Claire worked the problem below. Jane is having the carpet cleaned throughout her entire house. She plans to pay Carpets-R-Clean a service charge of $50 plus $25 per room. Write an equation to help Jane determine how much she will pay, y, if her home has x rooms with carpet.

Answer:

Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.

For the larger box:

Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²

Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)

For the smaller box:

Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²

Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.

Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)

The difference in cost between the larger and smaller boxes is:

20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)

The percentage savings can be calculated as follows:

Percentage savings = (difference in cost / cost of larger box) * 100%

= (5.33718 / 20.55986) * 100%

= 25.98%

Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

79-83= 2

84-88 =4

89-93= 5

94-98=2

Step-by-step explanation:

put in order then you can just count them

Answer:

2x - 3 = 11

x = -21

Step-by-step explanation:

The algebraic property illustrated is the commutative property of multiplication

The properties of algebra are those properties mostly used in simplifying algebraic expressions.

Algebraic properties are:

From the expression given we have

4/5 • 5/4 = 1

= 4/ 5 × 5/ 4

= 1

Thus, the algebraic property illustrated is the commutative property of multiplication

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Answer:

y = 3/2x-2

Step-by-step explanation:

slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 3/2x+b

Substitute the point in for x and y

1 = 3/2(2)+b

1 = 3+b

1-3 =b

-2=b

y = 3/2x-2

Answer:

100,000>56,313 56, 56,313<100,000

To reach a temperature of 100 degrees the pizza would take 750 minutes.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

Since the pizza was heated at a constant rate, we can model the experiment as a line, where the slope represents how fast the pizza was heated.

The slope is given as:

m = (y2 - y1)/(x2 - x1)

Let

(x1,y1) = (6, 40)

(x2,y2) = (8, 55)

m = (55 - 40) / ( 8 - 6 )

m = 7.5 degrees per minute.

The pizza heats up an average of 7.50 degrees per minute

To reach a temperature of 100 degrees the pizza would take:

(100)(7.50) = 750 minutes.

Hence, to reach a temperature of 100 degrees the pizza would take:

(100)(7.50) = 750 minutes.

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Answer:

-10, -6

6, 10

Step-by-step explanation:

Let the one number be x.

One number is 3/5 of the other number.

The numbers are x and 3x/5.

Add 4 to one number, the sum equals the other number.

There are two possibilities.

A) x + 4 = 3x/5

B) 3x/5 + 4 = x

Solve A)

5x + 20 = 3x

2x = -20

x = -10

Solve B)

3x + 20 = 5x

2x = 20

x = 10

According to A)

x = -10

3x/5 = -6

According to B)

x = 10

3x/5 = 6

Answer:

-10, -6

6, 10

Answer:

1/3 simplifed.

Step-by-step explanation:

To find the product of 3/7*7/9. We can multiply top and bottom. Top: 3*7=21 Bottom: 7*9=63. Our final answer is just the Top/Bottom= 21/63. We can also simplify this into 1/3 which is our final answer.

The money collected during the second week was :  840

Analysis:

Total number of persons.

number of persons that paid first week = 12

number that paid second week = 62 - 12 = 50

if each person is to pay 16.40, then 50 people would pay = 16.4 x 50 = 840 dollars.

Hence we can conclude that The money collected during the second week was :  840

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Option B is a correct representation of the given number line,  -3.8 < 1.5, and is located to the left of 1.5.

A number line is a visual depiction of numbers on a straight line drawn either horizontally or vertically. It is simple for humans to compare numbers and carry out simple arithmetic operations on them when they are written down on a number line. A number line is thought to begin at zero (0). Left of zero, there are only negative numbers, and right of zero, there are only positive numbers.

Given a number line and two points marked on it,

-3.8 and 1.5

we find from the number line that -3.8 lie left to 1.5,

and the negative numbers are always less than the positive numbers,

so -3.8 is less than 1.5,

-3.8 < 1.5, and lie left to 1.5.

Hence, option B is correct.

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Answer:

400 litres

Step-by-step explanation:

Answer:

a = 6.34, b = 2.64

Step-by-step explanation:

used stat function on calculator

Answer: a is 4 , b is 3

Step-by-step explanation:

We are asked to create a frequency table. We will create the table.

We know that we will have 205 dancers in total, so this can go in the bottom right hand corner.

Then, we need to find out how many in total were trained in tap and ballet. We are given the value of 72, so this goes under "Trained in Tap" and meets with "Trained in ballet."

Then, we are told that 43 train in ballet, but not in tap. Therefore, we will place 43 under "Trained in ballet" but line it up with "Not trained in tap."

Finally, we have that 62 dancers were not trained in either tap nor ballet, so 62 is placed in the cell that lines up "Not trained in tap" and "Not trained in ballet."

This gives us this frequency table:

Then, we need to perform some math to find out how to fill the cells. Let's find the total number of individuals trained in tap column.

We know that 72 are trained in tap, and that 205 is the total for the entire frequency. 105 are not trained in tap, so we can subtract 105 from 205 to get 100. That means the total for the Trained in tap column becomes 100.

Then we have to find how many are not trained in ballet but are trained in tap. This means that we need to subtract 72 from 100. This gives us 28, which means 28 dancers are not trained in ballet but are trained in tap.

Finally, we can find the total dancers not trained in ballet by adding 28 and 62, which gives us 90.

This gives us a final frequency table:

Now, we need to find the percent of dancers that were not trained in either discipline. This means that we need to use the value of 62 dancers. We were told that 62 dancers were not trained in either discipline. Therefore, we know that we have 205 dancers in total, which means we will divide 62 by 205.

Then, we need to multiply this decimal by 100% to find the percentage of dancers not trained in either discipline.

Therefore, 30.24% of dancers were not trained in either discipline.

Part B asks us to find what percent of tap dancers were also trained in ballet. Using our frequency table, we can see that 72 dancers were trained in both tap and in ballet. Therefore, we also know that 100 dancers were trained in tap. If 72 of those dancers were also trained in ballet, we can divide 72 by 100 and find the percentage using the same steps as above.

Then, we multiply the decimal by 100%.

Therefore, 72% of dancers that were trained in tap dance were also trained in ballet.

Answer:

23/20

Step-by-step explanation:

60+65/100

plz make me brainliest

Answer:

there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Step-by-step explanation:

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:

Select the first battery. There are 6 choices for the first battery.

Select the second battery. There are 5 choices left for the second battery, since we've already selected one.

Select the third battery. There are 4 choices left for the third battery.

Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:

6 x 5 x 4 = 120

Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Answer:

5 crayons

Step-by-step explanation:

A standard pack of crayons is 24, so I put b = 24.

24 + 6 - (x) = 25

30 - (x)  = 25

- 30          -30

- (x) =  -5

÷ -1     ÷ -1

(x) = 5

I really hope this helps!

Answer:

There are 20 odd numbers between 10 and 50

Step-by-step explanation:

Here are all the odd numbers! Hope this helps!

11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49

Answer:

5 × 4 = 20 not 40

Step-by-step explanation:

The Area of the two circle is 14.13 cm square. and  area of the blue section is 14.13 cm square.

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the shape is the sum of the area of the two smaller circle.

The circles have diameter of 3 unit.

Area of a circle = πr²

where: π = 3.14 = pi

D = diameter

r = radius

1. Radius = 3 cm

Now the area of the big circle =  πr²

Area = 3.14 x 3² = 28.26 cm square

2. Radius = 3/2

Area = 3.14 x 3/2² = 7.06 cm square

Area of the two circle = 7.06 + 7.06 = 14.13 cm square

3.  the area of the blue section = the area of the big circle - Area of the two circle

= 28.26  - 14.13

= 14.13

Therefore, the area of the blue section is 14.13 cm square.

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Answer:

\(A_{total} = 14\ in^2\)

Step-by-step explanation:

Step 1:  Determine the area of the left rectangle

We can tell that the total shape seems like two rectangles glued together.  We can separate the left rectangle and determine the area of it and then determine the area of the right rectangle and combine them.  Lets first solve the left rectangle.

\(A = l * w\)

\(A_{left\ rectangle} = 2\ in * 4\ in\)

\(A_{left\ rectangle} = 8\ in^2\)

Step 2:  Determine the area of the right rectangle

\(A = l * w\)

\(A_{right\ rectangle} = 3\ in * 2\ in\)

\(A_{right\ rectangle} = 6\ in^2\)

Step 3:  Determine the total area

\(A_{total}=A_{left\ rectangle} + A_{right\ rectangle}\)

\(A_{total} = 8\ in^2 + 6\ in^2\)

\(A_{total} = 14\ in^2\)

Answer: \(A_{total} = 14\ in^2\)

Area of right rectangle

Area of left rectangle

Total

The calculated value of the rate of the graph is 0.8

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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Answer:

Step-by-step explanation:

(cos A+ cos B)-cos C

\(=2cos \frac{A+B}{2}cos \frac{A-B}{2}-cos C~~~...(1)\\A+B+C=180\\A+B=180-C\\\frac{A+B}{2}=90-\frac{C}{2}\\cos \frac{A+B}{2}=cos(90-\frac{C}{2})=sin \frac{C}{2}\\cos C=1-2sin^2\frac{C}{2}\\(1)=2 sin \frac{C}{2} cos \frac{A-B}{2}-1+2sin^2\frac{C}2}\\=2sin\frac{C}{2}[cos \frac{A-B}{2}+sin \frac{C}{2}]-1~~~...(2)\\\\now~again~A+B+C=180\\C=180-(A+B)\\sin\frac{C}{2}=sin(90-\frac{A+B}{2})=cos \frac{A+B}{2}\\(2)=2sin\frac {C}{2}[cos \frac{A-B}{2}+cos \frac{A+B}{2}]-1\\\)

\(=-1+2sin\frac{C}{2}*2cos \frac{\frac{A-B}{2} +\frac{A+B}{2} }{2} cos \frac{\frac{A-B}{2} -\frac{A+B}{2} }{2} \\=-1+4sin\frac{C}{2} cos \frac{A}{2} cos\frac{-B}{2} \\=-1+4 cos \frac{A}{2} cos \frac{B}{2} sin \frac{C}{2}\\(cos(-B)=cos B)\)

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

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