Bentley is going to invest $98,000 and leave it in an account for 7 years. Assuming
the interest is compounded daily, what interest rate, to the nearest tenth of a percent,
would be required in order for Bentley to end up with $114,000?​

The range is: B. {12, 4, -6}

Step-by-step explanation:

Given

12x + 6y = 24

Here x is the input and y is the output

So,

Replacing y with f(x)

[tex]12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}[/tex]

Domain =  {-4, 0, 5},

We will put the elements of domain, one by one, to find range

[tex]f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6[/tex]

Hence,

The range is: B. {12, 4, -6}

Keywords: Range, Domain, functions

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{12, 4, -6}

Step-by-step explanation:

The relation is given by the equation as 12x + 6y = 24 ........... (1)

Now, the domain of this function is {-4, 0, 5}

We have to find the range of this function corresponding to the given domain.

Now, for x = - 4,  

12(-4) + 6y = 24 {From equation (1)}

⇒ 6y = 72

⇒ y = 12

Now, for x = 0,  

12(0) + 6y = 24 {From equation (1)}

⇒ 6y = 24

⇒ y = 4  

Now, for x = 5,  

12(5) + 6y = 24 {From equation (1)}

⇒ 6y = -36

⇒ y = -6

Hence, the range for the relation is {12, 4, -6} (Answer)

Answer:

x = 0.6 and x = -1.75

Step-by-step explanation:

80x2+92x−84=0

Use quadratic formula

x = (−b ±√(b2−4ac))/√2a

x = (-92 ± √(35344)) / 160

x = 95/160 and x = -280 / 160

x = 0.6 and x = -1.75

Option 3

The solution for given expression is [tex]\frac{(x - 4)(x - 4)}{(x + 3)(x + 1)}[/tex]

Given that we have to divide,

[tex]\frac{x^2 -16}{x^2 + 5x + 6} \div \frac{x^2 + 5x + 4}{x^2 -2x - 8}[/tex]   ---- (A)

Let us first factorize each term and then solve the sum

Using [tex]a^2 - b^2 = (a + b)(a - b)[/tex]

[tex]x^2 -16 = x^2 - 4^2 = (x + 4)(x -4)[/tex]  ----- (1)

[tex]x^2 + 5x + 6 = (x + 2)(x + 3)[/tex]   ----- (2)

[tex]x^2 + 5x + 4 = (x+1)(x + 4)[/tex]   ---- (3)

[tex]x^2 -2x - 8 = (x-4)(x + 2)[/tex]   ---- (4)

Now substituting (1), (2), (3), (4) in (A) we get,

[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \div \frac{(x+1)(x+4)}{(x-4)(x +2)}[/tex]

To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time. Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.

[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \times \frac{(x - 4)(x + 2)}{(x + 1)(x + 4)}[/tex]

On cancelling terms we get,

[tex]= \frac{(x -4)(x-4)}{(x + 3)(x + 1)}[/tex]

Thus option 3 is correct

Answer:

A. (x , y) = ( 1,  4) is the SOLUTION of the given system of equations.

Step-by-step explanation:

Here, the given set of equations is:

2 y + 5x = 13  ....... (1)

2y - 3x = 5    ...... (2)

Now, to solve this question by SUBSTITUTION:

From (1), we get:

2 y + 5x = 13   ⇒   2 y = 13 - 5 x

or, [tex]y = \frac{13 - 5x}{2}[/tex]

Put this value of y in (2) . We get

[tex]2y - 3x = 5  \implies 2\times\frac{(13-5x)}{2}  - 3x = 5\\\implies 13 - 5 x - 3x = 5\\\implies- 8x  = -8\\\implies x = 1[/tex]

Now, x = 1, put this value of x  in (1),

2 y + 5x = 13     ⇒ 2y + 5(1) = 13

or, 2 y = 13- 5 = 8

or, y = 8 / 2  = 4,   ⇒ y = 4

Hence, x  = 1, y = 4 is the SOLUTION of the given system of equations.

1. 8/64=1/8

2. 5/16

3. 33/84

4. 15/45=3/9=1/3

Answer:

1. 8/64=1/8

2. 5/16

3. 33/84

4. 15/45=3/9=1/3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Remember that slope=rise/run. You can find the right graph with the slope of 2/3 very easily by counting, upward 2 and rightward 3.

Answer:

y=125x+75

Step-by-step explanation:

Y= 125x+B

700=125(5)+B

700=625+B

700-625=625-625+B

75=B

The initial value, or deposit, for the vacation home is $75. The rate of change, or the cost per day, is $125. This constitutes a linear relationship where the total cost increases by a constant daily fee as the number of rental days increases.

In this problem, the total cost of the vacation home equals the deposit plus (daily rental fee * number of days). The total cost came out to be $700 when the family rented the home for 5 days. Given that the daily rental rate is $125, that means that the cost of the rental alone was $125 * 5 = $625.

Subtract the cost of the rental from the total cost to find the deposit: $700 - $625 = $75. Therefore, the initial value is $75, which represents the deposit.

The rate of change, which is the cost per day, is $125. This means for every additional day the family rents the vacation home, they are charged an additional $125. So the relationship is linear because the total cost increases by a constant rate - the daily fee - as the number of days increases.

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Answer:

n=-2

Step-by-step explanation:

-6n-2n=16

-8n=16

n=16/-8

n=-2

The distance from Indiana to Louisville is 1.37 inches on map.

Step-by-step explanation:

Distance from texas to milwaukee = 1000 miles

Distance on map = 13.7 inches

Distance from indiana to louisville = 100 miles

Distance on map = x

Using proportion;

Distance from texas to milwaukee: distance on map :: Distance from indiana to louisville : Distance on map

[tex]1000:13.7::100:x[/tex]

Product of mean = Product of extreme

[tex]100*13.7=1000*x\\1370=1000x\\1000x=1370[/tex]

Dividing both sides by 1000;

[tex]\frac{1000x}{1000}=\frac{1370}{1000}\\x=1.37\ inches[/tex]

The distance from Indiana to Louisville is 1.37 inches on map.

Keywords: Ratio, proportion, distance

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Answer:

9/20 yes, 4/15 not. See below

Step-by-step explanation:

Pick 9/20 and multiply numerator and denominator by 5:

9/20 = 45/100

We know that if we divide a number by 100 we need to move the coma as two places left, so:

9/20 = 45/100 = 0.45

And this is a terminal decimal as we know where it ends.

On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):

4 |_ 15

we can divide 4 by 15, so we use 40 and begin with a comma

40 |_ 15

      0.

15 enters 2 times in 40 with a rest of 10, so:

40 |_ 15

  30  0.2

  100

100 divided by 15 is 6 and we have 10 as rest again, and again and again...

40 |_ 15

  30  0.266.....

  100

    100

      ....

So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...

Answer:

y = 0.5x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 1, y = 0.5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5

y = 0.5x ← equation of variation

Answer: 0.5

Step-by-step explanation:

Answer:

A=lw is a formula for the area. L is length, W is width.

The ratios of the number of people to the number of rollercoaster cars are proportional because all the given ratios simplify to 6:1.

To determine if the ratios of the number of people to the number of rollercoaster cars are in a proportional relationship, we must see if the ratios are equivalent. If we look at the provided ratios, 18:3, 30:5, 36:6, and 48:8, we see that when simplified all become 6:1. This indicates that the relationship is indeed proportional because the same ratio is maintained throughout all given pairs.

Answer:

B 35%

Step-by-step explanation:

35/100 reduces to .35. To turn this into a percent, multiply it by 100 and add a percent sign. .35 * 100 = 35. 35%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Total number of squares = 100

Number of shaded squares = 35

The percentage of shaded squares is 35%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of squares = 100

Number of shaded squares = 35

The percentage of shaded squares.

= 35/100 x 100

= 35%

Thus,

The percentage of shaded squares is 35%

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D) 12 cm is the right answer

Step-by-step explanation:

Given

[tex]Radius\ of\ sphere = r_s = 6\ cm\\Height\ of\ cone = h = 6 cm\\[/tex]

As the volumes of cone and sphere are same

[tex]V_s = V_c\\\frac{4\pi {r_s}^3}{3} = \frac{\pi {r_c}^2h}{3}[/tex]

Putting the known values

[tex]\frac{4\pi {6}^3}{3} = \frac{\pi {r_c}^2*(6)}{3}[/tex]

Dividing both sides by pi

[tex]\frac{4\pi {(6)}^3}{3\pi } = \frac{\pi {r_c}^2*(6)}{3\pi }\\\frac{4*{(6)}^3}{3} = \frac{{r_c}^2*(6)}{3}[/tex]

Multiplying both sides by 3

[tex]4*(6)^3 = 6{r_c}^2\\{r_c}^2 = \frac{4*(6)^3}{6}\\{r_c}^2 = 4 * 6^2\\{r_c}^2 = 144[/tex]

Taking Square root on both sides

[tex]\sqrt{{r_c}^2}=\sqrt{144}\\r_c = 12\ cm[/tex]

Hence,

D) 12 cm is the right answer

Keywords: Volumes, areas

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Answer:

f=10

Step-by-step explanation:

Answer:

The answer is 34

To solve this, percentage calculations were used. The geologist visited 6 volcanoes in California, which is 15% of 40, and the remaining 34 in Alaska.

The question requires us to calculate the number of volcanoes the geologist visited in California and Alaska. The total number of volcanoes visited is 40, and 15% are in California. To find the number of volcanoes in each state, we employ basic percentage calculations.

First, to find the number of volcanoes in California, we multiply the total number by 15% (or 0.15):
Number of volcanoes in California = 40 * 0.15 = 6.

To find the number of volcanoes in Alaska, we subtract the number of volcanoes in California from the total:
Number of volcanoes in Alaska = 40 - 6 = 34.

Therefore, the geologist visits 6 volcanoes in California and 34 volcanoes in Alaska.

Answer:

a=-2 and b=-2

Step-by-step explanation:

So I just used Elimination I made the top part the same as b then I just subtract and did some other stuff,hope the pic helps

Answer:

i believe it is the 2nd one

Step-by-step explanation:

I think the answer is B because the line is a congruent to the line segment.

Answer:

6 large, 12 medium and 18 small

Step-by-step explanation:

Lets call small pizzas s, medium pizzas m and large pizzas l, with its respective prices $10, $15 and $40.

As they sell as many small as medium and large combined we can say that:

s = m + l [eq 1]

Also, as the number of medium is twice the larges we can say that:

m = 2l [eq 2]

Finally, as the get $600 we know that every amount sold multiplied by its price, and summing all together must bring $600:

10s + 15m + 40l = 600 [eq 3]

Lets replace s by its value in eq 1:

10s + 15m + 40l = 10 (m+l) 15m + 40l = 10m +10l + 15m + 40l = 600

25m + 50l = 600

Now we can replace m by its value in eq 2:

25m + 50l = 25 (2l) + 50 l = 50l + 50l = 100l = 600

100l = 600

Now divide both sides by 100:

l = 6

So, 6 large pizzas were sold.

Replace l=6 in eq 2:

m = 6*2

m = 12

12 medium pizzas were sold.

Finally, replace l=6 and m=12 in eq 1

s = m + l = 12 + 6 = 18

And 18 small pizzas were sold.

Lets verify our results in eq. 3:

10*(18) + 15*(12) + 40*(6) = 600

180 + 180 + 240 = 600

360 + 240 = 600 ---> Verified!

Answer:     edmentum 100%

f(x) − g(x)  = 2.5e-0.04x − (1.2 + 0.2x)

= 2.5e-0.04x − 1.2 − 0.2x

Step-by-step explanation:

The algebraic expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]

Given that the functions from part A are :

[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]

To find the expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term.

Step 1: Given two functions

[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]

Step 2: find f(x) - g(x),  subtract each term:

[tex]f(x) - g(x) = (2.5e^{(-0.04x)}) - (1.2 + 0.2x)[/tex]

Simplifying further, combine like terms:

[tex]f(x) - g(x) = 2.5e^{(-0.04x) }- 1.2 - 0.2x[/tex]

Therefore, the algebraic expression resulting from f(x) - g(x) is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]

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Answer:

Part a) [tex]V(h)=6.25\pi h\ in^3[/tex]

Part b) [tex]V(3)=18.75\pi\ in^3[/tex]  (see the explanation)

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of cylinder

h is the height of the cylinder

we have that

[tex]B=\pi r^{2}[/tex]

Part a) Write the function, V(h), that represents the volume of the cylinder

we have

[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]B=\pi (2.5)^{2}[/tex]

[tex]B=6.25\pi\ in^2[/tex]

The volume is

[tex]V(h)=6.25\pi h\ in^3[/tex]

Part b) Find V(3) and tell what it represents

V(3) represent the volume of the cylinder with a height of 3 inches

so

For h=3 in

substitute

[tex]V(3)=6.25\pi(3)\ in^3[/tex]

[tex]V(3)=18.75\pi\ in^3[/tex]

Final answer:

The function for the volume of the cylinder with diameter 5 inches is V(h) = π * (2.5 inches)² * h. To find V(3), we calculate the volume with height 3 inches, which represents the physical volume of the cylinder at that height.

Explanation:

To find the volume of the cylinder, V(h), we must use the formula V = πr²h, where r is the radius of the base, and h is the height of the cylinder.

Part A: Given that the diameter is 5 inches, the radius is half of the diameter, so r = 5 / 2 = 2.5 inches. Thus, the function representing the volume is V(h) = π * (2.5 inches)² * h.

Part B: To find V(3), we substitute h with 3 inches into the function: V(3) = π * (2.5 inches)² * 3 inches. This gives us the volume of the cylinder when the height is 3 inches.

Answer:

88°

Step-by-step explanation:

Alternate interior angles are congruent. So, set the angles equal to each other and solve for x.

2x + 30 = 3x + 1

x = 29

So, ∠5 = 3x + 1 = 3(29) + 1 = 88°

Answer:

94

Step-by-step explanation:

had question on usa test prep

Answer:

Filled table below

Step-by-step explanation:

There are three columns to fill out according to the requirements of the question:

The observed time will be taken from the given table (or scattered points in the graph)

The predicted time will be computed from the equation of the best fit line

The residual will be the difference between both  

For x=4.0, the time spent exercising is 4.5 hours

If we use the line, we have

[tex]y=-0.4x+7.02= -0.4(4.0)+7.02=5.42[/tex]

The residual is 5.42-4.5=0.92

For x=5.0, the time spent exercising is 6.5 hours

If we predict with the line, we have

[tex]y=-0.4x+7.02= -0.4(5.0)+7.02=5.02[/tex]

The residual is 5.02-6.5=-1.48

The values will be shown in the table below

Answer:

AD=23

Step-by-step explanation:

18+5=23      combined factors

Answer:

AD=23

Step-by-step explanation:

This solution uses the formula for the area of a triangle together with the Pythagorean theorem to determine the length of the missing side in a right triangle. Assuming one side and the area of the triangle are given, the step involves rearranging the area formula to solve for the missing side. The Pythagorean theorem guarantees the accuracy of this method.

The subject of this question is Mathematics. The grade of this question is Middle School. Based on the information given, we are asked to find a missing side of a triangle with a given area.

Since this is a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as x² + y² = h².

Assuming we know one side and the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height = 50. If we know one of the other sides, let's say 'y', we can solve for the other side 'x' by rearranging this formula to solve for 'x', then substituting the known values.

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Answer:

60 minutes

Step-by-step explanation:

There are 3 feet in a yard, so a football field is 300 feet long.

Dive 300 by 5 to find the total minutes.

300 / 5 = 60

Answer:

1 hour

Step-by-step explanation:

100 yards = 300 feet

300 / 5 = 60

60 min = 1 hour

Answer: It would take 1 hour for sloths to walk across a 100-yard football field.

M=4/5 y - intercept of -2

y= mx+b - slope formula

slope is also m

b is the y-intercept

answer:

y= 4/5x-2

Answer:

y = [tex]\frac{4}{5}[/tex] x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{4}{5}[/tex] and c = - 2

y = [tex]\frac{4}{5}[/tex] x - 2 ← equation of line

Answer:

There are 80 birds in the flock of cardinals.

Step-by-step explanation:

Given,

Number of seagulls in a flock = 20

Total number of birds of new flock = 100

To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.

Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock

Number of birds in cardinal = [tex]100-80=20[/tex]

Hence there are 80 birds in the flock of cardinals.

Answer:

3.45

Step-by-step explanation:

if you look at the picture all the steps are provided

GOOD LUCK!!