Determine whether the following procedure results in a binomial distribution or a distribution that
can be treated as binomial (by applying the 5% guideline for cumbersome calculations). If it is not
binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
In a Pew Research Center survey of 150 subjects, the ages of the respondents are
recorded.

Step-by-step explanation:

We have,

[tex]\begin{gathered} \bullet \: \bold{ - \dfrac{\pi}{4} < \beta < 0 < \alpha < \dfrac{\pi}{4} } \\ \\ \implies \: - \dfrac{\pi}{4} < \alpha + \beta < \dfrac{\pi}{4} \end{gathered}[/tex]

[tex]\begin{gathered} \rm\bullet \: \: \: \sin( \alpha + \beta ) = \dfrac{1}{3} \: \: \: \: \: and \: \: \: \: \: \cos( \alpha - \beta ) = \dfrac{2}{3} \\ \end{gathered} [/tex]

Now,

[tex]\begin{gathered} y= \bigg( \dfrac{ \sin( \alpha ) }{ \cos( \beta ) } + \dfrac{ \cos( \beta ) }{ \sin( \alpha ) } + \dfrac{ \cos( \alpha ) }{ \sin( \beta ) } + \dfrac{ \sin( \beta ) }{ \cos( \alpha ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \bigg( \dfrac{ \sin( \alpha ) }{ \cos( \beta ) } + \dfrac{ \sin( \beta ) }{ \cos( \alpha ) } + \dfrac{ \cos( \beta ) }{ \sin( \alpha ) } + \dfrac{ \cos( \alpha ) }{ \sin( \beta ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \bigg( \dfrac{ \sin( \alpha ) \cos( \alpha ) + \sin( \beta \cos( \beta ) ) }{ \cos( \beta ) \cos( \alpha) } + \dfrac{ \sin( \alpha) \cos( \alpha ) + \sin( \beta ) \cos( \beta ) }{ \sin( \alpha ) \sin( \beta ) } \bigg)^{2} \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \bigg( \dfrac{ \sin( \alpha + \beta ) }{ \cos( \beta ) \cos( \alpha) } + \dfrac{ \sin( \alpha + \beta ) }{ \sin( \alpha ) \sin( \beta ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \sin^{2} ( \alpha + \beta ) \bigg( \dfrac{ 1 }{ \cos( \beta ) \cos( \alpha) } + \dfrac{ 1 }{ \sin( \alpha ) \sin( \beta ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \sin^{2} ( \alpha + \beta ) \bigg( \dfrac{\cos( \beta ) \cos( \alpha) + \sin( \alpha ) \sin( \beta ) }{ \cos( \beta ) \cos( \alpha) \sin( \alpha ) \sin( \beta )} \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \sin^{2} ( \alpha + \beta ) \bigg( \dfrac{\cos( \alpha - \beta ) }{ \cos( \beta ) \cos( \alpha) \sin( \alpha ) \sin( \beta )} \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{2\cos( \alpha ) \cos( \beta ) \cdot 2\sin( \alpha ) \sin( \beta ) \right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{\cos( \alpha + \beta ) + \cos( \alpha + \beta ) \right \} ^{2} \left \{ \cos( \alpha - \beta ) - \cos( \alpha + \beta ) \right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{ \cos^{2} ( \alpha - \beta ) - \cos^{2} ( \alpha + \beta ) \right \}^{2} } \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{ \cos^{2} ( \alpha - \beta ) - 1 + \sin^{2} ( \alpha + \beta ) \right \}^{2} } \\\end{gathered}[/tex]

Putting the values given above, we get,

[tex]\begin{gathered} \implies y= \dfrac{4 \cdot \dfrac{1}{9} \cdot\dfrac{4}{9} }{ \left \{ \dfrac{4}{9} - 1 + \dfrac{1}{9} \right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \left \{ \dfrac{5}{9} - 1\right \}^{2} } \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \left \{ \dfrac{5 - 9}{9}\right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \left \{ \dfrac{- 4}{9}\right \}^{2} } \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \dfrac{16}{81}} \\\end{gathered} [/tex]

[tex]⟹y=1[/tex]

Answer:

can you send a link or photo of the angles?

Step-by-step explanation:

Answer:

A) 2 + 8x = -134

B) x = -17

Step-by-step explanation:

Note: I am assuming the question says use x as a variable, not z. Otherwise part B does not make sense

If we let variable x be the number then
8 times a number ==> 8x

2 and 8 times a number ==> 2 + 8x

2 and 8 times a number is -134 ==> 2 + 8x = -134

A) Equation form is 2 + 8x = -134

B) Equation is
2 + 8x = -134

Subtract 2 from both sides:
2 - 2 + 8x = -134 - 2
8x = -136

Divide both sides by 8 to give
8x/8 = -136/8
x = - 17

Step-by-step explanation:

The mean of a set of numbers is the average of those numbers. You can find the mean by adding the set of numbers and dividing by how many numbers are given. If you are given the mean and asked to find a missing number from the set, use a simple equation.

Add up the numbers you know. The problem states a mean of 58 with this set of numbers: 43, 57, 63, 52 and x. Assign the missing number a value of “x.” So add 43, 57, 63 and 52 to get 215.

Set up your equation by adding 215 plus “x” (the missing number), divided by 5, the number of values given. Set that side of the equation equal to the mean, 58. So, your equation would look like this: [tex] \frac{215+x}{5} = 58 [/tex]

Multiply each side by 5 since our goal is to get “x” by itself. This process cancels the 5 on the left side of the equation and gives you 290 on the right side (58 × 5). Now, your equation should look like this: [tex] 215+x=290 [/tex]

Subtract 215 from each side as you continue to work to get “x” alone. This cancels out the 215 on the left side of the equation and gives you 75 on the right side. Now, your equation should show that x = 75. Therefore, the missing number is 75.

Check the missing number by adding all the numbers together and dividing by 5.

[tex] \frac{43+57+63+52+75}{5} = \frac{290}{5} = 58 [/tex]

Answer:

8/3

Step-by-step explanation:

[tex]g^2 (x)=\frac{2\left(\frac{2x}{x-2} \right)}{\frac{2x}{x-2}-2} \\ \\ =\frac{4x}{2x-2(x-2)} \\ \\ =\frac{4x}{4} \\ \\ =x[/tex]

From this, we can see that g(x) is its own inverse. Thus, [tex]g^{13}(x)=g(x)[/tex]

So,

[tex]g^{13}(8)=\frac{2(8)}{8-2}=8/3[/tex]

Explanation:

"given it is an even number" tells us that the outcomes could be anything from this set {2,4,6}. We ignore the odd numbers entirely.

We have one copy of "6" out of three total items.

Therefore, we end up with a probability of 1/3

This is approximately equal to the decimal form 0.333 and the percent form 33.3%

I would stick to the fraction form since it's most exact. However, if your teacher instructs otherwise then be sure to follow said instructions of course.

The expression of the mathematical statement given as "Jaun's age, x, is 4 times his age 15 years ago" is x = 4 * (x - 15)

The mathematical statement is given as

Jaun's age, x, is 4 times his age 15 years ago

From the statement, we have:

x represent Juan's current age

This means that his age 15 years ago is

15 years ago = x - 15

4 times his age 15 years ago is

4 * 15 years ago = 4 * (x - 15)

The above equation is equivalent to his current age

So, we have

x = 4 * (x - 15)

Hence, the expression of the mathematical statement given as "Jaun's age, x, is 4 times his age 15 years ago" is x = 4 * (x - 15)

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The value of the probability of hitting the target is 0.1736.

According to the statement

We have to find that the value of the probability.

So, For this purpose, we know that the

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

From the given information:

A circular dartboard with a diameter of 24 inches has a circular bullseye at its center. The diameter of the target is 10 inches.

Then

Area of a circular dartboard = [tex]\pi r^{2}[/tex]

Area of a circular dartboard = [tex](3.14)* 12^{2}[/tex]

Area of a circular dartboard = [tex](3.14) *144[/tex]

Area of a circular dartboard = 452.16 inches

And then

Area of a circular bullseye = [tex]\pi r^{2}[/tex]

Area of a circular bullseye = [tex](3.14)* 5^{2}[/tex]

Area of a circular bullseye = [tex](3.14) * 25[/tex]

Area of a circular bullseye = 78.5

Then

Probability of hitting the target = Area of a circular bullseye / Area of a circular dartboard

Probability of hitting the target = 78.5 / 452.16

Probability of hitting the target = 0.1736.

So, The value of the probability of hitting the target is 0.1736.

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The difference between the dining set cost using the hire purchase method of payment is $37400.

It should be noted that when the hire purchase is used and there is a deposit of $37000 and 24 equal monthly installments of $4600 each.

The total amount will be:

= $37000 + ($4600 × 24)

= $37000 + $110400

= $147400

On the other hand, the dinner set can be bought for $110000 cash.

Therefore, the difference will be:

= Hire purchase - Cash.

= $147400 - $110000.

= $37400

Therefore, the difference between the dining set cost using the hire purchase method of payment is $37400.

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The solution to the equation 1/3|x - 8| = 10 is x = 38

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

1/3|x - 8| = 10

Multiply through by 3

So, we have

|x - 8| = 30

Remove the absolute bracket

So, we have

x - 8 = 30

Add 8 to both sides of the equation

So, we have

x = 38

Hence, the solution to the equation is x = 38

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Answer:

138cm^2

Step-by-step explanation:

Trianle area = (b*h)/2

b = 8cm + 15cm

h = 6cm

Triangle area = (23*6)/2

138/2 = 69cm^2

Upper triangle area

--------------------------------

since both triangles share the same base and height

69*2 = 138cm^2

Answer: this statement would be true because that would mean that 100x100=1

Step-by-step explanation:hope it helps, brainliest? i could really use it

Answer:

  97

Step-by-step explanation:

You want the value of the composition of functions f and g for x=4.

The ring operator signifies a composition of functions. It works right to left. That is, ...

  [tex](f\circ g)(x)=f(g(x))[/tex]

A composition is evaluated using the Order of Operations, working from inner parentheses outward.

  [tex](f\circ g)(4)=f(g(4)) = f(3-\dfrac{1}{2}4^2)=f(-5)\\\\=4(-5)^2-3=100-3=\boxed{97}[/tex]

The ratio of high school students who are in a music class to students who are not is 9 : 41.

So, 18% of high school students are in a music class which means the rest 82% are not in a music class.

Then the ratio:

Simplest form:

Therefore, the ratio is 9 : 41.

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Answer:

The probability of rolling a 2 the next time that same die is rolled is 0.167.

Step-by-step explanation:

In this question it is given that there is rolling dice that is six sided and which is rolled for a 100 times and it was further observed that the probability of rolling a 2 was 12%.

Firstly, let us understand what is probability;

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

Now,

Let us understand the concept of impossibility and certainty of an event;

An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Further, In the above-mentioned condition, it is observed that the die has been rolled a 100 times;

The probability of getting X is only 12%.

Now,

In the condition where the die is rolled in for an extra time being a six sided, the probability of getting a 2 is 1/6.

=> 1/6

=> 0.167

Therefore, the probability of rolling a 2 the next time that same die is rolled is 0.167.

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Answer:

Step-by-step explanation:

According to the question, the cupcake cafe makes 1/2 times as much revenue on doughnuts as muffins and the total revenue is total sales were $44,000. Let us assume that the revenue on muffins is X and then the revenue on doughnuts is 412X. 4 1 2 X . The amount of money earned from muffins is 20000 dollars

Answer: None of these

Step-by-step explanation:

First term

[tex]\int 12e^{12t} \text{ } dt=12 \int e^{12t} \text{ } dt=e^{12t}+C[/tex]

Second term

[tex]\int \sqrt[3]{27t} \text{ } dt=3\int t^{1/3} \text{ } dt=\frac{9}{4}\sqrt[3]{t^4}+C[/tex]

Third term

[tex]\int \frac{5}{t} \text{ } dt=5 \int \frac{1}{t} \text{ } dt=5\ln t+C[/tex]

Fourth term

[tex]\int 15 \text{ } dt=15t+C[/tex]

Adding these integrals, we get

[tex]\int g(t) \text{ } dt=e^{12t}+\frac{9}{4}\sqrt[3]{t^4}+5\ln t+15t+C[/tex]

which matches none of the options.

Answer:

A) product of a power law

Step-by-step explanation:

most sensible

Answer: 6.12315 × 105

Step-by-step explanation: No worry's just here for the fun of it

Answer:

x = 32

y = 5

Step-by-step explanation:

2y=10

X=6y+2

Put both equations in the same format

x - 6y = 2

Manipulate the equations so that they have a common coefficient

6y = 30

Solve for one coefficient

(x - 6y = 2) + (6y = 30)

x + (-6y + 6y) = 2 + 30

x = 2 + 30

x = 32

Solve for the other coefficient

2y = 10

y = 5

x - 6y = 2

32 - 6y = 2

-6y = 2 - 32

-6y = -30

y = -30/-6

y = 5

The value of x is 6 is proved by equating line segment PM and MR as M is the midpoint of line PR.

What is midpoint of line segment?

The midpoint divides the line segment into two equal parts. As the number line progresses, the leftmost numbers become smaller, and the rightmost numbers become larger. Adding, subtracting, and multiplying can also be done using a number line like for addition move towards right and for subtraction move towards left.

It is given that M is the midpoint of line segment PR which implies M will divide PQ into two equal parts that is PM (2x + 5) equals MR (4x - 7). now calculating x value first :

PM = MR

2x+5 = 4x -7

4x -2x = 5 + 7

2x = 12

x = 12/2

x = 6

Hence proved that the value of x is 6

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Answer:

a=25

b=90

c=45

d=25

e=90

g=130

h=50

i=130

k=85

l=95

n=95

Step-by-step explanation:

Hey, could you perhaps provide a little bit more info regarding what method/topic/skill you are required to use in order to solve the following? Also, are these three different expressions, or are they a part of the same question. Thanks!

The system of inequalities for the given situation is x+y≤11 and 2x+4y≥40.

Given that, the cost of each drink = $2 and the cost of each taco = $4.

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

x represents the number of drinks purchased and y represents the number of tacos purchased.

Juan has $40 to spend and must buy a minimum of 11 drinks and tacos altogether.

So inequalities are x+y≤11 and 2x+4y≥40

Therefore, the system of inequalities for the given situation is x+y≤11 and 2x+4y≥40.

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The length and width of the yard with perimeter of 400 feet are 136 ft and 64 ft respectively.

The yard has a perimeter of 400 feet.

Eight times the length of the yard equals seventeen times the width.

Therefore,

perimeter of a rectangular yard = 2(l + w)

where

Therefore,

8l = 17w

Hence,

l = 17 / 8 w

perimeter of a rectangular yard = 2(17 / 8 w + w)

perimeter of a rectangular yard = 2( 25  /8 w)

perimeter of a rectangular yard = 50/ 8 w

400 = 50 / 8 w

cross multiply

3200 = 50w

divide both sides by 50

w = 3200 / 50

w = 64 ft

l = 17 / 8 × 64 = 136 ft

Therefore, the length and width of the yard with perimeter of 400 feet are 136 ft and 64 ft respectively.

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The garden has a length of 37.5 yards and width of 37.5 yards as well as an opening of 12.5 yards.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width.

150 yards of fencing is available, hence:

2(x + y) = 150

x + y = 75

y = 75 - x     (1)

The area (A) of the garden is given as:

A = xy

A = x(75 - x)

A = 75x - x²

The maximum area is at A' = 0

A' = 75 - 2x

75 - 2x = 0

x = 37.5 yards

y = 75 - x = 75 - 37.5 = 37.5

Opening of the garden = 1/3 * 37.5 = 12.5 yards

The garden has a length of 37.5 yards and width of 37.5 yards as well as an opening of 12.5 yards.

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Answer:

2

Step-by-step explanation:

The graph looks to be like a parabola. Due to the end behaviour of the graph (Up in both quadrants 1 and 2) it can be said that the graph has a positive leading coefficient.

Hope that helps

Among the four options provided in the reference diagram for the question attached thereby along with the question statement, {(-5, 8), (-5, 2), (-3, 3), (-3, 1), (0, 4), (0, 5), (-5, 7), (-3, 6)} is the relation that has a domain of {(-5), (-3), 0} and a range of {1, 2, 3, 4, 5, 6, 7, 8}.

As per the question statement, we are required to determine the relation which has a domain of {-5, -3, 0) and a range of {1, 2, 3, 4, 5, 6, 7, 8).

To solve this question, we will use the trial-and-error method on the options provided. We have to find out possible (x, y) combination, where "x" belongs to the set of {(-5), (-3), 0} and "y" belongs to the set of {1, 2, 3, 4, 5, 6, 7, 8}, and match these combinations with the options.

The first option has x values from the set of {1, 2, 3, 4, 5, 6, 7, 8} and y values from the set of {(-5), (-3), 0}. Hence, it is not the correct answer.

The second option has x values from the set of {(-5), (-3), 0} and y values from the set of {1, 2, 3, 4, 5, 6, 7, 8}. Hence, it is one possible correct answer.

The third and fourth options have values out of the sets of {(-5), (-3), 0} and {1, 2, 3, 4, 5, 6, 7, 8}. Hence, they are not the correct answers.

Therefore,  {(-5, 8), (-5, 2), (-3, 3), (-3, 1), (0, 4), (0, 5), (-5, 7), (-3, 6)} is the relation that has a domain of {(-5), (-3), 0} and a range of {1, 2, 3, 4, 5, 6, 7, 8}.

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A∩B = {10, 20, 50}

The given two function is

A = { 10, 20, 30, 40, 50, 60}

B = { 10, 20, 50}

We have to find the value of function of A∩B

A∩B means the number which is common in both the function,

The number common in function A and B is 10, 20, 50.

Therefore the function A∩B = {10, 20, 50}

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The base 10 representation of the number 142 base 5 as required to be determined in the task content is; 47.

Since, the conversion of numbers from any base to base 10 requires imaginary exponents to represent place value in such number as follows;

142₅ can therefore be written as follows; 1²4¹2⁰₅.

On this note the evaluation is carried out by summing the product of each digits and 5 to the corresponding power as follows;

1²4¹2⁰₅ = (2 × 5⁰) + (4 × 5¹) + (1 × 5²)

= (2 × 1) + (4 × 5) + (1 × 25)

= 2 + 20 + 25.

= 45.

Ultimately, the base 10 representation of the number 142 base 5 as required to be determined in the task content is; 47.

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