Steve and carol live 405 miles apart, they start at the same time and travel toward each other, Steve speed is 6mph greater than carols. If they meet in 2.5 hours, find their speed

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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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:

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

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:

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

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

Answer:

0.46 repeating 6

Step-by-step explanation:

plug it into a calculator

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)

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:

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:

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 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:

1500 students

600 boys

Step-by-step explanation:

40% are boys, so 60% are girls.

Writing a proportion:

900 / 60% = x / 100%

x = 1500

There are 1500 students in the school, which means there are 600 boys in the school.

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 amount he will be spending now is : 0.65q

Using the information given ;

The amount which would be reduced from his spending would be :

Now we have ;

q × 35%

= 0.35q

The amount he will be spending now is :

Now we have;

q - 0.35q = 0.65q

Hence, the amount he will be spending now is : 0.65q

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

Answer:

7 + n

Step-by-step explanation:

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

Answer:

see explanation

Step-by-step explanation:

Sum the parts of the ratio, 2 + 3 + 3 = 8

Divide the sum to be shared by 8 to find the value of one part of the ratio

£96 ÷ 8 = £12 ← value of 1 part of the ratio, thus

David gets 2 × £12 = £24

Stephen gets 3 × £12 = £36

June also gets £36

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

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:

2(5a+2)

Step-by-step explanation:

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

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:

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

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:

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~  :)

-38(-3) = 114

-72/(-12) = 6

-9 x 23 = -207

-150/5 = -30

564 / -4 = -141

Given that, we have to find each product or quotient

-38(-3)

It is a product, so we have to find product value

[tex]-38(-3)=38 \times 3=114[/tex]

-72 / (-12)

It is division, so we have to find the quotient

[tex]\frac{-72}{-12}=\frac{72}{12}=6[/tex]

-9 x 23

It is a product, so we have to find product value

[tex]-9 \times 23=-207[/tex]

- 150 / 5

It is division, so we have to find quotient

[tex]\frac{-150}{5}=-30[/tex]

564 / -4

It is division, so we have to find the quotient

[tex]\frac{564}{-4}=-141[/tex]

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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