Suppose 50% of politicians are lawyers.

If a random sample of size 780 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%? Round your answer to four decimal places.

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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The type of sampling used in each case are:

Statement A → Stratified random sampling.

Statement B → Cluster sampling

Statement C → Simple random sampling

Statement D → systematic sampling

There are different ways that samples are classified such as:

1) Convenience sampling: This is where samples are drawn from a conveniently available pool.

2) Random Sampling: This is when we put all the options into a particular hat and drawn some of them.

3) Systematic Sampling: This is when every nth element is taken. For example, we want to survey something in the school, and then we interview every 10th person.

4) Cluster Sampling: This usually divides a population into groups, referred to as clusters, and each element in that cluster is surveyed.

5) Stratified Sampling: This will divide the population into groups. However, unlike cluster sampling, here, only some elements of the group are surveyed.

From the given problem:

Statement A is Stratified random sampling.

Statement B is Cluster sampling

Statement C is Simple random sampling

Statement D is systematic sampling

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The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

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Answer: answer is D

Step-by-step explanation:

i just took the quiz

Answer:

The answer is D :)

I got y’all homies

Answer: 29 :)

Step-by-step explanation:

The option (b) set y equal to a constant other than zero to get the curve of points where the slope is that constant.

A slope field is a visual representation of the slopes of a function's derivative at different points on the xy-plane. The slope at a particular point in the xy-plane is given by the derivative of the function at that point.

To match the given equations with their corresponding slope fields, you need to analyze the behavior of the slopes and isoclines. An isocline is a curve in the plane along which the slope of a function is constant. Isoclines are useful in constructing slope fields by hand, as they help in determining the slope at different points.

To start with, set y equal to zero and observe how the derivative behaves along the x-axis. Similarly, set x equal to zero and observe the behavior of the derivative along the y-axis. These observations will give you an idea of the direction and magnitude of the slope at different points in the xy-plane.

Next, consider the curve in the plane defined by setting y' = 0. This curve represents the points in the picture where the slope is zero. These points are known as critical points or equilibrium points. They are essential in analyzing the stability and behavior of a system.

These curves are called isoclines and can be used to construct the slope field picture by hand.

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Complete Question:

Match the following equations with their slope field. Clicking on each picture will give you an enlarged view. While you can probably sove this problem by guessing, it is useful to try to predict characteristics of the slope field and then match them to the picture Here are some handy characteristics to start with- you will develop more as you practice. Set y equal to zero and look at how the derivatiwe behaves along the x axis. Do the same for the y axis by setting x equal to 0. Consider the curve in the plane defined by setting y' = 0-this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slepe is that constant. These are called isoclines, and can be used to construct the slope field picture by hand.

Answer:

The food preferences among vole species are independent of one another.

Step-by-step explanation:

The hypothesis can be defined as follows:

H₀: The food preferences among vole species are independent of one another.

Hₐ: There is a relationship between voles and food preference.

The data provided is:

                                           meadow voles            common voles

                 apple slices                15                                   21

peanut butter-oatmeal               25                                    16

A Chi-square test for the Goodness of fit will be used.

The expected values are computed using the formula:

\(E_{i}=\frac{\text{ith Row Total}\times \text{jth Column Total}}{N}\)

Consider the Excel sheet attached.

The Chi-square statistic value is 2.861.

Compute the degrees of freedom as follows:

df = (r - 1)(c - 1)

   = (2 - 1)(2 - 1)

   = 1

Compute the p-value as follows:

\(p-value=P(\chi^{2}_{(1)}>2.861)=\text{CHISQ.DIST.RT(2.861,1)}=0.091\)

The p-value = 0.091 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that the food preferences among vole species are independent of one another.

Answer:

-12

Step-by-step explanation:

-7+(-5)=

-7-5=

-12

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

2x3=6.

so I think it is either 6 or 12

2x3=6

Answer:

it's 59 I hope this helps

Answer:

11(x+3) is correct answer. Please Mark it as brainlist answer.

Step-by-step explanation:

let's say the unknown number be x

Simplify it:

11(x+3)

Answer:

-50x

Step-by-step explanation:

The rate of change is the dependent variable, which means that is the number that can change due to another number or variable. The only dependent variable is -50x, Which means this is the rate of change.

Answer:

What is the normal rate of return?

Normal rate of return . ' means the average rate of return that a firm would receive in an industry when conditions of perfect competition prevail.

Step-by-step explanation:

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Answer:

X is 18 degrees

A ciricle total is 360 degrees so you add up all of the degrees that you have subtract it from 360 then divide that number by 17 to get x

Answer:

\(i)a + 2b = 2 + 2(3) = 2 + 6 = 8 \\ ii)a + b + c = 2 + 3 + 3 = 2 + 6 = 8\)

Answer:

a = 2, b = 3 and c = 3

a + 2b

2 + 2(3) = 2 + 6 = 8

a + b + c

2 + 3 + 3 = 8

Thus, The answer of i.) is 8 and ii.) is 8

-TheUnknownScientist 72

Answer:

6) F

7) B

Step-by-step explanation:

6)

\(\boxed{perimeter \: of \: rectangle = 2(length + breadth)}\)

60= 2[½(n -6) +2n +5]

Expand:

60= 2(½)(n -6) +2(2n) +2(5)

60= n -6 +4n +10

Simplify:

60= 5n +4

Minus 4 on both sides:

5n= 60 -4

5n= 56

Divide both sides by 5:

n= 56 ÷5

n= 11.2

Thus, option F is correct.

7)

\(\boxed{area \: of \: rectangle = length \: \times breadth}\)

13q +2= 9(q +6)

Expand:

13q +2= 9q +54

Bring q terms to one side, constant to the other:

13q -9q= 54 -2

Simplify:

4q= 52

Divide both sides by 4:

q= 52 ÷4

q= 13

Thus, option B is correct.

3.64 x \(10^8\) divided by 3.3 x \(10^4\) is equal to 110.12121212121212.

The division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into a number of equal parts. The symbol for division is typically a forward slash (/) or a horizontal line. For example, if you have 10 apples and you want to divide them equally among 5 people, each person would receive 2 apples (10 ÷ 5 = 2). The result of division is called the quotient.

Here is one way to divide 3.64 x 10^8 by 3.3 x 10^4 step by step:

Write the numbers as decimal numbers: 3.64 x 10^8 is equal to 364000000 and 3.3 x 10^4 is equal to 33000.

Divide the decimal numbers: 364000000 ÷ 33000 = 11006.06

The result is 11006.06.

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Answer:

What grade math is this?

Step-by-step explanation:

This math is hard.

Answer:

\(\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2} \right)\)

Step-by-step explanation:

The coordinate has the following polar form:

\(\vec r = (1, 0^{\circ})\)

The image of the coordinate rotated counterclockwise 60° is:

\(\vec s = (1, 60^{\circ})\)

Its equivalent form in rectangular coordinates is:

\(\vec s = (1\cdot \cos 60^{\circ}, 1 \cdot \sin 60^{\circ})\)

\(\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2} \right)\)

Answer:

m= -1/7

b=2

Step-by-step explanation:

The probability that you win at most once when the chances of winning are 0.2, if you play the lottery five times and outcomes are independent is 0.7373

Thus the answer is (d) 0.7373

This is a case of Binomial expansion. Here the chances of winning is the probability of successful trial, i.e. 0.2 and thus the probability of failure is (1-0.2) = 0.8. Total number of trials is 5.

Given probability that you win at most once, that is it includes probability of winning once and probability of not winning. So number of successful trial is 1 and 0 in case 1 and case 2.

Probability = 5C0×0.2^{0}×0.8^{5-0} + 5C1×0.2^{1}×0.8^{5-1}  

= 1×1×0.32768 + 5×0.2×0.4096

= 0.73728

≅ 0.7373

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Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

Answer:

a. P(O) = ¹/₂ = 0.5

As a percentage, this is 50%

b. P(> 2) = ²/₃ = 0.666...

As a percentage, this is 66.6...%

c. P(< 7) = 1

As a percentage, this is 100%

d. P(prime) = ¹/₂ = 0.5

As a percentage, this is 50%

Step-by-step explanation:

a.

1, 3 and 5 are odd, 3 of the outcomes

2, 4 and 6 are even, 3 of the outcomes

So, 3 of the 6 possible outcomes are odd and 3 are even;

Thus, the probability of an odd roll is ³/₆ (and the same applies to even);

This can be simplified to ¹/₂

b.

3, 4, 5 and 6 are the outcomes > 2;

1 and 2 are the outcomes ≤ 2;

So, 4 of the 6 possible outcomes are > 2;

Thus, the probability of rolling < 2 is ⁴/₆;

This can be simplified to ²/₃

c.

All outcomes are less than 7 since they are 1, 2, 3, 4, 5 or 6;

This means the probability of rolling less than 7 is ⁶/₆, or simply 1

d.

Prime numbers: 2, 3, 5, 7 ...

The possible prime number outcomes are 2, 3 and 5;

3 of the 6 possible outcomes, therefore, are prime so the probability of rolling a prime is ³/₆ or ¹/₂

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

There are 4 quarts in one gallon

Answer:

2.9%

Step-by-step explanation:

Answer:

k=r+7

Step-by-step explanation:

k=Kyle

r=Ryan

k=51+7

k=58

Kyle will be 58 years old when Ryan is 51 years old

Answer:

Kyle will be 58

Step-by-step explanation:

So it seems to be that Ryan and Kyle have a 7 year age gap. We know this because of the first half of the question "When Ryan is 10, his brother Kyle is 17." And doing simple math, Kyle is seven years older than Ryan.

Now that we know that, If Ryan is 51, then we just have to add 7.

\(51+7=58\)

And there we go! At the end it says to fill in the table, but I don't see one provided. Hopefully what I said helps filling it out though. Good luck!

The order of the matrices of each product is given as follows:

AB is nonexistent, BA is nonexistent.

Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.

For the product AB, we have that:

Hence the product is nonexistent.

For the product BA, we have that:

Hence the product is nonexistent.

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