If y varies inversely as the square of x and y=4 when x=5, find y when x is 2

What’s the algebraic expression for 8 squared

diamong [38]

Answer:

$8^2$

Step-by-step explanation:

Step 1: Convert words into an expression

What’s the algebraic expression for 8 squared

8 squared -> $8^2$

Answer: $8^2$

If needed, solve:

$8^2$

8 * 8

64

3 0

3 years ago

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distr

Marianna [84]

Answer:

(a) Decision rule for 0.01 significance level is that we will reject our null hypothesis if the test statistics does not lie between t = -2.651 and t = 2.651.

(b) The value of t test statistics is 1.890.

(c) We conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) P-value of the test statistics is 0.0662.

Step-by-step explanation:

We are given that a recent study focused on the number of times men and women who live alone buy take-out dinner in a month.

Also, following information is given below;

Statistic : Men Women

The sample mean : 24.51 22.69

Sample standard deviation : 4.48 3.86

Sample size : 35 40

Let $\mu_1$ = mean number of times men order take-out dinners in a month.

$\mu_2$ = mean number of times women order take-out dinners in a month

(a) So, Null Hypothesis, $H_0$ : $\mu_1-\mu_2$ = 0 {means that there is no difference in the mean number of times men and women order take-out dinners in a month}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2\neq$ 0 {means that there is difference in the mean number of times men and women order take-out dinners in a month}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n_1_-_n_2_-_2$

where, $\bar X_1$ = sample mean for men = 24.51

$\bar X_2$ = sample mean for women = 22.69

$s_1$ = sample standard deviation for men = 4.48

$s_2$ = sample standard deviation for women = 3.86

$n_1$ = sample of men = 35

$n_2$ = sample of women = 40

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(35-1)\times 4.48^{2}+(40-1)\times 3.86^{2} }{35+40-2} }$ = 4.16

So, test statistics = $\frac{(24.51-22.69)-(0)}{4.16 \sqrt{\frac{1}{35}+\frac{1}{40} } }$ ~ $t_7_3$

= 1.890

(b) The value of t test statistics is 1.890.

(c) Now, at 0.01 significance level the t table gives critical values of -2.651 and 2.651 at 73 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) Now, the P-value of the test statistics is given by;

P-value = P( $t_7_3$ > 1.89) = 0.0331

So, P-value for two tailed test is = 2 $\times$ 0.0331 = 0.0662

4 0

3 years ago

3x-9=3(x-3) how many solutions

Colt1911 [192]

Answer:

All Real Numbers

Step-by-step explanation:

Step 1:

3x - 9 = 3 ( x - 3 ) Equation

Step 2:

3x - 9 = 3x - 9 Multiply

Step 3:

- 9 = - 9 Subtract 3x on both sides

Answer:

All Real Numbers

Hope This Helps :)

4 0

3 years ago

Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list

lara31 [8.8K]

Sin(2θ)+sin(θ)=0
use double angle formula: sin(2θ)=2sin(θ)cos(θ).
=>
2sin(θ)cos(θ)+sin(θ)=0
factor out sin(θ)
sin(θ)(2cos(θ)+1)=0
by the zero product property,
sin(θ)=0 ...........(a) or
(2cos(θ)+1)=0.....(b)
Solution to (a): θ=k(π)
solution to (b): θ=(2k+1)(π)+/-(π)/3
for k=integer

For [0,2π), this translates to:
{0, 2π/3,π,4π/3}

8 0

3 years ago

Computer Action Company sells computers and computer parts by mail. The company assures its customers that products are mailed a

Scorpion4ik [409]

Answer:

The t distribution is used, because we have the standard deviation for the sample.

Step-by-step explanation:

When to use the z or the t distribution?

When we have the standard deviation for the population, we use the z distribution.

When we have the standard deviation for the sample, we use the t distribution.

In this question:

We have the standard deviation for the sample, which means that the t distribution is used.

8 0

3 years ago