On a map, the length of a river is 4.75 in. The actual length of the river is 247 miles. What is the scale of the map?

Answer:

Drain A [tex]54\ min[/tex]

Drain B [tex]21.6\ min[/tex]

Step-by-step explanation:

Let

x------> the time in minutes

y-----> the volume of the pool in gallons

we know that

The equation that represent the situation is equal to

[tex]y=mx[/tex]

solve for x

[tex]x=y/m[/tex]

Drain A

[tex]x=y/m[/tex]

In this case we have

[tex]m=2\frac{gal}{min}[/tex]

[tex]y=108\ gal[/tex]

substitute

[tex]x=108/2=54\ min[/tex]

Drain B

[tex]x=y/m[/tex]

In this case we have

[tex]m=5\frac{gal}{min}[/tex]

[tex]y=108\ gal[/tex]

substitute

[tex]x=108/5=21.6\ min[/tex]

To find the value of x in the equation x + 4/5 = 11, you subtract 4/5 from both sides and then simplify the resulting fraction, giving you x = 10.2.

To solve the equation x +  {4}/{5} = 11, we need to isolate the variable x. First, subtract  rac{4}{5} from both sides of the equation:

x +  {4}/{5} -  {4}/{5} = 11 -  {4}/{5}

This simplifies to:

x = 11 -  {4}/{5}

To subtract the fraction from 11, which is a whole number, we can write 11 as a fraction with the same denominator:

x =  {55}/{5} -  {4}/{5}

Now, subtract the numerators:

x =  {55 - 4}/{5}

x =  {51}/{5}

Finally, divide 51 by 5:

x = 10.2

Answer:

Each shrub is $9.

Step-by-step explanation:

You are looking for the price of the shrub plants. Since you know that the plants' price with the soil's price totals the purchase at $53.50, your equation should look like this:

[tex]4p + 17.50 = 53.50[/tex]

After that, use the order of operations to solve the price of the shrubs.

[tex]4p + 17.50 = 53.50 \\4p + 17.50-17.50 = 53.50-17.50\\4p = 36\\4p/4 = 36/4\\p=9[/tex]

The group of girls can purchase 16 sodas with $20. Because each soda costs $1.25, we find this by dividing the total amount of money ($20) by the cost of each soda ($1.25)

The question is asking how many sodas a group of girls can buy with $20 if each soda costs $1.25. To find this out, you need to divide the total amount of money they have ($20) by the cost of each soda ($1.25). Therefore, $20 divided by $1.25 equals 16, so the girls can buy 16 sodas with $20. Here is a chart to illustrate this:

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Answer:

20 books NOW WHERE IS MY BRAINLY CROWN

Step-by-step explanation:

The cost of one greeting card Marianne bought is $9.45/x.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Marianne spends $9.45 on greeting cards, and let she bought 'x' numbers of cards.

Therefore, As the cost of each greeting card is the same, The cost of one card can be obtained by dividing the total cost by the total number of cards which is,

= $(9.45/x).

So, The cost of one greeting card is $(9.45/x).

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To represent the ratio 1 to 3 using a model, you can draw one square divided into three equal parts. To find an equivalent ratio, you can multiply both parts of the ratio by the same number.

To draw a model to represent the ratio 1 to 3, you can use squares or rectangles. For example, you can draw one square and divide it into three equal parts. Then, label the first part as 1 and the other two parts as 2 and 3. This represents the ratio 1 to 3.

To find an equivalent ratio, you can multiply both parts of the ratio by the same number. For example, if you multiply both parts by 2, the new ratio would be 2 to 6, which is equivalent to the original ratio.

Answer:

y=-2x+3

Step-by-step explanation:

Given the slope intercept form of the general equation of a line below:

y=mx+c,

m is the gradient/slope

c is the intercept on the y-axis.

From the given information:

m=-2 and c=3

Therefore substituting into y=mx+c

The equation is y=-2x+3

To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. If we want to write [tex]\frac{1}{8}[/tex] as a percent, we need to find a fraction equivalent to [tex]\frac{1}{8}[/tex] that has a 100 in the denominator. We can do this by setting up a proportion.

[tex]\frac{1}{8}[/tex] = [tex]\frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

8n = 100

÷8     ÷8   ← divide by 8 on both sides

n = 12.5

Therefore, [tex]\frac{1}{8}[/tex] is equal to [tex]\frac{12.5}{100}[/tex] or 12.5%.

The value of 246 divided by 3 is 82 .

Given,

246/3

Here,

Divisibility rule of 3: A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

Here,

Sum of digits of number = 2+ 4 + 6 = 12

Thus 12 is divisible by 3 , so 246 will be divisible by 3.

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Answer:

20

Step-by-step explanation:

We have been given that Ken watches a marching band he sees 2 rows of flute players. Six people are in a row.

First of all, we will find number of flute players by multiplying 6 by 2 as:

[tex]\text{Number of flute players}=2\times 6[/tex]

[tex]\text{Number of flute players}=12[/tex]

Since Ken sees 8 trombone players, so total number of people would be 12 plus 8.

[tex]\text{Number of flute players and trombone players}=12+8[/tex]

[tex]\text{Number of flute players and trombone players}=20[/tex]

Therefore, Ken sees 20 flute players and trombone players.

The first error that Carlos made was B) Step 2 should have been 14(40) + 14(9).

We can analyze Carlos's work and the suggested steps to determine the first error:

Analysis of Errors:

Step 1:

49 was split into 40+9, which is correct.

Step 2:

This step should distribute 14 to both 40 and 9 and not only to 40.

Correct version:

14×40+14×9.

Step 3:

Carlos only computed 14×40 and ignored multiplying 14×9.

The correct version calculates both parts as

14×40 = 560 and 14×9 = 126.

Step 4:

The addition of 560+9 is wrong since it doesn't account for the correct 126 from 14×9.

Correct version should add 560+126 to get 686.

Thus, the first error Carlos made was in Step 2, where he incorrectly distributed 14 only to 40 and not to 9, failing to apply the distributive property.

Complete Question:

Carlos is using the distributive property to evaluate the expression 14 (49) by using friendlier numbers. His work is shown below. Carlos’s Work 14 (49)

Step 1: 14 (40 + 9)

Step 2: 14 (40) + 9

Step 3: 560 + 9

Step 4: 569

What was the first error that Carlos made?

A) Step 1 should have been 14(7 + 7).

B) Step 2 should have been 14(40) + 14(9).

C) Step 3 should have been 23(40).

D) Step 4 should have been 5,040.

The equivalent expression is a+ 2b.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

2(a+2b)-a-2b

Now, solving the expression we get

= 2(a + 2b) - a - 2b

= 2a + 4b - a -2b

= 2a - a + 4b - 2b

= a + 2b

Hence, the equivalent expression is a+ 2b.

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