Sarah and Bryan went shopping and spent a total of $47.50. Bryan spent $15.50 less than what Sarah spent. How much did Bryan spend?

Answer:

the answer is the first one

Step-by-step explanation:

The  functions will represent $500 placed into a mutual fund yielding 10% per year for 4 years is  A = 500(1.1)^4

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.

given:

P= $500

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 500.00\((1 + 0.1/1)(1)^4\)

A = 500.00\((1.1)^4\)

A = $732.05

Hence, the functions will represent $500 placed into a mutual fund yielding 10% per year for 4 years is  A = 500(1.1)^4

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Answer:

x| = 78.7 is satisfied by both x = 78.7 and x = -78.7.

Step-by-step explanation:

The interpret μ\(_x\) = 3 and the interpret σ\(_x\) = 1.5492 .

Given :

When an opinion poll calls a residential telephone number at random, there is only a 20% chance that the call reaches a live person. You watch the random digit dialing machine make 15 calls. Let X = the number of calls that reach a live person.

here n = 15 and p = 0.20

μ\(_x\) = n * p

= 15 * 0.20

= 3

Standard deviation σ\(_x\) = \(\sqrt{n * p ( 1- p )}\)

= \(\sqrt{15 * 0.20 ( 1- 0.20)}\)

= 1.5492

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The increase in the price of tacos shifts the demand curve to the left, causing a decrease in the equilibrium price and quantity of hamburgers.

The accompanying supply and demand diagram is depicting the market for hamburgers in your hometown. The event that is given is that the price of tacos increases. This will cause the demand curve to shift to the left, as consumers shift from hamburgers to tacos. As the demand curve shifts to the left, the equilibrium price will decrease and the equilibrium quantity will decrease. This is because the decrease in demand will cause the quantity demanded to fall and the decrease in demand will cause the price to fall. This shift in the supply and demand curves will cause the equilibrium point to move to the left and downward. The new equilibrium price will be lower than the original equilibrium price and the quantity will also be lower.

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Answer:

y=0, y=8

Step-by-step explanation:

y²-8y=0

y(y-8)=0

so either y=0 or y-8=0

so y=0, y=8

Answer:

the solution to the equation is m = 28/3, or approximately 9.3333

Step-by-step explanation:

To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:

3m/2/3 = 7

(2/3) * (3m/2/3) = (2/3) * 7

3m/2 = 7 * (2/3)

3m/2 = 14/3

Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:

(2) * (3m/2) = (2) * (14/3)

3m = 28/3

Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:

(3m) / 3 = (28/3) / 3

m = 28/3

Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.

Answer:

Maybe m = 14/9

Maybe m = 14

Step-by-step explanation:

It is not clear what you mean by the fraction on the left side.

Do you mean

3m/(2/3) = 7  ?

If so:

3m = 7 × 2/3

3m = 14/3

m = 14/9

Do you mean

(3m/2)/3 = 7   ?

If so:

3m/2 = 21

m = 21 × 2/3

m = 14

Do you mean something else?

Answer:

Step-by-step explanation:

3x=27

The volume of the right rectangular prism is 504 cubic feet.

To find the volume of a right rectangular prism with a base area of 112 square feet and a height of 4½ feet, we can use the formula:

Volume = Base Area x Height

First, we need to convert the height to feet and inches or decimal feet:

4½ feet = 4.5 feet

Now we can substitute the given values into the formula and calculate the volume:

Volume = 112 square feet x 4.5 feet

Volume = 504 cubic feet

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Step-by-step explanation:

First let solve the inequality

\(5 {x}^{2} + 2x - 3 < 0\)

Factor by grouping

\(5 {x}^{2} + 5x - 3x - 3 < 0\)

\(5x(x + 1) - 3(x + 1)\)

So the factor are

\((5x - 3)(x + 1)\)

So the factor are

\(x = \frac{3}{5} \)

and

\(x = - 1\)

Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics

creates 2 roots and/or double roots.

The inequality

\( |x - b| < c\)

works as

b is the midpoint between 2 roots. And c is the

\( |x + b| = c\)

We know that the midpoint between both roots is-1/5.

so

\( |x - ( - \frac{1}{5} )| < c\)

\( |x + \frac{1}{5} | < c\)

Let use roots 3/5

\( | \frac{3}{5} + \frac{1}{5} | = \frac{4}{5} \)

-1 works as well.

\( | - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5} \)

So the absolute value equation is

\( |x + \frac{1}{5} | < \frac{4}{5} \)

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

16 is 40% of 40

Step-by-step explanation:

16 = 40% x Y

16 = 40/100 x Y

y=3 x 100/40

y=40

Answer:

(11.6+7.3) - (6.2 × 2.1)

(18.9)-(13.02)

= 149.1

Answer:

.

Step-by-step explanation:

The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

16 feet per second

Step-by-step explanation:

Divide 480 feet by 30 seconds.

Answer:

\(2 \frac{2}{7}\) pounds, D

Step-by-step explanation:

1 pound of apples = 1.75 dollars.

Set the number of pounds of apples as x.

Then, we can write this equation.

1.75x = 4

\(\frac{7}{4}\)x = 4

Divide both sides by \(\frac{7}{4}\)

x = \(\frac{4}{1}\) * \(\frac{4}{7}\)

x = \(\frac{16}{7}\)

x = \(2 \frac{2}{7}\)

Thus, the answer is D, x = \(2 \frac{2}{7}\) pounds

Answer:

10

Step-by-step explanation:

15 ÷ 1.5 = 10

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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Answer: 6 x 3.14 = 18.84

Step-by-step explanation:

To find the circumference of a circle, you multiply the diameter by pi.

Answer:

  18.84 units

Step-by-step explanation:

You want to know the circumference of a circle with a diameter of 6 units.

The circumference C of a circle with diameter d is given by the formula ...

  C = πd

Using the given values of π and d, this becomes ...

  C = 3.14 × (6 units)

  C = 18.84 units

The circumference of the circle is 18.84 units.

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Using the normal distribution, it is found that:

a) 4.46% of finish times was higher than 72 minutes.

b) 55.11% of finish times was between 52 and 70 minutes.

c) The 40th percentile of finish times is 52.5 minutes.

d) The 95th percentile of finish times is 71.45 minutes.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

Item a:

The proportion is 1 subtracted by the p-value of Z when X = 72, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{72 - 55}{10}\)

\(Z = 1.7\)

\(Z = 1.7\) has a p-value of 0.9554

1 - 0.9554 = 0.0446

0.0446 x 100% = 4.46%

4.46% of finish times was higher than 72 minutes.

Item b:

Th proportion is the p-value of Z when X = 70 subtracted by the p-value of Z when X = 52, hence:

X = 70:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{70 - 55}{10}\)

\(Z = 1.5\)

\(Z = 1.5\) has a p-value of 0.9332.

X = 52:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{52 - 55}{10}\)

\(Z = -0.3\)

\(Z = -0.3\) has a p-value of 0.3821.

0.9332 - 0.3821 = 0.5511

0.5511 x 100% = 55.11%

55.11% of finish times was between 52 and 70 minutes.

Item c:

The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.253 = \frac{X - 55}{10}\)

\(X - 55 = -0.253(10)\)

\(X = 52.5\)

The 40th percentile of finish times is 52.5 minutes.

Item d:

The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 55}{10}\)

\(X - 55 = 1.645(10)\)

\(X = 71.45\)

The 95th percentile of finish times is 71.45 minutes.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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The percent increase of the profit is 15%

In this question, the figures are given as

Profit in March = £2750

Profit in April = £3162.50

The percentage of the increase of the profit is then calculated using the following equation

Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%

Substitute the known values in the above equation, so, we have the following representation

Increase percentage = (3162.50 - 2750)/2750 * 100%

Evaluate

Increase percentage = 15%

Hence, the increase in percentage is 15%

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Given:

The product of \(\dfrac{9}{5}\) and \(8\dfrac{1}{4}\) greater than 5.

To find:

By how much the product of \(\dfrac{9}{5}\) and \(8\dfrac{1}{4}\) greater than 5.

Solution:

First we need to find the product of \(\dfrac{9}{5}\) and \(8\dfrac{1}{4}\).

\(\text{Product}=\dfrac{9}{5}\times 8\dfrac{1}{4}\)

\(\text{Product}=\dfrac{9}{5}\times \dfrac{8(4)+1}{4}\)

\(\text{Product}=\dfrac{9}{5}\times \dfrac{33}{4}\)

\(\text{Product}=14.85\)

Now subtract 5 from the product.

\(14.85-5=9.85\)

Therefore, the product of \(\dfrac{9}{5}\) and \(8\dfrac{1}{4}\) is 9.85 greater than 5.

Answer:

???

Step-by-step explanation: