a rectangular prism has 312 cubes. The cubes have an edge length of 1/5 cm. What is the volume of this rectangular prism?
Answers
Answer:
[tex] {( \frac{1}{5}) }^{3} (312) = \frac{312}{125} = 2.496[/tex]
The volume of this rectangular prism is 2.496 cubic centimeters.
The volume of the rectangular prism is 2.496 cubic centimeters.
If the rectangular prism has 312 cubes with an edge length of 1/5 cm, we may calculate the total volume by multiplying the number of cubes by the volume of each cube.
V = x3 gives the volume of a cube with edge length x. Because the edge length, in this case, is 1/5 cm, the volume of each cube is (1/5)3 = 1/125 cm3.
We multiply the number of cubes by the volume of each cube to determine the volume of the rectangular prism:
312 cubes (1/125 cm3/cube) = 2.496cm3 volume
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Related Questions
Use the drawing tool(s) to form the correct answers on the provided graph.
Graph the system of equations given below on the provided graph.
32+y
Then, use the Mark Feature tool to plot the solution to the system.
Drawing Tools
Select
Mark Feature
Line
Click on a tool to begin drawing.
=
-5
10-
80
92
3 Delete
Answers
The solution of the given system of equations is (-3, 4).
Given two linear equations.
2x - 3y = -18
3x + y = -5
Multiplying the first equation by 3 and the second equation by 2,
6x - 9y = -54
6x + 2y = -10
Subtracting the equations,
-11y = -44
y = 4
Substituting,
x = -3
The graph of the system of equations is given below.
Hence the solution is (-3, 4).
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Which statement is true? (1 point)
a
An equilateral triangle is always an isosceles triangle.
b
A right triangle is never an isosceles triangle.
c
An obtuse triangle is sometimes an acute triangle.
d
An isosceles triangle is always a scalene triangle.
Please help!!
Answers
The True statement is An equilateral triangle is always an isosceles triangle.
An equilateral triangle is always an isosceles triangle is True because isosceles triangle have two sides equal and equilateral have three sides equal.
A right triangle is never an isosceles triangle is False statement.
An obtuse triangle is sometimes an acute triangle is False statement.
An isosceles triangle is always a scalene triangle is False statement.
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Evaluate the algebraic expression t + s - r when r=13, s=10, t = 7 and u=15,
A) 2
B) 4
C) 16
D) 30
Answers
Therefore the answer would be B. 4
Which of the following is not a characteristic of both experiments and
surveys?
O A. Data are collected about a population.
B. Subjects should be randomly selected.
OC. The data collected might be studied for patterns.
OD. The researcher exercises direct control over at least one variable.
SUBMIT
Answers
"Data are collected about a population," is not a characteristic of both experiments and surveys. Option A
What is the difference between survey and experiment?A survey is a technique for gathering data about a study variable from the respondents of the population. An experiment is a technique used in science to isolate the problem being examined and test a theory.
Options B, C, and D are characteristics obtained in the case of the experiments and surveys. In both types of research, subjects may be randomly selected (option B), the data collected may be studied for patterns (option C).
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help me please fr i just need these questions
Answers
The base area of the cylinder is 78.54 ft².
The height of the cylinder is 2 ft.
How to find the height and base area of the cylinder?The cylinder has a volume of 157.08 ft cube and the radius of the cylinder is 5 ft.
Therefore, the area of the base of the cylinder can be found as follows:
base area of the cylinder = πr²
base area of the cylinder = 3.1416 × 5²
base area of the cylinder = 3.1416 × 25
base area of the cylinder = 78.54 ft²
Therefore, let's find the height of the cylinder.
volume of the cylinder = πr²h
where
h = height of the cylinder157.08 = 78.54 h
divide both sides by 78.54
h = 157.08 / 78.54
h = 2 ft
Therefore,
height of the cylinder = 2 ft
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K
Let u = 4i-3j, and v= -2i+ 7j. Find u-v.
U-V= (Type your answer in terms of i and j.)
Answers
The value of u -v is 6i - 10j.
We have,
u = 4i-3j, and v= -2i+ 7j.
So, u - v
= (4i - 3j) - (-2i + 7j)
= 4i - 3j + 2i - 7j
= (4i + 2i) + (-3j - 7j)
= 6i - 10j
Thus, the resultant vector is 6i - 10j.
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Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
If one student is chosen at random,
Find the probability that the student was female:
Find the probability that the student was female AND got a "C":
Find the probability that the student was female OR got a "C":
If one student is chosen at random, find the probability that the student was female GIVEN they got a 'C':
Answers
a) The probability that the student was female is 43/76
b) The probability that the student was female AND got a "C" is 9/38
c) The probability that the student was female OR got a "C" is 45/76
We have,
A B C
Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
a) The probability that the student was female
= 43/76
b) The probability that the student was female AND got a "C"
= 18/76
= 9/38
c) The probability that the student was female OR got a "C"
= 43 /76 + 20/76 - 18/76
= 45/76
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The radius of the circle with a central angle of 6 radians that intercepts an arc with
length 53 cm is
____cm.
The radius of the circle with a central angle of 56° that intercepts an arc with length
19 miles is____miles
Answers
We are given that the length of the arc is 53 cm and the central angle is 6 radians. Solving for r, we get:
r = L/θ = 53/6 = 8.833 cm
Therefore, the radius of the circle is 8.833 cm.
For the second question, we need to convert the central angle from degrees to radians. We know that 360° is equal to 2π radians, so 1° is equal to (2π/360) radians, or approximately 0.01745 radians.
The central angle of 56° is equal to 56 x 0.01745 = 0.9772 radians.
We are given that the length of the arc is 19 miles. Using the same formula as before, we get:
r = L/θ = 19/0.9772 = 19.44 miles
Therefore, the radius of the circle is 19.44 miles.
Can u mark my answer as the Brainlyest if it work Ty
What function is represented in the table?
Select one:
y = .5(4^x)
y = 2(.5^x)
y = .5(2^x)
y = 4(.5^x)
Answers
The function that represents in the table is y = 0.5(2^x)
Option C is the correct answer.
We have,
Looking at the table,
We can observe that as the value of x increases, the value of f(x) doubles.
This doubling of f(x) indicates that the base of the exponential function is 2.
Also, when x = 0, the value of f(x) is 0.5, which means that the y-intercept of the exponential function is 0.5.
Thus,
The function can be represented as y = 0.5(2^x).
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A movie theater offers two containers which container is the better value use 3.14 as an approximation for pi 
Answers
Answer:
cylinder
Step-by-step explanation:
You want to know which of two popcorn containers is a better value:
cone: diameter 12 cm, height 19 cm, cost $6.75cylinder: diameter 8 cm, height 15 cm, cost $6.25VolumeThe volume formulas for the two shapes are ...
V = 1/3πr²h . . . . . cone
V = r²h . . . . . . . . . cylinder
RatioFor r = d/2, the ratio of these two volumes is ...
[tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]
The cone has less volume and costs more, so the cylindrical container is the better value.
Exponential model (10,160) (11,250)
Answers
The Exponential model is y = 0.74 (1.79)ˣ
We have,
(10, 160) and (11, 250)
Using the Exponential model
y = abˣ
where a is the initial amount and be is the constant.
Now, the value of b is
= 250/ 140
= 1.79
Now, y = abˣ
140 = a (1.79)⁹
a = 0.74
So, the Exponential model is y = 0.74 (1.79)ˣ
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which expression is equivalent to -16x squared +36 in factored form?
Answers
Expression for -16x squared +36 in factored form is [tex]-4(2x - 3)(2x + 3).[/tex]
The given equation is [tex]-16x^{2} +36[/tex]
simplifying the equation,
[tex]-16x^2 + 36 = 4(-4x^2 + 9)[/tex]
[tex]=-4x^2 + 9\\ = -(2x)^2 + 3^2 \\= -(2x - 3)(2x + 3)[/tex]
when compared together,
[tex]-16x^2 + 36 = 4(-4x^2 + 9) = 4(-(2x - 3)(2x + 3)) = -4(2x - 3)(2x + 3)[/tex]
The expression for the equation in factored form is -4(2x - 3)(2x + 3).
The question is incomplete. complete question will be "which of these expression is equivalent to [tex]-16x^{2} +36[/tex] in factored form?
options- 4(x+2)(3-2x) , -4(2x - 3)(2x + 3) or (4x+2x)(9x-2x)"
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What is the y-intercept of the line of fit?
b=?
m=5
Answers
The y-intercept of the line of best fit is: y = 20
What is the y-intercept?The formula for equation of a line of best fit is:
y = mx + c
where:
m is slope
c is y-intercept
Now, the y-intercept is simply defined as the point where the line crosses the y-axis.
In this case, the line crosses the y-axis at y = 20.
Thus, we can conclude that it is the y-intercept
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NEED HELP I HAVE 20 MIN WILL RATE AND GIVE BRAINLIEST!
Answers
Answer:
A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]
B) [tex]x = \dfrac{\ln(11)}{2}[/tex]
C) [tex]x = \dfrac{11}{5}[/tex]
Step-by-step explanation:
A) We can solve for x by taking log base 6 of both sides.
[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]
[tex]4x - 6 = \log_6(46)[/tex]
[tex]4x = \log_6(46) + 6[/tex]
[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]
B) First, we have to divide both sides by 2.
[tex]2e^{2x} / 2= 22 / 2[/tex]
[tex]e^{2x} = 11[/tex]
Then, we can solve for x by taking the natural log (log base e) of both sides.
[tex]\ln(e^{2x})= \ln(11)[/tex]
[tex]2x= \ln(11)[/tex]
[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]
C) We can solve for x by raising 2 to the power of each side.
[tex]2^{\log_2(5x + 5)} = 2^4[/tex]
This cancels the log base 2 on the left.
[tex]5x + 5 = 16[/tex]
[tex]5x = 11[/tex]
[tex]\boxed{x = \dfrac{11}{5}}[/tex]
I heard you might have to increase your prices by 12% if i normally pay $45 per order, how much would my order be if the price increse happens?
Answers
The order will be $50.4 with the price increase
How much would the order be with the price increase?From the question, we have the following parameters that can be used in our computation:
Order = $45
Percentage increase = 12%
Using the above as a guide, we have the following:
New order = Order * (1 + Percentage increase)
Substitute the known values in the above equation, so, we have the following representation
New order = 45* (1 + 12%)
Evaluate
New order = 50.4
Hence, the new order is $50.4
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if det [a 10 e b d 0] = [2 10 3 6 -1 0],find a,d and e
Answers
Answer:
The given equation is:
det [a 10 e b d 0] = [2 10 3 6 -1 0]
The determinant of a 3x3 matrix is calculated as follows:
|a b c|
|d e f| = a(ei - fh) - b(di - fg) + c(dh - eg)
Applying this formula to the given matrix, we get:
det [a 10 e b d 0] = a(d0 - b-1) - 10(ed - b0) + e(10*-1 - d*3)
= ab + 10b - 10ed - 3e
Substituting the given values, we get:
ab + 10b - 10ed - 3e = 2(6-0) - 10(3-(-1)) + 3(10-(-1))
ab + 10b - 10ed - 3e = 12 + 40 + 33
ab + 10b - 10ed - 3e = 85
We can simplify this equation by factoring out b and e:
b(a + 10) - e(10d + 3) = 85 - 10b
We can solve for a, d, and e by setting up a system of equations using the given values of the determinant:
ab + 10b - 10ed - 3e = 85
From this equation, we can solve for b:
b(a + 10) - e(10d + 3) = 85 - 10b
Substituting the value of b from the determinant equation, we get:
(a+10)(-1) - e(10d+3) = -8.5
Simplifying, we get:
-a - 10e - 3.3d = -8.5 ...(1)
Also, from the determinant equation, we have:
6a + 10d + 3e = 29
Solving for e in terms of a and d, we get:
e = (29 - 6a - 10d)/3 ...(2)
Substituting equation (2) into equation (1), we get:
-a - 10[(29 - 6a - 10d)/3] - 3.3d = -8.5
Simplifying and multiplying both sides by -3, we get:
3a + 20d - 29e = 25.5
Substituting equation (2) into this equation, we get:
3a + 20d - 29[(29 - 6a - 10d)/3] = 25.5
Simplifying, we get:
a + 6d - 29 = 1.5
a + 6d = 30.5
We have two equations in two variables:
-a - 10e - 3.3d = -8.5
a + 6d = 30.5
Solving for a and d using any method (substitution, elimination, etc.), we get:
a = 7
d = 4
Substituting these values into equation (2), we get:
e = (29 - 6a - 10d)/3 = (29 - 6(7) - 10(4))/3 = -3
Therefore, a = 7, d = 4, and e = -3.
Step-by-step explanation:
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
Answers
Answer:
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Step-by-step explanation:
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.
The amount of tickets is given as,
Ticket's amount = 3 x $13
Ticket's amount = $39
Then the amount spent on snacks is given as,
Snack's amount = 4 x $5
Snack's amount = $20
Then the total amount is given as,
Total amount = $39 + $20
Total amount = $59
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
PLEASE HELP (WILL GIVE BRAINLIEST
Answers
Answer:
A. V = 81π(7.25) = 1,844.90 cubic inches
V = 81(3.14)(7.25) = 1,843.97 cubic inches
B. Let p be the number of cans of paint.
1,843.97p = 10,000, so p = 5.42
Jessie will need 6 cans of paint.
C. Area of each storage area = π(9.5^2) = 283.53 square inches. Using 3.14 for π, this area is (3.14)(9.5^2) = 283.385 square inches. The base area of each paint can is 81π = 254.46 square inches (254.34 square inches if we use 3.14 for π). Jessie can't use the carrier because the area of each storage area exceeds the base area of each paint can.
3.
You have two credit cards. If you budget $375 to pay off your credit card debt and you payoff the highest interest card first while maintaining the interest accrued on the other card, how many months does it take you to pay it off?
Card Name (APR %) Existing Balance Credit Limit
Murk (5.6%) $675.49 $1,500.00
Mini (9.85%) $902.43 $1,000.00
5 months
2 months
4 months
3 months
Answers
It takes A. 5 months to pay off (Mini) the highest interest card.
How many months to pay off the highest interest card debt?To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.
First, calculate interest accrued on each card per month:
Murk: (5.6/100)/12 * $675.49 = $2.98 per month
Mini: (9.85/100)/12 * $902.43 = $7.42 per month
Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.
This should be a percentage of the balance.
Assuming it's 2% of the balance, which is $13.51.
So, in month 1, we will pay:
Mini: $375
Murk: $13.51
Leaving these balances:
Murk: $675.49 + $2.98 - $13.51 = $664.96
Mini: $902.43 - $375 + $7.42 = $534.85
In month 2:
Mini: $534.85 + $7.42 = $542.27
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $664.96 + $2.98 - $16.49 = $651.45
Mini: $542.27 - $375 + $7.42 = $174.69
month 3:
Mini: $174.69 + $7.42 = $182.11
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $651.45 + $2.98 - $16.49 = $638.94
Mini: $182.11 - $174.69 + $5.52 = $12.94
month4:
Mini: $12.94 + $7.42 = $20.36
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $638.94 + $2.98 - $16.49 = $625.43
Mini: $20.36 - $12.94 + $0.54 = $8.96
month 5:
Mini: $8.96 + $7.42 = $16.38
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $625.43 + $2.98 - $16.49 = $612.92
Mini: $16.38 - $8.96 = $7.42
So, Mini's balance is paid off here.
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Note:
And we can allocate the entire $375 budget to Murk.
This means we will pay off Murk in month 6:
Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39
What is the solid formed when rotated around the side length of 4?
O cylinder with a height of 3 units and a radius of 4 units
O cone with a height of 4 units and a radius of 3 units
cylinder with a height of 3 units and a radius of 5 units
O cone with a height of 5 units and a radius of 4 units
Find the volumes and surface areas of the solids. Give your answers in terms of .
Surface Area: square units
Volume: cubic units
Answers
Answer: B: cone with a height of 4 units and a radius of 3 units
Step-by-step explanation:
Surface Area: 9pi + 15pi = 24pi square units
Volume: 9pi x 4 x 1/3 = 12pi cubic units
How do I find the quadratic formula?
Answers
Answer:
x = -31 maybe
Step-by-step explanation:
The functions s and t are defined as follows. s (x) ニーx+5 t(x) =2x+2 Find the value of t (s (2)).
Answers
The value of the composite function t(s (2)) is 8
Finding the value of the composite function t(s (2))From the question, we have the following parameters that can be used in our computation:
s(x) = -x + 5
t(x) = 2x + 2
The composite function t(s(x)) is calculated as
t(s(x)) = 2s(x) + 2
Substitute the known values in the above equation, so, we have the following representation
t(s(x)) = 2(-x + 5) + 2
Again, substitute the known values in the above equation, so, we have the following representation
t(s(2)) = 2(-2 + 5) + 2
Evaluate
t(s(2)) = 8
Hence, the value of t(s(2)) is 8
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Can someone please help me solve this simple question for high reward
Answers
Answer:
D
Step-by-step explanation:
The Percentages are as follows
History: 80%
English: 82%
Reading: 84%
Math: 85%
Science: 86%
Population of a city grows by 14% every year. Initial population of the city is 5,741. Find how many people will be in the city after 3 years
Answers
The estimated population of the city after 3 years would be 8,537 people.
To find the population of the city after 3 years, we can use the formula for compound interest;
A = P ×[tex](1+r)^{t}[/tex]
where;
A = the final amount (population after 3 years)
P = the initial amount (initial population of the city) = 5,741
r = the annual growth rate (as a decimal) = 14% = 0.14
t = the number of years = 3
Plugging in the values, we get
A = 5,741 × (1 + 0.14)³
Simplifying the expression inside the parentheses first;
A = 5,741 × (1.14)³
Then, raising 1.14 to the power of 3;
A = 5,741 × 1.485136
A ≈ 8,536.98
So, the estimated population of the city after 3 years would be approximately 8,536.98 people. Since population cannot be in decimal numbers, we can round it to the nearest whole number;
A ≈ 8,537
Therefore, the estimated population of the city after 3 years would be 8,537 people.
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Help me please I don’t know
Answers
Answer:21y -78
Step-by-step explanation: Distribute the 7 to 3y and -10 to get 21y and -70.
Then combine like terms so the equation would be 21y -78
Step-by-step explanation:
-8+7(3y-10)
-8+21y-70
21y-70+8
21y-78
Last step because there is no more like terms to combine
Hope this helps
John is w years old. His sister is 16 years old and his brother is twice
John's age. All three siblings have a total age of 31.
a) Write an equation to represent this.
b) Solve your equation to find out John's age.
Answers
Answer: 16* 2
Step-by-step explanation:
I am unsure about how to do this problem, pictured below.
Answers
The time taken to reach a population of 500 is gotten from 500=50e^0.55t
What is the exponential growth?
Exponential growth is a process that increases quantity over time as in the bacterial culture here.
We know that from the question, we have;
P(t)=Poe^rt
P(t) = population at time t
Po= Initial population
r = growth rate
t = time taken
Then we have that;
150 = 50e^2r
3=e^2r
ln3 = 2r
r = ln3/2
r = 0.55
If the rate of growth is 0.55, then to reach a population of 500;
500=50e^0.55t
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PLEASE HELP WHAT IS 7 x 4
Answers
Answer:
THE ANSWER OF 7×4=28 !!!!!!!
Sean A y B dos sucesos tales que:
P(A)= 0. 4;
P(Bc)= 0. 7 y P(AUB)= 0. 6, donde Bc
es el suceso contrario de B. Determinar si son independientes A y B
Answers
Primero, se debe encontrar P(B) utilizando la probabilidad complementaria:
P(B) = 1 - P(Bc) = 1 - 0.7 = 0.3.
Luego, se puede encontrar P(A∩B) utilizando la fórmula de la unión:
P(A∩B) = P(A) + P(B) - P(AUB) = 0.4 + 0.3 - 0.6 = 0.1.
Finalmente, se puede verificar si A y B son independientes:
P(A)P(B) = 0.4 x 0.3 = 0.12.
Como P(A∩B) ≠ P(A)P(B), se concluye que A y B no son independientes
Three squares are placed to form a right triangle as shown.
Which statement must be true?
A The sum of the areas of the smaller
squares is always equal to the area of the largest square.
B The sum of the areas of the smaller squares is always greater than the area of the largest square.
C The difference of the areas of the smaller squares is always equal to the area of the largest square.
D The difference of the areas of the smaller squares is always greater than the area of the largest square.
Answers
If three squares are placed to form a right triangle as shown. The statement that must be true is: C .The difference of the areas of the smaller squares is always equal to the area of the largest square.
Which statement is true?Let's use the letters a, b, and c to denote the side lengths of the squares, with c standing for the hypotenuse of the right triangle. Assuming that an is the shortest side length to preserve generality a2 is the area of the smallest square. The largest square has a surface area of c2 whereas the medium square has a surface area of b2.
The Pythagorean theorem demonstrates that a + b equals c. If we rewrite this equation, we obtain:
c^2 - b^2 = a^2
c^2 - a^2 = b^2
This means that the size of the largest square is equal to the difference between the areas of the two smaller squares, which is either a2 or b2.
Therefore the correct option is C.
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