Use the following situation to answer the next 2 questions: A manufacturer claims that a particular car will get at least 50 miles per gallon on the highway. The researchers of a consumer-oriented magazine believe this claim is too high and plan a test with a simple random sample of 30 cars. Assume the population standard deviation for individual cars is 2.3 miles per gallon. The researchers found the sample mean to be 49 miles per gallon, and they decided on using a = 0.05. (Hint: H n SD = H. Find the value of the test statistic. A.-2.38 B.-1.645 C.-0.43 D. 0.0087 E. 2.38 What is the conclusion of the hypothesis test? There evidence to reject the manufacturer's claim because sufficient:________A. Is not; 49 miles per gallon is too close to the claimed 50 miles per gallon B. Is not; the p-value of 0.0087 is less than the significance level C. Is; the sample mean is less than the claimed mean D. Is; the p-value of 0.0087 is less than the significance level E. Is; the p-value of 0.0174 is less than the significance level

Answer:

Step-by-step explanation:

From the diagram, we can se that line l is parallel to m. This means that according to geometry, m<7 and m<9 are located on the same position on line n. Hence m<7 = m<9 (corresponding angle)

Given

m<7 = 9x+ 5

m<9 = x+37

Equaling both

9x + 5 = x+ 37

9x - x = 37-5

8x = 32

x = 32/8

x = 4

Hence the value of x is 4

Answer:

[tex]p = i - e[/tex]

Step-by-step explanation:

Given

[tex]i = income[/tex]

[tex]e = expenses[/tex]

Required

Determine the profit (p)

Profit (p) is the difference between income (i) and expenses (e)

.

Mathematically:

[tex]Profit = Income - Expenses[/tex]

i.e.

[tex]p = i -e[/tex]

Option D is correct.

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Formula to be used,

A = [tex]P(1+\frac{r}{n})^{nt}[/tex]

Here, A = Final amount

P = Principal amount

r = rate of interest

n = Number of compounding (In a year)

t = Duration of investment (In years)

Question (5)

P = $4250

r = 0.015

n = 4

t = 3 years

A = [tex]4250(1+\frac{0.015}{4})^{4\times 3}[/tex]

A = [tex]4250(1.00375)^{12}[/tex]

A = $4445.24

Part (C)

1). P = $6000

   r = 0.03

   n = 2

   t = 10 years

  A = [tex]6000(1+\frac{0.03}{2})^{2\times 10}[/tex]

      = [tex]6000(1.015)^{20}[/tex]

      = $8081.13

2). P = $9000

    r = 0.05

    n = 2

    t = 8 years

    A = [tex]9000(1+\frac{0.05}{2})^{2\times 8}[/tex]

        = [tex]9000(1.025)^{16}[/tex]

        = $13360.55

Answer:

40%

Step-by-step explanation:

26×100=2600÷65=40

40%×65=26

Answer:

quadrilateral

Step-by-step explanation:

A quadrilateral that has two pairs of parallel sides.

Answer:I am pretty sure the answer is

C. "They are perpendicular to each other."

Step-by-step explanation:

For a shape to be reflected, it must be reflected across a line.

The true statement about the relationship between segments M, M' and the x-axis is that (c) they are perpendicular to each other

Given that:

When the shape is reflected across the x-axis, we have the following perpendicular and congruent lines

Hence, the relationship between segments M, M' and the x-axis is that (c) they are perpendicular to each other

Read more about reflection at:

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Answer:

The alligator is 60 Inches long.

Step-by-step explanation:

5 feet is 60 inches.

hope it helps!

Answer:

60 inches

Step-by-step explanation:

There are 12 inches in 1 foot, therefore the ratio of inches to feet is 12:1.

If the alligator is 5 feet than the amount of inches increase.

In order to find how long the alligator is in inches, multiply 5 by 12

5 x 12 = 60

9514 1404 393

Answer:

  13 cm wide;  15 cm long

Step-by-step explanation:

Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...

  w(w+2) -(w-1)(w+1) = 27

 w^2 +2w -(w^2 -1) = 27

 2w +1 = 27

  w = (27-1)/2 = 13

The original piece of cardboard was 13 cm wide and 15 cm long.

Step-by-step explanation:

Triangles RQP and RBC are congruent.

Letters R and P are the 1st and 3rd letters in RQP.

Letters R and C are the 1st and 3rd letters in RBC.

Hence line RP = line RC = line CR (D).

D) CR

ΔRQP ≅ ΔRBC

They are congruent so if you highlight the line PR and find the similar one,

ΔRQP ≅ ΔRBC

The line would be line CR.

Answer:

The equation in slope-intercept form is y = 8/5x-4.

I hope this helps! Have a nice day!!

Answer:

b?

Step-by-step explanation:

b= v16.4

Answer:

the phone with me and I will be in the future of our games in call of duty Black ops game clip is not available for remote playback of the phone with me know if I can be used for

Step-by-step explanation:

explain the IF

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Answer:

Step-by-step explanation:

Hey if you give me your email i ca email you the aswer it wot let me link a photo lol

Answer:

12.5

Step-by-step explanation:

it's the awnser. I need to explain why

Answer:

226 cubed foot (rounded to 3 s.f.)

Step-by-step explanation:

Volume of cyclinder: [tex]\pi[/tex] × r² × h

Volume of cylindrical tank = [tex]\pi[/tex] × 3² × 8

                                           = 72[tex]\pi[/tex]

                                           = 226 cubed foot (rounded to 3 s.f.)

Answer:

1) the average time a car is in the system is 0.1587 min

2) the average number of cars in the system 0.1111

3) the average time cars spend waiting to receive service is 0.01587 min

4) the average number of cars in line behind the customer receiving service is 0.01111

5) the probability that there are no cars at the window is 0.9

6) the percentage of time that the postal clerk is busy is 10%

7) the probability that there are exactly two cars in the system is 0.1217

Step-by-step explanation:

Given that;

Arrival rate λ = the rate of 7 every 10 minutes = 7/10 = 0.7

Average service time μ = 7 minutes

The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

1) What is the average time a car is in the system?

Average in the system W = 1 / (μ - λ)

= 1 / (7 - 0.7) = 1 / 6.3 = 0.1587 min

therefore the average time a car is in the system is 0.1587 min

2) What is the average number of cars in the system?

Average number of cars L = λ / (μ - λ)

= 0.7 / (7 - 0.7) = 0.7/6.3 = 0.1111

Therefore the average number of cars in the system 0.1111

3) What is the average time cars spend waiting to receive service?

Average time spend waiting for services  Wq = λ / μ(μ - λ)

= 0.7 / 7(7 - 0.7) = 0.7/44.1 = 0.01587 min

Therefore the average time cars spend waiting to receive service is 0.01587 min

4) What is the average number of cars in line behind the customer receiving service?

average number of cars in line behind the customer receiving service

Lq = λ² / μ(μ - λ) = (0.7)² / 7(7 - 0.7) = 0.49 / 44.1 = 0.01111

Therefore the average number of cars in line behind the customer receiving service is 0.01111

5) What is the probability that there are no cars at the window?

probability that there are no cars at the window = 1 -  (λ / μ)

= 1 -  (0.7 / 7) = 1 - 0.1 = 0.9

Therefore the probability that there are no cars at the window is 0.9

6) What percentage of the time is the postal clerk busy?

percentage of the time is the postal clerk busy = (λ / μ)

= (0.7 / 7) = 0.1 ≈ 10%

Therefore the percentage of time that the postal clerk is busy is 10%

7) What is the probability that there are exactly two cars in the system?

the probability that there are exactly two cars in the system = (λ²e^-λ) / 2!

= (0.7²e^-0.7) / 2! = 0.2433 / 2 = 0.1217

Therefore the probability that there are exactly two cars in the system is 0.1217

Answer:

12

Step-by-step explanation:

a2 b

(    )2 (  )

(–2)2 (3)

(4)(3)

Answer:

360

Step-by-step explanation:

Six letters in twelve with a repeated e would be 6! ÷ 2

Answer:

sqrt(A/pi), -sqrt(A/pi)

Step-by-step explanation:

A=pi*r^2

r^2=A/pi

r=sqrt(A/pi), -sqrt(A/pi)

Answer:

you should use desmos graphing. When you get there in the top left corner there are 3 lines. press that and scroll down. when you see sarcastic linear regression press that and put the coordinates points I hope this helped :))

Answer:

1/8

Step-by-step explanation:

7/12= 14/24                                    14/24 + 7/24= 21/24                    

21/24= 7/8           1-7/8= 1/8

The fraction of the total number of puzzle pieces has not been used is 1/8.

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 Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces.

The fraction of the total number of puzzle pieces has not been used is calculated as,

7/12= 14/24      

21/24= 7/8        

1-7/8= 1/8

To know more about an expression follow

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Answer:

A) 0.1339

B) 0.8078

Step-by-step explanation:

The Poisson Distribution formula is given by;

P(x; μ) = (e^(-μ) × (μ^(x))/x!

We are given;

Variance = 0.5 per month

Now, in Poisson distribution, variance = mean.. Thus, mean μ = 0.5 per month

A) We want to find the probability that 4 typhoons will hit US in a year.

Thus, x = 4

But since it's for a year, then μ = 0.5 × 12 = 6

So;

P(x = 4) = (e^(-6) × (6^(4))/4!

P(x = 4) = 0.00247875 × 1296/24

P(X = 4) = 0.1339

B) probability that at least 2 typhoons will hit US in a given half-year is;

P(X ≥ 2) = 1 - P(X < 2)

P(X < 2) = P(X = 0) + P(X = 1)

In a half given year, μ = 0.5 × 6 = 3

P(X = 0) = (e^(-3) × (6^(0))/0!

P(X = 0) = 0.0498

P(X = 1) = (e^(-3) × (6^(1))/1!

P(X = 1) = 0.1494

P(X < 2) = 0.0498 + 0.1494

P(X < 2) = 0.1922

P(X ≥ 2) = 1 - 0.1922

P(X ≥ 2) = 0.8078

Answer:

21

Step-by-step explanation:

I am 90% sure but tell me if i'm wrong

Answer:

[tex]0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11[/tex]

Step-by-step explanation:

Given

[tex]0, 8, 9, 6, 5, 7, 2, 4, 3, 1, 11[/tex]

Required

Determine the mode

Though, not necessary; it is a good practice to order the given data either in ascending or descending order.

In ascending order, the ordered data are:

[tex]0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11[/tex]

Mode implies that: the data that has the highest number of occurrence.

In the given data, each data has a frequency of 1.

Hence, the mode is:

[tex]0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11[/tex]

Answer:

a) we get value of n: n=10.7 or n=1.2 when d=30

b) we get value of n: n=9.6 or n=2.3 when d=20

Step-by-step explanation:

a) solve for  n When  do= 30

Put d= 30 in the given equation:

[tex]d = n^2-12n + 43[/tex]

[tex]30=n^2-12n+43\\n^2-12n+43-30=0\\n^2-12n+13=0\\[/tex]

Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a=1, b=-12 and c=13

[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(13)}}{2(1)}\\n=\frac{12\pm\sqrt{144-52}}{2}\\n=\frac{12\pm\sqrt{92}}{2}\\n=\frac{12\pm9.59}{2}\\n=\frac{12+9.59}{2} , n=\frac{12-9.59}{2}\\n=10.7 , n=1.2\\[/tex]

So, we get value of n: n=10.7 or n=1.2

b) solve for n  when  d=20

[tex]d=n^2-12n+43\\20=n^2-12n+43\\n^2-12n+43-20=0\\n^2-12n+23=0\\[/tex]

Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a=1, b=-12 and c=23

[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(23)}}{2(1)}\\n=\frac{12\pm\sqrt{144-92}}{2}\\n=\frac{12\pm\sqrt{52}}{2}\\n=\frac{12\pm7.21}{2}\\n=\frac{12+7.21}{2} , n=\frac{12-7.21}{2}\\n=9.6 , n=2.3\\[/tex]

So, we get value of n: n=9.6 or n=2.3

Answer:   Slope = -1.000/2.000 = -0.500

 x-intercept = 0/1 = 0.00000

 y-intercept = 0/2 = 0.00000

Step-by-step explanation:

Answer:

I had this question and i got it right it is the measure is four

Step-by-step explanation:

Answer: 79 seconds.

Step-by-step explanation:1) we have to calculate the lenght of the baseball field.

perimeter of the baseball field=2(radius)+lenght of a semicircle.

2(radius)=2(175 ft)=350 ft

lenght of a semicircle=40% of a circumference=(40/100)(2πr)

Perimeter of the baseball field=2(175 ft) + (40/100)(2π175 ft)=

=350 ft + 140π ft=350 ft + 439.82 ft=789.82 ft,

2)Now, we calculate the amounts of time that it takes you to ruan arount the baseball field.

10 ft------------------------1 second

789,82 ft-----------------    x

x=(789.82 ft * 1 second) / 10 ft=78.98 s≈79 s

Answer: x = -2/3

[tex]\frac{x}{x+2}- \frac{4}{x-2}=1\\\\<=>\frac{x(x-2)}{(x+2)(x-2)}-\frac{4(x+2)}{(x+2)(x-2)}=1\\\\\\<=>\frac{x(x-2)-4(x+2)}{(x-2)(x+2)}=1\\\\\\=>x(x-2)-4(x+2)=(x-2)(x+2)\\\\\\<=> x^{2} -2x-4x-8=x^{2} -4\\\\\\<=>-6x-8=-4\\\\\\<=>-6x=8-4\\\\\\<=>-6x=4\\\\\\<=>x=-4/6=-2/3[/tex]

Step-by-step explanation: