Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.

How much is in her account at the end of one year?

Answer:

a. SST = 1816

SSR = 1511.804

SSE = 465.804

b. Coefficient of determination, R² = 0.832491079

c. The correlation coefficient r = 0.8636

Step-by-step explanation:

y = 23.194 + 0.318·x

Where:

x = Price

y = Overall score

The observed data are given as follows;

Brand                Price  Score

Bose                 180     76

Scullcandy       150      71

Koss                 95       62

Phillips/O'Neill 70       57

Denon              70       30

JVC                   35       34

[tex]SST = \sum \left (y - \bar{y} \right )^{2}[/tex]= 1816

[tex]SSR = \sum \left ({y}'-\bar{y{}'} \right )^{2}[/tex] = 1511.804

[tex]SSE = \sum \left (y - {y}' \right )^{2}[/tex] = 465.804

Coefficient of determination

[tex]Coefficient \, of \, determination = \dfrac{SSR}{SST}[/tex]= 0.832

Coefficient of correlation =

[tex]r = \dfrac{n\left (\sum xy \right )-\left (\sum x \right )\left (\sum y \right )}{\sqrt{\left [n\sum x^{2}-\left (\sum x \right )^{2} \right ]\left [n\sum y^{2}-\left (\sum y \right )^{2} \right ]}}[/tex]

Ʃxy  = 37500

Ʃx =600

Ʃy = 330

Ʃx² = 74950

Ʃy²  = 19966

[tex]r = \dfrac{6 \left (37500 \right )-\left (600 \right )\left (330 \right )}{\sqrt{\left [6\times 74950-\left (600 \right )^{2} \right ]\left [6 \times 19966-\left (330 \right )^{2} \right ]}} = 0.8636[/tex]

Answer:

Step-by-step explanation:

Hello!

So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.

Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.

The hypotheses are:

H₀: The variables are independent.

H₁: The variables are not independent.

α: 0.05

[tex]X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}[/tex]

r= total number of rows

c= total number of columns

i= 1, 2 (categories in rows)

j=1, 2, 3 (categories in columns)

To calculate the statistic you have to calculate the expected frequencies for each category:

[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]

[tex]O_{i.}[/tex] Represents the marginal value of the i-row

[tex]O_{.j}[/tex] Represents the marginal value of the j-column

[tex]E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7[/tex]

[tex]E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7[/tex]

[tex]E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7[/tex]

[tex]E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33[/tex]

[tex]E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33[/tex]

[tex]E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33[/tex]

[tex]X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34[/tex]

Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:

[tex]X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991[/tex]

Decision rule:

If [tex]X^2_{H_0}[/tex] ≥ 5.991, reject the null hypothesis.

If [tex]X^2_{H_0}[/tex] < 5.991, do not reject the null hypothesis.

The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.

At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.

I hope this helps!

Answer:

D

Step-by-step explanation:

divide 10 times starting with 100.

The answer is 25/256 or 0.09765625

The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the height of the ball after x bounce. Given that the ball rises to the height from which it has fallen, hence:

y = 100(1/2)ˣ

After the 10th bounce:

y = 100(1/2)¹⁰ = 0.09766

The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet.

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Answer:

A. d= 45t

Step-by-step explanation:

(assuming that you meant 67.5 in the last 1.5 hours)

67.5 miles = distance

1.5 hours = time

therefore:

[tex]\frac{d}{t\\}[/tex] = 67.5/1.5

making your answer 45

leaving a as your correct answer:

d= 45t

The proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Given that, A train travels at a constant speed and has travelled 67.5 miles in the last 1.5 hours. (assuming that you meant 67.5 in the last 1.5 hours)

67.5 miles = distance

1.5 hours = time

We know that, speed = distance / time

s = 67.5/1.5

s = 45 mph

Now, distance = speed × time

d = 45t

Hence, the proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).

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Answer:  A) 3 x 4

Step-by-step explanation:

The dimensions of a matrix are ROWS x COLUMNS.

The given matrix has 3 rows and 4 columns,

therefore the dimensions are: 3 x 4

Answer:

The expected value of profit is -$0.65.

Step-by-step explanation:

The rules of the lottery are as follows:

The probability of winning is, P (W) = 0.001.

Then the probability of losing will be,

P (L) = 1 - P (W)

       = 1 - 0.001

       = 0.999

Let the random variable X represent the amount of profit.

The probability distribution table of the lottery result is as follows:

Result      X        P (X)

Win      +349     0.001

Lose         -1       0.999

The formula to compute the expected value of X is:

[tex]E(X)=\sum X\cdot P(X)[/tex]

Compute the expected value of profit  as follows:

[tex]E(X)=\sum X\cdot P(X)[/tex]

         [tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]

Thus, the expected value of profit is -$0.65.

Area = length x width

Area = 5/6 x 3/4

= (5x3) / (6x4)

= 15/24

= 5/8 square miles

Answer: There is a 0.88% chance of pulling three red marbles in a row.

Step-by-step explanation:

First pull = 4/15 (26.67%)

second pull = 3/14 (21.43%)

Third pull = 2/13 (15.38%)

You need to multiply these three fractions to get the probability of pulling three reds in a row, doing that will get you 4/455 or 0.88%

Answer:

  -3i +-12j

Step-by-step explanation:

P2 -P1 = (-1-2, -6-6) = (-3, -12)

In terms of unit vectors i and j, this is -3i -12j.

Answer:

it is the mode.

Step-by-step explanation:

i. e 5 is the most occuring number in the set of data listed above

Answer:

12x+40

Step-by-step explanation:

A=l*w

A=20(3/5x+2)

A=4*3x+20*2

A=12x+40

Answer:

[tex] = 12x + 40[/tex]

Step-by-step explanation:

[tex]area = l \times b \\ = 20 \times (\frac{3}{5} x + 2) \\ = \frac{60x}{5} + 40 \\ = 12x + 40[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

The selection probability to be assigned to each of the package designs is 0.20

Step-by-step explanation:

Firstly, we need to assume that one design is just as likely to be selected by a consumer as any other design

so the probability of selecting any of the design is same and that is 1/5 = 0.20

Thus, what we are trying to say is that each of the package designs have an equal selection probability of 0.20

The building height is 32 feet.

Let us consider that building height is x feet.

From attached diagram shown below,

Two triangles are formed.

Apply law of similarity of triangles.

Corresponding sides are in equal proportion.

                  [tex]\frac{x}{24}=\frac{12}{9} \\\\9x=12*24\\\\x=\frac{12*24}{9}=32 feet[/tex]

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Answer:

a. Discrete random variable

b. Discrete random variable

c. Discrete random variable

d. Discrete random variable

e. Continous random variable

f. Continous random variable

Step-by-step explanation:

a. The number of points scored during a basketball game.

This is a random variable, that only takes integer values, so it is a discrete random variable.

b. The number of free dash throw attempts before the first shot is made.

This is a count, so it is a discrete random variable.

c. The response to the survey question "Did you smoke in the last week question mark".

This is a boolean random variable (only two values), and can be considered discrete.

d. The number of people in a restaurant that has a capacity of 150.

This is a count of people, so it is a discrete random variable.

e. The time it takes for a light bulb to burn out.

Time is continous, so it is a continous random variable.

f. The height of a randomly selected giraffe.

Height, as it is a distance, is also a continous variable, so it is a continous random variable.

Answer:

9.222222222

Step-by-step explanation:

7+21+2+17+3+13+7+4+9 = 83

7+21+2+17+3+13+7+4+9 = 83 83÷9 = 9.222222222

_____________________________

Hey!!

Solution,

Given data=7,21,2,17,3,13,7,4,9

summation FX= 83

N(total no. of items)=9

Now,

Mean=summation FX/N

= 83/9

=9.23

So the answer is 9.23

__________________________

Answer:

  0.5 units

Step-by-step explanation:

The dilation factor is ...

  (GZ')/(GZ) = (GZ')/(GZ' +Z'Z) = 1.5/(1.5 +7.5) = 1/6

Side WX is 3 units, so side W'X' is (1/6)(3 units) = 1/2 units

W'X' is 0.5 units.

Answer:

It is .5 on edge

Step-by-step explanation:

I took the test

Answer:

y = -3/4x-1/4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b

where m is the slope and b is the y intercept

y = -3/4x +b

We have a point (-5,4)

4 = -3/4 (-5) +b

Changing to a common denominator

16/4 = 15/4 +b

subtracting 15/4 from each side

16/4-15/4 = -15/4 +15/4 +b

1/4 = b

y = -3/4x-1/4

Answer:

book

Step-by-step explanation:

kmgktn

Answer:

199

Step-by-step explanation:

i dont know

Answer:

1/4 probability of getting a product that isn't divisible by 2.

Step-by-step explanation:

These are all the possible outcomes

1 x 1 = 1    2 x 1 = 2    3 x 1 = 3     4 x 1 = 4     5 x 1 = 5      6 x 1 = 6

1 x 2 = 2   2 x 2 = 4   3 x 2 = 6     4 x 2 = 8    5 x 2 = 10    6 x 2 = 12

1 x 3 = 3  2 x 3 = 6    3 x 3 = 9     4 x 3 = 12   5 x 3 = 15   6 x 3 = 18

1 x 4 = 4   2 x 4 = 8   3 x 4 = 12     4 x 4 = 16   5 x 4 = 20  6 x 4 = 24

1 x 5 = 5   2 x 5 = 10  3 x 5 = 15   4 x 5 = 20  5 x 5 = 25  6 x 5 = 30

1 x 6 =  6   2 x 6 = 12  3 x 6 = 18   4 x 6 = 24   5 x 6 = 30  6 x 6 = 36

All of the outcomes that aren't divisible by 2 are in bold

There are 9 out of 36 possible outcomes that aren't divisible by 2

9/36 = 1/4

Answer:

The velocity is v(t) = 2*t + a

a) we want to find the average velocity betwen t = 0 and t = 1.

We can do this as:

Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a

b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.

For this we can see the integral:

[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]

Answer:

A. The probability that a randomly selected sports car from this manufacturer will be white with gray upholstery is P=0.12.

B. Assuming that we know the car has tan upholstery, the probability that the car is either silver or white is P=0.50.

Step-by-step explanation:

We first start by stating that the events "exterior color" and "leather color" are independent, so the probability of the outcomes of each event is not affected by the outcomes of the other event.

A. The probability of having a car that is white (W) with gray upholstery (G) is equal to the probability of having a car that is white multiplied by the probability of having a car with gray leather upholstery. Mathematically, this is:

[tex]P(\text{W\&G})=P(W)\cdot P(G)=0.3\cdot 0.4=0.12[/tex]

B. As the events are independent, the probability of having a silver or white car, given that the car has tan upholstery, is the same as the probabiltiy of having a silver or white car:

[tex]P(S\,or\,W | T)=P(S\,or\,W)=P(S)+P(W)=0.20+0.30=0.50[/tex]

[tex]0.84 \div 3 = 84 \div 300 = 0.28[/tex]

Answer:

x = 41 ft

Step-by-step explanation:

35(35+23) = 29(29+x)

2030 = 29(29+x)

70 = 29 + x

x = 41 ft

Answer:

1) Estimated slope = b₁ = 0.215

2) Estimated y-intercept = b₀ = -4.185

3) Not all the points predicted fall on the same straight line, but the model gives a close to ideal estimate of the line of best fit.

4) The estimated value of y when x=46 is 5.705

5) The value of the dependent variable y^ at x=0 is -4.185

6) The coefficient of determination = 0.951

Step-by-step explanation:

To solve this, we apply regression analysis

y = b₀ + b₁x

Price in Dollars | 23 | 34 | 40 | 46 | 47

Number of Bids | 1 | 3 | 4 | 5 | 7

For this question, we want to predict the number of bids (dependent variable, y), given the list price of the item (independent variable, x)

So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.

Σxᵢ = sum of all the independent variables (sum of all the list prices)

Σyᵢ = sum of all the dependent variables (sum of all the number of bids in the table)

Σxᵢyᵢ = sum of the product of each dependent variable and its corresponding independent variable

Σxᵢ² = sum of the square of each independent variable (list prices)

Σyᵢ² = sum of the square of each dependent variable (number of bids)

n = number of variables = 5

The scatter plot and the line of best fit is presented in the second attached image to this solution

Then the regression analysis is then done

Slope; m = b₁ = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]

Intercept b: b₀ = [Σyᵢ - m×(Σxᵢ)] / n

Mean of x = (Σxᵢ)/n

Mean of y = (Σyᵢ) / n

Sample correlation coefficient r: r =

[n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}

And -1 ≤ r ≤ +1

All of these formulas are properly presented in the third attached image to this answer

The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.

Hence, the regression equation is

y = -4.185 + 0.215x

y = b₀ + b₁x

Intercept = b₀ = -4.185

Slope = b₁ = 0.215

And the regression coefficient = 0.951 (Which is very close to 1 and indicates statistic significance)

Hence, we can use this answer obtained to answer the questions attached

1) Find the estimated slope.

Estimated slope = b₁ = 0.215

2) Find the estimated y-intercept.

Estimated y-intercept = b₀ = -4.185

3) Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Taking a few of sample data

x = 23 when y = 1

y = -4.185 + 0.215x

y = -4.185 + 0.215 (23) = 0.76 ≈ 1

x = 34, y = 3

y = -4.185 + 0.215 (34) = 3.125 ≈ 3

Hence, it is evident that not all the points predicted fall on the same straight line, but the model gives a close to ideal estimate of the line of best fit.

4) Find the estimated value of y when x=46.

The linear model is

y = -4.185 + 0.215x

when x = 46

y = -4.185 + 0.215(46) = 5.705

5) Determine the value of the dependent variable y^ at x=0.

y = -4.185 + 0.215x

when x = 0

y = -4.185 + 0.215(0) = -4.185

6) Find the value of the coefficient of determination.

The coefficient of determination = regression coefficient = 0.951 (as calculated above)

Hope this Helps!!!

Answer:

a. In the explanation.

b. The point estimate of the difference can be calculated as the difference between the sample mean and the population mean:

[tex]d=M-\mu=24.95-23.8=1.15[/tex]

c. Test statistic t = 0.90

P-value = 0.1932

The null hypothesis failed to be rejected.

Step-by-step explanation:

We have a sample, wich mean and standard deviation are calculated as:

[tex]M=\dfrac{1}{14}\sum_{i=1}^{14}(27.8+23.84+25.25+21+17.52+19.61+...+26.94+27.24)\\\\\\ M=\dfrac{349.34}{14}=24.95[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{14}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(27.8-(24.95))^2+(23.84-(24.95))^2+...+(27.24-(24.95))^2]}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(8.106)+(1.238)+...+(5.23)]}\\\\\\ s=\sqrt{\dfrac{304.036}{13}}=\sqrt{23.39}\\\\\\s=4.8[/tex]

This is a hypothesis test for the population mean.

The claim is that the consumption of milk in the Midwest is significantly higher than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=23.8\\\\H_a:\mu> 23.8[/tex]

The significance level is 0.01.

The sample has a size n=14.

The sample mean is M=24.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.8}{\sqrt{14}}=1.28[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{24.95-23.8}{1.28}=\dfrac{1.15}{1.28}=0.9[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=14-1=13[/tex]

This test is a right-tailed test, with 13 degrees of freedom and t=0.9, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>0.9)=0.1932[/tex]

As the P-value (0.1932) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the consumption of milk in the Midwest is significantly higher than the national average.

Answer:

No.

Step-by-step explanation:

A point has no length, height or depth. It only has position.

A line has one dimensional length.

Answer:

8.32 × 10^4

Step-by-step explanation:

The formula for the area of a triangle is 1/2×b×h.

1/2(320)(520) = 83,2000

83,200 in scientific notation is 8.32 × 10^4

Answer:

The simple interest rate is 5%.

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.

[tex]E = P*I*t[/tex]

[tex]630 = 4200*I*3[/tex]

[tex]I = \frac{630}{4200*3}[/tex]

[tex]I = 0.05[/tex]

The simple interest rate is 5%.

Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of  return of 6%?

We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]

So

[tex]E = P*I*t[/tex]

[tex]E = 4200*0.06*4[/tex]

[tex]E = 1008[/tex]

[tex]T = E + P = 4200 + 1008 = 5208[/tex]

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.