Name three points that are collinear

The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.

Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.

The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .

So the function is good model.

The year 2014 means t=2014-1970=44

So to get the population,put t=44 in equation

f(t)=0.027(44)²+0.216(44)+53.296

f(t)=0.027(1936)+0.216(44)+53.296

f(t)=52.272+9.504+53.296

f(t)=115.072

And on rounding it we get 115%.

Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t

f(t)=0.027t²+0.216t+53.296=100

0.027t²+0.216t+53.296=100

0.027t²+0.216t+53.296-100=0

0.027t²+0.216t-46.704=0

Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0

[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]

for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get

[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]

As we all know time cannot be negative so t=-45.78 will be rejected.

So, t=37.78=38

Now, we will find the corresponding year

1970+38=2008

Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.

Learn more about the scatter plot from here brainly.com/question/27841050

#SPJ9

The interval at which the function x³ + 3x² - 4x - 12 increases is

x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).

We have,

x³ + 3x² - 4x - 12

We need to draw a graph to see at which interval the graph is increasing.

The graph is given below.

We see that the graph is increasing from x = -∞ to x = -2.5 and from  x = -2.5 it decreases till x = 0.5 and again from x = 0.5 it increases to x = ∞.

So we can write the interval as:

x ∈ (- ∞, - 2.5) and  x ∈ (0.5, ∞)

We can write it as one single interval as:

S = (- ∞, - 2.5) ∪ (0.5, ∞)

Thus the interval at which the function x³ + 3x² - 4x - 12 increases is

x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).

Learn more about functions here:

https://brainly.com/question/19030609

#SPJ1

The average rate of change of the function from x == -4 to x = 3 is calculated as: -26.

The formula for determining the average rate of change across a given interval of a function is expressed as:

Average rate of change = g(b) - g(a)/b - a.

Given the function, g(x) = -2x³ + 5 to find the average rate of change from x = -4 to x = 3, do the following:

a = -4

g(a) = g(-4) = -2(-4)³ + 5 = -2(-64) + 5 = 128 + 5 = 133

b = 3

g(b) = g(3) = -2(3)³ + 5 = -2(27) + 5 = -54 + 5 = -49

Substitute the values into g(b) - g(a)/b - a:

Average rate of change = (-49 - 133)/(3 - (-4))

Average rate of change = -182/7

Average rate of change = -26

Thus, the average rate of change of the function from x == -4 to x = 3 is calculated as: -26.

Learn more about the average rate of change on:

https://brainly.com/question/11627203

#SPJ1

The baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.

In this problem we know that a baseball coach spends a total of $ 118.25 on buying 11 pizzas. First, we need to estimate the amount of money spent per each pizza bought, which is found by means of multiplication tables and the supposition of truncation, that is, finding the maximum integer less than or equal to the real total cost.

By direct inspection we find that 10 times the 11 pizzas is equal to $ 110, which is the maximum integer less than or equal to the real total cost. Then, we estimate a cost of $ 10 per each pizza bought. Second, the exact unit cost is found by dividing the total by the number of pizzas:

c = $ 118.25 / 11

c = $ 10.75

In a nutshell, the baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.

To learn more on costs: https://brainly.com/question/13945982

#SPJ1

7 in 7.8 is 100 times greater than 7 in 23.97.

As the name suggests place value is where the digit is being placed in decimal number system.

We can multiply both these numbers by 100 in that way we'll get rid of the decimal and it doesn't effect our answer.

Now 7.8 and 23.97 multiplied by 100 becomes 780 and 2397.

We can observe that 7 in 780 is in hundreds place and 7 in 2397 is in ones place.

∴ If we divide (100/1) = 100.

So, it is 100 times greater.

learn more about place value here :

https://brainly.com/question/27734142

#SPJ1

The inequality that describes the possible temperatures on Mars is

 -133°c ≤T≤ -7°c .

Inequality compares two values by if they are less than or greater than each other.

According to the given question Mars has a maximum temperature of -7°c at the equator and a minimum temperature of -133°c at the winter pole.

We have to write an inequality that describes the possible temperatures on Mars.

Let us denote all the possible range of temperatures by T,

∴ T is less or equal to the maximum temperature and T is greater than or equal to the minimum temperature.

So,    -133°c ≤T≤ -7°c .

learn more about inequality here :

https://brainly.com/question/20383699

#SPJ1

Answer: 0.3574 miles

Step-by-step explanation:

22647 inches = 0.3574 miles

The total impact on Jakob's cash flow for the year is C. $6,400.

It should be noted that Jakob received a $1,000-a-year raise in January, sold stocks in March for $6,000 that were originally purchased for $4,000.

The impact will be:

= Raise + Sale of stock - Mortgage

= 1000 + 6000 - 600

= 6400

Therefore, the correct option is C

Learn more about cash flow on:

brainly.com/question/10922478

#SPJ1

Answer: 4 seconds

Step-by-step explanation:

c=cheetah. a=antelope

a=c+120

c/90=a/60

c/90=(c+120)/60

60*c/90=60*(c+120)/60

6*c/9=c+120

2c/3=c+120

(2c/3=c+120)*3   ==> multiply the equation by 3 to get rid of fractions

2c=3c+360

2c-3c=3c-3c+360

-c=360

c=-360  feet==> position of cheetah before catching up to the antelope. This means that the cheetah needs to travel 360 feet before reaching 0 ft when it catches the antelope.

360 feet * 1 second/90 feet=

360*1/90=

360/90=4 seconds

The reciprocal of 0.375 is gotten by Dividing 1 by 0.375 and Solving the equation 0.375x = 1

The reciprocal of a number is the multiplicative inverse of that number. For a number x, the reciprocal is x⁻¹

Hence, the reciprocal of 0.375 is:

a) Dividing 1 by 0.375

b) Solving the equation 0.375x = 1

Find out more on reciprocal at: https://brainly.com/question/1955429

#SPJ1

Answer:2

Step-by-step explanation:

[tex]\frac{14}{5} -5[/tex]

Divide 14 by 2 to get 7.

7−5

Subtract 5 from 7 to get 2.

Answer=2

Answer:

p=2

Step-by-step explanation:

8 halls would be required to accommodate 520 people in the hall.

As we know that a hall can accommodate 65 people.

To determine the number of hall required for 520 people,

first we need to find that how many halls would be required for one person,

So, we will divide the 1 by 6 to find :

The number of one person accommodate = 1/65 Hall

Then, 520 people required to accommodate = 1/65 × 520

                                                                      = 8 Halls.

[Accommodate: to have enough space for somebody/something, especially for a certain number of people]

To learn more about this Patterned Question visit :

https://brainly.com/question/17498351

#SPJ9

The percent increase in pay was 20%

Maddie's Boutique paid the members of its staff $20 per hour.

and,  the boutique merged with another store, and the staff members started making $24 per hour.

To find the what percent increase in pay ?

Now, According to the question:

Based on the given conditions,

= (24 - 20) ÷ 20

= [tex]\frac{24-20}{20}[/tex]

= 1/5

and, Covert to percentage

= 1/5 x 100

= 20%

Hence, The percent increase in pay was 20%

What is Percentage?

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is :

(value/ total value) x 100%

Learn more about Percentage at:

https://brainly.com/question/22847606

#SPJ1

Step-by-step explanation:

(5 ,_4) it the location this is the answer

The total cost functions are:

total charges for Hertz=32+42x

total charges for Enterprise=24+46x

What does the total rental cost of each company entails?

The total rental cost of each company consists the fixed service charges and the daily charge which can be multiplied by the total of number of days of rental to determine total charges overall.

Hertz:

total charges=32+42x

when x=6 days

total charges=32+(42*6)

total charges=$284

Enterprise:

total charges=24+46x

when x=6 days

total charges=24+(46*6)

total charges=$300

Renting for 4 days:

total charges(Hertz)=32+(42*4)

total charges(Hertz)=$200

total charges(Enterprise)=24+(46*4)

total charges(Enterprise)=$208

savings=$208-$200

savings=$8

The company that charges less when Avery decides to rent car for only 4 days is Hertz and Avery can $8 as result of choosing Hertz

Find out more about total rental cost on:brainly.com/question/17486314

#SPJ1

Answer:

13

Step-by-step explanation:

Simplify the following:

(7 - (sqrt(16))/4)^2 + 2 - 5^2

sqrt(16) = sqrt(2^4) = 2^2:

(7 - (2^2)/4)^2 + 2 - 5^2

2^2 = 4:

(7 - 4/4)^2 + 2 - 5^2

(-4)/4 = 4/4×-1 = -1:

(-1 + 7)^2 + 2 - 5^2

7 - 1 = 6:

6^2 + 2 - 5^2

5^2 = 25:

6^2 + 2 - 25

6^2 = 36:

36 + 2 - 25

36 + 2 - 25 = 13:

Answer:  13

Answer: probably like 1.8%

Step-by-step explanation:

$3,708.33 is withheld monthly for state taxes.

Some states have a graduated income tax that involves a different tax rate for each of several levels of income. The tax rate increases as income increases.

Tax Withheld per Pay Period = Annual Tax Withheld/ Number of Pay Periods per Year

Here, we are given that Kerry McCarthy is a news traffic reporter with an annual gross pay of $44,500.

Thus, the Annual Tax Withheld = $44,500.

He is paid on a monthly basis ⇒ Number of Pay Periods per Year = 12

Hence, we get-

Tax Withheld per Pay Period = 44,500/ 12

= 3,708.33

Thus $3,708.33 is withheld monthly for state taxes.

Learn more about tax rates here-

https://brainly.com/question/25783927

#SPJ9

Solution of  2x+y+z=−4, 3x+2y−z=6, x+2y−3z=2 value of

(x , y, z) =(10,-16,-8) in the simplest terms.

As given,

2x+y+z=−4 __(1)

3x+2y−z=6 __(2)

x+2y−3z=2 __(3)

Add (1) and (2)

2x+y+z=−4

3x+2y−z=6

5x + 3y=2  __(4)

Multiply 3 to (1) add it to (3)

6x+3y+3z=-12

 x+2y−3z=2

7x + 5y = -10  __(5)

Now [5× (4)] subtract [3×(5)] from it

25x + 15y=10

21x+15y=-30

4x= 40

⇒x=10

Substitute in (4)  

y=[2-5(10)]/3

  =-16

Substitute value of x and y in (1)

z=-4 -2(10)-(-16)

 =-8

Therefore, solution of  2x+y+z=−4, 3x+2y−z=6, x+2y−3z=2 value of

(x , y, z)=(10,-16,-8) in the simplest terms.

Learn more about simplest terms here

brainly.com/question/16745818

#SPJ1

Reason:

A rational number is a fraction of any two integers, as long as the denominator is nonzero. This applies to the first two answer choices.

Choices C and D are undefined because of the 0 in the denominator. You cannot divide by zero. This rules out the last two choices.

Answer: Y = -8 or Y = 8

Step-by-step explanation:

Y² = 64

Y = -8 or Y = 8 ==> yes there is more than one answer

Answer:

hi can we talk for a while I'm a little alone

Answer:

56/5 or 11 1/5

Step-by-step explanation:

Convert 1 3/5 to an improper fraction

1 3/5 = (1 x 5 + 3)/5 = (5 + 3)/5 = 8/5

7 x  1 3/5  = 7 x 8/5 = 56/5

In mixed fraction, 56/5 = 11 1/5

Answer: x^3y^2(x+y)

Step-by-step explanation:

x^4y^2+x^3y^3​=

x*(x^3y^2)+(x^3y^2)*y=x^3y^2(x+y)

Answer:

{-3/2, 3/2}

Step-by-step explanation:

Let's solve your equation step-by-step.

2(|x|)=3

Step 1: Divide both sides by 2.

2(|x|)/2 = 3/2

|x|= 3/2

Step 2: Solve Absolute Value.

|x|= 3/2

We know either x= 3/2 or x=−3/2

x=3/2

(Possibility 1)

x=−3/2

(Possibility 2)