The management of a large hardware store is interested in estimating the difference between the mean dollar amount of purchases made by customers who use the store's credit card and the mean dollar amount of purchases made by customers who use a different credit card. A random sample of 74 customers who used the store's credit card showed a mean purchase of $107 with a standard deviation of $12. A separate random sample of 58 customers who used a different credit card showed a mean purchase of $132 with a standard deviation of $9. Technology was used to calculate that the correct number of degrees of freedom is 129.78. Which of the following represents the margin of error for a 98 percent confidence interval to estimate the difference in the mean purchase amount for the two types of credit cards? 2.355 ® 2.355 © 2.326,+ B 2.326, the 2.326, +

The statement which says "The intersection of three planes can be a ray." is; True

In terms of line segments, the intersection of a plane and a ray can be a line segment.

Now, for the given question which states that the intersection of three planes can be a ray. This statement is true because it meets the definition of plane intersection.

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Answer:

False

Step-by-step explanation:

Saw a one star rating on the other answer, so I put false as my answer and got it correct.

Answer:

Area if figure = 22 m²

Step-by-step explanation:

Given:

Length of rectangle = 8 m

Width of rectangle = 1 m

Base of triangle = 8 m

Height of triangle = 3.5 m

Find:

Area if figure

Computation:

Area if figure = Area of rectangle + Area of triangle

Area if figure = [l x b] + [(1/2)(b)(h)]

Area if figure = [8 x 1] + [(1/2)(8)(3.5)]

Area if figure = 8 + 14

Area if figure = 22 m²

Answer:

x > 3/14

Step-by-step explanation:

Answer:

Step-by-step explanation:

-14x > -3

x < -3/-14

x < 3/14

The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).

The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.

The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.

The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.

(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.

So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Answer:2/16

Step-by-step explanation:

Answer:

= 64

do u need the working out?

Using a confidence level of 95%, the margin of error for the mean GRE score of graduate students is approximately 14.15. The upper bound of the confidence interval is 314.15, and the lower bound is 285.85. This means we are 95% confident that the true population mean GRE score falls between these two values.

To calculate the margin of error, we use the formula:

Margin of Error = Z * (Standard Deviation / √n)

In this case, the standard deviation is 47 and the sample size (n) is 50. The Z-value for a 95% confidence level is approximately 1.96. Plugging in these values, we get:

Margin of Error = 1.96 * (47 / √50) ≈ 14.15

This means that the sample mean of 300 is expected to be within 14.15 points of the true population mean GRE score.

The confidence interval is then constructed by adding and subtracting the margin of error from the sample mean:

Confidence Interval = (Sample Mean - Margin of Error, Sample Mean + Margin of Error)

= (300 - 14.15, 300 + 14.15) = (285.85, 314.15)

Interpreting the confidence interval, we can say that we are 95% confident that the true population mean GRE score for graduate students falls within the range of 285.85 to 314.15. This means that if we were to repeat the sampling process and calculate the sample mean GRE scores multiple times, approximately 95% of the confidence intervals obtained would contain the true population mean.

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The Freeze Zone batch does not align with Ari's ideal milkshake in terms of the scoop-to-caramel ratio.

To calculate the value of the expression \(2^5 * 6^(^-^5^)\), we can simplify it as follows:

\(2^5 = 2 *2 * 2 * 2 * 2 = 32\)

\(6^(^-^5^) = 1 / 6^5 = \frac{1}{(6 * 6 * 6 * 6 * 6) } = \frac{1}{ 7776}\)

So, the expression \(2^5 * 6^(^-^5^)\) can be written as:

\(32 *(1 / 7776) = \frac{32}{ 7776}\)

Now, let's address the second part of your statement. Ari thinks that the perfect milkshake has 555 scoops of ice cream for every 333 spoonfuls of caramel.

Freeze Zone makes batches of milkshakes with 101010 scoops of ice cream and 777 spoonfuls of caramel.

Comparing the quantities, we can see that the number of scoops of ice cream in the Freeze Zone batch (101010) is greater than the number Ari considers perfect (555). Similarly, the number of spoonfuls of caramel in the Freeze Zone batch (777) is not equal to the number Ari considers perfect (333).

Therefore, the Freeze Zone batch does not align with Ari's ideal milkshake in terms of the scoop-to-caramel ratio.

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Answer:

About 69cm²

Explanation:

A = d

A = 3.14(22)

A = 69.08

Answer:

The gradient is the same as the slope. To find the slope, let's convert this from standard form to slope-intercept form.

4x - 3y + 5 = 0

4x + 5 = 3y

4/3x + 5/3 = y therefore the answer is 4/3.

The researcher is assessing item equivalence, If a study is in parallel forms of the measurement instrument to the same person. The correct option is C).

When a study introduces parallel forms, the researcher is assessing item equivalence. Item equivalence refers to the extent to which the different forms of the measurement instrument produce similar results for the same individual.

This assessment is crucial in research because it allows researchers to evaluate the consistency and reliability of the measurement instrument across different versions. By administering parallel forms to the same person, any differences in responses can be attributed to individual factors rather than variations in the instrument.

This helps ensure that the instrument is measuring the intended construct consistently and accurately. The correct option is C).

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Answer: 0

Step-by-step explanation:

The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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Answer:

Choice C

According to the graph, f(2) = 2

Answer:

54.8 Nm

Step-by-step explanation:

Torque is the cross product of the radius vector and force vector:

τ = r × F

Another way to write it is the product of the radius and force magnitudes times the sine of the angle between the vectors.

τ = rF sin θ

Here, r = 0.366 meters and F = 155 Newtons.  F is in the +y direction, and r is 15° below the +x axis, so the angle between the vectors is 90° − 15° = 75°.

τ = (0.366 m) (155 N) (sin 75°)

τ = 54.8 Nm

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The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

2/3

Step-by-step explanation:

16/4=4

24/4=6

4/6 divided by 2= 2/3

Answer: 70

Step-by-step explanation:

Note that we can find the number of ways to choose 4 numbers out of the 8 to represent the unordered triple \((a,b,c,d)\). The other 4 numbers will represent the unordered triple \((e,f,g,h)\). For each of these triples, there is only one allowed permutation because the numbers need to be in sequential order.

So, the final answer is \(\binom{8}{4}=70\).

Answer:

The magnitude of a vector is the length of the vector. The magnitude of the vector a is denoted as ∥a∥.

Answer:

(C) It is warm year-round because it is close to the equator.

Step-by-step explanation:

This is what the tropical rainforest environment is like :)

Answer:

C)

Step-by-step explanation:

Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3\)

After you collect your data, you have several options in regards to the null hypothesis. First, you could fail to reject the null hypothesis.

The data did not provide enough evidence to support the alternative hypothesis, and you accept the null hypothesis as the most likely explanation. Second, you could reject the null hypothesis. This means that your data provided enough evidence to support the alternative hypothesis, and you reject the null hypothesis as the most likely explanation. To neither accept nor reject the null hypothesis. The less common option and occurs when your data does not provide enough evidence to reject the null hypothesis, but also does not provide enough evidence to accept it as the most likely explanation.

The null hypothesis after you collect your data include failing to reject it, rejecting it, or neither accepting nor rejecting it.

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The sin(x) = -3/5, cos(x) = -4/5, and tan(x) = 3/4.

Given that cos(x) = -4/5 and 180° < x < 270°, we can determine the values of sin(x) and tan(x) using trigonometric identities.

Using the identity \(sin^2(x) + cos^2(x) = 1\), we can find sin(x) as follows:

\(sin^2(x) = 1 - cos^2(x)\\sin^2(x) = 1 - (-4/5)^2\\sin^2(x) = 1 - 16/25\\sin^2(x) = 9/25\)

sin(x) = ±√(9/25) = ±3/5

Since 180° < x < 270°, the sine value should be negative:

sin(x) = -3/5

Next, we can find tan(x) using the identity tan(x) = sin(x)/cos(x):

tan(x) = (-3/5) / (-4/5)

tan(x) = 3/4

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The limit of the function f(x,y) = sin(√( 4x^2+y^2 ))/√( 4x^2+y^2 ) as (x,y) approaches (0,0) is -1.

To find the limit of the function f(x,y) as ( x,y ) approaches (0,0), we can use the squeeze theorem

First, note that -1 ≤ sin(t)/t ≤ 1 for all t, so we have

-1 ≤ sin(√( 4x^2+y^2 ))/√( 4x^2+y^2 ) ≤ 1

Multiplying all sides by -1, we get

-1 ≥ -sin(√(4x^2+y^2))/√(4x^2+y^2) ≥ -1

Now, we can apply the squeeze theorem:

\(\lim_{(x,y) \to \((0,0))}\) -1 = -1

\(\lim_{(x,y) \to \((0,0))}\)  -sin(√(4x^2+y^2))/√(4x^2+y^2) = -1

\(\lim_{(x,y) \to \((0,0))}\)  -1 = -1

Therefore, by the squeeze theorem, we have

\(\lim_{(x,y) \to \((0,0))}\) sin(√(4x^2+y^2))/√(4x^2+y^2) = -1

Thus, the limit of the function f(x,y) as (x,y) approaches (0,0) is -1.

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Answer:

Clarice is right because you can flip the triangle and it makes a different shape every single time.

Step-by-step explanation:

Hope i helped.

A brainliest is always apprciated.

Based on the information provided, it appears that the regression model has found a statistically significant relationship between the outcome variable and the response variables while controlling for the effects of the two co-variables.

However, the R2 value of only 11.5% suggests that the model is explaining only a small portion of the variability in the outcome variable. This may indicate that there are other important factors that are not being accounted for in the model. It is also possible that the co-variables included in the model are not strong predictors of the outcome variable. Further investigation and analysis may be needed to fully understand the relationship between the variables and to improve the predictive power of the model.

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Answer:

it is 1/5

Step-by-step explanation:

.............

(An algebraic expression) may be the answer

Answer:

fx/gx=10

Step-by-step explanation:

fx= (36x5)-(44x4)-(28x3)

fx=80

gx= 4x2

gx=8

To work out fx/gx:

fx/gx=80/8

fx/gx=10