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1 year ago

Tim and Jim are working on a school project together. If he had to work by himself, it would take

Mathematics

1 answer:

Vladimir [108]1 year ago

4 0

Answer: 6 hours

Step-by-step explanation:

Given, Tim and Jim are working on a school project together.

Tim takes 10 hours to complete the school project.

If Jim worked alone, it would take him 15 hours

Let t be the time they both take if they work together.

Then, $\dfrac{1}{t}=\dfrac{1}{\text{Time taken by Tim}}+\dfrac{1}{\text{Time taken by jim}}$

$\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3+2}{30}=\dfrac{5}{30}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow t=6$

So, it will take<u> 6 hours</u> to complete the school project together .

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What is the finance charge on $13,300 financed at 7.9 percent for 4 years if the monthly payment per $100 is $2.44?

luda_lava [24]

If you borrowed $100, then your monthly payment is $2.44

If you borrowed $200, then your monthly payment is 2*2.44 = 4.88

etc etc

We can set up a proportion

2.44/100 = x/13300

to figure out the monthly payment x. Cross multiply and solve for x

2.44*13300 = 100*x

100x = 2.44*13300

100x = 32452

x = 32452/100

x = 324.52

So the monthly payment is $324.52

An alternative way to get this monthly payment is to apply 2.44% to 13300, which is another way to view the phrase "monthly payment per $100 is 2.44"

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

There are 48 months in 4 years (start with 12 mon = 1 yr, then multiply both sides by 4) so we multiply 48 by the monthly payment to get the result 48*324.52 = 15,576.96. This is the total amount you have to pay back which is the principal plus interest.

Subtract off the principal (amount borrowed) to find the interest or finance charge: 15,576.96 - 13,300 = 2,276.96

Answer: Choice B

5 0

2 years ago

A random sample of 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The

lisov135 [29]

Answer:

$(75.1 -72.1) -1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= -1.96$

$(75.1 -72.1) +1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= 7.96$

And the confidence interval would be given by:

$-1.96 \leq \mu_1 -\mu_2 \leq 7.96$

And since the confidence interval contains the value 0 we have enough evidence to conclude that we don't have significant differences between the two means at 10% of significance.

Step-by-step explanation:

For this case we have the following info given :

$\bar X_1= 75.1$ represent the sample mean for the scores of the undergraduate students

$s_1 = 12.8$ represent the standard deviation for the undergraduate students

$n_1 =35$ the sample size for the undergraduate

$\bar X_2= 72.1$ represent the sample mean for the scores of the high school students

$s_2 = 14.6$ represent the standard deviation for the high school students

$n_2 =50$ the sample size for the high school

The confidence interval for the true difference of means is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

The degrees of freedom are given by:

$df=n_1 +n_2 -2= 35+50-2=83$

The confidence level is 90% and the significance level is $\alpha=0.1$ and $\alpha/2 =0.05$ then the critical value would be:

$t_{\alpha/2}= 1.99$

And replacing the info we got:

$(75.1 -72.1) -1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= -1.96$

$(75.1 -72.1) +1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= 7.96$

And the confidence interval would be given by:

$-1.96 \leq \mu_1 -\mu_2 \leq 7.96$

And since the confidence interval contains the value 0 we have enough evidence to conclude that we don't have significant differences between the two means at 10% of significance.

8 0

1 year ago

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

masha68 [24]

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

7 0

1 year ago

The junior class has 50 students. Twenty-five students take only french, 15 take only Latin, and 10 take both. If a student is c

zavuch27 [327]

There are 15 students who take Latin, and 10 students who take both.
Therefore:
15+10 =25 total students taking Latin
25students / 50 total students = 1/2

The answer is 1/2.

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2 years ago

Read 2 more answers

If x is the midpoint of ZW, then ZX=XW

sasho [114]

Answer:

True.

Step-by-step explanation:

By definition of a mid point, it is located in the middle of two connected points. This means that the split is equal on both sides.

IF X is the midpoint of ZW, then ZX = XW.

4 0

1 year ago