A part manufactured at a factory is known to be 12.05 cm long on average, with a standard deviation of 0.350. One day you suspect that that the part is coming out a little longer than usual, but with the same deviation. You sample 14 at random and find an average length of 12.20. What is the z-score which would be used to test the hypothesis that the part is coming out longer than usual?

Answer:

The mode is 23

Step-by-step explanation:

The function [tex]√(x^3 - 8)[/tex] at each x value is 0.25 * [-1.902 - 1.609].  The interval [2, 3] into subintervals and apply the respective formulas.

To approximate the integral ∫[2 to 3] √(x^3 – 8) dx using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule, we need to divide the interval [2, 3] into subintervals and apply the respective formulas. Let's compute the approximations for each rule.

Step 1: Determine the subinterval width, h.

We can calculate h using the formula:

h = (b - a) / n

Given:

a = 2

b = 3

Let's use different values of n for each rule.

For Trapezoidal Rule, let's set n = 4.

For Midpoint Rule, let's set n = 4.

For Simpson's Rule, let's set n = 2.

Step 2: Compute the approximations for each rule.

Using the Trapezoidal Rule:

Approximation = (h / 2) * [f(a) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(b)]

For n = 4:

h = (3 - 2) / 4 = 0.25

Approximation = (0.25 / 2) * [f(2) + 2f(2.25) + 2f(2.5) + 2f(2.75) + f(3)]

Evaluate the function √(x^3 - 8) at each x value:

f(2) ≈ √(2^3 - 8) ≈ -2

f(2.25) ≈ √(2.25^3 - 8) ≈ -1.726

f(2.5) ≈ √(2.5^3 - 8) ≈ -1.414

f(2.75) ≈ √(2.75^3 - 8) ≈ -1.125

f(3) ≈ √(3^3 - 8) ≈ -0.464

Approximation = (0.25 / 2) * [-2 + 2(-1.726) + 2(-1.414) + 2(-1.125) + (-0.464)]

≈ (0.125) * [-2 - 3.452 - 2.828 - 2.25 - 0.464]

≈ (0.125) * [-11.994]

≈ -1.49925

Using the Midpoint Rule:

Approximation = h * [f(x1) + f(x2) + ... + f(xn)]

For n = 4:

h = (3 - 2) / 4 = 0.25

Approximation = 0.25 * [f(2.125) + f(2.375) + f(2.625) + f(2.875)]

Evaluate the function √(x^3 - 8) at each x value:

f(2.125) ≈ √(2.125^3 - 8) ≈ -1.902

f(2.375) ≈ √(2.375^3 - 8) ≈ -1.609

f(2.625) ≈ √(2.625^3 - 8) ≈ -1.335

f(2.875) ≈ √(2.875^3 - 8) ≈ -1.073

Approximation = 0.25 * [-1.902 - 1.609]

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The chi-square test is used to test the claim of independence between marital status distribution in California and the expected distribution.

To test the claim that the distribution of marital status in California is as expected, the appropriate statistical test to use is the chi-square test for independence. The null hypothesis (H0) states that marital status and residency are independent, meaning the distribution of marital status in California is the same as it is nationally. The alternative hypothesis (Ha) suggests that the distribution of marital status in California is not the same as it is nationally.

The degrees of freedom for this test is calculated as (r - 1) * (c - 1), where r is the number of rows (4) and c is the number of columns (2). In this case, the degree of freedom is 3.

Using the observed frequencies and the expected frequencies, the chi-square test statistic is calculated. The p-value is then determined based on the test statistic and the degrees of freedom. The final conclusion is made by comparing the p-value to the significance level.

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Answer:

C. y = -x + 2

Step-by-step explanation:

Sana nakatulong

Answer:

B

Step-by-step explanation:

cus thats the formula

The number of people who received fewer than 100 spam messages in the university department is calculated below:

Total number of messages tagged as spam = 6693

Total number of people = 12

Total number of people who received more than 100 spam messages = 11

Number of people who received fewer than 100 spam messages = 1

The number of people who received fewer than 100 spam messages can be calculated by subtracting the total number of people who received more than 100 spam messages from the total number of people in the department.

Thus, the other 1 person received a total of: 6693 - (1818 + 1358 + 442 + 416 + 399 + 389 + 304 + 251 + 251 + 178 + 158 + 103) = 474

Graph illustrating the data collected from students and faculty in the department. it is clear that the majority of students and faculty members in the department received more than 100 spam messages. One person received fewer than 100 spam messages. The number of spam messages received seems to decrease with time, which may indicate that the spam filter is effective.

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The proportion of Shohei Ohtani's hitting the ball (batting average) decreased from 2018 to 2019. In 2018, Ohtani hit the ball 103 times out of 195 at-bats, resulting in a batting average of approximately 0.528.

In 2019, he hit the ball 54 times out of 179 at-bats, yielding a batting average of approximately 0.302. To determine whether Ohtani's batting average decreased from 2018 to 2019, we compare the proportions of hitting the ball in each year. Using a 1% significance level and assuming the Central Limit Theorem conditions hold, we can conduct a hypothesis test. The null hypothesis (H0) states that there is no difference in Ohtani's batting average between 2018 and 2019, while the alternative hypothesis (Ha) suggests a decrease in batting average.

To test the hypotheses, we can use a two-sample z-test for proportions. We calculate the sample proportions for hitting the ball in each year: p1 = 103/195 ≈ 0.528 in 2018 and p2 = 54/179 ≈ 0.302 in 2019. The standard error for the difference in proportions is given by the formula sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)), where n1 and n2 are the sample sizes.

Next, we calculate the test statistic z using the formula z = (p1 - p2) / sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)). The calculated z-value can be compared to the critical z-value at the 1% significance level (zα/2) to determine if we reject or fail to reject the null hypothesis.

In this case, the z-value is negative, indicating that the proportion of hitting the ball decreased from 2018 to 2019. By comparing the calculated z-value to the critical z-value, we can conclude that the decrease in Ohtani's batting average is statistically significant.

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Answer:

slope-intercept form: y= -5/4x-1

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

Angle A=68

Step-by-step explanation:

68+x+(x-24)=180

68+x+x-24=180

2x+44=180

2x=136

x=68

Answer:

33/12 or 2.75

Step-by-step explanation:

6 1⁄6 - 3 5⁄12

37/6 - 41/12

74/12 - 41/12

33/12 or 2.75

The subset satisfies all three conditions, it is a subspace of [tex]R^{3}[/tex].

To determine if the described set is a subspace, we need to check if it satisfies three conditions: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let's consider the subset of [tex]R^{3}[/tex] consisting of vectors of the form (a, b, c), where a = b = c.

Closure under addition: Let (a₁, b₁, c₁) and (a₂, b₂, c₂) be two vectors in the subset.

Their sum is (a₁ + a₂, b₁ + b₂, c₁ + c₂).

Since a₁ = b₁ = c₁ and a₂ = b₂ = c₂, we have (a₁ + a₂, b₁ + b₂, c₁ + c₂) = (a₁ + a₁, b₁ + b₁, c₁ + c₁) = (2a₁, 2b₁, 2c₁).

Since 2a₁ = 2b₁ = 2c₁, the sum is also in the subset.

Closure under scalar multiplication: Let (a, b, c) be a vector in the subset and let k be a real number.

The scalar multiple k(a, b, c) is (ka, kb, kc). Since ka = kb = kc, the scalar multiple is also in the subset.

Contains the zero vector: The zero vector is (0, 0, 0). Since 0 = 0 = 0, it is in the subset.

Therefore, the subset satisfies all three conditions, it is a subspace of [tex]R^{3}[/tex].

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Answer:

A is the answer.

Step-by-step explanation: It would go up about 2.2 i hope i helped! <3

Answer: A is your answer

Step-by-step explanation:

the answer would be b on scholar

Answer:

3 (x² + 5) (x - 2)

Step-by-step explanation:

3x³- 6x² + 15x - 30

=> 3 (x³ - 2x² + 5x - 10)

=> 3 [x²(x - 2) + 5 (x - 2)]

=> 3 (x² + 5) (x - 2)

Answer:

No

Step-by-step explanation:

Angle measures of a triangle must add up to 180 and this only adds up to 87

Answer:

(1,5) because, before it was at (3,8) and  

3 – 2 = 1      

8 – 3 = 5

For further explanation:

(3,8) / (2,3) = (1,5)

2 for 2 units left and 3 for 3 units down

Answer:

d . 19528

Step-by-step explanation:

maaf jika salah

Answer: 180 ft^3

Step-by-step explanation:

Answer: 180 ft is the answer

Step-by-step explanation:

Answer:

3.14 square inches or π square inches

Step-by-step explanation:

The radius of a circle is 1 inch. What is the area?

r=1 in

The formula for the area of a circle is given as:

πr²

The radius (r) = 1 inch

Hence,

Area of the circle = π × 1²

= 3.1415926536 square inches

Approximately = 3.14 square inches or we can say that the Area of the circle = π square inches

Answer:

400

1.05

Step-by-step explanation:

The athlete should take the second offer.

It is given by the formula,

A = P(1+r)ⁿ

where A is the value after n period of time, P is the initial amount, and,

r is the rate of increment or decrement.

Now, Total amount = $400,000(1+5%)⁷

                    = $400,000(1+0.05)⁷

                    = $400,000(1.4071)

                    = $562840.17

Now, the total amount that the pro-athlete will get in 8 years is,

Total amount = $425,000(1+4%)⁷

                    = $425,000(1+0.04)⁷

                    = $425,000(1.3159)

                    = $559,271

Since the total amount that the athlete will get in the next 8 years is more for the second offer, the athlete should take the second offer.

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Answer:

c

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

p=k√q

8=k√25

8=k5

k=8/5

p when q=100

p=8/5*√100

p=8/5*10

p=16

Answer: $10

Step-by-step explanation:

Let Josie's money be x

Since Joe has half as much as Josie. Joe's money will be: x/2 = 0.5x

Bob has four times as much money as Joe. Bob's money will be = (4 × 0.5x) = 2x

Therefore, we add all the amount together and equate to $35. This will be:

x + 0.5x + 2x = 35

3.5x = 35

x = 35/3.5

x = 10

Josie has $10

Answer:

*Pew Pew*

Step-by-step explanation:

Answer:

8!

Step-by-step explanation:

Answer) 8!

Explanation) i dont have one :')

Answer:

i think ist D correct me if im wrong

Step-by-step explanation:

Answer:

22.7

Step-by-step explanation:

if ∡M is 90° then you can do:

sin 65 = h/25

h = 25(sin 65°)

h = 22.65

Answer:

Step-by-step explanation:

Question 13.

By applying cosine rule,

cos(45°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{10}{y}[/tex]

y = 10√2

By applying sine rule,

sin(45°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{x}{y}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{x}{10\sqrt{2} }[/tex]

x = 10

Question 15.

By applying sine rule,

sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{y}{32}[/tex]

y = 16√3

By applying cosine rule,

cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{2}=\frac{x}{32}[/tex]

x = 16

Question 17.

By applying sine rule,

sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{11\sqrt{3} }{y}[/tex]

y = 22

By applying cosine rule,

cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{2}=\frac{x}{y}[/tex]

[tex]\frac{1}{2}=\frac{x}{22}[/tex]

x = 11

Answer:

3.9mm

Step-by-step explanation: