Consider the joint probability distribution below. Complete parts (a) through (c). X 1 2 Y 0 0.30 0.10 1 0.40 0.20 a. Compute the marginal probability distributions for X and Y. X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) (Type integers or decimals.) b. Compute the covariance and correlation for X and Y. Cov(X,Y)= (Round to four decimal places as needed.) Corr(X,Y)= (Round to three decimal places as needed.) c. Compute the mean and variance for the linear function W=X+Y. Hw= (Round to two decimal places as needed.) = (Round to four decimal places as needed.) ow

Answer:60

Step-by-step explanation:

180-75-60=45

90-45=45

180-45-75=?

A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

Answer:

-2

Step-by-step explanation:

Three times the sum of a number and ten is twenty-four.​

3 x (n + 10) = 24

24 / 3 = 8

n + 10 = 8

-2 + 10 = 8

3 x (-2 + 10) = 24

3 x 8 = 24

Answer:

\( - 2\)

Step-by-step explanation:

do the math

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

The answer is (3,-2)

Step-by-step explanation:

\( \frac{1}{3} x - 3 = - 2x + 4 \\ \frac{1}{3} x + 2x = 7 \\ \frac{7}{3} x = 7 \\ x = 3 \\ then \: \\ y = - 2\)

Step-by-step explanation:

The quotient of -256/6 represents the average rate of descent of the submarine, in feet per minute. To find this rate, we divide the total change in depth (-256 feet) by the time taken to descend (6 minutes):

-256 / 6 = -42.67...

The quotient is negative because the submarine is descending (i.e., decreasing in depth). The magnitude of the quotient is approximately 42.67 feet per minute, rounded to two decimal places.

Therefore, the correct answer is:

C. The depth of the submarine DECREASED by 42 2/3 feet per minute.

Answer:

First, we need to solve the equation in the problem for y to put it in slope-intercept form so we can determine its slope:

2y−6x=4

2y−6x+6x=6x+4

2y−0=6x+4

2y=6x+4

2y2=6x+42

2y2=(6x2)+(42)

y=3x+2

The slope-intercept form of a linear equation is: y=mx+b

Where m is the slope and b is the y-intercept value.

Therefore the slope of this equation is m=3

A perpendicular line will have a slope (let's call this slope mp) that is the negative inverse of this line. Or, mp=−1m

Substituting gives:

mp=−13

Answer:

-2

Step-by-step explanation:

The average waiting time in minutes is approximately 0.317 minutes.

To determine the average waiting time in minutes, we can use the queuing theory formula for average waiting time in an\($\mathrm{M} / \mathrm{M} / \mathrm{c}$\) queue:

\($$W_q=\frac{\rho^{c+1}}{c ! \cdot(1-\rho)} \cdot \frac{1}{\mu-\lambda}$$\)

Where:

\($W_q$\) is the average waiting time in the queue.

\($\rho$\) is the traffic intensity, given by $\frac{\lambda}{c \cdot \mu}$.

\($c$\) is the number of service channels (cashiers).

\($\mu$\) is the service rate (customers per hour).

\($\lambda$\)  is the arrival rate (customers per hour).

Given:

\($\lambda=85.5$\)customers per hour.

\($\mu=19$\) customers per hour.

\($c=5$\) cashiers.

First, let's calculate $\rho$ :

\($$\rho=\frac{\lambda}{c \mu}=\frac{85.5}{5 \cdot 19} \approx 0.9011$$\)

Now, let's calculate \($W_q$\) :

\($$W_q=\frac{\rho^{c+1}}{c ! \cdot(1-\rho)} \cdot \frac{1}{\mu-\lambda}\\=\frac{0.9011^{5+1}}{5 ! \cdot(1-0.9011)} \cdot \frac{1}{19-85.5} \\\approx 0.317 \text { (rounded to two decimal places) }$$\)

Therefore,the average waiting time in minutes is approximately 0.317 minutes.

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a. The length of the arc across the fair landing area is approximately 12.17 meters.

To find the length of the arc, we need to calculate the circumference of the sector defined by the central angle of 34.92°.

The formula to calculate the circumference of a sector is:

Circumference = (Central Angle / 360°) * 2π * Radius. In this case, the central angle is 34.92° and the radius is the distance from the center of the sector to the outer edge, which is the length of the winning shot, 21.89 meters.

Plugging the values into the formula:

Circumference = (34.92° / 360°) * 2π * 21.89 meters

Simplifying the expression:

Circumference = (0.097 * 2π * 21.89) meters

Circumference ≈ 12.17 meters

Therefore, the length of the arc across the fair landing area is approximately 12.17 meters.

b. The area of the sector bounded by the arc in part (a) is approximately 11.89 square meters.

To find the area of the sector, we need to use the formula for the area of a sector, which is given by:

Area = (Central Angle / 360°) * π * (Radius^2)

In this case, the central angle is 34.92° and the radius is the length of the winning shot, which is 21.89 meters.

Plugging the values into the formula:

Area = (34.92° / 360°) * π * (21.89^2)

Simplifying the expression:

Area = (0.097 * π * 21.89^2) square meters

Area ≈ 11.89 square meters

Therefore, the area of the sector bounded by the arc in part (a) is approximately 11.89 square meters.

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Answer: To find the number of liters of water in the first pool after x minutes have passed, we can use the formula:

972 + 17x

To find the number of liters of water in the second pool after x minutes have passed, we can use the formula:

44x

Note that both of these formulas assume that the pools are being filled continuously, without any interruptions. If the flow of water into either pool is interrupted at any point, the actual amount of water in the pools may be different from what these formulas predict.

Answer:

a)

17x + 972

44x

b)

972 + 17x = 44x

Step-by-step explanation:

Answer: $1.05 per orange

Step-by-step explanation:

12.33 - 2.88 = 9.45

9.45 ÷ 9 = 1.05

D) y = 2x + 8

Parallel lines are coplanar lines that never intersect.

Parallel Slopes

All parallel lines have the same relationship between their slopes. For 2 lines to be parallel, their slopes must be equal. The question tells us that the slope of the first line is 2. This means that only answer choices B and D are viable.

The slopes of answer choices A and C are perpendicular to the line given.

Testing the Answers

Both B and D could be parallel to the line given; however, we are also told that the line must pass through (-2, 4). To see which answer is correct, we can plug in the x and y-values and solve. If a line passes through a point, then the equation will be true when the values are plugged in.

Let's start with answer B.

Since this statement is not true, we know that y = 2x + 4 does not pass through the point (-2, 4).

Next, we need to test answer choice D.

This is true, so y = 2x + 8 must pass through the point (-2, 4). Since answer choice D has a parallel slope and passes through (-2, 4), it must be the correct answer.

Answer:

The interest rate was 5.24%.

Step-by-step explanation:

You can use the following formula to calculate the interest rate:

i=n*((A/P)^1/nt-1), where:

i= interest rate

n= number of times interest is compounded= 4

A=value of investment= 3425

P= principal= 2500

t=time= 6

Now, you can replace the values on the formula:

i=4*((3425/2500)^1/4*6-1)

i=4*(1.37^1/24-1)

i=4*0.0131

i=0.0524

According to this, the answer is that the interest rate was 5.24%.

Independent value: Quarts of oil

Dependent variable: Cost of oil

Constant of proportionality: 5.8

Answer:Wolverines

Step-by-step explanation:

The panthers <  tigers               Tiger  1

Tigers  <   Lions                          Lions  2

Lions< wolverines                      Panthers   0

Lions> Panthers                         Wolverines  1

Even though the lions scored more wolverines scored more than the panthers since the panthers didn't score a single point according to my calculations

To find the volume of a cone, we use the formula V = (1/3)πr²h or V = (1/3)π(d/2)²h, where r is the radius, d is the diameter, and h is the height of the cone.

Example 1: A cone with a height of 8 cm and a radius of 3 cm.

V = (1/3)π(3²)(8)
V = 24π
V ≈ 75.4 cm³

Example 2: A cone with a height of 12 cm and a diameter of 6 cm.

V = (1/3)π(6/2)²(12)
V = (1/3)π(3²)(12)
V = 36π
V ≈ 113.1 cm³

Example 3: A cone with a height of 5 cm and a diameter of 10 cm.

V = (1/3)π(10/2)²(5)
V = (1/3)π(5²)(5)
V = (1/3)π(25)(5)
V = 125/3π
V ≈ 130.9 cm³

Example 4: A cone with a height of 15 cm and a radius of 2.5 cm.

V = (1/3)π(2.5²)(15)
V = (1/3)π(6.25)(15)
V = (1/3)π(93.75)
V ≈ 98.2 cm³

Puzzle grid:

| 75.4 | 113.1 | 130.9 | 98.2 |
|  -   |   -   |   -   |   -   |
|  -   |   -   |   -   |   -   |
|  -   |   -   |   -   |   -   |

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Answer:

kk

Step-by-step explanation:

The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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x=19

add 45 to both sides 3

Answer:

x=7

Step-by-step explanation:

6x6=36

6x7=42

Sides of the right triangle are 6x bigger

Answer:

28%

Step-by-step explanation:

Lets say the fraction of speed and problem solved is 100/100

the number of problems solved increases by 60%

so now it is 160/100, also the speed increases by 25%

so now we do 160/125=1.28

finaly we do 1.28-1 = 28%

Therefore the answer is 28%.

hope this helps

Answer:

28%

Step-by-step explanation:

The number of mathletes on the team must increase by 28%.

Description of speed

The speed of the mathletes is total number of questions divided the total number of people on the team.

Speed = total number of questions / total number of people on the team

Determination of the percentage increase in the number of mathletes

Increase in the number of people on the team = total number of questions / speed

1.60 / 1.25 - 1 = 28%

The researcher should use the measure of e. standard deviation. This is because standard deviation provides an indication of the dispersion or spread of the data around the mean.

Helping to understand how close the ages are to the average (49 years).The measure that would most accurately answer the researcher's question is the median. The median is the middle value in a dataset, so if most respondents are close to 49 years old, the median would also be close to 49 years old.

The mean could also be used to answer this question, but it could be skewed if there are outliers in the dataset. The mode, range, and standard deviation are not as useful in determining if most respondents are close to 49 years old.

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(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer: 2

Step-by-step explanation:

Change the divisor 4.5 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

90 ÷ 45 = 2

and therefore:

9 ÷ 4.5 = 2

Answer:

\( \frac{10}{16} \)

Step-by-step explanation:

\( \frac{red \: pens}{total \: pens \: } = \frac{10}{16} \)

or 5/8

Answer:False.  

Step-by-step explanation:

Multiply both sides of the equation by a coefficient:begin equation begin cases5  5 x + 2 y = 7 * 52 13.

In the given IS-LM model, the equilibrium real output, Y, and the equilibrium value of consumption, C, can be determined using the IS and LM equations. The IS equation relates output to the interest rate, while the LM equation represents the equilibrium condition in the money market. By substituting the given values into the equations, we can find the equilibrium values.

The IS equation is given by: Y = 1,586.27 - 3,145.45i.

The LM equation is given as: i = 0.04.

To find the equilibrium real output, we substitute the value of i from the LM equation into the IS equation:

Y = 1,586.27 - 3,145.45 * 0.04.

Calculating the right side of the equation, we have:

Y = 1,586.27 - 125.82,

Y ≈ 1,460.

Therefore, the equilibrium real output, Y, is approximately 1,460.

To find the equilibrium value of consumption, we substitute the equilibrium real output, Y, into the consumption function:

C = 217 + 0.51Y.

Substituting Y = 1,460, we have:

C = 217 + 0.51 * 1,460.

Calculating the right side of the equation, we find:

C ≈ 984.

Therefore, the equilibrium value of consumption, C, is approximately 984.

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Answer: The accumulated amount after 5 years = $ 5352.90

The accumulated amount after 20 years = $ 12828.54

Step-by-step explanation:

Formula to find the accumulated amount after investing P amount at the rate of r ( in decimal) compounded annually for t years:

\(A=P(1+r)^t\)

As per given , we have

P =  $4,000

r= 6% = 0.06

Put thsese values in formula : \(A=4000(1+0.06)^t=4000(1.06)^t\)

The accumulated amount after 5 years = \(A(5)=4000(1.06)^5\)

\(=4000(1.3382255776)=5352.9023104\\\\\approx5352.90\)

Hence,  the accumulated amount after 5 years = $ 5352.90

The accumulated amount after 20 years = \(A(20)=4000(1.06)^{20}\)

\(=4000(3.20713547221)=12828.5418888\\\\\approx12828.54\)

Hence,  the accumulated amount after 20 years = $ 12828.54

Using the compound interest formula, the amount in the bank at the end of 5 years and 20 years would be $5325.90 and $12828.54 respectively

Using the compound interest formula :

After 5 years :

\( A = 4000(1 + 0.06)^{5} \)

Amount after 5 years = $5325.90

After 20 years :

\( A = 4000(1 + 0.06)^{20}\)

Amount after 5 years = $12828.54

Hence, the amount accumulated after 20 years will be $12828.54

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Answer:

603

Step-by-step explanation:

\(\mathrm{Write\:the\:problem\:in\:long\:division\:format}\)

\(\begin{matrix}14\overline{|\smallspace8442}\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

Divide 84 by 14 to get 6

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 14\overline{|\smallspace8442}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace8\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

Divide 4 by 14 to get 0

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 14\overline{|\smallspace8442}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace8\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

Divide 42 by 14 to get 3

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace6\emptyspace03\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 14\overline{|\smallspace8442}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace8\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

        \(\underline{42}\\0\)

\(\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{8442}{14}\:\mathrm{is}\:603\)

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