A grocer had 40 crates of tomatoes. Each crate contained 124 tomatoes. She threw away 24 rotten tomatoes and repack the rest into bag of 8 tomatoes each. How many bags of tomatoes were there?
A rectangular prism has a volume of 729ft3. The length, width and height are all the same. What is the length of each side of the prism?
What is the following product?
3 sqrt24 * 3sqrt 45
The product of 3√24 and 3√45 is approximately 295.77.
Explanation:To find the product, we can first simplify the individual square roots.
√24 = √(4 * 6) = 2√6
√45 = √(9 * 5) = 3√5
Substitute the simplified terms: 3 * 2√6 * 3 * 3√5 = 18√30
Factor out a 9: 18√30 = 9 * 2√(10 * 3)
Simplify the remaining square root: 9 * 2√30 ≈ 9 * 2 * 5.477 = 295.77 (rounded to two decimal places).
Therefore, the product of 3√24 and 3√45 is approximately 295.77.
the diagram shows an artificial lake. When Amanda jogged twice around the lake she jogged a distance of 2,700 meters. Find the value of x
Assuming that the attached file is the lake which you are mentioning in the question.
The perimeter is the distance around the lake, we need to set up an equation based on the statement "When Amanda jogged twice around the lake she jogged a distance of 2,700 meters" as below:
[tex] 2(Perimeter \; of\; the\; lake) =2700\\ \\ 2(x+140+x+x+250+x+x+3x)=2700\\ Group \; Like\; Terms\\ \\ 2(x+x+x+x+x+3x+140+250)=2700\\ Combine \; Like\; Terms\\ \\ 2(8x+390)=2700\\ Distribute\; 2\; in\; left\; side\; of\; the\; equation\\ \\ 16x+780=2700\\ Subtract \; 780\; on\; both\; sides\\ \\ 16x+780-780=2700-780\\ Combine \; like\; terms\\\\16x=1920 \\ Divide\; 16 \; on\; both\; sides\\ \\ \frac{16x}{16}=\frac{1920}{16}\\ Simplify\; fraction\; on\; both\; sides\\ \\ x=120 [/tex]
Conclusion:
The value of x is 120 meters
A space shuttle orbits earth at a rate of about 4,375 miles in 15 minutes. At the rate, how far does the space shuttle travel around earth in 1 hour?
Six different ways to show equal groups of 18
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
Answer:
5 roots
Step-by-step explanation:
just did it on edge
The radius of a sphere is increasing at a rate of 5 mm/s. how fast is the volume increasing when the diameter is 60 mm? evaluate your answer numerically. (round the answer to the nearest whole number.)
The rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].
According to the question, the radius of a sphere is increasing at a rate of [tex]5 mm/s[/tex] and the diameter is [tex]60 mm[/tex].
The volume of the sphere is, [tex]V=\dfrac{4}{3}\pi r^3[/tex] where, [tex]r[/tex] is the radius of the sphere.
Differentiate the volume of the sphere both sides with respect to [tex]t[/tex] as-
[tex]\dfrac{dV}{dt}=\dfrac{4\pi}{3}\dfrac{dr^3}{dt}\\\dfrac{dV}{dt}=\dfrac{4\pi}{3}\times 3r^2\dfrac{dr}{dt}\\\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}[/tex]
The radius of the sphere is-
[tex]r=\dfrac{60}{2}\\r=30mm[/tex]
Substitute the value of the parameter as-
[tex]\dfrac{dV}{dt}=4\pi\times (30)^2\times 5\\\dfrac{dV}{dt}=62.8\times 900\\\dfrac{dV}{dt}=56520\;\rm{mm/sec}[/tex]
Hence, the rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].
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without graphing decide whether the system of linear equations below has one solution, no solution, or infinitely many solutions. y=3x-8. 4y=12x-5
Answer:
B. no solution
Step-by-step explanation:
Multiplying the first equation by 4 gives ...
4y = 12x -32
This is inconsistent with the second equation, ...
4y = 12x -5
There can be no common point on these parallel lines, hence no solution.
Answer:
You will revise your narrative, indicating four instances in which you have added adjectives and/or adverbs.
You will also submit a reflection paragraph.
View the grading rubric as you complete your assignment. This is your guide to a super submission.
Add adjectives and adverbs. Mark your new additions with an (Adj) or (Adv).
Make other revisions suggested in your Discussion-Based Assessment.
Write a reflection paragraph discussing changes you made during the revision process. Explain how you feel these changes improved your narrative.
Submit your (1) final draft and your (2) reflection paragraph.
Save your work to your computer or drive.
Submit your work in 03.10 Kick It Up a Notch.
Step-by-step explanation:
if the area of a rectangle is 42 feet. what could be possible lengths and widths of the rectangle? 42=__×___
PLEASE HELP!!!!
Which is the following best describes the graph below?
A. it is many-to-one function
B. it is a function but it is not one to one.
C. it is a one to one function
D. it is not a function
Solution:
we are given with a graph and we have been asked to find Which of the given options best describes the graph ?
As we know from the vertical line test of a function that a curve reprsents a function , if we draw a vertical line and that line intersect that curve only once.
If that vertical line interscet the given curve more than once it mean that curve does not represent a function.
Here for the given curve if we will draw any vertical line, that line will intersect it more than once.
Hence the given curve does not represent a fimction.
Hence the correct option is D.
movie mania charges a subscription fee of $30 and an additional fee of 5 per movie
Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?
The width of the porch is 5 feet and the length is 10 feet. The perimeter of the porch is 30 feet.
Explanation:To find the perimeter of the porch, we first need to find the dimensions of the porch. Let's assume the width of the porch is x feet. According to the problem, the length of the porch is two times the width, so the length would be 2x feet. Since the area of the porch is 50 square feet, we can set up the equation: x * 2x = 50. Simplifying this equation, we get 2x^2 = 50. Divide both sides by 2 to isolate x^2: x^2 = 25. Taking the square root of both sides, we find that x = 5. Therefore, the width of the porch is 5 feet and the length is 2 * 5 = 10 feet.
To find the perimeter, we use the formula: perimeter = 2 * (length + width). Substituting the values, we get perimeter = 2 * (10 + 5) = 2 * 15 = 30 feet. So, the perimeter of the porch is 30 feet.
Identify the graph that displays the altitude of a skydiver as he is taken up in a plane and then jumps.
Answer:
A is your answer
Graph Below
Lesson 8 homework practice solve percent problems
To solve percent problems, we can use equivalent fractions, cross-multiply, solve for the unknown, or convert percent to a fraction and simplify. In context, a 24% positive rate among students indicates that 24 out of every 100 students are positive.
Explanation:In mathematics, specifically in percentage calculation, there are several methodologies to solve problems. One very common way, as mentioned in the reference material, is by setting up equivalent fractions with 100 as the denominator, and cross-multiplying. For example, if you have the fraction 9/37 representing some scenario (like 9 successful attempts out of 37), you can set up an equation like 9/37 = x/100, where 'x' is the equivalent percentage. Cross-multiply and solve for 'x' to get x = (9/37) * 100, giving you the percentage.
Also, note that a percent can be converted to a fraction by writing the value of the percent as a fraction with a denominator of 100. Simplify the fraction, if possible.
In context, if 24% of students are positive, that means for every 100 students, 24 would be positive. If only 70 are surveyed, then (24/100)*70 = 16.8 students, but since we can't have a part of a student, we would round it to 17 students are positive for this sample size.
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Tomas created a function table using the equation y = x + 4. Which table is correct?
find the probability of getting a king then an eight. Assume the cards are not replaced?
The perimeter of a rectangle is 12 inches. If the length and width are whole numbers, what are the least and greatest possible areas?
Answer:
5in and 9in
Step-by-step explanation:
ANSWER FAST 15 PTS
What is the length of PQ?
JKLM : PQRS
12 km
16 km
18 km
20 km
Answer:
20 KM
Step-by-step explanation:
God bless!!!
Answer: 20 Km
Step-by-step explanation: I did the assignment (Similar Polygons)
Pierce wishes to purchase a municipal bond with a par value of $500 from Arapahoe County, and he is trying to decide which broker he should employ to purchase the bond. Broker A charges a 3.1% commission on the market value of each bond sold. Broker B charges a flat $24 for each bond sold. If the bond has a market rate of 88.754, which broker will give Pierce the better deal, and by how much?
Answer:
Since the given problem statement and data is
Manicipal bond with par value=$500
commission rate =3.1%
charges of broker B=$24
bond market rate=$88.754
hence from the given data Broker A charges a 3.1% commission on the market value of each bond sold is a better deal.
Scientist determine that Antarctica average winter temperature was 34.44 Celsius the difference between the temperature and Antartica highest record temperature was 49.44 degrees what was the highest record temperature
Karina read a total of 20 2/4 pages in her science and social studies books combined she read 12 3/4 pages in her science book how many pages did she read in her social studies book?
Final answer:
To find out how many pages Karina read in her social studies book, you subtract the number of pages read in the science book from the total pages read. After doing the math, Karina read 8 1/4 pages in her social studies book.
Explanation:
Karina read a total of 20 2/4 pages in both her science and social studies books combined. It is mentioned that she read 12 3/4 pages in her science book. To find out how many pages she read in her social studies book, one must subtract the pages read in the science book from the total pages read.
The subtraction of mixed numbers involves the following steps:
First, make sure the fractions have the same denominator.
Then, subtract the fractions.
If necessary, borrow from the whole number and reduce the fractions further.
Finally, subtract the whole numbers.
In this case:
Total pages - Science book pages = Social Studies book pages
20 2/4 - 12 3/4 = 7 5/4 or 8 1/4 pages (since 5/4 is equal to 1 and 1/4).
Therefore, Karina read 8 1/4 pages in her social studies book.
Find the product of (4x − 3)(2x2 − 7x + 1).
On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t^2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is _______ feet
In playing Monopoly, rolling doubles three times in a row sends you to jail. What is the probability of rolling three consecutive doubles? a. 0.167 b. 0.5 c. 0.00463 d. 18.0
Answer:c 0.00463
Step-by-step explanation:
1/6×1/6×1/6=1/216
In a basic sine curve, where can the zeros NOT be found?
a. middle
b. beginning
c. maximum point
d. end
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we know that
[tex]f(x)=\sin x[/tex]
It is an odd function.
It has a period of 2π because the sine wave repeats after every 2π units.
It value lies between -1 and 1.
And we know that
[tex]\sin 0^\circ=0^\circ[/tex]
And 0 occurs exactly middle of -1 and 1.
So, the zeroes can be found in the middle, beginning and at the end.
But at maximum point, there will be no zero.
As when it attains its maximum point, it won't touch x-axis.
Hence, Option 'C' is correct.
robert ordered 11 pizzas for a pizza party for the softball team. when he ordered the pizzas, he told members they could each eat 3/5 of a pizza. if each person gets 3/5 of a pizza, how many people can eat this much pizza at the party
Final answer:
18 people can eat 3/5 of a pizza, with a little pizza left over.
Explanation:
To find out how many people can eat 3/5 of a pizza at the party, we need to divide the total number of pizzas by the fraction each person can eat.
Number of people who can consume 3/5 of a pizza = Total pizzas / (3/5)Number of people = 11 / (3/5)Number of people = 11 / (3/5) = 11 * (5/3) = 55/3 = 18.33Therefore, approximately 18 people can eat 3/5 of a pizza at the party.
write each fraction in simplest form. if the fraction is already in simplest form, write simplified
A.
[tex] \ \frac{4}{14} [/tex]
B.
[tex] \frac{15}{20} [/tex]
C.
[tex] \frac{21}{35} [/tex]
Answer:
4/14 = 2/7
15/20 = 3/4
21/35 = 3/5
Step-by-step explanation:
Formulate a decision model to determine whether there are any arbitrage opportunities with the spot currency rates given in table 1. note that an arbitrage opportunity could involve several currencies. if there is an arbitrage opportunity, your model should specify the exact set of transactions to achieve it. to us dollar pound ffranc dmark yen us dollar - 0.63900 5.37120 1.57120 98.8901 pound 1.56480 - 8.43040 2.45900 154.7733 from ffranc 0.18560 0.11860 - 0.29210 18.4122 dmark 0.63610 0.40630 3.42330 - 62.9400 yen 0.01011 0.00645 0.05431 0.01588 - table 1: cross-currency spot rates
Final answer:
To determine if there's an arbitrage opportunity, convert an amount through various currencies in the table and see if you end with more than you started. If more is ended up with, there's an opportunity, specifying the currencies and transactions. If not, the market is in equilibrium, and rates will adjust to prevent arbitrage.
Explanation:
To identify an arbitrage opportunity within the given spot currency rates, one must find a sequence of exchanges that results in more currency than initially started with, after accounting for the currency exchange rates in table 1. The decision model for discovering an arbitrage opportunity typically involves converting an amount from one currency to another across several pairs and ending up with more than one started with in the original currency. The following steps outline the process to determine if arbitrage is possible:
Start with a denomination of one currency (e.g., $1).
Convert this amount into another currency using the provided spot rates.
Repeat the conversion process for subsequent currencies.
Finally, convert back to the original currency.
If the final amount is greater than the starting amount, an arbitrage opportunity exists. In such a scenario, the model should indicate the currencies involved and the specific transactions to execute the arbitrage. However, if no sequence of transactions results in profit, then no arbitrage opportunity is present given the rates provided. The absence of arbitrage ensures that the markets are in equilibrium, and the exchange rates will adjust to eliminate any potential for arbitrage as per the efficient market hypothesis.
He radius r of a circle is increasing at a rate of 6 centimeters per minute. find the rate of change of the area when r = 35 centimeters. cm2/min
The rate of change of the area when the radius is 35 centimeters is 420π cm2/min.
Explanation:To find the rate of change of the area, we can use the formula for the area of a circle: A = πr2. We are given that the radius (r) is increasing at a rate of 6 centimeters per minute. We need to find the rate of change of the area when r = 35 centimeters.
First, differentiate the area formula with respect to time (t) using the chain rule:
dA/dt = 2πr(dr/dt)
Substitute the given values into the formula: dA/dt = 2π35(6) = 420π cm2/min.
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The rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.
Explanation:The subject of this question is related to the rate of change in the context of a circle's area, which is a topic in calculus. Given that the radius r of a circle is increasing at a rate of 6 centimeters per minute, we are to find the rate of change of the area when r = 35 centimeters.
The area A of a circle is given by the equation A = πr². If we differentiate this equation with respect to time t, we get dA/dt = 2πr(dr/dt). We know that dr/dt, the rate of change of the radius, is 6 cm/min. Substituting r = 35 cm and dr/dt = 6 cm/min into the derivative equation, we get dA/dt = 2π*35*6 = 420π cm²/min.
So, the rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.
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