Recall that two angle are complementary if the um of their meaure i 90 degree°. Find the meaure of two complementary angle if one angle i 20 degree° more than forty four time the other angle

The probability that both will be married before the age of 18 is 0.0036. The probability that both will be married by the age of 25 is 0.25. Finally, the probability that both will be married by the age of 30 is 0.5476.

According to the brief report by NCHS, approximately 6% of women in the United States married for the first time before their 18th birthday, and 50% of women married by their 25th birthday. 74% of women married by their 30th birthday.The probability of a family with two daughters marrying at different ages is asked in the question. The probability that both daughters will be married by the ages of 18, 25, and 30 will be determined

The question requires finding the probability that both daughters of a family will be married by the ages of 18, 25, and 30 respectively. Since each daughter's wedding is a separate event, the individual probability of a daughter marrying at a given age will be determined separately and then multiplied together to get the probability of both daughters being married at the given age. So, let's find the probabilities of each daughter marrying at a given age:

Probability of one daughter getting married by 18 years:

As per the brief report, 6% of women in the United States married before the age of 18.

Therefore, the probability of one daughter getting married before the age of 18 is 0.06

Probability of one daughter getting married by 25 years:

As per the brief report, 50% of women in the United States get married by the age of 25. Therefore, the probability of one daughter getting married by 25 years is 0.5.

Probability of one daughter getting married by 30 years:

As per the brief report, 74% of women in the United States get married by the age of 30. Therefore, the probability of one daughter getting married by 30 years is 0.74.

The probability of both daughters getting married at the same age is the product of each daughter's probability of getting married at that age.

The probability that both daughters will get married before the age of 18 is:

P(both daughters married at 18 years) = P(daughter1 married at 18) × P(daughter2 married at 18)= 0.06 × 0.06= 0.0036

The probability that both daughters will get married by the age of 25 is:

P(both daughters married at 25 years) = P(daughter1 married at 25) × P(daughter2 married at 25)= 0.5 × 0.5= 0.25

The probability that both daughters will get married by the age of 30 is:

P(both daughters married at 30 years) = P(daughter1 married at 30) × P(daughter2 married at 30)= 0.74 × 0.74= 0.5476

The probability that in a family with two daughters, both will be married before the age of 18 is 0.0036. The probability that both daughters will be married by the age of 25 is 0.25. Finally, the probability that both daughters will be married by the age of 30 is 0.5476.

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Answer:

The solution set consists of all the real numbers smaller than or equal to 11/4:

\(x\leq \frac{11}{4}\)

Step-by-step explanation:

We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:

\(3+\frac{x-2}{x-3} \leq 0\\\frac{x-2}{x-3} \leq -3\\x-2\leq -3\,(x-3)\\x-2\leq -3x+9\\x+3x\leq 9+2\\4x\leq 11\\x\leq \frac{11}{4}\)

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.

The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.

So, as one moves further from the mean, the probability of occurrence decreases exponentially.

So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.

Therefore, the statement is True.

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a. Simple interest: around 14.29 years.

b. Annual compound interest: about 5 years.

c. Continuous compound interest: roughly 4.95 years.



a. With a 14 percent simple interest rate, the time it takes for a sum to double can be calculated using the formula:Time = (100 / interest rate) * 2

In this case, the interest rate is 14 percent, so the time it takes for the sum to double is:Time = (100 / 14) * 2 = 14.29 years (approximately).

b. With a 14 percent interest rate compounded annually, the time it takes for a sum to double can be calculated using the compound interest formula:Time = log(2) / log(1 + (interest rate / 100))

Substituting the values, the time it takes for the sum to double is:

Time = log(2) / log(1 + (14 / 100)) = 5.00 years (approximately).

c. With a 14 percent interest rate compounded continuously, the time it takes for a sum to double can be calculated using the formula:

Time = ln(2) / (interest rate / 100)

Using the values, the time it takes for the sum to double is:

Time = ln(2) / (14 / 100) = 4.95 years (approximately).

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Answer: B.  No, y does not vary directly with x

Why not? Well we would find that k isn't the same when dividing each pair of x and y values like so:

Technically once you get to the result k = 2.5 in the second row, you could stop there. The third row is just extra practice. All of the k values must be the same if we want a direct variation equation in the form y = kx

Answer:

Step-by-step explanation:

y+ 20= x+ 15( Vertically opposite angles)

y+ 20- 15= x

x= y+ 5 __(1)

3x+ 5=4y- 15

Substituting (1)

3(y+5)+ 5= 4y-15

3y+15+5=4y- 15

y=15+20

y= 35

x= 40

The value of integral ∫(0,8)  [4f(x) + 6g(x)] dx on the interval of (0,8) is 264

when ∫(0,8) f(x) dx = 39 and  ∫(0,8)g(x) dx =18.

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

Given that,

∫(0,8) f(x) dx = 39 and  ∫(0,8)g(x) dx =18

∫(0,8)  [4f(x) + 6g(x)] dx

Apply linearity rule of integration,

= ∫(0,8) 4f(x) dx + ∫(0,8) 6g(x) dx

=4 ∫(0,8) f(x) dx + 6∫(0,8) g(x) dx

= 4(39) + 6(18)

= 156 + 108

= 264

therefore, the value of integral ∫(0,8)  [4f(x) + 6g(x)] dx on the interval of (0,8) is 264

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Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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Step-by-step explanation:

Time=distance/speed

67÷110

=36' 32sec

Answer:

B - {5, -5}

Step-by-step explanation:

Use the quadratic formula.

A total of 23, 950, 080 results are possible.

We are given;

10 women

12 men

5 men and 5 women, chosen and pared off, how many results in total?

Thus;

[10 choose 5] x [12 choose 5]=252 x 792 = 199584 ways

We then need to know how many ways there could put into pairs i.e. For the first woman, there will be 5 choices of men. For the second woman, there will be 4 choices remaining of men. For the third woman, there will be 3 choices remaining. For the fourth woman, there will be only 2choices remaining, and only 1 choice left for the last woman.

Therefore, there are 5x4x3x2x1 = 120 ways.

 In total there are 199584x120 = 23950080 total  ways

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Answer:

80-4(2)=72; 80-4(x) if he got x wrong.

It is a function. None of the x values repeat

Answer: x= 3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer: For number 8 it is 2  For number 9 it is confusing

Step-by-step explanation:

If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.

The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.

In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.

A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.

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Answer:

???

Step-by-step explanation:

Where's the image?

Answer:

52min

Step-by-step explanation:

5 people..............5 walls............52 min

1 people...............5 walls...........52 x 5=260 min

1 people................20 walls.........260 x 4 =1040 min

20 people................20 walls........1040:20=52 min

Answer:

116

Step-by-step explanation:

maybe don't try this i could be wrong.

An adult must spend 6 hours on leisure activities.

We have been given the mean, µ = 4.5 and

standard deviation, σ = 1.3 of the normal distribution and we need to find how much time must be spent on leisure activities by an adult living in household with no young children to be in the group of adults who spent the highest 3% of the time in a day in such activities

. Let x be the amount of time that should be spent on leisure activities by an adult to be in the group of adults who spent the highest 3% of the time in a day in such activities. Now, we know that the highest 3% of the

time in a day in such activities will correspond to the area to the right of z value of 0.97. Hence, we can write the z score as: 0.97 = (x - µ) / σz = (x - 4.5) / 1.3x - 4.5 = 0.97 × 1.3x = 6.011Therefore, an adult living in household with no young children must spend 6.011 hours on leisure activities to be in the group of adults who spent the highest 3% of the time in a day in such activities

.Thus, the answer is: An adult living in household with no young children must spend 6.011 hours on leisure activities

to be in the group of adults who spent the highest 3% of the time in a day in such activities.

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An adult living in a household with no young children must spend approximately 6.95 hours on leisure activities to be in the group of adults who spent the highest 3% of time in a day on such activities.

To find the amount of time an adult must spend on leisure activities to be in the highest 3%, we need to use the z-score formula and find the corresponding value.

First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value we want to find, μ is the mean (4.5 hours), and σ is the standard deviation (1.3 hours).

Next, we find the z-score corresponding to the highest 3% by subtracting 3% from 100% (97%). Using a z-table or a calculator, we find that the z-score corresponding to 97% is approximately 1.8808.

Now, we can solve for x:

1.8808 = (x - 4.5) / 1.3

Multiply both sides by 1.3:

1.8808 * 1.3 = x - 4.5

2.44504 + 4.5 = x

x ≈ 6.94504

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Answer:

??

Step-by-step explanation:

If that truly is homework I'd email your teacher.

Answer:

a leg of something

a piece of watch

or a piece of clothing

Step-by-step explanation:

c) It would be larger, because higher confidence requires a larger margin of error.

When increasing the confidence level from 95% to 99%, the margin of error of the confidence interval tends to increase. This is because a higher confidence level means we want to be more certain or have a higher level of confidence in capturing the true population parameter.

To achieve a higher confidence level, we need to widen the interval to account for more potential variability in the population. As a result, the margin of error increases, reflecting the increased uncertainty and the need for a larger range of values to capture the true population parameter with higher confidence.

Therefore, the margin of error of a 99% confidence interval, based on the same sample, would be larger compared to the 95% interval.

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According to the Empirical rule, approximately 95% of women had their first child between the ages of 16.5 years and 38.1 years. The correct option is b. 16.5 years and 38.1 years.

The given question states that a researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child and found an approximately normal distribution with a mean age of 27.3 and a standard deviation of 5.4. We are to find the range of age at which approximately 95% of women had their first child, according to the empirical rule.

There are three ranges for the empirical rule as follows:

Approximately 68% of the observations fall within the first standard deviation from the mean.

Approximately 95% of the observations fall within the first two standard deviations from the mean.

Approximately 99.7% of the observations fall within the first three standard deviations from the mean.

Now, we will apply the empirical rule to find the age range at which approximately 95% of women had their first child. The mean age is 27.3 years and the standard deviation is 5.4 years, hence:

First, find the age at which 2.5% of women had their first child:

µ - 2σ = 27.3 - (2 × 5.4) = 16.5

Then, find the age at which 97.5% of women had their first child:

µ + 2σ = 27.3 + (2 × 5.4) = 38.1

Therefore, approximately 95% of women had their first child between the ages of 16.5 years and 38.1 years. Hence, the correct answer is option b. 16.5 years and 38.1 years.

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Answer:

- 2

Step-by-step explanation:

Note that the values of x represent the input, while the values of f(x) represent the output.

From the column for f(x)

The only value on the list that is an output is - 2

Answer:

B.

Step-by-step explanation:

-2

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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To determine the residual for a data point based on a given trendline, we need to calculate the difference between the observed value (y-value) and predicted value (y-value) on the trendline at corresponding x-value.

Given that the trendline equation is y = 2x + 1, and the data point has an x-value of 1.3 and a y-value of 1.6, we can calculate the residual as follows:

Predicted y-value = 2x + 1

Substituting x = 1.3 into the equation:

Predicted y-value = 2(1.3) + 1

= 2.6 + 1

= 3.6

Residual = Observed y-value - Predicted y-value

= 1.6 - 3.6

= -2

Therefore, the residual for the data point with a measured y-value of 1.6 and an x-value of 1.3, based on the trendline y = 2x + 1, is -2.

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Answer:

C

C'

1

1. see attached

2. the figure is reflected in the y-axis

Step-by-step explanation:

1.

The given transformation moves each point horizontally to the same

distance on the other side of the y-axis. This is shown in the attachment.

2.

The given rule ...

(x, y) → (-x, y)

is the most precise description of the transformation. In English, it can be

described as a reflection in the y-axis

Step-by-step explanation:

Correct me if I'm wrong