A formula that approximates real-world phenomena is call a/an
Kasey has 8 packages of gelatin. She plans to fill molds that each take 1 1/3 packages of gelatin. Each mold can be divided into 6 servings. How many servings of gelatin can Kasey make?
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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Jan has 10 dolls. Kat has 7 dolls. choose yes or no to show if the equation can be used to find how many fewer dolls Kat has than Jan.
10-7=3 yes or no
3+7=10 yes or no
10+7=17 yes or no
7+3=10 yes or no
is (-4, 10) a solution to the equation 10 - 5x=y
Pete wants a loan of $1,500. Which of these terms describes the money he wants to borrow?
1. (Principal)
2. (Collateral)
3. (Credit)
Principal amount describes the money which he wants to borrow.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Pete wants a loan of $1,500.
Now,
Since, We know that;
The principal amount describe the money to borrowed.
Thus, Principal amount describes the money which he wants to borrow.
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the expression 14.50 X can use to find the total cost for x tickets on family night for Mission and the movie what is the cost for three tickets
Carly is 3 times older than her brother's age. The sum of their ages is no more than 24 years.
a. x+3x≤24
b. x+x+3≤24
c. x+3x<24
d. x+x+3<24
Using the inequality, find the oldest age Carly's brother can be
Jeanie sells M&Ms out of her giant bag at 4 for 5 cents. The machine at the store sells you 9 for 25 cents. Which is the better deal for you? Show your work. Justify your answers in the space below
Tom sells baseball cards at 10 for 35 cents. Is that a better deal than 12 for 40 cents? Prove your thinking.
The hardware store sells sparklers for the 4th of July. They charge 19 cents a piece. The fireworks stand charges 85 cents for four. Which is the better deal? How can you tell?
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. Which one has less sugar from an ounce of cereal? How can you tell for sure? Prove your answer.
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.
A _______________________ is a ratio that compares two quantities that are measured in different units.
A rate is a ratio that compares two quantities that are measured in different units.
What is Unit Rate?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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if 51,829 is rounded to the nearest thousand, how many zeros will the rounded number have?
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.
Explanation: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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Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. Last year, the hotel served a total of 660 gallons of orange juice to its guests. This year, the hotel served 1,133.2 gallons of orange juice. What is the percent of increase in the amount of orange juice served yearly? Round your answer to the nearest tenth of a percent.
Final answer:
The amount of orange juice served by Sleepwell Hotel increased approximately by 71.7% from last year.
Explanation: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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solve for c
2 ( 2c + 9 ) = c
c = ??
Which of the following statements best represents the relationship between a relation and a function.
1. A function is always a relation but a relation is not always a function.
2. A relation is always a function but a function is not always a relation.
3. A relation is never a function but a function is always a relation.
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.
06.01) Saturday morning there were 7 adults and 20 kids at Pump and Jump Land. The morning cash registers show $236 was collected. In the afternoon there were 21 adults and 50 kids for a total amount of $618. What is the cost for 1 adult?
The cost of 1 adult for the given games using the various parameters to create a simultaneous equation gives; $8
How to create simultaneous equations?
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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what is 7 over (fraction bar) (8×4)+90÷9 ÷ (6^3)^-2 × 9 over (fraction bar) 6(5+4) = ?????
Julian walks a total of 900 meters to work each day. How far does he walk in 10 days
900 * 10 = 9000 meters
9000/1000 = 9 km
a store has all board games on sale for 25% off the regular price. a checker set has a sale price of $12. It is then moved to a clearance table where every item is discounted 40% off its regular price. What is the clearance price of the checker set?
The clearance price of the checker set will be $9.6.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
A store has all tabletop games on special for 25% off the standard cost. A checker set has a deal cost of $12.
Then the regular price of the board games is given as,
⇒ $12 / (1 - 0.25)
⇒ $12 / 0.75
⇒ $16
It is then moved to a leeway table where each thing is limited to 40% off its normal cost.
Then the clearance price of the checker set will be given as,
⇒ (1 - 0.40) x $16
⇒ 0.60 x $16
⇒ $9.6
The freedom cost of the checker set will be $9.6.
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write an equation in slope -intercept form of the line through point p(6,-1) with slope 4
15 is 25% of the what number?
Which of the following numbers is irrational ??please help !!
how can you decide if finding common multiples and common factors is helpful in solving a problem?explain.
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)?
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.
Help with number 9 please!asap
in a typical wimbledon,42,000 balls are used and 650 matches are played.about how many balls are used per match
divide number of balls by number of matches
42,000 / 650 = 64.615 = 65 balls per match
Machine A produces 500 items per hour. Machine B produces 400 items per hour. Working together, the two machines produce 2250 items in t hours. Which equation can be used to find the value of t?
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.
Explanation: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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Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best represents Monica's income for the week?
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.
What is the unitary method?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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A cell phone service provider offers two plans. Plan A includes a fee of $25 per month and charges $0.25 for every call. Plan B includes a fee of $40 per month and offers unlimited calls. For what number of phone calls is the cost of plan B less than the cost of plan A?
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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Ms. Posillico shoes are in ratio of 6:2:3:4; Wedges, Stilettos, Sneakers, Sandals respectfully. She owns 18 pairs of wedges. How many pairs of shoes does she own? (Show your work)
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.
−13π/5 find the reference angle
At one time, the Texas Junior College Teachers Association annual conference was held in Austin. At that time a taxi ride in Austin was $1.15 for the first 1/5 of a mile and $0.35 for each additional 1/5 of a mile. If the distance from one of the convention hotels to the airport is 8.5 miles, how much will it cost to take at taxi from that hotel to the airport? (Round your answer to the nearest cent.)
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:
The initial fare covers the first 1/5 mile and costs $1.15.Since the total trip is 8.5 miles, we need to find out how much the remaining 8.3 miles (8.5 miles - 1/5 mile) will cost at $0.35 per each additional 1/5 mile.To find the number of 1/5 mile increments in 8.3 miles, we divide 8.3 by 1/5, which equals 41.5 increments.Now we multiply the number of increments (41.5) by the cost per increment ($0.35), which equals $14.525.Adding the initial fare of $1.15 to $14.525 gives us the total cost of the taxi ride, which is $15.675.Finally, we round $15.675 to the nearest cent to get $15.68 as the total cost of the ride.Therefore, the taxi fare from the hotel to the airport will be $15.68.