Consider the list (5, 4, 4, 8, 9). The average of this list is The standard deviation of the list is Round your answer to the nearest tenth. How many numbers in the list are within one standard deviation from the average?

Answer:

(-3,1)

Step-by-step explanation:

go to -3 to the right and 1 up

The results are statistically insignificant at  = 0.10. There is insufficient evidence to draw the conclusion that Presbyterians donate less than Catholics do in comparison to the population's mean amount of money they give away.

We can test a hypothesis to see if the typical Presbyterian gives less money to charity on Sundays than the typical Catholic does.

a. Given that the population standard deviations are unknown and the sample sizes are small (n  30), a t-test should be used for this study.

b. The following are the null and alternative hypotheses:

H0 is the null hypothesis: The populace mean gift for Presbyterians is equivalent to or more noteworthy than the populace mean gift for Catholics.

H1: A different hypothesis: Presbyterians' population mean donation is lower than Catholics' population mean donation.

c. The value given for the significance level () is 0.10.

d. The means of two distinct groups can be compared using the two-sample t-test. The following is how the test statistic can be calculated:

t = (x1 - x2) / ((s1 / n1) + (s2 / n2)) in the following locations:

x1 denotes the Presbyterian group's average donation of $23; x2 denotes the Catholic group's average donation of $24; s1 denotes the Presbyterian group's standard deviation of $7; s2 denotes the Catholic group's standard deviation of $12; n1 denotes the Presbyterian group's sample size of 57; n2 denotes the Catholic group's sample size of 46.

t = (23 - 24) / ((7/2 / 57) + (12/2 / 46)) t -1 / (0.878 + 0.938) t -1 / 1.816 t -1 / 1.347 t -0.7426 e. In order to determine the p-value, we need to compare the test statistic to the t-distribution using the degrees of freedom given by (n1 - 1) + (n2 101 degrees of freedom are the result of (57 - 1) plus (46 - 1) in this scenario. The p-value for a t-statistic of -0.7426 and 101 degrees of freedom is approximately 0.2312 when using a t-table or statistical software.

f. We are unable to reject the null hypothesis because the p-value (0.2312) is higher than the significance level ( = 0.10).

g. As a result, the results are statistically insignificant at  = 0.10, which is the final conclusion. There is insufficient evidence to draw the conclusion that Presbyterians donate less than Catholics do in comparison to the population's mean amount of money they give away.

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Answer:

\(2 + p = \frac{4}{5} + \frac{3}{5} p \\ p \: terms \: togather \\ p - \frac{3}{5} p = \frac{4}{5} - 2 \\ \frac{5p - 3p}{5} = \frac{10 - 4}{5} \\ \frac{2p}{5} = \frac{3}{5} \\ 2p = 3 \\ p = \frac{3}{2} \\ thank \: you\)

The value of p in the given equation 2 + p =4/5 + 3/5p is -5/2.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 2 + p =4/5 + 3/5p

Two plus p equal to four by five plus three by five times of p.

p is the variable in the given equation.

2 + p =4/5 + 3/5p

Take the variable terms on one side.

2-4/5 =3/5p-p

6/5= -2p/5

5=-2P

P=-5/2

Hence, the value of p in the given equation 2 + p =4/5 + 3/5p is -5/2.

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The sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.

We have sales record of communication industry.

We have to determine the increase in sales over the three-year period.

The advantage of using prepaid phone plans is you only pay for the data you use, and you're not tied into a lengthy service contract.

According to the question -

Initial Sales -  $500,000

Sales after 3 years -  $200,000,000

Therefore, the rate at which the sales increased is -

r = \($\frac{2\times 10^{8}- 5\times 10^{5} }{3}\) = $6,65,00,000

Hence, the sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.

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Answer:irrational

Step-by-step explanation:

Answer:

irrational Def is the answer

The six hundred thirty nine thousandths in decimal form is 0.639.

Here in the given situation  

Six hundred - the number 6

Thirty nine - the number 39

Now  

We have to Add them together with 0.

So, it should be 0.639

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Answer:

$32.25

Step-by-step explanation:

20% of $129 is $32.25

Answer:

y=4.95                     cost= 11.95

Step-by-step explanation:

duh

The domain and range of the function are [-3, 3] and [-2, 4], respectively and The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

Given that the graph of the function is shown below, the domain and range of the function need to be determined along with finding the function values for (a) f(−1), (b) f(0), (c) f(1) and (d) f(2).Graph of the function:Graph of the function for the given graph of the function, we can observe that the domain of the function is from -3 to 3 as the graph is defined within these limits.In order to find the range of the function, we need to look at the range of the y-coordinates.

The minimum value of y is -2 and maximum value of y is 4.Range of the function: [-2, 4]a) f(-1) means the function value for x = -1. As we can observe from the graph, the point where x = -1 is on the graph of the function is (1, 0). Therefore, f(-1) = 0b) f(0) means the function value for x = 0. As we can observe from the graph, the point where x = 0 is on the graph of the function is (0, -2).

Therefore, f(0) = -2c) f(1) means the function value for x = 1. As we can observe from the graph, the point where x = 1 is on the graph of the function is (2, 4). Therefore, f(1) = 4d) f(2) means the function value for x = 2. As we can observe from the graph, the point where x = 2 is on the graph of the function is (3, 3). Therefore, f(2) = 3

Thus, the domain and range of the function are [-3, 3] and [-2, 4], respectively. The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

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Answer:

The answer is 16 units.

Step-by-step explanation:

Now we have to use the distance formula i.e distance between two points =root under (x2-x1)^2+(y2-y1)^2

Answer:

22 is the distance between the points

Answer:

Zero Property of Multiplication

Step-by-step explanation:

Since this equation is displaying that the product of any number/variable is 0, it is the Zero Property of Multiplication

Answer:

It is different because perimeter is the outside and area is the inside.

Step-by-step explanation:

We can say that the value of n cannot be calculated since the series diverges. The value of n cannot be calculated since the series diverges.

To determine what should n be in order that the partial sum sn = n= 1 root 1/i+1 satisfies sn > 1000, we need to find the value of n that satisfies the given equation.

So,We know that the partial sum of the series to infinity can be given as,

S= ∑1∞ (1/i+1)

Now, the value of S can be given as,

S = 1/2 + 1/3 + 1/4 + … + 1/n + …

Let, Sn be the partial sum up to the first n terms of the series.

Then, Sn = 1/2 + 1/3 + 1/4 + … + 1/n, and we have to find the value of n for which Sn > 1000.

Using the comparison test, we can say that,

∑1∞ 1/i+1 > 1 + ∫[1,∞] 1/x+1 dx

So,S = ∑1∞ (1/i+1) > 1 + ∫[1,∞] 1/x+1 dx

= 1 + ln (x+1) from 1 to infinity= ∞

Therefore, from here, we can say that the value of n cannot be calculated since the series diverges.

Hence, the answer is that the value of n cannot be calculated since the series diverges.

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In linear algebra, the coordinate vector of a vector x relative to a basis b can be defined as the vector of coordinates with respect to the basis b. That is to say, it is a vector that is used to describe the components of x in terms of the basis b.

b = {b1, b2, b3}, where b1 = [1 0 4] , b2 = [5 1 18] , b3 = [1 -1 5] and x = [x1 x2 x3].In order to find the coordinate vector [x]b, we need to solve the system of equations:   x = [x1 x2 x3] = c1*b1 + c2*b2 + c3*b3where c1, c2, and c3 are the constants we need to solve for. Substituting the values of b1, b2, and b3, we get:x1 = 1*c1 + 5*c2 + 1*c3  x2 = 0*c1 + 1*c2 - 1*c3  x3 = 4*c1 + 18*c2 + 5*c3This can be written in matrix form as:    [1 5 1; 0 1 -1; 4 18 5] [c1; c2; c3] = [x1; x2; x3

]Using row reduction to solve the matrix equation above, we get:    [1 0 0; 0 1 0; 0 0 1] [c1; c2; c3] = [17; -5; -4]Therefore, the coordinate vector [x]b = [c1 c2 c3] = [17 -5 -4]. Hence, the final answer is [17 -5 -4].This is a total of 89 words.

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Answer:

47

Step-by-step explanation:

To find the mean, you sum all the numbers, then count the number of numbers you summed up (amount of numbers in the array which in this case is 8) and then divide the two. So you get

Σarray/arraysize = 75+14+48... / 8

Answer:

Mean = 47

Step-by-step explanation:

Given terms :

The mean is equal to the sum of the terms divided by the number of terms.

Therefore, the mean is equal to :

A geometric series is a sequence of numbers in which each term is found by multiplying the previous term by a constant factor.

Given: The series is\(\(x + x^2 + x^3 - x^4 + x^5 + x^6 + x^7 - x^8 + \ldots\)\) We can rewrite the terms as below: \(\begin{aligned}= x - x^4 + x^5 - x^8 + x^9 \ldots &\\= x + x^5 + x^9 + \ldots - x^4 - x^8 - x^{12} \ldots\\ & \\= x \left(1 + x^4 + x^8 + \ldots\right) - x^4 \left(1 + x^4 + x^8 + \ldots\right)\\ &\\= x \cdot \frac{1}{1 - x^4} - x^4 \cdot \frac{1}{1 - x^4}\\ &\\= \frac{x(1-x^4)}{(1-x^4)}\\ &\\= \boxed{\frac{x}{1+x^3}} \end{aligned}\)

Hence, the required expression is \(\(\boxed{\frac{x}{1+x^3}}\)\)

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The probability of rolling a 2 when rolling two dice is 1/36. This is because there are 36 possible outcomes when rolling two dice, and only one of those outcomes is a 2.

To calculate the probability of rolling a 2, we need to consider all of the possible outcomes. There are 6 possible outcomes for each die, so there are a total of 6 x 6 = 36 possible outcomes when rolling two dice. Only one of these outcomes is a 2, so the probability of rolling a 2 is 1/36.

It is also possible to calculate the probability of rolling a 2 by using the formula for the probability of two independent events. In this case, the two independent events are rolling a 2 on the first die and rolling a 2 on the second die.

The probability of rolling a 2 on any given die is 1/6, so the probability of rolling a 2 on both dice is 1/6 x 1/6 = 1/36.

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Answer:

Step-by-step explanation:

i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.

  U = {1, 2, 3, 4, 5, 10, 11, 12}

  A' = U - A = {10, 11, 12}

  A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}

__

ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.

The correct statement about the study is: "The result of the study is not reliable because there is no randomization and the confounding variables are not controlled."

Although the study found greater weight loss in the vegetarian group, we cannot confidently conclude that a vegetarian diet helps people lose more weight based on the given information. There are several reasons for this:

1. Lack of randomization: Randomization is a crucial aspect of experimental studies to ensure that participants are assigned to groups (vegetarian vs. control) in a random and unbiased manner. Without randomization, there is a risk of selection bias, as individuals may have chosen their diet based on personal preferences or other factors that could influence weight loss.

2. Confounding variables: Confounding variables are factors that may affect the outcome but are not controlled or accounted for in the study design. In this case, there could be various confounding variables that contribute to the difference in weight loss between the vegetarian and control groups. For instance, differences in calorie intake, exercise levels, or individual motivations could influence the results.

3. Sample size: While sample size plays a role in the statistical power and precision of a study, it alone does not determine the reliability of the results. Even with a large sample size, if the study design lacks proper control and randomization, the findings may still be compromised.

4. Lack of control group: The absence of a proper control group makes it difficult to establish a causal relationship between the vegetarian diet and weight loss. A control group is essential to compare the effects of the intervention (vegetarian diet) against a baseline or standard treatment (low-calorie diet with meat).

Therefore, the study described does not provide sufficient evidence to support the conclusion that a vegetarian diet helps people lose more weight. Further research with a randomized controlled design and careful control of confounding variables is necessary to draw reliable conclusions about the effectiveness of a vegetarian diet for weight loss.

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The two ways to write the expression k/3+16 are 1/3k + 16 and (k + 48)/3

From the question, the expression is given as

k/3+16

Start by factoring 1/3 out of the first term

So, we have the following expression

1/3k + 16

The above is one of the ways of rewriting the expression

Another way is by taking the LCM

So,we have

k/3+16 = (k + 48)/3

Hence, the equivalent expressions are 1/3k + 16 and (k + 48)/3

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To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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Every day, the mass of the sample shrinks by a factor of 0.04.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The growth or decay of an exponential function depends on the parameter b as follows:

The decay factor k of the exponential function, when |b| < 1, is obtained as follows:

b = 1 - k

k = 1 - b.

The parameter b for this problem is given as follows:

b = 0.96.

Hence it represents decay, and the factor is obtained as follows:

k = 1 - 0.96

k = 0.04.

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Answer:

pi^2

Step-by-step explanation:

If the diameter of a circular rug is 2 feet, we can determine that the rug's radius is 1 foot. We can apply the formula to find the area of a circle

(pi*radius)^2 which would give us and answer of pi^2

The circular rug takes up approximately 3.14 square feet of space on the floor.

The amount of space a circle encloses in a two-dimensional plane is measured by its area. It is computed as times the square of the circle's radius, where (pi) is a mathematical constant that denotes the relationship between a circle's circumference and diameter.

The area of a circle is given by the formula:

A = πr²

where r is the radius of the circle.

The diameter of the circular rug is 2 feet, which means the radius is:

r = 2/2 = 1 foot

Substituting this value of r into the formula, we get:

A = π(1 foot)² = π square feet

Using the approximation of π as 3.14, we get:

A ≈ 3.14 square feet

Therefore, the circular rug takes up approximately 3.14 square feet of space on the floor.

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Answer:

x =10

Step-by-step explanation:

angles are equivalent

170 = 2x + 6x + 90

170 - 90 = 8x +90 - 90

80 = 8x

10 = x

If the owner's beliefs are correct,  the probability of being awarded the second job (Event B) is 0.5 . Event A and Event B are not mutually exclusive and are independent and must be true for event A and event B.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative. In the sections that follow, let's go into greater detail on the fundamentals of probability.

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