The usual price of a book was $20. Miko sold the book to Elsa for $23. 60. Find the percentage increase in price

Answer:

he can get 6 shirts

Step-by-step explanation:

12.60 x 26.5

333.9 - 280

53.9 ÷ 8.6

6

Answer:

6

Step-by-step explanation:

given coordinates                           dilated coordinates

p' ( 4, 6 )                                               p'' ( 4, -6 )

Q' ( 2, 2 )                                              Q'' ( 2, -2 )

R' ( 6, 2 )                                               R'' ( 6, -2 )

S' ( 6, 6 )                                               S'' ( 6, -6 )  

Given data

p' ( 4, 6 )

Q' ( 2, 2 )

R' ( 6, 2 )

S' ( 6, 6 )

The given coordinates is gotten by ( x, y ) and the coordinates is gotten to be ( x, -y ). Applying the rule is solve as follows:

given coordinates                           dilated coordinates

( x, y )                                                     ( x, -y )

p' ( 4, 6 )                                               p'' ( 4, -6 )

Q' ( 2, 2 )                                              Q'' ( 2, -2 )

R' ( 6, 2 )                                               R'' ( 6, -2 )

S' ( 6, 6 )                                               S'' ( 6, -6 )  

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We must account for both the capital gain and the capital loss in order to determine your overall multiplied dollar return on this investment. Therefore, your total dollar return on this investment is $5,200.

We must account for both the capital gain (or loss) from the shift in stock price and the dividend payments made throughout the year in order to determine your overall dollar return on this investment.

To begin, let's figure out the financial gain per share:

Sales price minus purchase price per share equals capital gain per share.

Share price  $43.25 - $37

Shares with a capital return of $6.25

Thus, each share of your capital gain is worth $6.25.

Let's next determine the total quantity of dividend income earned during the year:

Dividend per share x shares outstanding equals dividend revenue per share.

Earnings per share from dividends = $0.25 * 800

$200 is the dividend yield per share.

As a result, you received $200 in dividend revenue overall.

When all is said and done, we can determine your overall dollar return on investment:

Dividend revenue per share multiplied by capital gain per share to calculate the total dollar return.

Total amount received: ($6.25 + $0.25) * 800

Return in dollars: $6.50 * 800

$5,200 is the overall profit.

Your overall dollar return on this investment is therefore $5,200.

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Answer:

Step-by-step explanation:

(3-1)/(-2-3)= -2/5

y - 1 = -2/5(x-3)

y - 1 = -2/5x + 6/5

y - 5/5 = -2/5x + 6/5

y = -2/5x + 11/5

standard form is

5y = -2x + 11

2x + 5y = 11

Answer:

c 2/3

Step-by-step explanation:

divide both numerator and denominator by 7

Answer:

0

Step-by-step explanation:

The slope is always 0 on a horizontal line.

Answer:

x=5 .........................................

Answer:

r = 100(\(\frac{A}{P}\) - 1 )

Step-by-step explanation:

Given

A = P(1 + \(\frac{r}{100}\) ) ← divide both sides by P

\(\frac{A}{P}\) = 1 + \(\frac{r}{100}\) ( subtract 1 from both sides )

\(\frac{P}{A}\) - 1 = \(\frac{r}{100}\) ( multiply both sides by 100 )

100 ( \(\frac{P}{A}\) - 1) = r

Answer:

the answer is 2 4/5

Step-by-step explanation:

there are two wholes plus 4 out of 5 pieces, so it is 2 and 4/5.

The four possible times that car B could take to complete one lap are: 120 seconds, 90 seconds, 60 seconds, and 30 seconds.

The equation used to solve this problem is (150 - 30) = N * B, where N is the number of laps and B is the total number of seconds for car B to complete one lap. Therefore, the four possible times for car B to complete one lap are 120 seconds, 90 seconds, 60 seconds, and 30 seconds.

When solving for the total time, it is important to remember that the two cars start the race together and that their speeds remain constant. This means that the time it takes for car B to complete one lap must be a factor of 150 seconds. If car B takes a time that is not a factor of 150, then it will not be able to finish the race in 150 seconds.

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Kenneth had $125 and after deducting the expenses for the zoo, candy store, and toy shop, he would have $125 - 0.04(125 - x) - 0.2(125 - x) dollars left, where x represents the amount spent on the zoo.

Let's break down Kenneth's expenses :

Kenneth spent some money on a trip to the zoo.

Let's assume he spent x dollars on the zoo.

After this expense, he has 125 - x dollars remaining.

At the candy store, Kenneth spent 4% of the remaining money. Since 4% is equivalent to 0.04, he spent 0.04(125 - x) dollars.

After this expense, he has (125 - x) - 0.04(125 - x) dollars left.

Finally, at the toy shop, Kenneth spent 0.2 of his remaining money.

Since 0.2 is equivalent to 0.2(125 - x), he spent 0.2(125 - x) dollars.

After this expense, he has (125 - x) - 0.04(125 - x) - 0.2(125 - x) dollars remaining.

To find out how much money Kenneth has left, we need to simplify the expression:

(125 - x) - 0.04(125 - x) - 0.2(125 - x) =

125 - x - 0.04 \(\times\) 125 + 0.04x - 0.2 \(\times\) 125 + 0.2x =

125 - 0.04 \(\times\) 125 - 0.2 \(\times\) 125 - x + 0.04x + 0.2x =

125 - 5 - 25 - x + 0.24x =

(125 - 5 - 25) + (0.24x - x) =

95 + (-0.76x) =

95 - 0.76x

Therefore, Kenneth has 95 - 0.76x dollars left.

The exact amount of money he has left depends on the value of x, which represents the amount he spent on the zoo.

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Answer:

(0,-2) is the correct answer.

Step-by-step explanation:

There are 20 many ways can three items be selected from a group of six items.

Here we consider simple random sampling which can be further of two types that are:

With replacement,  when the samples used in previous round of choosing are put back in the population for the upcoming rounds.

When the data are sampled with replacement the number of samples are \(N^{n}\), where N is population and n is sample number.

Without replacement, when the samples used in previous round are not returned back in the population for the upcoming rounds of sampling.

When the data are sampled without replacement  there are n P r  or n C r number of items as sample in given set.

The number of ways to select three items from a group of six items can be found using the combination formula:

C(6, 3) = 6! / (3! * (6 - 3)!) = 20

So there are 20 different combinations of three items that can be selected from the group of six items. Here they are listed as three-letter combinations:

ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF, BCD, BCE, BCF, BDE, BDF, BEF, CDE, CDF, CEF, DEF

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Answer:

\(x^{2} + 9x\)

Step-by-step explanation:

(x+3)(x+3)

distribute the x to both three and x.

x * x + 3x * 3x

add like terms.

X^2 + 9x

Answer:

\(m=\frac{-5}{3}\)

Step-by-step explanation:

We want to find the slope between the points (-2,5) and (1,0).

The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are points.

We are already given the values of the points, but let's label their values to avoid any confusion and mistakes.

\(x_1=-2\\y_1=5\\x_2=1\\y_2=0\)

Now, substitute into the formula.

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{0-5}{1--2}\)

Simplify this to:

\(m=\frac{0-5}{1+2}\)

\(m=\frac{-5}{3}\)

The slope is -5/3.

Answer: r - 3.5 <= 10    

Step-by-step explanation:

-12 - 3.5 = -15.5
-15.5 <= 10

The circumference and area of a circle are 44π feet and 484π square feet.

The circumference (s), in feet, is the perimeter of the circle, the formulas for the circumference and the area (A), in square feet, of the circle are, respectively:

Circumference

s = 2π · r

Area

A = π · r²

Where r is the radius, in feet.

If we know that r = 22 ft, then the circumference and area of the circle are, respectively:

Circumference

s = 2π · (22 ft)

s = 44π ft

Area

A = π · (22 ft)²

A = 484π ft²

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A)

If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:

B)

If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):

Answer:

R = V/I+E

Hope this helps!

To solve the problem of maximizing z=x1+2x2+x3 with the given constraints:
\(1) x1+x2+x3=7\\2) 2x1−5x2+x3≥1\\3) x1, x2, x3≥0\)

To solve the first problem for maximizing \(z=3x1−x2+3x3+4x4\), we need to find the values of \(x1, x2, x3, and x4\) that satisfy the given constraints.

The given constraints are:
\(1) x1+2x2+2x3+4x4≤40\\2) 2x1−x2+x3+2x4≤8\\3) 4x1−2x2+x3−x4≤10\\4) x1, x2, x3, x4≥0\)
To solve this problem, we can use linear programming techniques, such as the simplex method or graphical method.

Since the question does not specify which method to use, I will provide a general overview of the steps involved in solving this type of problem.

1) Convert the given inequalities into equations by adding slack or surplus variables as needed.

For example, we can rewrite the first constraint as: \(x1+2x2+2x3+4x4+s1=40\)

2) Formulate the objective function. In this case, the objective function is \(z=3x1−x2+3x3+4x4\)

3) Set up the initial tableau by writing the coefficients of the variables in the constraints and the objective function.

4) Use the simplex method or graphical method to find the optimal solution.

This involves iteratively improving the current solution by pivoting on the variables until no further improvement can be made.

5) Once the optimal solution is found, interpret the results.

The values of \(x1, x2, x3, and x4\) in the optimal solution will maximize the objective function z.

For the second problem, the two-phase method is mentioned.

The two-phase method is used when there are artificial variables involved in the initial setup of the tableau.

It involves solving an auxiliary problem to find an initial feasible solution and then proceeding with the regular simplex method.

To solve the problem of maximizing z=x1+2x2+x3 with the given constraints:
\(1) x1+x2+x3=7\\2) 2x1−5x2+x3≥1\\3) x1, x2, x3≥0\)

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ANSWER

Length of the playing alley = 9m

Width of the playing alley = 3m

STEP-BY-STEP EXPLANATION:

Given information

The perimeter of a rectangular playing alley = 24 m

The length of the alley is three times the width

Let l represents the length of the alley

Let w represents the width of the alley

Step 1: Write the formula for calculating the perimeter of a rectangle

Where l is the length and w is the width of the rectangle

Recall, length = 3 times the width of the alley

Mathematically,

Step 2: Substitute the value of l = 3w into the above formula

Step 3: Solve for w

From the calculations above, you will see that the width of the playing alley is 3m

Step 4: Solve for l

Hence, the length of the playing alley is 9m

The probability that exactly 2 of them are left handed is equal to  approximately 0.98415 or 98.4%.

Percent of people left handed is equal to 10%

Number of people selected at random = 6

Use the binomial distribution to find the probability of exactly 2 people out of 6 being left-handed,

With a probability of success being left-handed is equal to 0.1.

The probability of exactly x successes in n independent trials,

Each with probability of success p, is given by the binomial probability mass function,

P(k) = (ⁿCₓ) × pˣ × (1-p)ⁿ⁻ˣ

where  (ⁿCₓ) is the binomial coefficient, which represents the number of ways to choose x items out of n.

Here we have,

n = 6  as 6 people are selected.

p = 0.1 the probability of a success being left-handed.

x= 2

find the probability of exactly 2 people being left-handed.

Plugging these values into the formula, we get,

⇒P(2) = ⁶C₂ × 0.1² × 0.9⁴

Evaluate this expression as,

⇒P(2) = 0.98415

Therefore, the probability that exactly 2 out of 6 people selected at random are left-handed is approximately 0.98415 or 98.4%.

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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After applying a reflection over the x-axis and a shift of 5 units up, the transformed function is:

g(x) = -3x + 5

Here we start with the linear function:

f(x)= 3x

There are some transformations that we need to apply to this function, first we need to apply a reflection over the x-axis, let's define this for a general function f(x). The reflection can be written as:

g(x) = -f(x)

After that, we apply a shift upwards of 5 units, to get that we just need to add 5 units, so we get:

g(x) = -f(x) + 5

Now we just replace f(x) by the given function to get

g(x) = -3x + 5

That is the transformed function.

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Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

3 ice cream machines will make a total of 480 gallons for the same length of time

4 ice cream machines will make a total of 640 gallons for the same length of time

From the question,

We are to determine the number of gallons of ice cream that could be made.

From the given information,

2 ice cream machines make a total of 320 gallons in a certain amount of time.

If 2 ice cream machines can make a total of 320 gallons

Then,

3 ice cream machines will make a total of x gallons in the same amount of time

x = \(\frac{320 \times 3}{2}\)

x = 480 gallons

Hence, 3 ice cream machines will make a total of 480 gallons.

If 2 ice cream machines can make a total of 320 gallons

Then,

4 ice cream machines will make a total of y gallons in the same amount of time

y = \(\frac{320 \times 4}{2}\)

y = 640 gallons

Hence, 4 ice cream machines will make a total of 640 gallons.

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The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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Answer:

There was a 16% increase since 2010 to 2012.

Step-by-step explanation:

8% + 8% = 0.16 x 100 = 16%.