An angle measuring 3.6 radians is drawn in standard position?

Graph the first six terms of a sequence where a1 = -10 and d = 3.

ohaa [14]

Answer:

It's A.

Source: I took the test

4 0

3 years ago

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than

Sedbober [7]

Testing the hypothesis, it is found that:

a)

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

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

b)

The critical value is: $t_c = 1.74$

The decision rule is:

If t < 1.74, we do not reject the null hypothesis.
If t > 1.74, we reject the null hypothesis.

c)

Since t = 1.41 < 1.74, we do not reject the null hypothesis, that is, it cannot be concluded that the mean weight loss is of more than 10 pounds.

Item a:

At the null hypothesis, it is tested if the mean loss is of at most 10 pounds, that is:

$H_0: \mu \leq 10$

At the alternative hypothesis, it is tested if the mean loss is of more than 10 pounds, that is:

$H_1: \mu > 10$

Item b:

We are having a right-tailed test, as we are testing if the mean is more than a value, with a significance level of 0.05 and 18 - 1 = 17 df.

Hence, using a calculator for the t-distribution, the critical value is: $t_c = 1.74$ .

Hence, the decision rule is:

If t < 1.74, we do not reject the null hypothesis.
If t > 1.74, we reject the null hypothesis.

Item c:

We have the standard deviation for the sample, hence the t-distribution is used. The test statistic is given by:

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

The parameters are:

$\overline{x}$ is the sample mean.
$\mu$ is the value tested at the null hypothesis.
s is the standard deviation of the sample.
n is the sample size.

For this problem, we have that:

$\overline{x} = 10.8, \mu = 10, s = 2.4, n = 18$

Thus, the value of the test statistic is:

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

$t = \frac{10.8 - 10}{\frac{2.4}{\sqrt{18}}}$

$t = 1.41$

Since t = 1.41 < 1.74, we do not reject the null hypothesis, that is, it cannot be concluded that the mean weight loss is of more than 10 pounds.

A similar problem is given at brainly.com/question/25147864

3 0

2 years ago

What two numbers multiply to 44 and add up to 12?

djverab [1.8K]

This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.    x*y = 44 ..........(a)

Add up to 12. x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a

x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2

x = (12 + 4i√2 )/ 2 (12 - 4i√2 )/ 2

x = 12/2 + (4i√2)/2 12/2 - (4i√2)/2

x = 6 + 2i√2 or    6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2, y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2

x = 6 + 2i√2, y = 6 - 2i√2

x = 6 - 2i√2, y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2

8 0

2 years ago

Read 2 more answers

A car is driving towards home at 0.5 miles per minute. If the car is 4 miles from home at t=0 , which of the following can repre

Lostsunrise [7]

Answer:

the answer is D

7 0

2 years ago

Find the volume of a right circular cone that has a height of 7.4 in and a base with a diameter of 5.4 in. Round your answer to

JulijaS [17]

Answer:

approximately 56.51 cubic inches

Step-by-step explanation:

volume of a cone = 1 / 3 × pi × radius^2 × height

= 1/3 × 22/7 × 7.29 × 7.4

= 56.5148 cubic inches

8 0

2 years ago