To raise money, the Boy Scouts bought 60 kg of caramels for $130.80. They sold the caramels in 300 g bags for $2.37 each. How much profit did they make?

The equivalent linear equation to the line 3x + 4y = 15 is the one in the first option:

y = (15 - 3x)/4

Here we have the following linear equation:

3x + 4y = 15

And we want to find an equivalent linear equation where y is isolated in the left side of the equation. So let's isolate the variable.

If we subtract 3x in both sides of the linear equation we will get:

3x + 4y - 3x = 15 - 3x

4y = 15 - 3x

Now we can divide both sides by 4, so we will get:

4y/4 = (15 - 3x)/4

y = (15 - 3x)/4

This is the equation in option 1, so we conclude that the correct option is the first one.

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Approximately 95% of men must duck when walking through a door that is 72 inches high. Approximately 5% of women must duck when walking through the door. The door height that would allow at least 95% of men to walk through the door without ducking is 74 inches.

The mean height of men is 69.0 inches and the standard deviation is 2.8 inches, while the mean height of women is 63.6 inches and the standard deviation is 2.5 inches.

(a) To find the percentage of men who must duck when walking through a door that is 72 inches high, we first need to find the percentage of men whose height is less than 72 inches.

The height of the door is 72 inches, which is 3 inches above the mean height of men.

Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.

Therefore, approximately 95% of men are between 69.0 - 5.6 = 63.4 inches and 69.0 + 5.6 = 74.6 inches tall.

If the height of the door is 72 inches, approximately 95% of men must duck when walking through the door.

(b) To find the percentage of women who must duck when walking through a door that is 70 inches high, we first need to find the percentage of women whose height is less than 70 inches.

The height of the door is 70 inches, which is 6.4 inches above the mean height of women.

Since the standard deviation is 2.5 inches, this means that approximately 95% of women are within 2.5 * 2 = 5 inches of the mean height. Therefore, approximately 95% of women are between 63.6 - 5 = 58.6 inches and 63.6 + 5 = 68.6 inches tall.

If the height of the door is 70 inches, approximately 5% of women must duck when walking through the door.

(c) To find the door height that would allow at least 95% of men to walk through the door without ducking, we need to find the height that is within 2 standard deviations of the mean height of men.

Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.

Therefore, the door height that would allow at least 95% of men to walk through the door without ducking is 69.0 + 5.6 = 74

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Answer:

A: x=0, X=6

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

Answer:

Function: y = 2/x

Graph:

The graph of y = 2/x is a hyperbola whose asymptotes are the x-axis and y-axis.

y when x = 20:

y = 2/20 = 0.1

The length of the side a is 112.1664 cm.

The ratios of a triangle's side lengths to each of its opposite angles are related by the law of sines. There is no change in this ratio for the three sides or the opposing angles.

The Law of sines;

Sin A / a = Sin B / b = Sin C/ c

Here, we have two angles 35° and 25° and a side b = 5 ft

Now, sin35°/5 = sin25°/a

a = (0.42) x 5 / (0.57)

a = 3.68

Now the length in feet is 3.68 cm.

Therefore, the length of the side a is 112.1664 cm.

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The slope of the line in the graph is 2/3.

A line's slope is defined as

Slope = Rise / Run

Can also be written as,

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

Choose any two points on the line, such as A and B.

It is clear from the graph below that

Rise = y Change = -3-(-1) = -2

Run = x Change = 1 - 4 = -3

In the above formula, substitute these values.

Slope = -2 / -3

          = 2/3

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The new temperature is 91 degrees, if the temperature is raised by 13 degrees.

Two or more expressions with an Equal sign is called as Equation.

The temperature Thursday morning was 78 degrees

If the temperature rose 13 degrees by noon,

We need to find the new temperature

Temperature rose 13 degrees by noon means thirteen degrees is increased by 78.

78 degrees + 13 degrees

91 degrees.

Hence, the new temperature is 91 degrees, if the temperature is raised by 13 degrees.

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The number of Canadian dollars your 212 US dollars became is 264.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, you have saved $212 to take for spending money in vacation.

Here, 25 Canadian dollars is equivalent to $20.08 US dollars

Now, number of US dollars = 212/20.08

= 10.56

So, 25 Canadian dollars = 25× The number of US dollars

= 25×10.56

= 264 Canadian dollars

Therefore, the number of Canadian dollars your 212 US dollars became is 264.

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Answer: B: rational numbers

Step-by-step explanation: A rational number is a number that can be expressed as A/B or A over B. They also include integers, whole numbers, percents, decimals, etc...... For example, -2 can be expressed as -2/1 or -2 over 1.

The complete table of values of the equation y = 3x + 5 is

x = -2, -1, 0, 1 2

y = -1  2  5   8  11

The complete question is added at the end of this solution

From the question, we have the following equation that can be used in our computation:

y = 3x + 5

From the table of values added at the end of this question, we have the following x values

x = -2, -1, 0, 1 and 2

Substitute x = -2, -1, 0, 1 and 2 in y = 3x + 5

So, we have the following representation

y = 3(-2) + 5 = -1

y = 3(-1) + 5 = 2

y = 3(0) + 5 = 5

y = 3(1) + 5 = 8

y = 3(2) + 5 = 11

So, the complete table of values is

x = -2, -1, 0, 1 2

y = -1  2  5   8  11

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Answer: Range

Step-by-step explanation:

The amount of power y the solar panel can produce is linearly proportional to the size of x, the equation is y = 1200x, and the graph is attached below.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given data:

A certain model of a solar panel produces 1,200 KW of power for an area of one square meter,2,400 KW of power for an area of two square meters, and 3,600 KW of power for three square meters,

As you can see from the above, the power is linearly dependent on the area, and it can be seen by the following equation,

y = 1200x

Here, y = power and x = area,

Therefore, the amount of power y the solar panel can produce is linearly proportional to the size of x, the equation is y = 1200x, and the graph is attached below.

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Answer: 5, 12, 13

Step-by-step explanation:

the first one

THE FORMULA

a^2 + b^2 = c^2

5^2 + 12^2 = 13^2

5^2 = 25

12^2 = 144

13^2 = 169

IS IT CORRECT???

yes

169-144=25!

The full price when the sales price is ;

£32.24 = £96.72

£86.08 is  £258.24

£105.48 is £316.44

£230.62 is £691.86

The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.

Full price = sales price x 3

Full price when the sales price is £32.24 would be;

= 3 x £32.24

= £96.72

Full price when the sales price is £86.08  would be;

= 3 x £86.08 = £258.24

Full price when the sales price is £105.48 would be;

= 3 x £105.48 = £316.44

Full price when the sales price is £230.62  would be;

= 3 x £230.62 = £691.86

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Answer: The distributive property

Step-by-step explanation: The distributive property ALWAYS has 1 number that is outside the parentheses. I know you didn't ask for this, but you can use the distributive property to write an equivalent expression by multiplying (or distributing) the 13 by every # inside the parentheses, so your new equation would look like 260 x 65. I hoped this explanation and example help you understand now.

Answer:

yes ofc its a proportional ratio

Step-by-step explanation:

basic math

Answer:

17

Step-by-step explanation:

13 + 4 = 17

Answer:

31

Step-by-step explanation:

Answer: z=34 degrees

Step-by-step explanation:

the total angle of a triangle always adds up to 180

180=44+2z+2z

combine like terms

4z+44=180

4z+44-44=180-44

4z=136

z=34

Answer:

thnx needed the answer!!

Answer =》Absolute value of any number is positive. Here, The absolute value of (-40) is 40.Apr 29, 2019

Step-by-step explanation: if I not right I am sorry god bless you

The length of the mirror is [tex]3\frac{2}{33}[/tex] feet so it can fit into a wall of 4 feet.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, The area of a rectangular mirror is [tex]10\frac{5}{6}[/tex] square feet.

The width of the mirror is [tex]2\frac{3}{4}[/tex] feet and assuming the length to be x feet.

∴ (11/4)×x = 65/6.

x = (65/6)×(4/11).

x = 260/66.

x = 130/33.

x = [tex]3\frac{2}{33}[/tex] feet so the mirror can fit in the wall as it is less than 4 feet.

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4x is 25 percent of 16x.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Let the percentage be P.

Now,

P% of 16x = 4x

P/100 x 16x = 4x

P/100 = 4x/16x

P/100 = 1/4

P = 100/4

P = 25

This means,

25% of 16x is 4x.

We can cross-check.

= 25% of 16x

= 1/4 x 16x

= 4x

Thus,

25 percent of 16x is 4x.

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The value of n in the given equation is 1.

Define Algebraic Expression

In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Given equation,

-1/2 (2n + 4) + 6 = -9 + 4(2n + 1)

Now, solve for n

first, solve the brackets

-1/2 * 2n + (-1/2) * 4 + 6 = -9 + 4*2n + 4 * 1

-n - 2 + 6 = -9 + 8n + 4

Solve the constants on both the sides,

-n + 4 = 8n - 5

Now, take out n value one side and constant terms other side

-n - 8n = -5 - 4

-9n = -9

Cancel out -9 from both the sides,

n = 1

Hence, the value of n in the given equation is 1.

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Answer:

35 and 1/4

Step-by-step explanation:

6x47/8

6/1x47/8

282/8

35 1/4 or 35.25