8th grade math. Please help!!

In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B'

Daniel [21]

Original coordinates of the points:

A (8,15) ; B (12,13) ; C (8,10)

Dilated scale factor of 3.

A ⇒ 3x = 3(8) = 24 ; 3y = 3(15) = 45 ⇒ A' (24,45)

B ⇒ 3x = 3(12) = 36 ; 3y = 3(13) = 39 ⇒ B' (36, 39)

C ⇒ 3x = 3(8) = 24 ; 3y = 3(10) = 30 ⇒ C' (24, 30)

The given image forms a right triangle. So, I'll get the short leg and long leg of the right triangle to solve for the hypotenuse, length of CB.

Short leg: y value of B and C

39 - 30 = 9

Long leg: x value of B and C

36 - 24 = 12

a² + b² = c²

9² + 12² = c²

81 + 144 = c²

225 = c²

√225 = √c²

15 = c

The length of CB is 15 units. (option B).

4 0

2 years ago

Which angles are corresponding angles?

STALIN [3.7K]

Answer:

8 and 16

Step-by-step explanation:

3 0

3 years ago

A stereo speaker in the shape of a triangular pyramid has a height of 6 inches. The area of the base of the speaker is 11 square

Jet001 [13]

Answer:

The correct answer is A. 22 inches ³

Step-by-step explanation:

Let's recall that the formula of the volume of a triangular pyramid:

Volume = 1/3 * Area of the base * height

Replacing with the values we have:

Volume = 1/3 * 11 inches² * 6 inches

Volume = 66/3

Volume = 22 inches ³

The correct answer is A. 22 inches ³

5 0

3 years ago

The net weights (in grams) of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample fill

Andru [333]

Answer:

Since is a right tailed test we need to look on the t distribution with 12 degrees of freedom that accumulates 0.05 of the area on the right. And we can use the following excel code:

"=T.INV(0.95,12)" and we got $t_{crit}=+1.782$

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

The system of hypothesis on this case are:

Null hypothesis: $\mu_O \leq \mu_E$

Alternative hypothesis: $\mu_O > \mu_E$

Or equivalently:

Null hypothesis: $\mu_O - \mu_E \leq 0$

Alternative hypothesis: $\mu_O -\mu_E > 0$

Our notation on this case :

$n_E =6$ represent the sample size for group Edne

$n_O =8$ represent the sample size for group Orno

$\bar X_E =7$ represent the sample mean for the group Edne

$\bar X_O =10$ represent the sample mean for the group Orno

$s_E=1.414$ represent the sample standard deviation for group Edne

$s_O=2.268$ represent the sample standard deviation for group Orno

First we can begin finding the pooled variance:

$\S^2_p =\frac{(6-1)(1.414)^2 +(8 -1)(2.268)^2}{6 +8 -2}=3.834$

And the deviation would be just the square root of the variance:

$S_p=1.958$

And now we can calculate the statistic:

$t=\frac{(10 -7)-(0)}{1.958\sqrt{\frac{1}{6}+\frac{1}{8}}}=2.837$

Now we can calculate the degrees of freedom given by:

$df=6+8-2=12$

Since is a right tailed test we need to look on the t distribution with 12 degrees of freedom that accumulates 0.05 of the area on the right. And we can use the following excel code:

"=T.INV(0.95,12)" and we got $t_{crit}=+1.782$

Since our calculated value is higher than the critical value we have anough evidence to reject the null hypothesis, and on thsi case the mean for Orno is significanlty higher than the mean for Edne at 5% of significance.

4 0

3 years ago

Зу - 10 < 11 How to solve

zheka24 [161]

Answer:

y<7

Step-by-step explanation:

3y-10 < 11 add 10 to both sides of the equation

3y < 21 divide by 3

y < 7

3 0

2 years ago