Divide.

3/4÷2 1/2

Responses

3/10

1 1/2

1 7/8

3 1/3

The relation that is represented in the table is a function. YES.

For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).

In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.

Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.

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Answer:

Answer = 140

Step-by-step explanation:

360 = 9x + 14x + 4x + 90

360 - 90 = 27x
270 = 27x
x = 270 / 27
x = 10
14 x 10 Angle F

Measure of angle F = 140

Answer:

Answer = 140

Step-by-step explanation:

360 = 9x + 14x + 4x + 90

360 - 90 = 27x

270 = 27x

x = 270 / 27

x = 10

14 x 10 Angle F

Measure of angle F = 140

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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Answer:

Step-by-step explanation:

1 1/6 + (x/3 · 1/4) = 1 3/4

solve for x

1 1/6 + x/12 = 1 3/4

1 1/6 - 1 3/4 = -x/12

-7/12 = -x/12

-7 = -x

x = 7

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

check

1 1/6 + (7/12 * 1/4) = 1 3/4

1 1/6 + 7/48 = 1 3/4

1 15/16 = 1 3/4

1 3/4 = 1 3/4

the answer is good

The equation for the line is:

3y - x = 14

Given the line:

x - 3y = 7

This line can be written as:

y = (1/3)x - 7/3

The slope is 1/3

The y-intercept is -7/3

A line parallel to this has the same slope but different y-intercept, written as:

y = (1/3)x + b

Using the given point (-2, 4), with x = -2 and y = 4, we can obtain the value of b

4 = (1/3)(-2) + b

b = 4 + 2/3

= 14/3

Therefore, the line is:

y = (1/3)x + (14/3)

or

3y - x = 14

Answer:

1,2,5

Step-by-step explanation:

202 edg yakdvb

Larger than for the Purdue sample because the sample size is smaller. Therefore, the option A is the correct answer.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Given sample size = 500

Total outcomes = 37,000

The margin of error in a 95% confidence

The margin of error is given by

Margin of error (statistic) = Critical value x Standard error of the sample.

So, according to the given condition margin of  error in a 95% confidence is same as for the Purdue sample because both are samples of size 500, because it depends on sample size.

Therefore, the option A is the correct answer.

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Answer:

I getting the probability of the adult female that will rent the action movies in DVDs in by dividing the possible probability outcome which is 10% of all adults by the total number of possible outcome. So all of the population of the female is 51% and the ones who rent is only 10%. the probability is 19%

The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

Data:

A: the adult is a male, P(A) = 0.49

B: the adult rent action-movie DVDs

C: the adult is a female,  P(C) = 1 - P(A) = 1 - 0.49 = 0.51  

24% of the adults are male and rent action-movie DVDs, then P(A ∩ B) = 0.24

10% of the adults are female and rent action-movie DVDs, then P(C ∩ B) = 0.10

The conditional probability of B (the adult rents action-movie DVDs) given C (the adult is female) is computed as follows:

P(B|C) = P(C ∩ B)/P(C)

          = 0.1/0.51

          = 0.2

Hence, The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.

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The area of the surface generated by revolving the curve about the x-axis is 243π square units, and the area of the surface generated by revolving the curve about the y-axis is 1152π square units.

We are given the curve x = 8t, y = 9t, and the range of t is 0 ≤ t ≤ 3. We need to find the area of the surface generated by revolving this curve about the x-axis and the y-axis.

(a) To find the area of the surface generated by revolving the curve about the x-axis, we can use the formula for the surface area of revolution: S = 2π∫[a,b] y √(1 + (dy/dx)²) dx. In this case, a = 0 and b = 3, and the curve is given by x = 8t, y = 9t. We can differentiate y = 9t with respect to x to find dy/dx = 9. Plugging these values into the formula, we have S = 2π∫[0,3] 9t √(1 + 9²) dt = 162π ∫[0,3] t dt = 162π (t²/2)∣[0,3] = 243π.

(b) To find the area of the surface generated by revolving the curve about the y-axis, we use the same formula but with x as the variable. The curve is still given by x = 8t, y = 9t, and we differentiate x = 8t with respect to y to find dx/dy = 8/9. Plugging these values into the formula, we have S = 2π∫[c,d] x √(1 + (dx/dy)²) dy. The range of y is determined by the range of t, so c = 0 and d = 27. Evaluating the integral, we get S = 2π∫[0,27] (8/9)y √(1 + (8/9)²) dy = 2π(64/9) ∫[0,27] y dy = 1152π.

Therefore, the area of the surface generated by revolving the curve about the x-axis is 243π square units, and the area of the surface generated by revolving the curve about the y-axis is 1152π square units.

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Answer:

80+60+3x+4=180

140+3x+4=180

144+3x=180

3x=180-144

3x=36

x=12

Answer:

x = 12

Step-by-step explanation:

All triangles equal to 180 degrees so, we can set up this expression:

180 = (3x + 4) + 80 + 60

All we have to do is solve:

180 = (3x + 4) + 80 + 60

180 = 3x + 4 + 140

180 = 3x + 144

-144        -144

36 = 3x

/3     /3

12 = x

From the problem, we have :

We need to think of a square number that if we multiply it by 9, the result is 64.

That would be 64/9

The square root of 64/9 is 8/3.

Let u = 3x/8

8u = 3x

x = 8u/3 (This value is the same as we've got above 8/3)

du = 3/8 dx

dx = 8/3 du

Subsitute x = 8u/3 and dx = 8/3 du

Extract the square root of 64 which is equal to 8.

Note that the identity :

It follows that :

Bring back u = 3x/8, the answer is :

The highest point scored is by Carlos with 19 points. Mario's highest was 15. so, Carlos scored 4 points more than Mario.

In the 7th game, Carlos scored 19 points which is the highest point of his game. In the 1st game, Mario scored 15 points which was the highest point he scored. Therefore, Carlos had the highest scoring game between the two of them. Carlos scored 4 points more than Mario did in his highest-scoring game. You can also construct a box plot for this question which will help you visualise this better. The box plot can be made by drawing a number line and marking the following points: minimum, first quartile, median, third quartile and maximum.

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The full question is:

Mario and Carlos, two brothers, play for the same basketball team. Here are the

points they scored in 10 games:

Game 1 2 3 4 5 6 7 8 9 10

Mario 15 X X 12 7 11 12 11 10 11

Carlos 10 X 9 12 15 X 19 11 12 12

(Xs mark games each one missed.) Which brother had the

highest-scoring game? How many more points did he score in

that game than the other brother did in his highest-scoring game?

Answer/Step-by-step explanation:

Since you know that the answer is x = 36, Then you can substitute it in the equation.

3/4(36) - 11 = 16          → Multiply 3/4 by 36

27 - 11 = 16                  → Subtract 11 from 27

16 = 16                        → They are equal

Hence as you can see, x = 36.

RevyBreeze

The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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Answer: 1/13

Step-by-step explanation:

1/13 is the simplest form of 4/52, which is the number of king cards to the number of cards total.

The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

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Answer:

More info is needed

Step-by-step explanation:

Because there are many outcomes/answers which include.

x=4 and y=1

x=0 and y=4

Answer:

A = 36 pi m^2 or approximately 113.04 m^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

The radius is 6

A = pi 6^2

A = 36 pi m^2

Using the approximation of 3.14 for pi

A =113.04 m^2

Answer:

A≈113.1

Step-by-step explanation:

A=πr^2=π·6^2≈113.09734

The polynomial, f(x) expressed as a product of linear factors is; f(x) =(-5/2 + √ 5) and (-5/2 - √ 5)

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Given that ;

\(p(A) = 2x^3 - 3x^2 + 10x + 6\)

\(P(a)= (2x^3 - 3x^2) + (10x + 6)\)

therefore need to further factorise the quadratic expression (x² + 5x +3) using the quadratic formula;

Quadratic formula;

x = {-b ± √(b² +4ac)}/2a

where; a = 1, b = 5, c = 3.

Therefore; x = -5/2 + √ 5or x = -5/2 - √ 5

Therefore, the other factors are:

(-5/2 + √ 5) and (-5/2 - √ 5)

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The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Answer:

The answer is

Step-by-step explanation:

To convert an angle from degrees to radians multiply the value by \( \frac{\pi}{180} \)

From the question the value to be converted is - 420°

The value in radians is

\( - 420 \times \frac{\pi}{180} \\ = - \frac{420\pi}{180} \)

Reduce the fraction with 60

We have the final answer as

\( - \frac{7\pi}{3} \)

Hope this helps you

Answer:

1/7   and if you reduce its still 1/7

Step-by-step explanation:

To determine the number of ways the letters in the word "payment" can be arranged using 5 letters, we can utilize the concept of permutations.

A permutation is an arrangement of objects where the order matters. In this case, we want to arrange the letters of the word "payment" using only 5 out of the 7 letters available. To calculate the number of arrangements, we use the formula for permutations: nPr = n! / (n - r)!, where n is the total number of objects (letters) and r is the number of objects to be selected (5 in this case).

In the word "payment," there are 7 letters. Therefore, we have 7 options to choose from for the first position, 6 options for the second position, 5 options for the third position, 4 options for the fourth position, and 3 options for the fifth position. Hence, the number of arrangements is:
7P5 = 7! / (7 - 5)! = 7! / 2! = 7 * 6 * 5 * 4 * 3 = 2,520. Therefore, there are 2,520 different ways to arrange the letters of the word "payment" using only 5 letters.

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Answer:

40

Step-by-step explanation:

The middle dot of the box is the median.

Answer:

the median is 44.75

Step-by-step explanation:

first i add up all the numbers

40+37+48.5+53.5=175

then i divide them by how 4

179 divided by 4=44.75

To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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Answer:

5

Step-by-step explanation:

Answer:

it would also equal 50

Step-by-step explanation:

angle 4 and angle 8 are corresponding angles meaning that they are the same angle