The following scatter plot depicts the number of chicken pox cases after 1988. The variable x represents the number of years after 1988. The variable y represents the number of cases in thousands.
A graph has number of years after 1988 on the x-axis, and reported cases (thousands) on the y-axis. Points trend on a negative line.
Does there appear to be a linear relationship? Explain your answer.
a.
Yes, there is a linear relationship. The data appears to have a negative correlation.
b.
Yes, there is a linear relationship. The data appears to have a positive correlation.
c.
No, there is not a linear relationship. The data seems random.
d.
No, there is not a linear relationship. There is no line which goes through all the points.

1. When a fair die is tossed the expected value E[X1] = 3.5 and the variance var(X1) = 35/12.

When a fair die is tossed, each of the six possible outcomes has an equal probability of 1/6. Let X1 denote the score obtained in the first toss.

To calculate the expected value E[X1], we find the sum of all possible values of X1 multiplied by their respective probabilities:

E[X1] = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5

To calculate the variance var(X1), we use the formula:

var(X1) = E[X1^2] - (E[X1])^2

First, we find E[X1^2] by taking the sum of the squares of all possible values of X1 multiplied by their respective probabilities:

E[X1^2] = (1^2 * 1/6) + (2^2 * 1/6) + (3^2 * 1/6) + (4^2 * 1/6) + (5^2 * 1/6) + (6^2 * 1/6) = 91/6

Substituting the values into the formula, we calculate var(X1):

var(X1) = (91/6) - (3.5)^2 = 35/12

Therefore, E[X1] = 3.5 and var(X1) = 35/12.

2. The probability distribution of Y = |X1 - X2| is tabulated as follows:

Y |X1 - X2| P(Y)

0 0 1/6

1 1 2/6

2 2 2/6

3 3 1/6

To calculate E[Y], we find the sum of all possible values of Y multiplied by their respective probabilities:

E[Y] = (0 * 1/6) + (1 * 2/6) + (2 * 2/6) + (3 * 1/6) = 1

Therefore, E[Y] = 1.

3. The statements E(Z^2) = E(Y^2) and Var(Z) = Var(Y) are false.

E(Z^2) and E(Y^2) represent the expected values of the squares of the random variables Z and Y, respectively. Since Z = X1 - X2 and Y = |X1 - X2|, the squares of Z and Y have different probability distributions, leading to different expected values.

Similarly, Var(Z) and Var(Y) represent the variances of Z and Y, respectively. Since Z and Y have different probability distributions, their variances will generally not be equal.

Therefore, E(Z^2) ≠ E(Y^2) and Var(Z) ≠ Var(Y).

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Answer: 6 liters

Step-by-step explanation:

24 liters

He sells 75%

24 x 0.75 = 18 liters

24 - 18 = 6

He still has 6 liters left

Answer:

65 girls and 45 boys

Step-by-step explanation:

Add 4.5

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hope it helps

Answer: add 4.5 to both sides

Step-by-step explanation: this will allow the 4.5 to be removed from the y side and since you added it to one side you have to add it to the other side. This will give your y the value of 16.7.

Brainliest plz

Answer:

42+123+x=180

x=180-165

x=15 degrees

Step-by-step explanation:

Answer:

the answer is rotation

hope this helps

Answer:

Scalene

Step-by-step explanation:

Because all 3 sides have different length.

When all 3 sides have the same length: equilateral

When 2 sides have the same length but the 3rd side has a different length: isosceles

When all 3 sides have different length: scalene

Answer:

c. 322

Step-by-step explanation:

Surface area of cylinder = 2πr² + 2πrh.

SA in terms of π = π(2r² + 2rh) →

π(2(7)² + 2(7)(16)) →

π(2(49) + 2(112)) → π(98 + 224) → π(322)

The two way table given by option z is a possible representation of the data collected.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

From the first table, we have that:

Then, for the basic packages, we have that resorts were chosen 2.5 times more than tours, while cruises were chosen 1.5 times more than tours.

Option z shows these same ratios between the amounts, hence it is the correct option.

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Answer:

y = 8

Step-by-step explanation:

Both of the points have the same y, which is 8, meaning that if the line passed through both of those points, then it has to be horizontal, meaning the equation is y = 8   Also, there is no x in the equation because the slope is 0.

Answer:

3

Step-by-step explanation:

Answer:

y = 7x

Step-by-step explanation:

you mutiply 7 times 1=7

you just continue to do that

Answer:

46

Step-by-step explanation:

Answer:

x=46

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

4x +8 = 2x -8

4x = 2x - 16

2x = -16

x = -8

Answer:

12

Step-by-step explanation:

1/5 mint = 6

30 - 6 = 24

Half of 24 is 12

12 is chocolate

so 12 must be vanilla

Answer:

I would need to see the different tables to answer this question.

The corresponding z-scores for the given observations can be calculated using the formula:

[tex]\[z = \frac{{x - \mu}}{{\sigma}}\][/tex]

where [tex]\(x\)[/tex] is the observation, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.

For the baby born in week 34 weighing 2875 grams:

[tex]\[z_{34} = \frac{{2875 - 2500}}{{600}} = 0.625\][/tex]

For the baby born in week 41 weighing 3175 grams:

[tex]\[z_{41} = \frac{{3175 - 2800}}{{415}} = 0.904\][/tex]

To determine which baby weighs more relative to the gestation period, we compare the z-scores.

A. The baby born in week 34 weighs relatively more since its z-score 0.625 is smaller than the z-score 0.904 for the baby born in week 41.

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Answer:

x={3,-7}

Step-by-step explanation:

brackets for list

Solve with quadratic formula

separate the solutions

Square

Answer:

2 for the first box and 25 for the second one.

Step-by-step explanation:

Answer:

okay then

Step-by-step explanation:

Answer: gtyrehretr

Step-by-step explanation:

Answer:

15 by 2

Step-by-step explanation:

15 cubes in each layer with 2 layers

Answer:

Cubes in each layer: 15

Number of layers: 2

Volume : 30 cm^3

Step-by-step explanation:

Answer:

4324eqW

Step-by-step explanation:

3 + 5 =7

the test statistic (t = -12.857) is smaller than the critical value (-1.860), we have enough evidence to reject the null hypothesis.

To test the hypothesis regarding the population mean, we can perform a one-sample t-test.

Given:

- Null hypothesis (H₀): μ = 13

- Alternative hypothesis (Hₐ): μ < 13

- Sample mean ([tex]\bar{X}[/tex]) = 10

- Sample standard deviation (s) = 0.7

- Sample size (n) = 9

- Significance level (α) = 0.05

To conduct the t-test, we can calculate the test statistic and compare it with the critical value from the t-distribution.

The test statistic (t-score) is calculated as:

t = ([tex]\bar{X}[/tex] - μ) / (s / √n)

Plugging in the values:

t = (10 - 13) / (0.7 / √9)

t = -3 / (0.7 / 3)

t = -3 / 0.233

t ≈ -12.857

To determine the critical value, we need to find the appropriate degrees of freedom (df) for a one-sample t-test. In this case, df = n - 1 = 9 - 1 = 8.

Using a significance level of α = 0.05 and looking up the critical value for df = 8 in the t-distribution table, we find the critical value to be approximately -1.860.

Since the test statistic (t = -12.857) is smaller than the critical value (-1.860), we have enough evidence to reject the null hypothesis.

Decision: Based on the test results, at α = 0.05, we reject the null hypothesis (H₀: μ = 13). There is sufficient evidence to support the alternative hypothesis (Hₐ: μ < 13), suggesting that the population mean is less than 13.

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Given question is incomplete, the complete question is below

Assuming the sample was taken from a normal population, test at α = 0.05 and state the decision. Họ: μ = 13 HA: μ < 13 [tex]\bar{X}[/tex]= 10 s= 0.7 n = 9

Answer:what’s classification

Step-by-step explanation:

Answer: 9 x 6 x 6

Step-by-step explanation: 9 x 6=54  54 x 6 = 324 ft

Answer:

not a right triangle

Step-by-step explanation:

you can use the pythagorean theorem to prove whether not this is a right triangle

if this triangle is a right triangle then the following equality should be true

a²+b²=c²

(9.75)²+(3.45)²=(10.24)²

(95.06)+(11.90)=(104.86)

106.96≠104.86

since the following equality is not true, this is not a right triangle.