What is the quotient of 1 over (1 plus the square root of 3)?

Answers

Answer 1
Answer: You can rationalize the denominator by multiplying by 1 in the form of the conjugate of the denominator divided by itself.

(1)/(1+√(3))=(1)/(1+√(3))\cdot (1-√(3))/(1-√(3))\n\n=(1-√(3))/(1^(2)-(√(3))^(2))=(1-√(3))/(1-3)\n\n=(√(3)-1)/(2)

This eqvaluates to approximately 0.3660254037844386.

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In a study of government financial aid for college​ students, it becomes necessary to estimate the percentage of​ full-time college students who earn a​ bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.02 margin of error and use a confidence level of 99​%. Complete parts​ (a) through​ (c) below.a. Assume that nothing is known about the percentage to be estimated.n = ________b. Assume prior studies have shown that about 55% of​ full-time students earn​ bachelor's degrees in four years or less.n = _______c. Does the added knowledge in part​ (b) have much of an effect on the sample​ size?

Answers

Answer:

(a) The sample size required is 2401.

(b) The sample size required is 2377.

(c) Yes, on increasing the proportion value the sample size decreased.

Step-by-step explanation:

The confidence interval for population proportion p is:

CI=\hat p\pm z_(\alpha/2)\sqrt{(\hatp(1-\hat p))/(n)}

The margin of error in this interval is:

MOE=z_(\alpha/2)\sqrt{(\hatp(1-\hat p))/(n)}

The information provided is:

MOE = 0.02

z_(\alpha/2)=z_(0.05/2)=z_(0.025)=1.96

(a)

Assume that the proportion value is 0.50.

Compute the value of n as follows:

MOE=z_(\alpha/2)\sqrt{(\hat p(1-\hat p))/(n)}\n0.02=1.96* \sqrt{(0.50(1-0.50))/(n)}\nn=(1.96^(2)*0.50(1-0.50))/(0.02^(2))\n=2401

Thus, the sample size required is 2401.

(b)

Given that the proportion value is 0.55.

Compute the value of n as follows:

MOE=z_(\alpha/2)\sqrt{(\hat p(1-\hat p))/(n)}\n0.02=1.96* \sqrt{(0.55(1-0.55))/(n)}\nn=(1.96^(2)*0.55(1-0.55))/(0.02^(2))\n=2376.99\n\approx2377

Thus, the sample size required is 2377.

(c)

On increasing the proportion value the sample size decreased.

PLEASE HELP !!!!! 1) Find the equation of the trend line (line of best fit). SHOW WORK

2) Predict the number of tips that would be collected if 100 costumers were served at the restaurant on a given day. Explain your reasoning.

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(I don't know how to attach more than 1 picture by the way )​​

Answers

Answer:

1) y = 1.8741176487x + 3.655964863

2) About $191 using the equation, about $180 or more using the data you are given.

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Which graph represents the compound inequality

Answers

Answer: C

Step-by-step explanation:

When looking at compound inequalities, the inequalities are very important. You can see that on the graphs, there are some points that have a white open circle and others have blue, closed circle. The 2 different circles tells you the inequality itself. If you see ≤ or ≥, it is a closed circle. This is a closed circle because it is less than/greater than or equal to. That means it is also equal to the point, therefore it is a closed circle. If you see < or >, it is an open circle. That means it is not closed because it is greater than. It is not equal to on that specific point.

Now that we have covered the basics, we can start to eliminate. our first condition is n<-2. Above, we have established that < is an open circle. We can eliminate A and B because the points on -2 are both closed circles.

That leaves us with C and D. Since C and D both follow the points, let's look carefully at what the inequality tells us. n<-2 means n is less than -2. This means the arros should be pointing in the left side. As you go more towards the negative, the smaller the number becomes.

We can eliminate D because at -2, the numbers are going towards the right, not the left.

Therefore, our answer is C.

Help asap. yes i will give brainliest

Answers

Answer:

  1. A = 1.5
  2. B = -1/3
  3. C = -4/3

Step-by-step explanation:

For A:

  1. A is smack in the middle of 1 and 2, so it it 1 1/2 or 1.5 (same thing)

For B:

  1. Each tick mark between the numbers represents 1/3
  2. B is on the first tick mark between 0 and -1, so therefore it is -1/3

For C:

  1. C is on the first tick mark between -1 and -2
  2. That means C is -1 1/3
  3. -1 1/3 = -4/3

I hope this helps!

Answer:

A ----> +1.5

B------> -0.33

C-------> -0.1322

Step-by-step explanation:

A\ is\ +1.5\ as\ it\ is\ 1.5\ units\ upwards(positively)\ from\ 0.\nB\ is\ -(1)/(3)\ as\ it\ equates\ to\ -0.33\ which\ is\ between\ 0\ and\ -1.\nC\ is\ -(4)/(3)\ as\ it\ equates\ to\ -1.322\ which\ is\ between\ -1\ and\ -2.\n

An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?

Answers

The length of the line on the blueprint of the wall will be 18 inches.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

An architect uses a scale of 3/4 inches to represent 1 foot on a blueprint for a building.

Then the scale factor of the blueprint will be

Scale factor = 3/4 inches per foot

If the east wall of the building is 24 feet long.

Then the length of the line on the blueprint of the wall will be

Length = 24 feet x scale factor

Length = 24 x (3/4)

Length = 6 x 3

Length = 18 inches

Thus, the length of the line on the blueprint of the wall will be 18 inches.

More about the dilation link is given below.

brainly.com/question/2856466

#SPJ2

Answer:

16 in.

Step-by-step explanation:

We have the ratio

How about let's make this easier.  Easier is better, right?  Let's get rid of the fraction 2/3.  We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

Now we need to know how many inches there would be if the number of feet is 24:

Cross multiply to get

3x = 48 so

x = 16 in.

A.3(f) The line graphed on the grid represents the first of two equations in a system of linear equations.20
-16
12
-8
-20 -16 -12
-
-4
48
12
16 2024
-8
-12
16
If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?

Answers

I don’t any idea for this