You decide to invest $10,000 in an account where the interest compounds annually. Create an exponential function to represent how much money you will have after 20 years if the money grows at a rate of 7.5 percent

SOLUTION

In mathematics, a ratio indicates how many times one number contains another.

And when we write quantities in ratio form, we represent ratio with the symbol :

For example: The ratio of A to B is written mathematically as A:B

Another important thing we must note when writing ratios is to always express both quantities in their simplest form.

With the above explanation, we can proceed in answering the question.

The ratio of adults to children which is 400 to 150, can be written mathematically in ratio form as:

Final answer: The ratio of adults to children is:

Answer:

B and C

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Equation 9 x 4 / 2 = 18

First do 9 x 4 which is 36

Next do 36 / 2 which is 18

Also the "/" is another way to say to divide

the temperature in the morning was 1 degree celsius

then rise of 3 degree

so now the total temperature is 1 + 3 = 4 degree

so the temperature of the afternoon is 4 degrees.

Answer:

121 pi

Step-by-step explanation:

pi d =22 pi

divide both side by pi to find diameter

d=22

divide by 2 too find radius

11 is the radius

plugg 11 to pi r ²

121 pi

The dimensions of the golf hole found using the indicated variable expressions are as follows;

a. The area of the golf hole is 4·x² + 12·x

b. The perimeter of the golf hole is 8·x + 8

c. The perimeter of the golf hole if the area of the hole is 216 square feet is 56 feet

The perimeter of a geometric figure is found by the length of the boundary of the figure.

a. The area of the gulf hole is found as follows;

The area is a composite figure, which consists of a rectangle of length 3·x and width (x + 4) and a square of length x

Which indicates that the area is A = 3·x × (x + 4) + x×x = 3·x² + 12·x + x²

The area of the hole, A = 3·x² + 12·x + x² = 4·x² + 12·x

The area of the hole is A = 4·x² + 12·x

b. The perimeter of the hole is found as follows;

P = (x + 4) + 3·x + (x + 4) + x + x + x = 8·x + 8

The perimeter of the hole = 8·x + 8

c. The area of the golf hole = 216 square feet, which indicates;

4·x² + 12·x = 216

4·x² + 12·x - 216 = 0

x² + 3·x - 54 = 0

(x + 9)·(x - 6) = 0

x = 6 or x = -9

The perimeter of the golf hole is therefore;

P = 8 × 6 + 8 = 56

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Given:

Triangle ABC is mapped onto triangle ADE.

Required:

The transformation that maps triangle ADE similar to triangle ABC.

Explanation:

A dilation process from A by a factor 3 maps triangle ABC onto triangle ADE.

In the dilation process, the transformed angle value remains constant.

Also,

Therefore above transformation makes triangle ABC similar to triangle ADE.

Answer:

Thus from the explanation given above, the above transformation makes triangle ABC similar to triangle ADE.

Answer:

x=1

Step-by-step explanation:

Both graphs intersect at 1

Answer:

x=1

Step-by-step explanation:

They sectioned at 1

The frequency of the longitudinal wave is 5/2 cm.

Given:

A longitudinal wave has 20 compressions and 20 rarefactions in 0.1s.

we are asked to determine the frequency of the wave = ?

1 wave ⇒ 1 compression + 1  rarefactions

therefore,

20 waves:

0.2 s ⇒ 20 waves.

1 & ⇒ 20/0.02 × 10/1

1 & ⇒ 200/2

1 & ⇒ 100 hz

20 > = 50 cm

⇒ 50/20

= 5/2 cm

Hence we get the frequency as 5/2 cm

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Answer:

Explanation:

Answer:

slope is -3

y intercept is 2

Step-by-step explanation:

3x+y=2 [subtract 3x from both sides]

y=-3x+2

slope is -3

y intercept is 2

DEF is an acute angke because the measure we can notice is less than a right angle

then the value is less than 90°

then right option should be D and E

C isnt because we can notice the angle is

Answer: with what???

Answer: 10.8 seconds

Step-by-step explanation:

[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]

Answer:

Step-by-step explanation:

I got 22 my friend hope i helped.

Answer:

$18

Step-by-step explanation:

50% of 40 is 20, so 40-20=20

10% of 20 is 2, so 20-2=18

total price=$18

The Sine rule formula is,

Given:

Let us solve for solve for the measure of angle B

Therefore,

Hence, there are no possible solutions for this triangle (OPTION C).

Answer:

1)To find the mean, median, mode and midrange for each gender.

From the given data,

Male: 191,222,168,154,178,155,190,170,178,202,169,184,149,160,181,158

For Men:

Mean is,

Mean is 175.5625

Arrange the given data in ascending order,

149,154,155,158,160,168,169,170,178,178,181,184,190,191,202,222

Median is,

Median is 174

The mode is one of the values of the measures of central tendency. This value gives us a rough idea about which of the items in a data set tend to occur most frequently.

Mode is 178.

Female: 136,160,101,126,119,165,102,135,137,140,115,126,140,121,124

For Women:

Mean is,

Mean is 129.8

Arrange the given data in ascending order,

101,102,115,119,121,124,126,126,135,136,137,140,140,160,165

Median is 126

Mode is 126,140

Answer: The highest common factor of 91, 112 and 49 is 7

hope this helps :)

Answer:

-5+0=-5

(-6)+1=-5

-7+2=-5

Step-by-step explanation:

Angle of depression is 7.7 °  made by the line of sight from the canyon edge to the fire .

The angle of depression is the angle created by the object and the horizontal line as seen from the horizontal line. The distance between two objects is often calculated when the angles and spacing of an object from the ground are known.

let f be the the fire

b is the base of the sheer canyon wall

o be the cliffs of insanity point that is canyon edge

so OB = 7117 Feet

bf = 10 miles = 10 * 5280 = 52800 feet

angle of depression is < xof which is equal to < ofb

let the angle of depression is [tex]\theta[/tex]

now from triangle obf ; it is a right angle triangle , where of = hypotenuse

bf = base , ob = height < ofb = [tex]\theta[/tex]

so , tan [tex]\theta[/tex] = ob/bf = 7117/52800

[tex]\theta[/tex] = [tex]tan^{-1}[/tex] ( 7117/52800) = 7.68 ° = 7.7 °

so angle of depression is 7.7 °

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Answer: The answer would be

B. 1/2

C. 1/3

Step-by-step explanation:

The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

y in equation 1

-28=3 is false, therefore the system of equations has no solution

Mean is 5.25, Median is 5 and mode is 3.

Given,

In the question:

There are numbers:

3, 4, 5, 7, 6, 8, 8, 5, 3, 6, 4, 5, 3, 3, 7, 7.

To find the mean, median and mode.

Let's Know :

How do you find the mean median and mode?

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Now, According to the above statement :

To find Mean:

[tex]\frac{3+4+ 5+ 7+ 6+ 8+ 8+ 5+ 3+ 6+ 4+ 5+ 3+ 3+ 7+ 7}{16}[/tex]

= 84/16 = 5.25

For Median

Arrange in ascending order

3, 3, 3, 3, 4,4, 5,5,5, 6,6, 7, 7, 7, 8,8.

There is an even no. of observations. i.e., 16 numbers.

then, there is no single middle value; the median is then usually defined to be the mean of the two middle values: so the median of

Middle two values is : (5 + 5)/2 = 10/2 = 5

Middle value is 5

For Mode:

The mode is the number that occurs most often in a data set.

Mode is 3 .

Hence, Mean is 5.25, Median is 5 and mode is 3.

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Answer:x=12

y=−186

Step-by-step explanation:x=63x+4y=12

Consider the first equation. Subtract 63x from both sides.

x−63x=4y

Combine x and −63x to get −62x.

−62x=4y

Divide both sides by −62.

x=−

62

1

​

×4y

Multiply −

62

1

​

 times 4y.

x=−

31

2

​

y

Substitute −

31

2y

​

 for x in the other equation, 63x+4y=12.

63(−

31

2

​

)y+4y=12

Multiply 63 times −

31

2y

​

.

−

31

126

​

y+4y=12

Add −

31

126y

​

 to 4y.

−

31

2

​

y=12

Divide both sides of the equation by −

31

2

​

, which is the same as multiplying both sides by the reciprocal of the fraction.

y=−186

Substitute −186 for y in x=−

31

2

​

y. Because the resulting equation contains only one variable, you can solve for x directly.

x=−

31

2

​

(−186)

Multiply −

31

2

​

 times −186.

x=12

The system is now solved.

x=12,y=−186

The original speed of the train was 32 miles per hour.

We have a train. The train travels a distance equal to 288 miles. It is given that if the speed of a train is increased by 4 miles per hour from its original speed, then it takes 1 hour less to cover the distance. We need to find out the original speed of the train.

Let the original speed of the train be denoted by the variable "s". We can write the following equations using the given data:

s = 288/t

(s + 4) = 288/(t - 1)

We will substitute the value of "s" from the first equation into the second equation.

(288/t) + 4 = 288/(t - 1)

(288)×(t - 1) + 4×t×(t - 1) = 288×t

288t - 288 + 4t² - 4t = 288t

4t² - 4t - 288 = 0

t² - t - 72 = 0

t² - 9t + 8t - 72 = 0

t(t - 9) + 8(t - 9) = 0

(t - 9)(t + 8) = 0

The value of time cannot be negative, so the value of "t" is 9. Now, we will substitute this value into the first equation.

s = 288/t

s = 288/9

s = 32

Hence, the original speed of the train is 32 miles per hour.

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The constant of proportionality is 20.

What is constant of proportionality?

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

Given,

the recipe uses 5 cups of strawberries per 1/4 cup of sugar.

And let constant of proportionality is k.

that is

5 α 1/4

5 = k1/4

k = 5(4)

k = 20

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Answer:

46

Explanation:

In each number to the right of the equality sign, the tenths place is always the rightmost number in addition and the one place is the result of the addition.

For example, in 1 +3 = 34

Therefore, for 2 + 4 we have

Hence,

which is our answer!

SOLUTION:

Step 1:

In this question, we are given the following:

How many subsets does the set T = {salsa, sour cream, queso, guacamole, pico de gallo} have?

Step 2:

The details of the solution are as follows:

Recall that:

The empty set and the set itelf are also part of the subsets that must be included as part of the number of subsets.

If a set has “n” elements,

then the number of subset of the given set is

Hence, the total number of subsets will be:

CONCLUSION:

The final answer is:

Answer:

f(x)=(6x+6)(x+10)

Explanation:

Given the quadratic expression:

First, we can rewrite it in the form below:

Next, factor the terms:

Thus, the quadratics as a product of two binomials is: