Simplify completely, help me:(

we just have to use the Pythagoras theorem and then calculate the value of x and y.

Answer:

Option B is the correct option.

Here,

Adjacent=15

Hypotenuse=17

Now,

[tex]cos \: theta = \frac{adjacent}{hypotenuse} \\ cos \: 28 = \frac{15}{17} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

B. 15/17

Step-by-step explanation:

(see attached graphic for reference)

Because we have a right triangle (i.e one of the internal angles is 90 degrees), we can use trigonometry to solve

from the diagram, we can see that

cos 28° = adjacent length / hypotenuse

we can also see that the length adjacent to 28° = 15 units and the hypotenuse is 17 units,

hence, substituting these values into the equation:

cos 28° = 15 / 17   (answer)

edit: typo

Answer:

  6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

  x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

  h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

  V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

  dV/dx = 0 = 27 -(3/4)x²

  x² = (4/3)(27) = 36

  x = 6

  h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

Comment on maximum volume, minimum area

In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

Answer:

(38.8%...7/10), than (47%...8/17) I didnt know if u needrd it in fraction or percent.

Step-by-step explanation:

You want to first add up everyone. So in total there are 18 people.

There is than a 38.8% chance that a independent will be picked first. 7/18.

But since one person was picked already you have to subtract 1 person from the total, so now its out of 17.

There is now a 47% chance that a democrat will be picked next. 8/17.

The area bounded by region between the curve [tex]y = x^2- 24[/tex]  and [tex]y = 1[/tex] is

[tex]0[/tex] square units.

To find the Area,

Integrate the difference between the two curves over the interval of intersection.

Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .

The point of Intersection is the common point between the two curve.

Value of [tex]x[/tex] and [tex]y[/tex] coordinate  will be equal for both curve at point of intersection

In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].

[tex]1 = x^2-24[/tex]

Rearrange, like and unlike terms:

[tex]25 = x^2[/tex]

[tex]x =[/tex]  ±5

The point of intersection for two curves are:

[tex]x = +5[/tex]  and  [tex]x = -5[/tex]

Integrate the difference between the two curve over the interval [-5,5] to calculate the area.

Area =   [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]

Simplify,

[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]

Integrate,

[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]

Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.

[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]

= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]

[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]

[tex]= 0[/tex]

The Area between the two curves is [tex]0[/tex] square  units.

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Answer:

5n

Step-by-step explanation:

Think about it:

If Tommy has 4 friends (n = 4), then he will have to give 5 pencils to each person. The total number of pencils is 5 * n or 5 * 4 = 20.

Similarly, if Tommy has 0 friends (I can relate), then he will have to give 5 pencils to each of his imaginary friends. The total number of pencils he has to give out to his real friends is 5 * n or 5 * 0 = 0.

Answer:C

Step-by-step explanation:

The vertical line test

Answer:

Option C

Step-by-step explanation:

The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.

It tests the claim that the row and column variables are independent of each other.

The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.

Answer:

(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 ​minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Step-by-step explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

  The given standard deviation = 3.4 minutes

The value of  n sample size = 45

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

Unlevered beta ≈ 1.09

Step-by-step explanation:

Unlevered beta is basically the unlevered weighted average cost as it shows the volatility of returns without financial leverage. Unlevered beta is also known as asset beta, while the levered beta is commonly known as equity beta. Unlevered beta is calculated from the hamada equation as:

Unlevered beta = Levered beta/[1 + ((1 - Tax rate) × (Debt / Equity))]

We are given;

Levered beta = 1.4

Tax rate = 30% = 0.3

Debt = $6 million

Equity = $15 million

Thus, plugging these into the hamada equation, we have;

Unlevered beta = 1.4/[1 + ((1 - 0.3) × (6/15))]

Unlevered beta = 1.4/(1 + (0.7 × 0.4)

Unlevered beta = 1.4/(1 + 0.28)

Unlevered beta = 1.4/1.28

Unlevered beta = 1.09375

To 2 decimal places;

Unlevered beta ≈ 1.09

Answer:

85.932 cm³

Step-by-step explanation:

The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):

[tex]V=l*w*h[/tex]

The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:

[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]

The volume of this prism is 85.932 cm³.

Answer:

y = x/6 − 11/6

Step-by-step explanation:

y = 6x + 11

To find the inverse, switch x and y, then solve for y.

x = 6y + 11

x − 11 = 6y

y = x/6 − 11/6

Answer: CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F

Step-by-step explanation:

CITY C: Dew Point Temperature = 25°F, expected low Temperature = 20°F

CITY A: Dew Point Temperature = 65°F, expected low Temperature = 60°F

CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F

city B is going to have dew on their lawn in the morning as the dew point temperature is less than the lowest temperature.

When surface temperature drops, eventually reaching the dew point, atmospheric water vapor condenses to form small droplets on the surface. Thus dew will be formed as the conditions are suitable only for city B.

Answer: 0.0023

Step-by-step explanation:

Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.

probability of success p = 32% = 0.32

Sample size : n= 10

Binomial probability function :

[tex]P(X=x)= \ ^nC_xp^x(1-p)^{n-x}[/tex]

Now, the probability that eight receipts will show that the above three food items were ordered :

[tex]P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023[/tex]

hence, the required probability = 0.0023

Answer:

  68

Step-by-step explanation:

The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.

  [tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]

The technician can test 68 chips in that time period.

Answer:

[tex]\boxed{Option A ,D}[/tex]

Step-by-step explanation:

The remote (non-adjacent) interior angles of the exterior angle 1 are <4 and <6

Answer:

Betty should use T = 2.571 to construct the confidence interval

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571

Betty should use T = 2.571 to construct the confidence interval

Answer:

Use a graphing calc.

Step-by-step explanation:

Answer:

3, 12

Step-by-step explanation:

Et x and y be the required integers.

Case 1: x = 5y - 3...(1)

Case 2: xy = 36

Hence, (5y - 3)*y = 36

[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]

Hence, the required integers are 3 and 12.

let

x  = one integer

y = another integer

x = 5y - 3

If the product of the two integers is 36, then find the integers.

x * y = 36

(5y - 3) * y = 36

5y² - 3y = 36

5y² - 3y - 36 = 0

Solve the quadratic equation using factorization method

That is, find two numbers whose product will give -180 and sum will give -3

Note: coefficient of y² multiplied by -36 = -180

5y² - 3y - 36 = 0

The numbers are -15 and +12

5y² - 15y + 12y - 36 = 0

5y(y - 3) + 12 (y - 3) = 0

(5y + 12) (y - 3) = 0

5y + 12 = 0      y - 3 = 0

5y = - 12           y = 3

y = -12/5

The value of y can not be negative

Therefore,

y = 3

Substitute y = 3 into x = 5y - 3

x = 5y - 3

x = 5(3) - 3

= 15 - 3

= 12

x = 12

Therefore,

(x, y) = (12, 3)

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Answer:

1/7 = 0.142857... repeating

Step-by-step explanation:

7^(-1) = 1/(7^1) =1/7 = 0.142857... repeating

Answer:

Solution,

[tex] {7}^{ - 1} \\ = \frac{1}{ {7}^{1} } \\ = \frac{1}{7} [/tex]

[tex] {x}^{0} = 1[/tex]

[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]

( powers are added in multiplication of same base)

[tex] {( {x}^{m} )}^{n} = {x}^{m \times n} [/tex]

[tex] {x}^{ - m} = \frac{1}{ {x}^{m} } [/tex]

[tex] {x}^{ \frac{p}{q} } = \sqrt[q]{ {x}^{p} } [/tex]

Hope this helps ....

Good luck on your assignment...

Answer:

X = 50

Step-by-step explanation:

(5x - 100) + (x - 20) = 180 (sum of angle on a straight line is = 180)

5x + x -100 -120 = 180

6x - 120 = 180

6x = 180 + 120

6x = 300

x = 300/6

x = 50

For y

3y + y + 140 = 180

4y = 180 -140

4y = 40

y = 40/4

y = 10

Answer:

25%

Step-by-step explanation:

George is 33[tex]\frac{1}{3}[/tex]% ([tex]\frac{100}{3}[/tex]%) richer than Pete. Let Pete's percentage of wealth be 100%.

Thus George percentage of wealth = 100% + [tex]\frac{100}{3}[/tex]%

                                                           = [tex]\frac{400}{3}[/tex]%

                                                           = 133[tex]\frac{1}{3}[/tex]%

Pete's percent poorer than George can be determined by;

                                                           = [tex](\frac{100}{3})[/tex] ÷ [tex](\frac{400}{3} )[/tex] × 100

                                                           = [tex](\frac{100}{3})[/tex] × [tex]\frac{3}{400}[/tex] ×100

                                                           = 0.25 × 100

                                                           = 25%

Pete is 25% poorer than George.

Answer:

C. -4/3

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes.

We know that line m is perpendicular to line l.

Line l has a slope of 3/4. To find the slope of line m, find the negative reciprocal of 3/4.  Negate the fraction and find the reciprocal.

Negative: switch the sign

3/4 --> -3/4

Reciprocal: switch the numerator (top number) and denominator (bottom number)

-3/4 --> -4/3

Line m has a slope of -4/3 and C is correct.

Answer:

3,145,728

Step-by-step explanation:

x1.6

300000 x 1.6 = 4800000

480000 x 1.6 = 7680000

768000 x 1.6 = 1228800

122800 x 1.6 = 1966080

1966080 x 1.6 = 3145728

Answer:

the answer i got was (16/3,16/3)

Step-by-step explanation:

Answer:

x⁴ = -0.955939

x³ = 0.206897

x² = -2.07471

x = 2.65517

Step-by-step explanation:

Step 1: Rewrite equations in standard form

30x⁴ - 5x³ - 10x² + 3x = -1

-3x⁴ + 5x³ + 7x² + 4x = 0

-3x⁴ + x³ + x² = 1

6x⁴ - 10x³ - 2x² + x = -1

Step 2: Write in matrix form

Top Row: [30 -5 -10 3 | -1]

2nd Row: [-3 5 7 4 | 0]

3rd Row: [-3 1 1 0 0 | 1]

Bottom Row: [6 -10 -2 1 | -1]

Step 3: Plug in calc with RREF function

Top Row: [1 0 0 0 | -499/522]

2nd Row: [0 1 0 0 | 6/29]

3rd Row: [0 0 1 0 | -361/174]

4th Row: [0 0 0 1 | 77/29]

Answer:

Dy/Dx=1/√ (2x+3)

Yeah it's correct

Step-by-step explanation:

Applying differential by chain differentiation method.

The differential of y = √(2x+3) with respect to x

y = √(2x+3)

Let y = √u

Y = u^½

U = 2x +3

The formula for chain differentiation is

Dy/Dx = Dy/Du *Du/Dx

So

Dy/Dx = Dy/Du *Du/Dx

Dy/Du= 1/2u^-½

Du/Dx = 2

Dy/Dx =( 1/2u^-½)2

Dy/Dx= u^-½

Dy/Dx=1/√ u

But u = 2x+3

Dy/Dx=1/√ (2x+3)

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Answer:

a. Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. P(at least B) = 0.330

c. P(pass) = 0.855

Step-by-step explanation:

Professor Sanchez has been teaching Principles of Economics for over 25 years.

He uses the following scale for grading.

Grade     Numerical Score      Probability

A                       4                            0.090

B                       3                            0.240

C                       2                            0.360

D                       1                            0.165

F                       0                            0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

The cumulative probability distribution is given by

Grade = F

P(X ≤ x) = 0.145

Grade = D

P(X ≤ x) = 0.145 + 0.165 = 0.310

Grade = C

P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670

Grade = B

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910

Grade = A

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1

Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

At least B means equal to B or greater than B grade.

P(at least B) = P(B) + P(A)

P(at least B) = 0.240 + 0.090

P(at least B) = 0.330

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Passing the course means getting a grade of A, B, C or D

P(pass) = P(A) + P(B) + P(C) + P(D)

P(pass) = 0.090 + 0.240 + 0.360 + 0.165

P(pass) = 0.855

Alternatively,

P(pass) = 1 - P(F)

P(pass) = 1 - 0.145

P(pass) = 0.855

Answer:

5/16

Step-by-step explanation:

Use the formula to find slope when 2 points are given.

m = rise/run

m = y2 - y1 / x2 - x1

m = 3 - 8 / -10 - 6

m = -5 / -16

m = 5/16

The slope of the line is 5/16.

Answer: m=5/16

Step-by-step explanation:

Answer:

[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]

[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]\bar X= 7.72[/tex] represent the sample mean

[tex]s= 2.5[/tex] represent the sample deviation

[tex] n=20[/tex] represent the sample size

The confidence interval is given by:

[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:

[tex] df= n-1 = 20-1=19[/tex]

And the critical value would be:

[tex] t_{\alpha/2}= 2.539[/tex]

And replacing we got:

[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]

[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]

The 98% confidence interval is between 6.42 hamsters per liter to  9.02 hamsters per liter

Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98

α = 1 - C = 0.02

α/2 = 0.01

The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.

The margin of error E is:

[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]

The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)

Hence the 98% confidence interval is between 6.42 hamsters per liter to  9.02 hamsters per liter

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