A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes. A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes. Conduct a hypothesis test at the 5% significance level.

Answers

Answer 1

Answer:

Answer:

t = 2.9272 > 1.708 at 25 degrees of freedom

null hypothesis is rejected

The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes

Step-by-step explanation:

Step (i):-

A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes.

Given sample size 'n' = 26

The mean of the sample 'x⁻ = 21.1 min

Standard deviation of the sample 'S' = 5.4 min

The Population mean 'μ' = 18min

Step(ii):-

Null hypothesis: H₀ : The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes.

'μ' > 18min

Alternative hypothesis :H₁:

'μ' <18min

Level of significance : ∝=0.05

Degrees of freedom γ = n-1 = 26-1 =25

The test statistic

$t = (x^(-)-mean )/((S)/(√(n) ) )$

$t = (21.1-18)/((5.4)/(√(26) ) )$

t = 2.9272

Step(iii):-

The tabulated value t = 1.708 at 25 degrees of freedom

t = 2.9272 > 1.708 at 25 degrees of freedom

Null hypothesis is rejected at 5% significance level of significance

Conclusion:-

The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes

x = - 2/5

Step-by-step explanation:

$3(x+2)=2(2-x)\n\n\mathrm{Expand\:}3\left(x+2\right):\quad 3x+6\n\n\mathrm{Expand\:}2\left(2-x\right):\quad 4-2x\n\n3x+6=4-2x\n\n\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\n\n3x+6-6=4-2x-6\n\n3x=-2x-2\n\n\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\n\n3x+2x=-2x-2+2x\n\nSimplify\n\n5x=-2\n\nDivide\:both\:sides\:by5\n\n(5x)/(5)=(-2)/(5)\n\nx=-(2)/(5)$

An experiment is pulling a ball from an urn that contains 3 blue balls and 5 red balls. a.) Find the probability of getting a red ball. b.) Find the probability of getting a blue ball. c.) Find the odds for getting a red ball. d.) Find the odds for getting a blue ball.

Answers

Answer:

Step-by-step explanation:

The urn contains 3blue balls 5 red balls

a) probability of getting a red ball

P=no of favourable of outcomes /total no outcomes

P(red ball) = 5/8

b) Probability of blue ball

P(blue ball) = 3/8

c) Odds getting a red ball

odds in favour of any object = m/n

m : event to occur

n : event will not occur

Odds(red ball) = 5/3

Odds(blue) = 3/5

HELP ME PLEASE I DO NOT UNDERSTAND PLEASE THANK YOU HAVE A GOOD DAYa.) Draw a rectangular prism with these dimensions: 3 units x 9 units x 27 units.

b.) Draw a net of the rectangular prism and label each face with its surface area.

c.) Use the net of the rectangular prism to find the surface area of the solid.

Answers

You can draw a rectangular prison not to scale and just label these on the prism length= 3 width= 9 and height =27
Then you would draw a net the rectangular prism like if you were to unfold it then use the calculation from a and solve for the surface area
Then you add the surface areas together I believe sorry if I get this wrong and it should be the surface area of everything

There are two boxes of Lego pieces. One box has 200 pieces and the other box has 115 pieces. Which of the following best describes how 4 people will divide the Lego pieces as evenly as possible?three people will get 77 pieces
One person will get 76 pieces

Three people will get 78 pieces
One person will get 77 pieces

Three people will get 79 pieces
One person will get 78 pieces

Three people will get 76 pieces
One person will get 75 pieces

Answers

The answer is C: three people will get 79 pieces and one person will get 78 pieces.
79x3=237
237+78=315
There were 315 total pieces (200+115) so it has to be C.
Hope this helps!

three people will get 79 pieces
one person will get 78 pieces
200+115=315
79x3=237+78=315

Silvio wants to find the perimeter of quadrilateral ABCD. He begins by computing the length of side AB using the distance formula. Finish Silvio’s work to find the length of side AB.

Answers

Answer:

Step-by-step explanation:

AB = √(-4)² + (-3)²

AB = √ 16 + 9

AB = √ 25

AB = 5

AD = 4 ; DC = 4 ; BC = 7

Perimeter = 5 + 4 + 4 + 7 = 20 units

2. Solve the following problems involving simple interest. RecallSimple Interest-INT=PV*r*t
An investor decides to offer a business owner a $45,000 loan at simple interest of 3.5%
per year. Find the total amount in dollars, the investor will receive when the loan is
repaid after 7 years.

Answers

Answer:

A = $56025

Step-by-step explanation:

Given that,

An investor decides to offer a business owner a $45,000 loan at simple interest of 3.5% per year.

Principal, P = 45,000

Rate of interest, R = 3.5%

We need to find the total amount the investor will receive when the loan is repaid after 7 years.

The formula for the simple is given by :

$I=(PRT)/(100)\n\n=(45000* 3.5* 7)/(100)\n\n=\$ 11025$

We know that,

Amount = Principal + simple interest

So,

A = 45,000 + 11025

A = $56025

So, the required amount is equal to $56025.

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