The graph of the function f(x) = –(x + 1)2 is shown.

6:2:3:4

 for every 6 pairs of wedges she owns 2 Stillettos, 3 sneakers and 4 sandals

18/6 =3

3*2 =6 stilettos

3*3 = 9 sneakers

3*4 =12 sandals

18 + 6 + 9 + 12 = 45 pairs of shoes

Final answer:

Given the ratio 6:2:3:4 for different types of shoes and 18 pairs of wedges, we first find the value of one unit in the ratio by dividing 18 by 6, which equals 3. Multiplying each part of the ratio by 3 gives us the total for each type, and adding those up gives us 45 pairs of shoes in total.

Explanation:

The question asks us to determine the total number of pairs of shoes Ms. Posillico owns based on the given ratio of different types of shoes and the fact that she owns 18 pairs of wedges.

Step-by-step Solution

First, we are given a ratio of 6:2:3:4 for Wedges, Stilettos, Sneakers, and Sandals respectively.

Since we know that there are 18 pairs of wedges, which corresponds to the first number in the ratio (6), we can use this information to find the value of each unit in the ratio.Divide the number of wedges (18) by the ratio number for wedges (6) to find out the value of one unit in the ratio.

Calculate the total number of pairs of shoes by multiplying the number each type of shoe per the given ratio by the value of one unit.

Add up the total pairs for each type of shoes to get the grand total.

Calculation

18 pairs of wedges / 6 = 3 pairs per unit
Then, multiply each part of the ratio by 3 to get:
Wedges: 6 * 3 = 18
Stilettos: 2 * 3 = 6
Sneakers: 3 * 3 = 9
Sandals: 4 * 3 = 12
Add up the total: 18 + 6 + 9 + 12 = 45 pairs of shoes.

Therefore, Ms. Posillico owns 45 pairs of shoes in total.

Final answer:

The amount of orange juice served by Sleepwell Hotel increased approximately by 71.7% from last year.

The subject of this question is Mathematics and it deals with the concept of percentage increase. To calculate the percent of increase in the amount of orange juice served yearly by Sleepwell Hotel, we need to keep in mind that the formula to calculate percentage increase is:

(New Amount - Original Amount)/Original Amount * 100

In the given problem, the original amount is 660 gallons (the amount of orange juice served last year) and the new amount is 1133.2 gallons (the amount served this year). Inserting these values into the formula gives us:

(1133.2 - 660) / 660 * 100

After performing the arithmetic, we find that the percent increase of orange juice served by Sleepwell Hotel is approximately 71.7%.

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The correct statement is: "The average number of days the house stayed on the market before being sold for $150,000." So option (a) is correct.

To find the meaning of  f(150) , we need to understand that  f(p) represents the average number of days a house stays on the market before being sold for price ( p ) in $1,000s.

So,  f(150)  represents the average number of days a house stays on the market before being sold for $150,000.

This means the correct statement is: "The average number of days the house stayed on the market before being sold for $150,000."

To calculate this, let's say there are ( n ) houses that were sold for $150,000. The total number of days these houses stayed on the market would be the sum of days for each house. Then we divide this sum by (n ) to find the average.

Let's say [tex]\( D_i \)[/tex] is the number of days house [tex]\( i \)[/tex] stayed on the market before being sold for $150,000.

[tex]\[ f(150) = \frac{D_1 + D_2 + \cdots + D_n}{n} \][/tex]

Now, let's illustrate the calculation:

Let's assume 5 houses were sold for $150,000 and their days on market were 120, 140, 160, 180, and 200.

[tex]\[ f(150) = \frac{120 + 140 + 160 + 180 + 200}{5} \][/tex]

[tex]\[ f(150) = \frac{800}{5} = 160 \][/tex]

So, [tex]\( f(150) = 160 \)[/tex] which means the average number of days a house stayed on the market before being sold for $150,000 is 160 days. Therefore, the correct statement is: "The average number of days the house stayed on the market before being sold for $150,000."

Complete Question:

Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(150)?

a. This is the average number of days the house stayed on the market before being sold for $150,000.

b. The house sold on the market for $150,000 and stayed on the market for an average of 150 days before being sold.

c. The house sold for $150,000.

d. The house stayed on the market for an average of 150 days before being sold.

Answer: 8.50h+60

The reason is because she earns $8.50 per hour so the variable goes next to 8.50 instead of the 60.

The equation (8.50h + 60) will represent Monica's earnings for the week.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given; Monica earned a bonus = $60

Per hour earning in addition to bonus = $8.50

Let she worked for 'h' hours this week.

Then total earning from the hourly rate is $8.50h

The Total earning for the week = Earning of 'h' hours + Bonus earned

= $(8.50h + 60)

Therefore, The equation (8.50h + 60) will represent Monica's earnings for the week.

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Answer:

1.

Jeanie sells M&Ms out of her giant bag at 4 for 5 cents.

Each piece of M&Ms cost = [tex]\frac{5}{4}=1.25[/tex] cents

The machine at the store sells you 9 for 25 cents.

Each piece costs = [tex]\frac{25}{9}=2.78[/tex] cents

Hence, Janine is selling at a lower price. Hers is a better deal.

2.

Tom sells baseball cards at 10 for 35 cents.

Per card costs = [tex]\frac{35}{10}=3.5[/tex] cents

The second deal is 12 for 40 cents.

Per card costs = [tex]\frac{40}{12}=3.33[/tex] cents

Hence, 2 for 40 cents is a better deal.

3.

The hardware store sells sparklers for the 4th of July. They charge 19 cents a piece.

The fireworks stand charges 85 cents for four.

Per piece cost = [tex]\frac{85}{4}=21.25[/tex] cents cents

Hence, The hardware store's deal is a better deal.

4.

Frosted flakes has 11 grams of sugar in each 1 ounce serving.

Raisin Bran has 13 grams of sugar in each 1.4 ounce serving.

Per ounce sugar content in Raisin Bran= [tex]\frac{13}{1.4}=9.28[/tex] gram

Hence, Raisin Bran has less sugar from an ounce of cereal.

To find the value of t, set up a proportion using the rates of production for the machines. The equation is (500 + 400)t = 2250. Simplify the equation and solve for t to find that t = 2.5 hours.

To find the value of t, we need to determine how long it takes for the two machines to produce 2250 items together. We can set up a proportion to solve for t using the rates of production for each machine. The proportion is:

(500 + 400)t = 2250

Simplifying the equation, we get:

900t = 2250

Dividing both sides by 900, we find that:

t = 2250/900 = 2.5 hours

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Answer:

The number of servings of gelatin is 48

Step-by-step explanation:

step 1

Find out the number of molds

Divide the number of packages of gelatin (8)  by 1 1/3 to obtain the number of molds

Remember that

[tex]1\frac{1}{3}=\frac{1*3+1}{3}=\frac{4}{3}[/tex]

so

[tex]\frac{8}{(4/3)}=\frac{24}{4}=6\ molds[/tex]

step 2

Find out the number of servings of gelatin

we know that

Each mold can be divided into 6 servings

To obtain the number of servings multiply the number of molds by 6

[tex]8(6)=48[/tex]

therefore

The number of servings of gelatin is 48

Kasey can make 36 servings of gelatin based on the number of packages she has and the amount required for each mould.

This question involves a bit of fraction work. Kasey has 8 packages of gelatin and each mold requires 1 1/3 packages of gelatin. As we need to figure out how many molds can be made, we divide the total number of packages by the amount needed for one mold. This equals 8 ÷ 1 1/3, which equals to 6 molds when converted into an improper fraction.

Subsequently, we understand that each mold can be divided into 6 servings. Therefore, Kasey could make a total of 6 molds x 6 servings which equals 36 servings of gelatin.

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The cost of 1 adult for the given games using the various parameters to create a simultaneous equation gives; $8

Let cost of adults be x and let cost of kids be y.

Now,  there were 7 adults and 20 kids at Pump and Jump Land and the cash collected was $236. Thus, we can say that;

7x + 20y = 236    -----(1)

Similarly, there were 21 adults and 50 kids for a total amount of $618. Thus;

21x + 50y = 618   -----(2)

Solving both equations simultaneously gives;

x = $8 and y = $9

Thus, cost of 1 adult = $8

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A rate is a ratio that compares two quantities that are measured in different units.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity.

Rate is the ratio between two quantities which are measured in different units.

Unit rate is also a rate but the difference is that it is the rate corresponds to single unit of one quantity.

Numerator will be mainly the dependent variable and the denominator will be the independent variable.

For example, speed is the rate which is the function of distance and time.

Slope is also a rate.

Hence the rate is a ratio that compares two quantities that are measured in different units.

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Given 10.49 seconds to be rounded to the nearest second, we would round down 10.49 seconds to have: 10 seconds.

Recall:

When rounding a number, if the number that comes before it is 5, 6 and up to 9, you round the number up. i.e. 57 to the nearest ten would be rounded up to 60.

When rounding a number, if the number that comes before it is from 4 below, you round the number down. i.e. 54 to the nearest ten is 50.

Thus:

Given 10.49 seconds, we want to round the number to the nearest second.

We need to round it down.

10.49 to nearest seconds = 10 secs.

In summary, given 10.49 seconds to be rounded to the nearest second, we would round down 10.49 seconds to have: 10 seconds.

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Answer:

1. A function is always a relation but a relation is not always a function.

Step-by-step explanation:

A function is a relation in which each element of the domain is mapped to one element of the range.

This means that every function is a relation, but not every relation is a function.

There are 60 phone calls is the cost of plan B less than the cost of

plan A.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Plan A includes fee of $25 per month and charges $0.25 for every phone call.

And, Plan B includes a fee of $40 per month and offers unlimited calls.

Let number of phone calls for the cost of plan B less than the cost of

plan A = x

So, For plan A; we can formulate;

The total cost of the plan A ,

f (x) = 25 + 0.25x

And, For plan B;

The total cost of the plan B,

f (x) = 40

Now, To check the number of phone calls for the cost of plan B less than the cost of plan A, we can formulate;

40 < 25 + 0.25x

Solve for x, it gives the number of phone calls.

40 < 25 + 0.25x

Subtract 25 both side;

40 - 25 < 25 + 0.25x - 25

15 < 0.25x

Divide by 0.25;

60 < x

So, We can say that;

There are 60 phone calls is the cost of plan B less than the cost of

plan A.

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900 * 10 = 9000 meters

9000/1000 = 9 km

When the number 51,829 is rounded to the nearest thousand, it becomes 52,000 which has three zeros. The process of rounding helps simplify numbers for easy comprehension and calculation.

The question asks about rounding the number 51,829 to the nearest thousand. Rounding involves increasing or decreasing a number to its closest specific multiple. In this case, the closest thousand to 51,829 is 52,000. The rules of rounding dictate that if the number in the hundreds place is 5 or above, we round up. In 51,829, the number in the hundreds place is 8, which is greater than 5, indicating we should round up from 51,000 to 52,000.

If we check how many zeros 52,000 has, it has three zeros. Thus, the rounded number will have three zeros. It's important to remember that the number of zeros often increases when rounding to larger place values like thousands, ten thousands, etc.

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To calculate the taxi fare, we determine the cost for the first 1/5 mile at $1.15, and then add the cost for the remaining increments at $0.35 each. The total fare comes to $15.68 when rounded to the nearest cent.

To calculate the cost of a taxi ride in Austin from one of the convention hotels to the airport for an 8.5-mile distance, let's break it down step by step:

Therefore, the taxi fare from the hotel to the airport will be $15.68.