The radius of a cylindrical water tank is 4.5ft, and its height is 11ft. What is the volume of the tank?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.

Answer:

a)  0.0721

Step-by-step explanation:

Let the random variable X be the score on the ACT exam.

Given:

Therefore, the random variable X is normally distributed:

[tex]X \sim\textsf{N}(21,5^2)[/tex]

Z-score for a sample mean

[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]

[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]

Given:

Therefore, the test statistic is:

[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]

Using the Z-tables to find the probability:

[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]

The partition point is (-7/2, 23/4)

The given parameters are:

(x1,y1) = (-6,-1)

(x2,y2) = (4,8)

a = 1 and b = 3

The partition point is calculated as:

(x, y) = ((bx1 + ax2)/(a + b) ,( by1+ay2)/a+b)

So, we have:

(x, y) = ((3 * -6 + 1 * 4)/(1 + 3) ,(3 * 8 + 1 * -1)/1+3)

Evaluate

(x, y) = (-14/4, 23/4)

Simplify

(x, y) = (-7/2, 23/4)

Hence, the partition point is (-7/2, 23/4)

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The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C

The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.

Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.

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Answer:

The answer is C.

Answer:

The function has 4 roots.

Step-by-step explanation:

Since the degree of the polynomial has is 4, there are a total of 4 roots (both real and complex).

Answer:

4 roots, two real and two complex.

Step-by-step explanation:

The degree of the polynomial indicates the number of solutions

Hope this helps

Answer:

5:3:2

Step-by-step explanation:

see image

Jarek gets half. Then from the other half, Jerzy gets 3 pieces of 5 and Justyn gets the leftover 2 pieces. But Jarek's piece is all 5 pieces of the first half.

Jarek 5 parts:

Jerzy 3 parts:

Justyn 2 parts

5:3:2

see image

Answer:

the third answer (-3, -3, 3)

Step-by-step explanation:

the dotted lines indicate that these lines (or part of lines) are invisible due to being inside or behind the cube.

so, we know that A is the left-back-upper corner of the cube.

the x-axis goes front-back. front is positive.

the y-axis goes left-right. right is positive.

the z-axis goes up-down. up is positive.

since the origin (0, 0, 0) is the center of the cube, and the sides are all 6 units long, the corners can have only -3 or +3 coordinates (half of a side length on either side of the origin) in each direction.

as we said : left-back-upper corner.

left means negative y.

back means negative x.

upper means positive z.

so, the coordinates of A are

(-3, -3, 3)

The time it will take the roller coaster to reach the ground is 171.65 seconds

Given the roller coaster’s height given by the following parameters

h = –0.025t² + 4t + 50

On the ground level, the height will be zero. Substitute h = 0 and determine the value of t

–0.025t² + 4t + 50 = 0

0.025t² - 4t - 50 = 0

Factorize

On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds

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The value of x according to the given task is; 12.

It follows from the task content that the value of x is to be determined.

Since, lines AB and BC are both tangent to the circle and they both share a point of intersection; it follows that;

5x = 3x +24

2x = 24

x = 24/2

x = 12.

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The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

First, we must obtain the slope of the line perpendicular to BC

Given the coordinates B(7,5), and C(2,3)

Get the slope BC, exists

[tex]$m_{BC} = \frac{3-5}{2-7}[/tex]

= -2/-5 = 2/5

The slope of the line perpendicular to BC will be -5/2.

The slope of the required line in point-slope form exists expressed as;

[tex]$y - y_0 = m(x - x_0)[/tex]

m = -5/2

[tex](x_0, y_0) = (3, 8)[/tex]

Substitute the values into the formula we get

y - 8 = (-5/2)(x - 3)

2(y - 8) = (-5)(x - 3)

2y - 16 = (-5x + 15)

2y + 5x = 15 + 16

2y + 5x = 31

Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

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Answer:

when the question is rearranged so that y is by itself, any of the options that say - 2.5x will be parallel.

Step-by-step explanation:

5x + 2y = 1

to get y by itself, simple algebra rules must be applied.

1. subtract 5x from both sides.

5x - 5x + 2y = 1 - 5x

2y = 1 - 5x

divide both sides by 2

2y / 2 = 1 / 2 - 5x / 2

therefore the new equation is:

y = 0.5 - 2.5x

this is very close to standard form for a line which is y = mx + b

rearrange the right side of the equals sign:

y = -2.5x + 0.5

in a standard linear equation, the x value determines the gradient of the line. therefore, anything with the same gradient (in this case -2.5x) will be parallel to the given equation.

Hope this makes sense :)

Answer: D

Step-by-step explanation:

The graph is narrower, so the coefficient of [tex]x^2[/tex] has an absolute value more than 1.

Also, because g(x) opens down, the coefficient of [tex]x^2[/tex] is negative.

This leaves D as the answer.

The rules that define the piecewise function graphed are as follows:

y = x + 2, y = 5.

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:

m = (5 - 2)/(3 - 0) = 1.

The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:

[tex]y = x + 2, 0 \leq x \leq 3[/tex]

For x greater than 3, the function is constant at y = 5, hence the definition is:

y = 5, x > 3.

Hence, the rules that are used to define the piecewise function graphed are as follows:

y = x + 2, y = 5.

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Answer:

[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]

Step-by-step explanation:

The ball strikes the ground when h = 0.

[tex]-16t^2 - 20t + 120 = 0 \\ \\ 4t^2 + 5t - 30=0 \\ \\ t=\frac{-5 \pm \sqrt{5^{2}-4(4)(-30)}}{4(2)} \\ \\ t=\frac{-5 \pm \sqrt{505}}{8}[/tex]

However, as time most be positive, we only consider the positive case.

So,

[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]

Answer:

26 - R = C

3 cars

Step-by-step explanation:

26-R = C

26-23 = 3

The answers to the questions are

a. No they are not the same

b. The presence of outliers are known to affect the market.

How to solve the box plot

For these areas  we have

Q1 = 2.7 Q3 = 3 median = 2.8 out;ier 2.

Q1 =  2.5 Q3 = 2.7 median = 2.6 out;ier 3.1.

Q1 =  2.5 Q3 = 2.75 median = 2.65 out;ier 1.6

Q1 =  2.4 Q3 = 2.6 median = 2.5

We can see that the median prices in the markets are nearly similar except for the one that is conatined in the first market.

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Answer: A

Step-by-step explanation:

[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]

The unit rate of each of the brands are:

Brand A's unit rate = 37 cents per ounce.

Brand B's unit rate = 31 cents per ounce.

The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.

To find the unit rate of each brand, do the following:

Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.

Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.

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Step-by-step explanation:

4x2+8x−3=0

For this equation: a=4, b=8, c=-3

4x2+8x+−3=0

Step 1: Use quadratic formula with a=4, b=8, c=-3.

x=

−b±√b2−4ac

2a

x= −(8)±√(8)2−4(4)(−3)

2(4)

x= −8±√112

8  x=−1+

1 2 √7 or x=−1+

−1 2 √7

Answer:  x=−1+

1 2√7 or x=−1+

−1 2 √7

The triangle is an isosceles triangle and the four triangles are similar

The coordinates are given as:

A (0, 0), B (5, 0), and C (2, 4).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(0 -5)^2 +(0-0)^2} =5[/tex]

[tex]AC = \sqrt{(0 -2)^2 +(0-4)^2} =4.5[/tex]

[tex]BC = \sqrt{(5 -2)^2 +(0-4)^2} =5[/tex]

The above shows that two sides are congruent.

Hence, the triangle is an isosceles triangle

This is calculated using:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

AB = 0.5 * (0 + 5, 0 + 0) = (2.5, 0)

AC = 0.5 * (0 + 2, 0 + 4) = (1, 2)

BC = 0.5 * (5 + 2, 0 + 4) = (3.5, 2)

From the attached graph, we can see that the triangles are similar

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The statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A

They include;

Thus, the statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A

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Answer:

Step-by-step explanation:

false

Answer:

z=16

Step-by-step explanation:

10=z-6

10+6=z-6+6

16=z

Answer:

10=z-6

or, z= 10+6

or, z = 16

the vale of y is 16

Answer:

b)14/3 or 4 2/3  C) 256/15 or 14 1/15

Step-by-step explanation:

In the second fraction, the "of" means to multiply

Answer:

#b

[tex] \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}[/tex]

[tex]\frak{SOLUTION:}[/tex]

[tex]\displaystyle \frak{Here,}[/tex]

[tex]\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }[/tex]

[tex] = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }[/tex]

[tex]=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }[/tex]

[tex]\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }[/tex]

[tex]\displaystyle{ = \frac{8 \times 7}{12} }[/tex]

[tex] =\displaystyle{} \frac{56}{12} [/tex]

[tex]\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }[/tex]

[tex]\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } [/tex]

#c

[tex]\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}[/tex]

[tex]\displaystyle{ \frak{SOLUTION:}}[/tex]

[tex]\displaystyle \frak{Here,}[/tex]

[tex] \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }[/tex]

[tex]\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}[/tex]

[tex] = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }[/tex]

[tex]\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }[/tex]

[tex]\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }[/tex]

[tex]\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }[/tex]

[tex] = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }[/tex]

Answered by :

[tex]\frak{\pink{seolleaphrodite}}[/tex]

Answer: B

Step-by-step explanation:

The parabola has an open hole at x=2, and the line has a closed hole at x=2.

This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].

This eliminates everything except for B.

The standard deviation is 1.43 below the mean

The given parameters are:

Mean = 98.249

Standard deviation = 0.733

x = 97.2

To calculate the number of standard deviation below the mean, we use

[tex]x = \bar x - n\sigma[/tex]

So, we have:

[tex]97.2 = 98.249 - n * 0.7333[/tex]

Evaluate the like terms

[tex]-1.049 =- n * 0.7333[/tex]

Divide both sides by -0.733

n =1.43

Hence, the standard deviation is 1.43 below the mean

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Series are sum of a given sequence.. The sum of the given expression is -33

Series are sum of a given sequence. According to the given expression

∑∑k=1 (k^2-5k-3)

Taking the sum from k = 1 to k = 4

Sum = (1-5-3) + (4-10-3) +(9-15-3)+(15-20-3)

Sum = (-7) + (-9) + (-9) + (-8)

Sum = -33

Hence the sum of the given expression is -33

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Answer:

The answer is circle.

Step-by-step explanation:

For all the rest of the shapes, we use certain base x height formulas.  Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula  [tex]\pi r^{2}[/tex] where r= radius.

The solution of the system of equation of the matrix is as follows:

x = - 8

y = 3

3x + 10y = 6

x + 3y = 1

multiply equation(ii) by 3

3x + 10y = 6

3x + 9y = 3

Therefore,

y = 3

Hence,

x + 3y = 1

x + 3(3) = 1

x + 9 = 1

x = 1 - 9

x = -8

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Answer:

Give the opposite of each number : a. -3; b. 9; c. 5; d. -12

Solve each of the following problems : a. 3; b. 3; c. -18; d. 18; e. -6; f. -4

Solve each problem. Be sure to include the correct sign in your answer :

a. 24; b. -35; c. 54; d. -4; e. 8; f. -6

Answer:

Step-by-step explanation:

1.a. –3

b. 9

c. 5

d. –12

2. a. 9 + (–6) = 3

b. (–5) + 8 = 3

c. (–12) + (–6) = –18

d. 10 – (–8) = 18

e. (–4) – (+2) = –6

f. –9 – (–5) = –4

3. a. 8 × 3 = 24

b. –7 × 5 = –35

c. –6 × (–9) = 54

d. 8 ÷ (–2) = –4

e. –24 ÷ (–3) = 8

f. –36 ÷ 6 = –6

5. Multiply the service charge by the number of months in a year.

12 × 7 = $84

Answer: $84 is deducted per year.

6. Add the balance of each year to determine the closing balance.

–$1500 + (–$1200) = –$2700

penn foster