a cube of edge 15 centimeters is cut from a rectangular block of wood as shown find the volume of the remaining block​

Answers

Answer 1

The Volume of Remaining block is  (l w h - 1125) cm³

We have,

Edge of cube = 15 cm

So, Volume of cube

= 15 x 15 x 15

= 1125 cm³

Now, Volume of Remaining block

= Volume of cuboid - Volume of cube

= l w h - 1125 cm³

Here we just have to put the dimension of cuboid in place of l w h.

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Related Questions

One sesame cracker has a mass of 3.25 grams, which is 18 grams less than
the mass of 1 slice of cheese. Write an equation that represents the relationship
between the masses of 1 cracker and 1 slice of cheese in terms of the mass of a
package of 16 slices of cheese, m.
A. What expression represents the mass of 1 slice of cheese?
B. What expression represents the difference in the masses of 1 slice of
cheese and 1 cracker?
C. What equation represents the relationship between the masses of
1 cracker and 1 slice of cheese?

Answers

Answer:

Step-by-step explanation:

A. Let x be the mass of 1 slice of cheese.

B. The difference in the masses of 1 slice of cheese and 1 cracker is:

x - 3.25 grams

C. Since one package contains 16 slices of cheese, the total mass of the package is:

16x

According to the problem, the mass of one cracker is 18 grams less than the mass of one slice of cheese. Therefore, we can write:

x - 18 = 3.25 + m/16

where m is the mass of the package of 16 slices of cheese.

Simplifying the equation:

x = 3.25 + m/16 + 18

x = m/16 + 21.25

This equation represents the relationship between the masses of 1 cracker and 1 slice of cheese in terms of the mass of a package of 16 slices of cheese.

check that y = 1/2 x^2 x 3 satisfies the differential equation dy/dx = x 1.

Answers

The function y =[tex](3/2) x^2[/tex] indeed satisfies the differential equation [tex]dy/dx = x 1.[/tex]

To check if [tex]y = 1/2 x^2 x 3[/tex]satisfies the differential equation dy/dx = x 1, we need to find the first derivative of y with respect to x and then compare it to the given dy/dx expression.

Given y = 1/2 x^2 x 3, we can rewrite it as[tex]y = (3/2) x^2.[/tex]

Now, let's find the first derivative of y with respect to x:

[tex]dy/dx = d(3/2 x^2)/dx = 3x[/tex]
Now we compare this with the given [tex]dy/dx = x 1. Since 3x = 3x * 1[/tex], the function y = (3/2) x^2 indeed satisfies the differential equation dy/dx = x 1.

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Can you answer this please?

Answers

So, the equation of the plane tangent to the surface at point P(40, 80, 12) is: z = x - (9/5)y + 4.

What is equation?

An equation is a mathematical statement that shows the equality of two expressions. It usually consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

To find the equation of the plane tangent to the surface at point P(40, 80, 12), we need to first find the partial derivatives of the function z(x,y) with respect to x and y, and evaluate them at point P. Then we can use the gradient vector of the surface at point P to find the equation of the tangent plane.

Given,

r = (9u+v)i + 5u²j + (4u – v)k

We have, x = 9u + v, y = 5u², z = 4u - v

So, z(x, y) = 4u - v = 4(1/4(x-9y/5))-1/5(y-v) = (x-9y/5) - (y-v)/5

Taking partial derivatives of z with respect to x and y, we get:

∂z/∂x = 1, and ∂z/∂y = -9/5

Evaluating these at point P(40, 80, 12), we get:

∂z/∂x = 1, and ∂z/∂y = -9/5

So, the gradient vector of the surface at point P is:

grad z = (1)i - (9/5)j

Now, the tangent plane at point P is given by the equation:

z - z(P) = ∇z · (r - r(P))

where z(P) = z(40, 80) = 12, r(P) = <40, 80, 12>, and ∇z = (1)i - (9/5)j

Substituting the values, we get:

z - 12 = (1)(x - 40) - (9/5)(y - 80)

Simplifying, we get:

z = x - (9/5)y + 12 - 8

So, the equation of the plane tangent to the surface at point P(40, 80, 12) is:

z = x - (9/5)y + 4

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PLS HELP ME FAST BIG TEST!!!!!!!!!
I'LL MARK YOU BRAINLIST!!!!!!!!!

Answers

Answer:

(-2,-1)

Step-by-step explanation:

see photo

Is ΔP'Q'R' a 180° rotation about the origin of ΔPQR? Use the drop-down menus to explain your answer.


A coordinate plane showing triangles P Q R and P prime Q prime R prime. The coordinates of the first figure are P 2 comma 3, Q 4 comma 4, and R 4 comma 3. The coordinates of the second figure are P prime 8 comma 1, Q prime 6 comma 2, and R prime 6 comma 1.



Choose...
no , yes
.
Choose...
side lengths, sides , angles , coordinates

of the image and preimage

Choose...
are not , are

opposites.

Answers

Yes, ΔP'Q'R' is a 180° rotation about the origin of ΔPQR as the image coordinates obtained using the rotation formula are the opposite of the preimage coordinates. The comparison of coordinates indicates the transformation. The correct answers are A), D) and B).

The coordinates of the preimage triangle PQR are P(2, 3), Q(4, 4), and R(4, 3). To determine if triangle P'Q'R' is a 180° rotation about the origin of triangle PQR, we need to apply the transformation to each vertex of the preimage and compare the resulting image coordinates.

Using the rotation formula, we can find the image coordinates

P' = (x cos 180° - y sin 180°, x sin 180° + y cos 180°) = (-2, -3)

Q' = (x cos 180° - y sin 180°, x sin 180° + y cos 180°) = (-4, -4)

R' = (x cos 180° - y sin 180°, x sin 180° + y cos 180°) = (-4, -3)

Comparing the image coordinates with the preimage coordinates, we can see that P'Q'R' is a 180° rotation of PQR about the origin. Therefore, the answer is "Yes" for the first dropdown.

For the second dropdown, we choose "Coordinates" because we are comparing the image and preimage coordinates.

For the third dropdown, we choose "are" because the image and preimage triangles are opposites, as one is a rotation of the other. The correct options are A), D) and B).

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Question 25
. The "break-even point" for a company is the number of units sold (other than 0 units)
for which: Profit = Revenue - Cost = 0. Production is profitable only when revenue is
greater than cost. The monthly profit of a company selling x units is given by the
quadratic function: P(x) = 2x² + 30x. Which of the following equivalent
1
200
expressions displays the break-even point as a constant or coefficient?
((x-3,000)² - 9,000,000)
(x-3,000)² + 45,000

Answers

The expression that displays the break-even point as a constant or coefficient is: (x-3,000)² + 45,000, which is equivalent to 1,200 * (x-3,000)² - 9,000,000.

How to determine the expression that displays the break-even point as a constant or coefficient

To find the break-even point, we need to set the profit function equal to 0 and solve for x:

P(x) = 2x² + 30x = 0

We can factor out x:

x(2x + 30) = 0

So, x = 0 or x = -15. Since we are looking for a positive number of units sold, the break-even point is:

x = 0 units

Now, we can plug this value into the given expressions to see which one results in a constant or coefficient:

((0-3,000)² - 9,000,000) = 0-9,000,000-9,000,000 = -18,000,000

(x-3,000)² + 45,000 = (0-3,000)² + 45,000 = 9,000,000 + 45,000 = 9,045,000

Therefore, the expression that displays the break-even point as a constant or coefficient is:

(x-3,000)² + 45,000, which is equivalent to 1,200 * (x-3,000)² - 9,000,000.

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Nicole is on her way in her car. She has driven 20 miles so far, which is one-half of the way home. What is the total length of her drive

Answers

Answer:

40 miles

Step-by-step explanation:

If Nicole has driven 20 miles and this is only half the distance, then the total length of her drive would be 40 miles.

We can determine this with a simple algebraic equation:

Let x be the total length of her drive.

We know that Nicole has already driven one-half of the distance, which can be represented as:

20 = 1/2x

Multiplying both sides by 2, we get:

40 = x

Therefore, the total length of Nicole's drive is 40 miles.

If 20 miles is one-half of the way home, then the total length of her drive is 40 miles.

Here's the reasoning: if she has driven 20 miles and that is one-half of the way home, that means that the other half of the way home is also 20 miles. So the total length of her drive is the sum of the distance she has already driven (20 miles) and the distance left to go (20 miles), which is equal to 40 miles in total.

Consider the following. x = et, y = e−4t (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Answers

The curve starts at (1,1) and goes to the right, approaching the x-axis but never touching it. It also approaches the y-axis but never touches it. The curve is traced in the direction from (1,1) towards the positive x-axis as the parameter t increases.

To eliminate the parameter, we can solve for t in terms of x and substitute into the equation for y:

x = et  --> t = ln(x)
y = e⁽⁻⁴ᵗ⁾ = e⁽⁻⁴⁾ln(x)) = x⁽⁻⁴⁾
So the Cartesian equation of the curve is y = x⁽⁻⁴⁾.

To sketch the curve, we can notice that as x increases, y decreases rapidly (since it is raised to the negative fourth power). The curve approaches the y-axis but never touches it. It also approaches the x-axis but is never quite horizontal. To indicate the direction in which the curve is traced as the parameter increases, we can use an arrow pointing to the right (since t = ln(x) increases as x increases).

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calculate the sum of the series [infinity] an n = 1 whose partial sums are given. sn = 7 − 5(0.8)n

Answers

The sum of the series is 15 square units.

How to calculate the sum of the given series?

The formula for the nth partial sum of a series is given by Sn = a1 + a2 + a3 + ... + an, where a1, a2, a3, ... are the individual terms of the series.

In this case, we are given the nth partial sum sn = 7 − 5(0.8)n.

We can use this expression to find the individual terms of the series as follows:

s1 = 7 - 5[tex](0.8)^{1}[/tex] = 3

s2 = 7 - 5[tex](0.8)^{2}[/tex] = 4.6

s3 = 7 - 5[tex](0.8)^{3}[/tex] = 5.48

s4 = 7 - 5[tex](0.8)^{4}[/tex]= 5.984

We can see that the series is a decreasing geometric series with first term a1 = 3 and common ratio r = 0.8.

The sum of an infinite geometric series with first term a1 and common ratio r, where |r| < 1, is given by S = a1 / (1 - r).

Using this formula, we can find the sum of our series as:

S = a1 / (1 - r) = 3 / (1 - 0.8) = 15

Therefore, the sum of the series is 15 square units.

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let t(n) denote the number of addition or subtraction operations performed by square(n). write down a recurrence relation for t(n). (no justification needed.

Answers

Recurrence relation for t(n):

t(n) = 4t(n/2) + 1, where n > 1

Explain more about the answer provided?

When we compute the square of an n-bit number, we can express it as:

n² = (n/2)² + (n/2)² + n

This means that we can compute the square of an n-bit number by recursively computing the square of an (n/2)-bit number twice, and adding the result to the product of the two (n/2)-bit numbers.

Each recursion involves 4 additions/subtractions (for adding/subtracting the two intermediate results), and 1 addition (for adding the final result). Therefore, the number of operations t(n) required to compute the square of an n-bit number can be expressed as:

t(n) = 4t(n/2) + 1, where n > 1

The base case is t(1) = 0, since computing the square of a 1-bit number requires no operations.

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Recurrence relation for t(n):

t(n) = 4t(n/2) + 1, where n > 1

Explain more about the answer provided?

When we compute the square of an n-bit number, we can express it as:

n² = (n/2)² + (n/2)² + n

This means that we can compute the square of an n-bit number by recursively computing the square of an (n/2)-bit number twice, and adding the result to the product of the two (n/2)-bit numbers.

Each recursion involves 4 additions/subtractions (for adding/subtracting the two intermediate results), and 1 addition (for adding the final result). Therefore, the number of operations t(n) required to compute the square of an n-bit number can be expressed as:

t(n) = 4t(n/2) + 1, where n > 1

The base case is t(1) = 0, since computing the square of a 1-bit number requires no operations.

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Central Middle School has calculated a 95% confidence interval for the mean height (μ) of 11-year-old boys at their school and found it to be 56 ± 2 inches.
(a) Determine whether each of the following statements is true or false.
There is a 95% probability that μ is between 54 and 58.
There is a 95% probability that the true mean is 56, and there is a 95% chance that the true margin of error is 2.
If we took many additional random samples of the same size and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ.
If we took many additional random samples of the same size and from each computed a 95% confidence interval for μ, approximately 95% of the time μ would fall between 54 and 58.
(b) Which of the following could be the 90% confidence interval based on the same data?
56±1
56±2
56±3
Without knowing the sample size, any of the above answers could be the 90% confidence interval.

Answers

a)1. True

2.False

3.True

4).False

b)Without knowing the sample size and standard deviation, we cannot determine the exact 90% confidence interval.

(a) For the content loaded Central Middle School data:

1. True: There is a 95% probability that μ (mean height) is between 54 and 58 inches.

This is the correct interpretation of the 95% confidence interval.

2. False: The confidence interval doesn't tell us the probability of the true mean or the margin of error being exactly as given. It only tells us the range where the true mean is likely to fall with 95% confidence.

3. True: If we took many additional random samples of the same size and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ. This is the definition of a 95% confidence interval.

4. False: It's incorrect to say that μ would fall between 54 and 58 95% of the time. The correct interpretation is that if we computed multiple 95% confidence intervals, approximately 95% of those intervals would contain the true mean height.

(b) To determine the 90% confidence interval based on the same data:

Without knowing the sample size and standard deviation, any of the above answers could be the 90% confidence interval. Confidence intervals depend on the sample size, standard deviation, and desired confidence level. With the information given, we cannot determine the exact 90% confidence interval.

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Consider a random sample X1, X2,..., Xn from the shifted exponential pdfTaking u 5 0 gives the pdf of the exponential distribution considered previously (with positive density to the right of zero). An example of the shifted exponential distribution appeared in Example 4.5, in which the variable of interest was time headway in traffic flow and θ = .5 was the minimum possible time headway. a. Obtain the maximum likelihood estimators of θ and λ. b. If n 5 10 time headway observations are made, resulting in the values 3.11, .64, 2.55, 2.20, 5.44, 3.42, 10.39, 8.93, 17.82, and 1.30, calculate the estimates of θ and λ.

Answers

The maximum likelihood estimators of θ and λ are θ-cap = min(X1, X2, ..., Xn) and λ-cap = n / (Σ(Xi - θ-cap)). For the given data, the estimates of θ and λ are θ-cap = 0.64 and λ-cap = 10 / (Σ(Xi - 0.64)).

To find the maximum likelihood estimators (MLE) for the shifted exponential distribution, first obtain the likelihood function L(θ, λ) by multiplying the pdf of each observation.

Take the natural logarithm of the likelihood function to get the log-likelihood function, and then differentiate it with respect to θ and λ. Set these partial derivatives to zero to find the MLEs.

For the given data, to find θ-cap, choose the smallest value, which is 0.64. To find λ-cap, subtract θ-capfrom each observation, sum the differences, and divide the number of observations (10) by this sum. This gives λ-cap = 10 / (Σ(Xi - 0.64)).

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If a garden box that has 31/2 feet long and 4 feet wide and 1/2 foot deep how many cubic feet dirt do you need to fill the garden box completely

Answers

We will need 7 cubic feet of dirt to fill the garden box completely.

The formula for the volume of a rectangular box is:
Volume = Length × Width × Height

In this case, the dimensions of the garden box are:
Length = 3 1/2 feet
Width = 4 feet
Height = 1/2 foot
First, convert the mixed numbers to improper fractions:
Length = (3 × 2 + 1)/2 = 7/2 feet
Now, multiply the dimensions together:
Volume = (7/2) × 4 × (1/2)
Simplify the fractions:
Volume = (7 × 4 × 1) / (2 × 2) = 28 / 4
Finally, divide to find the volume in cubic feet:
Volume = 28 ÷ 4 = 7 cubic feet.

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1A)
Find the mass and center of mass of the plate that occupies the region Ω and has the density function λ.
Ω:0≤ x ≤5,0 ≤y≤ 25−x sqrt (25-x^2)
λ(x,y)=2xy
a) M=625/8,xM=8/3,yM=8/3
b) M=625/4,xM=1250/3,yM=1250/3
c) M=625/2,xM=8/3,yM=8/3
d) M=625/2,xM=16/3,yM=1/63
e) M=625/4,xM=8/3,yM=8/3
f) None of these.
1B)
Find the mass and center of mass of the plate that occupies the region Ω and has the density function λ.
1C)
Find the mass and center of mass of the plate that occupies the region Ω and has the density function λ.
Ω:−1≤x≤1,0≤y≤4
λ(x,y)=x2
a) M=16/3,xM=0,yM=2
b) M=8/3,xM=2,yM=0
c) M=8/3,xM=0,yM=2
d) M=8/3,xM=0,yM=16/3
e) M=4/3,xM=0,yM=2
f) None of these.
Ω:0 ≤x≤ 3,x^2≤y≤9
λ(x,y)=2xy
a) M=243,xM=2916/7,yM=6561/4
b) M=243,xM=12/7,yM=27/4
c) M=243/2,xM=12/7,yM=27/4
d) M=243,xM=27/4,yM=12/7
e) M=486,xM=12/7,yM=27/4
f) None of these.

Answers

A the center of mass is[tex]$(x_{M},y_{M})=(0,2)$.[/tex] The answer is (a).
B the center of mass is [tex]$(x_{M},y_{M})=(\frac{2916}{7\cdot243},\frac{6561}{4\cdot243})$[/tex]. The answer is (a).

C the center of mass is[tex]$(x_{M},y_{M})=(0,2)$.[/tex] The answer is (a).

1A) We can find the mass by integrating the density function over the region:
[tex]$$M=\iint_{\Omega}\lambda(x,y)dA=\int_{0}^{5}\int_{0}^{25-x\sqrt{25-x^2}}2xydydx$$[/tex]
Evaluating this integral gives [tex]$M=\frac{625}{8}$.[/tex] To find the center of mass, we need to compute the moments:
[tex]$$M_{x}=\iint_{\Omega}x\lambda(x,y)dA=\int_{0}^{5}\int_{0}^{25-x\sqrt{25-x^2}}2x^2ydydx=\frac{8}{3}M$$\\$$M_{y}=\iint_{\Omega}y\lambda(x,y)dA=\int_{0}^{5}\int_{0}^{25-x\sqrt{25-x^2}}2xy^2dydx=\frac{8}{3}M$$[/tex]
So the center of mass is [tex]$(x_{M},y_{M})=(\frac{8}{3},\frac{8}{3})$[/tex]. Therefore, the answer is (a).

1B) Since the question only asks for the mass and center of mass, we can use the same method as in 1A to get [tex]$M=\int_{-1}^{1}\int_{0}^{4}x^2dydx=\frac{16}{3}$[/tex]. To find the moments, we have:
[tex]$$M_{x}=\int_{-1}^{1}\int_{0}^{4}x^3dydx=0$$\\$$M_{y}=\int_{-1}^{1}\int_{0}^{4}xy^2dydx=2\int_{0}^{1}\int_{0}^{4}xy^2dydx=\frac{16}{3}$$[/tex]
Therefore, the center of mass is[tex]$(x_{M},y_{M})=(0,2)$.[/tex] The answer is (a).

1C) Using the same method as in 1A, we have:
[tex]$$M=\int_{0}^{3}\int_{x^2}^{9}2xydydx=\frac{243}{2}$$[/tex]
To find the moments, we have:
[tex]$$M_{x}=\int_{0}^{3}\int_{x^2}^{9}x2xydydx=\frac{2916}{7}$$\\$$M_{y}=\int_{0}^{3}\int_{x^2}^{9}y2xydydx=\frac{6561}{4}$$[/tex]
Therefore, the center of mass is [tex]$(x_{M},y_{M})=(\frac{2916}{7\cdot243},\frac{6561}{4\cdot243})$[/tex]. The answer is (a).

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(3, −5) (i) find polar coordinates (r, ) of the point, where r > 0 and 0 ≤ < 2.

Answers

The polar coordinates of the point (3, -5) are (r, θ) = (√34, 5.25) where r > 0 and 0 ≤ θ < 2π. Since tan() is negative, we know that lies in either the second or fourth quadrant.

To find the polar coordinates (r, ) of the point (3, -5), we can use the following formulas:
r = sqrt(x^2 + y^2)
tan() = y/x
Plugging in the values for x and y, we get:
r = sqrt(3^2 + (-5)^2) = sqrt(34)
tan() = -5/3
Since tan() is negative, we know that lies in either the second or fourth quadrant. To determine which one, we can use the fact that tan() = y/x. In the second quadrant, both x and y are negative, which would give us a positive value for tan(). Therefore, must be in the fourth quadrant.
To find the angle , we can use the inverse tangent function (tan^-1) on our calculator. However, we need to adjust the result to account for the fact that we are in the fourth quadrant. Specifically, we need to add 2 radians (or 360 degrees) to the result. So:
tan^-1(-5/3) = -1.03 radians
+ 2 radians = 0.97 radians
Therefore, the polar coordinates of the point (3, -5) are (sqrt(34), 0.97 radians).
To find the polar coordinates (r, θ) of the point (3, -5) where r > 0 and 0 ≤ θ < 2π, you can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Plugging in the Cartesian coordinates (3, -5) for x and y:
r = √(3^2 + (-5)^2) = √(9 + 25) = √34
Since the point is in the fourth quadrant (x > 0 and y < 0), we'll adjust the angle:
θ = arctan(-5/3) ≈ -1.03 radians
To convert θ to the range 0 ≤ θ < 2π, add 2π:
θ = -1.03 + 2π ≈ 5.25 radians
So, the polar coordinates of the point (3, -5) are (r, θ) = (√34, 5.25) where r > 0 and 0 ≤ θ < 2π.

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The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 12 square inches. Solve for the dimensions (length and width) of the poster

Answers

The dimensions of the poster are width = 2 inches & length = 6 inches. Let's assume the width of the poster to be x inches. According to the problem, the length of the poster is 2 more inches than two times its width, which can be represented as 2x+2.

We are also given that the area of the poster is 12 square inches.

We know that the area of a rectangle is given by length times width, so we can set up an equation:-

length × width = area

(2x+2) × x = 12

Expanding the left side, we get:-

2x² + 2x = 12

Subtracting 12 from both sides, we get:-

2x² + 2x - 12 = 0

Dividing both sides by 2, we get:-

x² + x - 6 = 0

This is a quadratic equation that can be factored as:

(x + 3) (x - 2) = 0

Therefore, either x+3=0 or x-2=0.

If x+3=0, then x=-3, which doesn't make sense since we can't have a negative width.

If x-2=0, then x=2, which is a valid width.

We can use this value of x to find the length:-

length = 2x + 2 = 2(2) + 2 = 6

Therefore, the dimensions of the poster are width = 2 inches & length = 6 inches.

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consider the following set of five independent measurements of some unknown random quantity: 0.1, 0, -0.3, -1.4, 0.

Answers

Sample standard deviation is approximately 0.6129.

How to find the sample mean of the given set of measurements?

We add all the numbers and divide by the sample size:

(0.1 + 0 - 0.3 - 1.4 + 0) / 5 = -0.32/5 = -0.064

Therefore, the sample mean is -0.064.

To find the sample variance, we need to first find the deviations of each measurement from the sample mean. We subtract the sample mean from each measurement to get:

0.1 - (-0.064) = 0.164

0 - (-0.064) = 0.064

-0.3 - (-0.064) = -0.236

-1.4 - (-0.064) = -1.336

0 - (-0.064) = 0.064

Then, we square each deviation:

0.164² = 0.026896

0.064² = 0.004096

(-0.236)² = 0.055696

(-1.336)² = 1.787296

0.064² = 0.004096

We take the average of these squared deviations to get the sample variance:

(0.026896 + 0.004096 + 0.055696 + 1.787296 + 0.004096) / 5 = 0.375416

Therefore, the sample variance is 0.375416.

To find the sample standard deviation, we take the square root of the sample variance:

sqrt(0.375416) = 0.6129

Therefore, the sample standard deviation is approximately 0.6129.

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True or false: a correlation coefficient of -0.9 indicates a stronger linear relationship than a correlation coefficient of 0.5.

Answers

The given statement is True.

What does a  correlation coefficient measures?

A correlation coefficient measures the strength and direction of the linear relationship between two variables. The range of possible values for a correlation coefficient is from -1 to +1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and +1 indicates a perfect positive linear relationship.

Therefore, a correlation coefficient of -0.9 indicates a strong negative linear relationship between the two variables, whereas a correlation coefficient of 0.5 indicates a moderate positive linear relationship between the two variables. Thus, the correlation coefficient of -0.9 indicates a stronger linear relationship than the correlation coefficient of 0.5.

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Vik spends £88 on a plane ticket and €50 on airport tax. Using £1 = €1.14, what percentage of
the total cost does Vik spend on airport tax?
1
Give your answer rounded to 1 dp.

Answers

Vik spends 33.28% of the total cost on airport tax, rounded to 1 decimal place.

What percentage of the total cost does Vik spend on airport tax?

Converting €50 to pounds using the exchange rate, we get:

€50 = £50/1.14 = £43.86 (rounded to 2 decimal places)

The total cost is:

£88 + £43.86 = £131.86

The proportion of the total cost that Vik spends on airport tax is:

£43.86 / £131.86 = 0.3328

To convert this to a percentage, we multiply by 100:

0.3328 × 100 = 33.28%

Therefore, Vik spends 33.28% of the total cost on airport tax, rounded to 1 decimal place.

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Please help me (timed)

Answers

Since it's going up and down, my guess would be the second answer slope = undefined.

Answer:

The Correct answer is slope=Undefined

use induction to prove that 6 divides 9n−3 n for all non-negative integers n.

Answers

Step-by-step explanation:

We can prove the statement by mathematical induction.

Base Case: For n = 0, we have 9n - 3n = 1, which is divisible by 6, since 1 = 6*0 + 1.

Inductive Step: Assume that 6 divides 9k - 3k for some non-negative integer k. We need to show that 6 also divides 9(k+1) - 3(k+1).

Starting with 9(k+1) - 3(k+1), we can simplify it as follows:

9(k+1) - 3(k+1) = 9k + 9 - 3k - 3

= (9k - 3k) + (9 - 3)

= 6k + 6

Since 6 divides both 6k and 6, it also divides their sum, 6k + 6. Therefore, we have shown that 6 divides 9(k+1) - 3(k+1).

By the principle of mathematical induction, we can conclude that 6 divides 9n - 3n for all non-negative integers n.

A substance with a half life is decaying exponentially. If there are initially 12 grams of the substance and after 2 hours there are 7 grams, how many grams will remain after 3 hours? Round your answer to the nearest hundredth, and do not include units.

Answers

Answer:

5.33

Step-by-step explanation:

The amount of a substance decaying exponentially with a half-life can be modeled using the formula A = A₀ * 2^(-t / h), where A is the amount remaining after time t, A₀ is the initial amount of substance, t is the time elapsed, and h is the half-life of the substance. Using the fact that initially there were 12 grams of the substance, and after 2 hours there were 7 grams, we can solve for the half-life h. Substituting the values into the equation 7 = 12 * 2^(-2 / h) and solving, we get that h is approximately 4.145 hours. Finally, we can use the formula A = A₀ * 2^(-t / h) to find the amount of substance remaining after 3 hours. Plugging in A₀ = 12, t = 3, and h ≈ 4.145, we get A ≈ 5.33 grams. Rounding to the nearest hundredth, we conclude that approximately 5.33 grams of the substance will remain after 3 hours.

Let Y(k) be the 5-point DFT of the sequence y(n) = {1 2 3 4 5}. What is the 5-point DFT of the sequence Y(k)? 1. [15 -2.5 + 3.4j -2.5 + 0.81j -2.5 - 0.81j -2.5 - 3.4j] 2. [1 5 4 3 2] 3. [5 25 20 15 10] 4. [5 4 3 2 1]

Answers

The 5-point DFT of the sequence Y(k) is [15 -2.5 + 3.4j -2.5 + 0.81j -2.5 - 0.81j -2.5 - 3.4j]. So, the correct answer is 1).

We can find the 5-point DFT of y(n) using the formula

Y(k) = sum_{n=0}^{4} y(n) exp(-2piikn/5), k = 0,1,2,3,4

Substituting the values of y(n) = {1, 2, 3, 4, 5}, we get

Y(0) = 1 + 2 + 3 + 4 + 5 = 15

Y(1) = 1 + 2exp(-2pii/5) + 3exp(-4pii/5) + 4exp(-6pii/5) + 5exp(-8pii/5) = -2.5 + 3.4j

Y(2) = 1 + 2exp(-4pii/5) + 3exp(-8pii/5) + 4exp(-12pii/5) + 5exp(-16pii/5) = -2.5 + 0.81j

Y(3) = 1 + 2exp(-6pii/5) + 3exp(-12pii/5) + 4exp(-18pii/5) + 5exp(-24pii/5) = -2.5 - 0.81j

Y(4) = 1 + 2exp(-8pii/5) + 3exp(-16pii/5) + 4exp(-24pii/5) + 5exp(-32pii/5) = -2.5 - 3.4j

Therefore, the 5-point DFT of the sequence Y(k) is [15, -2.5 + 3.4j, -2.5 + 0.81j, -2.5 - 0.81j, -2.5 - 3.4j], which is option 1.

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solve the given differential equation by undetermined coefficients. y'' 2y' y = sin(x) 7 cos(2x)

Answers

The general solution is y = y_h + y_p = c1 [tex]e^{ (-x) }[/tex] + c2 x e^(-x) - (1÷2) cos(x) - (1÷12) sin(2x) - (5÷24) cos(2x).

What is Differential Equation ?

A differential equation is a mathematical equation that relates a function or a set of functions with their derivatives or differentials. In other words, it is an equation that describes the behavior of a system in terms of the rates of change of one or more variables.

First, we find the homogeneous solution of the differential equation:

The characteristic equation is r*r + 2r + 1 = 0, which can be factored as (r+1)(r+1) = 0. Hence, the homogeneous solution is y_h = c1  [tex]e^{ (-x) }[/tex]  + c2 x[tex]e^{ (-x) }[/tex]

Now, we look for a particular solution of the form y_p = A sin(x) + B cos(x) + C sin(2x) + D cos(2x), where A, B, C, and D are constants to be determined.

Taking derivatives, we get y_p' = A cos(x) - B sin(x) + 2C cos(2x) - 2D sin(2x) and y_p'' = -A sin(x) - B cos(x) - 4C sin(2x) - 4D cos(2x).

Substituting y_p, y_p', and y_p'' into the differential equation, we get:

(-A sin(x) - B cos(x) - 4C sin(2x) - 4D cos(2x)) + 2(A cos(x) - B sin(x) + 2C cos(2x) - 2D sin(2x)) + (A sin(x) + B cos(x) + C sin(2x) + D cos(2x)) = sin(x) + 7cos(2x)

Simplifying and collecting like terms, we get:

(-3A - 3C + 4D) sin(2x) + (3B + 4C - 3D) cos(2x) + 2A cos(x) - 2B sin(x) = sin(x) + 7cos(2x)

Equating coefficients of sin(2x), cos(2x), sin(x), and cos(x), we get the following system of equations:

-3A - 3C + 4D = 0

3B + 4C - 3D = 7

2A = 0

-2B = 1

Solving for A, B, C, and D, we get:

A = 0

B = -1÷2

C = -1÷12

D = -5÷24

Therefore, the particular solution is y_p = (-1÷2) cos(x) - (1÷12) sin(2x) - (5÷24) cos(2x).

The general solution is y = y_h + y_p = c1   [tex]e^{ (-x) }[/tex] + c2 x  [tex]e^{ (-x) }[/tex] - (1÷2) cos(x) - (1÷12) sin(2x) - (5÷24) cos(2x).

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int result = bsearch(nums, 0, nums.length - 1, -100); how many times will the bsearch method be called as a result of executing the statement, including the initial call?

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The number of times the bsearch method is called depends on the implementation of the binary search algorithm and the contents of the nums array. The initial call to the bsearch method is counted as one call.

After that, each subsequent call is made as the algorithm narrows down the search space by dividing it in half. The maximum number of calls can be calculated as log2(nums.length) + 1, where log2 is the base-2 logarithm.

This includes the initial call. However, the exact number of calls may be less than the maximum, depending on the data and target value (-100 in this case).

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I NEED HELP ON THIS ASAP!!!

Answers

Each point (x, y) on the graph of h(x) becomes the point (x - 3, y - 3) on v(x).

Each point (x, y) on the graph of h(x) becomes the point (x + 3, y + 3) on w(x).

What is a translation?

In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image;

g(x) = f(x - N)

Since the parent function is v(x) = h(x + 3), it ultimately implies that the coordinates of the image would created by translating the parent function to the left by 3 units.

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Do a full function study and plot a graph
y=x^4-8x^2-9

Answers

Answer:

To do a full function study of y = x^4 - 8x^2 - 9, we need to determine the domain, intercepts, symmetry, asymptotes, intervals of increase and decrease, local extrema, and concavity.

Domain:

Since the function is a polynomial, it is defined for all real numbers. Therefore, the domain is (-∞, ∞).

x-Intercepts:

To find the x-intercepts, we set y = 0 and solve for x:

x^4 - 8x^2 - 9 = 0

We can factor the left-hand side to get:

(x^2 - 9)(x^2 + 1) = 0

This gives us x = ±√9 = ±3 as the x-intercepts.

y-Intercept:

To find the y-intercept, we set x = 0:

y = 0^4 - 8(0^2) - 9 = -9

Therefore, the y-intercept is (0, -9).

Symmetry:

The function is an even-degree polynomial, which means it has rotational symmetry of order 2 about the origin.

Asymptotes:

There are no vertical or horizontal asymptotes for this function.

Intervals of Increase and Decrease:

To find the intervals of increase and decrease, we need to find the critical points of the function by taking the first derivative and setting it equal to zero:

y' = 4x^3 - 16x = 0

Solving for x, we get x = 0 or x = ±√4 = ±2. Therefore, the critical points are (-2, 43), (0, -9), and (2, 43). We can use the second derivative test to determine that (-2, 43) and (2, 43) are local minima and (0, -9) is a local maximum.

The function increases on the intervals (-∞, -2) and (2, ∞) and decreases on the interval (-2, 2).

Local Extrema:

The local minimum points are (-2, 43) and (2, 43), and the local maximum point is (0, -9).

Concavity:

To determine the concavity of the function, we take the second derivative:

y'' = 12x^2 - 16

Setting y'' equal to zero, we get x = ±√4/3. Since y'' is positive for x < -√4/3 and x > √4/3, and negative for -√4/3 < x < √4/3, we have a point of inflection at x = -√4/3 and x = √4/3.

Plotting the Graph:

We can now use all of the information we have gathered to sketch the graph of y = x^4 - 8x^2 - 9. The graph has rotational symmetry of order 2 about the origin, and it passes through the points (-3, 0), (0, -9), and (3, 0). It has local minimum points at (-2, 43) and (2, 43) and a local maximum point at (0, -9). It changes concavity at x = -√4/3 and x = √4/3. Here is a rough sketch of the graph:

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find the curvature k of the curve where s is the arc length parameter

Answers

We can calculate the curvature k as:

k = |dT/ds| / |dr/ds|

[tex]= |d^2 r(s)/ds^2| / |dr/ds|^3[/tex]

How to find the curvature k of a curve given by the vector-valued function?

To find the curvature k of a curve given by the vector-valued function r(s), where s is the arc length parameter, we use the following formula:

k = |dT/ds| / |dr/ds|

where T(s) is the unit tangent vector and r'(s) is the velocity vector.

To find T(s), we differentiate r(s) with respect to s:

T(s) = dr(s)/ds

Then, we normalize T(s) to obtain the unit tangent vector:

T(s) = dr(s)/ds / |dr(s)/ds|

Next, we differentiate T(s) with respect to s to obtain the unit normal vector N(s):

[tex]N(s) = d^2 r(s)/ds^2 / |d r(s)/ds|[/tex]

Finally, we can calculate the curvature k as:

k = |dT/ds| / |dr/ds|

[tex]= |d^2 r(s)/ds^2| / |dr/ds|^3[/tex]

So, to find the curvature k of the curve given by the vector-valued function r(s), we need to calculate r(s), dr(s)/ds, and[tex]d^2 r(s)/ds^2[/tex] and plug them into the above formula.

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If 25% of a number is 65 and 40% of the same number is 104, find 15% of that number.

Answers

Answer: 260

Step-by-step explanation:

Use proportions:

65/25 = x/100

cross multiply the proportions:

25x = 6500

solve your equation:

x = 260

The number is 260.

Let's start by finding the number we're working with.

We know that 25% of the number is 65, so we can set up an equation:

0.25x = 65

where "x" is the number we're trying to find.

To solve for "x", we can divide both sides of the equation by 0.25:

x = 65 / 0.25

x = 260

So the number we're working with is 260.

Next, we need to find 40% of the same number:

0.40(260) = 104

Now we can use this information to find 15% of the same number:

We can set up a proportion:

40% is to 104 as 15% is to x

0.40/104 = 0.15/x

To solve for "x", we can cross-multiply:

0.40x = 104(0.15)

0.40x = 15.6

x = 39

So 15% of the same number is 39.

the radius of a star can be indirectly determined if the star's distance and luminosity are known.
true
false

Answers

The statement "The radius of a star can be indirectly determined if the star's distance and luminosity are known." is true because the radius of a star can be calculated using the Stefan-Boltzmann Law.

The Stefan-Boltzmann Law can be used to determine a star's radius. This law states that the luminosity of a star (the total amount of energy it emits in a given time) is proportional to the fourth power of its radius. Therefore, if the distance and luminosity of a star are known, its radius can be calculated by rearranging the equation.

This equation can be used to calculate the radius of a star even if its size cannot be directly measured. The equation is:

Radius = (L/4πσT⁴[tex])^{1/2}[/tex]

Where L is the luminosity of the star, σ is the Stefan-Boltzmann constant, and T is the temperature of the star.

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