A summer camp has 32 campers. A total of 22 of them swim, 20 play softball, and 5 do not swim or play softball. Which values complete the table?

a = 15, b = 10, c = 7, d = 5, e = 12
a = 15, b = 7, c = 5, d = 10, e = 12
a = 14, b = 7, c = 5, d = 12, e = 10
a = 14, b = 12, c = 7, d = 5, e = 10

Answer:

The value for the expression [tex](A+B)^{2}[/tex] is the largest

Step-by-step explanation:

Since both A and B must be greater than 0 and A>B then we can assume the least possible values for B=1 and A=2.

So,

i) 2(A+B) = 2(2+1) = 2*3 = 6

ii) [tex](A+B)^{2}[/tex] = (A+B)*(A+B) = (2+1)*(2+1) = 3*3 = 9

iii) [tex]A^{2} + B^{2}[/tex]  = [tex]2^{2} +1^{2}[/tex] = 4+1 = 5

iv) [tex]A^{2} - B^{2} = 2^{2} - 1^{2}[/tex] = 4-1 =3

Inspecting the answers of the above four expressions, we see that the value for the expression [tex](A+B)^{2}[/tex] is the largest.

Answer: (A+B)^2 is the largest because it equals 9 when A=2 and B=1 are plugged in and the rest are less than 9

Answer:

$307.5

Step-by-step explanation:

We have been given that Elena's aunt bought her a $150 savings bond when she was born. When Elena is 20 years old the bond will have earned 105% interest.

The bond's value after 20 years will be 150 plus 105% of 150.

[tex]\text{Bond's value when Elena will be 20 years old}=150+(\frac{105}{100}*150)[/tex]

[tex]\text{Bond's value when Elena will be 20 years old}=150+(1.05*150)[/tex]

[tex]\text{Bond's value when Elena will be 20 years old}=150+157.5[/tex]

[tex]\text{Bond's value when Elena will be 20 years old}=307.5[/tex]

Therefore, bond will be worth $307.5 when Elena will be 20 years old.

Answer:

16

Step-by-step explanation:

the 9 parts of the ratio is equivalent to 72 books

divide number of books by 9 to find one part of the ratio

[tex]\frac{72}{9}[/tex] = 8 ← 1 part of the ratio

2 parts = 2 × 8 = 16 ← number of bookmarks sold

Answer:$13

Step-by-step explanation:

Answer:

The correct explaination is Point G can be the centroid because 12:6 equals 2:1

Step-by-step explanation:

Given in  triangle ABC, the segments drawn from vertices intersect at point G.

Segment FG measures 6 cm and and segment FC measures 18 cm.

FG = 6 cm & FC = 18 cm

and also FC = FG + GC

               18 = 6 + GC   ⇒ GC = 12

Note: The centroid divides each median in a ratio of 2:1

& 12:6 give rise to 2:1

Hence, the correct explaination for this is Point G can be the centroid because 12:6 equals 2:1

Answer:

C

Step-by-step explanation:

Answer:

This system will have a. exactly one solution.

Step-by-step explanation:

When two lines have different slopes it means that they intersect exactly one time.

If they have the same slope, we need to look at the intercept to see if there is none or infinitely many solutions.

However, these have different slopes and therefore have just 1 solution.

The given set of equations has exactly one solution as y = -1 and x = 2.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

To put it another way, the equation needs to be subject to some restrictions.

A linear equation could contain more than one variable. If a variable's maximum power constantly equals one, an equation is considered to be linear.

Given a set of equations,

y = -3x + 5 and y = 3x - 7

By equate,

-3x + 5 = 3x - 7

6x = 12

x = 2 and y = -1

Hence "The given set of equations has exactly one solution as y = -1 and x = 2".

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Answers: (a→b), (b→a), (c→c)

Explanation:

Column A:

a) [tex]y = -3x + \dfrac{1}{3}[/tex]

  m = -3  ⇒  m⊥ = [tex]\dfrac{1}{3}[/tex]

b) 6x - 2y = 4

         -2y = -6x + 4

            y =  3x - 2

  m = 3  ⇒  m⊥ = [tex]-\dfrac{1}{3}[/tex]

c) y - 3 = [tex]\dfrac{1}{3}[/tex](x - 3)

  m = [tex]\dfrac{1}{3}[/tex] ⇒  m⊥ = -3

Column B

a) y - 3 = [tex]-\dfrac{1}{3}[/tex](x - 3)

  m = [tex]-\dfrac{1}{3}[/tex]

b) y = [tex]\dfrac{1}{3}x + 6[/tex]

   m = [tex]\dfrac{1}{3}[/tex]

c) 3x + y = 3

           y  = -3x + 3

  m = -3

******************************************************************************

Column A letter a matches to Column B letter b

Column A letter b matches to Column B letter a

Column A letter c matches to Column B letter c

2x/3=8

2x=24

x=12

It takes Molly 12 minues to run one mile.

The limit of any constant function is the value of the constant, so the limit is just 5.

For this case we have that by definition:

The limit of a constant function of the form [tex]y = f (x)[/tex], where [tex]f (x) = c[/tex], is the same constant, whatever the value to which the limit tends.

Thus, the limit of "5" when x tends to "2", results in "5".

Answer:

5

Option A

Answer:

x<=11

Step-by-step explanation:

2(x-3 ) <= 16

Distribute the 2

2x -6 <= 16

Add 6 to each side

2x -6+6<= 16+6

2x <= 22

Divide by 2

2x/2 <= 22/2

x<=11

Answer:

b = -5

Step-by-step explanation:

So we know

3a = -9

Divide 3 on both sides

a = -3

Plug a in to the other equation

-3b = 15

divide -3 on both sides

b = -5

Answer:

The correct answer is Option 4, the fourth graph

Step-by-step explanation:

We will go through why the other graphs are not the correct answer and then explain why the fourth is indeed the correct answer.

Option 1 is wrong because it has the general shape of the graph of an even valued function. These functions are either concave up or concave down.

Option 2 is wrong because it has the general shape of the cubic function. These functions are defined for both negative and positive values of x.

Option 3 is wrong because it is not defined for negative values of x. It has the general shape of the square root function.

Option 4 is correct because it has the general shape of the function [tex]f(x)=\sqrt[3]{x}[/tex]. Functions of this kind are defined for both negative and positive values of x.

Answer: the fourth Graph

Step-by-step explanation:

Probability of rolling a 5: 1/6

Probability of rolling a number greater than 3: 3/6

The probability of rolling a 5 or a number greater than 3 on a six-sided die is calculated by summing the individual probabilities of rolling a 4, 5, or 6, which are each 1/6. Therefore, the total probability is 3/6 or 1/2, equating to a 50% chance.

To solve this, we need to identify the favorable outcomes and divide them by the total number of possible outcomes. A six-sided die has six possible outcomes: {1, 2, 3, 4, 5, 6}. The event of rolling a 5 or a number greater than 3 includes the outcomes {4, 5, 6}. Hence, there are three favorable outcomes for the desired event (rolling a 4, 5, or 6).

The probability of any single outcome is 1/6, as there are six sides to the die. Therefore, the probability of rolling a 5 or a number greater than 3 is calculated by adding the probabilities of rolling each of these numbers:

Adding these probabilities gives us 3/6 or 1/2, making the probability of rolling a 5 or a number greater than 3 being 50%.

Answer:

6.6% Would be the answer.

You can check by multiplying 1000 people by 0.06 and get 66 people which is the number of families for that survey.

If you can please mark brainliest ¯\_(ツ)_/¯

Step-by-step explanation:

Answer:

Water = 1/5 of the volume of the syrup

Step-by-.step explanation:

Suppose we had  1000 cm^3 of syrup  and the new volume after adding water is x cm^3.  Now the amount of sugar stays the same so we have the equation 35 * 1000 =  25 * x

x = (30 * 1000) / 25 =  30,000 / 25

= 1200 cm^3

So we need to add 200 cm^2 of water .

In general terms,  we need to add water which equals 1/5 of the volume of the syrup,

0.80 per ounce

1.25 ounces

Answer: at this amount, there are 57.5 calories per ounce

therefore, there are 355 calories in 6 ounces of this ice cream

(since 57.5×6=355.0)

Answer:

345 calories

Step-by-step explanation:

Total Calories = 230 calories

Total amount = 4 ounces

TO find how many calories in 6 ounces of the ice cream

For this question we have to find out the number of calories in one ounce of an ice cream firs

as it is given to us that 230 calories in 4 ounces

so no of calories in one ounce = total calories / no of ounces

                                                   =230 / 4

                                                   =57.5 calories / ounce

Now we know that their are 57.5 calories in one ounce of the ice cream

We have to find no of calories in 6 ounces of ice cream

No of calories = 6 * 57.5

                       =345 calories

so amount of calories in 6 ounces are 345 calories

Answer:

Leading coefficient = - 15

Degree = highest power on a variable = 4

Step-by-step explanation:

It might be easier to see if you rewrote the polynomial in the order it is normally presented.

Highest power goes on the left.

y = -15x4  -  10x^2 - 2x + 9

The leading coefficient (-15) is the number in front of the variable with the  highest power (x^4 or 4)

The highest power on a variable is the degree.

There are 40 different ways could you choose a car black or blue Hyundai.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that Each dealership carries the same two car companies, and sells eight different models that all come in four colors.

The following steps can be used to determine the different ways could you choose a car:

Now Multiply 5 and 4 that is multiply five exterior color choices and six interior color choices.

5 x 4

Now Multiply the above expression with 2 that is with two model choices.

20 x 2

Further simplify the above expression.

= 40

There are 40 different ways could you choose a car.

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To determine the number of different Hyundais available in black or blue, you multiply the number of dealerships (6) by the number of Hyundai models (8) and the number of relevant colors (2), resulting in 96 different cars.

The question asks how many different cars you can buy if you want a black or blue Hyundai, given certain constraints. There are six dealerships, two car companies, eight models, and four colors available. To answer this, we calculate the total combinations possible with the given choices: dealerships (6), car companies (2), models (8), and colors (4). Since we are only interested in Hyundai cars in black or blue, we eliminate other colors and car companies from the choice set. The calculation is as follows:

Number of dealerships: 6
Car companies: 1 (only Hyundai)
Car models: 8
Car colors: 2 (black or blue)

To find the total number of possible combinations, we multiply the number of each category's choices together:

6 (dealerships)
* 1 (Hyundai)
* 8 (models)
* 2 (colors)
= 96 different cars

The problem can be solved using the power of a point theorem. First, let BD = x and EC = x + 12. Construct an equation: 8x = 6(x+12). Solving for x gives BD = 9 and EC = 21. The length of AC is then 35.

This problem can be solved using the concept of power of a point theorem in circle geometry. The power of a point theorem states that for any point outside a circle, the product of the lengths of the two line segments obtained by drawing secants from that point to the circle are always equal.

To apply this theorem to this problem, we'll first denote BD as x. Because the problem states that EC is 12 more than BD, we can denote EC as x + 12.

Now, using the power of a point theorem, we can write the equation (AD)*(DB) = (AE)*(EC). Substituting in the given values and the values we denoted for DB and EC, we get (8)*(x) = (6)*(x+12).

Solving this equation gives x = 9. Therefore, the length of BD is 9, and the length of EC is 21. To find the length of AC, we add the lengths AE, EC, and AD, which gives us AC = 6 + 21 + 8 = 35.

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ΔAED is the equilateral triangle. Therefore AH is a height of this triangle.

The formula of a height of an equilateral triangle:

[tex]h=\dfrac{a\sqrt3}{2}[/tex]

We have a = 5. Substitute:

[tex]\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]

You can use the Pythagorean theorem.

[tex]EH^2+AH^2=AE^2\\\\\left(\dfrac{5}{2}\right)^2+AH^2=5^2\\\\\dfrac{25}{4}+AH^2=25\\\\AH^2=25-\dfrac{25}{4}\\\\AH^2=\dfrac{100}{4}-\dfrac{25}{4}\\\\AH^2=\dfrac{75}{4}\to AH=\sqrt{\dfrac{75}{4}}\\\\AH=\dfrac{\sqrt{75}}{\sqrt4}\\\\AH=\dfrac{\sqrt{25\cdot3}}{2}\\\\\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]

If Circle A has a radius with the length of 5 units then the  exact length of the apothem is 5√3/2

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Circle A has a radius with the length of 5 units.

We have to find the length of apothem

The formula of a height of an equilateral triangle

h=a√3/2

We have a = 5. Substitute:

h=5√3/2

Apply Pythagorean theorem.

(5/2)²+AH²=5²

25/4+AH²=25

AH²=25-25/4

AH²=75/4

Take square root on both sides

AH=5√3/2

Hence, if Circle A has a radius with the length of 5 units then the  exact length of the apothem is 5√3/2

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Answer:

Step-by-step explanation:

Answer:

7665 arrangements

Answer: (a) 5

Step-by-step explanation:

[tex]\lim_{x \to 2} 5[/tex] means what is the y-value when x = 2 .

The given equation is: y = 5 so the y-value is 5 for all values of x

Answer: (c) 13

Step-by-step explanation:

f(x) = x² + 5x

f'(x) = 2x + 5

f'(4) = 2(4) + 5

      = 8 + 5

      = 13

Answer: (c) 2

Step-by-step explanation:

The question is asking what the y-value is when x = -2.  The graph shows that the coordinate (-2, 2) is on the curve. So, when x = -2, y = 2.

Answer:

lim x→2   5     =5

The slope is 13

lim x→-2   x^2 -2  =2

Step-by-step explanation:

lim x→2   5     =5

The limit of a constant is the constant

f(x) = x^2 +5x

We need to take the derivative

f'(x) = 2x+5

Then evaluate the derivative at x=4  (4,36)

f'(4) = 2*4 +5

     = 8+5

    = 13

The slope is 13

lim x→-2   x^2 -2  =2

Looking at the graph, the value of the function at -2  is about 2

We can also calculate it   (-2)^2 -2 =  4-2 = 2

Answer:

23 packages

Step-by-step explanation:

We are told that the school cafeteria needs to buy 200 new forks. Each package contains 9 forks.

To find the number of packages that school cafeteria should buy we will divide total number of needed forks by number of forks in each pack.

[tex]\text{The number of fork packages}=\frac{200}{9}[/tex]

[tex]\text{The number of fork packages}=22.22222[/tex]

Since forks come in package of 9, so cafeteria have to buy whole number packages.

Let us round up our answer to the whole number.

[tex]\text{The number of fork packages}=22.22222\approx 23[/tex]

Therefore, school cafeteria should buy 23 packages of forks.

Answer:

23 packages should the cafeteria buy.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

As per the statement: The school cafeteria needs to buy 200 new forks. If each package contains 9 forks.

then by definition of Proportion;

[tex]\frac{1}{9} = \frac{x}{200}[/tex]   , where x represents the package

By cross multiply;

200 = 9x

Divide both sides by 9 we get;

[tex]\frac{200}{9} =\frac{9x}{9}[/tex]

Simplify:

[tex]x = \frac{200}{9} =22.222[/tex]

Therefore, 23 package should the cafeteria buy.

Given is :

The annual income of Richard = $34200

Hence, his monthly income becomes = [tex]\frac{34200}{12}[/tex] = $2850

So, the maximum amount that he can spend per month paying off credit cards and loans and not be in danger of credit overload can be a maximum of 20% of this income.

So, 20% of 2850 is = $570

Hence, approximately $570 can be spent a month.

As, the question has no options to choose from, but the question is complete in itself, so this is the best possible answer.

Answer: $570

Step-by-step explanation: