A large poll showed that 42%, percent of adults approved of their nation's prime minister. Margot wants to test if it is now lower, so she takes a random sample of 1,000 adults in that nation and finds that 390—or 39% percent of those sampled—approved of the prime minister.

Let p represent the proportion of adults in this nation who approve of the prime minister.

Which of the following is an appropriate set of hypotheses for her significance test?

Choose 1 answer:

(Choice A)
A
\begin{aligned} &H_0: p = 0.39 \\ &H_\text{a}: p < 0.39 \end{aligned}
​

H
0
​
:p=0.39
H
a
​
:p<0.39
​


(Choice B)
B
\begin{aligned} &H_0: p = 0.39 \\ &H_\text{a}: p < 0.42 \end{aligned}
​

H
0
​
:p=0.39
H
a
​
:p<0.42
​


(Choice C)
C
\begin{aligned} &H_0: p = 0.42 \\ &H_\text{a}: p < 0.39 \end{aligned}
​

H
0
​
:p=0.42
H
a
​
:p<0.39
​


(Choice D)
D
\begin{aligned} &H_0: p = 0.42 \\ &H_\text{a}: p < 0.42 \end{aligned}
​

H
0
​
:p=0.42
H
a
​
:p<0.42
​

The Probability of drawing a three given that the card is not a face card is 1/9.

In summary:

- P(face card | queen) = 1/13

- P(three | not a face card) = 1/9

The probabilities, we need to consider the total number of favorable outcomes and divide it by the total number of possible outcomes.

1. P(face card | queen):

A face card is a jack, queen, or king. There are four queens in a standard deck of 52 cards. So the total number of favorable outcomes is 4 (there are four queens in the deck). The total number of possible outcomes is 52 (the total number of cards in the deck).

P(face card | queen) = Number of favorable outcomes / Total number of possible outcomes

                    = 4/52

                    = 1/13

Therefore, the probability of drawing a face card given that the card is a queen is 1/13.

2. P(three | not a face card):

A face card is a jack, queen, or king. So not a face card includes all the other cards in the deck except for jacks, queens, and kings. There are 12 cards of each suit, and there are four suits in a deck. So the total number of not face cards is (12-3) * 4 = 9 * 4 = 36.

The total number of favorable outcomes is the number of threes in the deck, which is four.

P(three | not a face card) = Number of favorable outcomes / Total number of possible outcomes

                         = 4/36

                         = 1/9

Therefore, the probability of drawing a three given that the card is not a face card is 1/9.

In summary:

- P(face card | queen) = 1/13

- P(three | not a face card) = 1/9

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The probability of a bouquet containing at most 2 roses can be calculated by considering the different combinations of roses and carnations.

To determine the probability, we need to calculate the number of favorable outcomes (bouquets with at most 2 roses) and divide it by the total number of possible outcomes.

Let's consider the different possibilities:

1. Bouquets with no roses: In this case, we can only choose carnations, and there is only one combination possible.

2. Bouquets with one rose: We have 6 choices for the position of the rose, and the remaining 5 flowers can be carnations. So, there are 6 × 5 = 30 combinations.

3. Bouquets with two roses: We have 6 choices for the position of the first rose, and 5 choices for the position of the second rose. The remaining 4 flowers can be carnations. So, there are 6 ×5 ×4 = 120 combinations.

The total number of possible outcomes is the sum of the combinations in the three cases: 1 + 30 + 120 = 151.

Therefore, the probability of the bouquet having at most 2 roses is favorable outcomes (151) divided by the total possible outcomes (151): 151/151 = 1.

Thus, the probability is 1, meaning it is certain that the bouquet will have at most 2 roses.

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Answer:

L = 3.5 in/sec  * 3 min  * 60 sec /min = 630 in

(L = S * T   where T is in sec and S is inches / sec)

Answer:440

Step-by-step explanation:

Answer:

Parece que quieres factorizar la expresión 3x^4 -+12. Sin embargo, el signo -+ no es válido en álgebra. ¿Quieres decir 3x^4 - 12 o 3x^4 + 12?

Step-by-step explanation:

Factorization of 3x⁴+ 12 , is 3(x²₋ 2x ₊ 2) (x²₊2x₊2)

we known that the given equation needs to be factorized.

therefore, let us use the basic principle of factorization here, then using the splitting the middle term theorem find out the factorization

Given;

3x⁴₊12

Here, let us take 3 common from the base equation

Therefore,

3( x⁴ ₊ 4)

Furthermore let us split the middle sub equation into simple terms,

Therefore,

3(x⁴ ₋ 2x + 2) (x²₊ 2x₊2)

Hence, Factorization of 3x⁴+ 12 , is 3(x²₋ 2x ₊ 2) (x²₊2x₊2).

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Answer:

(x+1) + -3/(x-1)

Step-by-step explanation:

x² / x = x.

multiply x by (x - 1) to get x² - x.

subtract (x² - x) from (x² + 0x) to get x.

x / x = 1

multiply 1 by (x-1) to get x -1.

subtract (x-1) from (x-4) to get -3.

cannot divide any further. so -3 is our remainder.

answer is (x+1) + -3/(x-1).

please see attachment.

The value of x which will make the equation 8 + x = 32 true will be 24 thus, option (B) is correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

8 + x = 32

Put x = 4

8 + 4 = 12 ≠ 32

Put x = 24

24 + 4 = 32 (so it will be the solution)

Hence "The value of x which will make the equation 8 + x = 32 true will be 24".

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Given, radius of the earth is 6.36 × 10^6 m and its mass is 5.98 × 10^24 kg.

Applying formula of weight, we have:

W = mg where m = 10 kg and g is the acceleration due to gravity.

To calculate acceleration due to gravity (g),

formula is: g = GM/R²

where G is the gravitational constant= 6.67 × 10^-11 Nm²/kg², M is the mass of the earth = 5.98 × 10^24 kg, R is the radius of the earth= 6.36 × 10^6 m.

Now putting these values in the formula, we have:

g = GM/R²= 6.67 × 10^-11 × 5.98 × 10^24/ (6.36 × 10^6)²g = 9.81 m/s²

Therefore,Weight of the object can be calculated as;

W = mg = 10 × 9.81W = 98.1 N

(a) Using formula [2.10]:

Formula [2.10] is given by;

W = mgh/ R²

Where, h = height at which object is placed above the earth's surface.

Since the object is on the surface of the earth, h = 0.

Therefore,

W = mgh/ R²= (10 × 9.81 × 0)/ (6.36 × 10^6)²W = 0 N

(b) Using formula [2.12]:

Formula [2.12] is given by;

W = m (GM/ (R+h))²

Here, h = 0, therefore;

W = m (GM/R)²

= 10 × (6.67 × 10^-11 × 5.98 × 10^24/ 6.36 × 10^6)²

W = 98.05 N (Approximately)

Therefore, the weight of an object whose mass is 10 kg by using a) [2.10] is 0 N, and by using b) [2.12] is 98.05 N (Approximately).

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Answer:

Dan paid $80 for his luggage

Step-by-step explanation:

$400

-$320

= $80

Jake wants to go to a lil uzi vert concert. A lil uzi vert concert ticket cost $320. The backstage pass is only $400, so Jake pays for that instead. He later figured out that he wanted to lose 50 pounds before the concert in 6 months and for every time he goes to the gym he has to pay $10 he only goes to the gym 8 times and his bank account has $500 on it. How much money did he have left over after going to the gym 8 times? - PS don't worry about this question its just a fake scenario i made for the second part of your question hope this helps!!!

Answer:

65,398

Step-by-step explanation:

In the numbers 5,638 and 38,641, the digit 6 is the SAME value as in 647. In the number 6,523,532, the digit 6 is 10,000 times larger than in 647. In the number 65,398 the digit 6 is 100 times larger than in 647.

Answer:

x = 10

Step-by-step explanation:

48 = x + 8 + 2x + x

    48 = 4x + 8

   -8           -8

40 = 4x

divide both sides by 4

10 = x or x =10

False, one of the most pieces of information with a var is whether each estimated coefficient for the lags is statistically significant (t-tests)

A statistical test called a t-test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

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The number of cars that must be made to minimize the unit cost is 300 cars which is determined by differentiation.

Differentiation is a mathematical process that determines the instantaneous rate of change of a function based on one of its variables. The most common example is velocity, which is the rate of change of displacement with respect to time. Anti-differentiation is the inverse of finding a derivative.
Differentiation is used to calculate the rate of change of quantities in real time.

Since, we have been given the cost function to be function \((cx)= 1.1^{2} - 660x+107,357\) then we have to find the first differentiation in order to get the value and this will be:-

\((cx)= 1.1^{2} -660x+107,357\\2.2x=660\\x=\frac{660}{2.2} \\x=300\)

Therefore, the number of cars that must be made to minimize the unit cost is 300 cars.

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To solve this problem, we'll use the concept of permutations.

First, we need to choose a woman for the position of president, then another woman for the position of vice president, and finally, a man for the treasurer position.

1. President: Since there are 20 women, we have 20 options for the president position.
2. Vice President: We're left with 19 women (since we already chose one for the president), so we have 19 options for the vice president position.
3. Treasurer: Since there are 17 men, we have 17 options for the treasurer position.

Now, multiply the number of options for each position together to find the total number of ways to form the committee:

20 (president) × 19 (vice president) × 17 (treasurer) = 6,460 ways.

So, there are 6,460 possible ways to choose three different members with women as president and vice president and a man as treasurer.

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Answer:

289 in

Step-by-step explanation:

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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When two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

We need to find the type of correlation when two variables vary along with each other but the data points are loosely scattered around the line of best fit.

A scatter plot helps find the relationship between two variables. This relationship is referred to as a correlation. Based on the correlation, scatter plots can be classified as follows.

A weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.

Therefore, when two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

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Answer:

339.6 cm²

Step-by-step explanation:

½×10.4×12

= 62.4 cm²

½×12×15.4×3

= 277.2 cm²

total = 277.2+62.4

= 339.6 cm²

a. The number of passengers for each cruise line in thousands:

4,133,000 passengers ÷ 1,000 = 4,133 passengers

2,369,000 passengers ÷ 1,000 = 2,369 passengers

1,295,000 passengers ÷ 1,000 = 1,295 passengers

928,000 passengers ÷ 1,000 = 928 passengers

679,000 passengers ÷ 1,000 = 679 passengers

So, the answer is 4,133; 2,369; 1,295; 928; 679.

b. The mean number of passengers can be found by adding the number of passengers for each cruise line and then dividing the total by the number of cruise lines, which is 5.

(4,133 + 2,369 + 1,295 + 928 + 679) ÷ 5 = 10,514 ÷ 5 = 2,102.8 passengers

So, the mean number of passengers is 2,102.8 passengers.

c. The range is the difference between the highest and lowest number of passengers, which is:

4,133 - 679 = 3,454 passengers

So, the range is 3,454 passengers.

d. The standard deviation can be calculated using the formula for the standard deviation of a sample. However, this calculation is quite complex and requires a significant amount of mathematical knowledge and computational resources. Without access to those resources, the standard deviation cannot be calculated

The standard deviation is a measure of the amount of variation or dispersion from the mean. It shows how spread out the values in a set of data are. To calculate the standard deviation, the difference of each value from the mean is squared and then divided by the number of items in the set. The standard deviation provides a way to quantify the degree of variation of the values around the mean. It is a useful tool for understanding how much each value in a set deviates from the average.

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a. To reach a savings goal of $180,000 by your 18th birthday, assuming starting from your first birthday and earning a 6.5% annual return, your parents would need to save a fixed amount each year.

b. If they adjust their goal to $220,000 and assume a five-year college duration, the annual savings required would change.

a. To calculate the amount your parents would need to save each year to reach the goal of $180,000, we can use the concept of present value. The present value (PV) of the savings should equal the future value (FV) of $180,000, given an annual interest rate of 6.5% and a time period of 17 years (from your first to 18th birthday). By using the formula for calculating present value of an annuity, we can determine the required annual savings amount.

b. If your parents adjust their goal to $220,000 and consider a five-year college duration, the time period would change from 17 years to 16 years (from your first birthday to the year before your 18th birthday). Using the new future value of $220,000 and the same interest rate of 6.5%, the required annual savings amount can be recalculated.

To obtain the specific annual savings amount in both scenarios, the calculations can be done using financial formulas such as the present value of an annuity formula or by utilizing financial calculators or spreadsheets.

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The value of sin 223° is equivalent to -sin 47°.

To prove this, we can use the trigonometric identity

sin(A - B) = sinA cosB - cosA sinB.

Here, A = 270° and B = 47°.

sin(223°) = sin(270° - 47°)

               = sin(270°) cos(47°) - cos(270°) sin(47°)

               = (-1) × sin(47°) = -sin(47°)

Therefore, the value of sin 223° is equivalent to -sin 47°.

Since, the value of sin 223° is equivalent to -sin 47°.

Hence, the value of sin 223° is equivalent to -sin 47°.

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Answer:

Similar by SSS

Hope it helps

Please mark me as the brainliest

Thank you

Cameron is left with 11/6 of a pan by using mathematical operation known as subtraction.

Given,

Total number of brownies = 2 pans

Cameron ate = 1/6 of a pan

In this question we will be using mathematical operation known as subtraction.

Subtraction is an arithmetic operation that involves finding the difference between two numbers. In other words, it is the process of removing a quantity from another. It is a fundamental mathematical concept that is widely used in everyday life, from calculating the change from a purchase to determining the difference between two quantities. Subtraction can be performed with whole numbers, decimals, fractions, and even with negative numbers. In all cases, the process of subtraction involves aligning the numbers to be subtracted, either vertically or horizontally, and then subtracting the smaller quantity from the larger one.

Brownies left = 2 pans - 1/6 of pan

                      = 12/6 -1/6

                      = 11/6 pan

Hence, she is left with 11/6 of a pan to eat.

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Answer:

48

My explanations is:

13.2:27.5*100 =

(13.2*100):27.5 =

1320:27.5 = 48

The expression f(5)=10 tells us that if Polly is an artist and sells posters at a local cafe then it means that Polly makes 10 dollars when she sells 5 posters.

According to the question,

We have the following information:

Polly sells x posters then she makes f(x) dollars.

We have the following expression:

f(5) = 10

So, it simply means that in place of x in f(x) we have f(5) then we have 5 in place of x.

f(x) is the amount made in dollars. So, the total amount Polly made is 10 dollars.

Hence, the expression f(5) = 10 clearly states that Polly sold 5 posters as an artist and made 10 dollars out of it.

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4x + 3y = 5  is the form of linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                              Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. ax+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

Points are (-7 ,11 ) and (8 , -9 )

 y - 11 = -4/3 (x + 7)   equation of the line into point slope form

the equation of the line into slope intercept form

  y = mx + b

  b is the y-intercept (value of y when the value of x is equal to zero)

For x=0

   y - 11 = -4/3(0 + 7)

  y =  - 28/3 + 11

   y = 5/3

substitute

   y = -4/3x + 5/3

Find the equation of the line in standard form

  Ax +By = C

    y = -4/3x + 5/3

Multiply by 3 both sides

 3y = -4x  + 5

4x + 3y = 5

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