Suppose the life time (in hours) of a battery brand is normally distributed. A random sample of 16 batteries results in a sample variance of
3.25
hours
2
. We want to test if there is significant/sufficient evidence in the sample data to claim that the variance of the battery life population is different than 4 hours
2
at significance level of
0.05
. Which of the following is INCORRECT? A.
H 0
​
:σ 2
=4 vs H 1
​
:σ 2

=4
B. The test statistic is found to be
12.1875
C. We should reject the null hypothesis and there is sufficient evidence to claim that the variance of battery life is different than 4 hours
2
at significance level of
0.05
. D. None of the above.

The PE ratio will be equal to $22. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jangles Co. earned $1.80 per share. Assuming a closing price of $40. The PE ratio will be calculated as,

Earning per share = $1.80

The price of the share = $40

PE ratio = Price of the share ÷ Earning per share

PE ratio = $40/$1.8-

PE ratio = $22.

Therefore, the PE ratio will be equal to $22. The correct option is B.

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Answer:

it's 25.7

Step-by-step explanation:

you just divide the 90 by 3.5

The probability that 75% or more of the women in the sample have been on a diet is 0.0371 or 3.71 %.

Here, n = 267, p = 0.7, 1 = 0.3

Mean, [tex]m_p = p[/tex]

⇒ [tex]m_p = 0.7[/tex]

Standard deviation, [tex]\sigma_p = \sqrt(\frac{pq}{n})[/tex]

⇒ [tex]\sigma_p[/tex] = 0.028

The conditions for a sampling distribution to be normal distribution, it must satisfy

1. Randomization condition(SRS)

2. logo condition

3. success/failure condition

Hence, the given sampling distribution in the problem statement is approximately normal distribution.

n×p = 267×0.7 = 186.9 ≥ 10

n×q = 267×0.3 = 80.1 ≥ 10

Norm cdf = (0.75, 999, 0.7, 0.028) ≈ 0.0371 ≈ 3.71%

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Answer:

n=20

Step-by-step explanation:

The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

A wall is to be worked to encase a rectangular area of 260 square feet. The wall along three sides is to be made of material that costs 3 bucks for every foot, and the material for the fourth side costs 15 bucks for each foot.

LW = 260

L = 260 / W

Then the minimum cost is given as,

y = 3L + 3W + 3L + 15W

y = 18W + 6L

y = 18W + 6(260 / W)

y = 18W + 1560 / W

Differentiate with respect to W and put it zero, then we have

y' = 0

18 - 1560/W² = 0

W² = 1560 / 18

W = 86.67 feet

Then the length is given as,

L = 260 / 86.67

L = 3 feet

The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.

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Answer:

-33/35

Step-by-step explanation:

turn mixed fraction into an improper fraction

-2 1/5 = -11/5

times both fractions

The values of x that make the expression undefined are 0 and 2

From the question, we have the following parameters that can be used in our computation:

Volume = 5 - x

Width = x - 2

Height = 5 - x/x(x -2)

Introduce brackets to the height expression to differentiate between the numerator and the denominator

So, we have

Height = (5 - x)/x(x -2)

The question implies that we calculate the domain

Set the denominator to 0

This gives

x(x - 2) = 0

So, we have

x = 0 or x - 2 = 0

Solve for x

x = 0 or x = 2

This means that the undefined height value of x are 0 and 2

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The value of the required probabilities are:

(a) E[X] = 6

(b) E[X|Y=1] = 1/36

(c) E[X|Y=5] = 5/36.

To find the values of P{X=x, Y=1} and P{X=x, Y=5}, we need to understand the concept of conditional probability and the properties of geometric distributions.

First, let's recall some properties of geometric distributions:

The probability of success (rolling a specific number on a fair die) in a single trial is denoted by p, and for a fair die, p = 1/6.

The probability of failure (not rolling the specific number) in a single trial is denoted by q, and for a fair die, q = 1 - p = 5/6.

The geometric distribution is the number of trials required to achieve the first success (rolling the specific number) in a sequence of independent trials.

For the random variable X (number of rolls necessary to obtain a 6), X follows a geometric distribution with parameter p = 1/6.

Now, let's find the values of P{X=x, Y=1} and P{X=x, Y=5}.

(a) E[X]:

The expected value of X (denoted as E[X]) for a geometric distribution is given by E[X] = 1/p. For a fair die, p = 1/6, so E[X] = 1 / (1/6) = 6.

(b) E[X|Y=1]:

This represents the expected number of rolls necessary to obtain a 6 given that the first roll resulted in a 5.

To find E[X|Y=1], we need to consider the conditional probability.

The event "Y=1" represents that the first roll resulted in a 5.

The probability of rolling a 6 in the next roll (X=1) given that Y=1 is P{X=1, Y=1}.

Since the rolls are independent, P{X=1, Y=1} = P{X=1} * P{Y=1}.

The probability of rolling a 6 in a single roll (P{X=1}) is 1/6, and the probability of rolling a 5 in a single roll (P{Y=1}) is also 1/6 (since we want the first roll to be a 5).

So, P{X=1, Y=1} = (1/6) * (1/6) = 1/36.

Now, to find E[X|Y=1], we need to sum the products of the number of rolls (x) and the corresponding probabilities for all possible values of x, given that Y=1:

E[X|Y=1] = ∑(x * P{X=x, Y=1})

Since the geometric distribution is defined over all non-negative integers, we need to consider all possible values of x (0, 1, 2, 3, ...).

E[X|Y=1] = (0 * P{X=0, Y=1}) + (1 * P{X=1, Y=1}) + (2 * P{X=2, Y=1}) + ...

Now, we already know that P{X=1, Y=1} = 1/36. For all other values of x, P{X=x, Y=1} = 0 because we cannot have any rolls beyond the first roll when Y=1 (since Y=1 means the first roll was a 5).

So, E[X|Y=1] = (1 * 1/36) + (0 * 0) + (0 * 0) + ... = 1/36.

(c) E[X|Y=5]:

This represents the expected number of rolls necessary to obtain a 6 given that the first roll resulted in a 5 followed by four rolls that resulted in other numbers (not 6).

Similarly to part (b), we need to consider the conditional probability.

The event "Y=5" represents that the first five rolls resulted in numbers other than 6.

The probability of rolling a 6 in the next roll (X=1) given that Y=5 is P{X=1, Y=5}.

Again, since the rolls are independent, P{X=1, Y=5} = P{X=1} * P{Y=5}.

The probability of rolling a 6 in a single roll (P{X=1}) is 1/6, and the probability of rolling a number other than 6 in a single roll (P{Y=5}) is 5/6 (since we want the first five rolls to be numbers other than 6).

So, P{X=1, Y=5} = (1/6) * (5/6) = 5/36.

To find E[X|Y=5], we need to sum the products of the number of rolls (x) and the corresponding probabilities for all possible values of x, given that Y=5:

E[X|Y=5] = ∑(x * P{X=x, Y=5})

Similarly to part (b), for all values of x other than 1, P{X=x, Y=5} = 0 because we cannot have any rolls beyond the first roll when Y=5 (since Y=5 means the first five rolls were other numbers).

So, E[X|Y=5] = (1 * 5/36) + (0 * 0) + (0 * 0) + ... = 5/36.

Hence, The value of the required probabilities are:

(a) E[X] = 6

(b) E[X|Y=1] = 1/36

(c) E[X|Y=5] = 5/36.

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Answer: 3

Step-by-step explanation:

The measure of the interior angle at vertex E is; B: 90

The formula for the sum of interior angles of an irregular polygon is;

Sum of interior angles = (n − 2) × 180°

where;

'n' is the number of sides of a polygon.

Thus;

Sum of interior angles of an irregular pentagon with 5 sides is;

Sum = (5 - 2) * 180

Sum = 540°

Thus;

3(4x) + 2(3x) = 540

12x + 6x = 540

18x = 540

x = 540/18

x = 30°

Thus, angle at vertex E = 3(30) = 90°

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Answer: The answer is B and D

Step-by-step explanation: The answer is B and D because B is -2 and D is 2, so when we combine them(combine means add) we get -2 + 2 which equals 0.

The probability that the randomly selected student  will chose running  can be written as  12/57.

The concept used is the probability which is the likelyhood of an event to take place.

Total number of students was given as  57

Total number of boys  that was given was  26

Total number of girls  can be written as 57-26=31`

Number of Girls that chose football  can be written as 15

Number of boys that chose football  can be wriitten as  9

Number of students that chose Tennis can be written as  18

Now, number of students that chose running will be;

Number of students that chose running = 57 - (24 + 18) = 15

Therefopre, probability that a randomly selected student chose running = 15/57

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The absolute maxima and minima of the function f(x) = xe^-(x²/32) along an interval [-3, 8] are (4, 4/e^1/2) ≅ (4, 2.43) and  (-3, -3/e^9/32) ≅ (-3, -2.26) respectively

An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.

Absolute minimum and maximum values of the function in the entire domain are the highest and lowest value of the function wherever it is defined. A function can have both maximum and minimum values, either one of them or neither of them. For example, a straight line extends up to infinity in both directions so it neither has a maximum value nor minimum value.

In this question given,

f(x) = xe^-(x²/32) along an interval [-3, 8]

The absolute maxima = (x, f(x)) = (4, 4/e^1/2) ≅ (4, 2.43)

The absolute minima = (x, f(x)) = (-3, -3/e^9/32) ≅ (-3, -2.26)

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Two examples of geometric sequence are {2, 6, 18, 54, 162, 486, 1458, ...} and {1, 2, 4, 8, 16, 32, 64, 128, 256, …}.

In mathematics, a geometric sequence or geometric progression refers to a sequence of non-zero numbers where the ratio between consecutive terms is constant. In such a sequence, each term (after the initial term) is determined by multiplying the previous one by a fixed, non-zero number called the common ratio. An example of geometric sequence is {2, 6, 18, 54, 162, 486, 1458,  ..} where each term is 3 times the previous term i.e., the common ratio is 3. Another example is {1, 2, 4, 8, 16, 32, 64, 128, 256, .. } where each term is 2 times the previous term i.e., the common ratio is 2.

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Answer:

-3

Step-by-step explanation:

6x + 4 = x - 11

6x - x = -11 - 4

5x = -15

5/5 x = -15/5

x = -3

The option a "The chi-square test for independence" is correct.

In the given question we have to find, a test of a single population and is to determine if there is an association between two characteristics of that population.

The given options are

A) The chi-square test for independence

B) Pearson product moment test

C) The chi-square test for homogeneity

D) Goodness-of-fit test

E) Welch’s t test

As we know that;

When a categorical variable has more than two levels, a chi-square test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

So, the chi-square test for independence is correct answer.

Option (B) and (E) are two-sample tests.

(C) involves two attributes.

(D) Doesn't check association.

Hence all these are incorrect.

So the option a "The chi-square test for independence" is correct.

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You did not copy the image with the question. Sometimes you have to screenshot or use the Snip-it app to get the image.

The equation that shows the relationship between the length of Carla’shair and how many months have passed since Carla’s haircut will be hair Length - 14 = 1/3(months - 3)

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Carla’s hair grows 1/2 inch a month 3 months after carla got her last haircut, carla’s hair was 14 inches long. The equation that illustrates this is Carla’s haircut will be hair Length - 14 = 1/3(months - 3). Therefore, the correct option is D.

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If the function f(x)= 2x – 3 and g(x) = 3/2x + 1 then g(4) < f(4) is a true statement?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

A function can also be said to be a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

Functions are generally represented as f(x).

Let , f(x) = [tex]x^{3\\}[/tex].

It is said as f of x is equal to x cube.

Functions can also be represented by g(), t(),… etc.

For g(4) < f(4);

g(4) = 3/2(4) + 1

g(4) = 3/9

f(4) = 2(4) - 3

f(4) = 8 - 3

f(4) = 5

Therefore; g(4) < f(4)

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Answer: the best estimate could be 20 liters

Step-by-step explanation: it is 20 liters because 1 liter is = 264 gallons so we round up the number and then use regular estimate methods.

Answer:

15 liters

Step-by-step explanation:

4 gal  /  .264 gal / liter   = 15.15 liters  = ~ 15 liters

the correct expression for the rate of this reaction would be A[B] 3At or A[G] 2Ît, but not -A[A] At.

A rate expression is a mathematical expression that describes the rate at which a chemical reaction proceeds. It is typically written in the form of a differential equation, with the reactants on the left-hand side and the products on the right-hand side. The coefficients of the reactants and products represent the stoichiometric coefficients of the reaction. In the expression 2A +3B -> F+ 2G, the reactants are A and B, and the products are F and G. Therefore, the correct expression for the rate of this reaction would be A[B] 3At or A[G] 2Ît, but not -A[A] At.

A rate expression is an equation that describes the rate at which a chemical reaction occurs. It is usually written in the form of a differential equation, with the reactants on the left-hand side and the products on the right-hand side. The coefficients of the reactants and products represent the stoichiometric coefficients of the reaction. In the expression 2A +3B -> F+ 2G, the reactants are A and B, and the products are F and G. Therefore, the correct expression for the rate of this reaction would be A[B] 3At or A[G] 2Ît, but not -A[A] At, which does not represent a proper rate expression for this reaction.

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The group of symmetries of a regular tetrahedron is known as the tetrahedral group, and is denoted by $T_d$. This group consists of all the symmetries of a regular tetrahedron, including orientation-reversing symmetries.

The regular tetrahedron is a three-dimensional object with four faces that are all equilateral triangles. It is one of the five Platonic solids, which are convex polyhedral with congruent faces and regular polygonal faces. The tetrahedral group $T_d$ contains a total of 24 symmetries, which can be divided into two classes: rotational symmetries and reflection symmetries. The rotational symmetries consist of 8 proper rotations, which are rotations that preserve the orientation of the tetrahedron, and 6 improper rotations, which are rotations that reverse the orientation of the tetrahedron. The reflection symmetries consist of 6 plane reflections that reflect the tetrahedron across one of its faces.

To understand the symmetries of the tetrahedron, it is helpful to think about the symmetries of an individual face. An equilateral triangle has 6 symmetries: 3 rotational symmetries (120 degree rotations about the center of the triangle), and 3 reflection symmetries (across the lines of symmetry of the triangle). The regular tetrahedron has four faces, so these symmetries can be applied to each face independently, resulting in a total of $6^4=1296$ symmetries. However, many of these symmetries are not distinct, and can be generated by combinations of the tetrahedral group's 24 symmetries. Thus, the tetrahedral group $T_d$ is the group of all the distinct symmetries of a regular tetrahedron.

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Answer:

-20

Step-by-step explanation:

We see the number line is counting by 5's so let's count down by 5's until we get to the blue dot!

5

0

-5

-10

-15

-20!

We moved down 3 points from -5 on the number line!

Answer:-20

Step-by-step explanation:

(c) is correct option as it is forming an arithmetic sequence with a common difference of -2.

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term." The following is an arithmetic sequence where each term is created by adding 4 to the one before it.

An arithmetic sequence's first term is 'a', its common difference is 'd', and n is the total number of terms. The AP has the following general forms: a, a+d, a+2d, a+3d, etc., up to n words.

(a) 1,2,3,5,7,9 is not an arithmetic sequence as 2-1=1 and 5-3=2. That shows common difference is not constant.

(b) 1,10,20,30 is not an arithmetic sequence as 10-1=9 and 20-10=10. That shows common difference is not constant.

(c) 1,-1,-3,-5 is an arithmetic sequence as (-1)-1=-2 and -3-(-1)=-2. That shows common difference is constant.

(d) 7,-7,7,-7 is not forming an arithmetic sequence because common difference is not constant.

Option (c) is correct option.

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Answer:

somone in my class is literaly a new York rat

Step-by-step explanation:

The error in computing the area of triangle is 10.75 and the percentage error in computing the area of triangle is 1.194%.

Given that, base of the triangle is 36 cm (a)

Altitude of the triangle is 50 cm (b)

Error in each measurement is 0.25 cm

We know that, area of the triangle (s) = 1/2 * base * altitude

Let us consider base as ' a ' and altitude as ' b '

So, the maximum error of ' s ' can be calculated as

⇒ ds/da * da + ds/db * db

⇒ 1/2* b * da + 1/2 *a * db

⇒ 1/2* 36 * 0.25 + 1/2* 50* 0.25

⇒ 4.5 + 6.25 = 10.75

Now, let us calculate the percentage error in computing the area of the triangle.

dA/A * 100 = [(1/2* b* da + 1/2* a * db)/ 1/2* b *h] * 100

⇒ [(1/2* 36 * 0.25 + 1/2* 50 * 0.25)/ 1/2* 36 * 50] * 100

⇒ [ 21.5/ 1800 ] * 100

⇒ 1.194%

Thus, the error in computing the area of the triangle is 10.75 and the percentage error in computing the area of the triangle is 1.194%.

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True , The adjusted R^2: is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model .

Given :

The adjusted R^2: is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model .

If the regression equation includes anything other than a constant plus the sum of products of constants and variables, the model will not be linear.

Adjusted R^2 is a corrected goodness - of - fit  ( model accuracy ) measure for linear models. It identifies the percentage of variance in the target field that is explained by the input or inputs.

So the above statement is true.

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Standard error of the  of the standard deviation of 2 years with the mean  and the sample size of n will be 3

The parameter list is abbreviated (lower value, upper value, μ,

, α / √n

normal cdf: (85,92,90, 15 / √25

= 0.6997

To find the value that is two standard deviations above the expected value 90, use the formula:

value = ux + ( # of STDEVs ( αx / √n )

value = 90 + 2 (15 / √25 )= 96

The value that is two standard deviations above the expected value is 96. The standard error of the mean is

σ / √n = 15√25

= 3.

standard error of the mean is a description of how far that the sample mean will be from the population mean in repeated simple random samples of size n.

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Answer:

Step-by-step explanation:

33.3%

well, we know the TV cost 200 bucks, now if we just bump it up by 45%, that'd do it.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{45\% of 200}}{\left( \cfrac{45}{100} \right)200}\implies 90~\hfill \underset{retail~price}{\stackrel{200~~ + ~~90}{\text{\LARGE 290}}}[/tex]