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2 years ago

Hi, I'm very confused and I need help.

Mathematics

1 answer:

Sphinxa [80]2 years ago

8 0

Answer:

x ≤ -5

Step-by-step explanation:

According to the 'key' on the far right :

First box has 4 x + 12 in it

second box has - 8 in it

4x+12 ≤ -8 subtract 12 from both sides

4x ≤ -20 divide through by 4

x ≤ -5

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In the year 2000, the United States had a population of about 281.4 million people; by 2010, the population had risen to about 3

IgorC [24]

Answer:

Part 1. 0.9259 % per year

Part 2. P = 281.4e^(0.009 259t); 338.6 million

Step-by-step explanation:

Data:

P₀ = 281.4 million

P = 308.7 million

Part 1. Growth rate

t = 2010 - 2000 = 10 yr

P = P₀e^(rt)

308.7 = 281.4e^(10r)

e^(10r) = 1.0970

10r = ln1.0970

r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259

r = 0.9259 % per year

The 10-year continuous growth rate is 0.9259 % per year.

Part 2. Population model

The population model is

P = 281.4e^(0.009 259t)

where P is in millions and t is the number of years since 2000.

By 2020,

P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203

P = 338.6 million

The estimated population in 2020 is 338.6 million.

8 0

3 years ago

13.

liubo4ka [24]

Answer:

6x +4 where x is amount for standard call

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Solve for p.<br> -p - 1 = 5 - 9p + 10p

Darina [25.2K]

Answer:

p= 1/3 or 0.33 repeating

Step-by-step explanation:

5-19p=-p-1

5=18p-1

6=18p

divide by 18

6/18 = 1/3 or 0.33 repeating

5 0

3 years ago

Read 2 more answers

Joe likes to go fishing. He knows that the stronger the fishing line is, the larger the fish that he can catch.

Trava [24]

The answer is
<span>B.

The size of the fish Joe can catch is a function of the strength of his fishing line.
</span>

6 0

3 years ago

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances

wariber [46]

Answer:

Step-by-step explanation:

Hello!

The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUV's equipped with tires made with compound 1 is shorter than the braking distance of SUV's equipped with tires made with compound 2.

So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUV's equipped with tires made using compound 2.

Two samples of 81 braking tests are made and the braking distance was measured each time, the study variables are determined as:

X₁: Braking distance of an SUV equipped with tires made with compound one.

Its sample mean is X[bar]₁= 69 feet

And the Standard deviation S₁= 10.4 feet

X₂: Braking distance of an SUV equipped with tires made with compound two.

Its sample mean is X[bar]₂= 71 feet

And the Standard deviation S₂= 7.6 feet

We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.

The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂

The statistical hypotheses are:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

α: 0.05

The statistic to use to compare these two populations is a pooled Z test

$Z= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} } }$

Z ≈ N(0;1)

$Z_{H_0}= \frac{69-71-0}{\sqrt{\frac{108.16}{81} +\frac{57.76}{81} } }= -1.397$

The rejection region if this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:

$Z_{\alpha } = Z_{0.05}= -1.648$

Decision rule:

If $Z_{H_0}$ > -1.648 , then you do not reject the null hypothesis.

If $Z_{H_0}$ ≤ -1.648 , then you reject the null hypothesis.

Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.

At a 5% significance level, you can conclude that the average braking distance of SUV's equipped with tires manufactured used compound 1 is greater than the average braking distance of SUV's equipped with tires manufactured used compound 2.

I hope you have a SUPER day!

4 0

4 years ago