A caterer charges $800 for a party of 25 guests. For a party of 60 guests, the cost is $1,430. Enter a linear model that represents the total cost, C, as a function of g, the number of guests at a party.

Answer:

  The line of reflection is at y = x+6.

Step-by-step explanation:

The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...

  y = 1(x +4) +2

  y = x + 6 . . . . . . . line of reflection

Answer:

  $300

Step-by-step explanation:

30% of $1000 is ...

  0.30 × $1000 = $300

Answer:

$300

Step-by-step explanation:

If there is a 30% reserve requirement on a $1,000 deposit, there must be $300 set aside as a member bank reserve.

30% of $1000 = $300

Answer:

Variance = 4.68

Step-by-step explanation:

The formula for the variance is:

[tex]\sigma^{2} =\frac{\Sigma(X- \mu)^{2}}{N} \\or \\ \sigma^{2} =\frac{\Sigma(X)^{2}}{N} -\mu^{2} \\[/tex]

Where:

[tex]X: Values \\\mu: Mean \\N: Number\ of\ values[/tex]

The mean can be calculated as each value multiplied by its probability

[tex]\mu = 0*0.4 + 1*0.3 + 2*0.1+3*0.15+ 4*0.05=1.15[/tex]

[tex]\frac{\Sigma (X)^{2}}{N} =\frac{(0^{2}+1^{2}+2^{2}+3^{2}+4^{2})}{5} =6[/tex]

Replacing the mean and the summatory of X:

[tex]\sigma^{2} = \frac{\Sigma(X)^{2}}{N} -\mu^{2} \\= 6 - 1.15^{2}\\= 4.6775[/tex]

Answer:

  C = (7, 6)

Step-by-step explanation:

The problem statement tells us the relation between the points is ...

  (B-A)/(C-A) = 2/7

  7(B -A) = 2(C -A) . . . . . . multiply by 7(C-A)

  7B -7A +2A = 2C . . . . . add 2A

  C = (7B -5A)/2 . . . . . . . divide by 2

  C = (7(2, -4) -5(0, -8))/2 = (14, 12)/2 . . . . . fill in the values of A and B

  C = (7, 6)

Answer:  [tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given : An opaque bag contains 5 green marbles, 3 blue marbles and 2 red marbles.

Total marbles = 5+3+2=10

Now, if it given that the a red marble is already drawn, then the total marbles left in the bag = 10-1=9

But the number of blue marbles remains the same.

Now, the probability of drawing a blue marble given the first marble was red :-

[tex]=\dfrac{\text{Number of blue marbles}}{\text{Total marbles left}}\\\\=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Hence, the required probability = [tex]\dfrac{1}{3}[/tex]

Answer:

The answer to your question is: 16x + 3

Step-by-step explanation:

Step 1 :      f(x) = 8x² + 3x

                f(x +h) =  8(x + h)² + 3( x + h)

                f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

                f (x + h) = 8x² + 16xh + 8h² + 3x + 3h

Step 2 f(x+h) - f(x) =  8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

                              = 8x² + 16xh + 8h² + 3x + 3h - 8x² -3x

                              = 16xh + 8h² + 3 h

Step 3 f(x + h) - f(x)/ h = h(16x + 8h + 3) /h

                                    = 16x + 8h + 3

Step 4 lim  f(x + h) - f(x)/ h = lim 16x + 8h + 3  = lim 16x + 8(0) + 3 = 16x + 3

        h ⇒0                           h ⇒0                     h ⇒0

Here, we are required to find the slope of the tangent line to the graph of the given function at any point.

The correct answer is 16x + 3.

The four step process to find the slope of the tangent line to the graph at any point is as follows;

First step (1):

f(x +h) = 8(x + h)² + 3( x + h) and yields;

f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

and, f (x + h) = 8x² + 16xh + 8h² + 3x + 3h.

Second step(2):

F(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

and, F(x+h) - f(x) = 16xh + 8h² + 3 h

Third step (3):

{F(x+h) - f(x)} / h = (16xh)/h + (8h²)/h + (3 h)/h

This in turn yields;

{F(x+h) - f(x)} / h = 16x + 8h + 3.

Fourth step(4):

lim f(x + h) - f(x)/ h =

h=>0

lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3

h=>0. h=>0

Therefore, the slope of the tangent line to the graph of the given function at any point is;

16x + 3.

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The values for x and y are as follows: ( x = 25 ) feet and ( y = 15 ) feet.

To find the values of x and y, we can set up a system of equations based on the given information. Let( x ) be the side length of the large square and ( y ) be the side length of the small square. The perimeter of the entire fence is given by ( 4x + 4y = 350) feet, and the total area enclosed by the fence is( xy + xy = 2xy = 6125 ) square feet.

First, we solve the perimeter equation for  x

4x + 4y = 350

[tex]\[ x + y = \frac{350}{4} \][/tex]

x + y = 87.5

Now, we have two equations:

x + y = 87.5

2xy = 6125

We can substitute the value of ( x + y ) from the first equation into the second equation:

2xy = 6125

2(87.5 - y)y = 6125

175y - 2y² = 6125

y² - 87.5y + 3062.5 = 0

Solving the quadratic equation, we find two possible values for  y  However, since the side length cannot be negative, we discard the smaller value, leaving us with y = 15  feet. Substituting this into the first equation, we find x = 25feet.

Therefore, the final answer is x = 25 feet and  y = 15  feet.

By the law of total probability,

[tex]P(A\cap B)=P[(A\cap B)\cap C]+P[(A\cap B)\cap C'][/tex]

but the events A, B, and C are mutually independent, so

[tex]P(A\cap B)=P(A)P(B)[/tex]

and the above reduces to

[tex]P(A)P(B)=P(A)P(B)P(C)+P(A\cap B\cap C')\implies P(A\cap B\cap C')=P(A)P(B)(1-P(C))=P(A)P(B)P(C')[/tex]

which is to say A, B, and C's complement are also mutually independent, and so

[tex]P(A\cap B\cap C')=0.5\cdot0.8\cdot(1-0.3)=0.12[/tex]

By a similar analysis,

[tex]P(A\cap B'\cap C)=P(A)P(B')P(C)=0.03[/tex]

[tex]P(A'\cap B\cap C)=P(A')P(B)P(C)=0.12[/tex]

These events are mutually exclusive (i.e. if A and B occur and C does not, then there is no over lap with the event of A and C, but not B, occurring), so we add the probabilities together to get 0.27.

Final answer:

The probability that exactly two of the independent events A, B, and C occur is 0.43, calculated by adding the probabilities of each possible pair of events occurring while the third does not.

Explanation:

The student is seeking the probability that exactly two out of the three events A, B, and C occur given their individual probabilities P(A) = 0.5, P(B) = 0.8, and P(C) = 0.3, and the fact that they are mutually independent events. To find this, we ned to consider the three scenarios where exactly two events occur: A and B, A and C, and B and C. The probability for each scenario is found by multiplying the probabilities of the two events occurring and then multiplying by the probability of the third event not occurring.

For example, the probability of A and B both occurring but not C is P(A) × P(B) × (1 - P(C)). To find the total probability that exactly two events occur, we sum up the probabilities of all three scenarios:

P(A and B but not C) = P(A) × P(B) × (1 - P(C))

P(A and C but not B) = P(A) × (1 - P(B)) × P(C)

P(B and C but not A) = (1 - P(A)) × P(B) × P(C)

We then calculate and sum these probabilities:

P(A and B but not C) = 0.5 × 0.8 × (1 - 0.3) = 0.5 × 0.8 × 0.7 = 0.28

P(A and C but not B) = 0.5 × (1 - 0.8) × 0.3 = 0.5 × 0.2 × 0.3 = 0.03

P(B and C but not A) = (1 - 0.5) × 0.8 × 0.3 = 0.5 × 0.8 × 0.3 = 0.12

Adding these probabilities together provides the final answer:

Σ P(exactly two events) = 0.28 + 0.03 + 0.12 = 0.43

Therefore, the probability that exactly two of the events A, B, and C occur is 0.43.

Answer:

  (a) |s - x| ≤ 3/16

  (b) 4 15/16 ≤ x ≤ 5 5/16

Step-by-step explanation:

(a) The absolute value of the difference from spec must be no greater than than the allowed tolerance:

  |s - x| ≤ 3/16

__

(b) Put 5 1/8 for s in the above equation and solve.

  |5 1/8 - x| ≤ 3/16

  -3/16 ≤ 5 1/8 -x ≤ 3/16

  3/16 ≥ x -5 1/8 ≥ -3/16 . . . . multiply by -1 to get positive x

  5 5/16 ≥ x ≥ 4 15/16 . . . . . . add 5 1/8

Pieces may be between 4 15/16 and 5 5/16 inches in length.

An absolute value inequality can be used to represent the acceptable range of lengths for a piece of wood in a woodshop class. For a specified length of 5 1/8 inches, the acceptable lengths for the piece would be between 4 15/16 inches and 5 5/16 inches.

Your task in woodshop class is to cut pieces of wood to within 3/16 inch of the teacher's specifications. The difference between the specification s and the measured length x of a cut piece is represented by (s-x).

(a) You can represent this situation with the absolute value inequality |s - x| ≤ 3/16, which shows that the difference between the specification and the measured length must be less than or equal to 3/16 inch.

(b) If the length of one piece is specified to be s = 5 1/8 inches, you can substitute that value into the inequality to find the acceptable range of lengths: |5 1/8 - x| ≤ 3/16. Solving the inequality gives you the range 5 - 3/16 inches ≤ x ≤ 5 + 3/16 inches, or between 4 15/16 inches and 5 5/16 inches.

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Answer:

The answer to your question is:  The last option is correct

Step-by-step explanation:

Just remember thta when we divide by a negative number, the inequality changes, then,

                            - 125 ≥ -135      divide by -5

                              25  ≤ 27

Answer:

25 < 27 not 25 ≤ 27

Step-by-step explanation:

-125 ≥ -135

on the number, you count through -125 before -135, so -125 is greater but not equal to -135.

-125/ -5  > -135/ -5

= 25 < 27

25 is less than 27. They are not equal.

Answer:

Step-by-step explanation:

Given that When n is divided by 21, the remainder is an odd number.

i.e. [tex]n=21m+k[/tex] where m is an integer and k a positive integer <21

When n is divided by 28, the remainder is 3

[tex]n=28c+3[/tex], where c is a positive integer

This can be written as

[tex]n=4(7c)+3\\n=7(4c)+3[/tex]

Since n is giving odd remainder when divided by 21,

we get r =3 as n is a multiple of 7 +3

125 liters of pure peroxide should be added to the 500 liters of the 10% solution to produce a new product that is 28% peroxide.

The concentration C of the new mixture is given by the formula:

C = (x + 0.1 * 500) / (x + 500)

We want to find out how many liters of pure peroxide (100% peroxide) should be added to produce a new product that is 28% peroxide.

In other words, we want to find the value of x that makes C equal to 0.28 (28%).

So, we set up the equation:

0.28 = (x + 0.1 * 500) / (x + 500)

Now, we can solve for x:

0.28(x + 500) = x + 0.1 * 500

Distribute 0.28 on the left side:

0.28x + 0.28 * 500 = x + 0.1 * 500

Simplify:

0.28x + 140 = x + 50

Subtract x from both sides:

0.28x - x + 140 = 50

-0.72x + 140 = 50

Subtract 140 from both sides:

-0.72x = -90

Divide by -0.72:

x = 125

So, 125 liters of pure peroxide should be added to the 500 liters of the 10% solution to produce a new product that is 28% peroxide.

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Final answer:

To achieve a 28% peroxide concentration, approximately 125 liters of pure peroxide should be added to the existing 500-liter, 10% peroxide solution.

Explanation:

The question asks how many liters of pure peroxide (x liters) must be added to a 500-liter solution with a 10% peroxide concentration to produce a new product that is 28% peroxide. To solve this, we'll set up the equation:

C = (x+0.1(500)) / (x+500) where C = 0.28 (the target concentration). So,

0.28 = (x + 50)/(x + 500)

Multiply both sides by (x + 500) to get 0.28(x + 500) = x + 50

Distribute 0.28 to get 0.28x + 140 = x + 50

Subtract 0.28x from both sides to isolate x on one side: 140 = 0.72x + 50

Subtract 50 from both sides: 90 = 0.72x

Divide both sides by 0.72 to solve for x: x ≈ 125 liters

Therefore, approximately 125 liters of pure peroxide should be added to the 500-liter solution to achieve a 28% peroxide concentration.

Because there are 4 inside angles the sum of the four angles must equal 360 degrees.

Add the angles to equal 360:

4x + 3x + 2x + 3x = 360

Simplify:

12x = 360

Solve for x by dividing both sides by 12:

x = 360 /12

x = 30

Now you have x, solve for each angle:

ABC = 4x = 4 x 30 = 120 degrees.

BCD = 3x = 3 x 30 = 90 degrees.

CDA = 2x = 2x 30 = 60 degrees.

DAB = 3x = 3 x 30 = 90 degrees.

C. It's important to know that a four sides figure needs the inside angles when added together need to equal 360 degrees.

Good morning ☕️

____________________

Step-by-step explanation:

Look at the photo below for the answer.

:)

Answer:

481 / 2142 = 22.46%

A pie chart is also commonly used to illustrate it.

Step-by-step explanation:

We can get the sample proportion of every case, applying the following relations:

1288 / 2142 (60.13%) answered "no"

481 / 2142 (22.46%) answered "yes"

373 / 2142 (17.41%) had no opinion

where 2142 (1288 + 481 + 373 = 2142) is the total of adults who were asked.

The opportunity cost of Susan attending college for a year is $51,400 ($11,400 of actual college expenses and $40,000 of foregone income from her previous job).

The opportunity cost of attending college is determined not only by the actual expenditure but also by the income you forgo by not working. In Susan's case, her actual expenses include $8,000 for tuition, $900 for books, and $2,500 for food, which total to $11,400. However, since she quit her $40,000 a year job to attend college, that lost income is also part of her opportunity cost. So, we add the lost income to her college expenses to get the total opportunity cost. Therefore, the opportunity cost of Susan attending college for the year would be $51,400 ($40,000 + $11,400).

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The best approximation of the solution is represented by the ordered pair, (0.7,-1.5), the correct option is C.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The system of equations are equations that have a common solution.

The equations are:

y = 2x-3

y = -5x +2

The ordered pair that is the best approximation of the solution is the point at which for a given value of x, the system of the equation has the same y value.

From the table, it can be seen that for x = 0.7, the y value for both the equation is similar, -1.5 and -1.6.

Therefore, (0.7, -1.5).

Your question seems incomplete, the complete question is attached with the answer.

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Answer:

  225%

Step-by-step explanation:

You can figure the percentage change from ...

  percentage change = ((new value)/(old value) -1) × 100%

  = (26/8 -1) × 100% = (3.25 -1) × 100% = 225%

Answer:  20

Step-by-step explanation:

Given : Angel can choose from 4 different types of chocolate and 5 different flavors of gum.

By the fundamental counting principle , the total number of outcomes is the product of the number of outcomes for each event.

i.e. The number of different types of grab bags can she put together if she puts one chocolate and one flavor of gum in each bag will be :_

[tex]4\times5=20[/tex]

Hence, The number of different types of grab bags can she put together if she puts one chocolate and one flavor of gum in each bag =20

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

[tex]A=b^{2}[/tex]

where b is the length side of the square

we have

[tex]A=49\ units^2[/tex]

substitute

[tex]49=b^{2}[/tex]

[tex]b=7\ units[/tex]

therefore

[tex]AB=BE=ED=AD=7\ units[/tex]

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

[tex]A=(AC)(AG)[/tex]

substitute the given values

[tex]A=(9)(10)=90\ units^2[/tex]

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

[tex]A=(DE)(DG)[/tex]

we have

[tex]DE=7\ units[/tex]

[tex]DG=AG-AD=9-7=2\ units[/tex]

substitute

[tex]A=(7)(2)=14\ units^2[/tex]

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

[tex]A=(EF)(CF)[/tex]

we have

[tex]EF=AC-AB=10-7=3\ units[/tex]

[tex]CF=BE=7\ units[/tex]

substitute

[tex]A=(3)(7)=21\ units^2[/tex]

step 5

sum the shaded areas

[tex]14+21=35\ units^2[/tex]

step 6

Divide the area of  of the shaded region by the area of ACIG

[tex]\frac{35}{90}[/tex]

Simplify

Divide by 5 both numerator and denominator

[tex]\frac{7}{18}[/tex]

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

Answer:

Step-by-step explanation:

You know that 3 pennies are involved, because $0.68 cannot be made without them.

Then 6 coins must make up 65¢. If 1 is a quarter, then the remaining 40¢ must be made using 5 coins. 4 dimes is too few, and 8 nickels is too many. However 3 dimes and 2 nickels is just right.

Bobby gave the cashier 1 quarter, 3 dimes, 2 nickels, 3 pennies.

Answer:

Discrepancy = 665,15 L

Step-by-step explanation:

Data: 1 Apple Barrel: 7056 cubic inches

         1 Cranberry Barrel: 5826 cubic inches

The merchant sells 33 cranberry barrels, so we need to find out the total volume of that. So we multiply our cranberry volume (data) 33 times:

33 x 5826 cubic inches = 192258 cubic inches

Now, the customer thinks that he is receiveing apple barrels. To calculate this volume, we need to multiply the apple volume (data) 33 times:

33 x 7056 cubic inches = 232848 cubic inches

(You can see that 33 apple barrels have more volume that 33 cranberry barrels, so the customer will receive less volume than he is expecting)

The problem is asking the discrepancy in the shipment in liters (L). First we calculate the discrepancy (difference) in cubic inches.

Discrepancy (cubic inches) = 232848 cubic inches - 192258 cubic inches = 40590 cubic inches

Finally we need to transform the units. As a general rule, we know that:

1 litre (L) = 61,0237 cubic inches. Using a simple rule of three we can solve it:

Discrepancy (L) = [tex]\frac{40590 cubic inches}{61,0237 cubic inches\\}[/tex] x 1 L

Discrepancy (L) = 665,15 L

So Julia... 6 miles in 30 minutes. Let's find out how much she travelled in 1 hour. Multiply it by 2, since 30 x 2 = 60 mins = 1 hour, you get 12 miles per hour for Julia.

For Alex... 2 miles in 12 minutes. Multiply it by 5, as 12 x 5 = 60 mins = 1 hour, you get 10 miles per hour for Alex.

Julia travelled faster. She travelled 12 miles per hour while Alex travelled 10 miles per hour.

Julia travelled at a greater speed at 12 miles per hour.

Unitary method is a mathematical way of first deriving the value of a single unit and then deriving the required unit by multiplying with it.

According to the given question Julia rode a bicycle 6 miles in 30 minutes.

∴  In 60 minutes Julia rode (6×60)/30 miles which is

= 12 miles per hour.

Alex rode his skateboard 2 miles in 12 minutes.

So, In 60 minutes he rode (60×2)/12 miles which is

= 10 miles per hour.

Therefore the average speed of Julia is more by 2 miles per hour.

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Answer:

Function [tex]sin(60^o)\,\,s=h[/tex]

Height of an equilateral angle of side length 88m: [tex]76.21\,m=h[/tex]

Step-by-step explanation:

An equilateral triangle has 3 equal sides and 3 equal angles. The height of the triangle could be expressed as:

[tex]sin(\theta)=\frac{O}{H}[/tex]

[tex]sin(60^o)=\frac{h}{s}[/tex]

Moving s to the other side we find the function for the height:

[tex]sin(60^o)\,\,s=h[/tex]

As we know that s=88m we have

[tex]sin(60^o)\,\,88m=h[/tex][tex]\frac{\sqrt{3}}{2}88m=h[/tex]

[tex]44\sqrt3 \,m=h[/tex]

[tex]76.21\,m=h[/tex]

Explanation of the height of an equilateral triangle as a function of its side length and calculation for a triangle with a side length of 88m.

Justify that the triangles are similar: Equilateral triangles have all sides equal and all angles equal, therefore they are similar.

Write an equation that relates the sides of the triangles using words to describe the quantities: The height h of an equilateral triangle is equal to √3/2 times the side length s.

Rewrite your equation using your symbols: h = √3/2 * s

Algebraically isolate the unknown quantity: Given s = 88 m, plug it into the formula h = √3/2 * s to find the height h.

Plug-in numbers and calculate answer: h = √3/2 * 88 m ≈ 76.12 m

Check answer: The calculated height of approximately 76.12 m seems reasonable for an equilateral triangle with a side length of 88 m.

Answer:

0.65

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

In this problem we have

[tex]x=4+4+13+13=34[/tex]

because

total of three=4

total of jack=4

total of club=13

total of diamond=13

[tex]y=52\ cards[/tex]

substitute

[tex]P=\frac{34}{52}=0.65[/tex]

The money that club make $ 639.75.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The Spanish club began the year with $15.00 in its account.

At the end the club had = $654. 75

so, the Club earned

= 654. 75- 15

= 639.75

Hence, the money club make $ 639.75

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Answer:

C

Step-by-step explanation:

Answer:

1/4

decimal- 0.25

percent- 25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation: