What is 3 times the sixth power of 10

If ray JG is an angle bisector of ∠FJH, find m∠FJH.

miss Akunina [59]

Answer:

m∠FJH=60°

Step-by-step explanation:

The complete question is

JG bisects FJH, FJG= (2x + 4)° and GJH = (3x -9)°

What is FJH

we know that

m∠FJH=m∠FJG+m∠GJH -----> equation A

If ray JG is an angle bisector of ∠FJH

then

m∠FJG=m∠GJH -----> equation B

substitute the given values in equation B and solve for x

(2x + 4)°=(3x -9)°

3x-2x=4+9

x=13

Find the measure of angle FJH

m∠FJH=(2x + 4)°+(3x -9)°

substitute the value of x

m∠FJH=(2(13) + 4)°+(3(13) -9)°

m∠FJH=(30)°+(30)°

m∠FJH=60°

3 0

2 years ago

Doug has a bag full of crayons. There are 6 red crayons, 7 blue ones, and 4 green crayons. Doug wants to color a blue sky. What

larisa86 [58]

Answer:

Blue 7/17 = Nearly 0.41

Red 6/17= Nearly 0.35

4/17= Nearly 0.23

Step-by-step explanation:

The Probability is 13/17 if im wrong then sorry i havent done this in a while

8 0

2 years ago

I rent a gym for $150.00 for 30 students. Another time I rent the gym for $270.00 for 70 students. I need to find a fixed rate.

masha68 [24]

Answer: y = 3x + 60

<u>Step-by-step explanation:</u>

Set up two equations and solve the system:

270 = 70x + b

- <u>(150 = 30x + b)</u>

120 = 40x

3 = x

Input "x" into one of the equations and solve for "b":

150 = 30x + b

150 = 30(3) + b

150 = 90 + b

60 = b

Equation: y = 3x + 60

This means that there is a flat fee of $60 plus a rate of $3 per student

5 0

2 years ago

The owners of Prim's Pizza are concerned that many of their customers are starting to purchase pizza from The Pizza Palace becau

AleksandrR [38]

Answer:

$(240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953$

$(240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047$

And the confidence interval for the difference is between:

$27.953 \leq \mu_1 -\mu_2 \leq 32.047$

Step-by-step explanation:

We have the following info given:

$\bar X_1 = 240$ sample mean for medium Pizzas from Prim's

$\bar X_2 = 210$ sample mean for medium Pizzas from Pizza Place

$s_1 =8.6$ sample deviation for Prim's

$s_2 =5.7$ sample deviation for Pizza Palca

$n_1 =n_2 = 100$ sample size selected for each case

The confidence interval for the difference of means is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

And for the 95% confidence we need a significance level of $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ , the degrees of freedom are given by:

$df= n_1 +n_2 -2= 100+100-2 =98$

And the critical value would be

$t_{\alpha/2}= 1.984$

And replacing we got:

$(240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953$

$(240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047$

And the confidence interval for the difference is between:

$27.953 \leq \mu_1 -\mu_2 \leq 32.047$

8 0

2 years ago

At a bake shop, the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month. The cost of cocoa is $6.00 per

Vesna [10]

Answer:

Step-by-step explanation:

We will find two equations for this system, one representing flour and the other representing cocoa. For the flour, we start with $2.50, and the cost goes up .07 per month, x. The equation for that is

y = .07x + 2.50

For the cocoa, the equation is written in the exact same way, but the cost goes down. Down is a negative thing while up is a positive thing. The cost starts at $6.00 and goes down .03 per month, x. The equation for that is

y = -.03x + 6.00

Comparing the first equation to the second, the .07 is positive because the cost goes UP that amount per month and the .03 is negative because the cost goes DOWN that amount per month. Get it?

If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same. If the first y is equal to .07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then

.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y). This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.

Combining like terms we get

.10x = 3.5 so

x = 35

Now back sub in what x equals to solve for y. If x = 35, then in the first equation,

.07(35) + 2.50 = y and

y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value. Promise!)

What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa. But immediately after 35 months, the costs will not be the same anymore. It is only AT 35 months. At 36 months, the costs will be different.

7 0

2 years ago