A right triangle has a leg of length 12 and a hypotenuse of length 23 yards. Find the length of the other leg (nearest tenth).

Answer:

C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11​%±3​%.

Step-by-step explanation:

Data provided in the questions

Number of respondents = 1,000

Choose chocolate pie = 11%

margin of error = ±3 percentage points

Based on the above information,

The lower limit is

= 0.11 - 0.03

= 0.08

And, the upper limit is

= 0.11 + 0.03

= 0.14

So based on the above computation, the option c is correct as it represents the true population percentage of people with respect to the chocolate pie preference

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

Answer:

the answer is 8472373n3

Answer:

12:8

Step-by-step explanation:

Bill receives £12, and Sue receives £8.

In order to divide £20 between Bill and Sue in the ratio 3:2, we first need to find the total number of parts in the ratio. The sum of the parts in a 3:2 ratio is 3 + 2 = 5.

Next, we determine the value of one part by dividing the total amount (£20) by the total number of parts (5): £20 ÷ 5 = £4.

Now, we can allocate the money to Bill and Sue according to their shares in the ratio. For Bill, who gets 3 parts, we multiply his share of one part (£4) by 3: £4 × 3 = £12. For Sue, who gets 2 parts, we multiply her share of one part (£4) by 2: £4 × 2 = £8.

Thus, Bill receives £12, and Sue receives £8.

In mathematical terms, we can represent the division of £20 between Bill (B) and Sue (S) as follows:

Let the ratio be represented as B:S = 3:2.

Total parts in the ratio = 3 + 2 = 5.

Value of one part (Vp) = Total amount / Total parts = £20 ÷ 5 = £4.

Amount received by Bill (Ab) = 3 parts × Vp = 3 × £4 = £12.

Amount received by Sue (As) = 2 parts × Vp = 2 × £4 = £8.

Thus, Bill receives £12, and Sue receives £8.

In summary, when dividing £20 between Bill and Sue in the ratio 3:2, we follow the steps of finding the total parts in the ratio, calculating the value of one part, and then distributing the amount based on each individual's share in the ratio.

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Answer:

each row can sit 6•4+2 people for a total of 26 people. 130 ÷ 26 = 5 rows

Answer:

Step-by-step explanation:

6 tables in a row can take:

Each row can take 26 people, the number of rows is:

Answer:

The percent increase is 74%

Step-by-step explanation:

Copy and Paste

Answer:B. y=0.5x+0.3

Step-by-step explanation:a. p. e. x.

The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation thus option (B) is correct.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given points,

Let's take two-point (1,1)  and (2,1.5)

The slope associated with the above points will be as,

(1.5 - 1)/(2 - 1) = 0.5

Thus, the line will be y = 0.5x + 0.3

Hence "The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation".

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y = e^((1/2)(tan(x) + C)) is the solution to the given differential equation.

To solve the given differential equation (y^2 + 2) dx = y sec^2(x) dy, follow these steps:

Step 1: Rewrite the equation as a separable differential equation.
To do this, divide both sides by y(y^2 + 2) to isolate dx and dy:

(dy/y) = (sec^2(x) dx) / (y^2 + 2)

Step 2: Integrate both sides of the equation.
Integrate the left side with respect to y, and the right side with respect to x:

∫(1/y) dy = ∫(sec^2(x) / (y^2 + 2)) dx

Step 3: Evaluate the integrals.
For the left side, the integral of 1/y with respect to y is ln|y| + C₁ (where C₁ is a constant).
For the right side, let u = y^2 + 2, then du = 2y dy, so the integral becomes:

∫(sec^2(x) / u) (1/2) du = (1/2) ∫(sec^2(x) du)

Now, the integral of sec^2(x) with respect to u is tan(x) + C₂ (where C₂ is another constant).

Step 4: Combine the constants and express the solution.
The general solution is given by:

ln|y| = (1/2)(tan(x) + C), where C = 2(C₁ - C₂).

To express y in terms of x, take the exponential of both sides:

y = e^((1/2)(tan(x) + C))

This is the solution to the given differential equation.

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The sum of the absolute deviations from the mean for the given data is 4. Answer (c) 4 is correct.

To compute the sum of the deviations from the mean, we first need to calculate the deviation of each data point from the mean. The mean is given as 7.

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 5 from the mean = |5 - 7| = 2

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 7 from the mean = |7 - 7| = 0

Deviation of 9 from the mean = |9 - 7| = 2

To find the sum of the absolute deviations, we add up the deviations from the mean:

|0| + |0| + |2| + |0| + |0| + |0| + |0| + |0| + |0| + |2| = 4

Therefore, the sum of the absolute deviations from the mean for the given data is 4. Answer (c) 4 is correct.

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Question 10

\(\frac{\sin x}{7}=\frac{\sin 85^{\circ}}{8}\\\\\sin x=\frac{7\sin 85^{\circ}}{8}\\\\x \approx 60.7^{\circ}, 119.3^{\circ}\)

However, the second case does not satisfy the angle sum of a triangle, so \(x \approx 60.7^{\circ}\).

Question 12

\(\frac{\sin x}{19}=\frac{\sin 34^{\circ}}{12}\\\\\sin x=\frac{19\sin 34^{\circ}}{12}\\ \\ x \approx 62.3^{\circ}, 117.7^{\circ}\)

Both of these cases satisfy the angle sum of a triangle.

Answer:

The answer would be letter J

The inequality for total expenditure & number of breakfasts is 5 > 1.25b

Assumed : Number of breakfasts = b

Number of breakfast meals x Price per breakfast meal = Total Expenditure

Total expenditure should be less or than equal to $1.25

So, 1.25b < 5

It implies that inequality : 5 > 1.25b

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Answer: 12:2, 6:1, 24:4

Step-by-step explanation:

The solution to the absolute-value inequality is x > 9; and x < -1

An inequality is an expression that shows the nonequal comparison of two or more numbers and variables.

Let x represent the unknown number, hence:

|x - 4| > 5

(x - 4) > 5; and -(x - 4) > 5

x > 9; and x < -1

The solution to the absolute-value inequality is x > 9; and x < -1

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unbiased

If the expected value of a sample statistic is equal to the parameter it is estimating, we can call the sample statistic:

a. unbiased.

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

The appropriate z-value to use in the situation given in the question is 1.28.

Given,Total number of adults in the sample = 2092

Number of adults using the internet = 1318

Number of internet users who expect businesses to have websites that give product information = 1041

Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8

To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:

SEp = √[p(1-p)/n]

where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.

Substituting the given values in the formula,

SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019

z-value is given by:

z = (p - P)/SEp

where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.

Substituting the given values in the formula,

z = (0.8 - 1041/1318)/0.019

z = - 1.28

The appropriate z-value to use in this situation is -1.28.

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The problem says you have 10 books arranged on a shelf and then you are choosing 4 books in alphabetical order.

Given that you are choosing books with an order (alphabetical) it means the order does matter, then it is a permutation (which is an ordered combination).

In this case, no repetitions are allowed because you can't repeat a book in the selection, they'll be 4 different books from the shelf, the formula you have to use is:

Then n=10 and r=4, replace these values:

Then, can be chosen 5040 different groups of books.

The answer is option D.

Answer:

the answer is B.

Step-by-step explanation:

The cost of one knife will be 5.23 which is calculated by using the given information about knives and spoons.

From the given information in the question we can form two equations:

We will consider the variables representing the cost of spoons and knives as k and f respectively.

now we will build the equations to find out the relation between knives and spoons from the given information.

k = s + 3

As the cost of knives is three times more than spoons we add 3 to the cost of spoons

the other information given is about the sum of 9 spoons and 12 knives

which we will write as:

9s + 12k = 82.80

By substituting the first equation in the second equation we will get an equation containing only one variable which is easier to solve

9s + 12(s + 3) = 82.80

9s + 12s + 36 = 82.80

21s = 82.80 - 36

21s = 46.8

s = 46.8 / 21

s = 2.23

now by substituting the value of s in the first equation

k = s + 3

k= 2.23 + 3

k = 5.23

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Answer:

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.

Step-by-step explanation:

The characteristic of a binomial experiment is that the trials are independent. This means that the outcome of one trial does not affect the outcome of any other trial. Additionally, at least two outcomes are possible in a binomial experiment.

A binomial experiment is a statistical experiment that has the following characteristics: the experiment consists of a fixed number of trials, each trial has only two possible outcomes (success or failure), the trials are independent, the probability of success remains constant for each trial, and the outcome of one trial does not affect the outcome of any other trial.

The characteristic that the probability of success remains constant is known as the "fixed probability" or "fixed success rate" characteristic. This means that the probability of success is the same for each trial and does not change based on the outcome of any previous trial. This is an important characteristic of a binomial experiment, as it allows for the calculation of probabilities using simple formulas.

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Answer:

A.

Step-by-step explanation:

the square root of 6 is roughly 1.57

so that means the ordered pair would read (2,1.57).

if you were to plot that point it would be on the circle.

Also the distance from the origin (0,0) to (3,0) is 3 units

We will see that the correct option is:

"No, the distance from (0, 0) to (2, 6) is not 3 units."

We know that the circle has a radius of 3 units, then we need to see if the distance between (0, 0) and (2, 6) is 3 units.

Here we have:

\(D = \sqrt{(6 - 0)^2 + (2 - 0)^2} = \sqrt{36 + 4} = \sqrt{40} \neq 3\)

So the distance between (0, 0) and (2, 6) is different than 3 units, meaning that the point is not in the circle.

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Answer:

Your answer is: \(-4c+23/3\)

Simplify the expression.

Step-by-step explanation:

Hope this helped : )

The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Given data:

7, 11, 12, 18, 20, 22, 43.

To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.

That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.

The formula to find standard deviation is:

S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}

Where, N = sample size,

             x = each value of the data set,

    \bar{x} = mean of the data set

To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:

Mean = $\frac{7+11+12+18+20+22+43}{7}$

          = $\frac{133}{7}$

          = 19

Now, calculate the standard deviation:

$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D

                                                                                                                               = $\sqrt{\frac{1442}{7-1}}$

                                                                                                                                ≈ 10.31

To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.

Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$

                                                                                                                      = $\frac{43-19}{10.31}$

                                                                                                                      = 2.32

Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.

Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

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The value of dy/dt is 0 units per second.

a) Given: y= √x Differentiating with respect to t, we get; \(dy/dt = 1/2√x * dx/dt\)

On substituting the values of x and dx/dt in the above equation, we get; dy/dt = 1/2 * √16 * 3= 1.5 units per second

Therefore, the value of dy/dt is 1.5 units per second.

b) Given: \(y= √x\)

Differentiating with respect to t, we get;

\(dy/dt = 1/2√x * dx/dt\)

Let us assume that y = k, where k is a constant that can be determined by the given value of x.

Substituting the values of x and y in the equation, we get; 25 = √x

Therefore, x = 625dx/dt

= 0

(Given)\(dy/dt = 1/2√x * dx/dt\)

dy/dt = 1/2√625 * 0

= 0

Therefore, the value of dy/dt is 0 units per second.

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The alternative hypothesis, in this case, would be that the cycle time of Team A is not better than the cycle time of Team B.

An assertion used in statistical inference experiments is known as the alternative hypothesis. It is indicated by \(H_a\) or \(H_1\) and runs counter to the null hypothesis. Another way to put it is that it is only a different option from the null. An alternative theory in hypothesis testing is a claim that the researcher is testing.

The alternative hypothesis is a statement that contradicts the null hypothesis and suggests the presence of an effect, relationship, or difference between the variables being studied.

In the context of comparing the cycle times of Team A and Team B, the null hypothesis (\(H_0\)) would typically be that there is no difference or superiority in the cycle times between the two teams. In other words, the null hypothesis assumes that the cycle times of Team A and Team B are equal or that any observed difference is due to chance.

The alternative hypothesis (\(H_A\)), on the other hand, asserts that there is a difference or superiority in the cycle times of Team A compared to Team B. It suggests that the observed difference, if any, is not due to chance and that there is a real effect or advantage associated with Team A's cycle time.

Formally, the alternative hypothesis would be stated as \(H_A\): The cycle time of Team A is better than the cycle time of Team B.

By formulating the alternative hypothesis in this way, we are proposing that Team A's cycle time is faster, more efficient, or otherwise superior compared to Team B. It sets the stage for conducting statistical tests or gathering evidence to support or refute this claim.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

=12pl+B

Step-by-step explanation:

where p represents the perimeter of the base, l the slant height and B the area of the base.

Answer:

4 + 4 sqrt 10

Step-by-step explanation:

The scale factor of 10cm to 5m is 50.

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;

scale factor = new dimension / old dimension

Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm

therefore 5m = 5× 100 = 500cm

therefore scale factor = 500/10 = 50

This means the scale factor of 10cm = 5m is 50

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