The pentagonal prism below has a height of 11 units and a volume of 451 units. Find the area of one of its bases.
Answers
Given:
The height of the pentagonal prism = 11 units.
The volume of the pentagonal prism = 451 cube units.
Required:
We need to find the baser area.
Explanation:
Consider the formula to find the volume of the pentagonal prism.
\(V=Base\text{ area}\times Height\)Substitute V =451 and height = 11 in the formula.
\(451=Base\text{ area}\times11\)Divide both sides by 11.
\(\frac{451}{11}=Base\text{ area}\times\frac{11}{11}\)\(41\text{ units}^2=Base\text{ area}\)Final answer:
\(Base\text{ area=}41\text{ units}^2\)Related Questions
The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
Answers
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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10 freshmen, 9 sophomores, 8 juniors, and 9 seniors are eligible to be on a committee.
In how many ways can a dance committee of 15 students be chosen?
Answers
6,480 ways
←
In 2007, a census counted 2817 of a certain animal. This was 292 fewer than the number counted in 2006. What was the
population of the animal in 2006?
The population of the animal in 2006 was
Points: 0
(Simplify your answer.)
Answers
The population of the animal found in 2006 was 3109.
What is defined as population census count?A population census is the overall method of collecting, compiling, evaluating, analyzing, and publishing and otherwise disseminating demographic, economic, and social data pertaining to all persons in a country or a well-defined portion of a country at a specific time.Natural population change is calculated by subtracting births from deaths, while net migration is the number of immigrants (people moving into the country) from the number of emigrants.For the given data in the question.
Population count of animals in 2007 is found as 2817.
The population count in 2007 is less than 292 than the population count in 2006.
Thus,
2007 population = 2006 population - 292.
2006 population = 2007 population + 292
2006 population = 2817 + 292
2006 population = 3109.
Therefore, the population count for the animals in 2006 is found to be 3109.
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Rauol made an investment in 155 shares of stock in a load fund for $3,117.05. After one year the stock had a net asset value of $18.35 per share. If Rauol redeems all 155 shares, which of the following is a correct statement?
a.Rauol will have a loss of $272.80.
b.Rauol will have a profit of $272.80.
c.Rauol will have a profit of $2,844.25.
d.There is not enough information to calculate profit or loss.
Answers
Answer:
The answer is A
Step-by-step explanation:
i got it right on edge <3
Answer:
It is A
Step-by-step explanation:
The other guy is right
M = I1+I₂ 31 +32 2 Now let's substitute in our given values. (-2 , 2) = ((-5 Find 2 and y2 We will now set up two equations to solve for our two unknowns of x2 and y₂. (-5 X2 (-5+₂) -5+22), (7+)) 2 - +₂)/2 = We will first want to multiply by 2 on both sides and will get −5+₂= -4 Adding 5 to both sides we get = 7 This is the coordinate of point B. Now we will set up the equation to solve for y2 +y2)/2 =
Answers
The coordinates of point B are (-3, 17).
The given equation is M = I₁ + I₂ = 31 + 32.
Now let's substitute in our given values:
(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)
We will now set up two equations to solve for our two unknowns, x₂ and y₂:
Equation 1: (-5 + x₂) / 2 = -4
Multiply both sides by 2:
-5 + x₂ = -8
Add 5 to both sides:
x₂ = -3
This gives us the x-coordinate of point B.
Equation 2: (-5 + 2 + y₂) / 2 = 7
Simplify:
(-3 + y₂) / 2 = 7
Multiply both sides by 2:
-3 + y₂ = 14
Add 3 to both sides:
y₂ = 17
This gives us the y-coordinate of point B.
Therefore, the coordinates of point B are (-3, 17).
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Find the annual interest rate.
I= $562.50, P=$1500, t= 5 years
The annual interest rate is_____%
Answers
The annual interest rate is 7.5%.
What is Simple interest?
Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.
The formula for simple interest is:
I = P × r × t
where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.
In this case, we know I = $562.50, P = $1500, and t = 5 years.
we ca substitute values into the formula,
562.50 = 1500× r ×5
Simplifying, we get:
r = 562.50 / (1500 ×5)
r = 0.075
r = 7.5%
Therefore, the annual interest rate is 7.5%.
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sokal and roy have a sack of 50 apples.All apples are either red or green.If sokal has 3 times as many red apples as roy does and half as many green apples.How many red apples sokal have?
Answers
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
Answers
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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Lin’s scale of 1 inch to 1 foot can be written as
Answers
Answer: 1i=1f
Step-by-step explanation:
Can someone help me please? ASAP
Answers
Answer:
triangle XYZ is similar to triangle RPQ
scale factor = 2/5
Step-by-step explanation:
Angles X and R are given as congruent.
Angles Z and Q are right angles, so they are congruent.
Then, angles Y and P must be congruent.
The similarity statement is
triangle XYZ is similar to triangle RPQ
To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.
10/25 = 2/5
The scale factor is 2/5.
a pentagon with sides 3 4 5 6 and 7 has area 48m. find the perimeter of a similar pentagon whose area is 27m
i give brainliest to first answer
Answers
Answer & step-by-step explanation:
Please see image attached below:
19.8 rounded to 20m
Step-by-step explanation:
reason;
Area=1/2 x perimeter x apothem
27=1/2 x p x 2.726
Divide both sides by 1/2
54= p x 2.726
Now divide both sides by 2.726 to isolate p
Answer p=19.8
Trey caught a 3 1/4 pound fish. How much did it weigh in ounces?
Answers
Answer: 52 ounces
multiply the mass value by 16
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Answers
4x - 5 = 2x + 7
First, let's simplify the equation by combining like terms:
4x - 2x = 7 + 5
2x = 12
Next, divide both sides of the equation by 2 to solve for x:
x = 12 / 2
x = 6
Therefore, the value of x that satisfies the equation is 6. None of the provided answer options (27, 37, 47, 57) are equal to 6.
Please help me find the length of OP. (See attached picture)
Answers
The length of OP in the given circle figure is 2.
We know that the area of a sector which obtain 'A' degree at center in a circle with radius 'r' is given by,
A = (A/360)*πr²
Here length of OP represents the radius of the circle with center O.
Let OP = R.
The area of the whole circle will be = πR²
Given that the sector which intends an angle of 72 degrees in center has area 4π/5.
According to the condition,
(72/360)* πR² = 4π/5
R²/5 = 4/5
R² = 4
R = 2 [since length cannot be negative so the negative value of square root is ignored.]
Hence the length of OP is 2.
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Find the values of x and y
(5y+38)
(8x+26)
3x
Answers
Y=20
3x+8x+26=180
The line is equal to 180 so u set the line to 180 and then solve for x
3x+8x+26=180
Combine like terms and subtract 26 on each side
11x=154
Divide by 11
X=14
And for y
Set it equal to 14
So it would be 180= 5y+38+42 (same as before, the line is equal to 180)
Or 138=5y+38 (Bc the ones across from each other are equal to each other)
180=5y+38+42
Combine like terms
180=5y+80
Subtract 80 on both sides
100=5y
Divide by 5
Y=20
Or
138=5y+38
Subtract 38 on each side
100=5y
Divide by 5
20=y
What is the constant up a proportionally in a equation y=x/g
Answers
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).
What is the volume of a sphere with a diameter of 12 cm.
Answers
Answer:
288π cm³, 904.32 cm³, and 904.778683 cm³
Step-by-step explanation:
The volume of a sphere can be found using the following formula.
\(V=\frac{4}{3} \pi r^3\)
We are given the diameter, so we must find the radius.
The radius is half of the diameter.
r= d/2
The diameter is 12 cm.
r= 12 cm/2
r= 6 cm
The radius is 6 centimeters. Let's return to the formula and substitute 6 cm in for r.
\(V=\frac{4}{3} \pi (6cm)^3\)
Evaluate the exponent.
\((6 cm)^3= 6 cm * 6 cm * 6cm = 36 cm^2 * 6cm= 216 cm^3\)
\(V=\frac{4}{3} \pi * 216 cm^3\)
Multiply 4/3 and 216 cm^3
\(V= (\frac{4}{3} * 216 cm^3)\pi\)
In terms of pi:
\(V= 288\pi cm^3\)
Using 3.14 as pi:
\(V= 288 \pi cm^3\)
\(V= (288 * 3.14) cm^3\)
\(V= 904.32 cm^3\)
Using 3.14159265 as pi:
\(V= 288 \pi cm^3\)
\(V= (288 * 3.14159265) cm^3\)
\(V=904.778683 cm^3\)
The volume of the sphere is 288π cm³, 904.32 cm³, and 904.778683 cm³
Answer:
Volume of sphere by formula is V= 4/3πr^3
Since d= 12
Then r = d/2
Radius = diameter / 2
r = 12/2
r = 6
V = 4/3 x 22/7 x 6^3
V = 1.33 x 3.14 x 216
V = 902.1cm^3....
Thanks
Inputs: People at concession stand Outputs: Cost of their order
this relation a function?
it a constant function?
it a 1-1 function?
Answers
People at the concession stand as input Cost of their order's output.
(1) The relation in question is a function.
(II) This function is not constant. (Each category of concession has a different order cost.)
Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)
A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.
The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.
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Anna is working at a fast food restaurant and made $45.00 for 6 hours. Allison is working at a retail store and made $50.75 for 7 hours.
If both girls worked for 10 hours, which girl would make more money and how much would she make?
Answers
Answer:
anna would make more money; she would make $75
Step-by-step explanation:
Answer:
anna 75.00
Step-by-step explanation:
To rent a moving truck for the day it costs $33 +1 dollar for each mile driven you drive the truck 300 miles how much do you pay right in expression that represents the cost in dollars to rent the truck
Answers
The amount paid for the truck for 300 miles is $333
How to determine the amount paid for the truckFrom the question, we have the following parameters that can be used in our computation:
Amount paid per day = $33
Amount paid per mile = $1
Number of miles driven = 300
The amount paid for the truck is then calculated as
Amount paid for the truck = Amount paid per day + Amount paid per mile x Number of miles driven
Substitute the known values in the above equation, so, we have the following representation
Amount paid for the truck = 33 + 300 * 1
Evaluate the products
Amount paid for the truck = 33 + 300
Evaluate the sum
Amount paid for the truck = 333
Hence, the amount is $333
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Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday.
He also has a part-time job that pays $8 per hour. How many hours will he need to
work to have $250 in his bank account?
.
Answers
Answer: 13h
Step-by-step explanation:
126 + 20 = 146
250 - 146 = 104
104 : 8 = 13
He will need 13h
Answer:
13.5
126 plus 20 is $146
250 minus 146 is 108
108 divided by 8 is 13.5
Write an equation in slope intercept form for a line that passes through the point (1,6) and a slope of 2
Answers
Answer:
The answer is
y = 2x + 4Step-by-step explanation:
To find an equation of a line when given the slope and a point we use the formula
\(y - y_1 = m(x - x_1) \\ \)
where
m is the slope
( x1 , y1) is the point
From the question the point is (1,6) and slope 2
The equation of the line is
\(y - 6 = 2(x - 1) \\ y - 6 = 2x - 2 \\ y = 2x - 2 + 6\)
We have the final answer as
y = 2x + 4Hope this helps you
Arnold Landis made a deposit of $720 to open a savings account that pays interest at an annual rate of 5%, compounded quarterly.
a. If he keeps his original deposit in the saving account and is paid interest for four quarters, how much interest will he earn in the first year?
Answers
Answer:
Hope It Help
Step-by-step explanation:
Brainliest please
30 POINTS!!!!!!!!!!!!!!!!!!!! HELP PLZ
A scatter plot is shown below:
A graph shows numbers from 0 to 10 on the x axis at increments of 1 and the numbers 0 to 15 on the y axis at increments of 1. The ordered pairs 0, 14 and 1, 11 and 2, 9 and 3, 10 and 4, 7 and 5, 7 and 6, 5 and 7, 5 and 8, 3 and 9, 1 and 10, 0 are shown on the graph.
Which two ordered pairs can be joined to best draw the line of best fit for this scatter plot?
(4, 15) and (10, 7)
(1, 6) and (6, 0)
(0, 13) and (10, 11)
(0, 13) and (10, 0)
Answers
Answer:
kk
Step-by-step explanation:
(0, 13) and (10,11)
The given equation has been solved in the table.
Step
Statement
2
1
Źr – 9 = –13
2
- 9 + 9 = -13 + 9
3
= -4
4
ယ်
NICO
=
5
r = -6
In which step was the addition property of equality applied?
A.
step 2
B.
step 3
OC.
step 4
D.
The addition property of equality was not applied to solve this equation.
Answers
Answer:
step 2
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
step 2
Does perpendicular lines have something same to intersecting lines
Answers
Answer:
They are similar in a way. Perpendicular lines can intersect, but they must make a 90 degree angle to be prerpendicular lines. A cross is an example of this.
Step-by-step explanation:
Runners at a cross-country meet run 2 miles south and then 4 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line. Brainliest and 20 points
Answers
Answer:
√20 miles
Step-by-step explanation:
a² + b² = c²
|
? | 2 miles ↓
|
------------------------------
← 4 miles
2² + 4² = c²
4 + 16 = c²
20 = c²
√20 = c
I hope this helps!
The length of the straight path they must run to get back to the starting line is 4.47 miles.
What is displacement?Displacement [x] of an object is the length of the straight line joining the initial and final position of the object. Mathematically, displacement can be written as-
Δx = x[2] - x[1]
Now -
Δx = vΔt {[v] is velocity}
So we can write -
vΔt = x[2] - x[1]
Given are the runners at a cross-country meet such that they ran 2 miles to south and then 4 miles to west from the starting line.
We can find the straight path they must run to get back to the starting line using the Pythagoras theorem. The base will be equal to distance ran towards south and height will be equal to the distance ran towards west. The length of the hypotenuse will be equal to that of displacement or the straight path they must run to get back to the starting line. Using Pythagoras theorem -
[h]² = [b]² + [p]²
[h]² = (2 x 2) + (4 x 4)
[h]² = 4 + 16
[h]² = 20
[h] = 4.47 miles
Therefore, the length of the straight path they must run to get back to the starting line is 4.47 miles.
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How would you describe the difference between the graphs of f(x) = 2x² and
g(x) = -2x²?
A. g(x) is a reflection of f(x) over the y-axis.
B. g(x) is a reflection of f(x) over the line y = -1.
OC. g(x) is a reflection of f(x) over the line y = x.
D. g(x) is a reflection of f(x) over the x-axis.
SUBMIT
Answers
How would you describe the difference between the graphs of f(x) = 2x² and g(x) = -2x²: D. g(x) is a reflection of f(x) over the x-axis.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
In this context, we can reasonably infer and logically deduce that a graph of transformed function g(x) = -2x² would be created by applying a reflection over or across the x-axis to the graph of the parent function f(x) = 2x² as shown in the image attached below.
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A bag of red grapes costs $4.00 per pound. Two bags of green grapes is 7.50. Which is the lower unit rate and the better deal for your budget
Answers
Answer:
red grapes
Step-by-step explanation:
Answer:
The two bags of green grapes are a lower unit rate.
Step-by-step explanation:
A bag of red grapes is $4 and two bags of green grapes is $7.50. If you buy two bags of red grapes the total amount of money you are spending is $8. If you buy two bags of green grapes the total is $7.50. If you divide $7.50 by two you get $3.50. This means that for one bag of green grapes it is $3.50. Therefore the two bags of green grapes are a lower unit rate.
Hope This Helps :)
The expression (4k + 8)/4 simplifies to an expression of the form ak+b where a and b are integers. find a/b.
Answers
If the expression (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2
The expression is (4k + 8) / 4
The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.
The given expression is (4k + 8)/ 4
Solve the expression
(4k + 8) / 4 = 4k/4 + 8/4
Divide the terms
=k + 2
The result is in the form of ak + b
The value of a = 1
The value of b = 2
The value of a/b = 1/2
Therefore, the value of the expression a/b is 1/2
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