Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
a) The height of the red prism is one-third the height of the blue prism.
b) The height of the red prism is the same as the height of the blue prism.
c) The height of the red prism is six times the height of the blue prism.
d) The height of the red prism is three times the height of the blue prism.
Answers
Let hb represent the height of the blue prism; let hr represent the height of the red prism.
216*hb = V = (1/3)*(216)*hr
3*hb = hr . . . . . . . . . . . . . . . divide by the coefficient of hr
The 4th selection is appropriate.
Answer:
D
Step-by-step explanation:
Related Questions
Let u = <6, -9>, v = <1, -4>. Find u - v.
A) <5, -5>
B) <10, -10>
C) <15, 5>
D) <7, -13>
Answers
In terms of a formula if we had the vectors u and v such that
u = <a,b>
v = <c,d>
then
u - v = <a-c, b-d>
Let's use that to get...
u - v = <6,-9> - <1,-4>
u - v = <6-1,-9-(-4)>
u - v = <6-1,-9+4>
u - v = <5,-5>
----------------------
Answer: A) <5,-5>
Final answer:
To find the difference between vectors u and v, subtract the components of v from the corresponding components of u, resulting in the vector A) <5, -5>.
Explanation:
The question involves finding the difference of two vectors u and v. To find the vector u - v, you subtract each corresponding component of vector v from vector u.
For the first component, subtract the x-component of v (1) from the x-component of u (6), which equals 5.For the second component, subtract the y-component of v (-4) from the y-component of u (-9), which equals -5.Thus, the vector u - v is A) <5, -5>.
Sal can mop a certain floor in 8 minutes by himself.If Sal and ben can mop the floor together in 6 minutes,how long does it take Ben to mop the floor alone?
Answers
After losing 30 pounds, an individual weigh 110 pound more than one-third his previous weight
Answers
For an instance, x is the previous weight
"After losing 30 pounds" could be written as (x - 30)
"110 pounds more than one-third his previous" could be written as (110 + [tex] \frac{1}{3} [/tex]x)
Join the expression and solve for x
x - 30 = 110 + [tex] \frac{1}{3} [/tex]x
Move 1/3 x to the left side, and the constant of 30 to the right side, so like terms will be on equal side
x - [tex] \frac{1}{3} [/tex]x = 110 + 30
Equalize the denominators of the fractions
[tex] \frac{3}{3} [/tex]x - [tex] \frac{1}{3} [/tex]x = 140
[tex] \frac{2}{3} [/tex] = 140
x = 140 × [tex] \frac{3}{2} [/tex]
x = 420/2
x = 210
The previous weight was 210 pounds
The new weight is 210 - 30 = 180 pounds
Rewrite 17/20 and 21/25, so that they have a common denominator then use <,>or = to order 17/20 and 21/25
Answers
20 = 2 * 2 * 5
25 = 5 * 5
The least common denominator has two 5s and two 2s.
LCD = 2*2*5*5 = 100
17/20 = 17 * 5/ 20*5 = 85 / 100
21/25 = 21* 4/25*4 = 84 / 100
Talk about close
17/20 > 21/25 <<<< answer
But I hate to have predicted that before hand.
10 POINTS!!!
Premier Tire sells three categories of tires: good, better, and best. The good tires cost $106, the better tires cost $156, and the best tires cost $190. The good tires sell 3 times as fast as the best tires and the better tires sell 2.5 times as fast as the best tires. If the total amount of tire sales in January was $233,480, how many of each category of tire was sold? (Round your answer to the nearest whole number.)
Answers
.. 106g +156b +190t = 233,480
.. g -3t = 0
.. b -2.5t = 0
You can put these equations into your friendly equation solver to find
.. g = 780
.. b = 650
.. t = 260 (no rounding necessary)
780 good tires were sold
650 better tires were sold
260 best tires were sold
_____
If you want to solve these equations "by hand," substitution will work well. Substitute for b and g and solve for t. Then the values of b and g fall out immediately.
.. 106(3t) +156(2.5t) +190t = 233480
Point R is located at (11,5).point S is located at (-1,5). what is the distance between point R and point S
Answers
d=√(x2-x1)² + (y2-y1)²
d=√(-1-11)² + (5-5)²
d=√(-12)² + 0
d=12
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft if there are four blades on the windmill, what is the total area of the blades.
Answers
A=(1/2)b*h=(1/2)7*4=28/2=14
for four blades
14*4=56
Solution :
As per the problem we have
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft.
There are four blades on the windmill.
we have been asked to find the total area of the blades.
Area of one blade[tex] =\frac{1}{2}*base*height=\frac{1}{2}*7*4 =14 \ ft^2\\ [/tex]
Total are of blades[tex] =4*\text{Area of one blade}\\ [/tex]
Total are of blades[tex] =4*14=56 \ ft^2\\ [/tex]
1/6 of 3 yards=______feet
I know I just ask one but u get 17 points so plz help I'm stuck
Answers
In this question, first we have to see how many feets are in 1 yard .
And there are 3 feets in 1 yard.
So in 3 yards, there are 9 feets
Therefore we will get
[tex] \frac{1}{6}*3 yards= \frac{1}{6} * 9 feet = 1.5 feet [/tex]
Therefore the answer of the given question is 1.5 feet.
Final answer:
To find the equivalent feet for 1/6 of 3 yards, multiply 1/6 by 3 feet per yard to get 1.5 feet.
Explanation:
1/6 of 3 yards=_____feet
Step 1: 1 yard is equal to 3 feet.
Step 2: To find the equivalent feet for 1/6 of 3 yards, calculate 1/6 x 3 = 0.5 x 3 = 1.5 feet.
how many radians are in a semicircle? a.2π, b.π, c.π/2, d.3π/2
Answers
A semicircle, which is half of a full circle, consists of half the total amount of radians in a full circle. Since a full circle has 2π radians, a semicircle contains π radians. Therefore, the correct answer is b.π.
Explanation:To answer your question, let's review the structure of a circle.It is divided by its radius into 360 degrees or by its diameter into a full rotation of 2π radians. Therefore, a semicircle, which is half of a circle, must consist of half the total amount of radians in a full circle.
In a full circle, there are 2π radians. Hence, in a semicircle, which is exactly half of the full circle, there would be 2π/2. This simplifies to π radians.
So, the correct answer to your question 'How many radians are in a semicircle?' is b.π.
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An artist wants to reduce the size of a drawing using a scale factor of 3:13:1 . The original drawing has an area of 720 square inches. What is area of the new drawing? Enter your answer in the box.
Answers
Answer: 80
MsEHolt is correct, the answer is 80[tex]in^2[/tex]
given than segment FE is parallel to segment DG, which of the following statements is no true
Answers
D <<<< answer.
To the nearest tenth, find the perimeter of ∆ABC with vertices A(-1,4), B(-2,1) and C(2,1). Show your work
Answers
The perimeter of ∆ABC = 11.4 units
ANSWER
The perimeter is 11.4 units
EXPLANATION
Perimeter is the distance around the figure.
We use the distance formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
to determine the length of all the sides and add them.
[tex]|AB|=\sqrt{(-2--1)^2+(1-4)^2}[/tex]
[tex]|AB|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]|AB|=\sqrt{1+9}[/tex]
[tex]|AB|=\sqrt{10} \approx 3.162[/tex]
[tex]|AC|=\sqrt{(2--1)^2+(1-4)^2}[/tex]
[tex]|AC|=\sqrt{(2+1)^2+(1-4)^2}[/tex]
[tex]|AC|=\sqrt{(3)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{9+9}[/tex]
[tex]|AC|=\sqrt{18} \approx 4.24[/tex]
[tex]|BC|=\sqrt{(2--2)^2+(1-1)^2}[/tex]
[tex]|BC|=\sqrt{(2+2)^2+(1-1)^2}[/tex]
[tex]|BC|=\sqrt{(4)^2+(0)^2}[/tex]
[tex]|BC|=\sqrt{14}=4[/tex]
Therefore perimeter=[tex]|AB|+|BC|+|AC|[/tex]
=[tex]4.00+3.16+4.24[/tex]
=[tex]11.40[/tex] units
One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3). What is the equation of the hyperbola?
Answers
Answer:
C) (y+3)^2/64-(x+1)^2/36=1
Step-by-step explanation:
Just took the review in edg
To solve this problem, we just need to substitute the values into the equation and solve. the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
Equation of a HyperbolaThe standard equation of a hyperbola is given as
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\\[/tex]
The data given are;
focus = (-1, 7)vertex = (-1, 5)center = (-1, -3)Let's substitute the values into the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
Learn more on equation of hyperbola here;
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What is the value of 4.05 divide by 1.5?
Answers
The value of the expression 4.05 / 1.5 using the division property will be 2.7.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
4.05 and 1.5
Then the division of the numbers 4.05 and 1.5 will be given by putting a division sign between them. Then we have
⇒ 4.05 / 1.5
⇒ 2.7
The value of the expression 4.05 / 1.5 using the division property will be 2.7.
More about the Algebra link is given below.
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Final answer:
The result of dividing 4.05 by 1.5 is 2.7.
Explanation:
The value of 4.05 divided by 1.5 can be calculated by simply performing the division.
When you divide 4.05 by 1.5, you get 2.7.
This is because 4.05 is equivalent to 405 tenths, and when you divide 405 by 15 (since 1.5 is the same as 15 tenths), you end up with 27, or 2.7 when you adjust for the decimal placement.
The hypotenuse of a right triangle measures 10 inches, and the side opposite to ∠θ, one of the non-right angles, is 5 inches long. The measure of ∠θ is
Answers
This is a 30-60-90 triangle where the short leg is half that of the hypotenuse. The short leg is opposite the smallest angle 30 degrees.
You can use trig to find that
sin(angle) = opposite/hypotenuse
sin(theta) = 5/10
sin(theta) = 0.5
theta = arcsin(0.5)
theta = 30 degrees
Sherri uses her credit card to pay for new transmission that ended up totaling $1,050.25. She can pay off up to $400 a month. The card has an annual rate of 18.5%. How much will she pay in interest?
Answers
Please tell Sherri that it is less expensive to get a bank loan than to use the credit card.
Principal, P=1050.25
interest rate, i = 18.5%/12 per month
Monthly Repayment, A = 400
We need to calculate the monthly balance to know how many months it takes her to pay off the debit, and hence the interest charge.
As usual, we assume the debit is made at the beginning of the month, and the $400 paid at the end of the month. In actual practice, all these debits and credits are calculated on a daily balance basis, and interest accumulated at the end of the month.
The monthly interest is calculated as the balance from last month multiplied by the interest rate, 18.5%/12. The amount owing (at the end of the month)
F=Balance(1+0.185/12)
month Owing Paid Balance Calculation of owing next month
0 1050.25 0 1050.25 1050.25*(1+0.185/12)=1066.44
1 1066.44 400 666.44 666.44(1+0.185/12)=676.72
2 676.72 400 276.72 276.72(1+0.185/12)=280.98
3 280.98 290.98 ................... loan paid off
Total interest paid = 400+400+290.98 - 1050.25 = 40.73
Sherri will pay approximately $30.69 in interest on her credit card debt of $1,050.25 with an 18.5% annual interest rate, assuming she makes payments of $400 per month and the interest compounds monthly.
To calculate how much interest Sherri will pay on her credit card debt, we need to know how the interest compounds. Typically, credit card interest is compounded daily, but since we do not have the compound frequency, we'll use a simplified approach to estimate the interest assuming the interest is compounded monthly.
The annual interest rate is 18.5%, which translates to a monthly rate of 18.5%/12 = 1.54%. Since Sherri can pay $400 a month, we can calculate the time it will take for her to pay off the principal without considering interest. This gives us $1,050.25 / $400 < 3 months.
Since the debt would be paid off in less than three months, we can estimate the interest for each month and sum it up:
First month interest: $1,050.25 < 0.0154 = $16.17Second month principal: $1,050.25 - $400 + $16.17 = $666.42Second month interest: $666.42 < 0.0154 = $10.26Third month principal: $666.42 - $400 + $10.26 = $276.68Third month interest: $276.68 < 0.0154 = $4.26Adding up these interest payments gives us approximately:
$16.17 + $10.26 + $4.26 = $30.69 in interest.
Please note, this is an estimation that assumes a linear payment model. Actual interest charges could be higher due to daily compounding.
A spherical helium balloon has a diameter of 30 cm. How much helium is needed to fill the balloon, in cubic centimeters? Round your answer to the nearest centimeter
Answers
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\quad \begin{cases} r=radius\\ -----\\ r=15 \end{cases}\implies V=\cfrac{4\pi 15^3}{3}[/tex]
If $200 is put in the bank and each year the account earns 5% simple interest, then how much interest will be earned in two years?
Answers
Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.
Answers
After cutting one of the dowels, the lengths will then be
x/2, x/2,x.
He cannot form a triangle using the three dowels because the triangle inequality requires that the sum of the two shorter sides of a triangle must be greater than the third side. Here x/2+x/2=x equals the third side, so a triangle cannot be formed.
By the way, if he cuts the long dowel a little shorter, he will then be able to make a triangle.
Answer:
The dowels are congruent, so they have the same length. If one is cut, the sum of the lengths of the two cut pieces will equal the length of the longer piece. If the pieces are to make a triangle, the sum of the lengths of the two cut pieces must be greater than the length of the third piece.
Step-by-step explanation:
Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice cream. What will Ari think about Freeze Zone's milkshakes?
Answers
Answer: Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Step-by-step explanation:
Since we have given that
Ari has 3 ounces of caramel for every 5 scoops of ice-cream .
Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice-cream.
According to Ari,
For every 5 scoops of ice-cream, he needs 3 ounces of caramel
For every 1 scoop of ice-cream, he needs
[tex]\frac{3}{5}\text{ ounces of caramel}[/tex]
For every 8 scoops of ice-cream, he needs
[tex]\frac{3}{5}\times 8=\frac{24}{5}=4.8\text{ ounces of caramel}[/tex]
So, Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Explanation:To determine what Ari will think about Freeze Zone's milkshakes, we need to compare the ratio of caramel to ice cream in Ari's perfect milkshake to the ratio in Freeze Zone's milkshakes.
Ari's perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream, so the ratio is 3:5.
Freeze Zone's milkshakes have 6 ounces of caramel for every 8 scoops of ice cream, so the ratio is 6:8.
To simplify both ratios, we can divide the numbers by their greatest common divisor. The GCD of 3 and 5 is 1, so the simplified ratio for Ari's perfect milkshake is 3:5. The GCD of 6 and 8 is 2, so the simplified ratio for Freeze Zone's milkshakes is 3:4.
Since both ratios are the same, we can conclude that Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
A bond is a small, interest-bearing loan made by an individual to a corporate or government entity.
Please select the best answer from the choices provided
T
F
Answers
Answer: TRUE
Step-by-step explanation:
Is the given sequence arithmetic? If so, identify the common difference. 3.2, 3.5, 3.8, 4.1, . . .
Answers
A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is full. after how many minutes is the bucket half full? show work
Answers
The water in the bucket doubles every minute. After 8 minutes the bucket is full. This means a minute earlier (i.e. at 7th minute) the water in bucket was half as compared to water in bucket after 8 minute.
So, if after 8 minutes bucket is full, after 7 minutes bucket will be half full. So the answer is 7 minutes.
What is the slope of a line that is parallel to to the one shown? (-3, 2) (0, -2)
Answers
slope = (2 + 2)/(-3 - 0) = -4/3
parallel lines have same slope
so answer is -4/3
Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a radius of 10 meters and a height of 11 meters
Answers
so, the volume of a cylinder is V = πr²h.
now, we know the radius is 10, and the height is 11, so then V = π10²*11 is its volume.
The exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.
To calculate the exact volume of an oblique cylinder using Cavalieri's Principle, follow these steps:
1. Consider a right cylinder with the same base and height as the oblique cylinder. The volume of the right cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
2. Since the oblique cylinder and the right cylinder have the same base and height, their volumes are equal according to Cavalieri's Principle.
3. The formula for the volume of a right cylinder can be applied to the oblique cylinder, giving the volume as V = πr^2h.
4. Substituting the values of the radius (r = 10 meters) and height (h = 11 meters) into the formula gives V = π(10)^2(11) = 110π cubic meters.
5. Therefore, the exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.
Help please ...........MATH
Answers
N=N0e^(-kt)
where
N is amount of C-14 at time t
N0 is the initial amount
k is the constant
t is the time taken
given that the amount found was 30% percent of the initial amount, the age of the mammal will be found as follows:
let N=x, N0=0.3x, k=0.0001, t=?
Plug in the formula we get:
0.3x=xe^(-0.0001t)
x will cancel and we shall remain with:
0.3=e^(-0.0001t)
introducing natural logs we get:
ln 0.3=-0.0001t
hence
t=ln0.3/(-0.0001)
t= 12039.7 years
Please help me with questions 24
Answers
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After the translation, the triangle stays in quadrant IV. It then reflects over to quadrant I, only to rotate back to quadrant IV again. The size and shape does not change. These transformations are known as "rigid transformations" which preserve segment lengths (aka keep them the same). So the final triangle is congruent to the original triangle. All that has happened is that it has moved around.
in 2012 the population of a city was 6.25 million the exponential growth rate was 3.22% per year
find the exponential growth function estimate the population of the city in 2018
Answers
[tex]F=A(1+r)^t[/tex]
F=final amount
A=initial amount
r=growth rate iin decimal form
t=time in years elapsed
so given
A=6.25 million
r=3.22%=0.0322
t=2018-2012=6
so
[tex]F=6.26(1+0.0322)^6[/tex]
[tex]F=7.57[/tex]
so it will be about 7.57 million in 2018
A combination lock has a code consisting of 3 numbers, each of which can be 0 to 39, with numbers repeated. Jillian says that there are only 120 possible codes. Is Jillian correct? If not, explain her error.
Answers
Answer:
Jillian is not correct
Jillian has summed up the possible number of codes for each digit instead of multiplying it
Step-by-step explanation:
The lock has a code that consists of 3 number
It is given that the number in the lock code can be used between [tex]0[/tex] to [tex]39[/tex]
Thus, out of total [tex]40[/tex] set of numbers (i.e [tex]0-39[/tex]), the numbers can be repeated.
This means for all three code numbers the opportunity of choosing a number is same i.e. between [tex]0-39[/tex]
Now, the first digit of the code can be any number between [tex]0-39[/tex]
Like wise the second and third digit of the code can be any number between [tex]0-39[/tex]
Thus. the possible number of codes with repetition allowed are
[tex]40 * 40* 40\\64000[/tex]
Hence, Jillian is not correct
Jillian has summed up the possible number of codes for each digit instead of multiplying it
Answer:
No, Jillian is not correct. According to the fundamental counting principle, the total number of possible codes would be (40)(40)(40) = 64,000. Jillian multiplied by 3 instead of multiplying the number of possibilities for each digit.
Step-by-step explanation:
A bathtub is filling with water at a rate of 60 liters per minute.How many liters of water are in the bathtub after t minutes?
Answers
Answer:
[tex]60t\text{ Liters}[/tex]
Step-by-step explanation:
We have been given that a bathtub is filling with water at a rate of 60 liters per minute. We are asked to find the water filled in the bathtub after t minutes.
To find the number of liters of water filled in tub after t minutes we will multiply rate of water filling by time.
[tex]\frac{60\text{ Liters}}{\text{Minute}}\times t\text{ minutes}[/tex]
[tex]60\text{ Liters}\times t[/tex]
[tex]60\times t\text{ Liters}[/tex]
[tex]60t\text{ Liters}[/tex]
Therefore, there were [tex]60t\text{ Liters}[/tex] of water in the bathtub after t minutes.