Cassie and Amy are playing a card flash game. Cassie has a card with the fraction - 2/7 and Amy has a card with the fraction - 3/4. Write an equation to represent the product of theirs fractions then solve that equation.
( The minus is not plain -3 or -2 it’s the whole fraction)

The flat fee that the store charges is $14 and the cost for 7 hours is $56

A linear equation is on the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

let f for the total rental cost of a vacuum cleaner for x hours

Using the points (1, 20) and (3, 32) from the table:

\(f-f_1=\frac{f_2-f_1}{x_2-x_1} (x-x_1)\\\\f-20=\frac{32-20}{3-1} (x-1)\\\\f(x)=6x+14\)

The flat fee that the store charges is $14

The reasonable domain is 1 ≤ x ≤ 12

The cost for 7 hours is:

f(7) = 6(7) + 14 = 46

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The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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The correct option b. Debit Accounts Payable $1,000; Credit Cash $980; Credit Merchandise Inventory $20, is the required journal entry for Toys R Fun.

For the stated question;

Toys R Fun is offered a discount of two percent if he settles within 10 days as well as the payable is required in 30 days, as indicated by the terms "2/10,n/30."

$20 (2 percent of $1,000) is the result.

On the 17th, which falls inside the discount days, the payment for the journal entry for Toys R Fun is:

$1,000 - Dr. Accounts Payable

Cr money - $980

$20 worth of Cr inventory.

Let's say, however, that the payment is made by December 30 rather than that day.

The submission will be:

$1,000 Dr. Accounts Payable.

$1,000 cash in Cr.

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The complete question is-

On Dec. 7, Toys R Fun purchased $1,000 of merchandise with terms of 2/10,n/30. If payment is made on December 30, demonstrate the required journal entry for Toys R Fun to record the payment under the perpetual inventory system.

a. Debit Cash $1,000; Credit Accounts Payable $1,000

b. Debit Accounts Payable $1,000; credit Cash $980; credit Merchandise Inventory $20.

c. Debit Accounts Payable $1,000; credit Cash $1,000

Answer:

0.5904

Step-by-step explanation:

For each number, there are only two possible outcomes. Either it is in the 20s, or it is not. The probability of a number being in the 20s is independent of other numbers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

4 generated numbers:

This means that \(n = 4\)

Probability of a number in the 20s:

From 1 to 50, there are 50 numbers. Of those(from 20 to 29), there are 10 in the 20s. So \(p = \frac{10}{50} = 0.2\)

What is the probability that at least one of the first 4 generated numbers is in the 20s?

Either none is, or at least one is. The sum of the probabilities of these events is 1. So

\(P(X = 0) + P(X \geq 1) = 1\)

We want \(P(X \geq 1)\). So

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = 0) = C_{4,0}.(0.2)^{0}.(0.8)^{4} = 0.4096\)

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.4096 = 0.5904\)

Answer:

The answer is 300

Answer:

300 students

Step-by-step explanation:

hope this helps!

The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Net operating profit = (22 million - 19 million)*(1 - 0.36)

                                = $1.92  million

EVA = net operating profit after taxes - invested capital*WACC

       = 1.92 million - 15 million*0.10

       = $0.42 million

Therefore, The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million.

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Answer:

The question asks us to identify which of the provided graphs represents a function.

A relationship can be called a function only if one x-value corresponds to exactly one y-value.

To know if a relationship is a function from its graph, we can use something called the vertical line test. This is where you draw (or imagine) a vertical line going through the graph. If the line touches the curve exactly once, it passes the test and is a function.

In this question, for the first option, if we imagine a vertical line going through the graph, we can see that it touches the graph continuously at x = 1. Therefore, it is not a function.

Similarly, for the second and third options, the vertical lines would touch the graph twice. Therefore, they aren't functions either.

Finally, for the last option, we can see that a vertical line would touch the graph exactly once at every value of x. Therefore, it is a function.

Answer:

yes, they are by SSS

Step-by-step explanation:

EF=AB

ED=BC

DF=AC

therefore, both triangles are congruent

The given product is

To solve this multiplication, we multiply the coefficients between each other, and the power between each other.

Which is approximated to

The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Answer:  A) £7.49

               B) £2.25

Step-by-step explanation:

Step 1:

Let the cost of a football be \(f\)and the cost of a tennis ball be \(t\).

Step 2:

Write the 2 equations we have from the given information:

\(2f + 3t = 21.73\) \( \textsf{(from the cost of 2 footballs and 3 tennis balls)} \)

\(5f + 7t = 53.20\) \( \textsf{(from the cost of 5 footballs and 7 tennis balls)} \)

Step 3:

Solve for one variable in one of the equations. For example, we can solve for \(f\)in the first equation:

Step 4:

Substitute this expression for \(f\) into the second equation and solve for \(t\):

So, the cost of a tennis ball is £2.25.

Step 5:

Substitute this value of \(t\) into the expression for \(f\) and solve for \(f\):

So, the cost of a football is £7.49

Step 6:

Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.

Answer:

22

Step-by-step explanation:

3.85+2.75= 6.6

6.6÷0.30= 22

Answer:

The answer is 22 loaves of bread.

Step-by-step explanation:

You add 3.85 pounds + 2.75 pounds to get the total number of pounds she bought, which is 6.6 pounds of bananas.

Then you divide your total answer of 6.6 pounds by 0.30 pounds for each loaf, to get 22 loaves of bread.

Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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Answer: 287.&. Multiply 365 x 10 Great, you get 3650 . . . Multiply 287 by 3650 which then equals 1049375 . . . Wow! The interest will then be a total of 60929$ with the 8450 that she recieved that should equal 3 years total keeping it open . . .

Step-by-step explanation: Hope This Helps! Pls mark Branliest!

Answer:

6n + 20

Step-by-step explanation:

10 + 2n + 10 +4n

6n +20

Answer:

\(10 + 2n + 10 + 4n \\ 6n + 20 \\ 2(3n + 10)\)

The definite integral for this problem has the result given as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)

The definite integral for this problem is defined as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx\)

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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There were 0-5 Listeners when the song was released.

The approximate number of listeners who had heard the song after the hour 5 was 15- below 50

The number of listeners was about 29,458 after hour 5842.62/

Alternative forms

Y= 4,637(1.26)ˣ

292131/50,5842,31/50,5.84262 =10³

5842.62

Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.

Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.

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Answer:

a. $90,000

b. 15 advertisement slots

c. 0.53

Step-by-step explanation:

Let the purchase price of the slots, c = 4,500

The salvage value of the slots, s = 2,000

The selling price of the slots, p = 8,000

a. If the store manager sells all the advertising slots in advance, the revenue received, 'R', is given as follows;

R = The number of slots, n × The purchase price for selling immediately, c

∴ R = 20 × $4,500 = $90,000

The revenue the station will receive by selling all the advertising slots in advance, R = $90,000

b. The Cost of Overage, \(C_o\) = Purchase price - Salvage value

∴ The Cost of Overage, \(C_o\) = 4,500 - 2,000 = 2,500

The Cost of Underage, \(C_u\) = Selling price - Purchase price

∴ The Cost of Underage, \(C_u\) = 8,000 - 4,500 = 3,500

P; 0.03, 0.05, 0.1, 0.15, 0.2, 0.15, 0.1, 0.05, 0.05, 0.05, 0.05, 0.02

With help of MS Excel, we get the following cumulative frequency

F(Q); 0.03, 0.08, 0.18, 0.33, 0.53, 0.68, 0.78, 0.83, 0.88, 0.93, 0.98, 1

The expected monetary value for the decision to sell the 8th slot at the last minute is given by the following relation;

\(C_u\) × [1 - F(Q)] - \(C_o\) × F(Q)

Where F(Q) = The cumulative frequency for the 8th stock

Therefore, we have;

3,500 × (1 - 0.03) - 2,500 × 0.03 = 3,300

For the 8th slot, the TV station is expected to make an extra $3,300

Using MS Excel, we get;

For the 9th slot, the profit over the purchase price = $3,020

Fot the 10th slot, the profit over the purchase price = $2,420

The profit over the purchase price for the 11th slot = $1,520

The profit over the purchase price for the 12th slot = $320

The profit over the purchase price for the 13th slot = $(-580)

The 14th = $(-1,180)

15th = $(-1,480)

16th = $(-1,780)

17th = $(-2,080)

18th = $(-2,380)

19th = $(-2,500)

Therefore, to maximize profit, only the 8th, 9th, 10th, 11th, and 12th, slots which are 5 slots should be sold late while 20 - 5 = 15 slots should be sold in advance

c. The probability that the total revenue will exceed the identified amount in part 'a' is the cumulative probability at the 12th slot which is given as follows;

P(D ≤ 12) = F(12) = 0.53.

The probability that the total revenue will exceed the identified amount in part 'a' is the cumulative probability at the 12th slot is 0.53.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

Given information

The demand for these last minute slots is estimated

8 9 10 11 12 13 14 15 16 17 18 19

Probability 0.03 0.05 0.1 0.15 0.2 0.15 0.1 0.05 0.05 0.05 0.05 0.02

The purchase price of the slots = 4,500

The salvage value of the slots = 2,000

The selling price of the slots = 8,000

a. The revenue received

R = The number of slots × The purchase price of the slot

R = 20 × $4,500 = $90,000

The revenue the station will receive by selling all the advertising slots in advance, R = $90,000

b. The Cost of Overage = Purchase price - Salvage value

The Cost of Overage,  = 4,500 - 2,000 = 2,500

The Cost of Underage,  = Selling price - Purchase price

The Cost of Underage,  = 8,000 - 4,500 = 3,500

Probability 0.03, 0.05, 0.1, 0.15, 0.2, 0.15, 0.1, 0.05, 0.05, 0.05, 0.05, 0.02

Cumulative frequency

F(Q); 0.03, 0.08, 0.18, 0.33, 0.53, 0.68, 0.78, 0.83, 0.88, 0.93, 0.98, 1

The expected monetary value for the decision to sell the 8th slot at the last minute

The Cost of Underage × [1 - F(Q)] -  × F(Q)

Where F(Q) = The cumulative frequency for the 8th stock

Therefore, we get

3,500 × (1 - 0.03) - 2,500 × 0.03 = 3,300

For the 8th slot, the TV station is expected to make an extra $3,300

For the 9th slot, the profit over the purchase price = $3,020

For the 10th slot, the profit over the purchase price = $2,420

Similarly,

The profit over the purchase price for the 11th slot = $1,520

The profit over the purchase price for the 12th slot = $320

The profit over the purchase price for the 13th slot = $(-580)

The profit over the purchase price for the 14th = $(-1,180)

The profit over the purchase price for the 15th = $(-1,480)

The profit over the purchase price for the 16th = $(-1,780)

The profit over the purchase price for the 17th = $(-2,080)

The profit over the purchase price for the 18th = $(-2,380)

The profit over the purchase price for the 19th = $(-2,500)

Therefore, only the 8th, 9th, 10th, 11th, and 12th slots should be sold in advance to maximize profit.

c. The probability that the total revenue will exceed the identified amount in part 'a' is the cumulative probability at the 12th slot.

P(D ≤ 12) = F(12) = 0.53.

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Answer:

Step-by-step explanation this is a tough one but i know everything the answer is 69

The function modelled for the given condition is \(y = -16x^{2} + 6x +22\) and the time after which the skier is 5 feet above the water is 1.23 seconds.

A competitive water skier's heights y, x seconds after soaring off a ramp.

For x = 0, y = 22

for x = 0.25, y = 22.5

For x = 0.75, y = 17.5

For x = 1, y = 12

For x = 1.1, y = 9.24

The general equation of a quadratic equation is y = \(ax^{2} + bx +c\)

Putting x = 0 and y = 22 in the equation, we get :

\(y = ax^{2} +bx +c\)

c = 22

Now, putting x = 1 and y =12, we get,

12 = a*1 + b*1 + 22

a +b = 12 - 22 = -10 equation (1)

Putting x = 0.25, y = 22.5,

22.5 = a* \(22.5^{2}\) +b*22.5 +22

506.25 a +22.5b = 0.5 equation(2)

Solving equation (1) and equation(2), we get :

a = -16 and b = 6 and c = 22

So, the quadratic equation becomes,

\(y = -16x^{2} + 6x +22\)

Now, Time when the skier is 5 feet above the water,

\(x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds\)

Hence, the function modelled for the given condition is \(y = -16x^{2} + 6x +22\) and the time after which the skier is 5 feet above the water is 1.23 seconds.

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Given:

8x + 2y = 6

Let's identify the slope and y-intercept of the equation.

To identify the slope and y-intercept, we are to the slope-intercept form of a linear equation:

y = mx + b

Where:

m represents the slope.

b represents the y-intercept.

Now, let's rewrite the given equation to the slope-intercept form.

Subtract 8x from both sides of the equation:

Divide all terms by 2:

Therefore, the equation in slope-intercept form is:

y = -4x + 3

Now, compare both equations:

y = mx + b

y = -4x + 3

Thus, we have the following:

Slope, m = -4

y-intercept, b = 3

Therefore, the slope of the line is -4 , while the y-intercept is 3 .

ANSWER:

• Slope = -4

• y-intercept = 3

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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the answer is D : 4

According to the problem statement, one side of the rectangle is of length 5 cm. The other side can have any length greater than 4 cm (since the area of the rectangle should be greater than 4 cm^2).

Let's call this other side "x".

We know that the area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.

Therefore, we can write the equation: 5*x = A, where A is the area of the rectangle.

We can also say that the area of the square and the rectangle is equal to 4 cm^2.

If we call the side of the square "y", then we can write the equation: y^2 = 4 cm^2.

Solving for y, we get: y = 2 cm.

Therefore, the length of the rectangle that can be cut into a square and a rectangle of area 4 cm^2 is 5 cm - y = 5 cm - 2 cm = 3 cm.

So, there are 4 possible rectangles that can be cut into a square and a rectangle of area 4 cm^2: (5,3), (3,5), (6,4), and (4,6).

So the answer is D : 4

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The probability according to the given scenario is:

(a) 0.0395

(b) 0.95

(c) 0.076

The given values are:

(a)

The probability that the  b/w has tuberculosis as well as having (+) test will be:

→ \(P(A \cap B) = P(B/A).P(A)\)

By substituting the values, we get

→                  \(= 0.79\times 0.05\)

→                  \(= 0.0395\)

(b)

The probability that a person does not have tuberculosis will be:

→ \(P(A') = 1-P(A)\)

→            \(=1-0.05\)

→            \(= 0.95\)

(c)

The person does not have tuberculosis as well as have a (+) test, the probability will be:

→ \(P(A' \cap B) = P(A').P(B/A')\)

→                  \(= 0.95\times 0.08\)

→                  \(= 0.076\)

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Answer:

200

Step-by-step explanation:

Answer:

6 boxes

Step-by-step explanation:

4boxes = 140RS

x. = RS 210

x = RS210×4/140

x= 6 boxes

Answers:

=============================================

Explanation:

The first blank represents the distance that corresponds to t = 1 hour.

We'll replace t with 1 to get...

d = 54t

d = 54*1

d = 54

Therefore, 54 goes in the first blank. It means that Isaac traveled 54 miles after 1 hour.

------------------

We repeat these steps for t = 3

d = 54*t

d = 54*3

d = 162

This means he traveled 162 miles after 3 hours

So 162 goes in the second blank

-------------------

Side note: your teacher wrote 180 but s/he should have written 108 instead because 54*2 = 108