Compute the standard deviation for the set of data.

Write an equation of the line below.

Blizzard [7]

Answer:

y=1/2x+4

Step-by-step explanation:

Refer to the picture that given :)

4 0

3 years ago

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Barbara requires 2 gallons of paint to cover an area of 800 square feet. Identify the graph for the relationship from quantity t

mote1985 [20]

Answer:

6

Step-by-step explanation:

x = area to be painted

y = gallons of paint needed

we know already one point of that function/graph :

x = 800

y = 2

so, for a simple relationship between the 2 variables we can assume

y = ax

2 = a×800

a = 2/800 = 1/400

so, we get

y = (1/400) x

for 2400 ft²

y = 1/400 × 2400 = 1/4 × 24 = 24/4 = 6

she needs 6 gallons of paint for 2400 ft².

4 0

3 years ago

What is the measure of EBC ? ___ degrees

erma4kov [3.2K]

Answer:

The measure of arc EBC is 220°

Step-by-step explanation:

step 1

Find out the measure of angle COB

we know that

m∠COB+m∠DOC=90° -----> given problem

we have that

m∠DOC=m arc DC -----> by central angle

m arc DC=50°

so

m∠DOC=50°

Find m∠COB

m∠COB+50°=90°

m∠COB=40°

step 2

Find out the measure of arc BC

we have that

m arc BC=m∠COB -----> by central angle

m∠COB=40°

therefore

m arc BC=40°

step 3

Find out the measure of arc EBC

we know that

m arc EBC=m arc EB+m arc BC

m arc EB=180° -----> because the diameter divide the circle into two equal parts

so

m arc EBC=180°+40°=220°

8 0

3 years ago

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A linear equation in two variables has infinitely many solution the set of all solutions to a linear equation in two variables f

Greeley [361]

1, During a 1-hr television program, there were 22 commercials, Some commercials were 15 sec and some were 30 sec long. Find the number of 15- sec commercials and the number of 30 sec commercial if the total playing time for commercial was 9.5 minutes.

a) show how to formulate your system of equations for your problem,

Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language

b) state the two equations:

- translate the word statement into algebraic equations:

* there were 22 commercials => x + y = 22
* the total playing time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 

Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y = 570

c) state which method you will use to solve either addition or substitution

Answer:
adition: multiply the first equation times - 15 and add the two equations.

d) solve your system showing and explaining each step of the process

Answer:
- muliply eq (1) times - 15

-15x - 15y = - 330

- add that to the eq (2):

-15x + 15x - 15y + 30y = -330 + 570

- add like terms: 15y = 240

- divide both members by 15: 15y/15 = 240 / 15 => y = 16

- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6

Solution: x = 6, y = 16

e) Be sure to check your solution!

x + y = 22
6 + 16 = 22
22 = 22 --> check

15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check

f) Once a solution is found explain what this solution means in the context of the problem, write the answer to the word problem in words

The solution means that during a 1-hr television program, there were 6 commercials of 15 sec and 16 commercials of 30 sec.

2, How many quarts of water should be mixed with a 30% vinegar solution to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).

a) variables:

- state the variables
x: number of quarters of water
y: number of quarters of vinegar

- translate the words into mathematical language

12 qt 25% vinegar solution

=> total number of quarts = 12 = x + y

balance in vinegar:

vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution

0 + 0.3y = 0.25 (x + y)

c) Equations

Eq (1) x + y = 12

Eq (2): 0.3y = 0.25x + 0.25y

=> 0.25x - 0.05y = 0

d) solve

- multiply eq (1) times 0.05 and add to eq (2)

0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6

x = 0.6 / 0.3 = 2

x + y = 12 => y = 12 - y = 12 - 2 = 10

Solution: x = 2, y = 10

e) check:

x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check

vinegar:

10*0.3 = 12*0.25
3 = 3 -> check

f) Explanation of the solution

The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.

5 0

3 years ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .