Factor the following polynomial completely 4x^2-100

A fair die with sides numbered 1, 2, 3, 4, 5, and 6 is to be rolled until a number greater than 4 first appears. what is the pro

AnnyKZ [126]

First two rolls have to be 1-4 that is 2/3 chance twice and the third can be 4or 5
2/3*2/3*1/3 + the chance that the fourth is the 5 or 6.
2/3*2/3*2/3*1/3

So the solution is : P=2/3*2/3*1/3 + 2/3*2/3*2/3*1/3

7 0

4 years ago

Drag the tiles to list the sides of △MNO from shortest to longest.

sweet [91]

The smaller the angle subtended by a side, the smaller the length of the

side.

The correct responses are;

Question 1: The list of sides from shortest to longest are;

MO/Shortest MO/Medium and MO/Longest

a) Friday

b) 70 minutes

c) 40%

d) Yes, the sum of the mean number of minutes spent on aerobic training and the mean number of minutes spent on strength training is equal to the mean total number of minutes spent training.

From the given diagram, we have, the measure of the third angle, ∠O, is

found as follows;

∠O = 180° - 54° - 61° = 65°

Therefore, ∠O = The largest angle

We get;

The longest side is opposite the largest angle, which gives;

The shortest side is the side opposite ∠N (54°)= $\frac{}{MO}$

The next shortest side is the side opposite ∠M(61°) = $\frac{}{NO}$

The longest side is the side opposite ∠O(65°) = $\frac{}{MN}$

a) The time spent training on Tuesday = 60 + 10 = 70 minutes

The time spent training on Thursday = 50 + 30 = 80 minutes

The time spent training on Friday = 45 + 40 = 85 minutes

Therefore, the day the athlete spent the longest total amount of time training is on Friday

b) The time spent training on Monday = 10 + 20 = 30 minutes

The time spent training on Wednesday = 20 + 15 = 35 minutes

Therefore, we get;

30, 35, 70, 80, and 85

The median total number of minutes the athlete spent training each day = 70 minutes

c) The time spent strength training = 20 + 10 + 15 + 30 + 45 = 120

The total number of minutes the athlete spent training = 70 + 80 + 85 + 30 + 35 = 300

$The$ $percentage$ $spent$ $on$ $strength$ $training$ = $\frac{120}{300}$ × $100 =$ $\frac{40}$ %

d) The mean number of minutes spent on strength training is found as follows;

$Mean_{strength} =\frac{120}{5} =24$

The mean number of minutes spent on aerobic training is found as follows;

$Mean_{aerobic} =\frac{10+60+20+50+40}{5} =36$

$Mean_{strength} +Mean_{aerobic} =24+36=60$

The mean total number of minutes spent training, $Mean_{total}$ = $\frac{300}{5}$ = 60

Therefore;

$Mean_{strength}+Mean_{aerobic} = Mean_{total} \\$

Learn more here:

brainly.com/question/2962546

4 0

3 years ago

What is the approximate area of the shaded sector in the circle shown below

jeyben [28]

Answer: B

Step-by-step explanation:

The area of a circle is pi*radius^2. But only a diameter is given, so in order to find the radius, you must divide the diameter by 2:

3.6/2 = 1.8

Now, you can plug the radius, 1.8, into the equation pi*radius^2 ( $\pi r^{2}$ ):

$\pi (1.8)^2 = \pi(3.24)$ = about 10.18

Lastly, you must divide the area 10.18 by 2 because you are looking for only half the area.

10.18/2 = 5.09

6 0

3 years ago

A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equat

jolli1 [7]

Answer:

7000 type A
6000 type B

Step-by-step explanation:

We assume your equations are intended to be ...

$C(x,y)=x^2-2xy+9y^2+3x-87y-6\\R(x,y)=5x+7y$

Then the profit equation is ...

$P(x,y)=R(x,y)-C(x,y)=5x+7y-x^2+2xy-9y^2-3x+87y+6\\=-x^2+2xy-9y^2+2x+94y+6$

The partial derivatives of profit with respect to x and y are zero when profit is maximized.

∂P/∂x = 0 = -2x +2y +2

∂P/∂y = 0 = 2x -18y +94

Simplifying, these equations are ...

y = x -1
x -9y = -47

Substituting the first into the second gives ...

x -9(x -1) = -47

-8x = -56

x = 7

y = 7 -1 = 6

The company will maximize profit by selling 7000 panels of type A and 6000 panels of type B.

5 0

3 years ago

The length is _____ the width is______ and the area of the actual room is ___ _______

RSB [31]

Answer:

98 square inches.

Step-by-step explanation:

The length is 14 inches. The width is 7 inches.

7 * 14 = 98 square inches.

The area is 98 square inches.

8 0

4 years ago