A successful author invests some of his earnings in two accounts for 1 year. the function f(x)=.05 models the interest he earns on x dollars invested in the first account. the function g(x)=.075(x+2500) models the interest he earns from the second account, in which he invests $2500 more than in the first account.
Evaluate (f+g)(18,500) and interpret what it means in this situation

Hey there!

You can find a number halfway between two numbers by simply adding them together and then dividing by two!

13/15+14/15=1 4/5

1 4/5÷2=9/10

Your number is 9/10.

I hope this helps!

Sure, let's find the rational number between 13/15 and 14/15.

A straightforward way to get a rational number between any two given rational numbers is to calculate their average, or arithmetic mean. This is because the mean of any two numbers always falls between those two numbers.

So, let's calculate the mean of 13/15 and 14/15:

1. Begin by adding these two fractions: 13/15 + 14/15

2. In order to add fractions, we need a common denominator, which we already have in this case: 15.
 
  Just add the numerators: 13 + 14 = 27

  So, the sum of 13/15 and 14/15 is 27/15.

3. Now, calculate the mean of the two numbers by dividing their sum by 2 since mean = (a+b) / 2

  So, we have: (27/15) / 2 = 27/30

Here you have it - the rational number between 13/15 and 14/15 is 27/30 or 0.9 in decimal form.

Answer:

Step-by-step explanation:

2. To find area, you use this equation: A = l*w

Let's input the values we do know to find the width.

96 = 12 * w

Divide both sides by 12 to isolate the w.

8 = w

The width is 8 cm.

3. We need the find the area of the floor to figure out how many square meters they need. to find area, we multiply the length by the width.

3 * 2 = 6

You need 6 sq. m.

4. To find the circumference, use the equation: C = 2 * pi *r

To find the radius, divide the diameter by 2.

3/2 = 1.5

C = 2pi(1.5)

C = 3pi

The circumference is 3pi. This can also be simplified to 9.42 or 9.4

5. To find the amount of square cm. it covers, multiply the length and width.

40 * 35 = 1,400

The surface covers 1,400 sq. cm.

6. To find circumference, use this equation: C = d * pi

Input the values you do know to find the diameter

15.7 = d * pi

divide both sides by pi to isolate d

4.77 = d

The diameter is approximately 4.8 cm.

7. To find area, multiply length by width. Since we know all sides of a square are the same, you can multiply 15 by 15 to get the answer.

15 * 15 = 225

The area is 225 sq. cm.

8. To find area, use this equation: A = l * w

put the values you know into the equation to find the length.

60 = l * 6

divide both sides by 6 to isolate the l

10 = l

The length is 10 cm.

9. To find the area of a square, the equation is: A = s^2

Input the values you know to find the length of a side.

81 = s^2

Find the square root of both sides to isolate the s.

9 = s

The length of one side is 9 cm.

10. To find the area of a circle, use this equation: A = pi * r^2

Input the values you know and solve for r.

201 = pi * r^2

Find the square root of both sides and divide both sides by pi to isolate the r.

7.998 = r

The radius is approximately 8 cm. Multiply this value by 2 to find the length of the diameter.

8 * 2 = 16

The diameter is approximately 16 cm.

Answer: 42 square feet.

Step-by-step explanation:

1/2 times 12 times 7 is 42.

Answer:

42

Step-by-step explanation:

Answer:

put the ^ when you do exponents!

Step-by-step explanation:

There are three parts to graphing an inequality.

1. determine if the line will be dashed or solid

2. determine where you will shade in

3 graph with the appropriate line and shade

1. it is just > and not ≥ so the line will be dashed, which means the line itself is not part of the answer.

2. it is y> so you shade in the area inside the parabola.  if y was an actal number it might be more complicated

3. graph x^2 - 6x + 11.  If that seems a bit hard, put it into vertex form by completing the square.

y = x^2 - 6x + 11

y = (x - 3)^2 +2

Since x^2 is positive it opens upward and then plug in 0 for x and y in y = (x - 3)^2 +2 to get the x and y intercepts and the -3 and +2 tells you the vertex (in this case the minimum) is at (3,2),  then remember the points are mirrored on either side of the vertex.  so if the y intercept is 2 to the left and one higher than the vertex, there will also be a point 2 to the RIGHT and 1 up.  then just connect the dots.  Keep in mind there may not be any x intercepts if it never goes below the x axis *hinthintwinkwink*

if all else fails just graph a handful of points to get the idea of the shape.  Just remember you are shading inside of the parabola and using dashed lines.  

Answer:

326.56

youre welcome

Step-by-step explanation:

Answer:

Both answers are 3.

Step-by-step explanation:

10^3 = 10 * 10 * 10 = 1000

When you multiply 42.12 by 10^3, you are multiplying 42.12 by 1000.

When you multiply a number by a power of 10, such as 10, 100, 1000, etc., move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10.

42.12 * 1000 = 42,120

Final answer:

To find the product of 42.12 and 10³, move the decimal point in 42.12 three places to the right because 10³ has three zeros. Thus, the product is 42120.

Explanation:

To find the product of 42.12 and 10³, you need to move the decimal point in 42.12 three places to the right because 10³ has three zeros. Multiplying by powers of ten is simplified by moving the decimal point to the right for each zero in the power of ten. For instance, multiplying 2.4 by 100 involves moving the decimal two places to the right to get 240, since 100 has two zeros.

When you multiply 42.12 by 10³, which is the same as multiplying by 1000 (10 x 10 x 10), you're effectively shifting the decimal point three places to the right. If there aren't enough digits, you can use zeros as placeholders. However, in this case, there are sufficient digits to move the decimal without adding additional zeros.

Therefore, 42.12 multiplied by 10³ would be 42120. This is because you move the decimal point three places to the right to account for the three zeros in 10³, changing 42.12 into 42120.

Answer:

x=  0.5

or x=  -1.5

Step-by-step explanation:

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

4x2+4x−3=0

Step 1: Factor left side of equation.

(2x−1)(2x+3)=0

Step 2: Set factors equal to 0.

2x−1=0 or 2x+3=0

x= 1/2 or x= −3/2

Answer:

A. x = –1.5, 0.5

Answer:

X²+6X=112

Step-by-step explanation:

area=1/2 base x height

56=x(x=6)/2

Multiply each side by two to eliminate the denominator

112=x(x=6)

112=x²+6x

Answer:

2a² + a   (   or a(2a+1)   )

Step-by-step explanation:

(6a²+3a) - (4a² + 2a)  (expand parentheses)

= 6a²+3a - 4a² - 2a   (group like terms)

= 6a²- 4a²+3a- 2a

= 2a² + a

= a(2a+1)

Answer:

2a^2+a

Step-by-step explanation:

This is an algebra. An algebra is an expression with no equality sign, and it will be expressed till the simplest form.

(6a^2+3a) - (4a^2 + 2a)

Remove the brackets

6a^2+3a-4a^2-2a

6a^2-4a^2+3a-2a

2a^2+a

Good morning ☕️

Answer:

Step-by-step explanation:

-7x + 5 = 8x - 25

then

25 + 5 = 8x + 7x

then

15x = 30

then

x = 2

___________________

:)

Answer:

    [tex]x=2[/tex]

Step-by-step explanation:

Given equation:

[tex]-7x + 5 = 8x - 25[/tex]

To find the value of 'x', take the terms of 'x' to one side and the constants to the other side:

Subtracting '[tex]5[/tex]' to both side:

   [tex]-7x+5-5=8x-25-5\\\\-7x=8x-30[/tex]

Subtracting '[tex]8x[/tex]' both side:

   [tex]-7x-8x=8x-8x-30\\\\-15x=-30[/tex]

          [tex]x=\frac{-30}{-15}[/tex]

          [tex]x=2[/tex]

Answer:

6

Step-by-step explanation:

18/3=6 You have to divide 18 by 3 in order to know how many times older Jill is than her sister.

Answer:

-1 case D)

Step-by-step explanation:

5-x=-(x-5) so the unknown factor is -1

b-k=-(k-b), again, -1

Similar for third case.

Answer:

36

Step-by-step explanation:

30% as a decimal is 0.30, take that and multiply it by 120 to find 30% of 120

120 × 0.30 = 36

Answer:

The total income from wages, bank interest, dividends, and the prize = $ 94577

Step-by-step explanation:

Total wages of Mike and Lisa in last year = $ 91301

Total bank interest of Mike and Lisa = $ 792 + $ 667 = $ 1459

Total income from dividends = $ 287 + $ 530 = $ 817

Prize of Lisa won = $ 1000

Thus the total income from wages, bank interest, dividends, and the prize =

$ 91301 + $ 1459 + $ 817 + $ 1000 = $ 94577

Final answer:

The total income from wages, bank interest, dividends, and the prize is $94,577.

Explanation:

To find the total income from wages, bank interest, dividends, and the prize, we need to add up all the amounts mentioned.

First, we add Mike and Lisa's wages: $91,301. Then we add their bank interests: $792 + $667 = $1,459. Next, we add their stock dividends: $287 + $530 = $817.

Finally, we add Lisa's prize: $1,000. Adding all these amounts together, the total income from wages, bank interest, dividends, and the prize is $91,301 + $1,459 + $817 + $1,000 = $94,577.

Answer:

x= -1/2

Step-by-step explanation:

-2(4x-3)=10​

Divide each side by -2

-2/-2 *(4x-3)=10​/-2

4x-3 = -5

Add 3 to each side

4x-3+3 = -5+3

4x = -2

Divide each side by 4

4x/4 = -2/4

x = -1/2

Answer:

x=-0.5 or x=-1/2

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

Answer:

20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.

Step-by-step explanation:

We are given the following in the question:

Let x quarts of 6% butterfat milk be used and y quarts of 3% butterfat milk be used to make 60 quarts of 4% butterfat milk.

Thus, we can write the equation:

[tex]6\%\times x + 3\%\times y = 4\%\times 60\\6x + 3y = 240[/tex]

Total amount of 3% butterfat milk = 60

Thus, we can write the equation:

[tex]x+y = 60[/tex]

Solving the two equation, we get,

[tex]6x + 3y-(3x+3y) = 240 - 3(60)\\3x = 240-180\\3x = 60\\x = 20\\y = 60-20 = 40[/tex]

Thus, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.

To get 60 quarts of 4% butterfat milk, mix 20 quarts of 6% butterfat milk with 40 quarts of 3% butterfat milk by setting up and solving a system of linear equations.

To solve this problem, we can set up a system of equations based on the quantities and percentages of butterfat in the milk types. Let's call the amount of 6% butterfat milk x quarts and the amount of 3% butterfat milk y quarts. According to the question, we want to end up with 60 quarts of 4% butterfat milk. Therefore, we have:

First, we multiply the second equation by 100 to simplify the percentages:

6x + 3y = 4 × 60

Simplify the right side:

6x + 3y = 240

Now, divide by 3 to get:

2x + y = 80

We can subtract the first total volume equation from this new equation:

(2x + y) - (x + y) = 80 - 60

Omit the similar terms to solve for x:

x = 20

We substitute x back into the initial total volume equation:

20 + y = 60

And solve for y:

y = 60 - 20

y = 40

Therefore, to get 60 quarts of 4% butterfat milk, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk must be mixed together.

Answer:

3/4

Step-by-step explanation:

Parallel lines will always have the same slope, but their y-intercepts can be any real number.

Answer:

Coefficient of y is 1 since the answer is y-1

Step-by-step explanation:

In the attached file

Answer:

n = 5

n = 8

Step-by-step explanation:

n^2 - 13n = -40

Equate everything to zero

n^2 - 13n + 40 = 0

Factorise

(n - 5)(n - 8) = 0

Either

n - 5 = 0

Add 5 to both sides

n - 5 + 5 = 0 + 5

n = 5

Or

n - 8 = 0

Add 8 to both sides

n - 8 + 8 = 0 + 8

n = 8

n = 5 or

n = 8

It has two real solutions

Answer:100cm

Step-by-step explanation:

Frank's error is that his function suggests a linear growth model instead of an exponential one. The correct function should be B(h) = 150 * (1.2)^h to represent an exponential growth where the population increases by 20 percent every hour.

Frank's error in his prediction function lies in the incorrect representation of the exponential growth of bacteria. His function reads B(h) = 150(.2)h, which implies a linear growth model, adding only 20% of the original amount, rather than a certain percentage of the current population. In reality, as the context describes the bacteria population growing by 20 percent every hour, the function should represent an exponential growth model accurate to the situation. Hence, the correct function should be B(h) = 150 * (1.2)^h, where 1.2, which signifies 120 percent (the original 100% plus the additional 20%), raised to the power h, accounts for the continuous multiplication or compounding of the bacteria every hour.

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Frank's error lies in the formulation of his prediction function. It should reflect exponential growth rather than linear growth. The population is 1.20 times what it was the previous hour, not 0.20 times.

The function he created, [tex]\( B(h) = 150(0.2)^h \),[/tex] incorrectly implies that the population increases by a factor of 0.2 each hour, which would represent a decrease since 0.2 is less than 1. Additionally, the initial population is multiplied by 0.2 instead of being increased by 20% each hour.

The correct way to model the population growth, assuming it grows by 20% each hour, is to use an exponential growth formula where the population is multiplied by [tex]\( 1 + \text{growth rate} \)[/tex] each hour that passes. Since the growth rate is 20%, or 0.20 in decimal form, the correct prediction function should be: [tex]\[ B(h) = 150(1 + 0.20)^h \][/tex]

This can be simplified to: [tex]\[ B(h) = 150(1.20)^h \][/tex]

This function correctly represents a 20% increase in the population each hour, starting with an initial population of 150 cells.

Frank's error was in the growth factor used in his function. It should have been [tex]\( 1 + \text{growth rate} \)[/tex] (which is 1.20 for a 20% increase) instead of just the growth rate (0.20). The correct function reflects that each hour, the population is 1.20 times what it was the previous hour, not 0.20 times.

Answer:

It would be C=(6, -9); D= (-5,-9)

Step-by-step explanation:

If you plot -6,9 and 5,9 on a four quadrant graph you can see the answer. (sorry I'm not good at explaining, I'm on the same question as you currently and this is the answer I got, I'm pretty sure the one above isn't correct.)

The locations of points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9), respectively depending on the orientation of the rectangle.

To calculate the locations of points C and D in the rectangle ABCD, consider that opposite sides of a rectangle are parallel and have equal lengths.

Given points A=(-6,9) and B=(5,9), know that points A and B lie on a horizontal line at y=9. Since opposite sides of a rectangle are parallel, points C and D should also lie on a horizontal line parallel to AB.

So, the y-coordinate of points C and D should be 9 as well.

The x-coordinate for points C and D, consider that opposite sides of a rectangle are of equal length. The length of AB represents the width of the rectangle.

The length of AB =  x-coordinate of B -  x-coordinate of A

AB = 5 - (-6)

AB = 11 units.

Since, opposite sides are parallel, points C and D should also have the same y-coordinate as A and B. Their x-coordinates must differ by 11 units to maintain equal side lengths.

Possible coordinates for C and D:

C = (5+11, 9) = (16, 9)

D = (-6+11, 9) = (5, 9)

Alternatively:

C = (-6-11, 9) = (-17, 9)

D = (5-11, 9) = (-6, 9)

Therefore, the possible locations for points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9) .

Learn more about Parallel line here:

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Answer:

Option B

Step-by-step explanation:

Using the law of logarithms

[tex]n log x= log x^{n}[/tex]

Therefore, since all the logs are to the same base, I will assume the base.

Also, when the bases are the same

log y+ log x= log (x+y)

[tex]\frac {1}{2}(log 4+ log 16)=log 4^{0.5}+log 16^{0.5}=log 2+log 4=log 6[/tex]

Now log 6-log 2= log (6-2)= log 4

Therefore, option B is correct

Answer:

8% is 0.08

275 + 0.08s > 560

0.08s > 285

s > 3562.5

Step-by-step explanation:

Total profit = Revenue - expenses

= $1200 - ($600 + $105 + $115 + $130)

= $1200 - $950

= $ 250

Answer:

100 : 175

Step-by-step explanation:

Divide 275 into two parts which are in the ratio 4:7?

To divide 275 into 4 :7, we will follow the steps below

First, We will add the ratio numbers together, that is; 4 + 7 = 11  

4 : 7 of 275 will be;

4/11  × 275

=4 × 275    /   11

=1100/11

=100

Then we will now proceed to the second part;

7/11  × 275

=  7 × 275  / 11

=1925/11

=175

Therefore dividing 275 into 4 : 7 yields    100 : 175

Step-by-step explanation:

[tex]5y + 1 = 1 \\ subtracting \: 1 \: from \: both \: sides \\ \red{ \boxed{ \bold{ 5y + 1 - 1 = 1 - 1}}} \\ 5y = 0 \\ y = 0[/tex]

Answer:

5

Step-by-step explanation:

Answer: its 5

Step-by-step explanation:

the coefficient is the leading number

Answer: -(x+8)(x-8)

Step-by-step explanation:

-(x^2-64)

x^2-8^2x^2

x^2-8^2=(x+8)(x-8)

-(x+8)(x-8)