A 2-gallon jug of juice costs $14.72. What is the price per cup?

Answer:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]

Step-by-step explanation:

We want to write the trignometric expression:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]

Take the secant of both sides:

[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]

By substitutition:

[tex]\displaystyle= \sin(2\theta)[/tex]

Using an double-angle identity:

[tex]=2\sin(\theta)\cos(\theta)[/tex]

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]

Simplify. Therefore:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]

Answer:

Answer:

5:51 P.M.

Step-by-step explanation:

You first add 36 and 10 which you get 46 then add the 46 to the total so, 46 + 5 is 51 so she will get back at 5:51 P.M

Answer:

u first add 36 to 5:05=5:41 then add 10 more min and that is 51

Answer:

60

Step-by-step explanation:

if it has a square in the center of the angle it means it is 90 degrees

so a straight line adds up to 180b

90 +30+x=180

x=60

Using the triangle inequality theorem, we can figure this out.

2-  Yes

3- No

4- No

5- Yes

6-  Yes

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Therefore we have;

[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

Therefore, we have;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]

The z-value is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

μ₁ - μ₂ = 5

When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]

[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]

When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]

[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

For more question on interest visit:

https://brainly.com/question/25720319

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Answer:

5,8  8,3

Step-by-step explanation:

hoped this helped <33

Answer:

Greater

Step-by-step explanation:

It is greater because 3 & 1/5 is technically 3.20 which obviously results with 3.65 being greater than 3.2. Also if you go into detail with it 3.65 is kinda 3 & 3/5. Thanks. Let me know if you find any fault in my answer. Have a good day!

Answer:

12.57

Step-by-step explanation:

same as last time you know

Answer:

since we have four groups, the number of population k = 4

Option C. 4 is the correct answer

Step-by-step explanation:

Given the data in the question;

Number of group k = 4

the number of cases in each group = 30

so

n = 4 × 30

n = 120

SS_total  = df = n - 1

= 120 - 1

= 199

SS_between = k - 1

= 4 - 1

= 3

since we have four groups, the number of population k = 4

Option C. 4 is the correct answer

Answer:

1=94 max  2=96 max

Step-by-step explanation:

9514 1404 393

Answer:

  7×10⁻¹ +6×10⁻² +5×10⁻³

Step-by-step explanation:

Place value in any place-value number system increases by a factor of the base for each place to the left of the "decimal" point. It is reduced by a factor of the base for each place to the right of the "decimal" point.

For base-10 numbers, the powers of 10 are -1, -2, -3, ... as you go to the right of the decimal point. Hence the number 0.765 decomposes as ...

  7×10⁻¹ +6×10⁻² +5×10⁻³

Answer: 2a/3 + b/3

Since it has two different variables, there is no final answer. To find the answer, you must first expand the equation and then apply the fraction rule.

Answer:

y = 18

x = 15.588

Answer:

The value of X should be 0

The value of Y should be 30

However your teacher gave next to no context, so these might be wrong

Step-by-step explanation: protractor

Answer: here is your answer

Step-by-step explanation:

A= 16

B= -8

C= 6

D= -16

E= -4

Answer:

The total number of students is 800.

Step-by-step explanation:

Given that in an examination, 40% students passed in Maths only, 30% passed in Science only and 10% students failed in both the subjects, to determine the total number of students if 400 students passed in Science the following calculation must be performed:

100 - 40 - 30 - 10 = 20

20 + 30 = 50

50 = 400

100 = X

100 x 400/50 = X

800 = X

Thus, the total number of students is 800.

Answer:

19

Step-by-step explanation:

9+15=24

24-5=

19 is the answer

Answer:

X=-2 x=1 x=3 and x=-1

Step-by-step explanation:

When the problem asks you to find the zeros all they are asking for is the solution so to solve all you need to do is set each individual piece equal to zero.

9514 1404 393

Answer:

  f(x) = {-x for x < 2; 2x-3 for x ≥ 2}

Step-by-step explanation:

The blue line extending to the left has a slope of -1 and a y-intercept of 0. Its equation is y = -x. That part of the definition of f(x) is applicable for values of x less than 2. (The open dot at (2, -2) tells you that point is not included.)

The red line extending to the right has a slope = rise/run = 2/1 = 2. The y-intercept can be found by extending the line to the y-axis, or from the computation ...

  b = y -mx

  b = 1 -2(2) = -3 . . . . . for the point (x, y) = (2, 1)

Then the slope-intercept equation for the red line is ...

  y = 2x -3

That part of the definition of f(x) is applicable for values of x ≥ 2. The solid dot tells you the point (2, 1) is included.

Putting these parts together, we get ...

  [tex]f(x)=\left\{\begin{array}{cc}-x&\text{if $x<2$}\\2x-3&\text{if $x\ge2$}\end{array}\right.[/tex]

Answer:

2/3 or .66666666

Step-by-step explanation:

Answer:

b. The difference in the distance traveled by the tortoise and hare during that time.

Step-by-step explanation:

First the intersection points are found out on the graph. Then the area between the curves is found out.

Putting the values

H(t) = sin(t)

H(t) = sin(1) = 0.01745

T(t) = cos(t),

T(t) = cos(1)= 0.9998

As T(t) ≥ H(t)

Area is found out by taking the integral of it.

Area = Integral ( limit 0 to 0.998)  T(t)-H(t) dt

The difference represents how far the turtle is from the hare.

So it represents the difference in the distance traveled by the tortoise and hare during that time.

Answer:

Step-by-step explanation:

radius of the cylindrical construction pipe = 2.5 ft

height of cylinder = 25 ft

volume of cylinder = [tex]\pi r^{2} h[/tex]

                             = 3.14 x 2.5 x 2.5 x 25

                             = 490.625

                             = 490 [tex]ft^{3}[/tex]

Hope this helps

please mark as brainliest!!!

Answer:

490 ft³

Step-by-step explanation:

The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? 490 ft³

Answer:

Here is the formula of what u want . so the answer would be A≈841.78 .

plz check the final answer yourself again ^^

hope it helps u . ⚘

Answer: 3

Step-by-step explanation:

12.9/4.3 will give you the number it was multiplied by.