Factor. Check by multiplying
2a - 14 = ?

Answer:

C.

Step-by-step explanation:

We need to apply Mean Value theorem here.

We just need to calculate the average rate of change for each interval.

A) x=0 to x=4

We have the points (0,8) and (4,0) are the points that correspond to the endpoints of the given interval.

(8-0)/(0-4)

8/-4

-2

Not this choice

B) x=4 to x=8

We have the points (4,0) and (8,2) are the points that correspond to the endpoints of the given interval.

(2-0)/(8-4)

2/4

1/2

Not this choice

C) x=8 to x=12

We have the points (8,2) and (12,10) are the points that correspond to the endpoints of the given interval.

(10-2)/(12-8)

8/4

2

This one works.

D) x=12 to x=16

We have the points (12,10) and (16,1) are the points that correspond to the endpoints of the given interval.

(1-10)/(16-12)

-9/4

The table is an illustration of mean value theorem

[tex]\mathbf{f'(c) =2}[/tex] on the interval (8,12)

If a function is differentiable, then:

[tex]\mathbf{f'(c) =\frac{f(b) - f(a)}{b - a}}[/tex]

(a) (0,4)

This gives

[tex]\mathbf{f'(c) =\frac{f(4) - f(0)}{4 - 0}}[/tex]

[tex]\mathbf{f'(c) =\frac{f(4) - f(0)}{4}}[/tex]

From the table, we have:

[tex]\mathbf{f'(c) =\frac{0 - 8}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{- 8}{4}}[/tex]

[tex]\mathbf{f'(c) =-2}[/tex]

(b) (4,8)

This gives

[tex]\mathbf{f'(c) =\frac{f(8) - f(4)}{8 - 4}}[/tex]

[tex]\mathbf{f'(c) =\frac{f(8) - f(4)}{4}}[/tex]

From the table, we have:

[tex]\mathbf{f'(c) =\frac{2-0}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{2}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{1}{2}}[/tex]

(c) (8,12)

This gives

[tex]\mathbf{f'(c) =\frac{f(12) - f(8)}{12 - 8}}[/tex]

[tex]\mathbf{f'(c) =\frac{f(12) - f(8)}{4}}[/tex]

From the table, we have:

[tex]\mathbf{f'(c) =\frac{10-2}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{8}{4}}[/tex]

[tex]\mathbf{f'(c) =2}[/tex]

Hence, [tex]\mathbf{f'(c) =2}[/tex] on the interval (8,12)

Read more about mean value theorems at:

https://brainly.com/question/3957181

Answer:

n = 6

m = 6√3

Step-by-step explanation:

Reference angle = 30°

Opposite = n

Adjacent = m

Hypotenuse = 12

✔️To find n, apply the trigonometric ratio, SOH:

Sin 30° = Opp/Hyp

Sin 30° = n/12

n = Sin 30° × 12

n = ½ × 12 = 6

✔️To find m, apply the trigonometric ratio, CAH:

Cos 30° = Adj/Hyp

Cos 30° = m/12

m = Cos 30° × 12

m = √3/2 × 12 (cos 30 = √3/2)

m = √3 × 6

m = 6√3

Answer:

notify me when you finish the question so i can answer ok

Step-by-step explanation:

Answer:

This means that there is 3/4 gallon or quarts left of milk that the teacher has.

Step-by-step explanation:

Answer:

1.98 × 10^10

Step-by-step explanation:

First solve for how many text messages were sent out per one month:

22,000,000 × 900

19,800,000,000

Convert into scientific notation:

1.98 × 10^10

In scientific notation, there can only be one number before the decimal. The rest of the numbers must be after the decimal; hence, why I put the numbers 9 and 8 after the decimal. If the rest of the numbers are zeros, you do not have to add them after the decimal. Instead, starting from right to left, count the number places until you reach your decimal. The number you have counted will be your exponent. I counted nine 0's, one 8, and one 9 which made this exponent 10 as there were 10 decimal placements.

Answer:

78.54

Step-by-step explanation:

Answer:

d= +3

Step-by-step explanation:

1st term = -19

2nd term = -16

d = 2nd - 1st

d= -16-(-19)

d = +3

Answer:24

Step-by-step explanation:

Answer:

The  95% confidence interval of the mean is

(17.8658, 20.5342)

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 15.9

Given that the size of the sample 'n' =12

Mean of the sample   x⁻ = 19.2

Given that the variance of the sample = 4.41

The standard deviation of the sample (S) = 2.1

Step(ii):-

Degrees of freedom = n-1

ν = n-1 = 12-1=11

t₀.₀₅ =  2.2010

The  95% confidence interval is determined by

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](19.2 - 2.2010 \frac{2.1}{\sqrt{12} } , 19.2 + 2.2010 \frac{2.1}{\sqrt{12} } )[/tex]

(19.2 - 1.3342 , 19.2+1.3342)

(17.8658 , 20.5342)

Final answer:-

The  95% confidence interval of mean is

(17.8658 , 20.5342)

Answer:

measure of <DFH=56

Step-by-step explanation:

The two triangles are similar, so their angles are the same, but their lengths are different.

If their angles are the same, then 98-6x=63-x.

98-6x=63-x (subtract: 98-63)

35-6x=-x (add 6x-x)

35=5x (divide by 5)

7=x (Then make sure you answer the question and put x in 63-x.)

63-(7)=56

Answer: -19x +1

Step-by-step explanation: Do -10x -9x which is -19x and you have 1 which is unlike terms .So your final answer is -19x +1 .

Answer:

x > -3

Step-by-step explanation:

-3x + 6 < 15

-3x < 15 - 6

-3x < 9

-x < 3

x > -3

A. x > -3

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

−3x + 6 − 6 < 15 − 6

−3x < 9

Step 2: Divide both sides by -3.

−3x/−3 < 9/−3

x > −3

Answer:     C

Step-by-step explanation:

Plz tell me if i am wrong

Answer:

The probability of spinning yellow or blue is [tex]\frac{4}{5}[/tex] or 80%.

Step-by-step explanation:

Since the circle is split evenly into 5 parts, and 4 parts are either blue or yellow, that means the probability of spinning blue or yellow is the number of blue or yellow sections divided by the total sections, which is [tex]\frac{4}{5}[/tex] or 80%.

Answer:22

Step-by-step explanation:

Answer:

The answer is b.

Step-by-step explanation:

Answer:

a) 1:48000 b)1.6128km

Step-by-step explanation:

Step-by-step explanation:

1 case- 8 cans

If you have 32 cans and you know that 1 case can have 8 cans you do this:

32:8=4 cases

Then if you have 10 cases in each you get 8 cans so it equals:

10*8=80cans

And last:

You have 96 cans and again you know that one case can contain 8 cans so it is:

96:8=12 cases

When you write that:

1. answer: 8

2.answer:4

3.answer:80

4.answer:12

Answer:

00.6inches 0.03 and o.1 or 5 times 0.006

Answer:

Since the pvalue of the test is 0.2743 > 0.1, the threshold probably was met.

Step-by-step explanation:

The widget manufacturing company had established a threshold of 60% preferring the proposed new widget to move forward with producing the new widgets.

This means that at the null hypothesis we test if the proportion is at least 60%, that is:

[tex]H_{0}: p \geq 0.6[/tex]

And the alternate hypothesis is:

[tex]H_{a}: p < 0.6[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.6 is tested at the null hypothesis:

This means that:

[tex]\mu = 0.6[/tex]

[tex]\sigma = \sqrt{0.6*0.4}[/tex]

Three hundred thirty-eight of 575 respondents reported preferring the proposed new widget.

This means that [tex]n = 575, X = \frac{338}{575} = 0.5878[/tex]

Value of the test-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.5878 - 0.6}{\frac{\sqrt{0.6*0.4}}{\sqrt{575}}}[/tex]

[tex]z = -0.6[/tex]

Pvalue of the test and decision:

We want to find the probability of a proportion of 0.5878 or lower, which is the pvalue of z = -0.6.

Looking at the z-table, z = -0.6 has a pvalue of 0.2743.

Since 0.2743 > 0.1, the threshold probably was met.

Answer:

48(c)

Step-by-step explanation:

Answer:

D. 16.7%

Step-by-step explanation:

Rate of return is:

R = (Vf - Vi) / Vi

R is the rate of return, Vf is the final value, and Vi is the initial value. Essentially, you're finding the change in value and dividing by the initial value.

R = (1750 - 1500) / 1500 = 0.167 = 16.7%

Make sure that you divide by the initial value, not the final. If you divided by 1750 instead, you would have gotten 14.3% which is not correct.

Make sure you check your sign as well. The value increased, so the rate of return is positive.

Answer:

300000000

Step-by-step explanation:

Answer:11:58 duh

Step-by-step explanation I can count

Answer:

SYDNEY FINISH CLEANING HER ROOM AT 11:58 a.m.

Answer:

115 degrees

Step-by-step explanation:

Since <4and <5 are alternate interior angles, this means that they are equal because alternate interior angles of a geometry are equal. Hence since

<4 = 115 degrees, <5 is also equal to 115 degrees

Answer:

Hello There!!

Step-by-step explanation:

You order them but in this case they are already ordered and the middle number is 81 so that is the median(also knows as the middle).

hope this helps,have a great day!!

~Pinky~

Answer:

The median is 81.

Step-by-step explanation:

You can find the median in the middle if it all of them add up to odd.(like your’s say 70, 77, 80,... so that You will count them all. In total you have seven numbers and it’s odd).

if it is an even numbers, you mulitply the middle two numbers and divide them by two. That is the median for even numbers.

Answer:

144

Step-by-step explanation:

Answer: x greater-than or equal-to 2,236

Step-by-step explanation:

5,000-2,764= 2,236

so Li's family still needs to save at least $2,236

Answer:

A

Step-by-step explanation:

bc

Answer:

x = 2.93

Step-by-step explanation:

The sum of angles of the triangle is 180degrees, hence;

9x - 72 + 73x + 11 = 180

82x - 61 = 180

82x = 180 + 61

82x  = 241

Divide both sides by 82

82x/82 = 241/82

x = 2.93

Note that the functions might not be accurate but the same methos should be employed for any function given

Step-by-step explanation:

Area of rectangle is Length × Breadth

We need to multiply these 3 terms.

[tex]\rm{2y^2 \times (6y^4 + 3y^3 - y^2 - 8)}[/tex]

Use distributive property

= 12 y⁶ + 6y⁵ - 2 y⁴ - 16 y²

Hope it helps :)