simplify the following 10^9÷10^7​

The volume of the cuboid as a function of x is V(x) = x * 3x * y.

the volume of the cuboid as a function of x is V(x) = 675/4 - (9/4)x^2.

The surface area of the cuboid is given as 450 cm, which can be expressed as:

2(x * 3x) + 2(x * y) + 2(3x * y) = 450.

Simplifying this equation, we get:

6x^2 + 2xy + 6xy = 450,

6x^2 + 8xy = 450,

3x^2 + 4xy = 225.

Now, we need to express y in terms of x. From the given dimensions, we know that the surface area is formed by six rectangular faces of the cuboid. Therefore, the length of one face is x, the width is 3x, and the remaining face (height) is y.

To find y, we can use the equation for the surface area. Rearranging the equation above, we have:

3x^2 + 4xy = 225,

y(4x) = 225 - 3x^2,

y = (225 - 3x^2) / (4x).

Now we can substitute the value of y into the expression for the volume:

V(x) = x * 3x * [(225 - 3x^2) / (4x)].

Simplifying further:

V(x) = (3/4) * (225 - 3x^2),

V(x) = 675/4 - (9/4)x^2.

Therefore, the volume of the cuboid as a function of x is V(x) = 675/4 - (9/4)x^2.

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The 99.9% confidence interval for a sample of size 176 with 118 successes is (0.558, 0.778).

The formula for finding the confidence interval for a sample proportion is given as follows:

Confidence interval = sample proportion ± zα/2 * √(sample proportion * (1 - sample proportion) / n)

Where,

zα/2 is the z-value for the level of confidence α/2,
n is the sample size,
sample proportion = successes / n

Here, level of confidence, α = 99.9%, so α/2 = 0.4995. The value of zα/2 for 0.4995 can be found from the z-table or calculator and it comes out to be 3.291.

Putting all the values in the formula, we get:

Confidence interval = 0.670 ± 3.291 * √(0.670 * 0.330 / 176)

                   = (0.558, 0.778) (rounded to three decimal places and put in parentheses)

Thus, the 99.9% confidence interval for a sample of size 176 with 118 successes is (0.558, 0.778).

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Answer:

7/20

Step-by-step explanation:

The probability that the girls would randomly choose their two favorite movies to watch is 0.0034.

The number of favorable outcomes is 2 (since Rhonda has two favorite movies).

Using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n = 35 (total number of movies) and r = 2 (number of movies to be chosen).

C(35, 2) = 35! / (2! x (35 - 2)!)

C(35, 2) = 35! / (2! x 33!)

= (35 x 34 x 33!) / (2! x 33!)

= (35 x 34) / 2

= 595

Therefore, there are 595 possible outcomes when choosing any two movies from Laura's collection.

Now, Probability = Favorable Outcomes / Total Outcomes

Probability = 2 / 595

Therefore, the probability that the girls would randomly choose their two favorite movies to watch is 0.0034.

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Quarter 1: $300,000Quarter 2: $300,013Quarter 3: $250,000Quarter 4: $500,000 the adjusted chart representing the Sales .

The given chart to represent the sales each quarter, we need to find out the sales of each quarter first and then represent them in the chart. Let's calculate the sales of each quarter one by one:

Sales of Quarter 1Let the sales of Quarter 1 be xSales of Quarter 2As per the given data, Quarter 2 produced 13 more sales than Quarter 1Therefore, sales of Quarter 2 = x + 13Sales of Quarter 3Let the sales of Quarter 3 be sales of Quarter 4As per the given data, Quarter 4 produced 17% of total sales for the year

therefore, 17% of $1,254,000 = (17/100) x 1,254,000= 213,180Sales of Quarter 4 = 213,180Sales increased 100% over the previous quarter

Therefore, sales of Quarter 4 = 2 x sales of Quarter 3= 2yNow, we can form the equation as follows: Total Sales = Sales of Quarter 1 + Sales of Quarter 2 + Sales of Quarter 3 + Sales of Quarter 4$1,254,000 = x + (x + 13) + y + 2y + 213,180$1,254,000 = 4x + 3y + 213,193or 4x + 3y = $1,040,807

Now, we can assume some values of x and y and then calculate the values of other variables. Let's assume x = $300,000 and y = $250,000Therefore, sales of Quarter 1 = $300,000Sales of Quarter 2 = $300,000 + $13 = $300,013Sales of Quarter 3 = $250,000Sales of Quarter 4 = 2 x $250,000 = $500,000Now, we can represent these sales in the chart as follows:

Quarter 1: $300,000Quarter 2: $300,013Quarter 3: $250,000Quarter 4: $500,000

Therefore, the adjusted chart representing the sales each quarter is shown above.

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1/5 cups of sugar.

have a nice day

The given trigonometric equation is sin x + 2 = 0.

It is important to note that sine values range from -1 to 1 and never exceed those bounds. Thus, it can be determined that sin x + 2 will never equal zero.This is because the lowest possible value of sine is -1, which is not equal to zero. When 2 is added to that value, the sum is still negative. Therefore, the equation sin x + 2 = 0 has no solutions.

A trigonometric equation is one that has a variable and a trigonometric function. For instance, sin x + 2 = 1 is an illustration of a mathematical condition. The equations can be as straightforward as this or more complicated than that, such as sin2 x – 2 cos x – 2 = 0.

The six mathematical capabilities are sine, secant, cosine, cosecant, digression, and cotangent. The trigonometric functions and identities are derived by referencing a right-angled triangle as a reference: Sin is the opposite side or the hypotenuse.

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Answer:

44

Step-by-step explanation:

because it a millon and not a bilolon

The volume of the oblique cylinder is calculated as: B. 96π units³.

Volume = πr²h, where h is the height and r is the radius of the given cylinder.

Given the following:

Volume = πr²h = π(4²)(6)

Volume = 96π units³ (option B)

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Answer:

x = -8 and y = -7

Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

8x−12y=20;4x−4y=−4

Step: Solve8x−12y=20for x:

8x−12y+12y=20+12y(Add 12y to both sides)

8x=12y+20

8x

8

=

12y+20

8

(Divide both sides by 8)

x=

3

2

y+

5

2

Step: Substitute

3

2

y+

5

2

forxin4x−4y=−4:

4x−4y=−4

4(

3

2

y+

5

2

)−4y=−4

2y+10=−4(Simplify both sides of the equation)

2y+10+−10=−4+−10(Add -10 to both sides)

2y=−14

2y

2

=

−14

2

(Divide both sides by 2)

y=−7

Step: Substitute−7foryinx=

3

2

y+

5

2

:

x=

3

2

y+

5

2

x=

3

2

(−7)+

5

2

x=−8(Simplify both sides of the equation)

Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.

Step-by-step explanation: Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.

The function is an even function because the function is symmetric with respect to the y-axis (i.e.) { -x) = {x). So, the Fourier series has only cosine terms. Therefore, the Fourier cosine series of the given function is given by:

f(x) = a0/2 + Σ an cos(nπx/L),

where L is the period of the function.

Since the function is even, the Fourier series reduces to  f(x) = a0/2 + Σ an cos(nπx/L) ...(1) , where a0 = 1/L ∫f(x)dx, an = 2/L ∫f(x)cos(nπx/L)dx for n = 1, 2, 3, ..., n. Let L = 1,

then a0 = 1/1 ∫0^1 f(x)dx = 1/2 an = 2/1 ∫0^1 f(x)cos(nπx)dx for n = 1, 2, 3, ..., n.
a1 = 2 ∫1/2^1 cos(nπx)dx = 1/nπ sin(nπx) from 1/2 to 1
= [1/nπ sin(nπ/2) - 1/nπ sin(0)]
= 2/nπ sin(nπ/2)

Hence, the Fourier cosine series is given by f(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(2)for n = 1, 2, 3, ...Similarly, the Fourier sine series of the given function is given by: f(x) = Σ bn sin(nπx/L)where L is the period of the function. Since the function is even, there are no sine terms in the Fourier series. So, the Fourier sine series is zero, i.e., bn = 0 for n = 1, 2, 3, ....Hence, the full Fourier series is the same as the Fourier cosine series, which is given byf(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(3)for n = 1, 2, 3, ...The Fourier series converges pointwise to f(x) for x in (0, 1/2) U (1/2, 1).The Fourier series does not converge at x = 0 and x = 1/2 because the function is not continuous at these points.

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The time it takes for the principle to triple in value is t = 18.792 years.

To determine how long it would take for a principal of $10,000 to triple in value at an interest rate of 3.75% compounded semi-annually, we can use the compound interest formula. By rearranging the formula and solving for time, we can find the answer.

The compound interest formula can be expressed as A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.

In this case, we have P = $10,000, r = 3.75% (or 0.0375 as a decimal), and n = 2 since compounding occurs semi-annually.

We want to find the time it takes for the principal to triple, so A = 3P. Substituting the known values into the compound interest formula, we have:

3P = P(1 + r/n)^(nt)

Canceling out the common factor of P on both sides, we get:

3 = (1 + r/n)^(nt)

Taking the natural logarithm (ln) of both sides to isolate the exponent, we have:

ln(3) = nt ln(1 + r/n)

Now, we can solve for t by dividing both sides of the equation by n ln(1 + r/n) and simplifying:

t = ln(3) / (n ln(1 + r/n))

Substituting the given values of r = 0.0375 and n = 2, we can calculate the value of t.

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Answer:

[tex]Range = 3.169m[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the difference between the shortest and the longest

This question implies that we calculate the range.

[tex]Range = Longest - Shortest[/tex]

From the table, we have:

[tex]Longest = 8.7m[/tex]

[tex]Shortest = 5.531m[/tex]

So, we have:

[tex]Range = 8.7m- 5.531m[/tex]

[tex]Range = 3.169m[/tex]

There are many possible solutions, but one example in the case of three functions f, g, and h would be: f(0) = 0, f(1) = 1g(0) = 1, g(1) = 0h(0) = 0, h(1) = 1

We have the set J2 = {0,1} and we need to estimate three functions f, g, and h such that f:

J2→ J2, g: J2→ J2, and h:

J2→ J2, and f = g = h.

To do this, we can simply assign values to each element of the set J2 for each of the three functions. For example, we can let f(0) = 0 and f(1) = 1, which means that the function f maps 0 to 0 and 1 to 1. We can also let g(0) = 1 and g(1) = 0, which means that the function g maps 0 to 1 and 1 to 0.

Finally, we can let h(0) = 0 and h(1) = 1, which means that the function h maps 0 to 0 and 1 to 1. Note that all three functions have the same values for each element in J2, so we can say that f = g = h.

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In multilevel signaling over an Additive White Gaussian Noise (AWGN) channel, the received signal can be represented as:

Y = X + N

where Y is the received signal, X is the transmitted signal, and N is the AWGN with zero mean and variance σ^2.

In this case, M = 4, which means we have 4 symbols: -2v, -v, +2v, +v. The pulse values assigned to these symbols are: -2v, -v, +2v, +v.

To find the optimum threshold values, we need to consider the decision regions between adjacent symbols. Let's denote the threshold values as T1, T2, and T3, corresponding to the decision boundaries between -2v and -v, -v and +2v, and +2v and +v, respectively.

For correct transmission of the symbol -2v, the received signal Y should be greater than T1 and less than or equal to T2. Mathematically, this can be expressed as:

T1 < Y ≤ T2

The probability of correct transmission for the symbol -2v can be obtained by integrating the probability density function (PDF) of the received signal Y over the region T1 < Y ≤ T2.

Now, let's find the expression for the total probability of error. The total probability of error (P_e) can be obtained by summing the probabilities of error for each symbol. In this case, we have four symbols, so the expression for P_e is:

[tex]P_e = P_error(-2v) + P_error(-v) + P_error(+2v) + P_error(+v)[/tex]

where P_error(-2v) is the probability of error for symbol -2v, P_error(-v) is the probability of error for symbol -v, and so on.

Finally, to evaluate the total probability of error when σ^2 = 0.40 and v = 0, we need more information. Specifically, we need the signal-to-noise ratio (SNR) or the value of σ^2 in order to proceed with the calculation.

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Answer:

x=2

Step-by-step explanation:

The axis of symmetry goes through the vertex and is the line that makes the image the same on one side as the other

Since this is a vertical parabola, the axis is symmetry is  of the form x=

The vertex is at x=2  so the axis of symmetry is x=2

Answer:

12

..................................................

Step-by-step explanation:

2 + 2 + 1 + 2 + 1 + 4 = 12

Answer:

12 centimeters

Step-by-step explanation:

The double dashes are both the same number. Since the base is 4cm and they have to be two of the same number, the double dashes are each 2cm long. Meanwhile, the height is 2cm, and the single dashes are two of the same numbers (but not 2cm, because that's what the double dashes are). So, each dash must be 1cm long. When you add them up: [tex]4+2+2+2+1+1=12[/tex]

Answer:

A. Third period

Step-by-step explanation:

- hope this helped!

Answer:

3rd

Step-by-step explanation:

The values of N and p that define the random graph ensemble G(N, p) with an average degree (k) of 40 and a variance of the degree distribution (σ²) of 50 are N = 201 and p = 0.2.

The values of N and p that define a random graph ensemble G(N, p) with an average degree (k) of 40 and a variance of the degree distribution (σ²) of 50, we can use the following formulas:

k = (N-1) × p

σ² = (N-1) × p × (1-p)

Plugging in the given values:

k = 40

σ² = 50

We can solve these equations to find the values of N and p:

From the first equation:

40 = (N-1) × p

From the second equation:

50 = (N-1) × p × (1-p)

By substituting the value of (N-1) × p from the first equation into the second equation, we can solve for p.

40 = 50 × (1-p)

1-p = 40/50

1-p = 0.8

p = 1 - 0.8

p = 0.2

Now, we can substitute the value of p back into the first equation to solve for N:

40 = (N-1) × 0.2

200 = N-1

N = 200 + 1

N = 201

Therefore, the correct values of N and p that define the random graph ensemble G(N, p) with an average degree (k) of 40 and a variance of the degree distribution (σ²) of 50 are N = 201 and p = 0.2.

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Answer:8 cars

Step-by-step explanation:

to find the least amount of cars dived 30/4 which equilds 7.5

Since there are 2 remaining students, an additional car will be needed bringing the total to 8 cars.

Given the expression |x - 4|, condition on |x - 4| that will assure that:(a)|x - 2| < 2/1(b)|x - 2| < 0.01

Given expression |x - 4|, the two possible values are: x - 4 if x > 4 -(x - 4) if x < 4Let us solve each part of the question separately:

(a)Part (a) can be expressed as follows:|x - 2| < 2/1Subtracting 2 from both sides of the in equality |x - 2| - 2 < 0Adding 4 to both sides of the inequality. |x - 2| - 2 + 4 < 0|x - 2| - 2 + 4 = |x - 4| < 0Since it is impossible to have an absolute value less than 0, therefore there is no solution.

(b)Part (b) can be expressed as follows:|x - 2| < 0.01 Subtracting 2 from both sides of the inequality |x - 2| - 2 < -0.01Adding 4 to both sides of the inequality. |x - 2| - 2 + 4 < -0.01|x - 2| - 2 + 4 = |x - 4| < -0.01Since it is impossible to have an absolute value less than 0, therefore there is no solution.

Thus, there are no solutions for the given conditions.

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Answer:

If you are looking at a graph then yes it will have a y-axis

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

A horizontal line goes on infinitely on both ends will eventually cross the y-axis, making a y-intercept.

Answer

6.

Steps

30/100×30

=6

Answer:

6

Step-by-step explanation:

There are 30 students

So,

20÷100×30=6

Answer:

960

Step-by-step explanation:

Let P, R and T denote principal amount, rate of interest and time period.

Principal amount of loan (P) = 4,000

Time period (T) = 4 years

Rate of interest (R) = 6%

Simple interest is calculated using the following formula:

Simple interest [tex]=\frac{4000(4)(6)}{100} =960[/tex]

So,

Simple interest is equal to 960

Both the given statements are true

1. Two equilateral triangles are always similar: True.

An equilateral triangle is a triangle in which all three sides are equal. Since two equilateral triangles have the same shape and size, they are always similar. Similarity means that the corresponding angles are equal, and the corresponding sides are in proportion.

2. The diagonals of a rhombus are perpendicular to each other: True.

In a rhombus, opposite sides are parallel, and all sides have equal length. The diagonals of a rhombus bisect each other at right angles, which means they are perpendicular to each other. This property holds true for all rhombuses, regardless of their size or orientation.

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Given question is incomplete, the complete question is below

State true or false

1. Two equilateral triangles are always similar.

2. The diagonals of a rhombus are perpendicular to each other.

Answer:

x = 43

Step-by-step explanation:

x = 98 - 55

x = 43

Answer:

x=43

Step-by-step explanation:

have a nice day and stay safe:)

Answer:

15(6.5% * 7000)+7000=y

Step-by-step explanation:

15(6.5% * 7000)+7000=y

im not sure tho

Answer:

B

Step-by-step explanation:

A or constant is the answer

Answer:

36 cubic feet

Step-by-step explanation:

Answer:

To find volume use the solution of l x w x h

Length x Width x Height

Step-by-step explanation:

16. 2 x 3 x 6 = 36 cubic feet

???. 5/8 x 3/4 x 2  = 15/16

???. 2 x 1 1/4 x 1 1/2 = 3 3/4 cubic inches

25.

1 = 4.89 / 3 = 1.63

3 = $4.89

9 = 4.89 + 4.89 + 4.89 = 14.67

10 = 14.67 + 1.63 = $16.30

???. Interquartile Range = Q3 - Q1

65 - 62 = 3

If i remember correctly

Answer:

14

Step-by-step explanation:

42:?

3:1

42/3=14

42:14

3:1