find the f-test statistic to test the claim that the population variances are equal. both distributions are normal. the standard deviation of the first sample is 2.1971 7.32 is the standard deviation of the second sample.

The sample proportion of the business travelers who use a laptop computer on overnight trips is 0.6417.

Given:

a survey that found that 351 of 547 business travelers use a laptop computer on overnight business trips.

we are asked to find the sample proportion based on this survey, who use a laptop computer on overnight business trips = ?

sample proportion:

The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.

P = X/N

P = 351/547

P = 0.641681

round off to four decimal places.

P = 0.6417

Hence we get the sample proportion as 0.6417

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According to the perpendicular bisector theorem, the statement that is true is: B. BI = BK.

The perpendicular bisector theorem states that if a line segment bisects another line segment perpendicularly, therefore, any point on the perpendicular would be the same distance from the endpoints of each of the line segment that was bisected.

In the diagram above, we are told that line segment AB is a perpendicular bisector of line segment IK. This means that, according to the perpendicular bisector theorem, any point on line segment AB, would be equidistant to the endpoints of line segment IK.

This implies that:

The length of BI is the same as the length of BK. Thus, the correct answer is: B. BI = BK.

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Probability of randomly selecting four committee members with only sophomores or juniors is equal to 0.77.

As given in the question,

Total number of group members including 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors = 14

Number of members required to form a committee = 4

Condition apply:

Committee consists of only sophomores or juniors

Let 'A' represents the sophomores

'B' represents the juniors

Total number of possible outcomes = ¹⁴C₄

Event A and B are independent of each other.

Favourable outcomes are :

2(⁴C₀⁴C₄ + ⁴C₁⁴C₃) +⁴C₂⁴C₂

Required probability

= 2(⁴C₀⁴C₄ + ⁴C₁⁴C₃) +⁴C₂⁴C₂ / ( ¹⁴C₄)

= [2( 1 + 16) + 36 ] / ( 7 × 13 )

= 70 /  91

=0.77

Therefore, the probability of the committee consists of only sophomores or juniors is equal to 0.77.

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Option B, The center 95% of players had an average weight of 151 pounds.

Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.

So, let x represent a football player's weight.

X ≅ N(200, (25)²)

The minimal weight of the center 95% of the members is

P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)

P(X > 95) = P(-4.2 < z)

P(X > 95) = - P(z < -4.2)

P(X > 95) = 0.1512

The needed percentage is 0.1512 × 100 = 151.2 percent.

A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

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The amount that would be in the account in 30 years will be $245,371.

An ordinary annuity is when a series of payment is made at the end of the period over a number of years.

The formula that can be used to determine the future value of an ordinary annuity is: monthly deposit x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$350 x (1.0033)^360 - 1} / 0.0033 = $245,371

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The volume of the  soup pot is 427.04 inches³

The soup pot is 8. 5 inches tall with a radius of 4 inches

We need to find the volume of the soup pot

What is volume?

Volume, is defined as the space that a body occupies. it is the ratio of the mass of object to its density.

Volume of cylinder = 3.14r²h

Where r represents the radius of the cylinder and h represents the height of the cylinder.

Volume of cylinder = 3.14 x 4 x 4 x 8.5

Volume = 427.04 inches³

Thus, the required volume of the soup pot when it is s 8. 5 inches tall with a radius of 4 inches is 427.04 inches³

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Answer:

b=-3

Step-by-step explanation:

11=2b+17

subtract 11 from both sides

then you get 2b+6=0

so b=-3

Answer: -3

Step-by-step explanation:

Hey! Here's a simple solution -

Step 1 - Subtract 17 from both sides -

11 - 17 = 2B + 17-17

-6 = 2B

Step 2 - Divide both sides by 2

-3 = B

Hope this helped you! Peace out!

Answer:

17 pennies, 14 nickels

Step-by-step explanation:

let p = pennies and n = nickels

p + n = 31 coins

p = 31 - n

0.01p + 0.05n = $0.87

0.01(31 - n) + 0.05n = 0.87

0.31 - 0.04n = 0.87

0.04n = 0.56

n = 14

p = 31 - 14

p = 17

hope this made sense :)

The amount of sugar in final recipe will be 5/8

Fractions are used to represent smaller pieces (or parts) of a whole.

Given that, You decide to subtract ⅛ of a cup of sugar from the original amount of ¾ of a cup.

3/4-1/8 = 5/8

Hence, The amount of sugar in final recipe will be 5/8

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The inequality x ≤  20 represents the all possible values of x.

Inequality shows relation between two expression which are not equal to each others.

Given that,

Kelli walks not more than 25 dogs on Mondays,

Also,

Kelli walks 5 dogs that belongs to Ms. Lincoln

The inequality to find the number of dogs Kelli walks on Monday x, in addition to Ms. Lincoln's dogs, can be written as,

x+5 ≤ 25

Subtract 5 from both the sides,

x + 5 - 5 ≤ 25 - 5

x ≤  20

The required inequality is x ≤  20.

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The equation of line that passes through the point (8,6) and has a slope of 0 is y = 6.

As the sated question-

The passing point; (x1, y1) =  (8,6)

slope m = 0

Thus, equation lo line by slope intercept form is-

y - y1 = m(x - x1)

y - 6 = 0(x - 8)

y = 6

Thus, the equation of the line that passes through the point (8,6) and has a slope of 0 is y = 6.

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Answer:

Step-by-step explanation:

Let p be the number of pennies and n be the number of nickels. As you have $8.80 in total (given that pennies are worth $0.01 and nickels are worth $0.05)

0.01p + 0.05n = 8.80

You also know that there are twice as many nickels than pennies (or alternatively, there are 2 nickels for every penny).

n = 2p

You can substitute this value of n into the first equation

0.01p + 0.05n = 8.80

0.01p + 0.05(2p) = 8.80

0.01p + 0.10p = 8.80 (multiplying out the brackets)

0.11p = 8.80 (collecting the p's)

p = 80

Putting this back into the second equation

n = 2p

n = 2(80) = 160

So there are 160 nickels and 80 pennies.

You can put this back into the first equation to check it.

0.01p + 0.05n = 8.80

0.01(80) + 0.05(160) = 0.80 + 8 =8.80

By using the expanded form of a number, it can be concluded that

Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99

What is expanded form of a number?
Every number can be written as a sum of the place value of its digit. This is known as expanded form of a number

Let the three digit positive integer be n = abc where a, b and c are distinct positive integers

n can be written as 100a + 10b + c

Its reverse is n' = cba

n' can be written as 100c + 10b + a

Difference between the number and its reverse

= 100a + 10b + c - 100c - 10b -a

=  99a - 99c

= 99(a - c)

= Since a and c are distinct, a - c [tex]\neq[/tex] 0

Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99

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Answer: 18°

Step-by-step explanation:

     The question doesn’t state where F is in relation to A, B or E, so we have to guess. Here are two guesses.

If ABF is a straight line then ∠ABE+∠EBF=180, so 2n+7+4n-13=180, 6n-6=180.

Divide each side by 6: n-1=30 so n=31 and m∠ABE=2n+7=2×31+7=62+7=69°.

If BF bisects ∠ABE, then ∠ABE=2×∠EBF, so 2n+7=2(4n-13)=8n-26. So 6n=33 and, dividing both sides by 3: 2n=11. Therefore m∠ABE=2n+7=11+7=18°.

Answer:22

Step-by-step explanation:

The linear equation that represents the total amount in her emergency fund after x number of months be

y = 320x + 2000

Given, Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month.

we have to model the situation in a linear equation,

Let the number of months be, x

and the total amount in her emergency fund be, y

As, she starts with $2000 so the y-intercept will be 2000

also she save $320 every month so the slope be 320

So, the equation be,

y = 320x + 2000

Hence, the linear equation that represents the total amount in her emergency fund after x number of months be

y = 320x + 2000

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A constant does not change its value over time. A variable, on the other hand, changes its value dependent on the equation.

A term is either a number, a variable, or the product of a number and a variable. A coefficient is your term's numerical factor. A constant term is one that only contains a number. In other words, a constant term contains no variables.

Constants are algebraic expression terms that only contain numbers. That is, they are the terms that do not have variables. We call them constants because their value never changes because the term contains no variables that can change its value.

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Answer:

estimate - 455

actual sum 376

Answer:

85 sociology books

255 history books

Step-by-step explanation:

h = history textbooks

s = sociology textbooks

h + s = 340

h = 3s

3s + s = 340

4s = 340

s = 85

h = 3s = 3(85) = 255

Answer:

255 history textbooks

85 sociology textbooks

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}x+y=340\\\;\;\;\:\:\:\:x=3y\end{aligned}[/tex]

Substitute the second equation into the first equation and solve for y:

[tex]\implies 3y+y=340[/tex]

[tex]\implies 4y=340[/tex]

[tex]\implies y=340 \div 4[/tex]

[tex]\implies y=85[/tex]

Substitute the found value of y into the second equation and solve x:

[tex]\implies x=3 \times 85[/tex]

[tex]\implies x=255[/tex]

Therefore, the number of each type of textbooks sold were:

The total number of hours spent on reading in a week is 14/3 hours.

For the given question-

Number of hours spent of reading = 2/3 hours.

Total number of days in a week = 7.

Total number of hours spent on reading = 2/3 x 7

Total number of hours spent on reading = 14/3

Thus, the total number of hours spent on reading in a week is 14/3 hours.

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Answer:

Answer

Step-by-step explanation:

10. is (-1,0)

12. is (3,0)

14. is (1,0)

Since the mean height of all children this age is 38 inches, the z-score is 1.282, and the child's height is 40 inches, the standard deviation of all children's heights will be 1561.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

Here,

The z-score which separates the top 10% of a normally distributed

population is 1.282.

Since z = (x-u)/sigma

1.282 = (40-38)/sigma

sigma = 2/1.282

sigma = 1/0.641 = 1561

The standard deviation of the heights of all children of this age will be 1561 as mean is 38 inch and z-score is 1.282 as well as the height of child is 40 inch.

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Deborah can choose from a total of 60 combinations.

Here, we are given that Deborah has two pairs of​ slacks, six ​shirts, and five sweaters.

She has to choose a pair of​ slacks, a​ shirt, and a sweater each​ day.

She can choose a pair of slacks in 2 ways

Similarly, she can choose a shirt to wear in 6 ways and a sweater in 5 ways.

Since, she wears each one of these items each day, the total number of combinations can be found by multiplying the possibilities for each item as follows-

2 × 6 × 5

= 60

Thus, Deborah can choose from a total of 60 combinations.

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Answer:

4/5

Step-by-step explanation:

The two points are (5, 7) and (-5, -1). The slope is the difference of y over the difference in x, or [tex](7--1)/(5--5)[/tex]. This simplifies to 8/10, or 4/5.

The assumptions are- Sample of students are independent and samples are simple random samples. Distribution is normal (t distribution). The independent variable measures on interval scale.

The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are within the purview of statistics, a branch of natural science. Research in stats has application in almost all scientific domains, and software concerns in the many science disciplines inspire the creation of new statistical methods and theories. Statistics is a very multidisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the concept that supports such methods.

Uncertainty and variation are two cornerstones of the statistical profession. In science, as well as more broadly in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air.

How to solve?

ts < tc Do not reject H0

P value > α Do not reject H0

There is insufficient data to determine that the mean scores of the two groups of pupils differ.

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The degrees of freedom for the F- statistic is:

(a) the degree of freedom of the numerator= 3

(b) the degree of freedom of the denominator= 58

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do.

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean".

If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,...,p[/tex]we have [tex]n_{j}[/tex] individuals on each group we can define the following formulas of variation.

We know, we have this property

[tex]SST=SS_{between} +SS_{within}[/tex]

The degrees for the numerator are [tex]df_{num}=k-1=4-1=3[/tex], where k represents the number of groups (k = 4)

The degrees for the denominator are [tex]df_{den} =N-K=62-4=58[/tex], where N represent the total number of people (N = 14+16+19+13=62)

And the total degrees of freedom are given by:

[tex]df_{tot} =df_{num} +df_{den} =3+58=61[/tex]

Hence, degree of freedom of the numerator is 3 and the degree of freedom of the denominator is 58.

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In one hour, the car covered a distance of 26.66 miles

Given,

The time when the trip begins = 2.00 pm

Distance travelled till 5.00 pm = 80 miles

Here,

Mean value Theorem;-

The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a, b] if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

The Mean Value Theorem is as follows. F is constant over I if f′(x)=0 over a period I. If f′(x)=g′(x) over I for two differentiable functions f and g, then f(x)=g(x)+C for some constant C.

Here,

2 pm to 5 pm = 3 hours

80 miles in 3 hours

That is,

80/3 = 26.66 miles per hour

That is,

The car travelled a distance of 26.66 miles in an hour.

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Answer:

Step-by-step explanation:

Since two angles of △ABC are congruent to two angles of △PQR, the third pair of angles must also be congruent, so ∠C≅∠R, and △ABC≅△PQR by ASA. The corresponding congruent angles are: ∠A≅∠P, ∠B≅∠Q, ∠C≅∠R. The corresponding congruent sides are: AB ≅ PQ, BC ≅ QR, AC ≅ PR.

There is a 1/4 probability that the family's next child will be a girl.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability that the next child born will also be a girl:

We know that:

There is a 50% chance that a female will be the only kid born.

That is: 1/2

The likelihood that the family's subsequent kid will be a girl is:

1/2 * 1/2 = 1/4

Therefore, there is a 1/4 probability that the family's next child will be a girl.

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