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2 years ago

Spencer is 32 years younger than Jennifer. 3 years ago, Jennifer’s age was 3 times Spencer’s age. How old is Spencer now?

Mathematics

1 answer:

natali 33 [55]2 years ago

6 0

Answer:

Step-by-step explanation:

The sentences 'Spencer is 32 years younger than Jennifer' can be modeled by x = y-32 (x representing spencer's age and y representing Jennifer's). The sentence '3 years ago, Jennifer's age was 3 times Spencer's age' can be modeled by the equation x-3 = 1/3(y-3). Solving the second equation for y gives you y = 3x-6. Substitute into the first equation to get x = (3x - 6) - 32. Solve for x, which represents Spencer's age, to get x = 17

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What ratio is proportional to 18/21

Doss [256]

Answer:

There are many.

Step-by-step explanation:

When you say proportional, you are looking for a ratio that is equivalent to the ratio given. In your case, there are many so you might need to be more specific. But still, we can help you figure it out.

An easy way to do this would be to scale it down to its simplest form and then move upwards. To find proportional ratios, just multiply denominator and the denominator with the same factor.

$\dfrac{18}{21} = \dfrac{6}{7}$

That is your ratio in its simplest form. Now we can scale up, I'll show you how to do one completely:

$\dfrac{6}{7} x \dfrac{2}{2} = \dfrac{12}{14}$

That's the same ratio scaled up by a factor of 2.

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

$\dfrac{6}{7} x \dfrac{3}{3} = \dfrac{18}{21}$

That's the ratio given

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$\dfrac{6}{7} x \dfrac{4}{4} = \dfrac{24}{28}$

Scaled up by a factor of 4

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$\dfrac{6}{7} x \dfrac{5}{5} = \dfrac{30}{35}$

Scaled up by a factor of 5.

The list goes on and on.

3 0

3 years ago

Person who answers first and correctly will be named the brainiest answer.

Korvikt [17]

1) From building 1 to 2: 5 - (-3) = 8

2) From 2 to 3: 4 - (-5) = 9

3) From 3 to 4: 5 - (-3) = 8

4) From 4 to 1: 4 - (-5) = 9

Total: 8 + 9 + 8 + 9 = 34 units = 34*100 feet = 3400 feet.

Answer: 3400 feet

6 0

3 years ago

Simon has $40 to buy baseballs for her team's practice. Each baseball cost $3. Which inequality represents this situation?

Liula [17]

3b<40 because no matter what the price cannot be over 40 because she only has 40

4 0

3 years ago

Read 2 more answers

A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life

alisha [4.7K]

Answer:

The null hypothesis is $H_0: \mu \leq 10$

The alternative hypothesis is $H_1: \mu > 10$

b-1) The value of the test statistic is t = 1.86.

b-2) The p-value is of 0.0348.

Step-by-step explanation:

Question a:

Test if the battery life is more than twice of 5 hours:

Twice of 5 hours = 5*2 = 10 hours.

At the null hypothesis, we test if the battery life is of 10 hours or less, than is:

$H_0: \mu \leq 10$

At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:

$H_1: \mu > 10$

b-1. Calculate the value of the test statistic.

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

10 is tested at the null hypothesis:

This means that $\mu = 10$

In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.

This means that $n = 45, X = 10.5, s = 1.8$

Then

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}$

$t = 1.86$

The value of the test statistic is t = 1.86.

b-2. Find the p-value.

Testing if the mean is more than a value, so a right-tailed test.

Sample of 45, so 45 - 1 = 44 degrees of freedom.

Test statistic t = 1.86.

Using a t-distribution calculator, the p-value is of 0.0348.

5 0

2 years ago

Rachel has a bag of marbles. She added 6 marbles to the bag but then took out 8 marbles. The bag now has 14 marbles. How many ma

Anna35 [415]

Answer:

to my knowledge of this it is 28

Step-by-step explanation:

because just pay attention to the math in it she ended up with 14 in the end so add 14 and the 6 she added in the beginning and then you get 20 so then you add the 20 marbles and the 8 marbles she took out so you end up with 28 total marbles i hope this helps

6 0

3 years ago