MATHEMATICS COLLEGE

Write each decimal in figures.1) five hundred forty-four and four-tenths
2) three and twenty-five hundreds
3) twenty-five and one-tenth
4) fifty-two and seventy-six hundred
5) eight hundred seventy-two and one tenths

Answers

Answer 1

Answer:

Step-by-step explanation:

1 544.4

2. 3.025

3. 25.1

4. 52.076

5. 872.1

for your information

1 tenth is equal to 0.1

1 hundredth is equal to 0.01

1 thousandth is equal to 0.001

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Answers

Answer:

A, f(x) ≥ -36

Step-by-step explanation:

The range is all the possible y values, also called f(x) values.

In this case, the range of the graph extends from -36 to infinity, so the correct answer is f(x) ≥ -36.

Let me know if this helps!

Answer:

C I think

Step-by-step explanation:

Fill in the blank with the missing term in the pattern. 216, 72, 24, ____

Answers

The Answer is 216, 72, 24, 8

A city currently has 31,000 residents and is adding new residents steadily at the rate of 1200 per year. If the proportion of residents that remain after t years is given by S(t) = 1/(t + 1), what is the population of the city 7 years from now?

Answers

Answer:

Population of the city after 7 years from now, P(7) = 6370

Given:

Initial Population, $P_(i) = 31000$

rate, r(t) = 1200 /yr

S(t) = [/tex]\frac{1}{1 + t}[/tex]

Step-by-step explanation:

Let the initial population be $P_(i) = 31000$

The population after T years is given by the equation:

$P(T) = P_(i)S(T) + \int_(0)^(T)S(T - t)r(t) dt$ (1)

Thus, the population after 7 years from now is given by using eqn (1):

$P(7) = (3100)/(1 + 7) + 1200\int_(0)^(7)(1)/(8 - t) dt$

$P(7) = 3875 - 1200ln(8 - t)|_(0)^(7)$

$P(7) = 3875 - 1200(ln(1) - ln(8))$

$P(7) = 3875 + 2495 = 6370$

Find the zeros of f(x) =x^3+2x^2-3x

Answers

Answer: 0, 1, -3

Step-by-step explanation:

f(x) = x^3 +2x^2 -3x

f(x) = x(x^2 +2x-3)

f(x) = x(x-1)(x+3)

to find zeroes, plug into f(x) and solve for each value of x. doing this gives 0, 1, and -3

The time needed for all college students to complete a certain paper-and-pencil maze follows a normal distribution with a population mean of 30 seconds and a population standard deviation of 3 seconds. You wish to see if the mean time μ (where μ stands for population mean) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. It takes them an sample average of 31.2 seconds to complete the maze. Use this information to test the hypotheses:

H0: μ = 30,

Ha: ≠30

at the significance level of 0.01.

You conclude:

a) There is not enough evidence to support the claim.

b) There is enough evidence to support the claim.

Answers

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 30\ seconds$

The standard deviation is $\sigma = 3 \ seconds$

The sample size is n = 9

The null hypothesis is $H_o: \mu = 30$

The alternative hypothesis is $H_a : \mu \ne 30$

The level of significance is $\alpha = 0.01$

The sample mean is $\= x = 31.2$

Generally the test statistics is mathematically represented as

$z = ( \= x - \mu )/( (\sigma)/(√(n) ) )$

=> $z = ( 31.2 - 30)/( (3)/(√(9) ) )$

=> $z = 1.2$

From the z table the area under the normal curve to the right corresponding to 1.2 is

$P(Z > 1.2) = 0.11507$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.2)$

=> $p-value = 2 *0.11507$

=> $p-value = 0.230$

From the value obtained w can see that

$p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

Final answer:

To test the hypotheses, use a one-sample t-test to compare the sample mean to the population mean. Calculate the t-value and compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Explanation:

To test the hypotheses, we can use a one-sample t-test since we know the population standard deviation and the sample size is small. The null hypothesis (H0) is that the population mean (μ) is equal to 30 seconds, while the alternative hypothesis (Ha) is that the population mean is not equal to 30 seconds.

Using the given information, we can calculate the t-value by using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, we reject the null hypothesis. If not, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

Learn more about Hypothesis testing here:

brainly.com/question/31665727

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