Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 30 mpgwith a standard deviation of 7 mpg. Thirty-one non-hybrid sedans get a mean of 20 mpg with a standard deviation of three mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test at the 5% level to evaluate the manufacturers claim.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
State the null hypothesis
State the alternative hypothesis.
In words, state what your random variable Xhybrid − Xnon−hybrid represents.
State the distribution to use for the test.
What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
What is the p-value?
what is the Alpha?
Explain how you determined which distribution to use.

The inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number would be x

The sum of a number and -4 is at least 8

According to the given question, translate the phrase into an algebraic form :

x - 4 ≥ 8

Add 4 both sides of the above inequality,

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Therefore, the inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

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The curve with parametric equations x = [tex]e^{- t}[/tex] + t, y = [tex]e^t[/tex] − t, − 2 ≤ t ≤ 2 can be plotted on a graph. The arrow shows the direction where t increases in the interval (-2,2).

The length of a curve of the provided parametric equations is indicated by the arrow pointing in the direction wherein the curve is traced given data.

Think about the equations for the parameterized curve in the x-y plane.

x = x( t )

y = y( t )

where the argument is t. The graph of the curve is created by charting the series of points as the variable t changes (x,y).

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The question is -

Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t increases. x = [tex]e^{- t}[/tex] + t , y = [tex]e^t[/tex] − t , − 2 ≤ t ≤ 2

Answer:

What is the value of √m = ∓ 17

The value of √m = ∓ 17 is undefined.

There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.

Given that,

The bookstore reduced the price of various notepads from $2.00 to $1.00 while maintaining the price. The whole lot was sold. The selling of the pads generated a total profit of $29.45.

We have to find what number of notepads were sold and how much did each notepad cost.

We know that,

One approach to solving this issue is to divide $29.45 by each of the values from $1.01 to $1.99. That is the price for each notepad if one of them fits evenly with no leftovers. The number of pads is the quotient (result of division). The number has to be placed evenly because we cannot use half of the pad (leave no remainder).

Although we can check each of them, I realized that $29.45 ends in a 5 and is therefore divisible by 5, so I chose to check 1.05 as a potential price and it entered evenly. 13 is the quotient.

Therefore, There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.

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Answer:

The answer is x=20

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

(x+21)+(2x+9)=90

x + 21 + 2x + 9 = 90

combine numbers on left side:

x + 30 + 2x = 90

combine x terms on left side:

3x + 30 = 90

subtract 30 from both sides:

3x + 30 -30 = 90 - 30

3x  = 60

divide  both sides by 3:

3x/3  = 60/3

x = 20

From the given information given, the mean and standard deviation of the probability distribution is; Y will be 0.4899 and 0.699 respectively.

How to create the probability distribution?

From the given probability distribution, it should be noted that the probability distribution for y will be:

Y                   0        1.         2

Probability 0.63.   0.25.   0.12

The mean of Y will be:

Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)

Mean = 0 + 0.25 + 0.25

Mean = 0.49

The variance will be 0.4899. Therefore, the standard deviation will be:

standard deviation = ✓0.4899

Standard Deviation = 0.699

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Answer:

Step-by-step explanation: find a point and find another point

y=1x+1/2

The slope of a function is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.

m = Δy/Δx

∆y --> net change in the y coordinate

∆x ---> net change in x coordinate

m ---> slope of fution

The y-intercept of both functions 'f' and 'g' are equal and slope of f(x) is less than the slope of g(x). So, the correct option is option (A).

We have given a function, g (x) = 2x + 1

comparing the g(x) with standard equation

y = mx + b

where m is slope of this line

b --> y-intercept

Thus we get m = 2 , b= 1 . So, the slope of g(x) is 2 and y-intersecpt is 1 .

Now, we have a table for function f(x) that is function f(x) passing through all points as given in table. The slope of function passing through (h,k) and (a,b) is expressed as (k-b)/(h-a)

Thus, slope of function 'f' passing through (0,1) and (2,4) = (1-4)/(0-2) = -3/-2

= 3/2

=> f (x) = (3/2)x + b

where , b --> y-intercept

plug the value x= 4 and corresponding to it

f(x) = 7 we get , 7 = 3/2× 4 + b

=> b = 7-6 = 1

Therefore, slope of function g(x) is greater than slope of function f(x) and y-intercept of f(x) is equal to y-intercept g(x) .

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Complete question:

The Table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

x / f(x)

0/1

2/4

4/7

g(x)= 2x+1

A. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

B. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

C. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

D. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

Answer: 7/12

Step-by-step explanation: First, flip the 4/3 to its reciprocal and change it to multiplication. Then, you can simplify the 9 and 3 to 3 and 1. After that, multiply straight across. Hope this helps! :)

Answer:

1. 7/9 ÷ 4/3 As a fraction) 21/36

2. 7/9 ÷ 4/3=21/36 as a simplified fraction) 7/12

3. 7/9 ÷ 4/3 As a decimal) 0.583

4. 7/9 ÷ 4/3 As a percentage) 58.3%

Let's see how it's done!

7/9 ÷ 4/3:

7/9 ÷ 4/3 (Invert or flip the second fraction and multiply across)

7/9 x 3/4 = 21/36

How to simplify 21/36

21/36 ÷ 3 (Divide the numerator "the top part of the fraction" and the denominator "the bottom part of the fraction" by 3. This will equal 7/12

How to turn 21/36 into a decimal

21 divided by 36 = 0.5833333333333333...

Round to the nearest thousandth: 0.583

How to turn 0.583 into a percent

Move the decimal point 2 places to the left, drop the zero(s)

and add the percent sign! 58.3%

These are all the same answer but in different forms and how to do them!

Hope it helps!

the polynomial will be 2x² + 11x+6, with degree less than 3 and be the subspace.

What is vector space?

A collection of vectors collected collectively and multiplied ("scaled") by scalars forms a vector space, also known as a linear space. Real numbers are typically thought of as scalars. Nevertheless, there aren't many instances of scalar multiplication with vector spaces using rational, complex, etc. numbers. Axioms and other preconditions must be met by the vector addition and scalar multiplication techniques. A space made up of vectors is referred to as a vector space when the addition of vectors is governed by the associative and commutative law and when vectors are multiplied by scalars is governed by the associative and distributive process.

W = span (9x-4-2x²,5+x+2x²)

Now, a(9x42x²)+b(5+x+2x²) = 0

⇒(9a+b)x+(2b-2a)x² + (5b-4a) = 0

⇒9a+b= 0; 2b2a = 0; 5b-4a=0

a = b =0

p(x)=(9x-4-2x²) + 2(5+x+2x²) = 9x-4-2x² + 10 + 2x + 4x² = 2x² + 11x+6

Hence the polynomial will be 2x² + 11x+6.

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By solving a linear equation, it can be calculated that-

Kenji needs 12 gallons of gas for the drive

What is a linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let Kenji requires x gallons of gas

Kenji's car gets 33.5 miles per gallon of gas when he is driving on the highway.

Kenji can travel 33.5x miles with x gallons of gas

Distance to be travelled = 402 miles

By the problem,

The required linear equation is

33.5x = 402

x = [tex]\frac{402}{33.5}[/tex]

x = 12 gallons

Kenji needs 12 gallons of gas for the drive

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The measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

Applying intersecting secants theorem:

4(4 + 2) = 3(3 + 2x + 5)

8 = 8 + 2x

x = 0

LK = 2x + 5 = 5 units

In the second circle:

4(4 + x - 8) = 3(3 + x - 5)

x = 10

NL = x - 8 + 4 = 10 - 8 + 4 = 6 units

Thus, the measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.

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Answer: (3,0)

Hope this helps! :)

Step-by-step explanation: Think of graphing, like regular number lines. The numbers are either positive or negative and depending on the integer you add or subtract, the number on the line will either move left or right.

x= 5 (x on a coordinate plane is left to right)

2 units left

5-2=3

y= -5 (y on a coordinate plane is top to bottom)

5 units up

-5+5=0

(3,0)

Answer:

(3,0)

Step-by-step explanation:

x= 5-2 = 3

y= -5+5 =0

There are 65, 19-bit sequences of 0s and 1s that start with a 0 and end with a 0 that exist.

Any subsequent 0 in the sequence must come exactly two or three spots down from the previous one.

We begin at point 1 and finish at position 19 in this instance.

That is, we advance along the line a whole of 18 positions.

In order to achieve 18, we must add all series consecutive 2s and 3s.

There are numerous methods for doing this:

Case 1: There is just one possible arrangement for nine 2s.

Case 2: Two 3s with six 2s - thus ⁸C₂ ways = 28 ways

Case 3: Four 3s with three 2s - thus ⁷C₄ ways = 35 ways

Case 4: Six 3s - Only 1 way to arrange.

Thus, the number of arrangements = 1 + 28 + 35 + 1 = 65 .

Therefore ,the total possible number of the sequence that cane be made is 65 .

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Step-by-step explanation:

so, if I understand correctly :

angle A = 22°

angle B = 53°

angle D = 38°

remember : the sum of all 3 angles in every triangle is always 180°.

so,

180 = 22 + 53 + AEB

angle AEB = 180 - 22 - 53 = 105°

per the attributes of crossing lines the angles between them are the same on both sides of any of the lines (just left-right mirrored).

so, CB and AD are crossing lines, therefore

angle AEB = angle CED = 105°

and then

180 = 105 + 38 + C

angle C = 180 - 105 - 38 = 37°

Answer:

x=2/3

Step-by-step explanation:

3x - 1 = 1

   + 1   + 1

---------------

3x = 2

÷3    ÷3

------------------

x=2/3

-----------------------

using subtraction and division properties of equality, you can simplify the expression to solve it. you can use other properties of equality for different equations as well, but for this one you only need subtraction and division. :)

The period of the solar system's orbit is 2.05 x 108 years.

What is the time period?

A period is a number that in algebraic geometry can be expressed as the integral of an algebraic function over an algebraic domain. Periods form a ring because their sums and products always remain in the same period.

Don Zagier and Maxim Kontsevich presented some theories and gave a survey of the eras. Periods also appear when computing the integrals that result from Feynman diagrams, and extensive work has been done to understand the relationships.

Solution Explained:

Given,

Radius of the solar system, r=25000 light year

Speed v=230 km/s

Calculate time period by

T = 2πr / v

T = 2πr X (25000 X 3 X 10^8 X 365 X 24 X 60 X 6) / (230 X 10^3)

  = 6.46 X 10^15 X (1 year / 365 X 24 X 60 X 60)
  = 2.05 X 10^8 years

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Answer:

3

Step-by-step explanation:

75/15=

             __3_________

   15    /   75

          -    75

     ---------------------------------

                   0

Have a great day

The likelihood that a shooter will hit the target at least 13 times is 27.92%.

For such a binomial distribution, the probability density function equals the amount of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of achievements is five (i.e., x = 13), as we are keen in the development that the objective will be hit exactly five times.

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit the target at most 13 times.

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Answer:

  y = 120°

Step-by-step explanation:

Given a triangle with external angle y and remote internal angles 33° and 87°, you want the measure of y.

The external angle is the sum of the remote internal angles:

  y = 33° +87°

  y = 120°

__

Additional comment

Angle x is supplementary to y, so its measure is ...

  x = 180° -y = 180° -120°

  x = 60°

Hopefully, you notice that the value of x is ...

  x = 180° -(33° +87°)

This is the same value you get when you solve the equation for the sum of angles in the triangle:

  33° +87° +x = 180°

Effectively, the rule regarding the external angle being the sum of remote internal angles is another way of saying the sum of angles in a triangle is 180°.

A 90​% confidence interval about μ if the sample​ size, n, is 25 is (111.6, 118.4), a 90​% confidence interval about μ if the sample​ size, n, is 20 is (111.1, 118.9), a 80​% confidence interval about μ if the sample​ size, n, is 25 is (112.4, 117.6) and we need population to be normal. So we can not make intervals.

In the given question,

Sample​ mean, x​, is found to be 115.

Sample standard​ deviation, s, is found to be 10.

(a) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7109

Using these values, the margin of error is

ME = 1.7109× 10/√25

ME = 3.4

So confidence interval is

CI = (115-3.4, 115+3.4)

CI = (111.6, 118.4)

(b) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 20.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7291

Using these values, the margin of error is

ME = 1.7291× 10/√20

ME = 3.9

So confidence interval is

CI = (115-3.9, 115+3.9)

CI = (111.1, 118.9)

(c) We have to construct a 80​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 80% confidence interval. So p=0.80.

t-score for confidence interval is given by the excel code is

t=1.3178

Using these values, the margin of error is

ME = 1.3178× 10/√25

ME = 2.6

So confidence interval is

CI = (115-2.6, 115+2.6)

CI = (112.4, 117.6)

​(d) Now we have to check, could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

To use t-distribution, the population has to be normal.Otherwise we need a sample size of at least 30. Here sample size is less than 30.

So we need population to be normal. So we can not make intervals.

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The right question is:

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 115​, and the sample standard​ deviation, s, is found to be 10.

(a) Construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

​(b) Construct an 90​% confidence interval about μ if the sample​ size, n, is 20.

​(c) Construct an 80​% confidence interval about μ if the sample​ size, n, is 25.

​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

So for the maximum area, the values of the width and length of the  rectangle will  be  2.121.

Since we know that the formula for the area of a rectangle is:

A = XY, where x and y are the width and length

since we are given the are, y=√(9-x²), so

A = √(9-x²)

taking the derivative on both sides and considering it to be zero, we get

A' = (x/√(9-x²)(-2x) + √(9-x²) = 0, after multiplying by √(9-x²)

A' = -x² + 9 -x² = 0

=>-2x² =-9

=>x² = 9/2

=> x = 3/√2

so x=2.121 so the for y = √(9-(2.121)^2) =  √(9-4.498) = 2.121

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A rectangle is bounded by a  semicircle y = radical 9 − x^2 and the x-axis. What length and width should the rectangle be to maximize the area

The domain and range of the function C(t) based on the context of the problem is

The range is calculated from minima and maxima, this will be achieved using derivative

C(t) = -5t² + 10t

C'(t) = 0 = -10t + 10

t = 1

substituting t = 1

C(t) = -5(1)² + 10t = 5

so at point (1, 5) it is either minima or maxima,

The second derivative test will help to confirm if point (1, 5) is minima or maxima

C'(t) = -10t + 10

C''(t) = -10

a negative value means it is a maxima

Hence the highest value of the concentration C(t) is 5 mg/L and this is at t = 1

The concentration cannot be less than zero or negative hence the lowest concentration is 0. and the range is 0 to 5

0 ≤ C ≤ 2

The time cannot be below zero so the lowest time will be zero

The domain is controlled by the input values. considering the least concentration of the drug which will be at C = 0

C(t) = -5t² + 10t

0 = -5t(t - 2)

-5t = 0

t = 0

t - 2 = 0

t = 2

The roots of the quadratic equation gives the domain to be 0 to 2

0 ≤ t ≤ 2

The graph is attached

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Answer:

565.9

Step-by-step explanation:

The rate of change of the area of a square is 12m^2/sec.

What do you mean by rate of change?

The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.

Rate of Change is equal to [tex]\frac{Change in y}{Change in x}[/tex].

Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.

Solution Explained:

Given,

S = 2m and ds/dt = 3m/s

So, we use

Area = s^2

dA/dt = 2s ds/dt

         = 2 X 2 X 3

Therefore, the rate of change of the area is 12m^2/s.

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The monthly payment amount a woman has to pay for the car is $462.91.

Here we have to find the monthly payment amount.

The cost of car = $23,800

Down payment = $3,500

Rate(r) = 4.5%

time(t) = 4 years

Periodic interest(i) = 0.045/12

Formula to calculate monthly payment:

A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1

Loan amount = 23800 - 3500

                      = $ 20300

A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1

  = 20300× 0.004488 / 0.196814

  = 462.91

Therefore the monthly payment is $462.91.

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It will cost his parents $187.5 to invite 15 friends to his party because it cost $12.5 to invite just one.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, may be used to calculate how many kilometers a car would go on one litre of gas if it travels 44 km on two litres of fuel.

Here,

For inviting 20 friends, The cost of party was $250.

So for 1 friend,

=250/20

=$12.5

Now he wish to invite 15 friends,

=12.5*15

=$187.5

The cost of inviting 15 friends to his party will cost $187.5 to his parents as cost of inviting 1 friend was $12.5.

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