A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3

Answer:

The Answer is 25.5 in

Step-by-step explanation:

What you basically do is

17² * 17²= 289

19² * 19²= 361

Then add 289+361=650

Then u have to Divide

Then you should get 25.495

Then Round to the nearest Tenth and you Get (25.5 in)

Hope This was Right

Answer:

25.49

Step-by-step explanation:

To find the hypotenuse for right triangles, we use the Pythagorean Theorem or

[tex]A^{2} +B^{2} = C^{2}[/tex]

Keep in mind we only use this for right triangles

With that in mind, lets solve for side c

[tex]A^{2} + B^{2} = C^{2} \\19^{2} +17^{2} = C^{2} \\(19*19) + (17*17) = C^{2} \\361+ 289 = 650\\C^{2} = 650\\\sqrt{650} = C\\C = 5\sqrt{26} or 25.49[/tex]

Hope This Helps!

Answer:

0.64 ± 0.1117 or

[tex]0.64\pm 1.645*\sqrt{\frac{0.64*(0.36)}{50}}[/tex]

Step-by-step explanation:

Sample size (n) = 50

Z-score for a 90% confidence interval (z) = 1.645

Proportion of students that read at least one book (p):

[tex]p=\frac{32}{50}=0.64[/tex]

The confidence interval is given by:

[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]

Applying the given data:

[tex]0.64\pm 1.645*\sqrt{\frac{0.64*(1-0.64)}{50}}\\ 0.64\pm 0.1117[/tex]

The confidence interval is 0.64 ± 0.1117

The 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month is [tex]0.64\pm 0.11178[/tex].

Given information:

From a random sample of 50 (n) students, Alma found that 32 students read at least 1 book last month.

Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book.

It is required to find the 90 percentage confidence interval for the proportion of all students in her district who read at least 1 book last month.

Now, from tha table, the z-score of 90 percent confidence level is,

[tex]z=1.645[/tex]

The probability p for the proportion of students who read atleast one book is,

[tex]p=\dfrac{32}{50}\\p=0.64[/tex]

So, the 90 percent confidence interval will be calculated as,

[tex]p\pm z\sqrt{\dfrac{p(1-p)}{n}}=0.64\pm 1.645\times \sqrt{\dfrac{0.64(1-0.64)}{50}}\\=0.64\pm 0.11178[/tex]

Therefore, the 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month is [tex]0.64\pm 0.11178[/tex].

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Answer:

A^B = A*A*A*... (B number of times)

Answer:

20%  

Step-by-step explanation:

Find the increase (subtract original number with final):

42-35= 7

Find the percent change (divide the increase by original number, then multiply by 100 to find the percentage):

[tex]\frac{7}{35}[/tex]*100=20

The percent change from 35 students to 42 students is 20%. This is calculated by using the formula for percent change: ((New Amount - Original Amount) / Original Amount) * 100.

In this case, we are trying to calculate the percent change in the number of students in Mrs. Mroc's class. The formula for percent change is:

((New Amount - Original Amount) / Original Amount) * 100

The New Amount is 42 (the number of students next year), and the Original Amount is 35 (the current number of students). So the percent change would be (((42-35)/35)*100), which equals 20%.

So, if Mrs. Mroc's class increases from 35 students to 42 students next year, the percent change will be 20%.

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Answer:

[tex]BC=6\sqrt{2}\ units[/tex]

Step-by-step explanation:

In this problem i will assume that the side AB is the hypotenuse

The picture in the attached figure

we know that

In a right triangle, if one angle is 45 degrees, then the other angle complementary is equal to 45 degrees too

so

[tex]m\angle B=45^o[/tex]

In the right triangle ABC

[tex]cos(B)=\frac{BC}{AB}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

we have

[tex]cos(45^o)=\frac{\sqrt{2}}{2}[/tex]

[tex]AB=12\ units[/tex]

substitute

[tex]BC=cos(B)(AB)[/tex]

[tex]BC=\frac{\sqrt{2}}{2}(12)=6\sqrt{2}\ units[/tex]

Answer: 6 square root 2

Step-by-step explanation:

In the given data set, 12, 8, 6, 6, 9, 8, 7, 11, 6, the value 6 represents the mode.

We are given the following dataset: 12, 8, 6, 6, 9, 8, 7, 11, 6.

Count the frequency of each number:

12 appears 1 time.

8 appears 2 times.

6 appears 3 times.

9 appears 1 time.

7 appears 1 time.

11 appears 1 time.

The number 6 appears 3 times, more frequently than any other number.

By the definition of mode, it is the value that appears most frequently in a data set.

Since 6 occurs more times than any other number in the list, then it is the mode

Answer:

Ok. so the Place value is 70000 and the face value is 7. Face value of a digit in a number is the digit itself.

More clearly, face value of a digit always remains same irrespective of the position where it is located

Place value of a digit in a number is the digit multiplied by thousand or hundred or whatever place it is situated.

Hope this helped.

Step-by-step explanation:

Answer:

1/2 chances if getting heads 1/2 for getting tails

Answer:

heads or tails

Given:

Given that the radius of the circle is 12 inches.

The angle of the shaded sector is 210°

We need to determine the area of the shaded sector.

Area of the shaded sector:

The area of the shaded sector can be determined using the formula,

[tex]Area =(\frac{\theta}{360}) \pi r^2[/tex]

Substituting [tex]\theta=210[/tex] and r = 12, we get;

[tex]Area =(\frac{210}{360}) (3.142)(12)^2[/tex]

Simplifying, we get;

[tex]Area =(\frac{210}{360}) (3.142)(144)[/tex]

[tex]Area =263.9 \ in^2[/tex]

Thus, the area of the shaded sector is 263.9 square inches.

Hence, Option c is the correct answer.

Answer:

A. when working on an online class students have more freedom to choose an environment in which they are most comfortable

Step-by-step explanation:

some students do better at home some do better in a traditional setting but being online lets you change your setting to anywhere with online access

Step-by-step explanation:

One year is 12 months.  12 mm is 1.2 cm.

Write and solve a proportion

1.2 cm / 4 months = x / 12 months

x = 3.6 cm

Answer: slope and x-intercept

y-intercept and a point that is not an intercept is the information about the graph of the relationship is given. So, the correct answer is E. y-intercept and a point that is not an intercept

Let's analyze the information given in the problem:

1. The charity organization sold 18 tickets to cover necessary production costs.

2. They sold each ticket for $45.

3. They want to determine the net profit when they have sold 2 tickets.

We are given a specific point on the graph: (x = 2, y = net profit when 2 tickets are sold).

Now, let's calculate the net profit when 2 tickets are sold:

Net profit when 2 tickets are sold = Total revenue - Total production costs

Total revenue = 2 tickets * $45 per ticket = $90

Total production costs = $18 (to cover necessary production costs)

Net profit = $90 - $18 = $72

Now, let's look at the options:

A. Slope and x-intercept: We do not have the slope or the x-intercept of the graph.

B. Slope and y-intercept: We do not have the slope or the y-intercept of the graph.

C. Slope and a point that is not an intercept: We have a point on the graph, but we do not have the slope.

D. x-intercept and y-intercept: We do not have the x-intercept or the y-intercept of the graph.

E. y-intercept and a point that is not an intercept: We have the y-intercept (net profit when 0 tickets are sold, which is $18) and a point on the graph (net profit when 2 tickets are sold, which is $72).

F. Two points that are not intercepts: We have one point on the graph (net profit when 2 tickets are sold, which is $72), but we do not have another point.

So, Based on the information given, the correct option is:

E. y-intercept and a point that is not an intercept

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Correct Question is:

A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs.

They sold each ticket for $45.

Let y represent the net profit (in dollars) when they have sold 2 tickets.

Which of the following information about the graph of the relationship is given?

A. Slope and x- intercept

B. Slope and y-intercept

C. Slope and a point that is not an intercept

D. x-intercept and y intercept

E. y-intercept and a point that is not an intercept

F. Two points that are not intercepts

Answer:

5040$

Step-by-step explanation:

28000 x .18 = 5040

We are given that if Tiffany closes any car on a car she gets 18% as commission. For a car that cost $28,000 her commission will be  $5,040

Given data

Commission = 18%

Cost of car  =  $ 28,000.00

Let us find 18% of  $28,000.00

Commission = 18/100* 28,000.00

Commission = 0.18* 28,000.00

Commission = $5,040

Hence her commission will be: $5,040

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Given:

In ΔABC, ∠C = 90°, ∠A = 50° and AB = 3 unit.

To find the value of BC.

Formula:

By Trigonometric Ratio we get,

[tex]sin \ \theta=\frac{opposite}{Hypotenuse}[/tex]

Now,

With respect to θ = 50°, AB is the hypotenuse and AB is the opposite side.

So,

[tex]sin \ 50^{\circ}=\frac{BC}{AB}[/tex]

[tex]sin \ 50^{\circ}=\frac{BC}{3}[/tex]

     [tex]BC = 3 \times sin 50^{\circ}[/tex]

     [tex]BC = 2.298 = 2.3[/tex] (approx)

Hence,

The value of BC is 2.3 units.

Answer:

13 cards

Step-by-step explanation:

One deck has 52 cards.

2 decks have 2 * 52 cards, or 104 cards.

104 cards are divided among 8 players.

104/8 = 13

Answer: 13 cards

Answer:

Three hundred fifty-five and three tenths.

Step-by-step explanation:

The word form for 355.3 kilograms is "Three hundred fifty-five point three kilograms." This representation breaks down the number into its hundreds, tens, ones, tenths, and specifies the unit of measurement, kilograms.

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a) True. Some residuals will be positive and some will be negative. b) True. Least squares minimizes the squares of the residuals. c) False. y with a caret denotes predicted values.

a) True. Some of the residuals from a least squares linear model will be positive and some will be negative. Residuals measure the difference between the observed values and the predicted values, and they can be positive if the observed value is higher than the predicted value, or negative if the observed value is lower.

b) True. Least squares regression aims to minimize the sum of squared residuals. By minimizing the squares of the residuals, we ensure that the line of best fit is as close as possible to the data points.

c) False. We write y with a caret (^) to denote the predicted values and y without a caret to denote the observed values.

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Answer:

The randomization will be centered around 0.5

Step-by-step explanation:

n = 30

Null hypothesis, H₀ : p = 0.5

Alternative hypothesis,  : p > 0.5

The randomization will be centered around 0.5

The indication of where the randomization distribution will be centered shows that the randomization distribution is always centered at the value of the parameter given in the null hypothesis, which is p = 0.5.

Thus, the randomization distribution is always centered at the value of the parameter given in the null hypothesis, which is p = 0.5.

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Answer:

With n = 50, both conditions(np > 5, n(1-p) > 5) are satisfied, so a random sample of 50 cars would have been large enough.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to the normal distribution if:

np > 5, n(1-p) > 5

70% of the drivers traveling on a major interstate highway exceed the speed limit.

So p = 0.7.

Would a random sample of 50 cars have been large enough and why?

With n = 50

np = 50*0.7 = 35 > 5

n(1-p) = 50*0.3 = 15 > 5

With n = 50, both conditions(np > 5, n(1-p) > 5) are satisfied, so a random sample of 50 cars would have been large enough.

Answer:

2/16

Step-by-step explanation:

1/8 x 2 = 2/16

Both 2 and 16 divide by 8, so one can know this is correct.

Also, both 8 and 16 are divisible by 8, so one can see this is the common denominator.

Answer:

θ   [tex]0.75\pi[/tex]     [tex]1.75\pi[/tex]

r   10.551  244.151

Step-by-step explanation:

The maximum value for [tex]\theta[/tex] is:

[tex]\theta_{max} = \ln r[/tex]

[tex]\theta_{max} = 2.199\pi\,rad[/tex]

The formula for the slope of the tangent line in polar coordinates is:

[tex]m = \frac{r'\cdot \sin \theta + r \cdot \cos \theta}{r' \cdot \cos \theta - r \cdot \cos \theta}[/tex]

Horizontal tangent lines have a slope of zero. So, the following relation must be satisfied:

[tex]r'\cdot \sin \theta + r \cdot \cos \theta = 0[/tex]

[tex]r'\cdot \sin \theta = - r \cdot \cos \theta[/tex]

[tex]\tan \theta = - \frac{r}{r'}[/tex]

[tex]\tan \theta = -\frac{e^{\theta}}{e^{\theta}}[/tex]

[tex]\tan \theta = -1[/tex]

[tex]\theta = \tan^{-1}(-1)[/tex]

[tex]\theta = \frac{3}{4}\pi + i\cdot \pi[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex].

The maximum value of i is:

[tex]i = \frac{\theta_{max}-\frac{3}{4}\pi }{\pi}[/tex]

[tex]i = \frac{2.199-0.75}{1}[/tex]

[tex]i = 1.449[/tex] ([tex]i_{max} = 1[/tex]).

Then, values are listed below:

θ   [tex]0.75\pi[/tex]     [tex]1.75\pi[/tex]

r   10.551  244.151

Answer:

{ ( 2.193 , π / 4)   , ( 10.551 , 3π / 4) ,  ( 50.754 , 5π / 4)  , ( 244.151 , 7π / 4)  }

Step-by-step explanation:

Given:-

- The polar curve has the equation:

                           r = e^θ

- list the points starting with the smallest value of r such that:

                1 ≤ r ≤ 1000   ,  0 ≤ θ < 2π.

Find:-

List all of the points (r,θ) where the tangent line is horizontal

Solution:-

- We will first transform the polar curve to cartesian coordinate system using the parametric relations:

                  x = r*cos (θ)

                  y = r*sin (θ)

- The tangent line is horizontal when the " dy / dθ  " = 0 and " dx / dθ  " = 0, so:

                  x = e^θ*cos (θ)      ,    y = e^θ*sin (θ)

                  dx / dθ = e^θ*cos (θ) - e^θ*sin(θ)

                               = e^θ*[cos (θ) - sin(θ)]

                  dx / dθ = e^θ*[cos (θ) - sin(θ)] = 0,

                  e^θ = 0    ,      [cos (θ) - sin(θ)] = 0

                  e^θ ≠ 0 for the given interval 0 ≤ θ< 2π  

                  cos (θ) - sin(θ) = 0 , tan ( θ ) = 1 - (1st quad and 3rd quad)

                  θ = { π / 4 , 5π / 4 } , 0 ≤ θ< 2π    

- Similarly, evaluate dy/dθ = 0;

                   dy/dθ = e^θ*cos (θ) + e^θ*sin(θ)

                              = e^θ*[cos (θ) + sin(θ)]

                  dy / dθ = e^θ*[cos (θ) + sin(θ)] = 0,

                  e^θ = 0    ,      [cos (θ) + sin(θ)] = 0

                  e^θ ≠ 0 for the given interval 0 ≤ θ< 2π  

                  cos (θ) + sin(θ) = 0 , tan ( θ ) = -1 , (2nd quad and 4th quad)

                  θ = { 3π / 4 , 7π / 4 } , 0 ≤ θ< 2π

- All possibilities of " θ " over the interval satisfying the a horizontal tangent line to the given polar curve:

                  θ = { π / 4, 3π / 4 , 5π / 4 , 7π / 4 } , 0 ≤ θ < 2π  

- We will plug the evaluated list of values of "θ " in the given polar curve and determine the corresponding values of "r":

                  r = e^θ

                  θ = π / 4  , r = e^(π / 4) = 2.193        

               1: ( r , θ ) = ( 2.193 , π / 4)        

                  θ = 3π / 4  , r = e^(3π / 4) = 10.55072        

               2: ( r , θ ) = ( 10.551 , 3π / 4)  

                  θ = 5π / 4  , r = e^(5π / 4) = 50.754      

               3: ( r , θ ) = ( 50.754 , 5π / 4)  

                 θ = 7π / 4  , r = e^(7π / 4) = 244.151      

               4: ( r , θ ) = ( 244.151 , 7π / 4)          

Answer:

d = 11

Step-by-step explanation:

The average rate of change can be calculated using the formula: (g(b) - g(a)) / (b - a), substituting -5 for a and 5 for b in our case.

In order to find the average rate of change of a function, in this case, function g, from x = -5 to x = 5, we use the formula: (g(b) - g(a)) / (b - a), where b is the ending value and a is the starting value. This gives us the slope of the tangent line that connects these two points on the graph, which reflects the average rate of change of the function over the interval. In this case, to find the average rate of change of function g from x = -5 to x = 5, we would substitute -5 for a and 5 for b in the formula to get: (g(5) - g(-5)) / (5 - (-5)). From here we can solve based on the known values of g(5) and g(-5).

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Answer:

A

Step-by-step explanation:

[tex]81[/tex] is [tex]9^2[/tex] which happens to be [tex](3^2)^2[/tex] or [tex]3^4[/tex].

So [tex]\sqrt[4]{81} =3[/tex]

this eliminates options C and D

It can't be option B as both b and c aren't 4th rooted.

Answer:

136=x

Step-by-step explanation:

When an angle is shown, the one opposite of it is equal to the forst equation. The bottom angles are equal to 360ñ so if you take 46x2=92. Subtract 92 by 360 to get 268. Divide it by 2 to get one of the bigger angles, which is 134 degrees. And as for the top, one angle on the bottom is equal to the same spot on the top. so, 136=x

Answer :

x = 134°

Step by step :

46° + x = 180°

x = 180° - 46°

x = 134°

Final answer:

The point estimate for the proportion of college students who prefer drink A is found by averaging the lower and upper bounds of the 95% confidence interval, which yields an estimate of 0.442 or 44.2%.

Explanation:

The point estimate for the true proportion of college students who prefer drink A is the midpoint of the 95% confidence interval. To find the point estimate, you sum the lower and upper bounds of the interval and divide by 2. In this case, the confidence interval is (.262, .622). The calculation for the point estimate is (0.262 + 0.622) / 2, which equals 0.442. Therefore, the point estimate is 0.442, which means that approximately 44.2% of college students prefer drink A.

Answer: A. $1300

Step-by-step explanation:

The initial value is $7000

The Salvage value is $500

The car will depreciate under a straight-line method, meaning it will lose $6500 value in 5 years.

6500 / 5 = 1300