60 cups of popcorn feed 15 students. How many cups of popcorn are needed to feed 70 students ?

A 280 cups
B 900 cups
C 1,050 cups
D 4,200 cups

It takes 10.155 years until you have $3,000 ⇒ 3rd

Step-by-step explanation:

The formula for compound interest, including principal sum is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where

∵ You decide to put $2,000 in a savings account

∴ P = 2000

∵ You want to save for $3,000

∴ A = 3000

∵ The account has an interest rate of 4% per year and is

   compounded monthly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 12 ⇒ compounded monthly

- Substitute all of these values in the formula above to find t

∵ [tex]3000=2000(1+\frac{0.04}{12})^{12t}[/tex]

- Divide both sides by 2000

∴ [tex]1.5=(1+\frac{1}{300})^{12t}[/tex]

∴ [tex]1.5=(1\frac{1}{300})^{12t}[/tex]

- Change the mixed number to an improper fraction

∴ [tex](1.5)=(\frac{301}{300})^{12t}[/tex]

- Insert ㏒ for both sides

∴ [tex]log(1.5)=log(\frac{301}{300})^{12t}[/tex]

- Remember [tex]log(a)^{n}=nlog(a)[/tex]

∴ [tex]log(1.5)=(12t)log(\frac{301}{300})[/tex]

- Divide both sides by [tex]log(\frac{301}{300})[/tex]

∴ 121.84 = 12 t

- Divide both sides by 12

∴ 10.155 = t

It takes 10.155 years until you have $3,000

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Answer:[tex]\frac{15}{28}[/tex]

Step-by-step explanation:

Number of strawberry = 2

Number of cherry = 3

Number of  = 3

Total number = 8

Brent randomly takes 2 yogurt containers from the bag

without replacement ,we are to find the probability that hat neither will be strawberry yogurt.

Let r represent  raspberry and c represents  Cherry ,then Bent selection could be :

{ rr , cc , rc , cr}

Calculating this , we have

([tex]\frac{3}{8}[/tex] x  [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x  [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x  [tex]\frac{3}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x  [tex]\frac{3}{7}[/tex] )

= [tex]\frac{30}{56}[/tex]

= 15/28

Therefore , the probability that neither will be strawberry yogurt= 15/28

The answer: d. < 1 and < 8

Answer:

The area at time t is given  by [tex]A(t) =\pi (4t^2+2t+0.25).[/tex]

Step-by-step explanation:

We know the radius [tex]r(t)[/tex] of the oil spill as a function of time, and we know the area [tex]A(r)[/tex] as a function of radius, and we want the area at time t. In other words we are looking for area as a function of time [tex]A(t)[/tex]

We find [tex]A(t)[/tex] by putting [tex]r(t)[/tex]  into [tex]A(r)[/tex] as a substitute to r:

[tex]A(t) = A(r(t))= \pi r(t)^2 =\pi (0.5 + 2t)^2={\pi (4t^2+2t+0.25).}[/tex]

[tex]\boxed{A(t) =\pi (4t^2+2t+0.25).}[/tex]

Which is our answer.

To find the composite function for the area of the oil spill over time, replace 'r' in A(r) = πr2 with the function r(t). The function becomes A(t) = π(0.5 + 2t)2.

In order to find the function that represents the area of the oil spill over time, we need to write a composite function. This means we plug the function r(t) into A(r). Since r(t) = 0.5 + 2t, you can replace every instance of 'r' in A(r) = πr2 with (0.5 + 2t) to get the area as a function of time 't'. So, the composite function becomes A(t) = π(0.5 + 2t)2. Now we have a composite function that represents the area of the oil spill, denoted by A(t), as a function of time. The function is: A(t) = π(0.5 + 2t)2.

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Answer:

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

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take two points from the data

(0,8), and (8,-24).

substitute

[tex]m=\frac{-24-8}{8-0}[/tex]

[tex]m=\frac{-32}{8}[/tex]

[tex]m=-4[/tex]

step 2

Find the equation of he line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-4[/tex]

[tex]b=8[/tex] ----> the y-intercept is given

substitute

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

Answer:

238°

Step-by-step explanation:

In a cyclic quadrilateral, the pair of opposite angles add up to 180 degrees.

So, the angle "21x - 2" and the angle "38x + 5"  add up to 180.

So, we can write an equation and solve for x first:

[tex]21x-2+38x+5=180\\59x+3=180\\59x=180-3\\59x=177\\x=3[/tex]

x = 3

Now, Arc FGH is DOUBLE of Angle A. Angle A is "38x + 5". We know x, so angle A is:

Angle A = 38x + 5 = 38(3) + 5 = 119

Thus, Arc FGH = 2 * 119 = 238°

Step-by-step explanation:

[tex]\text{The distributive property:}\\\\a(b-c)=ab-ac\\\\8(y-7)=(8)(y)-(8)(7)=8y-56\\\\\text{If you want whole solution:}\\\\8(y-7)=-16\\8y-56=-16\qquad\text{add 56 to both sides}\\8y-56+56=-16+56\\8y=40\qquad\text{divide both sides by 8}\\\dfrac{8y}{8}=\dfrac{40}{8}\\\boxed{y=5}[/tex]

Answer:

y=5

Step-by-step explanation:

8(y-7)= -16

(8)y-(8)7= -16

8y-56= -16

-16+56= 40

40/8= 5

y=5

(when you get y by itself)

hoped this helped a little bit.

Answer:

The required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

Step-by-step explanation:

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

The given situation can be written as: y = m x +  C  ......[A]

Now, Profit for 40 hot dogs = $90 profit

So, here this can be written as:

90 = 40 m + C ......[1]

Profit for 80 hot dogs = $210 profit

So, here this can be written as:

210 = 80 m + C ......[2]

Now, solving both the equations, we get:

Subtracting  [1] and [2], we get

210  - 90  = 80 m + C  - (40 m + C)

or, 120 = 40 m

or, m = 120/40 = 3

or, m = 3

Solving for the value of C , we get: C = - 30

Putting the value of m back in the equation : y   = m x + C

y = 3 x -30

Hence, the required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

Final answer:

The perimeter of the square playground can be found by adding the lengths of all four sides. Two equivalent expressions for the perimeter are 8n + 8 and 4(2n + 2).

Explanation:

To find the perimeter of the playground, we need to add up the lengths of all four sides. Since the playground is a square, all four sides are equal in length.

The length of each side of the playground can be found by subtracting twice the width of the sidewalk from the overall length of the sidewalk. This is because the sidewalk wraps around the playground on all sides.

So, the length of each side of the playground is (2n+3) - 2(0.5) = 2n + 2.

The perimeter of the playground is then 4 times the length of each side, which is 4(2n + 2) = 8n + 8 yards.

Two equivalent expressions for the perimeter of the playground are 8n + 8 and 4(2n + 2).

The number of unripe apples in a sack, given that there are N total apples and 3 are ripe, is calculated by subtracting 3 from N (N - 3).

The question posed is asking for a basic subtraction calculation within the context of ripe and unripe apples.

Given that there are N apples in total and 3 of them are ripe, we need to find out how many are not ripe.

The number of not ripe apples is N - 3, where N is the total number of apples in the sack.

To solve this, we subtract the number of ripe apples from the total number of apples:

For example, if a sack has 10 apples and 3 are ripe, then there would be 10 - 3 = 7 unripe apples.

Answer:

20. 3

Step-by-step explanation:

23.6 - 2 × 3 ÷ 2 = 23.6 - 3

                         = 20.3

Answer:

Step-by-step explanation:

Set this up as a proportion with granola on the top and chocolate chips on the bottom:

[tex]\frac{g}{cc}:\frac{1.75}{\frac{1}{3} }=\frac{x}{1}[/tex] and cross multiply to solve for x:

1/3x = 1.75 Multiply both sides by 3 to get

x = 5.25

This means for every 1 cup of chocolate chips, he needs 5 1/4 cups of granola.

Step-by-step explanation:

making x subject in eq 1

x= (-1-9y)/-14

substituting the value of x in eq 2

17(-1-9y/-14)=7+9y

(-17-153y)/-14=7+9y

-17-153y=-98-126y

-17+98=153y-126y

81=27y

y=3

substituting this value of y in eq 1

-14x=-1-9(3)

-14x=-28

x=2

(x,y) = (2,3)

Answer:

56652.3 ft^3

Step-by-step explanation:

The formula for the volume of a right circular cone is V=13pi*r^2*h where r is the radius of the base.

So V=13pi*(15.6)^2*(5.7)=56652.3

Answer:

45,2316

Step-by-step explanation:

You have to move the numbers to their new respective places as told by the description of the new place

The given statement written in symbolic language is x = 3y + 4 and x + y = 72 where "x" is the cost of one book and "y" is the cost of another book

Solution:

Given that Bruce bought two books

One book costs $ 4.00 more than three times the other

Let the two books be denoted as Book A and book B

Let "x" be the cost of book A

Let "y" be the cost of Book B

From given,

One book costs $ 4.00 more than three times the other

Let Cost of book A = $ 4.00 more than three times the other book B

x = 4 + 3 times cost of Book B

x = 4 + 3y

x = 3y + 4 --- (i)

Also given that Together, the two books cost him $72

cost of book A + cost of Book B = 72

x + y = 72 ------- (ii)

Therefore the given statement written in symbolic language is:

x = 3y + 4 and x + y = 72

George shovels at a rate of 8.33 square yards per hour. In 5 1/2 hours, he will shovel approximately 45.815 square yards of his driveway.

The student asked about how many square yards of driveway George would shovel in 5 1/2 hours after shoveling 12 2/4 square yards in 1 1/2 hours. To find this, we first need to calculate the rate at which George is shoveling.

George shovels 12 2/4 square yards in 1 1/2 hours. Simplifying these fractions, we have 12.5 square yards in 1.5 hours. The rate is therefore 12.5 ÷ 1.5 yards per hour = 8.33 square yards per hour.

Next, we multiply this rate by the total time George will be shoveling to find how much he would shovel in 5 1/2 hours:

8.33 yards/hour × 5.5 hours = 45.815 square yards

So, George will shovel approximately 45.815 square yards of his driveway in 5 1/2 hours.

Final answer:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information and multiply the rate by the time.

Explanation:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information. In 1 1/2 hours, he shovels 12 2/4 square yards of snow. We can write this as a fraction: 12 2/4 / 1 1/2. To simplify this fraction, we can convert the mixed numbers to improper fractions: 50/4 / 3/2.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (50/4) × (2/3). Multiplying the numerators and denominators, we get (50 × 2) / (4 × 3) = 100/12.

So, in 1 1/2 hours, George shovels 100/12 square yards of snow. To find out how many square yards he would shovel in 5 1/2 hours, we can multiply this rate by 5 1/2: (100/12) × (5 1/2). Multiplying the numerators and denominators, we get (100 × 11) / (12 × 2) = 1100/24. Simplifying this fraction, we get 275/6.

Therefore, George would shovel approximately 275/6 square yards of driveway in 5 1/2 hours.

Answer:

18

Step-by-step explanation:

Finding the remainder of 28254 divided by 52.

1. Use calculator to divide 28254 by 52:

2. Take whole part of the quotient and multiply by divisor:

3. Subtract this number from the initial dividend:

This is the remainder: 18

Final answer:

The remainder when 28,254 is divided by 52 is 9. This is found by dividing the number step by step until no more digits can be brought down, leaving the remainder.

Explanation:

The student is asking for the remainder when 28,254 is divided by 52. To solve this, we perform the division process until we reach a point where we cannot divide any further without going into decimals. The number that is left over at this point is the remainder. Below is a step-by-step explanation of the process.

The remainder when 28,254 is divided by 52 is 9.

Answer:

26 years of age.

Step-by-step explanation:

The average annual income, I, in dollars, of a lawyer with an age of x years is modeled with with the following function:

I = - 425x² + 45500x - 650000 .......... (1)

If the average annual income of the lawyer at the age of x years is $250000, then from the equation (1) we can write

- 425x² + 45500x - 650000 = 250000

⇒ - 425x² + 45500x - 900000 = 0

⇒ - 17x² + 1820x - 36000 = 0

Now, using the quadratic formula,

[tex]x = \frac{- 1820 \pm \sqrt{(1820)^{2} - 4(-17)(- 36000) } }{2(- 17)} = \frac{-1820 + 929.73}{- 34} = 26[/tex] years (Approximate)

{We have neglected the other root as we need the youngest age}(Answer)

Answer: 27

Step-by-step explanation:

Other answer is wrong

Answer:

(-9, 3)

Step-by-step explanation:

To rotate a point 270°:

R₂₇₀ (x, y) = (y, -x)

So the answer would be (-9, 3).

Answer:

Probability of getting blue both times = [tex]\frac{16}{81}[/tex]

Step-by-step explanation:

A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green.  

It is spun twice.  

We have to find the probability of getting blue both times?.

For both times , the probability of getting blue is the same.

Probability = [tex]\frac{number of favorable cases}{total number of cases}[/tex]

The number of favorable cases for blue = 4

Total number of cases = 9

Hence the probability = [tex]\frac{4}{9}[/tex]

We have to get it two times so final probability = [tex]\frac{4}{9}\times \frac{4}{9} = \frac{16}{81}[/tex]

Answer:

x = 90.

Step-by-step explanation:

< 1 and < 4 are corresponding angles and are congruent if line  a is parallel to line b. So:

3x - 160 = x + 20

2x = 180

x = 90.

Firstly they are not numbers, they are ordered pairs or points with a form [tex](x,f(x))[/tex] yes they probably lie on a function graph but that would be rather impossible to find out. The function may be linear, exponential, logarithmic etc. we can't tell. All we can tell is that if these ordered pairs [tex]P_{1,2,3}[/tex] lie on a function graph [tex]P_{1,2,3}\in G_f[/tex] where [tex]G_f=\{(x,f(x)):\forall x\in D_f\wedge f(x)\in T_f\}[/tex] where D is definition set of function defined x's and T a transformation set of f(x)'s for this function. So yes they may lie on some lambda function but they themselves are nothing but an ordered pairs with no meaningful connection.

Hope this helps.

Answer:

no

Step-by-step explanation:

there are two coordinates with the same x value

Answer:

The Width of the garden will be 9 feet.

Step-by-step explanation:

Given:

Manny has wood =48 feet

Length of the garden = 15 feet

The equation which can be used  [tex](2l+2w) = 48[/tex].

We need to find the width of the garden.

Solution :

Now Length of the garden is given we will substitute in the given equation to find the width.

[tex]2l+2w=48\\\\2\times15+2w=48\\\\30+2w=48[/tex]

Now Using Subtraction property we will subtract both side by 30 we get;

[tex]30+2w-30=48-30\\\\2w =18[/tex]

Now Using Division Property we will divide both side by 2 we get;

[tex]\frac{2w}{2}=\frac{18}{2}\\\\w= 9\ ft[/tex]

Hence the Width of the garden will be 9 feet.

Answer:

its A 9 ft

Step-by-step explanation:

i know things...

Answer:

[tex]\frac{61}{90}[/tex]

Step-by-step explanation:

We require to create 2 equations with the repeated value 7 after the decimal point

Let x = 0.6777777... ← multiply both sides by 10 and 100

10x = 6.777...... → (1)

100x = 67.777..... → (2)

Subtract (1) from (2) thus eliminating the repeating value

90x = 61 ( divide both sides by 60 )

x = [tex]\frac{61}{90}[/tex]

The decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.

To rewrite the decimal 0.67 with the repeating 7 as a simplified fraction, we can use the concept of infinite geometric series.

Let x = 0.677777...

Multiply both sides of the equation by 10 to shift the decimal point:

10x = 6.777777...

Now, subtract the original equation from the shifted equation to eliminate the repeating 7s:

10x - x = 6.777777... - 0.677777...

Simplifying, we get:

9x = 6

Divide both sides of the equation by 9 to solve for x:

x = 6/9

The fraction 6/9 can be further simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

x = (6/3) / (9/3)

x = 2/3

Therefore, the decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.

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Question is Incomplete, Complete question is given below.

Julia exercises at the gym. For every 3 minutes she spends running, she spends 5 minutes lifting weights.

Which of the following could be how Julia spends time at the gym?

A  Run for 10 mins and lifting weights for 12 mins.

B  Run for 15 minutes and lift weights for 25 mins.

C  Run for 20 mins and lift weights for 30 mins.

D  Run for 24 mins and lift weights for 48 mins.

E  Run for 30 mins and lift weights for 50 mins.

Answer:

B  Run for 15 minutes and lift weights for 25 mins.

E  Run for 30 mins and lift weights for 50 mins.

Step-by-step explanation:

Given:

Julia Spend s 3 minute for running and weight lifts for 5 mins.

We need to find which choices are correct match for the given data.

Hence we will check each.

A  Run for 10 mins and lifting weights for 12 mins.

Since given that she runs for 3 mins and in the above choice the given date is she is running for 10 mins it is neither 3 nor multiple of 3.

Hence this is Choice is Incorrect.

B  Run for 15 minutes and lift weights for 25 mins.

Now Given in choice is that she runs for 15 minutes and in given data she runs for 3 minutes hence 15 is multiple of 3 and is multiplied by 5 also given lift weights for 25 mins and in given data she lift weights for 5 mins since 25 is multiple of 5 and is multiplied by 5.

Hence the above Choice is Correct.

C  Run for 20 mins and lift weights for 30 mins.

Since given that she runs for 3 mins and in the above choice the given date is she is running for 20 mins it is neither 3 nor multiple of 3.

Hence this is Choice is Incorrect.

D  Run for 24 mins and lift weights for 48 mins.

Now Given in choice is that she runs for 24 minutes and in given data she runs for 3 minutes hence 24 is multiple of 3 and is multiplied by 8 also given lift weights for 48 mins and in given data she lift weights for 5 mins and 48 is not the multiple of 5.

Hence this is Choice is Incorrect.

E  Run for 30 mins and lift weights for 50 mins.

Now Given in choice is that she runs for 30 minutes and in given data she runs for 3 minutes hence 30 is multiple of 3 and is multiplied by 10 also given lift weights for 50 mins and in given data she lift weights for 5 mins since 50 is multiple of 5 and is multiplied by 10.

Hence the above Choice is Correct.

Answer:

Graph is attached below.

The graph illustrates the music that Jada may have downloaded with the $15 (s)he spent. The x-axis represents the number songs and the y-axis represents the number of albums. The data shows what combination of music she may have downloaded. The number of songs and albums have a negative correlation because if more money is spent on one variable, there is less money available to spend on the other.

Step-by-step explanation:

How to create a graph:

Using the data from part 1, plot the points (6, 3) (22, 1) and (30, 0) onto the graph. Label the x and y axis as the question asks. The axis should have arrows at the end. Include a title for the graph.

Do not connect the points because this indicates that all the space between the points are possible. Connecting the points includes decimal numbers and you can't buy part of a song or album, only a whole song or album.

Answer:

Step-by-step explanation:

94 beats per minute during one workout.

If the rate was maintained for 25 minutes, the heart beats = 94×25

= 2350 beats