A sphere and a cylinder have the same radius, and the height of the cylinder is equal to its radius; which figure has the greater volume?

Answer:

D. 1,248 cubic units

Step-by-step explanation:

the formula for the volume of a rectangular prism is length *width*height. the length=12, width=8 and height equals 13 sooo 12*8*13= 1248

Hope this helps!!

60,000/52 weeks in a year gives a month paycheck of $1153.8. Divide this by 2 to get the semi monthly paycheck. Therefore your final answer should be $576.9230769

The semimonthly paycheck is  $2500

As we know that there are 12 month in a year

And semimonthly means 15 days

Monthly income is 60,000 / 12 = 5000

Now semimonthly means monthly divided by 2

So semimonthly will be 5000/2 = $2500

Answer:

Step-by-step explanation:

Angles inside a quadrilatril add up to 360°.

Opposite angles in a cyclic quadrailtaril (a quadrilateral with every corner touching the circle) add up to 180°.

A + B+ C + D = 360°

A + C = 180°

B + D = 180°

(x + 6) + B + (x - 2) + (x - 10) = 360

(x + 6) + (x - 2) = 180

Simplify:

(x + x) + (6 - 2) = 2x + 4 = 180

Solve to find x:

2x + 4 = 180

2x = 180 - 4

2x = 176

x = 88°

Substitute it in to check it's right.

(x + 6) + (x - 2) = 180

(88 + 6) + (88 - 2) = 180

94 + 86 = 180

Substitute this into the other equation to find B:

(x + 6) + B + (x - 2) + (x - 10) = 360°

(88 + 6) + B + (88 - 2) + (88 - 10) = 360°

94 + B + 86 + 78 = 360°

Rearrange to find B:

B = 360 - 94 - 86 - 78

B = 102°

A = 94°

B = 102°

C = 86°

D = 78°

Answer:

A = 94°

B = 102°

C = 86°

D = 78°

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

An exponential function which crosses through (1,3) and (2,9) will have a base of 3 since the y values are multiples of 3.

3^1 = 3

3^2 = 9

This means that the function is y = 3^x.

y = 3x

Substitute the two points into the equation y = abx, giving 3 = ab1 and 9 = ab2.

Since a = a, then  

3

b1

=  

9

b2

, rearranged yields 3b2 = 9b1 → 3b2 − 9b = 0 → b(3b − 9) = 0

Thus, b = 0 or b = 3.

A curve of exponential function never drop below the x-axis, ignore any values of b that are less than or equal to zero.

Therefore, insert b = 3 into  

3

b1

= a and  

9

b2

= a → a = 1 for both equations.

y = abx

y = (1)(3x)

y = 3x

Answer:

Area_shaded  = 2543.742 ft^2

Step-by-step explanation:

First we find the area of the external triangle

A_triangle = base*height*0.5

A_triangle = (92 ft)*(84 ft)*0.5 = 3864 ft^2

Then we find the area of the pool (circle)

A_circle = pi*radius^2

A_circle = 3.1416*(20.5 ft)^2 = 1320.257 ft^2

The area of the shaded region

Area_shaded = A_triangle - A_circle

Area_shaded  = 3864 ft^2 - 1320.257 ft^2 = 2543.742 ft^2

yes, please coffee would be nice today.

Answer:

Yes I would love some coffee, that is the answer!

Step-by-step explanation:

The mean of the data set is calculated to be 4.05, the median is 2, and there are two modes. The error in the box and whisker plot is that the lower whisker extends below the minimum value. The second quartile has the largest range, and the correct statement is that 75% of the days had 7 or more parts per million of pollution.

A. To calculate the mean, median, and mode of the data, we first need to arrange the data in increasing order. The stem and leaf plot represents the following data: 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 5, 6, 7, 7, 8, 9, 9.

The mean can be calculated by summing up all the data points and dividing it by the total number of data points. In this case, we have 20 data points, so the sum is 81. The mean is then 81/20 = 4.05.

The median is the middle value of the data set when arranged in increasing order. In this case, the middle value is the 10th value, which is 2.

The mode is the value that appears most frequently in the data set. In this case, both 0 and 3 appear 5 times, so the data set has two modes.

B. The error in the box and whisker plot is that the lower whisker extends below the minimum value in the data set. The correct plot should have the lower whisker ending at the minimum value.

C. The quartile with the largest range is the second quartile, which is the median. The range of the second quartile is the difference between the maximum and minimum values in the data set.

D. The correct statement is: '75% of the days had 7 or more parts per million of pollution.' This statement is true because the 75th percentile corresponds to the value 7 in this data set.

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Final answer:

The mean, median, and mode are statistical measures calculated from the given data points. For part B, we cannot provide corrections to the box and whisker plot without seeing it. The quartile with the largest range is determined by comparing quartile differences, and the statement about 75% of days with values ≥ 20 ppm is false because more than 25% of the values are below 20 ppm.

Explanation:

To calculate the mean, median and mode of Stephen's two-week air pollution data from the stem and leaf plot:

Convert the stem and leaf plot to a data set:

5, 7, 9, 12, 12, 16, 17, 20, 24, 28, 31, 32, 35, 39

Calculate the mean (average) by adding all the numbers together and dividing by the number of data points.

Find the median by ordering the data from least to greatest and finding the middle value (or the average of the two middle values if there is an even number of data points).

Determine the mode by identifying the value(s) that appear most frequently.

For part B, without the provided box and whisker plot, we cannot determine the error or provide the correct answer.

For part C, to identify which quartile has the largest range, we need to calculate the quartiles (Q1, Q2, Q3), and then compare the differences between them: Q1 to Q2, Q2 to Q3, and Q3 to the maximum value.

For part D, the statement “75% of the days had 20 or more parts per million of pollution” is false because:

Not all values are above 20 ppm. From the data, we can calculate that more than 25% of the values are below 20 ppm, thereby making the statement incorrect.

Correct Statement: Less than 75% of the days had 20 or more parts per million of pollution.

Answer:

see explanation

Step-by-step explanation:

To find the zeros equate g(x) to zero, that is

(3x - 1)(2x + 5)(7x - 14)² = 0

Equate each factor to zero and solve for x

3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]

(7x - 14 )²  = 0 ⇒ 7x - 14 = 0 ⇒ x = 2 with multiplicity 2

Answer:

The correct answer option is c.  $8.05.

Step-by-step explanation:

We are given that a lawnmower costs $284, and the six-year extended warranty on the lawnmower costs 17% as much as the lawnmower itself.

We are to find its effective price per year of the extended warranty.

So, the amount of six year warranty = [tex] \frac { 17 } { 100 } \times 284 [/tex] = $48.28

Price of warranty per year = [tex] \frac { 48.28 } { 6 } [/tex] = $8.05

Answer:

The answer is C on edge 2020.

Step-by-step explanation:

Answer:

For the first one is 340.

Step-by-step explanation:

The SA formula is SA = s^2 + 2 × s × l

so 10^2+2*10*12=340.

Answer:

20

Step-by-step explanation:

find the upper quartile(44), and the lower quartile(24) and subtract them to get the IQR

After a translation of 4 units to the right and 2 units up, the image point of the original point (9, 8) is (13, 10).

When translating a point in the Cartesian coordinate system, you are essentially moving the point from its original location to a new position based on specific instructions. In this case, the original point is (9, 8), and you are instructed to translate it right 4 units and up 2 units.

For the horizontal translation to the right, you add 4 to the x-coordinate. So, the new x-coordinate becomes 9 + 4, which equals 13.

For the vertical translation upwards, you add 2 to the y-coordinate. The new y-coordinate becomes 8 + 2, resulting in 10.

Therefore, the image point after the translation is (13, 10). This means that the point originally at (9, 8) has been shifted right by 4 units and up by 2 units, landing at the new position (13, 10).

In the context of coordinates and geometry, such translations are a fundamental concept, and they describe the movement of points in the plane. This is essential in various mathematical applications and real-world scenarios, such as navigation, computer graphics, and architectural design. The process involves simple arithmetic operations and is a key building block in understanding transformations in mathematics and science.

For more such information on: translation

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The image point of (9,8) after a translation right 4 units and up 2 units is (13,10). The rightward translation increased the x-coordinate by 4, and the upward translation increased the y-coordinate by 2.

In translation, when a point moves right or left, this affects the x-coordinate, and up or down movements affect the y-coordinate. In the case of point (9,8), if it makes a translation right by 4 units, the x-coordinate is increased by 4, resulting in the new x-coordinate as 9 + 4 = 13. If the point then moves up by 2 units, the y-coordinate increases by 2, and the new y-coordinate is 8 + 2 = 10. Therefore, the image point of (9,8) after a translation right 4 units and up 2 units is (13,10).

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Answer:

77.47%

Step-by-step explanation:

We have to use Bayes Theorem in solving this problem.

This theorem's formula is:

P(A | B) = [tex]\frac{P(A and B)}{P(B)}[/tex]

Where the " | " means "given that".

For our problem, using bayes theorem, we can write:

P(Student has lice | positive ) = [tex]\frac{P(StudentHasLice and Positive)}{P(Positive)}[/tex]

So P(Student has lice | Positive ) = [tex]\frac{0.1692}{0.2184}=0.7747[/tex]

To find the full class size, since Yuet's class has 4 people (25% of the full), divide 4 by 0.25 to get 16. Therefore, a full class has 16 people.

To find out how many people are in a full gymnastics class, we can use the given information that Yuet's class, with 4 people, is 25% full.

Let's represent the number of people in a full class as ( x ).

We know that the number of people in Yuet's class is 25% of the full class. Mathematically, this can be expressed as:

[tex]\[\frac{4}{x} = 0.25\][/tex]

To solve for ( x ), we can multiply both sides by ( x ):

[tex]\[4 = 0.25x\][/tex]

Then, to isolate ( x ), we divide both sides by 0.25:

[tex]\[x = \frac{4}{0.25}\][/tex]

Now, let's calculate:

[tex]\[x = \frac{4}{0.25} = 16\][/tex]

So, a full gymnastics class would have 16 people.

Split the second term in 3a^2 - 8a + 4 into two terms

3a^2 - 2a - 6a + 4 = 0

Factor out common terms in the first two terms, then in the last two terms.

a(3a - 2) -2(3a - 2) = 0

Factor out the common term 3a - 2

(3a - 2)(a - 2) = 0

Solve for a;

a = 2/3,2

Answer : B. (2/3,2)

inverse proportionality between 2 variables follows this .

y = k/x

where k is proportional constant

as value of one variable increases/decreases , value of other variable decreases/increases

so

if x increases, y will decrease

if x decreases , y will increase

Answer:

Step-by-step explanation:

The formula of a slope:

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

We have the slope m = 1 and the points (-4, y) and (-2, 8). Substitute:

[tex]1=\dfrac{8-y}{-2-(-4)}[/tex]

[tex]1=\dfrac{8-y}{2}[/tex]         multiply both sides by 2

[tex]2=8-y[/tex]         subtract 8 from both sides

[tex]-6=-y[/tex]          change the signs

[tex]6=y\to y=6[/tex]

Answer:

b. T <7,-2> (RSTU); (2,-1)

Step-by-step explanation:

The given triangle has vertices R(-5, -5), S(-1,-5), T(-1,1) and U(-5,1).

Let the translation rule be T(a,b).

Then the mapping for the translation will be;

[tex](x,y)\to (x+a,y+b)[/tex]

Then the point R(-5,-5) has the image;

[tex]R(-5,-5)\to R'(-5+a,-5+b)=R'(2,-7)[/tex]

This implies that;

[tex]-5+a=2[/tex]

[tex]\Rightarrowa=2+5=7[/tex]

and

[tex]-5+b=-7[/tex]

[tex]\Rightarrow b=-7+5[/tex]

[tex]\Rightarrow b=-2[/tex]

Therefore the translation rule is T(7,-2)

Hence;

[tex]U(-5,1)\to U'(-5+7,1-2)=U'(2,-1)[/tex]

the correct choice is B.

41 cents per pound

12/4.92=0.41

For this case we have to:

12 pounds of potatoes equals $ 4.92. You want to know the unit cost, that is, the cost per pound of potatoes.

For this, we make a rule of three:

12lb -----------------> $ 4.92

1lb --------------------> x

Where the varibale "x" determines the cost per pound of potatoe

[tex]x = \frac {1 * 4.92} {12}\\x = 0.41[/tex]

Thus, each pound of potatoe costs $ 0.41

Answer:

Each pound of potatoe costs $ 0.41

Answer:

Step-by-step explanation:

Function: A special relationship where each input has a single output.

#1 It's a function:

Jan → 150

Feb → 400

March → 430

#2 It's not a function:

Jan → 150

Feb → 400

March → 400 and March → 430 (two values for March)

#3 It's a function:

Jan → 150

Feb → 150

March → 400

#4 It's a function:

Jan → 400

Feb → 400

March → 400

The 2nd choice is not a function. Hope this helps you out!

Answer:

The "3y" in the first term is a factor

The "9" in the second term is a coefficient

The "(7 + 2x)" in the first term is a factor

Step-by-step explanation:

Given in the question an expression

3y(7 + 2x) + 9xy - 10

6y

6 is coefficient

    2.Constants are terms without variables

 10

    3.The factors in a mathematical expression are parts of the expression that are connected with multiplication.

(4x+1)(3x+7)

(4x+1) and (3x+7) both are factors

Answer:

7.) B

8.) D

Step-by-step explanation:

For #7, look at the graph and plot y = 6, go down and you'll see that x = -1 (approximately).

For #8, 1 < x < 9 basically means any number in the x-axis between 1 to 9. In those range, you can plot (1, 9), (1.1, 8.9), (1.2, 8.8), (1.25, 8.75), (1.5874875, 8.2858426) etc. There are an infinite number between 1 to 2 alone, so D is the answer.

Answer:

72 cm

Step-by-step explanation:

Lets split the net into 3 rectangles, one is the big one in the middle while the other two are the smaller protruding ones on top and on the bottom.  The small rectangles have an area of 3*2 = 6 and the big rectangles have an area of 6(3+2+3+2) = 6*10 = 60.  Adding these up we get 60 + 6*2 = 60+12 =72.

Answer:

NO SOLUTION

Step-by-step explanation:

Here  you're asked to solve a system of equations, linear equations in this case.

Since y = 2x, we can subst. 2x for y in the 2nd equation:

-6x + 3(2x) = 16

Combining the x terms results in 0 = 16, which is never true.  

Thus, this system of linear equations has NO SOLUTION.

Answer:

336

Step-by-step explanation:

The graph and solution are given in attached image

Ok so you have to replace all x by 4:

F(4)= 4.4+7= 23

Replace all x with 4

f(4)= 4*4+7

f(4)=16 +7

=23

Answer:

The first choice

Step-by-step explanation:

it is mostly saying you will be testing multiple students or just predicting either way it will be experimental meaning there likely are outliers. however the question is not super clear so this could always be wrong but i hope i helped u

Answer:

f(x) = x² - 1

f(f(x)) = f(x² - 1) = (x² - 1)² - 1

= x⁴ - 4x² + 1 - 1

= x⁴ - 4x²

f(f(0)) = 0