Write the prime factorization of 21. Order the factors from least to greatest (for example, 2 × 2 × 3 × 5).

What is a positive angle less than 360 degrees that is conterminal with -289 degrees

wel

Answer:

The positive angle that less than 360° and is conterminal with -289° is 71°

Step-by-step explanation:

When a terminal of an angle moves anticlockwise, then it makes a positive angle with the positive part of the x-axis

When a terminal of an angle moves clockwise, then it makes a negative angle with the positive part of the x-axis

To find the positive angle which has the same terminal of a negative angle add the measure of the negative angle by 360°

Let us solve the question

∵ The measure of the angle is -289°

→ Add its measure by 360° to find the positive angle that is conterminal

with it

∵ The measure of the positive angle = -289° + 360°

∴ The measure of the positive angle = 71°

The positive angle that less than 360° and is conterminal with -289° is 71°

4 0

3 years ago

Given gif and GHF, write three proportions involving geometric mean.<br>

almond37 [142]

Answer:

$\frac{z}{h}=\frac{h}{y}\\\\\frac{a}{x}=\frac{x}{z}\\\\\frac{a}{w}=\frac{w}{y}$

Step-by-step explanation:

For this exercise it is important to remember that a Right triangle is a triangle that has an angle that measures 90 degrees.

According to the Altitude Rule, given a Right triangle, if you draw an altitude from the vertex of the angle that measures 90 degrees (The right angle) to the hypotenuse, the measure of that altitude is the geometric mean between the measures of the two segments of the hypotenuse.

In this case, you can identify that the altitude that goes from the vertex of the right angle ( $\angle G=90\°$ ) to the hypotenuse of the triangle, is:

$GF=h$

Then, based on the Altitude Rule, you can set up the following proportion:

$\frac{z}{h}=\frac{h}{y}$

According to the Leg Rule, each leg is the mean proportional between the hypotenuse and the portion of the hypotenuse that is located directly below that leg of the triangle.

Knowing this, you can set up the following proportions:

$\frac{a}{x}=\frac{x}{z}\\\\\frac{a}{w}=\frac{w}{y}$

6 0

3 years ago

Read 2 more answers

Determine whether the given value is a solution of the equation.

nlexa [21]

Answer:

16 is not the solution to the equation

Step-by-step explanation:

5 0

3 years ago

(e+3)(e-5) expanded and simplified

Zarrin [17]

Step-by-step explanation:

$(e + 3)(e - 5) \\ e \times e + e \times ( - 5) + e \times e + e \times 3 \\ { e}^{2} + ( - 5e) + {e}^{2} + 3e \\ {2e}^{2} + ( - 2e)$

In this type of math equation, you have to multiply all members from the first part with the second part.

Expanded:

$e \times e+e \times (-5)+e \times e+e \times 3$

simplified:

${2e}^{2} + ( - 2e)$

8 0

2 years ago

Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 bab

Leviafan [203]

Answer:

$z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936$

The p value can be founded with this formula:

$p_v =P(z$

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

Step-by-step explanation:

Information given

$\bar X_{1}=7.6$ represent the mean for Gibbs products

$\bar X_{2}=8.1$ represent the mean for the competitor

$\sigma_{1}=2.3$ represent the population standard deviation for Gibbs

$\sigma_{2}=2.9$ represent the sample standard deviation for the competitor

$n_{1}=40$ sample size for the group Gibbs

$n_{2}=55$ sample size for the group competitor

$\alpha=0.05$ Significance level provided

z would represent the statistic

Hypothesis to verify

We want to check if babies using the Gibbs brand gained less weight, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2}=0$

Alternative hypothesis: $\mu_{1} - \mu_{2}< 0$

The statistic would be given by:

$z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

Replacing the info given we got:

$z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936$

The p value can be founded with this formula:

$p_v =P(z$

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

5 0

3 years ago