3 serving of a fruit punch recipe serves 36 people. How many people can be
served by 8 servings of a fruit punch recipe?

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Explanation:

Along the top row, label the two triangles A and B.

In the bottom row, label the figures as C, D, E. We have C and E as the two surrounding triangles and D as the rectangle.

To find the area of triangle A, we need to find the horizontal side first. Use the pythagorean theorem to get 3 inches across the horizontal portion. We have a 3-4-5 right triangle. The area of triangle A is base*height/2 = 3*4/2 = 6 square inches. Triangle B is a reflected copy of triangle A, so it has the same area.

Triangle C has an area of base*height/2 = 1*5/2 = 2.5 square inches, so does triangle E because it is a mirrored congruent copy.

The rectangle D has an area of base*height = 4*5 = 20 square inches.

-----------------------

We have these areas:

To wrap things up, add up those areas

A+B+C+D+E = 6+6+2.5+20+2.5 = 37 square inches

Answer:

  y = 7 +ln(x)/4

Step-by-step explanation:

Maybe your parameterized equation is ...

  (x, y) = (e^(4t), t +7)

Using t = y-7, we can substitute for t in the expression for x:

  x = e^(4(y -7))

  ln(x) = 4(y -7)

  ln(x) +28 = 4y

  y = 7 +ln(x)/4

Step-by-step explanation:

4/100*100000+5/100*100000+5.1/100*100000=14100

Answer:

3,570

Step-by-step explanation:

To find the answer, you have to multiply 1,000 and 3.57

3.57 x 1,000 = 3,570

The remaining amount of salt that Tom needed to pour was 67.59 grams.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

As per the given,

The total amount that Tom needs to pour = 84.99 grams

Amount poured = 17.4 grams

Remaining = 84.99 grams - 17.4 grams = 7.59 grams

Hence "The remaining amount of salt that Tom needed to pour was 67.59 grams".

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Answer:

Step-by-step explanation:

208

Answer:

26

Step-by-step explanation:

One leg measures 7.

One leg measures 8.

a² + b² = c²

7² + 8² = c²

c² = √113 = 10.630 = 11

perimeter = 7 + 8 + 11

perimeter = 26

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Using the normal distribution, it is found that the the travel time such that 26.11% of the 60 days have a travel time that is at least is of 42.19 minutes.

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

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

The travel time such that 26.11% of the 60 days have a travel time that is at least X when Z has a p-value of 1 - 0.2611 = 0.7389, hence X when Z = 0.64, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(0.64 = \frac{X - 35.6}{10.3}\)

\(X - 35.6 = 0.64(10.3)\)

\(X = 42.19\)

The travel time such that 26.11% of the 60 days have a travel time that is at least is of 42.19 minutes.

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He would have saved $87,221.02  after 1 year

He would have saved $268,335.90   after 3  years

What is an ordinary annuity?

An ordinary annuity means a fixed amount invested at specific intervals, in this case, $7,185.51 is invested monthly, which means that its future value can be computed using the future value formula of an ordinary annuity as shown below:

FV=PMT*(1+r)^N-1/r

FV=future value of an ordinary annuity

PMT=monthly payment invested every month

r=monthly interest rate=annual interest/12

N=number of months that monthly payments were

FV after 1 year:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in 1 year=12

FV=$7,185.51*(1+0.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*(1.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*0.02528845698324970/0.00208333333333333

FV=$87,221.02

FV after 3  years:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in  3 years=36

FV=$7,185.51*(1+0.00208333333333333)^36-1/0.00208333333333333

FV=$268,335.90

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The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3

and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%

so the answer is 1 whole batch and 81% of another

or 1 9/3

Answer:

Hi, since their are 12 months in the year, you divide 60,000 (the annual salary), by the amount of months in the year to find the monthly salary. The answer is 5,000.

Answer:

TRUE

Step-by-step explanation:

If that's not the answer you wanted just comment if you need help

Answer:

0.00003km

....................

kilo means 1000

and centi means 1/100

Answer:

92 cents

Step-by-step explanation:

If each box has the cost of 23 cents, and you decided to buy 4, you would multiply the amount of boxes you want with the cost of each one, therefore, the 92 cents. 4 * 23 = 92

Answer:

I will set this up for you and you work the math.

f(n) = f(n - 1) + 3

n = 7

f(7) = f(7 - 1) + 3 = f(6) + 3

Do the same for f(6).

f(6) = f(5) + 3 ⇒

f(7) = f(5) + 3 + 3

Similarly,  

f(5) = f(4) + 3 ⇒

f(7) = f(4) + 3 + 3 +3

Do you see the pattern emerging here?  Keep going until you are down to

f(2) = f(1) + 3 = 6 + 3 = 9

Then carefully plug the intermediate answers into their proper place in

f(7) = f(6) + 3

Step-by-step explanation:

recursive equation

Answer:

The point A is a representation of the number -3.

Answer:

24:5

Step-by-step explanation:

4 yards is 3 feet, so 4*3=12. There are 12 inches in a foot, so 12*12=144. 144:30= 72:15 = 24:5

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Answer:

55

Step-by-step explanation:

25% = 1/4

1/4 of 44 is 11

44+11= 55.

Answer: 44 increased by 25%  = 55

Step-by-step explanation:

25% x 44 = 11

44 + 11 = 55

Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Step-by-step explanation:

Hi, there!!!

According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,

So, let's simply work with it,

Firstly, finding the area of rectangle,

length = 11cm.

breadth = 11cm.

now, area= length× breadth.

or, a = 11cm× 11cm.

a= 121cm^2

Now, let's work out the area of circle.

radius= 5cm

and pi. = 3.14 {using pi value as 3.14}

now,

area of a circle = pi× r^2

or, a= 3.14×5^2

or, a = 78.5 cm^2.

Therefore, The area of a circle is 78.5cm^2.

Now lastly finding the area of shadedregion,

area of shaded region = area of rectangle - area of circle.

or, area of shaded region = 121cm^2 - 78.5cm^2

Therefore, the area of shaded region is 42.5 cm^2.

Hope it helps...

Answer:

Year 2022

Step-by-step explanation:

Let number of years = x

Samantha :

Bonus + yearly earning

50 + 5x

Emily :

40 + 10x

Curent earning in 2018:

Years worked by Samantha = 6

50 + 5(6) = 50 + 30 = 80

Years worked by Emily = 2

40 + 10(2) = 60

Year when they'll both receive same amount :

80 + 5x = 60 + 10x

5x - 10x = 60 - 80

-5x = - 20

x = 20/5

x = 4 ; x = 4 years

2018 + 4 = 2022

Answer:

68

Step-by-step explanation:

85/10= 8.5 (sp he's running each km in 8.5 mins)

8.5x8= 68

Answer:

9) 44 ( I'm not sure yet)

10) 14

Step-by-step explanation:

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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