What is the predicted end-of-year value of a portfolio that begins the year with $200, in stocks and $100 in bonds?

Answer:

4/3

Step-by-step explanation:

GH =√90²-72²=

√8100-5184=

√2916= 54

so, tan (H) = 72/54 = 4/3

⁴/3 is a required answer.

Answer:

Solution given:

FG=72

FH=90

By using Pythagoras law

GH=[tex]\sqrt{90²-72²}=54[/tex]

Step-by-step explanation:

we have

Tan H=[tex] \frac{opposite}{adjacent}[/tex]

[tex]TanH=\frac{GF}{GH}=\frac{72}{54}=\frac{4}{3}[/tex]

Answer:

2, probably

Step-by-step explanation:

Answer:

11......................

Volume = (1/3) . π . r² . h

475.17 = (1/3) . π . r² . 15

475.17 = 5πr²

r² = 475.17/5π

r² = 30.25

r = √30.25 = 5.5

Diameter = 2r = 2 × 5.5 = 11 yd

[tex]_____________________________________[/tex]

[tex]\tt \sqrt{9} \\ = \tt \sqrt{ {3}^{2} } \\ = \large\boxed{\tt{\green{3}}}[/tex]

[tex]_____________________________________[/tex]

Answer:

Step-by-step explanation:

The common ratio of the terms is 0.6 (180/300=6/10;108/180=6/10). This is a geometric sequence .

nth term=500(0.6)^n-1

Answer:

1000

Step-by-step explanation:

1,080,000,000/1,047,000

Answer:5

Step-by-step explanation:

Answer:

16.8 cups

Step-by-step explanation:

3.5 percent of 30 gallons

Answer:

Just two corrections!  See attached image.

Step-by-step explanation:

The product of 8 and b taken from 10 means begin with 10 and subtract 8b from it.

8 times the difference of 10 and b means find 10 - b first, then multiply by 8.

Answer:

2^5/2-8 may equivalent

Answer:

8

Step-by-step explanation:

send the -5 to where the +3 is then you can now add the value together.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the number line is not given. The general explanation is as follows;

First, record the time she hung up (say, time = x)

To rewind 15 minutes back means, x - 15

So, point on the number line will be x - 15

Take for instance

[tex]x = 45[/tex]

The point on the number line will be:

[tex]x - 15 = 45 - 15[/tex]

[tex]x - 15 = 30[/tex]

See attachment for illustration

Answer:

x = 12, x = 7

Step-by-step explanation:

The 2 legs of the triangle are congruent, both 2x + 7, then

2x + 7 + 2x + 7 + x + 11 = 85 ← equation for perimeter

5x + 25 = 85 ( subtract 25 from both sides )

5x = 60 ( divide both sides by 5 )

x = 12

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

Opposite sides are congruent, then

2(2x) + 2(5x + 3) = 104 ← distribute and simplify both sides

4x + 10x + 6 = 104

14x + 6 = 104 ( subtract 6 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

Answer:

x=12 x=7 yup thank me later

Answer:

the sqare root of 19.9 is 4.46094160464

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A:

Given:

Pooled sample size: [tex]n=15[/tex]

Sample size (with academic scholarships): [tex]n_1=6[/tex]

Sample size (no academic scholarships): [tex]n_2=9[/tex]

Population standard deviations: Unknown

Sample mean (with academic scholarships): [tex]\bar{x}=\frac{25+24+23+21+22+20}{6}=22.5[/tex]

Sample mean (no academic scholarship):[tex]\bar{x}=\frac{23+25+30+32+29+26+27+29+27}{9}=27.\bar{5}[/tex]

Sample standard deviation (with academic scholarships): [tex]s_1=1.7078[/tex]

Sample standard deviation (no academic scholarships): [tex]s_2=2.5868[/tex]

Degrees of freedom: [tex]df=n-2=15-2=13[/tex]

Significance level: [tex]\alpha =0.02[/tex]

Decide which test is most appropriate to conduct:

Therefore, we will conduct a 2-sample t-test assuming our conditions are satisfied.

List null and alternate hypotheses:

[tex]H_o:\mu_1=\mu_2[/tex] -> There's no difference in ACT scores between students with and without an academic scholarship

[tex]H_a:\mu}_1\neq\mu_2[/tex] -> There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)

Determine the value of the test statistic:

We will use the formula [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }[/tex] to compute the test statistic [tex]t[/tex]. Therefore, the test statistic is [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }=\frac{27.\bar{5}-22.5}{\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9} } }=4.5592[/tex]

Calculate the p-value:

Because the test is two-sided, [tex]p=2tcdf(4.5592,1e99,13)=2(0.0003)=0.0006[/tex]

Interpret p-value and conclude test:

Given our significance level is [tex]\alpha =0.02[/tex], since [tex]p<\alpha[/tex], we reject the null hypothesis and conclude that there is significant evidence that suggests that there is a difference in ACT scores between students with and without an academic scholarship (it's more likely that the alternate hypothesis is true)

Part B:

The formula for a confidence interval for the difference in 2 population means is [tex]CI=(\bar{x}_1-\bar{x}_2)\pm t^*\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}[/tex] where [tex]\bar{x}_1-\bar{x}_2[/tex] is the difference of the 2 sample means and [tex]t^*[/tex] is the critical score for the desired confidence level.

The critical score for our 98% confidence interval would be [tex]t^*=invT(0.99,13)=2.6503[/tex]

Therefore, our 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is [tex]CI=(27.\bar{5}-22)\pm 2.6503\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9}}}=[2.6167,8.4944][/tex]

This means that we are 98% confident that the true difference in the ACT scores between students with and without an academic scholarship is contained within the interval [tex][2.6167,8.4944][/tex]

The evaluation of sub-parts results in:

Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02

Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]

If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.

Let we have:

Then, the value of t-test statistic is obtained as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]

If the level of significance is [tex]\alpha[/tex], then as we have:

the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex], the critical value of t is found to be [tex]t_{\alpha/2}[/tex], then if we get:

[tex]|t| < t_{\alpha/2}[/tex]null hypothesis

and if we get [tex]|t| > t_{\alpha/2}[/tex] null hypothesis, and thus, accept the alternate hypothesis.

For this case, we want to test if there is

Thus, we form the hypotheses as:

Null hypothesis: There's no difference in ACT scores between students with and without an academic scholarship

or: [tex]H_0: \mu_1 = \mu_2[/tex]

Alternative hypothesis:  There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)

or [tex]H_1: \mu_1 \neq \mu_2[/tex]

where we have:

For this case, we evaluate the mean and standard deviation as:

Sample size = [tex]n_1 = 6[/tex]

Mean = sum of all observation/ number of observations = 135/6 =22.5

Thus, standard deviation = [tex]s_1 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_1})^2}} = \sqrt{\dfrac{17.5}{6}} \approx1.71[/tex]

Sample size = [tex]n_2 = 9[/tex]

Mean = sum of all observation/ number of observations = 248/9 ≈27.56

Thus, standard deviation = [tex]s_2 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_2})^2}} \approx \sqrt{\dfrac{60.22}{9}} \approx 2.59[/tex]

The t-test statistic is evaluated as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}} = \dfrac{22.5 -27.56}{\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}}} \approx -4.56[/tex]

Degree of freedom = [tex]n_1 + n_2 - 2 = 6 + 9 - 2 = 13[/tex]

Level of significance = 0.02 = 2%

The critical value of t is found to be [tex]t_{0.02/2} =2.65[/tex]

Thus, we get: [tex]|t| \approx 4.56 > 2.65 =t_{\alpha/2}[/tex]

Thus, we may reject the null hypothesis.

That means, there is enough evidence of a difference in ACT scores between students with and without an academic scholarship at 0.02 level of significance.

Now, the 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is calculated as:

[tex]CI = (\overline{x}_1 - \overline{x}_2) \pm t_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}\\\\CI = -5.06 \pm 2.65(\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}})\\\\CI \approx -5.06 \pm 2.65 \times 1.11\\CI \approx -5.06 \pm 2.94\\CI \approx [-5.06 - 2.94, -5.06 + 2.94] = [-7.00, -2.14][/tex]

Thus, the evaluation of sub-parts results in:

Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02

Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]

Learn more about two sample t-test here:

https://brainly.com/question/16285453

Answer:

x = 80.96

Step-by-step explanation:

9x * 3x +1 = 2187

27x +1 = 2187

27x = 2187-1

27x = 2186

x = 2186/27 = 80.96(2dp)

Answer: [tex]78.55\ m^2[/tex]

Step-by-step explanation:

Given

The goat is tied by a rope to one corner of a rectangular field with length of rope 10 m.

Zoe can graze in an area equal to quadrant of circle with radius 10 m

Area of grazing is

[tex]\Rightarrow \dfrac{1}{4}\times \pi r^2\\\\\Rightarrow \dfrac{\pi r^2}{4}\\\\\Rightarrow \dfrac{\pi \times 10^2}{4}=78.55\ m^2[/tex]

Answer:

72 ft^2

Step-by-step explanation:

A = bh

A = 12 ft * 6 ft

A = 72 ft^2

Answer:

72

Step-by-step explanation:

you have to do base times height

Answer: The equation for the line is “y = 6x - 4”

Step-by-step explanation: To find this answer we will put it in slope-intercept form which is y = mx +b. To first find m which is the slope you subtract the the second y by the first y over the second x by the first x. It looks like this y2 - y1/ x2 - x1. After we find the slope which is 6, to find the y-intercept which is b we just plug a point we used to find the slope into the equation we have. It looks like this y = 6x + b —> 2 = 6(1) + b... I used (1,2). Then you solve for b by multiplying 1 by 6 and then subtracting 6 to both sides to get b by itself. So it goes from 2 = 6(1) + b into -4 = b. Then you just put -4 into b and you get the answer y = 6x - 4.

Have a nice day!

Answer:

m equals 4

Step-by-step explanation:

m represents the slope of the line.

The line equation is y = mx + b, which means that m = 4 and b = 0

Answer:

D

Step-by-step explanation:

"x" represents the hours.

so 8 is the fee for the hours, rather than insurance.

6 is the insurance fee.

if the cost per hours is doubled, it'll now be 16.

the answer is "6 + 16x" (D)

Answer:

Kindly check explanation

Step-by-step explanation:

Learning could be explained as a process of acquiring knowledge about a certain subject, trade or other aspects of life. In terms of learning about certain school subjects, a student needs to discover him or herself in other to make acquiring knowledge easy and less tedious for him or her. Now, there are designated tools more than evwr which could aid learning. A very important recommendation which could aid acquiring matematicka knowledge is the use of models to gain an insight to the fundamentals of a mathematical problem and thus seeing how it works. After this one can then break down the mathematical procedure embedded or used it aid the model manually in other to grasp the full concept of the principle.

Answer:

Step-by-step explanation:

This is a right triangle, and side c, our unknown, is the hypotenuse, the longest side in a right triangle. Using Pythagorean's Theorem, we have

[tex]17^2+19^2=c^2[/tex] which simplifies to

[tex]289+361=c^2[/tex] and

[tex]650=c^2[/tex] and

c = 25.5"

Answer:

C) 4,0

Step-by-step explanation:

Basically to find zeros you set up the expression equal to zero.

First pair is (0,0) they derived this by setting the leftmost x to 0 so x=0, this meant that when x was plugged back into the equation y = x(x-4) the y value we got out was 0 because y = 0 (0-4) = 0, thus the pair (0,0).

For second pair, we set up x-4= 0, solve this to get x = 4 (add 4 to both sides). Now plug this back into full equation y= 4 (4-4)= 0, you get y=0 and your ordered pair is (4,0) which is the second pair of zero.

Zero are x-intercept where y is zero which is the main reason why we setup x=0 or x-4=0 to start with.

Hi there!  

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I believe your answer is:  

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Here’s why:  

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See graph attached.

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

(3, - 1)

Step-by-step explanation:

We want to solve the system of equations:

2*x - y = 7

x - 2*y = 5

graphically.

To do it, we need to graph both lines, it will be easier if we rewrite both lines in a more general way, like in the slope-intercept form:

y = -7 + 2*x

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

Now, a solution of the system is a point (x, y) such that the point is a solution to both equations, then, when we graph the lines, as that point belongs to both equations, we should see that both lines pass through that point.

Then to find the solution of the system, we just need to graph the lines and find the point where the lines intersect.

Below, you can see a graph of the lines, and is easy to see that the lines do intersect at the point (3, - 1)