What expressions are equivalent to the expression (x-y) 5/8-1/4 x + y? Please help

Answers

Answer 1

The equivalent expression is (3x + 3y)/8 or (3/8)x + (3/8)y

We have,

The given expression:

(x - y)(5/8) - (1/4)x + y.

This can be written as,

By distributive property:

(5/8)x - (5/8)y - (1/4)x + y

Find LCM.

(5x - 5y - 2x + 8y)/8

Combining the like terms.

(3x + 3y)/8

or,

3x/8 + 3y/8

Thus,

The equivalent expression is (3x + 3y)/8 or (3/8)x + (3/8)y.

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Related Questions

A function is translated from f(x)=2⋅3x+4
to g(x)=2⋅3x−1.
What is the effect on f(x)?

Answers

The effect on f(x) is that it is shifted one unit to the left on the x-axis to obtain g(x). In other words, the graph of g(x) is obtained by taking the graph of f(x) and shifting it to the right by one unit.

What is graph?

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, and the connections between them, called edges or links.

The function f(x) is translated to g(x) by subtracting 1 from the exponent of 3. This means that g(x) is obtained by shifting f(x) one unit to the right on the x-axis.

The coefficient of 2 remains unchanged, which means that the overall scaling of the function remains the same.

Therefore, the effect on f(x) is that it is shifted one unit to the left on the x-axis to obtain g(x). In other words, the graph of g(x) is obtained by taking the graph of f(x) and shifting it to the right by one unit.

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A taxi company uses this formula to calculate the cost (C) of a journey .
C = 5 + 1.5m + B
where m is the number of miles travelled and B is a booking fee.
(a) Mae booked a taxi with the company.
She travelled 6 miles and paid 15.50
Work out the booking fee.
(b) Noreen also booked a taxi with the company.
She travelled 10 miles.
Work out how much Noreen paid.

Answers

Answer:

(a) We can use the given formula to set up an equation:

C = 5 + 1.5m + B

Mae travelled 6 miles and paid 15.50, so we can substitute these values into the formula to get:

15.50 = 5 + 1.5(6) + B

Simplifying and solving for B, we get:

15.50 = 14 + B

B = 1.50

Therefore, Mae paid a booking fee of 1.50.

(b) We can use the given formula to calculate the cost for Noreen's journey:

C = 5 + 1.5m + B

Noreen travelled 10 miles, so we can substitute this value into the formula to get:

C = 5 + 1.5(10) + B

We don't know the value of B, but we can use the information that the cost of Noreen's journey is proportional to the distance she travelled. This means that the ratio of the cost to the distance travelled should be the same as the ratio of the cost of Mae's journey to the distance she travelled:

C / 10 = 15.50 / 6

Solving for C, we get:

C = 10 * (15.50 / 6) = 25.83 (rounded to two decimal places)

Therefore, Noreen paid 25.83 for her journey.

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Compute S_{4} (the 4th partial sum) of the following series. S=\sum_{n=1}^{\infty}\frac{1}{1 n^5} Answer: Estimate the error in using S_{4} as an approximation of the sum of the series. (i.e. use \int_{4}^{\infty} f(x)\, dx \geq R_{4} Answer: Use n = 4 and S_n + \int_{n+1}^{\infty} f(x)\, dx \leq S \leq S \leq S_n + \int_{n}^{\infty} f(x)dx to find a better estimate of the sum.Answer :

Answers

The series estimate of the sum is between 1.000020993 and 1.000031132.

Compute the 4th partial s4 given series is S = [tex]1/1^5 + 1/2^5 + 1/3^5[/tex] + ...?

The given series is S = [tex]1/1^5 + 1/2^5 + 1/3^5[/tex] + ...

We need to compute the 4th partial sum S4.

S4 =[tex]1/1^5 + 1/2^5 + 1/3^5 + 1/4^5[/tex]

Using a calculator, we get:

S4 ≈ 1.000015873

To estimate the error in using S4 as an approximation of the sum of the series, we can use the integral test. Let f(x) = 1/[tex]x^5[/tex].

Then, ∫f(x) dx from 4 to ∞ = ∫(1/[tex]x^5[/tex]) dx from 4 to ∞

= [-1/([tex]4x^4[/tex])] from 4 to ∞

= (1/[tex]4^4[/tex]) - (1/∞)

= 1/256

Since f(x) is positive, decreasing, and continuous for x ≥ 1, the integral test applies and we have:

S - S4 = ∫f(x) dx from 4 to ∞

≥ 1/256

Therefore, the error in using S4 as an approximation of the sum of the series is at least 1/256.

To find a better estimate of the sum, we can use the following inequality:

S_n + ∫f(x) dx from n+1 to ∞ ≤ S ≤ S_n + ∫f(x) dx from n to ∞

where Sn is the nth partial sum of the series.

For n = 4, we have:

S4 + ∫f(x) dx from 5 to ∞ ≤ S ≤ S4 + ∫f(x) dx from 4 to ∞

Substituting the values, we get:

1.000015873 + ∫(1/[tex]x^5[/tex]) dx from 5 to ∞ ≤ S ≤ 1.000015873 + ∫(1/[tex]x^5[/tex]) dx from 4 to ∞

Simplifying the integral, we get:

1.000015873 + [(1/[tex]4^4[/tex]) - (1/5^4)] ≤ S ≤ 1.000015873 + (1/[tex]4^4[/tex])

Solving for the bounds, we get:

1.000015873 + 0.00000512 ≤ S ≤ 1.000015873 + 0.000015259

1.000020993 ≤ S ≤ 1.000031132

Therefore, a better estimate of the sum is between 1.000020993 and 1.000031132.

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Write the equation, in slope-
intercept form, of the line that
passes through the points (-4,4)
and (2,-5). If needed, write your
slope as a decimal and NOT as a
fraction.

Answers

Answer:

Step-by-step explanation:

To find the equation of a line in slope-intercept form (y = mx + b), we first need to find the slope (m) and the y-intercept (b).

1. Calculate the slope (m) using the two given points (-4, 4) and (2, -5):m = (y2 - y1) / (x2 - x1) = (-5 - 4) / (2 - (-4))m = -9 / 6 = -1.5

So, the slope of the line is -1.5.

2. To find the y-intercept (b), we can use one of the given points and plug in the values for x, y, and m in the slope-intercept equation. Let's use the point (-4, 4):4 = -1.5 * (-4) + b4 = 6 + bb = -2Now we have the slope (m) and y-intercept (b), so we can write the equation in slope-intercept form: y = -1.5x - 2

Americans are stressed out!
A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a
significant source of stress for me." To help form an estimate, the psychologist randomly selected 938
Americans and found that 62.6% of the sample agreed with the statement "the future of the nation is a
significant source of stress for me."
Using a 90% confidence level, determine the margin of error, E, and a confidence interval for the true
proportion of all Americans that say the "the future of the nation is a significant source of stress for me."
Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.

Answers

The margin of error is of: 0.026.The 90% confidence interval is of: (0.6, 0.652).

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters for this problem are given as follows:

[tex]\pi = 0.626, n = 938[/tex]

Hence the margin of error of the interval is of:

M = 1.645 x sqrt(0.626 x 0.374/938)

M = 0.026.

The lower bound of the interval is of:

0.626 - 0.026 = 0.6.

The upper bound of the interval is of:

0.626 + 0.026 = 0.652.

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is the following a power function, a polynomial, both, or neither? f(x)=−14x−−√3? Select the correct answer below: O Power function O Polynomial function O Both Power and Polynomial O Neither Power nor Polynomial

Answers

The given function f(x) = -[tex]14x^(^-^\sqrt3)[/tex] is a power function.

How to find the function of the equation?

A power function is a function of the form f(x) = [tex]kx^m[/tex], where k and m are constants, and x is the independent variable raised to the power of m.

On the other hand, a polynomial function is a function of the form f(x) = [tex]a_nx^n[/tex] + [tex]a_{n-1}x^{n-1}[/tex] + [tex]...[/tex] + [tex]a_1x[/tex] + a_0, where n is a non-negative integer and [tex]a_n[/tex], [tex]a_{n-1}[/tex], [tex]...[/tex], [tex]a_1, a_0[/tex] are constants.

Since the given function cannot be written in the form of a polynomial function, it is not a polynomial function. Therefore, the correct answer is: Power function.

The given function f(x) = -[tex]14x^(^-^\sqrt3)[/tex]is a power function because it can be written in the form f(x) = , where k = -14 and m = -√3.

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The volume of this cone is 1,271.7 cubic millimeters. What is the radius of this cone?

Answers

The radius of the cone is 7.79 millimeters when the volume of this cone is 1,271.7 cubic millimeters.

The volume of the cone is 1,271.7 cubic millimeters.

Height of cone is 20 millimeters

We have to find the radius of the cone

Volume of cone = πr²h/3

1,271.7 = 3.14×r²×20/3

1,271.7 =20.93r²

Divide both sides by 20.93

1,271.7/20.93 = r²

60.75= r²

r=7.79

Hence, the radius of the cone is 7.79 millimeters when the volume of this cone is 1,271.7 cubic millimeters.

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What would the critical value be for a correlational study consisting of 18 individuals (n = 18). Assume the study is nondirectional with an alpha level of 0.05.Group of answer choicesa. 0.321b. 0.468c. 0.433d. 0.444

Answers

The critical value for a correlational study consisting of 18 individuals (n = 18), assuming a nondirectional study with an alpha level of 0.05, would be 0.444.

To determine the critical value for a non-directional correlational study with 18 individuals (n = 18) and an alpha level of 0.05, you can follow these steps:

1. Determine the degrees of freedom: Subtract 2 from the number of individuals (n - 2). In this case, df = 18 - 2 = 16.

2. Look up the critical value for a two-tailed test with an alpha level of 0.05 and 16 degrees of freedom in a table of Pearson correlation coefficients.

Based on the given answer choices, the critical value for this correlational study with 18 individuals and an alpha level of 0.05 is: 0.444

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7/13=x/5 rounded to the nearest tenth.

Answers

Step-by-step explanation:

x/5 = 7/13      multiply both sides of the equation by to get

x = 5 * 7/13  =  35/ 13     then use calculator = ~  2.7

Answer:

7/13 = x/5 can be solved by cross-multiplication of the terms.

13*x = 5 *7

13x = 35

x = 35/13 = 2.69 = 2.7

Justin found a house for $112,000. He needs a 20% down payment. How much money does Justin need for the down payment?

Answers

Answer: 22400

Step-by-step explanation:

Answer:

Justin needs $22,400 for the down payment on the house.

Step-by-step Explanation:

To find out the amount of money Justin needs for the down payment, we can use the following formula:

Down payment amount = (down payment percentage / 100) x total cost of the house

Given that Justin needs a 20% down payment on a house that costs $112,000, we can substitute the values into the formula:

Down payment amount = (20 / 100) x $112,000

Simplifying the expression within the parentheses, we get:

Down payment amount = 0.20 x $112,000

Multiplying 0.20 by $112,000, we get:

Down payment amount = $22,400

Therefore, Justin needs $22,400 for the down payment on the house.

5. An apartment complex developer is considering building apartments in College Town, but first wants to do a market study. A sample of monthly rent values (S) for studio apartments in College Town was taken. The data collected from the 70-apartment sample resulted in a sample mean of $490.80. (Based on past experience, the developer assumes a known value of σ: $55 for the population standard deviation.) Develop a 95% confidence interval for the mean monthly rent for all studio apartments in this city monthly rent for all studio

Answers

To develop a 95% confidence interval for the mean monthly rent for all studio apartments in College Town, we can use the following formula:

CI = x ± z*(σ/√n)

where:
- CI is the confidence interval
- x is the sample mean ($490.80)
- z* is the z-score for a 95% confidence level (1.96)
- σ is the known population standard deviation ($55)
- n is the sample size (70)

Plugging in the values, we get:

CI = $490.80 ± 1.96*($55/√70)
CI = $490.80 ± $12.15

Therefore, the 95% confidence interval for the mean monthly rent for all studio apartments in College Town is $478.65 to $503.95. We can be 95% confident that the true population mean monthly rent for all studio apartments in College Town falls within this range.
Based on the provided information, we can construct a 95% confidence interval for the mean monthly rent of studio apartments in College Town. Here are the relevant terms and values:

- Sample size (n): 70 apartments
- Sample mean (x): $490.80
- Population standard deviation (σ): $55

To calculate the confidence interval, we will use the formula:

Confidence interval = x ± (z * (σ / √n))

For a 95% confidence interval, the z-value is 1.96. Now, let's plug in the values:

Confidence interval = $490.80 ± (1.96 * ($55 / √70))

Confidence interval = $490.80 ± ($13.61)

So, the 95% confidence interval for the mean monthly rent for all studio apartments in College Town is approximately $477.19 to $504.41. This means that we can be 95% confident that the true mean rent for all studio apartments in this city falls within this range.

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if the observed t value exceeds the critical t value, then the difference between the sample means is most likely ____.

Answers

If the observed t-value exceeds the critical t-value, then the difference between the sample means is most likely statistically significant.

In other words, the difference between the sample means is unlikely to have occurred by chance and is likely due to a real difference in the population means. The direction and magnitude of the difference must be further examined using effect size measures and confidence intervals.

Therefore, the most suitable value to be fit in the blank space of the given incomplete statement is, statistically significant.

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Calculate limx→0 4f (x) 15g(x 1) −5 −12x2 . if the limit is infinite, make sure to determine if it is [infinity] or −[infinity]. if the limit is finite, simplify your final answer.

Answers

The limit is finite and equals 37.

How to calculate the limit?

To calculate the limit, we need to know the functions f(x) and g(x). Without that information, we cannot provide an exact answer to the question.

However, we can provide some general guidance on how to approach such limits.

One method is to use algebraic manipulation to simplify the expression, and then use known limits or other techniques to evaluate the result.

Another method is to use L'Hopital's rule, which involves taking the derivatives of the numerator and denominator of a fraction separately and then evaluating the limit of the resulting quotient.

For example, let's suppose that f(x) approaches 3 as x approaches 0, and that g(x) approaches -2 as x approaches -1. Then, we can rewrite the limit expression as:

lim x→0 4f(x) -15g(x+1) - 5 - [tex]12x^2[/tex]

= lim x→0 4(3) - 15(-2) - 5 - [tex]12x^2[/tex] (substituting the limits of f(x) and g(x))

= 12 + 30 - 5 - 0 (simplifying)

= 37

Therefore, the limit is finite and equals 37.

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3 The coordinates (-2,-3) lie on line r. Which equation could represent line r? ​

Answers

The equation that represents line r is:  4x - 3y = 1

To find the equation of a line, we need either two points or a point and the slope of the line. In this case, we have one point (-2,-3) on the line but not the slope. However, we can still find the equation of the line using the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Since we don't know the slope, let's leave it as m for now:

y - (-3) = m(x - (-2))

Simplifying this equation gives:

y + 3 = m(x + 2)

Now, we need to eliminate the variable m by substituting another point on the line to solve for it. Let's choose the point (1,1) and substitute it into the equation:

1 + 3 = m(1 + 2)

4 = 3m

m = 4/3

Substitute this value of m back into the point-slope form of the equation:

y + 3 = (4/3)(x + 2)

Multiplying both sides by 3 gives:

3y + 9 = 4x + 8

Subtracting 4x from both sides and simplifying:

4x - 3y = 1

Therefore, the equation that represents line r is:  4x - 3y = 1

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I need the answer to no. 5.

Answers

Step-by-step explanation:

to find the area you first need to find the area of the square which is

[tex]14 \times 14 = {196m}^{2} [/tex]

then to find the area of the top triangle its

[tex]14 \times 14 \div 2 = {98m}^{2} [/tex]

then to find the area of the bottom triangle its

[tex](38 - 28) \times 14 -( (38 - 28) \times (14 \div 2)) = {70m}^{2} [/tex]

then add all of them together and its 364 m squared.

PLEAASE HELP ASAP please

Answers

The expression without the absolute value symbol is:

|x - 8| = x - 8, if x > 8|x - 8| = 0, if x = 8|x - 8| = 8 - x, if x < 8What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

|(x - 19) + 11|

This can be written as,

= |x - 19 + 11|

= |x - 8|

Now,

|x - 8| = x - 8, if x > 8

|x - 8| = 0, if x = 8

|x - 8| = 8 - x, if x < 8

Thus,

The expression without the absolute value symbol is:

|x - 8| = x - 8, if x > 8

|x - 8| = 0, if x = 8

|x - 8| = 8 - x, if x < 8

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1. If AP = P D, where P= [−1 4 1 1] and D= [−1 0 0 2], find A5. Their both a 2x2 -1 and 4 are the top ones and both ones at the bottom same for the second one too.
2. Let A= [1 0 1 0 2 0 1 0 1]. If AB + I= A2+B, find B. It is a 3x3 1 01 are the top ones

Answers

The value of B = [0 0 2; 0 3 -1; 2 0 0]. Since AP = PD, we can solve for A by multiplying both sides by [tex]P^{-1}[/tex]:

A =[tex]P^{-1}[/tex] PD = D = [-1 0; 0 2]

How to find A5?

To find [tex]A^{5}[/tex] we can simply raise A to the fifth power:

[tex]A^{5}[/tex] =[tex]D^{5}[/tex] = [[tex]-1^{5}[/tex] 0; 0 [tex]2^{5}[/tex]] = [-1 0; 0 32]

We can simplify the given equation as follows:

AB + I = [tex]A^{2}[/tex] + B

AB - B = [tex]A^{2}[/tex] - I

B(A - I) = [tex]A^{2}[/tex] - I

B = ([tex]A^{2}[/tex]- I)[tex](A - I)^{-1}[/tex]

To find B, we need to first calculate [tex]A^{2}[/tex] and A - I:

[tex]A^{2}[/tex] = [1 0 1; 0 4 0; 1 0 1]

A - I = [0 0 1; 0 1 0; 1 0 0]

Next, we need to calculate the inverse of A - I:

[tex](A - I)^{-1}[/tex] = [-1 0 1; 0 1 0; 1 0 -1]

Finally, we can substitute these values into the expression for B:

B = ([tex]A^{2}[/tex] - I)([tex](A - I)^{-1}[/tex]

B = ([1 0 1; 0 4 -1; 1 0 1] - [1 0 0; 0 1 0; 0 0 1])([-1 0 1; 0 1 0; 1 0 -1])

B = [0 0 2; 0 3 -1; 2 0 0]

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Write down, without any deduction, the roots of: ax² + bx + c = 0​

Answers

x = (-b + sqrt(b² - 4ac)) / 2a and x = (-b - sqrt(b² - 4ac)) / 2a

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.

The quadratic formula gives the roots of a quadratic equation in the form of ax² + bx + c = 0. The formula is:

x = (-b ± sqrt(b² - 4ac)) / 2a

So the roots of ax² + bx + c = 0 are:

x = (-b + sqrt(b² - 4ac)) / 2a

and

x = (-b - sqrt(b² - 4ac)) / 2a

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if the population variance of the raw scores equals 169 and the sample size is 100, what is the standard error of the mean? group of answer choices 15.36 1.18 16.90 1.30

Answers

The standard error of the mean (SEM) can be calculated using the formula:
SEM = √(population variance) / √(sample size)
Given that the population variance is 169 and the sample size is 100, the SEM can be calculated as:
SEM = √(169) / √(100)
SEM = 13 / 10
SEM = 1.3
So, the standard error of the mean is 1.3.

To find the standard error of the mean, we use the formula:
Standard error of the mean = population standard deviation / square root of sample size

Since we're given the population variance (169), we can first find the population standard deviation by taking the square root of the variance:

Population standard deviation = sqrt(169) = 13

Now we can plug in this value along with the sample size (100) to find the standard error of the mean:
Standard error of the mean = 13 / sqrt(100) = 1.30

Therefore, the answer is 1.30.

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Use the data given in the table below to compute the probability that a randomly chosen voter from the survey will satisfy the following. Round to the nearest hundredth.
The voter is under 50 years old.

Answers

The probability that a randomly chosen voter from the survey is under 50 years old is approximately 0.75 or 75%.

To compute the probability that a randomly chosen voter from the survey is under 50 years old, we need to first calculate the total number of voters who are under 50 years old. We can do this by adding the number of voters in the 18-28, 29-38, and 39-49 age groups.

Total number of voters under 50 years old = 847 + 804 + 773 = 2424

Next, we need to calculate the total number of voters in the survey, which is given as 3228.

Using these values, we can calculate the probability that a randomly chosen voter from the survey is under 50 years old as:

Probability = Number of voters under 50 years old / Total number of voters in the survey

Probability = 2424 / 3228

Probability ≈ 0.75 or 75%.

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the time it takes to edit a successful resume is normally distributed with a population standard deviation of 8 minutes and an unknown population mean. a random sample of 25 resume editors is taken and results in a sample mean of 58 minutes. identify the parameters needed to calculate a confidence interval at the 99% confidence level. then use a calculator to find the confidence interval. round the final answer to two decimal places. provide your answer below: $\overline{x}\

Answers

The parameters needed to calculate a confidence interval at the 99% confidence level are the sample mean ($\overline{x}$), the population standard deviation ($\sigma$), the sample size ($n$), and the confidence level ($1-\alpha$).

In this case, we are given that $\sigma = 8$ minutes, $n=25$, and $1-\alpha = 0.99$. We also know that the sample mean is $\overline{x} = 58$ minutes.

To find the confidence interval, we first need to find the critical value for a 99% confidence level. Using a t-distribution with $n-1=24$ degrees of freedom, we can find this value using a t-table or a calculator. For a 99% confidence level, the critical value is approximately 2.797.

Next, we can use the formula for a confidence interval for a population mean:

$\overline{x} \pm t_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Plugging in our values, we get:

$58 \pm 2.797\cdot \frac{8}{\sqrt{25}}$

Simplifying this expression, we get:

$58 \pm 5.58$

So the confidence interval is:

$(52.42, 63.58)$

Rounded to two decimal places, the confidence interval is:

$(52.42, 63.58)$
To calculate the 99% confidence interval for the time it takes to edit a successful resume, we'll need the following parameters:

1. Sample mean (x) = 58 minutes
2. Population standard deviation (σ) = 8 minutes
3. Sample size (n) = 25 resume editors
4. Confidence level (CL) = 99%

Now, we need to find the critical value (z*) for a 99% confidence level. Using a standard normal (z) table or calculator, we find that z* ≈ 2.576.

Next, we'll use the formula for the confidence interval:

CI =x ± z*(σ/√n)

CI = 58 ± 2.576*(8/√25)

CI = 58 ± 4.12

So, the 99% confidence interval is (53.88, 62.12). This means we can be 99% confident that the true population mean for the time it takes to edit a successful resume lies between 53.88 and 62.12 minutes.

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Help me with this please

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Answer: sorry i can't read the question

Step-by-step explanation:

Find the area of a semi-circle with diameter 34. Leave your answer in terms of pi.

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since we know the diameter is 34, that means its radius is half that, or 17.

[tex]\textit{area of a full circle}\\\\ A=\pi r^2 ~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies A=\pi (17)^2\implies \stackrel{ \textit{half that for a semicircle} }{A=\cfrac{\pi (17)^2}{2}\implies A=144.5\pi}[/tex]

in this problem, and are positive integers. when is written in base , its last digit is . when is written in base , its last two digits are . when is written in base , what are its last two digits? assume is positive.

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This shows that has a remainder of 217 when divided by 343. Therefore, its last two digits in base 343 are 7 and 217.

To approach this problem, we need to use some basic rules of number systems.

When a number is written in base 10 (decimal), its last digit is determined by its remainder when divided by 10. For example, if a number ends with a 7, we know it leaves a remainder of 7 when divided by 10.

Similarly, when a number is written in base n, its last digit is determined by its remainder when divided by n. For example, if a number in base 5 ends with a 3, we know it leaves a remainder of 3 when divided by 5.

Now let's apply this to the given problem. We know that leaves a remainder of 1 when divided by 7 (since its last digit is 1 in base 7). This means that can be expressed as 7k + 1 for some positive integer k.

Similarly, we know that leaves a remainder of 36 when divided by 49 (since its last two digits are 36 in base 49). This means that can be expressed as 49m + 36 for some positive integer m.

To find the last two digits of in base 343, we need to find its remainder when divided by 343. We can start by expressing as a sum of multiples of 7 and 49:

= (7k + 1) + 6(49m + 36)

= 7k + 294m + 217

Now we need to express this sum as a multiple of 343 plus a remainder. We can do this by dividing 294m + 217 by 343:

294m + 217 = 343m + (294m + 217 - 343m)

= 343m + 7m + 217

= 343(m + 1) + 7m - 126

So we have:

= 7k + 343(m + 1) + 7m - 126

= 343(m + 1) + 7(k + m) - 126

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(2.1) T/F The solution of a system of linear equations is the point (x,y) where the lines intersect.

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True. The solution of a system of linear equations in two variables is the point (x, y) where the two lines intersect. This point satisfies both equations in the system simultaneously.

A system of linear equations in two variables is a set of two equations that can be written in the form:

a₁x + b₁y = c₁
a₂x + b₂y = c₂

where x and y are the variables and a₁, b₁, c₁, a₂, b₂, and c₂ are constants. The goal is to find the values of x and y that satisfy both equations in the system.

Geometrically, each equation in the system represents a line in the two-dimensional plane. The solution of the system is the point (x, y) where the two lines intersect. This point satisfies both equations simultaneously and is the only point that does so.

To find the solution of a system of linear equations, we can use various methods such as substitution, elimination, or matrices. These methods involve manipulating the equations in the system to eliminate one of the variables and solve for the other. Once we have the value of one variable, we can substitute it back into one of the equations to solve for the other variable. The solution of the system is then the ordered pair (x, y) that satisfies both equations.

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consider a medical test that could be used to diagnose a form of cancer. the form of cancer is rare and effects a population at a rate of 0.001. the test has a false positive rate of 0.005. for individuals with this form of cancer the test has a perfect detection rate of 1. (a) out of a population of 1 million, how many people are expected to have this form of cancer? (b) out of a population of 1 million, how many people would test positive for this form of cancer? (c) if a particular person tested positive, what is the probability that this person actually has this form of cancer?

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(a) Out of a population of 1 million, we can expect 1000 people to have this form of cancer, as the rate of the disease is 0.001 (0.1% of the population) multiplied by 1 million.
(b) Out of a population of 1 million, 5000 people would test positive for this form of cancer, as the false positive rate is 0.005 (0.5% of the population) multiplied by 1 million.
(c) The probability that a person who tested positive actually has this form of cancer is 16.69%.


(a) Out of a population of 1 million, how many people are expected to have this form of cancer?

To calculate this, we'll multiply the population by the rate of cancer occurrence:
1,000,000 (population) × 0.001 (rate) = 1,000 people with cancer.

(b) Out of a population of 1 million, how many people would test positive for this form of cancer?

First, we need to find out how many false positives there would be:
1,000,000 (population) × 0.005 (false positive rate) = 5,000 false positives.

Next, since the test has a perfect detection rate (1) for individuals with cancer, all 1,000 people with cancer would test positive.

Total positive tests = 1,000 (true positives) + 5,000 (false positives) = 6,000 positive tests.

(c) Bayes' theorem. The probability of having the disease given a positive test result can be calculated as follows:

P(A|B) = P(B|A) * P(A) / P(B)

where A is the event of having the disease, B is the event of testing positive, P(A) is the prior probability of having the disease (0.001), P(B|A) is the probability of testing positive given that you have the disease (1), and P(B) is the probability of testing positive, which can be calculated as the sum of the true positive and false positive rates:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
P(B) = 1 * 0.001 + 0.005 * 0.999
P(B) = 0.005995

Now we can plug in the values and solve:

P(A|B) = 1 * 0.001 / 0.005995
P(A|B) = 0.1669

So the probability that a person who tested positive actually has this form of cancer is 16.69%.

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What is 0.8322 ÷ 0.57

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When the value 0.8322 is divided by 0.57, then we get the result that is equal to 1.46.

To divide decimals, you should align the decimal points in the dividend and divisor.

In this case, the dividend is 0.8322 and the divisor is 0.57. To align the decimal points, you can add a zero to the dividend and move the decimal point one place to the right in the divisor, as follows:

0.8322 ÷ 0.57

0.8322 ÷ 0.5700

Now, you can perform the division as usual, ignoring the decimal point for the moment.

   

Next, you should insert the decimal point in the quotient above the line and add a zero at the end of the dividend to continue the division:

0.8322 ÷ 0.57 = 1.4600

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A student bought a pair of sunglasses in the USA. He paid $35.50 In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42 In which country were the sunglasses cheaper, and by how much? Show all your working.

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The sunglasses cost $38.4178 in England

The sunglasses cost $2.9178 less in the USA

To compare the prices of the sunglasses in the two countries

We must convert the costs to a common currency in order to compare the costs of the eyewear in the two nations.

Let's first translate the cost from pounds to dollars:

£26.99 * $1.42/£1 = $38.4178

Therefore, the sunglasses cost $38.4178 in England.

We may now evaluate the costs:

$35.50 is the cost in the USA.

After conversion, the cost in England is $38.4178.

The sunglasses are cheaper in the USA by:

$38.4178 - $35.50 = $2.9178

Therefore, the sunglasses cost $2.9178 less in the USA.

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Which of the following is not true about a square? (2 points) a It has no right angles. b All its sides are of equal lengths. c It has opposite parallel sides. d It can be classified as a rectangle.

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The statement that is not true about a square is this: a It has no right angles.

What is untrue about squares?

The untrue statement about squares is that they have no right angles. This statement is false because a square actually has 4 right angles. Each of these angles measures 90 degrees.

The four corners of a square contain these angles. Recall that the angle on a straight line equals 180 degrees and we can obtain this by merging two angles of a square. Finally, the wrong statement of all listed is option A.

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Answer:

It has no right angles.

Step-by-step explanation:

What is untrue about squares

The untrue statement about squares is that they have no right angles. This statement is false because a square actually has 4 right angles. Each of these angles measures 90 degrees.

14. sat test when making a random guess for an answer to a multiple choice question on an sat test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.

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That's correct. When making a random guess on a multiple-choice question on the SAT test, with five answer choices (a, b, c, d, e), there is a 1 in 5 or 20% chance of being correct.

What is a proccedure of making a random guess multiple choice question on an sat test?

The SAT (Scholastic Assessment Test) is a standardized test used for college admissions in the United States.

The test measures a student's readiness for college-level work and is generally taken by high school juniors and seniors.

The SAT has several sections, including reading, writing and language, math (with calculator), math (without calculator), and an optional essay. Each section of the SAT includes multiple-choice questions, with four or five answer choices for each question.

When making a random guess for an answer to a multiple-choice question on the SAT, you simply select one of the answer choices without any prior knowledge or reasoning about the question.

To make a random guess, you can choose an answer choice that feels lucky, use a systematic method like always choosing "C" or "B," or close your eyes and point to an answer choice.

However, keep in mind that random guessing is not likely to result in a high score, and may even decrease your score due to penalties for incorrect answers.

Therefore, it is generally recommended to only guess on a question when you can eliminate at least one or two answer choices as incorrect.

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