The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if the average exam score will be higher for students who are given colored pens on the first day of class. The final exam scores for the 17 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 78, 74, 89, 76, 92, 81, 87, 77, 79, 75, 81, 52, 80, 98, 72, 78 What can be concluded at the 0.05 level of significance

Answer:

18

Step-by-step explanation:

It is 18. Just simply count the dots and sum them all up together, and you get 18. Unless there is a specific thing needed.

Answer:

11/20

Step-by-step explanation:

55% = 55/100

55/100 = 11/20

Answer: javier is taller

Step-by-step explanation:

68inches=5' 8"

Answer:

I'm pretty sure no because a square always has 4 right angles and all sides are the same length

the parallelogram could possibly be a rectangle tho

I could be completely wrong but I hope this helps

Answer:

x = -6.4 and y = -3.6

Step-by-step explanation:

The given system of equations are :

[tex]y=\dfrac{3}{2}x+6[/tex] ....(1)

and

[tex]y=\dfrac{x}{4}-2[/tex] ....(2)

We need to solve equation (1) and (2).

From equation (1) and (2),

[tex]\dfrac{3}{2}x+6=\dfrac{x}{4}-2[/tex]

Taking like terms together,

[tex]\dfrac{3}{2}x-\dfrac{x}{4}=-2-6\\\\\dfrac{6x-x}{4}=-8\\\\x=-6.4[/tex]

Put the value of x in equation (1).

[tex]y=\dfrac{3}{2}(-6.4)+6\\\\=-3.6[/tex]

So, the values of x and y are x = -6.4 and y = -3.6

Answer:

7

Step-by-step explanation:

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The Poisson distribution with a parameter λ = 1 accurately models the production stoppages, where on average, the company experiences one stoppage per month with a relatively small amount of variability.

The  scenario describes a company's production stoppages, which can be modeled using a Poisson distribution with a parameter (mean) of λ = 1. In a Poisson distribution, the mean, variance, and standard deviation are all equal.

The mean (μ) represents the average number of stoppages per month, which in this case is 1. This means that, on average, the company experiences one production stoppage per month.

The variance (σ^2) also has a value of 1 in a Poisson distribution. It measures the spread or variability of the data around the mean. In this case, the variance of 1 indicates that there is some fluctuation in the number of stoppages, but it is relatively small.

The standard deviation (σ) is equal to the square root of the variance, which is also 1 in this scenario. It represents the average amount of deviation from the mean. A standard deviation of 1 suggests that most of the observations will be within one unit of the mean.

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The number of degrees of freedom for treatment are 4.

Degrees of freedom is a statistical term that refers to the number of values in a calculation that are free to vary. It is a common concept in statistical inference. In general, degrees of freedom represent the number of observations in a statistical analysis that are free to vary.To find the degrees of freedom for treatment, the formula is (k - 1), where k is the number of treatment groups. In this case, there were 5 treatment groups, so the degrees of freedom for treatment would be (5 - 1) = 4.

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The sum of - -5, 3, -269, -243, 1, -3 and +9 is -507.

Integers are all whole numbers, either positive, negative or zero. In other words, integers are numbers that don’t have any fractional part. Integers can be represented as follows: {...-3, -2, -1, 0, 1, 2, 3...}

To add integers: Keep the sign of the number that is farthest from zero.

Perform the indicated operation for the rest of the numbers.

Addition of integers is easy.

When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value.

The sign of the answer is the same as the sign of the integer with the larger absolute value.

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Answer:

y=5000(1.04)^t

Step-by-step explanation:

Given data

Cost of painting=$5000

Rate of increase=4%

the exponential increase expression is

y=P(1+r)^t

      Where y= the total amount after growth

                  P= the initial cost of the painting

                  r= the rate of increase

                  t= the time interval

y=5000(1+0.04)^t

y=5000(1.04)^t

Answer: 3,3

Step-by-step explanation:

The expected characteristic path length (average distance) of a random network with 104 nodes and an average degree (k) of 10 is approximately 2.

The characteristic path length of a network measures the average distance between any two nodes in the network. For a random network, the expected characteristic path length can be approximated using the formula:

L ≈ ln(N) / ln(k),

where N is the number of nodes and k is the average degree.

Substituting N = 104 and k = 10 into the formula, we have:

L ≈ ln(104) / ln(10) ≈ 2.040

Rounding to the nearest integer, we get L ≈ 2.

Therefore, the expected characteristic path length of the network is approximately 2.

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The 95% confidence interval for the mean sodium content of the "reduced sodium" hot dogs is calculated to be (297.70 mg, 322.30 mg).

To find the 95% confidence interval, we use the formula:
Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √sample size)
Given that the sample mean sodium content is 310 mg, the standard deviation is 36 mg, and the sample size is 40, we need to determine the critical value for a 95% confidence level.The critical value corresponds to the level of confidence and the degrees of freedom, which is the sample size minus 1. Looking up the critical value for a 95% confidence level and 39 degrees of freedom in the t-distribution table, we find it to be approximately 2.024.
Plugging in the values into the formula, we get:
Confidence Interval = 310 mg ± (2.024) * (36 mg / √40)
Simplifying the expression, we find:
Confidence Interval ≈ (297.70 mg, 322.30 mg)Therefore, we can say with 95% confidence that the mean sodium content of this brand of "reduced sodium" hot dogs falls within the range of 297.70 mg to 322.30 mg.

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Answer:

-5x-16

Step-by-step explanation:

Combine like terms

Step-by-step explanation:

If you want to multiply a parenthesis by a number, you simply distribute the number to all the terms in the parenthesis.

So, if you want to multiply the parenthesis

(3x−7) by 5, you need to multiply by 5

both 3x and −7.

We have that 5⋅(3x)=5⋅(3⋅x)=(5⋅3)⋅x=15x and −7⋅5=−35

So, 5(3x−7)=15x−35

a. Calculation of Coefficient of Variation for each data set

Data set 1: 16 24 17 22$${\rm Mean }\ \overline{x} = \frac{16 + 24 + 17 + 22}{4} = 19.75$$

Variance σ² $= \frac{1}{N} \sum_{i=1}^{N}(x_i - \overline{x})^2$ $= \frac{(16-19.75)^2 + (24-19.75)^2 + (17-19.75)^2 + (22-19.75)^2}{4}$ $= 16.1875$

Standard deviation $σ = \sqrt{16.1875} = 4.0218$ Coefficient of variation, $CV = \frac{σ}{\overline{x}}$ $= \frac{4.0218}{19.75} = 0.2031$Therefore, the coefficient of variation for data set 1 is 20.31%.Data set 2: 2 7 1 8 200 5${\rm Mean}\ \overline{x} = \frac{2 + 7 + 1 + 8 + 200 + 5}{6} = 36.833$Variance σ² $= \frac{1}{N} \sum_{i=1}^{N}(x_i - \overline{x})^2$ $= \frac{(2-36.833)^2 + (7-36.833)^2 + (1-36.833)^2 + (8-36.833)^2 + (200-36.833)^2 + (5-36.833)^2}{6}$ $= 10627.0246$ Standard deviation $σ = \sqrt{10627.0246} = 103.0792$

Coefficient of variation, $CV = \frac{σ}{\overline{x}}$ $= \frac{103.0792}{36.833} = 2.7971$

Therefore, the coefficient of variation for data set 2 is 279.71%.

b. Identifying the data set with less consistency (or more variability) To determine which data set has less consistency (or more variability), we need to compare their coefficients of variation. A higher coefficient of variation implies higher variability or inconsistency in the data. Therefore, the correct answer is option C: Data set 2 has less consistency (or more variability) because its coefficient of variation is greater.

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Answer: 1/12

Step-by-step explanation:

The null hypothesis (H0): μ = 4 and alternative hypothesis (Ha): μ ≠ 4. The correct option is C.

The null hypothesis states that the mean age at which American children first read is equal to 4 years. The alternative hypothesis states that the mean age is not equal to 4 years.

In this case, the researcher is interested in whether the mean age has changed from 4 years. Therefore, the alternative hypothesis is two-tailed, meaning that the mean age could be either greater than or less than 4 years.

The null hypothesis is always tested against the alternative hypothesis. If the null hypothesis is rejected, then the researcher can conclude that there is evidence to support the alternative hypothesis. In this case, if the null hypothesis is rejected, then the researcher can conclude that the mean age at which American children first read has changed from 4 years.(Option-c)

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Ill-conditioned means that the problem or system being considered is sensitive to small changes in the input or data, leading to unstable or inaccurate results.

When solving a least squares problem using the normal equations, ill-conditioning refers to situations where the matrix involved is nearly singular or has a high condition number.

This means that small perturbations or errors in the data can result in large changes in the computed solution.

In the context of QR factorization, if the normal equations for a least squares problem are ill-conditioned, it implies that the matrix being decomposed using QR factorization is close to being singular or has a high condition number. QR factorization can help in such cases by providing a more stable and accurate solution compared to directly solving the normal equations.

QR factorization decomposes a matrix into the product of an orthogonal matrix Q and an upper triangular matrix R. This factorization can help mitigate the effects of ill-conditioning by providing a numerically stable way to solve the least squares problem.

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Answer:

38.5

Step-by-step explanation:

(a) The area under the curve is 154 square units.

(b) The exact area of the region between the curve y= f(x) and the x-axis is (118 / 3) square units.

(a) The given function is f(x) = 25 - x² .

We need to estimate the area under the graph between x = - 3 and x = 5 by dividing the interval [-3, 5] into 4 subintervals each of the same length by using left-hand and midpoint approximation and sketch the 4 rectangles that approximates the area under the curve.

The width of each rectangle is given by Δx, where Δx = (b - a) / n = (5 - (-3)) / 4 = 2.

The height of each rectangle is determined by either left-hand approximation or midpoint approximation.

1. Left-hand approximation: In the left-hand approximation method, the height of each rectangle is taken from the left endpoint of each subinterval. We have:

Left endpoint of the 1st subinterval is x₁ = -3 Left endpoint of the 2nd subinterval is x₂ = -1 Left endpoint of the 3rd subinterval is x₃ = 1 Left endpoint of the 4th subinterval is x₄ = 3

Thus, the heights of the four rectangles are: f(x₁) = f(-3) = 16f(x₂) = f(-1) = 24f(x₃) = f(1) = 24f(x₄) = f(3) = 16

We sketch the four rectangles as follows:

The total area of the four rectangles is the sum of the individual areas of the rectangles.

We have: Area ≈ [f(-3) + f(-1) + f(1) + f(3)] Δx= [16 + 24 + 24 + 16] × 2= 80 square units.2.

Midpoint approximation: In the midpoint approximation method, the height of each rectangle is taken from the midpoint of each subinterval.

We have: Midpoint of the 1st subinterval is x₁* = -2 Midpoint of the 2nd subinterval is x₂* = 0 Midpoint of the 3rd subinterval is x₃* = 2 Midpoint of the 4th subinterval is x₄* = 4

Thus, the heights of the four rectangles are: f(x₁*) = f(-2) = 21f(x₂*) = f(0) = 25f(x₃*) = f(2) = 21f(x₄*) = f(4) = 9

We sketch the four rectangles as follows:

The total area of the four rectangles is the sum of the individual areas of the rectangles.

We have:

Area ≈ [f(-2) + f(0) + f(2) + f(4)] Δx= [21 + 25 + 21 + 9] × 2= 154 square units.

(b) The exact area of the region between the curve y = f(x) and the x-axis on the interval [-3, 5] is given by the limit of a Riemann sum as the number of subintervals n approaches infinity.

We have:

Area = ∫[(-3, 5)] f(x) dx= ∫[-3, 5] (25 - x²) dx

= [25x - (x³ / 3)]|[-3, 5]

= [125 - (125 / 3)] - [-75 + (27 / 3)]

= (100 / 3) + (18 / 3)

= (118 / 3) square units.

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Answer:

B

Step-by-step explanation:

bdeehvdvjwjkwkwwjehheeh

If you dont know the anwser its always B

Answer:

80

Step-by-step explanation:

the answer is 80 because 8×10=80

Answer:

116

Step-by-step explanation:

Area of whole thing is 196 and area of grass is 80 so you do 196-80 to get 116.

Answer:

Its cost about 1.5625

if you rounded its 1.56 :)

Step-by-step explanation:

Answer:

I believe she would have to spend 2 days on vacation.

Step-by-step explanation:

She already have 7 pictures and she takes 1 a day. Therefore, she would have to spend 2 days on vacation to get 9 pictures.

After considering the given data we conclude that one tailed test can be utilised for this claim.

To test the claim about the proportion of students involved in extracurricular activities, we would employ a one-tailed test.
A one-tailed test is applied when the alternative hypothesis is directional, which projects the it predicts the direction of the difference between the sample proportion and the claimed proportion. For the given case, the alternative hypothesis will be that the proportion of attending students involved in at least one extracurricular activity is greater than 70%.
Hence, we would use a one-tailed test to test this claim.
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(a) The basis for the null-space N(T) is any vector Y that equals -1

(b) The basis for the range R(T) is the set {-10/23, -20/23}.

The basis for the null-space N(T) of the linear operator T, we need to solve the equation T(Y) = 0. Let's express this equation and find its solutions

1 - 23T(Y) = X + 4Y - 22 × 3.0 + 2Y - X + 4Y + 32

Simplifying the equation, we get:

-23T(Y) = 10Y + 10

Dividing both sides by -23, we have:

T(Y) = (-10/23)Y - (10/23)

To find the null-space, we set T(Y) equal to zero:

(-10/23)Y - (10/23) = 0

Simplifying further, we get:

(-10/23)Y = (10/23)

Multiplying both sides by -23/10, we obtain:

Y = -1

Therefore, any vector Y that equals -1 will satisfy the equation T(Y) = 0.

Now, let's find the basis for the range R(T) of the linear operator T. The range is the set of all possible values that T(Y) can take. To find this, we need to consider all possible values for Y and calculate T(Y) for each value.

Let's choose two arbitrary values for Y and calculate T(Y):

For Y = 0

T(0) = -10/23 × 0 - 10/23

T(0) = -10/23

For Y = 1

T(1) = -10/23 × 1 - 10/23

T(1) = -20/23

Therefore, the range R(T) consists of the values -10/23 and -20/23.

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