A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. Is there evidence to suggest the logic course improves abstract reasoning? You may assume that the differences for the dependent samples are normally distributed . Before 74, 83, 75, 88, 84, 63, 93, 84, 91, 77 After 73, 77, 70, 77, 74, 67, 95, 83, 84, 75
Note : define d = before - after, then đ = 3.7 and s = 4.95
Please sketch the rejection region and show computation for the test statistic

Answer:

a) 6.00

b) 3.00

c) 1.50

Step-by-step explanation:

Sample error of the mean is expressed mathematically using the formula;

SE = σ /√n where;

σ  is the standard deviation and n is the sample size.

a) Given σ = 18, n = 9

Standard error of the mean = σ /√n

Standard error of the mean = 18/√9

Standard error of the mean = 18/3

Standard error of the mean = 6.00

b) Given σ = 18, n = 36

Standard error of the mean = σ /√n

Standard error of the mean = 18/√36

Standard error of the mean = 18/6

Standard error of the mean = 3.00

c) Given σ = 18, n = 144

Standard error of the mean = σ /√n

Standard error of the mean = 18/√144

Standard error of the mean = 18/12

Standard error of the mean = 3/2

Standard error of the mean = 1.50

The probability that the average price is between $153 and $155 is 0.04.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The average price of a math textbook =$158

The standard deviation =$26

The mean= 158

n =number of textbooks randomly chosen which is 40

n=10

Then

σ = 26

σₓ = σₓ/√n

= 26/√40

Therefore. σₓ² = 16.90

For the group of 48, find the probability that the average price is between $153 and $155.

The probability that the average price is between $153 and $155

= 0.04

Learn more about probability here;

https://brainly.com/question/11234923

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Answer:

I know the answer

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Answer:

1.86

Step-by-step explanation:

Given the following :

X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4

P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12

The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.

Summation of [P(x) * X] :

(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)

= 0 + 0.28 + 0.44 + 0.66 + 0.48

= 1.86

Answer:

-12

Step-by-step explanation:

-7+(-5)=

-7-5=

-12

Answer:

-20x / (x-12) = y

Step-by-step explanation:

3/x  - 5/y  = 1/4

Multiply each side by 4xy to clear the fractions

4xy ( 3/x  - 5/y  = 1/4)

Distribute

12y - 20x = xy

Subtract 12y from each side

-20x = xy -12y

Factor out y

-20x = y(x-12)

Divide each side by (x-12)

-20x / (x-12) = y

Answer:

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

Step-by-step explanation:

Given that:

A baseball player has a batting average (probability of getting on base per time at bat) of 0.215

i.e

let x to be the random variable,

consider [tex]x_1 = \left \{ {{1} \atop {0}} \right.[/tex]  to be if the baseball player has a batting average or otherwise.

Then

p(x₁ = 1) = 0.125

What is the probability that they will get on base more than 6 of the next 15 at bats

So

[tex]\mathtt{x_i \sim Binomial (n,p)}[/tex]

where; n =  15 and p = 0.125

P(x>6) = P(x ≥ 7)

[tex]P(x>6) = \sum \limits ^{15}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=0} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 -0.9735[/tex]

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

Answer:

the work done by the force field = 24 π

Step-by-step explanation:

From the information given:

r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk

= xi + yj + zk

∴

x = 3 cos (t)

y =  3 sin (t)

z = 2t

dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt

Also F(x,y,z) = 6xi + 6yj + 6k

∴  F(t) = 18 cos (t) i + 18 sin (t) j +6 k

Workdone = 0 to 2π ∫ F(t) dr

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]

[tex]\mathbf{= 12 \times 2 \pi}[/tex]

= 24 π

Answer:

Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.

Anyways hoped this helped and I got to this question in time c:

Answer:

No solution

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write out systems of equations

-x + 3y = 3

x - 3y = 3

Step 2: Rewrite equations into slope-intercept form

3y = 3 + x

y = 1 + x/3

-3y = 3 - x

y = -1 + x/3

Step 3: Rewrite systems of equations

y = x/3 + 1

y = x/3 - 1

Since we have the same slope for both equations but different y-intercepts, we know that both lines are parallel. If that is the case, they will never touch or intersect each other. Therefore, we have no solution.

Answer:

Circle Equation : x² + y² = 21

Step-by-step explanation:

So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.

The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,

( √5 )² + ( 4 )² = r²,

5 + 16 = r²,

r = √21

In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -

( x - 0 )² + ( y - 0 )² = (√21 )²

Circle Equation : x² + y² = 21

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Answer:

I canot answer this

Step-by-step explanation:

Answer: -10

Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.

1. -4+2(-3)

2. -4+(-6)

3.-4-6

4.-10

Answer:

8

Step-by-step explanation:

-b + 2y

if

b = 4

and

y = 3

then:

-b + 2y = -4 + 2*6 = -4 + 12

= 8

Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99   using the cumulative standard normal distribution table

Answer:

6.642

Step-by-step explanation:

Given that mean = 2

standard deviation = 2

Let X be the random Variable

Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])

X [tex]\sim[/tex] N(2,2)

By Central limit theorem;

[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]

[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]

P(X<x) = 0.09

[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]

[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]

P(X < x) = 0.99

[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]

[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]

[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]

[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]

[tex]( \dfrac{X-2}{2})= 2.321[/tex]

X -2 = 2.321 × 2

X -2 = 4.642

X = 4.642 +2

X = 6.642

Responder:

Juanita = 11, madre = 33

Explicación paso a paso:

Dado lo siguiente:

Suma de sus edades = 44

En 11 años, Juanita tendrá la mitad de la edad de su madre

Sea la edad de la madre = my la edad de juanita = j

m + j = 44 - - - - (1)

(j + 11) = 1/2 (m + 11)

j + 11 = 1/2 m + 5,5; j - 1/2 m = - 5,5; 2j - m = - 11

2j - m = - 11 - - - - (2)

Desde (1): m = 44 - j

Sustituyendo m = 44- j en (2)

2j - (44 - j) = - 11

2j - 44 + j = - 11

3j = - 11 + 44

3j = 33

j = 11

De 1)

m + j = 44

m + 11 = 44

m = 44 - 11

m = 33

Answer:

The second quartile in the data set is $130 per night.

Step-by-step explanation:

Quartile is a type of quantile which divides the number of data set into even numbered sub groups. The second quartile is median of data set. This means that 5% of data lies within this point. The middle value between the median and highest value of data set. The second quartile in the data set must be 50% so the statement is not correct.

Answer:

1,377/2 and 688 1/17

Step-by-step explanation:

Answer:

x <-3

Step-by-step explanation:

15 <-5x

divide both sides by 5 but since the coefficient of x is negative after dividing the sign changes.

x <-3

Answer:

x < −3

I hope this helps!

Answer:

A.

Step-by-step explanation:

So we are given the function:

[tex]f(x)=7x+8[/tex]

To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:

[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]

So the answer is A.

Answer:

[tex]\large \boxed{\mathrm{Option \ A}}[/tex]

Step-by-step explanation:

f(x) = 7x+8

Write f(x) as y.

y = 7x + 8

Switch variables.

x = 7y + 8

Solve for y to find the inverse.

x - 8 = 7y

[tex]\frac{x-8}{7}[/tex] = y

Answer:

Step-by-step explanation:

Given that:

p = 0.61

If X is the the number of students in a randomly selected group  of a sample size n = 50

The expected value and the standard deviation can be computed as follows:

The expected value E(X) = np

The expected value E(X) =  50 × 0.61

The expected value E(X) = 30.5

The required standard deviation = [tex]\sqrt{np(1-p)}[/tex]

The required standard deviation = [tex]\sqrt{30.5(1-0.61)}[/tex]

The required standard deviation = [tex]\sqrt{30.5(0.39)}[/tex]

The required standard deviation = [tex]\sqrt{11.895}[/tex]

The required standard deviation = 3.4489

The required standard deviation =  3.45

(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)

There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.

From the given information:

Now, we can deduce that:

the mean = 30.5

standard deviation = 3.45

Using the empirical rule:

At 95% confidence interval;

[μ - 2σ,  μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]

[μ - 2σ,  μ + 2σ] =  [ 30.5 - 6.9 , 30.5 + 6.9]

[μ - 2σ,  μ + 2σ] = [ 23.6, 37.4]

The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.

The required number of teenagers is = the upper limit of the 95% confidence interval = 37

There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.

Answer:

  the product of a number and 33

Step-by-step explanation:

The operation "times" is what is used to form the product of two operands.

  "t times 33" is "the product of t and 33"

Step-by-step explanation:

[tex]Area = \: \frac{bh}{2} \\ : b = 16.9 \: h = 10.4 \\ [/tex]

[tex]Area = \frac{16.9 \times 10.4}{2} = \frac{175.76}{2} = 87.88 {ft}^{2} [/tex]

Base = 16.9

height = 10.4

Area = ½b×h

A = ½(16.9×10.4)

A = ½(175.76)

Area = 175.76/2

A = 87.88ft²

Answer:

[tex]\Large \boxed{\mathrm{87.88 \ ft^2 }}[/tex]

Step-by-step explanation:

[tex]\displaystyle area \ of \ triangle \ = \ \frac{base \times height }{2}[/tex]

[tex]\displaystyle area \ of \ triangle \ = \ \frac{16.9 \times 10.4 }{2}[/tex]

[tex]\displaystyle area \ of \ triangle \ = \ \frac{175.76}{2}[/tex]

[tex]\displaystyle area \ of \ triangle \ = \ 87.88[/tex]

Answer:

25  Answer A

Step-by-step explanation:

Use similar triangles, and the proportion derived from the quotient of a leg to the hypotenuse:

[tex]\frac{15}{9} =\frac{x}{15} \\x=\frac{15^2}{9} \\x=25[/tex]

Answer:

The answer is 4 + 4 + 4 - 4 = 8

Step-by-step explanation:

The four fours problem is one of the problems given in the book "The Man Who Calculated" by Malba Tahan, a Brazilian-born professor of mathematical sciences.

There are many complicated problems in this book made with the intention of using logic to find a value.

The 4 fours problem is based on using these numbers and using any operation to result in the numbers 1 through 10.

Answer:

The Width = 65.44 inches

The Height = 36.81 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Using Pythagoras Theorem we known that:

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 75²

We are given ratio: 16:9 as aspect ratio

Width = 16x

Height = 9x

(16x)² +(9x)² = 75²

= 256x² + 81x² = 75²

337x² = 5625

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately x = 4.09

For the newer 75 inch tv set

The Height = 9x

= 9 × 4.09

= 36.81 inches

The Width = 16x

= 16 × 4.09

= 65.44 inches.

Step-by-step explanation:

n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

Answer:  1) $300     2) $624

Step-by-step explanation:

[tex]\begin{array}{l||l|l}\underline{\quad \text{Item}\qquad \qquad \qquad \qquad}&\underline{\text{Income} }&\underline{\text{Expense}}\\\text{Net Pay}&5000&\\\text{Interest on Deposits}&0&\\\text{Income from Investments}&225&\\\text{Rent}&&3000\\\text{Utilities}&&250\\\text{Satellite Dish}&&175\\\text{Cell Phone Plan}&&135\\\text{Car Payment}&&385\\\text{Groceries}&&200\\\text{Insurance}&&380\\\underline{\text{Recreation}\qquad \qquad \qquad}&\underline{\qquad \quad }&\underline{400\qquad}\\\end{array}[/tex]

TOTALS                              5225      4925

Net Cash Flow = Income - Expenses

                        = 5225 - 4925

                        = 300

*************************************************************************************

[tex]\dfrac{25\ hours}{week}\times \dfrac{\$8}{hour}\times 4\ weeks\times 78\%\\\\\\=25\times \$8 \times 0.78\\\\= \$624[/tex]

Answer:

third option

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Given

g(x) = [tex]3^{x}[/tex] + 5 ← this represents a shift up of 5 units

Thus g(x) is the graph of f(x) translated up by 5 units

Answer:

[tex]\boxed{\sf{Option \: 3}}[/tex]

Step-by-step explanation:

g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted  in the direction of the y-axis.