The time 'x' that both Harper and Liam are running for is 0.25 hours. This is calculated by setting the total distance covered by both runners equal to each other and solving for 'x'.
Explanation:The subject of your question is Mathematics, specifically dealing with concepts of race pacing and distance calculations. Here's an answer to your question:
Let's denote the time it takes for both Harper and Liam to finish the race as 'x' hours. Given that Liam runs at 4 miles per hour and has a 0.25-mile head start, the total distance he runs is 4x + 0.25 miles. Harper, on the other hand, runs at 4.5 miles per hour (0.5 mile per hour faster than Liam) for 'x' hours, so Harper runs a total of 4.5x miles.
Since both runners run the same total distance, we can set these two equations equal to each other and solve for 'x':
4x + 0.25 = 4.5x
Solving this equation gives x = 0.25 hours.
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solve for c
2 ( 2c + 9 ) = c
c = ??
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.
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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−13π/5 find the reference angle
Solve the two-step equations.
1. k-3/4 = 10
2. z+5/7 = -3
3. 9+t/12 = -3
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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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.
write an equation in slope -intercept form of the line through point p(6,-1) with slope 4
Dilation of 1.5 j (-1,-1 ) u(1,3) w(0,-2)
Jasmine bought 7 yards of fabric. The total cost was $45.43. What was the average cost per yard of the fabric she bought?
Answer: $6.49
Step-by-step explanation:
$45.43 / 7=$6.49
find an equivalent expression to 3 (4m-2)-2(m+5). write your answer as an expression with two terms
Answer:
10m - 16
Step-by-step explanation:
3 (4m-2) -2(m+5)
The equivalent expression can be simplified as an expression with two terms as follows:
3 (4m-2) -2(m+5)
Open each parenthesis by multiplying the outside value with the values in the parenthesis.
3 (4m-2) = 12m - 6
-2(m + 5) = -2m -10
Bring the value together
12m - 6 -2m - 10
collecting like terms
12m -2m - 6 - 10
10m - 16
is (-4, 10) a solution to the equation 10 - 5x=y
What is 10.49 seconds rounded to the nearest second
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.
Therefore: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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how can you decide if finding common multiples and common factors is helpful in solving a problem?explain.
what is 7 over (fraction bar) (8×4)+90÷9 ÷ (6^3)^-2 × 9 over (fraction bar) 6(5+4) = ?????
1713 hours is the same as which of the following times a.7:13 a.m b.5:13 p.m c.7:13 p.m d.5:13 a.m. i pick d.5:13 a.m
Answer:
5:13 pm
Step-by-step explanation:
Since a day has 24 hours and if midnight is 000 hours and noon is 1200 hours you just have to count to 17 and think, or you could count on your fingers, what is the distance between 12 and 17, which is 5, and since it is after noon it is p.m, so 5 pm plus the 13 minutes it is 5:13 p.m.
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
Brad wants to buy flowers for his friend with 45$. The daisies are 1$ each and the roses are 2$ each. He buys 3 more daisies than roses. How much did the roses cost?
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
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
Joesl's father is 45. He is 15 years older than twice joe's age. How old Is joe?
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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Help with number 9 please!asap
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.
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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Ciara brought $240 to spend on gifts for her family. She found 8 identical statues at a gift shop. She had $72 leftover. How much did each statue cost?
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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A square is 8 inches along each side. A rectangle is 6 inches wide and 10 inches long. Which shape has the greater perimeter? Explain.
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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You deposit $200 in an account that earns 5% simple interest. How long will it be before the total amount is $400?