An aspiring business owner is planning their college course of study and would like to know whether they should pursue a doctoral degree before they open their own business. Explain what you would recommend to them using two specific examples from the bar graph to support your response.

Step-by-step explanation:

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

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.

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Using the Factor Theorem, the non-real solutions are given as follows:

[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the function is:

f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.

The function can be written as:

f(x) = g(x)h(x).

In which:

Using a calculator, as the graph is not given, the real solutions are given as follows:

[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]

Hence:

g(x) = (x + 6)(x + 4)(x - 1)

g(x) = (x² + 10x + 24)(x - 1)

g(x) = x³ + 9x² + 14x - 24.

f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:

f(x) = g(x)h(x)

3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)

Hence:

-24bx + 14cx = 76x

-24b + 28 = 76

-24b = 48

b = -2.

Then the equation with the non-real solutions is:

h(x) = 3x² - 2x + 2.

Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:

Hence the non-real solutions are:

[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]

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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

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 .

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Answer: 0.3574 miles

Step-by-step explanation:

22647 inches = 0.3574 miles

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 model that best described the statement is an exponential model and the function that models the situation is A(t) = 4^t

The statement is given as:

The above statement is a population function

Population functions are best represented by an exponential function

Hence, the model that best described the statement is an exponential model.

Here, we have

Initial value, a = 1

Rate, r = 3

The function is represented as

A(t) = A * (1 + r)^t

So, we have

A(t) = 1 * (1+3)^t

Evaluate

A(t) = 4^t

Hence, the function that models the situation is A(t) = 4^t

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[tex] \green\star\:{\underline{\underline{\sf{\orange{Answer:}}}}}[/tex]

¡Hello :D!

To solve the similar terms we must eliminate the parentheses and then put the parentheses back but this time it would be like this: (4 x + x) + ( 2 - 2)

Once we have done that we must restore the ones on the right side which gives us the result of 1 then as we see that there is + in the Parenthesis and another + outside the Parenthesis we do not care + since we are using the law of signs .

We proceed to solve:

[tex]\: \: \: \: \: \: \bold \: \bold \: \bold \: ( \bf4x+2)+(x-2)[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \bf \bold4x + 2 + x - 2[/tex]

[tex] \: \: \: \: \: \: \: \: \bf\tt( \bf4x + x) + (2 - 2)[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf5x[/tex]

So the result is 5x

I hope I've helped XD

Answer:

10

Step-by-step explanation:

1 Simplify 10-910−9 to 11.

1+8-7+{(6-(5+4)\div 3)}^{2}-1

1+8−7+(6−(5+4)÷3)

2

−1

2 Simplify 5+45+4 to 99.

1+8-7+{(6-9\div 3)}^{2}-1

1+8−7+(6−9÷3)

2

−1

3 Simplify 9\div 39÷3 to 33.

1+8-7+{(6-3)}^{2}-1

1+8−7+(6−3)

2

−1

4 Simplify 6-36−3 to 33.

1+8-7+{3}^{2}-1

1+8−7+3

2

−1

5 Simplify {3}^{2}3

2

to 99.

1+8-7+9-1

1+8−7+9−1

6 Simplify 1+81+8 to 99.

9-7+9-1

9−7+9−1

7 Simplify 9-79−7 to 22.

2+9-1

2+9−1

8 Simplify 2+92+9 to 1111.

11-1

11−1

9 Simplify.

10

Answer: probably like 1.8%

Step-by-step explanation:

Answer: Y = -8 or Y = 8

Step-by-step explanation:

Y² = 64

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

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.

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

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this is what you need?if yes than look and write

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.

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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.

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The original amount for the laptop that Candace bought when the markup rate is 20% will be $4375.

It should be noted that she added 875 markup amount to the original price and the markup rate used was 20%,

Therefore, 20% of x = 865

0.2x = 875

Divide

x = 875 / 0.2

x = 4375

Therefore, the original amount for the laptop is $4375.

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The correct option is b. -30x + 32 = 182.

After combining the like terms, the equation that represents -8x + 23 - 22x + 9 = 182 is -30x + 32 = 182, where x = -5.

In its most basic form, an equation is a statement that demonstrates that 2 mathematical expressions have been equal.

Now, as per the given question;

The stated equation in the question is is,

-8x + 23 – 22x + 9 = 182

Considering like terms together;

-8x – 22x + 23 + 9 = 182

Further simplifying;

– 30x + 32 = 182

Subtracting 32 from the both sides.

– 30x + 32 - 32 = 182 - 32

On solving;

– 30x = 150

⇒ x = -5

Therefore, the expression which defined the equation after taking alike terms is -30x + 32 = 182 for which the value of 'x' comes to be -5.

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The complete question is;

Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms?

-8x + 23 – 22x + 9 = 182

a. 14x + 32 = 182

b. -30x + 32 = 182

c. 14x + 14 = 182

d. -30x + 14 = 182

Answer: 17/14 or 1 3/14 simplified

Step-by-step explanation:

14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.

$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.

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As per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.

As given,

Total number of potential customers =40

Number of  respondents from bar graph

At grocery stores= 40

At drugstores respondents =32

At health food stores =8

At big box stores =20

Average number=(40 +32+8+20)/40

                            = 100 /40

                            =2.5

Therefore, as per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.

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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]

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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:

No solution.

Explanation:

Given expression:

when x = 3, y = 4

Substitute these values inside expression:

6(3) + 4(4) = 36

18 + 16 = 36

34 = 36

As the statement "34 = 36" not true. The solution is false or no solution.

Answer:

The given values are wrong.

Step-by-step explanation:

Given information,

→ x = 3

→ y = 4

Solving the given equation,

→ 6x + 4y = 36

→ (6 × 3) + (4 × 4) = 36

→ 18 + 16 = 36

→ 34 ≠ 36

Hence, there is no solution.

From the graph of the function, we have that:

a) The domain is all real values.

b) The range is y ≤ 4.

c) The x-intercepts are x = -4 and x = 1.

d) The y-intercept is y = 3.

e) f(-2) = 3, f(2) = -5.

Hence, for this problem:

a) The domain is all real values.

b) The range is y ≤ 4.

Hence:

c) The x-intercepts are x = -4 and x = 1.

d) The y-intercept is y = 3.

For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:

f(-2) = 3, f(2) = -5.

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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)