Given the cosine equation y = 2cos(4x) - 1, What is the midline?

Answer:

8.3

Step-by-step explanation:

Use the pythagorean theorem: a2 + b2 = c2 a2 would be 24.1 and c2 would be 25.5. square them then subtract a2 from b2. then find the square root of your answer which is 8.3

Answer:

Family a got 120kg, b got 240 kg and c got 120 kg

Step-by-step explanation:

Given that 480kg of rice is shared by families a, b, c. let these alphabets represent the amount received by each family.

a + b + c = 480

Given that B receives twice as much as a, c receives half of b then,

b = 2a and

c = 1/2 b = b/2

from b = 2a,

a = b/2

substituting into the first equation

b/2 + b + b/2 = 480

b + b = 480

2b = 480

b = 480/2

= 240 kg

a = c = b/2

hence a = c = 240/2 = 120kg

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:

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Answer:

30 sq cm

Step-by-step explanation:

The area of a parallelogram is the base times the height. We can see that the base is 10 cm, and 3 cm would be the height because it is perpendicular to the base. We get the equation:

Area = 10 cm x 3 cm

Area = 30 sq cm

Answer:

p=3+8=11

Step-by-step explanation:

Answer:

p = 11

Step-by-step explanation:

add 8 to both sides of the equation, so p = 3 + 8

p = 11

Answer:

Put x's on the numbers on the line that are above the line

Step-by-step explanation:

I BELIVE IN YOU

Answer:

3

Step-by-step explanation:

11g - 9k + 3

Let g = 9 and k =11

11 * 9 - 9*11 +3

Multiply

99 - 99 +3

Add

3

Answer:

3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

11g - 9k + 3

g = 9

k = 11

Step 2: Evaluate

Answer:

XZ = 26.7

ZY = 11.7

Area =  140.4 sq inches

Step-by-step explanation:

m∠Z = 180-(26+90) = 64°

to get XZ you can use the law of sines:

sin 90°/XZ = sin 64°/24

1/XZ = sin(64°)

cross-multiply to get:

XZ·sin(64°) = 24

XZ = 24/sin(64°)

XZ = 26.7

to get ZY you can use the law of sines again:

sin 64°/24 = sin 26°/ZY

cross-multiply to get:

ZY·sin(64°) = 24·sin(26°)

ZY = 24·sin(26°) ÷ sin(64°)

ZY = 11.7

Area = 1/2(11.7)(24)

= 12(11.7)

= 140.4 sq inches

Answer:

a pi = 3.14

Step-by-step explanation:

The symbol which compares the two angles is "< ".

What is an angle?

Angles around a point define the sum of angles that can be arranged together so that they construct a full arch. Angles around a point add to 360 °.

π/3 =180/3 = 60 degree

π/3 > 45 degree

45 degree <  π/3

Therefore, the correct answer is option A. <.

To learn more about angles

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Answer:

12.86 sq ft

Step-by-step explanation:

Find area of square and subtract out area of semi-circle; the diameter of the semi-circle equals the side of the square, which is 4 so radius is 2

A(square) = 4 x 4 = 16

A(semi-circle) = πr²/2

= 4π/2 or 2π

Area of Shaded Region = 16-3.14 which is 12.86

Since their were no numbers to the questions i had to write it by the problem

Circle with 9 feet question

C=2(pi)r or C=(pi)d

Circular table question

A=(pi)r^2

Interest question

I=Prt

Volume of a rectangular prism

V=Bh

Triangular pyramid

V=1/3Bh

Answer:

78,125

Step-by-step explanation:

5 × 5 × 5 × 5 × 5 × 5 × 5 = 78125

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Have a good day :)

Answer:

Step-by-step explanation:

143=5x+13(being corresponding angles)

143-13=5x

130/5=x

26=x

=======================================================

Explanation:

The angles shown are corresponding angles. Notice how they are in the northeast corner of their respective four-corner configuration.

If m is parallel to n, then the corresponding angles are congruent, and we can say...

5x+13 = 143

5x = 143-13 .... subtract 13 from both sides

5x = 130

x = 130/5 .... divide both sides by 5

x = 26

So taking this logic in reverse: if x = 26, then that leads to 5x+13 equal to 143, making the corresponding angles congruent. Therefore, it would lead to lines m and n being parallel.

Answer:

X = -2

Step-by-step explanation:

Hope this helps

Answer:

I believe it is C

It's the only one that makes sense

Answer:

[tex]y = {3x}^{2} - 2x + 3 \\ y = ( \frac{1}{3} + i) {}^{2} [/tex]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $7,000

Interest rate (i)= 2.5%

To calculate the future value after x years, we need to use the following formula:

FV= PV*(1 + i)^x

Now, for 9 years:

x= 9

FV= 7,000*(1.025^9)

FV=$8,742.04

Answer:

radius

Step-by-step explanation:

Answer:

Radius

Step-by-step explanation:

Center of the circle to a point on a circle would be the radius, seeing how as diameter is one edge of the circle to the other edge,of the circle, crossing the middle of the circle

Answer:

20(pi)

Step-by-step explanation:

• equation for the circumference of a circle= 2(pi)r

• You are given the diameter ( 20ft) but you need the radius (r) for the equation.

• divide 20 by 2 to get the radius since it is half of the diameter.

• 20/2=10 so c= 2(pi)(10)

• 2(10)=20

• plug in pi and your final answer is 20(pi)

Answer:

The mean of the data is of 3.7143%.

Step-by-step explanation:

Mean of the data:

Sum of all returns divided by the number of returns.

Returns:

6% 5% -2% 10% 3% 8% -4%

7 returns.

Sum: 6 + 5 - 2 + 10 + 3 + 8 - 4 = 26%

Mean: 26%/7 = 3.7143%

The mean of the data is of 3.7143%.

The third one is the correct graph for the equation

hope it helps !!

The equation  [tex]\left(x-3\right)^{2}+\left(y-1\right)^{2}=3^{2}[/tex]  is the equation of a circle. Graph B shows the given equation.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

The standard equation of the circle is;

[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^{2}[/tex]

Where,

(h,k) are the coordinates of points on the x and y-axis.

r is the radius

The equation  [tex]\left(x-3\right)^{2}+\left(y-1\right)^{2}=3^{2}[/tex]  is the equation of a circle.

Hence, graph B shows the given equation.

To learn more about the graph, refer to the link;

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Answer:

x/100 x 8 = 6

8x/100 = 6

x100    x100

8x = 600

Divide by 8 on both sides:

X = 75

Consider a percent out of 100. 'Of' meaning multiplication. 'is' meaning equal to that number.

(unknown number/percent)x/100 x 8(of 8) = 6(is 6)

Answer:

4 meters

Step-by-step explanation:

Assuming that the garden is a rectangular garden, its area would be length ×width.

Let the length be L meters and the width be W meters.

Area= L ×W

48= LW -----(1)

Given that the length is 3 times the width,

L= 3W -----(2)

Substitute (2) into (1):

48= 3W(W)

3W²= 48

Divide both sides by 3:

W²= 48 ÷3

W²= 16

Square root both sides:

[tex]W = \sqrt{16} [/tex]

W= 4 (reject negative as width cannot be a negative number)

Thus, the width of the garden is 4 meters.

Answer:

1368

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

[tex]x=10\sqrt[3]{2}[/tex]

Step-by-step explanation:

The Volume of a box with a square base  

x by  x  cm and height  h  cm is  

V =x^2h

The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.

The surface area of the box described is  

A = x ^2 +4 x h

We need  

A  as a function of  x  alone, so we'll use the fact that

V= x^2h = 1000 cm^3

This imples  [tex]h=\frac{1000}{x^2}[/tex]

This makes

[tex]A= x^2 + 4x(1000/x^2)\\A= x^2+4000/x[/tex]

Differentiating A w.r.t. x

[tex]A' = 2x-4000/x^2[/tex]

Now, A'=0

[tex]x=10\sqrt[3]{2}[/tex]

Therefore, minimum value x = [tex]x=10\sqrt[3]{2}[/tex]

Answer:

mean = (4 + 7 + 10 ) / 3

         = 21 / 3

         = 7

Step-by-step explanation:

Answer:

Average of 4,7 and 10:

Add all together 4+7+10=21

Then 21 divided by number of scores so 3.

21 divided by 3=7

So the mean is 7

Answer:

£140 increased by 5% is £147.00

Answer:

it should be 147.00 , I'm so sorry if I'm wrong!