Question is in the picture above

Answer:

Awnser "y = 10x + 60"

Step-by-step explanation:

So, the chart coordinate should looks like this:

(1, 75)

(2, 70)

(3, 80)

(4, 95)

(4, 100)

And there is a line passing (0, 60) and (2, 80)

So we just need to find the y-intercept and the slope by the line:

Slope: [change in x over change in y] = 20 ÷ 2 = 10

y-intercept: [the value of y when x equal 0] = 60 (because the line passed through (0, 60) )

Step-by-step explanation:

Answer; 10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test

Step-by-step explanation:

The arithmetic sequence with the given values a1 = 5  n= 10 and a10 =32 is 5,8,11,14 and soon

What is Arithmetic sequence ?

An arithmetic sequence is a sequence of numbers where each term is obtained by adding a fixed number, called the common difference (d), to the preceding term. In other words, an arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is the same.

Given a1 = 5  n= 10 and a10 =32

so we know that,

a10 = a+ 9 d

32 = 5 + 9*d

9d = 27

d = 3

so the sequence could be

a1 = 5

a2 = a+ d = 5 + 3 = 8

a3 = 8+ 3 = 11

a4 = 11+ 3  = 14

therefore, The arithmetic sequence with the given values a1 = 5  n= 10 and a10 =32 is 5,8,11,14 and soon

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The solution for \(\tan \theta\) is \(\frac{v\sqrt{3}}{u\sqrt{1-\frac{1}{3} v^{2}}}\).

To solve for \(\tan \theta\), we need to simplify the equation by combining the fractions and simplifying the square roots.

First, let's combine the fractions on the right side of the equation:
\[ \tan \theta=\frac{v}{\sqrt{3}} \cdot \frac{3}{\sqrt{9-3 v^{2}}} \cdot \frac{\sqrt{3}}{u} \]

Next, we can simplify the square roots:
\[ \tan \theta=\frac{v}{\sqrt{3}} \cdot \frac{3}{\sqrt{9}\sqrt{1-\frac{1}{3} v^{2}}} \cdot \frac{\sqrt{3}}{u} \]

\[ \tan \theta=\frac{v}{\sqrt{3}} \cdot \frac{3}{3\sqrt{1-\frac{1}{3} v^{2}}} \cdot \frac{\sqrt{3}}{u} \]

Now we can simplify the fractions:
\[ \tan \theta=\frac{v}{\sqrt{3}} \cdot \frac{1}{\sqrt{1-\frac{1}{3} v^{2}}} \cdot \frac{\sqrt{3}}{u} \]

Finally, we can combine the terms to get the final expression for \(\tan \theta\):
\[ \tan \theta=\frac{v\sqrt{3}}{u\sqrt{1-\frac{1}{3} v^{2}}} \]

Therefore, the solution for \(\tan \theta\) is \(\frac{v\sqrt{3}}{u\sqrt{1-\frac{1}{3} v^{2}}}\).

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The transformation between the points is (x, y) = (x, -y + 10)

From the question, we have the following parameters that can be used in our computation:

G(9, 12), H(−2, −15), J(3, 8) and

G'(9, -2), H'(-2, 25), J'(3, 2)

We can see that the x coordinates of the image and the preimage are equal

However, the relationship between the y-coordinates is

y' = -y + 10

This means that

(x, y) = (x, -y + 10)

The above rule is a translation transformation

Translation transformation is a transformation that moves each point in a figure or object by a fixed distance in a specified direction.

Hence, the transformation is (x, y) = (x, -y + 10)

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Complete question

26. G(9, 12), H(−2, −15), J(3, 8) and G'(9, -2), H'(-2, 25), J'(3, 2)

Write out the transformation rule from GHJ to G'H'J'

Applying Trigonometric ratios, the missing sides, expressed as radicals in simplest form are:

26. u = 3√2; v = 3

27. a = 3/2; b = 3/2

28. x = 7√2; y = 7

29. u = 5√2; v = 5√2

Radicals are mathematical expressions that involve the square root or nth root of a number or a variable.

We can express each of the missing sides in radicals using the appropriate Trigonometry ratio in each case as follows:

26. Use sine ratio to find u:

sin 45 = 3/u

u = 3/sin 45

u = 3 / 1/√2 [sin 45 = 1/√2]

u = 3 * √2/1

u = 3√2

Use tangent ratio to find v:

tan 45 = 3/v

v = 3/tan 45

v = 3/1 [tan 45 = 1]

v = 3

27. Use sine ratio to find a:

sin 45 = a / 3√2

a = 3√2 * sin 45

a = 3√2 * 1/√2 [sin 45 = 1/√2]

a = 3/2

Use cosine ratio to find b:

cos 45 = b / 3√2

b = 3√2 * cos 45

b = 3√2 * 1/√2 [cos 45 = 1/√2]

b = 3/2

28. Use cosine ratio to find x:

cos 45 = 7 / x

x = 7/ cos 45

x = 7 / 1/√2 [cos 45 = 1/√2]

x = 7 * √2/1

x = 7√2

Use tangent ratio to find y:

tan 45 = y/7

y = 7 * tan 45

y = 7 * 1 [tan 45 = 1]

y = 7

29. Use sine ratio to find u:

sin 45 = u/10

u = 10 * sin 45

u = 10 * 1/√2 [sin 45 = 1/√2]

u = 10/√2

Rationalize

u = 5√2

Use cosine ratio to find v:

cos 45 = v/10

v = 10 * cos 45

v = 10 * 1/√2 [sin 45 = 1/√2]

v = 10/√2

Rationalize

v = 5√2

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About 22,500 people at the Super Bowl game will not be wearing team jerseys.

Here the entire population is proportional to the number of people who entered the main gate without wearing team jerseys.

Find the proportion of people not wearing team jerseys by dividing 150 by 500. Now multiply the resultant proportion by the actual population.

Here we have

150 out of the first 500 people who entered the main gate were not wearing team jerseys,

The proportion of people not wearing team jerseys  

=> p = 150/500 = 0.3

Given that the sample is representative of the entire population of 75,000 people attending the game,

The population that will not be wearing team jerseys can be calculated as follows

75,000 x 0.3 = 22,500

Therefore,

About 22,500 people at the Super Bowl game will not be wearing team jerseys.

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The simplified form of the expression ( -3 )² + ( -2 )² is 13.

Given the expression in the question;

( -3 )² + ( -2 )²

To solve the expression (-3)² + (-2)², we first need to simplify each term inside the parentheses by multiplying each term by itself.

It involves squaring the values of -3 and -2, and then adding them together.

First, we can simplify;

(-3)² as (-3) x (-3), which gives us 9.

Similarly,

(-2)² can be simplified as (-2) x (-2), which gives us 4.

So, substituting these values back into our original expression, we get:

(-3)² + (-2)² = 9 + 4 = 13

(-3)² + (-2)² = 12

Therefore, (-3)² + (-2)² simplifies to 13.

Option C) 13 is the correct answer.

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Answer:It will hit the ground when 84 - 16t^2 = 0

Step-by-step explanation:

16t^2 = 84

t^2 = 5.25

t = 2.29

The total distance traveled by the taxi driver is 7 1/2 miles.

To find out how many miles the taxi driver travels for the two stops, we need to add up the distance to the first stop and the distance to the second stop.

The distance to the first stop is 4 5/8 miles.

To find the distance to the second stop, we need to subtract 1 3/4 miles from the distance to the first stop:

4 5/8 miles - 1 3/4 miles = 2 7/8 miles

Now we can add the distance to the first stop and the distance to the second stop to find the total distance traveled:

4 5/8 miles + 2 7/8 miles

= 7 1/2 miles

Therefore, the taxi driver will travel 7 3/2 miles for the two stops.

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Answer: y = -2x + 2 3/7

Step-by-step explanation:

The slope-intercept form is y = mx + b

Start:

14x + 7y = 17

Subtract 14 from each side to get y alone:

7y = -14x + 17

Divide by 7 on each side:

y = -2x + 2 3/7

Hope this helps!

The correlation coefficient relating is 0.76 thath mean  the accompaniment rates for wives and sons is the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

To find the correlation coefficient relating the accompaniment rates for wives and sons, we can use the formula:

r = (nΣxy - (Σx)(Σy)) / √[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Where:
- r is the correlation coefficient
- n is the number of observations (in this case, 9)
- x and y are the accompaniment rates for wives and sons, respectively
- Σxy is the sum of the products of x and y
- Σx and Σy are the sums of x and y, respectively
- Σx^2 and Σy^2 are the sums of x squared and y squared, respectively

Using the data from the table, we can calculate the following:

Σx = 27.2 + 40.1 + 35.7 + 37.8 + 38 + 38.4 + 38.7 + 29.8 + 23.8 = 309.5
Σy = 2.2 + 1.5 + 0.3 + 3.5 + 5.4 + 11 + 11.9 + 8.6 + 7.4 = 51.8
Σxy = (27.2)(2.2) + (40.1)(1.5) + (35.7)(0.3) + (37.8)(3.5) + (38)(5.4) + (38.4)(11) + (38.7)(11.9) + (29.8)(8.6) + (23.8)(7.4) = 1164.41
Σx^2 = 27.2^2 + 40.1^2 + 35.7^2 + 37.8^2 + 38^2 + 38.4^2 + 38.7^2 + 29.8^2 + 23.8^2 = 11491.89
Σy^2 = 2.2^2 + 1.5^2 + 0.3^2 + 3.5^2 + 5.4^2 + 11^2 + 11.9^2 + 8.6^2 + 7.4^2 = 349.98

Plugging these values into the formula, we get:

r = (9)(1164.41) - (309.5)(51.8) / √[(9)(11491.89) - (309.5)^2][(9)(349.98) - (51.8)^2] = 0.76

This value of r indicates a strong positive correlation between the accompaniment rates for wives and sons. This means that as the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

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The expression to represent the total cost of hiring a plumber is y = 50 + 40x

From the question, we have the following parameters that can be used in our computation:

Charges = $50 for visiting

Rate = $40 every hours

Represent the number of hour with x and the total charge with y

Using the above as a guide, we have the following:

y = Charges + Rate * x

Substitute the known values in the above equation, so, we have the following representation

y = 50 + 40x

Hence, the equation is y = 50 + 40x

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Yes, Tanner has enough spray paint for his arrow.

What is an Area?

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. A planar figure's area is the area that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm2 and m2.

Given : paint available in can = 12 ft²

We know that the arrow is comprised of a triangle and a rectangle.

So, the area of given arrow = area of rectangle + area of triangle

Now, area of triangle = 1/2 ×base × height

                                   = 1/2 × 3 × (6 - 5 1/3)

                                   = 3/2 × ( 6 - 16/3)

                                   = 3/2 × ( 18-16)/3

                                   = 3/2 × 2/3

                                    = 1 ft²

Similarly, area of rectangle =  length × breadth

                                            = 5 1/3 × 2

                                            = 16/3 × 2

                                            = 32/3 ft²

Hence, area of arrow = area of triangle +area of rectangle

                                   = 1 + 32/3

                                   = 35/3 ft²

                                   = 11.67 ft²

So, he has sufficient paint to cover the arrow.

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Answer:

see explanation

Step-by-step explanation:

the diagonals of a rhombus are perpendicular to each other, then

∠ 1 = 90°

AB and CD are parallel ( opposite sides of a rhombus are parallel )

∠ 2 and 51° are alternate angles and are congruent , then

∠ 2 = 51°

the diagonals bisect the angles , then

∠ 3 = ∠ 2 = 51°

the sum of the 3 angles , in the triangle with ∠ 4 sum to 180°

∠ 1 + ∠ 3 + ∠ 4 = 180°

90° + 51° + ∠ 4 = 180°

141° + ∠ 4 = 180° ( subtract 141° from both sides )

∠ 4 = 39°

then

∠ 1 = 90° , ∠ 2 = 51° , ∠ 3 = 51° , ∠ 4 = 39°

This distribution of inequities ensures that the total amount of ticket sales revenue stays within the budget, that no more than 150 tickets are sold overall, and that no negative ticket sales occur.

Let x represent the quantity of single tickets sold and y represent the quantity of pair tickets sold. The entire revenue from ticket sales, R, is then calculated as follows:

R = 45x + 70y

The entire amount of ticket sales revenue is limited by the budget to $5000:

45x + 70y ≤ 5000

No more than 150 tickets may be sold in total.

x + y ≤ 150

X and Y must both be non-negative since we cannot sell negative tickets:

x ≥ 0\sy ≥ 0

As a result, the system of disparities that best captures this circumstance is:

5000 x + y 45x + 70y 150x 0y 0

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The Cartesian equation of the curve is y = 0. This is a horizontal line at y = 0.

To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the parametric equations.

First, let's rearrange the first equation to isolate θ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x
1/(sinθ) - 1/(tanθ) = -2x
1/(sinθ) - (cosθ)/(sinθ) = -2x
(cosθ)/(sinθ) = 1/(sinθ) + 2x
cosθ = 1 + 2x*sinθ

Now, let's rearrange the second equation to isolate θ:
4y = 2cscθ - 2cotθ
2y = cscθ - cotθ
2y + cotθ = cscθ
cotθ - cscθ = -2y
1/(tanθ) - 1/(sinθ) = -2y
(cosθ)/(sinθ) - 1/(sinθ) = -2y
(cosθ)/(sinθ) = 1/(sinθ) - 2y
cosθ = 1 - 2y*sinθ

Now we can set the two equations equal to each other and solve for sinθ:
1 + 2x*sinθ = 1 - 2y*sinθ
4x*sinθ = -4y*sinθ
sinθ = -4y/4x
sinθ = -y/x

Finally, we can use the Pythagorean identity, sin^2θ + cos^2θ = 1, to find the Cartesian equation:
(-y/x)^2 + cos^2θ = 1
y^2/x^2 + cos^2θ = 1
cos^2θ = 1 - y^2/x^2
cosθ = √(1 - y^2/x^2)

Substituting this back into one of the original equations, we get:
1 + 2x*sinθ = 1 - 2y*sinθ
1 + 2x*(-y/x) = 1 - 2y*(-y/x)
1 - 2y^2/x = 1 + 2y^2/x
4y^2/x = 0
y^2 = 0
y = 0

So the Cartesian equation of the curve is y = 0. This is a horizontal line at y = 0.

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The distance across the lake is 120 feet.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given is a right angled triangle.

Pythagoras theorem states that,

Square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the two legs of the triangle.

The distance across the lake is one of the leg of the right triangle.

Length of hypotenuse = 208 feet + 104 feet

                                     = 312 feet

Length of other leg = 192 feet + 96 feet

                                = 288 feet

Distance across the lake = √(312² - 288²)

                                         = √14,400

                                         = 120 feet

Hence 120 feet is the distance across the lake.

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Step-by-step explanation:

the angles which occupy the same relative position at each intersection where a straight line crosses two others, are called corresponding angles. If the two lines are parallel, the corresponding angles are equal.

two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines, are called alternate angles. If the original two lines are parallel, the alternate angles are equal.

since we are only dealing with parallel lines here, the angles are always equal.

a)

a = 60°, alternate

b)

a = 75°, corresponding

c)

a = 108°, corresponding

The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.

In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).

Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).

So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

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Box plot of the given data for the scores of the statistics is represented by minimum value = 51, maximum value = 93, Median = 75, lower quartile = 67 and upper quartile = 87.

Box plot is attached.

Scores of the statistics test  is equal to

83,72,91,73,74,51,62,52,76,93

Arrange the scores into ascending order we get,

51, 52, 62, 72, 73, 74, 76, 83, 91, 93

Minimum value = 51

Maximum value = 93.

Median= Average of the two middle values.

Two middle values are 74 and 76

Median

= (74 + 76) / 2

= 75

Lower quartile = Median of the lower half of the data

Upper quartile = Median of the upper half of the data

Lower half= 51, 52, 62, 72, 73

Upper half = 76, 83, 91, 93

Lower quartile

= (62 + 72) / 2

= 67

Upper quartile

= (83 + 91) / 2

= 87

Constructed box plot is attached.

Therefore, to construct box plot minimum value = 51, maximum value = 93, Median = 75, lower quartile = 67 and upper quartile = 87 for the given test scores.

Box plot is attached.

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The value in the red box would be 19√7.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is a pyramid as shown in the image.

We can write -

b{4} = 2√7 - 4√7 = - 2√7

b{4} = - 2√7

- 4√7 + b{9} = 3√28

b{9} = 3√28 + 4√7

b{9} = 6√7 + 4√7

b{9} = 10√7

b{6} = 10√7 - √7

b{6} = 9√7

b{2} =  - 2√7 + 6√7

b{2} = 4√7

b{3} = 3√28 + 9√7

b{3} = 6√7 + 9√7

b{3} = 15√7

b{1} = 4√7 + 15√7

b{1} = 19√7

Therefore, the value in the red box would be 19√7.

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{QUESTION IN ENGLISH -

Look at the following pyramid, in which each box has a number that is formed by adding the two bottom boxes.

What is the number that occupies the red box?}

The researcher's study aims to examine how exercise and diet affect weight loss. The researcher collected data from 12 volunteers with similar weights and health conditions and randomly assigned them to one of three programs: Program I with diet only, Program II with exercise only, and Program III with a combination of diet and exercise. After three months, the weight loss of each participant was recorded and summarized. The researcher wishes to carry out nonparametric tests at a significant level of 0.05 to examine the effectiveness of the three programs and to compare the effectiveness of Program III to Program I.

a) To examine the effectiveness of the three programs, we can use the Kruskal-Wallis test, a nonparametric test that compares the medians of three or more groups. The null hypothesis is that the medians of the three programs are equal, and the alternative hypothesis is that at least one of the medians is different. We can use the R function kruskal.test() to carry out the test:

```
> weight_loss <- c(2,0,1,1,1,2,1,3,2,1,4,4)
> program <- factor(c(rep("I",4), rep("II",3), rep("III",5)))
> kruskal.test(weight_loss ~ program)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of the three programs.

b) To compare the effectiveness of Program III to Program I, we can use the Wilcoxon rank-sum test, a nonparametric test that compares the medians of two groups. The null hypothesis is that the medians of Program III and Program I are equal, and the alternative hypothesis is that the medians are different. We can use the R function wilcox.test() to carry out the test:

```
> weight_loss_I <- c(2,0,1,1)
> weight_loss_III <- c(3,2,1,4,4)
> wilcox.test(weight_loss_I, weight_loss_III)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of Program III and Program I.

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The expected net gain (or loss) for playing one game is -$3.125, which rounds to -$3.25. The correct answer is d. -$3.25.

I am a question answering bot and do not have personal experiences to share. However, I can help you find the expected net gain (or loss) for playing one game in this scenario.

First, let's calculate the probability of each possible outcome:
- Probability of winning: 1/8
- Probability of placing 2nd or 3rd: 2/8
- Probability of placing 4th through 8th: 5/8

Next, let's calculate the net gain (or loss) for each possible outcome:
- Net gain for winning: $125 - $25 = $100
- Net gain for placing 2nd or 3rd: $0 (since you receive your money back)
- Net gain for placing 4th through 8th: -$25 (since you lose your money)

Finally, let's use these probabilities and net gains to calculate the expected net gain (or loss) for playing one game:
Expected net gain = (Probability of winning) x (Net gain for winning) + (Probability of placing 2nd or 3rd) x (Net gain for placing 2nd or 3rd) + (Probability of placing 4th through 8th) x (Net gain for placing 4th through 8th)
= (1/8) x ($100) + (2/8) x ($0) + (5/8) x (-$25)
= $12.50 + $0 - $15.625
= -$3.125

Therefore, the expected net gain (or loss) for playing one game is -$3.125, which rounds to -$3.25. The correct answer is d. -$3.25.

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In the word problem,  the 16 cups equals to a gallon.

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here A pint is equal to 2 cups (example: a large glass of milk!)

=>1 pint = 2 cups = 16 fluid ounces

When measuring many cups of liquid all put together we might want to use quarts.

A quart (qt) is the same thing as 4 cups or 2 pints.

=>1 quart = 2 pints = 4 cups = 32 fluid ounces

A gallon (gal) is the same as 16 cups or 8 pints or 4 quarts.  It is the largest liquid measurement.

Hence the 16 cups equals to a gallon.

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Answer:

  32°

Step-by-step explanation:

You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).

The angles of a linear pair total 180°, so we have ...

  (3g +23) +(7g +127) = 180

  10g = 30 . . . . . . . . . subtract 150

  g = 3 . . . . . . . . . divide by 10

The smaller angle is ...

  ∠PKT = (3·3 +23)°

  ∠PKT = 32°

Answer:

Step-by-step explanation:

A cylinder has a base diameter of 12 foot and a height of 12 foot what is its volume in cubic feet to the nearest 10s place

The volume of a cylinder can be calculated using the formula:

V = πr^2h

where:

V is the volume of the cylinder

π is a mathematical constant, approximately equal to 3.14159

r is the radius of the base of the cylinder

h is the height of the cylinder

We are given the diameter of the base, which is 12 feet. The radius (r) is half of the diameter, so we have:

r = 12/2 = 6 feet

The height (h) is also given as 12 feet.

Substituting the values we have into the formula, we get:

V = π(6)^2(12) ≈ 1357.17

Rounding to the nearest 10's place, the volume is approximately 1360 cubic feet. Therefore, the volume of the cylinder is 1360 cubic feet to the nearest 10's place.

Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.

What is a geometric progression?

A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.

We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.

From this, we get the common ratio to be 51/50 i.e. 1.02.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₈ = a₁ r⁽⁸⁻¹⁾

⇒a₈ = a₁ r⁷

⇒a₈ = 1500 (1.02)⁷

⇒a₈ = 1500 (1.1487)

⇒a₈ = $1723.05

Hence, Leo's balance after 8 months will be $1723.05.

Learn more about geometric progression from the given link

https://brainly.com/question/29632351

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