Solve it below:
...............

The area of rectangle with has its vertices defined on parabola is 32 square units.

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

Square, figure, oblong, parallelogram, plane a.re terms to describe rectangle

Equation of Parabola is y = 12 - x^2 is an even function.

Therefore, its rectangle form also is even at the origin.

We know area of rectangle = length × width

Here,

length = 2x, width = y

Area, A = 2x(12 - x2)

⇒ A = 24x - 2x^3

Take derivative of A with respect to x

⇒ A' = 24 - 6x^2

The area is largest when A' = 0

⇒ 24 - 6x^2 = 0

⇒ x^2 = 4

⇒ x = 2

Put the value of x in y = 12 - x^2

⇒ y = 12 - 4

⇒ y = 8

Area = 2(2)(8) = 32

Therefore, the largest area of a rectangle is 32 square units.

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The common ratio is 1/5. By dividing each word by the term before it, we may find the geometric progression's common difference.

The common ratio in geometric progression is the ratio of any term in the sequence to divided by the first term.

The Formula to calculate the common ratio in geometric progression, a, ar, ar2, ar3, ar4, ar5… is,

Common ratio = ar/ a = ar2/ ar = ……. = an/ an-1

As stated in the definition, we can compute the common difference of a geometric progression by dividing any term by its preceding term.

Given, the geometric sequence is 625, 125, 25, 5, 1,....

We have to find the common ratio of the given geometric sequence.

In geometric sequence, a, b, c, d, … the common ratio r is given by

r = b/a = c/b = d/c.

So, r = 125/625 = 25/125 = 5/25 = 1/5;

r = 1/5

Therefore, the common ratio is r = 1/5.

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Answer:

B. 25/125

Step-by-step explanation:

The colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

Given is that a colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm.

The logistic model is given as -

y(t) = {c/(1 + a[tex]e^{-bt}[/tex])}

For y(t) = 2000

2000 = {c/(1 + a[tex]e^{-bt}[/tex])}

(2000/c) = 1/(1 + a[tex]e^{-bt}[/tex])

(1 + a[tex]e^{-bt}[/tex]) = (2000/c)

a[tex]e^{-bt}[/tex] = (2000/c) - 1

a[tex]e^{-bt}[/tex] = (2000 - c)/c

[tex]e^{-bt}[/tex] = (2000 - c)/(ac)

(-bt)log{e} = log {(2000 - c)/(ac)}

- bt = log(2000 - c) - log(ac)

- bt = log(2000 - c) - log(a) + log(c)

t = - {log(2000 - c) - log(a) + log(c)}/b

Therefore, the colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

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The relationship's slope and common difference are both 70 and constant.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
As the  relationship given in the table is linear,
The slope of the relationship is given as,
M = (y₂ - y₁) /  (x₂ - x₁)
Now, putting values from the table,
m = 140 - 70 / 2 - 1
m = 70 jumps per minute

Now,
The common difference between the consecutive minutes of jumping,
d = 140 - 70 = 210 - 140
d = 70 = 70

From the above evaluation, it can be said that the common difference and rate are constant.

Thus, the slope of the relationship and the common difference is 70, as well as constant.

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Part (A)

Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.

P/Q = R/S

where,

In this case,

Therefore, we go from this

P/Q = R/S

to this

(1.8)/6 = h/60

Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.

--------------

====================================================

Part (B)

Let's cross multiply and solve for h.

(1.8)/6 = h/60

1.8*60 = 6h

108 = 6h

6h = 108

h = 108/6

h = 18

--------------

Answer:

A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

B). 18 meters tall

Step-by-step explanation:

We see TWO right triangles in this problem:

These triangles are proportional so we can make a ratio out of them

the height of the man over the side of the triangle (6m)

and the height of the tower over the length of its triangle (60m)

Set these equal to each other to complete part A

[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

And by using cross multiplication (which is what you do for ratios), solve for h!

For a quick example of cross multiplication, I've attached a picture.

Now let's do it!

1.8 × 60 = 6 × h

108 = 6h

108/6 = h

h = 18

The height of the cell phone tower is 18 meters.

We can write an equation to represent the relationship between the three integers n - 1, n, and n + 1 by multiplying these three numbers together:

We can then solve this equation to find the value of n.

To solve the equation, we can first factor the left-hand side to get (n - 1) * (n + 1) * n = 210. This expression can be further simplified to n^2 - 1 = 210. We can then solve this equation by adding 1 to both sides to get n^2 = 211, and then taking the square root of both sides to get n = sqrt(211).

The value of n must be an integer, so the only possible value for n is 14. This means that the three consecutive integers are 13, 14, and 15.

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The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.

To find p(a) for a given polynomial p(x) we need to substitute x = a in the given polynomial i.e in place of x.

Here we have

Function c is defined by the equation c(n) = 50 + 4n.

It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.  

Activity 1 of 2

Find the value of c(7).

=> c(7) = 50 + 4(7)

=> c(7) = 50 + 28

=> c(7) = 78

Activity 2 of 2

Explain what the value of c(7) you found means in this situation.

In c(n) = 50 + 4n, n represents the number of visits in a month and 50+4n will represent the monthly cost in dollars

If we apply the above statement to c(7) = 78

then 7 represents the number of visits and 78 represents the monthly cost of visiting the gym 7 times

Therefore,

The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.

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By definition, perpendicular strains are strains intersecting at a proper attitude. The letters T and L are examples of perpendicular strains. By definition, parallel strains are strains at the equal aircraft that in no way intersect.

The letters N and Z include pairs of parallel linetwo non-vertical strains which are withinside the equal aircraft has the equal slope, then they may be stated to be parallel. Two parallel strains might not ever intersect. If non-vertical strains withinside the equal aircraft intersect at a proper attitude then they may be stated to be perpendicular.

We can decide from their equations whether or not strains are parallel with the aid of using evaluating their slopes. If the slopes are the equal and the y-intercepts are different, the strains are parallel. If the slopes are different, the strains aren't parallel. Unlike parallel strains, perpendicular strains do intersect.

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The domain and range of the given function are  {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.

The given function is

f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)

The domain of the function can be given as;

Domain : {-2, 0, 1, 2, 3}

Range : {-3, 0, 2, 3, 4}

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The value of 1204.2 + 4.72613 is 1208.92613.

What is meaning of significant figures of a number?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Given number is 1204.2 and  4.72613.

If add zeros after the last digit of the decimal number, then the number will remains same.

The rewrite form of 1204.2 is 1204.20000.

Before combining two decimal integers, make sure they both have the same number of digits after the decimal point. If they don't, move a number's right by a number of zeros until they do.

Then, place the decimal points vertically and write one number on top of the other. Bring the decimal point directly below the decimal point and add as you would with full numbers.

The sum of 1204.20000 and 4.72613

1204.20000

    +4.72613

__________

1208.92613

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The data Customers on file who visited the store during coupon promo is 32% .

a) We use Z-test for testing hypothesis in this case because it is single proportion.

b) The P-value is 0.0017.

c) As P value < α = 0.05 , So we reject the null hypothesis.

d) Yes, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.

The Null and Alternative hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.

Sample size ,n = 4,500

Significance level, 0.05

a) We use z-test, because this is single proportion hypothesis test.

Below are the null and alternative Hypothesis,

Null Hypothesis, H₀ : p = 0.3

Alternative Hypothesis, Hₐ : p > 0.3

b) Test statistic,

z = (p-cap - p)/sqrt(p×(1-p)/n)

z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)

z = 2.93

Using the Z-table, the P value at significance level 0.05 and z = 2.93 is 0.0017

As we see P-value < α = 0.05, so, reject the null hypothesis.

Yes, Lotions and Potions should continue to offer this promotion in order to increase visits.

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Answer:

5x+48=130

Step-by-step explanation:

5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.

The height of the cliff in terms of A, B and h are 40 meters.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

A man standing on the deck of a ship.

Let C be the position of man.

And the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively 60° and 30°.

That means, ∠DCH = 60° and  ∠BCD = 30°.

The diagram is given in the attached image.

HD = x And BD = 10 meters.

In right-triangle ΔCDH,

we have,

tan60° = HD / CD

√3 = x / CD

CD = x/√3

In right-triangle  ΔCDB,

we have,

tan30° = BD/CD

CD = 10√3

So, the distance of the ship from the cliff is 10√3 meters.

Comparing, the both values of CD,

 10√3 =  x/√3

x  =  10√3 × √3

x = 10 × 3

x = 30 meters.

Now, the total height of cliff  = BD + DH

= 10 + 30

= 40 meters.

Therefore, the height of the cliff is 40 meters.

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Answer:

  20^2 = 400, the 2nd power of 20

Step-by-step explanation:

Given that k=20^20 and 20^k/k^20 = 20^n, you want the largest power of 20 that divides n.

Taking the base-20 logarithm of both equations, we have ...

  [tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]

Substituting for k and log(k), we get ...

  [tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]

This shows us the largest power of 20 that is a factor of n is 20².

The least to greatest of the ratio is 18 : 32, 5 : 8, and 11 : 16

Least to greatest arrangement can also be referred to as ascending order. Ascending order is the order such that each element is greater than or equal to the previous element.

5 : 8

= 5/8

= 0.625

11 : 16

= 11/16

= 0.6875

18 : 32

= 18/32

= 0.5625

Therefore, the ratio can be arranged as 18 : 32, 5 : 8, and 11 : 16 in ascending order.

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Answer:

$44,334.34

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=6000e^{0.05 \times40}[/tex]

[tex]\implies A=6000e^2[/tex]

[tex]\implies A=6000(7.3890560...)[/tex]

[tex]\implies A=44334.33659...[/tex]

Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).

The solution is once more 1.28 since a combined area of 0.10416 to the right implies that it must also have an area of 0.90 to the left.

Since each normally distributed random variable has a slightly different distribution shape, standardizing the variable to give it a mean of 0 and a standard deviation of 1 is the only method to determine regions using a table. How do we go about doing that? Employ the z-score!

Z = ( x - μ)/σ

If a mean and standard deviation are present for the random variable X,

Then a random variable with a mean of 0 and a standard deviation of 1 is produced by converting X using the z-score!

With that in mind, all that remains is to understand how to find areas under the standard normal curve, which can then be applied to any random variable with a normal distribution.

Since an area of 0.10416 to the right means that it must have an area of 0.90 to the left, the answer is once again 1.28.

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Answer: 224 pens more sold in 2nd shop

Step-by-step explanation:

Given,    

1st shop, 6 pens are sold more than previous day,

      1st day : 60

      2nd day : 60+6 =66

      3rd day : 66+6 =72

      4th day : 72+6 =78

      5th day : 78+6 =84

      6th day : 84+6 =90

      7th  day : 90+6 =96  

Then,

2nd shop, each day doubles the previous sold,

      1st day: 5

      2nd day:5*2 =10

      3rd day:10*2 =20

      4th day:20*2 =40

      5th day:40*2 =80

      6th day:80*2 =160

      7th day:160*2 =320

Therefore, second shop sells more in a week which is calculated by 320-96=224 more sold than the 1st shop.

The time that is left before the fossil fuel reserves run out would be= 2000 years.

A fossil fuel is defined as the type of fuel that is gotten from dead and decayed organic matter that has been buried for years underneath the earth surface.

The quantity of usable fossil fuel existing on earth = 2.1 x 10⁸metric tonnes.

The rate of fossil fuel used per year = 1 x 10⁵

Mathematically,

If 1 year = 1 x 10⁵

X years = 2.1 x 108

make X years the subject of formula;

X years = 2.1× 10⁸/1× 10⁵

X years = 2.1 × 10³ or 2100

X year = 2000( to one significant figure)

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Answer:

6/1.5

Step-by-step explanation:

You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!

[tex] \Large{\boxed{\sf Slope = 3}} [/tex]

[tex] \\ [/tex]

The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.

[tex] \\ [/tex]

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]

Where m is the slope of the line.

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]

[tex] \\ [/tex]

Now, substitute these values into the formula:

[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer:

slope = 3

How to Solve:

The question is asking us to find the slope, given two points.

These points are (0,0) and (4,12).

We will use the slope formula:

[tex]\boldsymbol{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

Plug in the data:

[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]

[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]

Simplify the fraction to its lowest terms:

[tex]\boldsymbol{m=3}[/tex]

Therefore, the slope is 3.

The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:

p(s) = 4s

Integral = ∫2s5s ds

= ∫2s5s dx

= [s2/2]2s5s

= (25/2) - (4/2)

= 20/2

= 10

Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.

To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.

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Answer:

Step-by-step explanation:

To find the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0, we can use the following steps:

Rewrite the equation of the circle in standard form: (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius.

In this case, the equation of the circle is already in standard form, so we can skip this step.

Find the slope of the line 3x + 5y + 7 = 0. The slope is -3/5.

Find the slope of the tangent to the circle. The slope of the tangent will be equal to the slope of the line, which is -3/5.

Substitute the slope of the tangent and the coordinates of a point on the circle into the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the circle and m is the slope.

In this case, we can substitute the coordinates of the center of the circle (which is (0, 0)) and the slope of the tangent (-3/5) into the point-slope form to get:

y - 0 = (-3/5)(x - 0)

Simplify to get the equation of the tangent: y = -3/5x.

Therefore, the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0 is y = -3/5x.

Part A:

The graph of the line intersects the x-axis at the point (4, 0).

Part B:

The point represents the distance of Shari from the home.

After 4 minutes, Shari rushed past her house.

A function graph is a visual representation of a relation. A function is actually equal to its graph in set theory and current mathematical foundations. For instance, when deciding whether or not a function is onto (surjective), a codomain should be taken into account. The graph of a function alone does not reveal the codomain. Although they relate to the same thing, the terms "function" and "graph of a function" communicate different perspectives on it, which is why they are commonly employed.

The line's x-intercept is 4 minutes.

The time Shari will arrive at her house is indicated by the 4 minutes.

Shari's distance from home on her run across town is represented by the line 6x - 3y = 24......... (1), where y stands for blocks, and x for minutes.

Therefore, when y = 0, we obtain 6x - 0 = 24, which equals x = 4, from equation (1) above.

As a result, 4 minutes is the x-intercept of the line (1).

It is stated that Shari will get at her house in 4 minutes, and there are no blocks between them.

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Answer:

x=6

Step-by-step explanation:

9-3=6 or 6+3=9

Answer:

5

Step-by-step explanation:

The slope or gradient of the line

using this formula as our guide line

y = mx +b

where m = slope

x = x– intercept

b = y– intercept

so

y = 5x + 12

the slope will be 5

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