MATHEMATICS COLLEGE

1. An equation is shown below.3 (x-2) + 7x= 1/2(6x-2)
How many solutions, if any, does the equation have?

Answers

Answer 1

Answer:

Answer:

x=5/7

Step-by-step explanation:

3(x-2)+7×=1/2×(6×-2)

3x-6+7×=1/2×2(3×-1)

3×-6+7×=3×-1

-6+7×=-1

7×=-1+6

7×=5

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Prove that if a,b and c are odd integers such that a + b +c = 0, then abc < 0. (you are permitted to use well-known properties of integers here.) be sure to show all work.

Answers

The sum of three odd integers will never be an even integer (0).

This proof is impossible.

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:

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

A survey in Men’s Health magazine reported that 39% of cardiologists said that they took vitamin E supplements. To see if this is still true, a researcher randomly selected 100 cardiologists and found that 36 said that they took vitamin E supplements. At α = 0.05, test the claim that 39% of the cardiologists took vitamin E supplements. A recent study said that taking too much vitamin e might be harmful how might this study make the results of the previous study invalid?

Answers

Answer:

$z=\frac{0.36 -0.39}{\sqrt{(0.39(1-0.39))/(100)}}=-0.615$

The p value for this case would be:

$p_v =2*P(z<-0.615)=0.539$

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39

Step-by-step explanation:

Information given

n=100 represent the random sample taken

X=36 represent the number of people that take E supplement

$\hat p=(36)/(100)=0.36$ estimated proportion of people who take R supplement

$p_o=0.39$ is the value that we want to test

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true proportion is equatl to 0.39 or not, the system of hypothesis are.:

Null hypothesis: $p=0.39$

Alternative hypothesis: $p \neq 0.39$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

Replacing the info we got:

$z=\frac{0.36 -0.39}{\sqrt{(0.39(1-0.39))/(100)}}=-0.615$

The p value for this case would be:

$p_v =2*P(z<-0.615)=0.539$

The area of a circle is 127 square units. What would the circumference of the circle be?

Answers

Answer:

Area of the circle = π×r²

127 = 3.14 × r²

=> 127/3.14 = r²

=> 40.44 = r²

=> √40.44 = r

=> r = 6.35

Circumference of the circle = 2πr

= 2×22/7×6.35

=279.4/7

= 39.91

= 40 units

Wendi is 6 years older than Zaviel. The sum of their ages is 30. Which of these systems of equations can be used to find Wendi's age (w) and Zaviel's age (z)?

Answers

The system of equations for the ages of Wendi and Zaviel can be obtained as x = y + 6 and x + y = 30 respectively.

What is a system of linear equations?

A system of linear equations is a group of equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

Suppose the age of Wendi and Zaviel be x and y respectively.

Then, the equation for their age can be written as,

x = y + 6

And, the equation for the sum of ages is given as,

x + y = 30

Hence, the equations that represent the given case are x = y + 6 and x + y = 30 respectively.

To know more about system of equations click on,

brainly.com/question/24065247

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For Wendy’s age you can’t do 30-6=24 and then for Zaviel’s you can do 24-6=18 so Wendy is 24 years old and Zaviel is 18 years old.
30-6=w
W-6=z
30-6=24(w)
24-6=18(z)

Michael started a savings account with $300. After 4 weeks, he had $350 dollars, after 9 weeks, he had $400. What is the rate of change of money in his savings account per week?