Gerald has a punch bowl in the shape of a hemisphere as shown below.

One cup is equivalent to approximately 15 cubic inches. Which of the following is closest to the maximum number of cups the punch bowl can hold?

A. 60 cups
B. 45 cups
C. 30 cups
D. 18 cups

Answer:

they are all called numbers

Step-by-step explanation:

Using conditional probability, it is found that the correct statement is given by:

C. If P(A | B) = P(A) and P(B | A) = P(B), then the events are independent.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

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

In which:

If two events are independent, we have that:

[tex]P(A \cap B) = P(A)P(B)[/tex].

Hence:

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

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

Which means that option C is correct.

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Answer:

First, we have to add 3 to both sides.
[tex]\sqrt{2x} - 3 + 3 = 2 + 3[/tex]

Then we simplify the equation,
[tex]\sqrt{2x} = 5[/tex]

Divide both sides of the equation by [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2x} }{\sqrt{2}} = \frac{5}{\sqrt{2}}[/tex]

Finally, simplify.
[tex]x = \frac{5\sqrt{2}}{2}[/tex]

Therefore, our answer is [tex]x = \frac{5\sqrt{2}}{2}[/tex]

3.5

Step-by-step explanation:

square means 1/2.so,1/2(2x-3)=(2)^2

then square cancel by square. 2x-3=4

2x=4+3, 2x=7then divided by 2.

x=3,5

Considering it's vertical asymptotes, the rational function graphed below is given by:

B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem, the vertical asymptotes are at [tex]x = \pm 1[/tex], hence the function is given by:

B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]

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The axis on a graph that shows the dependent variable is the: vertical or y-axis.

The dependent variable is the variable that is affected by an independent variable. That is, a change in the independent variable, causes the dependent variable to change.

On a graph, the dependent variable (outcome) is usually plotted on the y-axis (vertical axis).

Thus, the axis that shows the dependent variable is the vertical or y-axis.

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If the distance between the cliff and the boat is 400 feet. Then the height of the cliff will be 186.52 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The angle of elevation to the top of a cliff is 25 degrees from a boat on the lake.

If the distance between the cliff and the boat is 400 feet.

Then the height of the cliff will be

Let x be the height of the cliff. Then we have

tan θ = height of cliff/ distance between cliff and boat

tan 25° = x/400

x = 400 tan 25°

x = 186.52 feet

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The cardinality of a set refers to the number of elements in the set. It is found by counting  the elements in the set.

The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.

a) There are 6 elements in this set hence the cardinality is 6.

b) There is only one element in the set hence its cardinality is 1.

c) There are two elements in the set hence the cardinality is 2.

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Answer:

-1

Step-by-step explanation:

Rise/Run equates it to be -1/1 wich is -1

Answer:

750

Step-by-step explanation:

FORMULA FOR VOLUME

L×W×H

L:5

W:25

G:H

5x25x6=750

The book has the greater mass is book A and It is 60 grams greater.

The table of values is given as;

              1-kilogram   500-gram   100-gram    10-gram

Book A       1                    0                7                    4

Book B       0                    3                1                    8

The weights of the books are calculated as:

Book A = 1 * 1kg + 0 * 500g + 7 * 100g +4 * 10g = 1740 g

Book B = 0 * 1kg + 3 * 500g + 1 * 100g +8 * 10g = 1680 g

1740 is greater than 1680 by 60

This means that the book has the greater mass is book A and It is 60 grams greater.

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[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]

The average rate of change for f(x) and g(x) are respectively 2.25 and -2 and so we can say that f(x) is moving more quickly.

Formula for the average rate of change is;

f'(x) = (f(b) - f(a))/(b - a)

Thus;

1)  Average rate of change of f(x) over the interval from x = 2 to x = 6 is;

f'(x) = (f(6) - f(2))/(6 - 2)

We are given;

f(6) = 10 and f(2) = 1

Thus; f'(x) = (10 - 1)/4 = 2.25

2)  Average rate of change of g(x) over the interval from x = 0 to x = 4 is;

g'(x) = (g(4) - g(0))/(4 - 0)

We are given;

g(4) = 0 and g(0) = 8

Thus; g'(x) = (0 - 8)/4 = -2

3) From the average rate of change of both functions, we see that f(x) is positive and has a higher rate of change and so we can say that f(x) is moving more quickly.

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The problem with the study is that Some of the sample data are missing.

A survey is a study that aims at obtaining the responses of people based on a questionnaire. The subjects are selected at random in such a way that the sample is representative of the population.

In this study, the problem with the study is that Some of the sample data are missing.

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Answer: D) The results is a precise number

Answer:

Step-by-step explanation:

the cost of each ticket is 7 dollars.  Peter brought 2 tickets.  7 x 2 = 14

Peter spent $14 dollars on two movie tickets.

Answer:

204.35

Step-by-step explanation:

500-295.65+204.35

Answer:

c

Step-by-step explanation:

I took the test, and that was the correct answer. I hope this helps!

Answer:  1/3  The spaces are equal, and there are 2 favorable outcomes; out of 6 possible outcomes.  That comes out to 2/6, and 2/6 reduced is 1/3

Answer:

See the attachment photo!

Answer:

150.72

Step-by-step explanation:

V = 4/3(pi r squared)

V = 4/3 3.14 (6 squared)

V = 150.72

Answer:

I think it's 2275 square feet

Answer:

it is1125

Step-by-step explanation:

first 45x50=2250

next divide 2250 by 2 equals 1125

Answer:

it should be the third one

Step-by-step explanation:

I just learn this all today and I'm pretty sure its the third one

Answer:

o 0.5(6+12) ● 3

Step-by-step explanation:

because when you 2x2 is 6 +2 is 12 so the answer is that

The area of the circle will be equal to 11309.733 square centimetres.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

The area of the circle will be calculated by the following formula:-

Area = πr²

Area = π x ( 60 x 60 )

Area = 3.14 x 60 x 60

Area = 11309.733 square centimeters.

Therefore the area of the circle will be equal to 11309.733 square centimetres.

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Each transaction has been an analyzed in the trial balance below by showing its effects on the accounting equation-specifically, identifying the accounts and amounts.

The Journal Entries are:

Cash                                                                                 6500

Photography equipment                                                33500

                  Capital                                                                       40000

Prepaid Insurance                                                           2100

                   Cash                                                                         2100

Office Supplies                                                                  880

                  Cash                                                                          880

Cash                                                                                   3331

           Revenue                                                                          3331

Utilities Expense                                                                 675

           Cash                                                                                 675

Cash account = 6500 - 2100 - 880 + 3331 - 675

Cash Account = 6176

                                                     Trial Balance

                                                                              Debit                         Credit

Cash                                                                       6176

Prepaid Insurance                                                  2100

Supplies                                                                   880

Revenue                                                                                                      3331

Utilities Expense                                                      675

Capital                                                                                                       40000

Photography Equipment                                         33500

Total                                                                         43331                       43331

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The value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given:

sinx = -5/13

and cosx > 0

We know,

cos2x = 1 - 2sin²x

sinx = -5/13

Squaring on both sides:

sin²x = 25/169

Multiply by 2 on both the sides:

2sin²x = 2(25/169)

Add -1 on both sides:

-1 + 2sin²x = -1 + 2(25/169)

or

1 - 2sin²x = 1 - 2(25/169)

cos2x = 1 - 50/169

cos2x = 119/169    (as the cosx > 0)

Thus, the value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.

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Answer:

The guy above me is correct

Step-by-step explanation:

Look at the screen shot I got it correct

Answer:

Step-by-step explanation:

1) 5a² - 15

5a²  = 5 * a²

15    = 5 * 3

GCF = 5

5a² - 15 = 5*a² - 5*3

            = 5a(a - 3)

5) 36x²y - 48xy²  

36x²y =  2 * 2 * 3 * 3 * x² * y

48xy² = 2 * 2 * 2 * 2 * 3 * x * y²

GCF = 2 * 2 * 3*x*y  = 12xy

36x²y - 48xy²  = (12xy * 3x)  - (12xy*4y)

                        = 12xy*(3x - 4y)

6)75b²c³ + 60bc⁶  

75b²c³ =  3 * 5 * 5 * b² * c³

60bc⁶  = 2 * 2 * 3 * 5 * b * c⁶

GCF = 3*5*b*c³ = 15bc³

75b²c³ + 60bc⁶ = [15bc³* 5b]  + [15bc³ * 4bc³]

                          = 15bc³ * (5b + 4bc³)

Answer:

Step-by-step explanation:

when a number x is added to it's square, the total is 12. find two possible values of x

x+x^2=12

x^2+x=12

x^2+x−12=12−12

x^2+x−12=0

(x−3)(x+4)=0

x−3=0 or x+4=0

x=3 or x=−4

x=3 or x=−4

Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 65, \sigma = 3.5[/tex]

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{54.5 - 65}{3.5}[/tex]

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.

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