9 inches of rain in 72 hours as a unit rate

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

Note : Figure given is for reference to understand better.

Where redline is for given line and blueline for new line

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

[tex]8x-4y=5[/tex]

[tex]8(0)-4y=5[/tex]

[tex]y=\frac{-5}{4}[/tex]

When y=0, x=?

[tex]8x-4y=5[/tex]

[tex]8x-4(0)=5[/tex]

[tex]x=\frac{5}{8}[/tex]

We get points [tex]A(0,\frac{-5}{4}), B(\frac{5}{8},0)[/tex]

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B  will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point [tex]A(0,\frac{-5}{4})[/tex] from origin is [tex]( \frac{-5}{4})[/tex]  unit in x-direction and zero [tex]\frac{-5}{4})[/tex]  unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is [tex]A'(0,-10)[/tex]

For point B:

Distance of point [tex]B(\frac{5}{8},0)[/tex] from origin is [tex](\frac{5}{8})[/tex] unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is [tex]B'(5,0)[/tex]

Step 3: Find Equation of new line.

Points [tex]A'(0,-10)[/tex] and [tex]B'(5,0)[/tex] make a new line

The equation of given as

[tex]\frac{y-Y1}{x-X1} = \frac{Y2-Y1}{X2-X1}[/tex]

[tex]\frac{y-(-10)}{x-0} = \frac{0-(-10)}{5-0}[/tex]

[tex]\frac{y+(10)}{x} = 2[/tex]

[tex]\frac{y+(10)}{x} = 2[/tex]

[tex]y+10= 2x[/tex]

[tex]y= 2x-10[/tex]

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

Answer:

55 m  she is far from the beginning of the track

Explanation:

The linear track begins at  0 m

Since She is at the 10 m mark while practicing for the race so the initial point becomes 10 m further from the 0 m point

After running she is at 45 m from the 10 m meter  

Therefore, from the beginning of the track which is 10 m beyond from the initial point

Distance = (45m + 10m ) = 55 m

She is  55 m away from the beginning of the track.

Answer: I think that the answer is 55 meters.

Answer:

The other 2 angles are 67 and 67 degrees OR 46 and 88 degrees.

Step-by-step explanation:

If the vertex angle is 46 degrees then , as the other 2 angles are congruent, they are  (180 - 46) / 2 =   67 degrees.

The triangle has angles (46, 67 and 67).

If the  2 equal angles are both 46 then the other angles is 180 - 2(46) = 88 degrees.

The other  triangle has angles (46, 46 and 88).

Answer:

[tex]\frac{31548}{7} x[/tex]

Step-by-step explanation:

Answer:

31548/7 x

Step-by-step explanation:

Answer:

(-36/6)+(-6)

Step-by-step explanation:

Answer:

[tex] \frac{ - 36}{6} + ( - 6)[/tex]

-12

Step-by-step explanation:

-36/6 = - 6

-6 + (-6) = -12

Chloe made 4 three-point shots and 5 two-point shots.

Let's solve this problem using a system of equations.

Let x be the number of three-point shots Chloe made and y be the number of two-point shots she made.

We have the following equations:

x + y = 9 (equation 1)

3x + 2y = 22 (equation 2)

From equation 1, we can solve it for x:

x = 9 - y

Substitute this value of x into equation 2:

3(9 - y) + 2y = 22

27 - 3y + 2y = 22

-y = -5

y = 5

Substitute this value of y back into equation 1:

x + 5 = 9

x = 4

Therefore, Chloe made 4 three-point shots and 5 two-point shots.

Answer:

- v

Step-by-step explanation:

Given

(- 2 - 5v) - (- 4v - 2) ← distribute parenthesis, noting second is multiplied by - 1

= - 2 - 5v + 4v + 2 ← collect like terms

= (- 5v + 4v) + (- 2 + 2)

= - v + 0

= - v

(- 2 - 5v) - (- 4v - 2) =

= - 2 - 5v + 4v + 2

= - 5v + 4v - 2 + 2

= - v + 0

= - v

Using the normal distribution, it is found that:

a) 64.8% of years will have an annual rainfall of less than 44 inches.

b) 68.4% of years will have an annual rainfall of more than 39 inches.

c) 31.1% of years will have an annual rainfall of between 37 inches and 42 inches.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The proportion is the p-value of Z when X = 44, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{44 - 41.8}{5.8}[/tex]

[tex]Z = 0.38[/tex]

[tex]Z = 0.38[/tex] has a p-value of 0.648.

0.648 x 100% = 64.8%

64.8% of years will have an annual rainfall of less than 44 inches.

Item b:

The proportion is 1 subtracted by the p-value of Z when X = 39, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{39 - 41.8}{5.8}[/tex]

[tex]Z = -0.48[/tex]

[tex]Z = -0.48[/tex] has a p-value of 0.316.

1 - 0.316 = 0.684

0.684 x 100% = 68.4%

68.4% of years will have an annual rainfall of more than 39 inches.

Item c:

The proportion is the p-value of Z when X = 42 subtracted by the p-value of Z when X = 37, hence:

X = 42:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{42 - 41.8}{5.8}[/tex]

[tex]Z = 0.035[/tex]

[tex]Z = 0.035[/tex] has a p-value of 0.514.

X = 37:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{37 - 41.8}{5.8}[/tex]

[tex]Z = -0.83[/tex]

[tex]Z = -0.83[/tex] has a p-value of 0.203.

0.514 - 0.203 = 0.311

0.311 x 100% = 31.1%

31.1% of years will have an annual rainfall of between 37 inches and 42 inches.

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To calculate the percentage of years with an annual rainfall between 37 inches and 42 inches, we need to use the standard normal distribution. First, we can convert the rainfall values to z-scores, and then use a z-table or calculator to find the area under the curve between the corresponding z-scores.

To calculate the percentage of years with an annual rainfall between 37 inches and 42 inches, we need to use the standard normal distribution. First, we can convert the rainfall values to z-scores using the formula:

z = (x-mu)/sigma.

So, for 37 inches, the z-score is (37-41.8)/5.8 = -0.8276, and for 42 inches, the z-score is (42-41.8)/5.8 = 0.0345.

Now, we can use a z-table or calculator to find the area under the curve between these two z-scores. The percentage of years with an annual rainfall between 37 inches and 42 inches is the difference between these two areas.

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Answer:

Yes

Step-by-step explanation:

3 and 9 are both divisible by 3. Divide 3 and 9 by 3. You would get the fraction 1/3. You cannot simplify this fraction anymore.

~Stay golden~  :)

this is the answer of question 4x-9/ 12

Answer:

4+1.25x(number of rides)=total cost

Answer:

Given: entrance is a flat fee of $4, and each ride costs $1.25

Treat the rides as x

$4 + x*$1.25 = the total cost of going to the carnival

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The unit rate, expressed in price per pound is $0.80​.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

The slope of the line running through coordinates (0,0) and coordinates (30,24) is,

m= (24-0)/(30-0) = 0.8

Hence, the unit rate, expressed in price per pound is $0.80​.

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Step-by-step explanation:

[tex]4 < x - 7[/tex]

It's a straight line so plug in two numbers and connect the points.

And the result is everything under the line. Expect the line because its only < instead of <=

To check your answer use Mathaway or something Desmos

Answer:

1. -16

2. 1 (12 x 0 = 0 but its not the right)

3. 43

4.80

5. 5 4 (5 x 5 x 5 x 5 = 625)

Answer:-16 and 1

Step-by-step explanation:

To make a minimum profit of $100 with each snack priced at $4.00, a total of 47 snacks need to be sold at the concession stand. This includes 22 snacks to cover the total cost of $86.56 and an additional 25 snacks to achieve the profit goal.

The question is about finding out how many snacks need to be sold at a concession stand to achieve a minimum profit. To get the answer, we first need to determine how many snacks would make up the total cost, and then calculate how many additional snacks would be necessary to attain the profit goal.

Given that each snack at the concession stand costs $4.00 and that the total cost of the snacks is $86.56, we can find out how many snacks were initially purchased by dividing the total cost by the price of each snack: $86.56 ÷ $4.00 = 21.64 snacks. Since we can't sell a fraction of snack, we round up to 22 snacks to cover the total cost.

To calculate the number of additional snacks needed to attain a $100 profit, we divide the profit goal by the price of each snack: $100 ÷ $4 = 25 snacks.

Therefore, to cover the total cost and also make a minimum profit of $100, the concession stand needs to sell 22 snacks for the cost and additional 25 snacks for the profit, totaling 47 snacks altogether.

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Answer:

Average mark of the semester

EXPLANATION

This is done by adding the total score divided by the number of scores of the semester in that way Matthews average test score would be gotten

The cafeteria can make 14 full stacks of milk cartons with 18 cartons in each stack.

To determine how many full stacks of milk cartons the cafeteria can make, we need to divide the total number of cartons by the number of cartons per stack. The total number of cartons is 269, and each stack is to contain 18 cartons.

We perform the division as follows:

[tex]\[ \text{Number of full stacks} = \frac{\text{Total number of cartons}}{\text{Number of cartons per stack}} \] \[ \text{Number of full stacks} = \frac{269}{18} \][/tex]

When we divide 269 by 18, we get 14 with a remainder. The quotient, 14, represents the number of full stacks, and the remainder indicates that there will be some cartons left over that will not form a full stack.

Since we are only interested in the number of full stacks, we disregard the remainder. Therefore, the cafeteria can make 14 full stacks of 18 cartons each. The remaining cartons will either form a partial stack or be set aside, depending on the cafeteria's policy for stacking.

Answer:

The cups of other type of juice is 615

Step-by-step explanation:

Given as :

The total cups of punch made by Jessica = 619

The two different types of juice is x and y

Let The one type of juice = x = 4

And According to question

x + y = 619

So, 4 + y = 619

Or, y = 619 - 4

∴ y = 615

Hence The cups of other type of juice is 615 . Answer

Answer:

2(5a+2)

Step-by-step explanation:

10a+4=2(5a+2)

Answer:

960 cubic cm.

Step-by-step explanation:

We have to find the volume of a solid figure as detailed in the attached photo.

The topmost part of the solid is a pyramid with a square base.

The square base has a dimensions 6 cm by 6 cm and the height of the pyramid is 4 cm, then the volume is  

[tex]\frac{1}{3} \times (\textrm {Area of base} \times {\textrm {Height}}) = \frac{1}{3} \times 4 \times 6^{2} = 48[/tex] cubic cm.

Now, the volume of the bottom cuboid of the pyramid is  

= Height × Length × Width

= 12 × 6 × 6

= 432 cubic cm.

And finally, the volume of the other cuboid = 10 × 8 × 6 = 480 cubic cm.

Hence, the total volume of the solid is (48 + 432 + 480) = 960 cubic cm. (Answer)

Answer:

7 + n

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Since 30%/3 is 10%, 6 is 10% of the total number of garden beds, since 18/3 is 6.

And 10% times 10 is 100%, or all of it, so 60 is the total amount of garden beds, since 6 times 10 is 60.

60 garden beds in the students plans.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Present flower bed= 18

This is 30% of the total number of garden beds.

let the total flower bed be x.

So, 30% of x= 18

30/100 x = 18

x= 1800/ 30

x= 60

Hence, 60 garden beds in the students plans.

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Rs 100 of the average total cost is made up of variable costs.

Step-by-step explanation:

Given:

Number of output the firm produces= 7 units

Average cost of the output= Rs. 150

fixed factors of production = Rs.350

To Find:

How much of the average total cost is made up of variable costs=?

Solution:

we know that,

Average total cost= total cost/ number of output units produced

substituting the values, we get

[tex]150=\frac{\text{Total cost}}{7}[/tex]

Total cost= 1050

we know that Total fixed cost = 350

Total cost = Total fixed cost + Total variable cost

plug in the known values.

1050= 350 + Total variable cost

Total variable cost = 1050-350

Total variable cost =700

For 7th unit [tex]\frac{700}{7}[/tex] = 100

Answer:

$969.3

Step-by-step explanation:

The DVDs are sold in packages of 50

Divide the total number you need by 50, therefore 2700/50 = 54 packages are needed

The packages are sold at $17.95 for one, hence amount needed is 54 * 17.95 = $969.3

Answer:

13

Step-by-step explanation:

26 * 50/100 = 26 * 1/2 = 13

Answer:

13

Step-by-step explanation:

50% = 50/100 = 1/2

That means that 1/2 of the children have blue eyes.

26*(1/2) or 26/2 = 13

She planted [tex]\frac{3}{4}[/tex] arcs of each type

Step-by-step explanation:

The given is:

We need to find how many acres of each type she planted

∵ The farmer planted [tex]4\frac{1}{2}[/tex] arcs of land

∵ She planted 6 types of wheat

∵ She planted an equal amount of each type of wheat

- Divide the total number of arcs by 6 to find the number of arcs

  for each type

To divide the total number of arcs change it from the mixed number

[tex]4\frac{1}{2}[/tex] to improper fraction

∵ [tex]4\frac{1}{2}=\frac{(4*2)+1}{2}=\frac{9}{2}[/tex]

∴ The total number of arcs = [tex]\frac{9}{2}[/tex]

∴ The number of arcs of each type = [tex]\frac{9}{2}[/tex] ÷ 6

- Change the division sign to multiplication sign and reciprocal

   the number after the division sign

∴ The number of arcs of each type = [tex]\frac{9}{2}[/tex] × [tex]\frac{1}{6}[/tex]

∴ The number of arcs of each type = [tex]\frac{9*1}{2*6}[/tex]

∴ The number of arcs of each type = [tex]\frac{9}{12}[/tex]

- Reduce the fraction by dividing up and down by 3

∴ The number of arcs of each type = [tex]\frac{3}{4}[/tex]

She planted [tex]\frac{3}{4}[/tex] arcs of each type

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Answer:

0.46 repeating 6

Step-by-step explanation:

plug it into a calculator

Answer:

26

Step-by-step explanation:

15 3/5=78/5

(78/5)/(3/5)=(78/5)(5/3)=78/3=26

There are 26 three-fifths in fifteen and three-fifths.

To find out how many times [tex]\frac{3}{5}[/tex] is in [tex]15 \frac{3}{5}[/tex], we follow these steps:

Convert the mixed number [tex]15 \frac{3}{5}[/tex] into an improper fraction.

[tex]15 \frac{3}{5} = 15 + \frac{3}{5} = \frac{15 \times 5}{5} + \frac{3}{5} = \frac{75}{5} + \frac{3}{5} = \frac{75 + 3}{5} = \frac{78}{5}[/tex]

Divide [tex]\frac{78}{5}[/tex] by [tex]\frac{3}{5}[/tex].

To divide fractions, we multiply by the reciprocal:

[tex]\frac{78}{5} \div \frac{3}{5} = \frac{78}{5} \times \frac{5}{3} = \frac{78 \times 5}{5 \times 3} = \frac{390}{15}[/tex]

Simplify [tex]\frac{390}{15}[/tex].

Divide the numerator and the denominator by their greatest common divisor (GCD), which is 15:

[tex]\frac{390 \div 15}{15 \div 15} = \frac{26}{1} = 26[/tex]

The original height of the water level in pool is 5 feet

Given that , A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.  

After the leak is fixed, the height of the water is 4.75 feet.  

The equation 4.75 = x + (- 0.25) can be used to find x, the original height of the water in a pool.

So by solving the given equation and finding value of "x" gives the original height of water in pool

We have to find the original height of the water level in the tank.

So, let us solve the given equation

[tex]\begin{array}{l}{\rightarrow 4.75=x+(-0.25)} \\\\ {\rightarrow 4.75=x-0.25} \\\\ {\rightarrow x=4.75+0.25} \\\\ {\rightarrow x=5}\end{array}[/tex]

Hence, the original height of the water level is 5 feet

Answer5 feet

Step-by-step explanation: