The unit rate is calculated by dividing the total quantity by the total number of units. In this case, it takes 4 minutes to fill the aquarium to a depth of 2/5 meters. So, the unit rate for filling the aquarium is 10 minutes per meter.
Explanation:To calculate the unit rate, you divide the total quantity by the total number of units. In this case, it takes 4 minutes to fill the aquarium to a depth of 2/5 meters. So, for the unit rate in minutes per meter, you would set up the division as follows:
4 minutes / (2/5) meters
When you divide 4 by 2/5, you actually multiply 4 by the reciprocal of 2/5, which is 5/2.
So, 4 * (5/2) = 10
Therefore, the unit rate for filling the aquarium is 10 minutes per meter.
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What is the slope of the line that contains these points?
x -4, 1, 6, 11
y -3,-2,-1,0
Answer:
slope = 1/5
Step-by-step explanation:
[tex]\frac{0-(-3)}{11-(-4)} =\frac{3}{15} =1/5[/tex]
What is the difference of (Negative 3.4 x + 4.7) minus (3 + 2.9 x)?
Negative 0.5 x + 1.7
Negative 6.3 x minus 1.7
Negative 0.5 x minus 1.7
Negative 6.3 x + 1.7
Answer:
A.-0.5x+1.7
Step-by-step explanation:
-3.4x+4.7-3+2.9x
-0.5x+1.7
Answer:
-0.5x+1.7
Step-by-step explanation:
What is the distance between the coordinates (5,5) and (7,2)? Round your
answer to the nearest tenth.
Answer:
4
Step-by-step explanation:
when you write them down and draw a diaganal line from 7,2 to 5,5 it passes 4 intersections, so it would be 4 units. When you round if it is 4 or less it stays the same and if it is 5 or more then it changes so it would still be 4.
Stay Safe
find the radius of a discus woth a circumference 8.6 pi inches
Answer:
4.3π or 13.51 = r
Step-by-step explanation:
C=2πr To find the circumference of a circle, you must have the formula
8.6π = 2πr Substitute the C for 8.6π
4.3π = r Divide both sides by 2π
13.51 = r Simplify 4.3π if needed
146+8 1/5
How do I solve this
Step-by-step explanation:
[tex]146 + 8 \frac{1}{5} \\ \\ = 146 + \frac{8 \times 5 + 1}{5} \\ \\ = \frac{146 \times 5 + 40 + 1}{5} \\ \\ = \frac{730 + 41}{5} \\ \\ = \frac{771}{5} \\ \\ = 154 \frac{1}{5} \\ \\ thus \\ \\ \huge \orange{ \boxed{146 + 8 \frac{1}{5} = 154 \frac{1}{5}}}[/tex]
A cylinder has a height of h meters, and the base has a radius of 7 meters. If the volume of the cylinder is 539π find the height
Answer:
Therefore,
The Height of Cylinder is 11 meters.
Step-by-step explanation:
Given:
Cylindrical Shape
Radius = r = 7 meter
Volume of Pipe = 539π
To Find:
Height = ?
Solution:
Formula for Volume of Cylinder is given by
[tex]\textrm{Volume of Cylinder}=\pi (Radius)^{2} \times Height[/tex]
Substituting the given values we get
[tex]539\pi=\pi(7)^{2}\times Height\\\\Height=\dfrac{539}{49}=11\ meter[/tex]
Therefore,
The Height of Cylinder is 11 meters.
A pitcher struck out 11 out of 40 batters. Write an equivalent decimal.
Answer:
0.275
Step-by-step explanation:
We want to write 11 out of 40 batters as a decimal.
We can write 11 out of 40 as a fraction to get:
[tex] \frac{11}{40} [/tex]
Note that:
[tex] \frac{11}{40} = \frac{1}{4} \times \frac{11}{10} [/tex]
This implies that:
[tex] \frac{11}{40} = 0.25 \times 1.1[/tex]
This gives us
[tex] \frac{11}{40 } = 0.275[/tex]
Warm up your day with a easy math problem! Which quantity is proportional to 35⁄80?
Comment all that are true.
A. 3⁄5
B. 14⁄36
C.26⁄52
D.21⁄48
E. 7⁄16
D and E are the only ones true.
Answer:
E
Step-by-step explanation:
You simplify the fraction by dividing both top and bottom by 5
35÷5=7
80÷5=16
Solve the following by using mathematical Induction. For >/ 1
1^2+2^2+3^3+......+ n^2 = 1/6 n(n+1)(2n+[)
Answer:
See explanation
Step-by-step explanation:
Prove that
[tex]1^2+2^2+3^3+...+n^2=\dfrac{1}{6}n(n+1)(2n+1)[/tex]
1. When [tex]n=1,[/tex] we have
in left part [tex]1^2=1;[/tex] in right part [tex]\dfrac{1}{6}\cdot 1\cdot (1+1)\cdot (2\cdot 1+1)=\dfrac{1}{6}\cdot 1\cdot 2\cdot 3=1.[/tex]2. Assume that for all [tex]k[/tex] following equality is true
[tex]1^2+2^2+3^3+...+k^2=\dfrac{1}{6}k(k+1)(2k+1)[/tex]
3. Prove that for [tex]k+1[/tex] the following equality is true too.
[tex]1^2+2^2+3^3+...+(k+1)^2=\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)[/tex]
Consider left part:
[tex]1^2+2^2+3^2+...+(k+1)^2=\\ \\=(1^2+2^2+3^3+...+k^2)+(k+1)^2=\\ \\=\dfrac{1}{6}k(k+1)(2k+1)+(k+1)^2=\\ \\=(k+1)\left(\dfrac{1}{6}k(2k+1)+k+1\right)=\\ \\=(k+1)\dfrac{2k^2+k+6k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+7k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+4k+3k+6}{6}=\\ \\=(k+1)\dfrac{2k(k+2)+3(k+2)}{6}=\\ \\=(k+1)\dfrac{(k+2)(2k+3)}{6}[/tex]
Consider right part:
[tex]\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)=\\ \\\dfrac{1}{6}(k+1)(k+2)(2k+3)[/tex]
We get the same left and right parts, so the equality is true for [tex]k+1.[/tex]
By mathematical induction, this equality is true for all n.
One side of a triangle is 2 times the second side. The third side is 5 feet longer than the second side. The perimeter of a triangle is 81 feet. Find the length of each side.
Answer:
The length of the side of the triangles are;
First side = 38 ft
Second side = 19 ft
Third side =24 ft
Step-by-step explanation:
To solve the question we are going to take;
Second side is x ft
Since, the first side is 2 times the second side then;
First side of the triangle is 2x ft
Since the third side is 5 ft less than the second side, then;
The third side is (x+5) ft
But, the perimeter of the triangle is 81 ft
Perimeter of a triangle is given by the sum of sides;
Therefore;
x + 2x +(x +5) = 81 ft
4x + 5 = 81
4x = 76
x = 19 ft
Therefore;
Second side = 19 ft
First side = 38 ft
Third side = 24 ft
8904 divided by 21 long dividion
Answer:424
Step-by-step explanation:
2x246-2x3-194 add brackets to make the question right.
Answer:
(2*246)-(2*3)-194=492-6-194=292
Step-by-step explanation:
Shira has 20 books on her bookshelf. Of those 15 are about horses, the rest are nature books. What fraction of Shiras books are about nature.
Answer:
1/4
Step-by-step explanation:
15 out of the 20 books are horses. 5 of those are nature. 5/20 is the fraction, but can be simplified to 1/4
Shira has 5 out of 20 books about nature on her bookshelf, which simplifies to a fraction of 1/4 of her books being about nature.
Explanation:Shira has 20 books in total on her bookshelf. Out of these, she has 15 books about horses, meaning the remaining books are about nature.
To find the fraction that represents the nature books, we need to subtract the number of horse books from the total number of books.
So, the number of nature books is 20 total books - 15 horse books = 5 nature books. The fraction of books about nature would therefore be the number of nature books divided by the total number of books, which is 5/20.
This fraction can be simplified by dividing both the numerator and the denominator by 5, resulting in 1/4. Therefore, 1/4 of Shira's books are about nature.
List 3 rational numbers between 3 and 3.9
The number are "3.4, 3.7, and 3.8"
Rational numbers:List of number 3 rational numbers in 3 and 3.9.
The number sequence has the form a/b, where a and b are integers, and b is not equivalent to 0.As there were numerous quantities or measures that numerals alone could not effectively explain, rational numbers were required. The most typical application of rationals is the measurement, either of length, mass, time, or whatever.Therefore the number are "3.4, 3.7, and 3.8".
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Final answer:
Three rational numbers between 3 and 3.9 are 3.2, 3.3, and 3.6.
Explanation:
To list 3 rational numbers between 3 and 3.9, we can consider the numbers that lie between these two values.
We can start by looking for numbers with a tenths place greater than 3 but less than 9.
To find three rational numbers between 3 and 3.9, we simply need to choose numbers that have a finite number of digits after the decimal point.
Some examples of rational numbers in this range are 3.2, 3.3, and 3.6.
These satisfy the condition of being between 3 and 3.9.
What is larger? -1 or -4/3
Answer:
-4/3
Step-by-step explanation:
-4/3 is equal to -1 1/3 which is greater than just -1
Answer: -1 is ;larger
pls help me for part A and B if correct I will mark brainslit :)) !!
Answer:
answer choice b is the correct answer
Step-by-step explanation:
5/8 times 2 1/2
1 3/4
1 3/4 > 1 1/4
for every $50 of candy you sell, you get to keep 7% of it. how much commission do you make if you sell $200 worth of candy?
You'll make 14 dollars.
7% of 50 is 3.5.
If you add 3.5 four times you'll get 14.
200 - 7% is 186.
200 - 14 is 186.
Answer:
$14
Step-by-step explanation:
Well, first find 7% of 50. To do this you need to make the percent a decimal by moving the decimal that is already(7 is the whole number, if there were any fractions it would be 7.00%) there two space to the left, adding zeros as needed.
0.07 x 50 = x
3.5 = x
Now you can multiply it by whatever you want. In this case it would be 4 since 50 time 4 is 200.
3.5 x 4 = 14
So the amount of money that you would make would be $14.
Hope this helped you out.
what is 738 divided by 13 in fraction form
Answer:
56.76923076...
Step-by-step explanation:
738 divided by 13 should be [tex]\frac{738}{13}[/tex] as an improper fraction.
As a mixed fraction, it is: [tex]56\frac{10}{13}[/tex]
And as a decimal it is approximately 56.769
I did this problem on a calculator after doing some written work on it.
What is 5(z+4) + 5(2-z) simplified?
Answer: 30
Step-by-step explanation:5(Z+4) + 5(2-Z).
Open the brackets by multiplying true by the number out of the bracket.
5Z + 20 + 10 - 5Z
Now, collect like terms, we have.
5Z - 5Z + 20 + 10. Now we have
0 + 30 = 30//
A water pipe floods 50 square feet every 1/5 minute.what is the flooded area after 6 minutes
Final answer:
To find the flooded area after 6 minutes, calculate the number of 1/5-minute intervals in 6 minutes, which is 30. Then, multiply by the area flooded in each interval. The flooded area after 6 minutes would be 1500 square feet.
Explanation:
The question is asking to calculate the area that would be flooded by a water pipe after 6 minutes, given that the pipe floods 50 square feet every 1/5 of a minute. To find the answer, we need to determine how many 1/5-minute intervals are in 6 minutes, and then multiply that number by the area flooded in each interval.
First, calculate the number of intervals: 6 minutes × (5 intervals/minute) = 30 intervals.
Next, multiply the number of intervals by the area flooded per interval: 30 intervals × 50 square feet/interval = 1500 square feet.
Therefore, after 6 minutes, the flooded area would be 1500 square feet.
The box plots below show the ages of college students in different math courses.
A box-and-whisker plot labeled Math 1 is shown. The number line goes from 16 to 22. The whiskers range from 17 to 21, and the box ranges from 18-20. A line divides the box at 19. A box-and-whisker plot labeled Math 2 is shown. The number line goes from 16 to 24. The whiskers range from 17 to 23, and the box ranges from 18-20. A line divides the box at 19.
Math 1 Math 2
Which statement is true?
The median age of the students in Math 1 is greater than the median age of the students in Math 2.
The median age of the students is Math 1 is less than the median age of the students in Math 2.
The mean and median age are most likely the same for both sets of data.
The mean and median age are more likely to be the same for the students in Math 1.
Answer:
The correct option for this is C.) The mean and median age are more likely to be the same for the students in Math 1.
Step-by-step explanation:
i) The median age of the students is Math 1 is less than the median age of the students in Math 2.
This statement is NOT TRUE as the median age of students in Math 1 = median age of students in Math 2 = 19
ii) The mean and median age are most likely the same for both sets of data.
This statement is NOT TRUE. The mean age of students in Math 2 should be greater than mean age of students in Math 1.
iii) The mean and median age are more likely to be the same for the students in Math 1.
This statement is TRUE.
Answer:
The mean and median age are more likely to be the same for the students in Math 1.
Step-by-step explanation:
The median age of the students for the student is Math 1 is less than the median age of the students in Math 2.
The statement is not true as the median age of students in Math 1 is equal to the median age of the students in Math 2 = 19.
Also, the mean and median age are the most likely to be the same for both sets of data.
The above statement is also not true as the mean age of students in Math 2 should be greater than the mean age of students in Math 1.
in an arithmetic series a1= -14 and a5=30 find the sum of the first 5 terms
The sum of the 5 terms in the arithmetic series is 40.
Step-by-step explanation:
Step 1; First we need to determine the three values between a1= -14 and a5=30. The difference between the first and fifth value = 30 - (-14) = 30 + 14 = 44.
Since there are 4 values after a1 we divide the difference by the number of terms, the difference between each term = 44 / 4 = 11. So the difference between each term is 11.
Step 2; To find out the terms we just add the difference to the previous number.
a1 = -14.
a2 = -14 + 11 = -3.
a3 = -3 + 11 = 8.
a4 = 8 + 11 = 19.
a5 = 19 + 11 = 30.
So a1 + a2 + a3 + a4 + a5 = -14 -3 + 8 + 19 + 30 = 40.
The sum of the first 5 terms in this arithmetic series is 40, calculated based on the formulas for an arithmetic series involving the first term, the fifth term, and the common difference.
Explanation:In an arithmetic sequence or series, the difference between each term (the common difference) is constant. We can represent this as: an = a1 + (n - 1) * d, where d is the common difference. Given in this problem that a1 = -14, a5 = 30, and n = 5.
First, we can find the common difference d using the formula: d = (a5 - a1) / (5 - 1) . So, d = (30 - (-14)) / (5 - 1) = 44 / 4 = 11.
Then, we can find the sum of the first 5 terms using the formula: Sn = n / 2 * (2a1 + (n - 1) * d). That gives us: S5 = 5 / 2 * (2(-14) + (5 - 1) * 11) = 5 / 2 * (-28 + 44) = 5 / 2 * 16 = 40.
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Classify the following triangle. Check all that apply.
A. Right
B. Scalene
C. Acute
D. Equilateral
E. Obtuse
F Isosceles
Answer:
A, E
Step-by-step explanation:
I think it is obtuse and scalene, but I don't think that is the only answer. Hope that can help a little.
The triangle is an isosceles and an obtuse triangle.
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of ∠ABC = 120°
So , it is an obtuse triangle with angle > 90°
Now , the measure of sides AB = measure of BC
So , an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base
Therefore , it is an Isosceles obtuse triangle
Hence , the triangle is isosceles
A oth grade student can complete 20 multiplication facts in 1 minute. If he works at the same rate, how long should it
take him to complete 35 multiplication facts? (Type your answer as a decimal number]
minutes
It should take the student 1.75 minutes to complete 35 multiplication facts.
To determine how long it will take the 5th grade student to complete 35 multiplication facts at the same rate as 20 facts in 1 minute, we can set up a proportion or use unit rates. Since the student can complete 20 facts in 1 minute, we find the time per fact by dividing the total time by the number of facts:
1 minute / 20 facts = 0.05 minutes per fact
Then, we multiply the rate by the number of new facts:
0.05 minutes per fact * 35 facts = 1.75 minutes
Therefore, it should take the student 1.75 minutes to complete 35 multiplication facts.
What is diversification?
A. investing in volatile stocks
B. investing in various types of investments
C. investing in low-risk investments
(20 points!!!!!! )
Answer:
b. investing in various types of investments
Step-by-step explanation:
i hope this helps!
brainliest is appreciated... :}
Answer:
1. diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk.
A. Stock market volatility is arguably one of the most misunderstood concepts in investing.
(B i) Stocks.
(ii) Bounds
(III) mutual funds
(iv) index funds
(C). Bank Savings.
Certificates of Deposit (CDs) ...
Treasury Securities. ...
Money Market Accounts. ...
Stable Value Funds. ...
Fixed Annuities. ...
Immediate Annuities
A factory is shipping 9 bicycles to a store. Each bicycle has a mass of 11.6 kg and is packed in a box with a mass of 3.41kg. What is the total mass of all the bicycles and their packing boxes?
Answer:
135.09 kg
Step-by-step explanation:
First, we must determine the total weight of each bicycle including their boxes. To do this, we must add 3.41 kg and 11.6 kg. 3.41 + 11.6 = 15.01.
Next, multiply the weight of one bike and its box to the total amount of bicycles there are. There are 9 bikes, so 15.01*9 = 135.09 kg.
To find the total mass of all bicycles and their boxes, add the mass of one bicycle (11.6 kg) and its box (3.41 kg) to get the total mass for one unit (15.01 kg), and then multiply by the total number of bicycles (9), resulting in a total mass of 135.09 kg.
The total mass of all the bicycles and their packing boxes can be calculated by first determining the mass of one bicycle with its box, and then multiplying that by the total number of bicycles being shipped. The mass of one bicycle is 11.6 kg and the mass of its packing box is 3.41 kg. Adding these together gives us the total mass for one bicycle and its box.
Mass of one bicycle: 11.6 kg
Mass of one box: 3.41 kg
Total mass for one bicycle and its box: 11.6 kg + 3.41 kg = 15.01 kg
This total mass for one bicycle and its box must then be multiplied by the number of bicycles to obtain the total mass for all bicycles and their boxes.
Number of bicycles: 9
Total mass for all bicycles and boxes: 9 * 15.01 kg = 135.09 kg
Therefore, the total mass of all the bicycles and their packing boxes is 135.09 kg.
If a triangle has side lengths 27, 79, and 84 is it a right triangle
Answer:
Nope
Step-by-step explanation:
A right triangle must have a 90 degree angle.
GRADE 8 UNIT 5 LESSON 5 OPEN UP RESOURCES
#3 A car is traveling on a small highway and is either going 55mph or 35mph, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55mph, and y being the time in hours that the car is going 35mph, an equation describing the relationship is:
55x + 35y = 200
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
c. If the car spends no time going 35mph, how long would the trip take?
a. It spends 2.04 hours going 55 mph.
b. It will spend 1 hour going 35 mph.
c. The trip will take 3.64 hours.
Step-by-step explanation:
Given equation is;
55x + 35y = 200
Where
x represent the time when speed is 55 mph
y represent the time when speed is 35 mph
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
Putting y=2.5 in given equation
[tex]55x+35(2.5)=200\\55x+87.5=200\\55x=200-87.5\\55x=112.5\\[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{112.5}{55}\\x=2.04\ hours[/tex]
It spends 2.04 hours going 55 mph.
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
Putting x=3 in given equation
[tex]55(3)+35y=200\\165+35y=200\\35y=200-165\\35y=35[/tex]
Dividing both sides by 35
[tex]\frac{35y}{35}=\frac{35}{35}\\y=1[/tex]
It will spend 1 hour going 35 mph.
c. If the car spends no time going 35mph, how long would the trip take?
Putting y=0 in given equation
[tex]55x+35(0) = 200 \\55x+0=200\\55x=200[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{200}{55}\\x=3.636[/tex]
Rounding off
x = 3.64
The trip will take 3.64 hours
Keywords: linear equation, division
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How do you find a volume of a sphere? Please explain. (Also if you can please someone answer the other questions I asked but it has not been answered.)
Thanks!
Answer:
V = (4/3)πr³
Step-by-step explanation:
The formula usually used to find the volume of a sphere is ...
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
where r represents the radius of the sphere.
The actual math involved will depend on what information about the sphere you are given. If you are given the radius or diameter (twice the radius), then this formula will be directly useful.
To determine the volume of a sphere, use the formula V = ([tex]\frac{4}{3}[/tex])πr³. Measure the radius, cube it, multiply by pi, and then multiply by 4/3.
To find the volume of a sphere, you use the formula:
V = ([tex]\frac{4}{3}[/tex])πr³
Here, V stands for volume, r represents the radius of the sphere, and π (pi) is approximately 3.14159.
Step-by-Step Explanation:
Measure the radius r of the sphere.Cube the radius (multiply it by itself three times): r³.Multiply the cubed radius by π (pi).Multiply the result from step 3 by 4/3.Determine the equation of the linear function that has a slope of -4 and passes through the point (2,-4). Write the equation in slope-intercept form and draw/graph the equation
Answer:
Part 1) [tex]y=-4x+4[/tex]
Part 2) The graph in the attached figure
Step-by-step explanation:
Part 1)
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=-4\\point\ (2,-4)[/tex]
substitute in the linear equation
[tex]-4=-4(2)+b[/tex]
solve for b
[tex]-4=-8+b\\b=8-4\\b=4[/tex]
substitute
[tex]y=-4x+4[/tex]
Part 2) Draw the equation
we know that
To graph a line we need two points
we have the y-intercept (0,4) and (2,-4)
Plot the points, connect them and join to draw the line
see the attached figure