Two rectangular prisms have the same volume. The area of the base of the blue prism
is 4 1/8 square units. The area of the base of the red prism is one-half that of the blue
prism. Which statement is true?
CLEAR
CHECK
A.The height of the red prism is four times the height of the
blue prism.
B.The height of the red prism is two times the height of the
blue prism.
C.The height of the red prism is one-half the height of the
blue prism.
D.The height of the red prism is the same as the height of
the blue prism.
Answers
The height of the red prism must be twice the height of the blue prism.
Volume of a prism can be calculated as the area of the base multiplied by the height. Since the height of the blue prism is twice that of the red prism, the height of the red prism must be twice as much as that of the blue prism to make the volumes equal.
Related Questions
john made two candles in the shape of rectangular prisms. The first candle is 12cm high, 4 cm long, and 6 cm wide. The second candle is 4 cm higher, but has the same length and width. How much additional wax was needed to make the taller candle?
Answers
Answer:
96[tex]cm^3[/tex]
Step-by-step explanation:
To determine how much additional wax was needed to make the taller candle, we determine the volume of each of the candles and find the difference in their volumes
First Candle
Height=12cmLength=4 cmWidth= 6 cmVolume=Height X Length X Width
=12 X 4 X 6
=288[tex]cm^3[/tex]
Second Candle
The second candle is 4cm higher
Height=12+4=16cmLength=4 cmWidth= 6 cmVolume=Height X Length X Width
=16 X 4 X 6
=384[tex]cm^3[/tex]
Difference in Volume = 384-288 =96[tex]cm^3[/tex]
Therefore, 96[tex]cm^3[/tex] of additional wax was used to make the second candle.
Multiplying polynomials and simplifying expressions
Answers
Given:
[tex](y-4 x)\left(y^{2}+4 y+16\right)[/tex]
Resulting form = [tex]y^{3}+4 y^{2}+a y-4 x y^{2}-a x y-64 x[/tex]
To find:
The value of a in the polynomial.
Solution:
[tex](y-4 x)\left(y^{2}+4 y+16\right)[/tex]
Using distributive property:
[tex]a(b+c)=a b+a c[/tex]
[tex](y-4 x)(y^{2}+4 y+16)=y(y^{2}+4 y+16)-4 x(y^{2}+4 y+16)[/tex]
Now multiply each of the first term with each of the second term.
[tex]=y y^{2}+y \cdot 4 y+y \cdot 16+(-4 x) y^{2}+(-4 x) \cdot 4 y+(-4 x) \cdot 16[/tex]
Applying plus minus rule: [tex]+(-a)=-a[/tex]
[tex]=y^{2} \cdot y+4 y\cdot y+16 y-4 y^{2} x-4 \cdot 4 y x-4 \cdot 16 x[/tex]
Apply the exponent rule: [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex]
[tex]=y^{3}+4 y^2+16 y-4 y^{2} x-16 y x-64 x[/tex]
Let us compare this with the given resulting form:
[tex]=y^{3}+4 y^{2}+a y-4 x y^{2}-a x y-64 x[/tex]
On comparing above two expression, we get a = 16.
The value of a in the polynomial is 16.
If the technician charged $327.50, then the technician worked ___
hours.
Answers
If the technician charges $327.50, then the technician worked 5.95 hours.
To determine how many hours the computer technician worked, we need to set up an equation based on the information provided. Let:
- [tex]\( F \)[/tex] represent the flat rate for home visits.
- [tex]\( h \)[/tex] represent the number of hours worked.
- [tex]\( 55h \)[/tex] represent the hourly charge ($55 per hour).
The total charge is given as $327.50. The equation for the total charge is:
[tex]\[F + 55h = 327.50\][/tex]
Without the flat rate [tex]\( F \)[/tex] provided, we can't determine [tex]\( h \)[/tex] exactly. However, let's assume that [tex]\( F \)[/tex] is included in the total cost as a constant and solve for [tex]\( h \)[/tex] based on the given rate per hour.
First, let's isolate [tex]\( h \):[/tex]
[tex]\[55h = 327.50 - F\\\\h = \frac{327.50 - F}{55}\][/tex]
Since the exact flat rate [tex]\( F \)[/tex] isn't given, let's assume it's zero for this case:
[tex]\[h = \frac{327.50}{55}\][/tex]
Now, calculate [tex]\( h \):[/tex]
[tex]\[h = \frac{327.50}{55} = 5.95 \text{ hours}\][/tex]
Therefore, if the technician charges $327.50 for 5.95 hours worked and assuming no flat rate, the technician worked approximately [tex]\( 5.95 \)[/tex] hours.
The complete question is:
A computer technician charges a flat rate for home visits plus $55 per hour. If the technician charged $327.50, then the technician worked how many hours?
The rent for an apartment is $800 per month. The landlord charges one month’s rent as a deposit plus a nonrefundable damage cost of $250. The expression 800(n + 1) + 250 represents the cost of the renting the apartment for n months. Simplify the expression.
How much does the apartment cost to rent for 2 years?
Answers
The cost of renting the apartment for n months can be simplified to 800n + 1050. To rent the apartment for 2 years, the cost is $20,250.
Explanation:To simplify the expression, we can distribute the 800 to both terms inside the parentheses:
800 * n = 800n800 * 1 = 800Combining these terms gives us:
800n + 800 + 250
By combining like terms, we get the simplified expression:
800n + 1050
To find the cost of renting the apartment for 2 years (24 months), we substitute n = 24 into the simplified expression:
800(24) + 1050 = 20,250
Therefore, the apartment costs $20,250 to rent for 2 years.
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(Algebra Word Problems) Janice, Rene, and Lucinda shared a summer
babysitting job. Janice babysat twice as many hours as Rene. Lucinda
babysat 10 more hours than Janice. If r represents the number of hours
that Rene babysat, which expression represents the number of hours that
Lucinda babysat? *
R+10
2r + 10
2(r + 10)
10 x 20
Answers
Answer:
r2+A
Step-by-step explanation:
lalalalalalalalalalalalala
Simplify.
(2x^2-5x+3) - (-x^2+4x-5)
Answers
Answer:
x^2-9x+8
Step-by-step explanation:
(2x^2-5x+3)-(-x^2+4x-5)
Open the bracket first
2x^2-5x+3+x^2-4x+5
Collect like terms
2x^2+x^2-5x-4x+3+5
x^2-9x+8
So the final answer is x^2-9x+8
A bag contains 24 blue tiles, 6 navy tiles, 10 pink tiles, and 10 orange tiles. A tile is drawn at random. What is the theoretical probability, as a decimal, of drawing a blue tile?
Answers
Answer:
.48
Step-by-step explanation:
The total number of tiles is
24+6+10+10 =50 tiles
P(blue) = number of blue tiles/total
= 24/50
=.48
NEED HELP URGENTLY!!!!
The population of the United States in 2005 was approximately 295,500,000 and the land area was 3,806,000 square miles. The population increased by 5.1% in 2015. To the nearest whole number, how much did the population density, in people per square mile, increase from 2005 to 2015?
3
4
5
6
Answers
Answer:
4 people per square mile
Step-by-step explanation:
----Population density = number of people divided by land area.
Back I 2005,the population density of the US was: 295500000/3806000= 77.6 people per square miles.
----If the population increased by 5.1%,the new population of residents in the US will be
100% + 5.1% = 105.1%
105.1/100 × 295500000
= 310,570,500.
--- The new population density of the US in 2015 will be
310,570,500 ÷ 3,806,000
= 81.6 persons per square mile
---- To find out the difference in population from 2005 to 2015,we have to do nothing else but subtract the Population Density (PD) of 2015 from 2005
81.6 - 77.6 = 4 persons per square mile
What information do you need to write a sine or cosine equation?
Answers
Answer:
of a stretched cosine curve, trigonometric videos, worksheets, games and activities that are suitable for ... More Lessons on Finding An Equation for Sine or Cosine Graphs ... We have included a tool that with plot the sine graph f(x) = A sin(B(x-h))+ k, given the values A, B, h and k.
Step-by-step explanation:
What is the equation used to find the nth term of the arithmetic sequence: -9, -4 1, 6, 11...
a^n =-9-5n
a^n =5-9 (n-1 )
a^n =−9+(n−1)⋅5
a^n=-9 (5)^(n-1)
Answers
Answer:
a^n=-9+(n-1).5
Step-by-step explanation:
Arithmetic sequence=a+(n-1)d
a=-9
n=?
d=+5
Arithmetic sequence=-9+(n-1)5
=-9+5n-5
Collect like terms
-9-5+5n
-14+5n
So the final answer is
an=-9+(n-1).5
Which system of equations represents this situation? 25 Points!! Look at pictures
Answers
Answer:
C
Step-by-step explanation:
the variables in this system of equations are b and p these represent distance walked.
4b + 5p = 2 represents the total amount of time the walk takes
b + p = 8 represents the total distance walked :)
The answer isn't A only because the word problem states that from her house to the beach, it should be represented as b. And p for the beach to the park.
A person invests 9500 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12600 dollars?
Answers
To determine the time necessary for an investment to grow from $9,500 to $12,600 at an interest rate of 5.75% compounded quarterly, the compound interest formula is rearranged and solved for time, yielding approximately 6.6 years.
Explanation:To find out how long it takes for an investment to grow from $9,500 to $12,600 with an interest rate of 5.75% compounded quarterly, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per unit t.t is the time the money is invested for in years.In this case, we're solving for t, so we rearrange the formula: t = ln(A/P) / (n * ln(1 + r/n)). Substituting the provided values:
P = $9,500A = $12,600r = 0.0575 (5.75% expressed as a decimal)n = 4 (since interest is compounded quarterly)Thus, t = ln(12600/9500) / (4 * ln(1 + 0.0575/4)). After calculating, we find that t ≈ 6.6 years, rounded to the nearest tenth of a year.
The person must leave the money in the bank for approximately 5.4 years until it reaches $12600, with interest compounded quarterly.
To find out how long it takes for the investment to reach $12600 at a 5.75% interest compounded quarterly, we can use the formula for compound interest:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- A is the amount of money accumulated after t years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times interest is compounded per year.
- t is the time the money is invested for, in years.
We want to find t, so we can rearrange the formula to solve for t:
[tex]\[ t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)} \][/tex]
Given:
- P = 9500
- A = 12600
- r = 0.0575 (5.75% expressed as a decimal)
- n = 4 (quarterly compounding)
Substituting these values into the formula:
[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + \frac{0.0575}{4}\right)} \][/tex]
[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + 0.0575/4\right)} \]\[ t \approx \frac{\log(1.32631579)}{4 \cdot \log(1.014375)} \]\[ t \approx \frac{0.12224324}{4 \cdot 0.00570388} \]\[ t \approx \frac{0.12224324}{0.02281552} \]\[ t \approx 5.361 \][/tex]
Rounded to the nearest tenth, it takes approximately 5.4 years for the investment to reach $12600 at 5.75% interest compounded quarterly.
Line segment MN is shown below. If point P(x,y) partitions the line segment
into the ratio MP:PN = 1:2 then determine the values of x and y.
Line segment:
Point M: (-6,2).
Point N: (9. – 4)
Answers
Answer:
P (-1 , 0)
Step-by-step explanation:
M (-6 , 2) N (9 , -4) P (x , y)
horizontal distance of M and N = 9 - (-6) = 15
vertical distance of M and N = 2 - (-4) = 6
1/3 from x coordinate of M (-6): -6 + 15/3 = -1 This is x coordinate of point P
1/3 from y coordinate of M (2): 2 - 6/3 = 0 This is y coordinate of point P
P (x , y) i.e P (-1 , 0)
check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385
distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77
MP / PN = 5.385 / 10.77 = 0.5 = 1/2
The values of x and y that partition the line segment MN into the ratio 1:2 are x = 3 and y = -4.
Explanation:To determine the values of x and y that partition the line segment MN into the ratio MP:PN = 1:2, we can use the section formula. The section formula states that the coordinates of a point P(x,y) that partitions a line segment with endpoints M(x1, y1) and N(x2, y2) into the ratio m: n are given by:
x = (nx1 + mx2) / (m + n)
y = (ny1 + my2) / (m + n)
In this case, M(-6, 2) and N(9, -4), and the ratio is 1:2. Plugging these values into the section formula, we get:
x = (2*9 + 1*(-6)) / (1 + 2) = 3
y = (-4*2 + 2*(-4)) / (1 + 2) = -4
Therefore, the values of x and y that partition the line segment MN are x = 3 and y = -4.
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PLZZ HELP IM STUPITT SORRY AND HURRYYYY
Answers
Answer:
9.9 cm²
Step-by-step explanation:
Base = 2.6x3 which is 7.8/ 2 is 3.9.
Faces = 4x3 which is 12/2 is 6
Then, add those together to get 9.9
There are 7 math folders on a classroom shelf. This is 1/3 of the total number of math folders in the classroom. what is the total of number of math folders in the classroom?
Answers
Answer: 21
Step-by-step explanation:
1/3 = 7
7 * 3 = 21
1/3 = 7/21
Answer:
21
Step-by-step explanation:
How do you write that in Standard Form?
Please help I will mark brainliest and worth 50 points.
Answers
Hope this will help u...
Answer:
9u(v²u+v³-5u³)
Hope this Helps You !!!
Please mark me as Brainliest
A bowling team participates in a two-day tournament and records the scores for each team member on both days. The scores for both days are represented by the box plots below.
A. The scores on Friday and the scores on Saturday have the same median and interquartile range.
B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.
C. The scores on Friday have a greater interquartile range than the scores on Saturday, but both data sets have the same median.
D. The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.
Answers
The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
From the given boxplot we can deduce the following points:
On Friday: Q₁ = 200, Q₂ = 215, Q₃ = 220 and IQR = 20.
On Saturday: Q₁ = 190, Q₂ = 205, Q₃ = 210 and IQR = 20.
And , the median of the data on Friday is M₁ = 220
And , the median of the data on Saturday is M₂ = 205
So , scores on Friday have a greater median than the scores on Saturday
Hence , the median is solved
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The complete question is attached below :
A bowling team participates in a two-day tournament and records the scores for each team member on both days. The scores for both days are represented by the box plots below.
A. The scores on Friday and the scores on Saturday have the same median and interquartile range.
B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.
C. The scores on Friday have a greater interquartile range than the scores on Saturday, but both data sets have the same median.
D. The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.
6 × 3 = (? × 5) - (? × 2)
Answers
6 × 3 = ( 10 × 5 ) - ( 16 × 2 )
Hope this helps you!
Answer:
6 x 3=(6 x 5) - (6 x 2)
Step-by-step explanation:
:) How
any nore novies does Student B have than Student A?
Sudent A OOOO
Sudent B 0000000
2 more
8 times as many
4 more
4 times as many
Answers
Answer:
student b has 4 more movies
Step-by-step explanation:
Answer:
4 more
Step-by-step explanation:
- Match each sentence with the appropriate equation.
a. x + (x + 2) = 24
1. The sum of two consecutive even integers is
24.
b. x + (x + 1) = 25
2. 5 less than the sum of a number and two is
25.
C. X + 2 = 24
3. The sum of a number and two is 24.
d. (x + 2) - 5 = 25
4. The sum of two consecutive integers is 25.
Answers
Step-by-step explanation:
[tex]a \: \: \: \: 1 \\ \\ b \: \: \: \: 4 \\ \\ c \: \: \: \: 3 \\ \\ d \: \: \: \: 2[/tex]
What is the complete factorization of x2 + 4x - 45?
OOO
A. (x + 15)(x - 3)
OB. (x-9)(x + 5)
C. (x+ 9)(x - 5)
D. (x - 15)(x+3)
Answers
Answer: c
Step-by-step explanation:
[tex]x^2+4x-45[/tex]
[tex](x+9)(x-5)[/tex]
Answer:
c
Step-by-step explanation:
Find the measure of the angle indicated.
Answers
Answer:
110 degrees
Step-by-step explanation:
the angles are alternate exterior angles which means that they are the same
Answer:
110
Step-by-step explanation:
The angles are the same according to the corresponding angle postulate.
Find the 5th term of the expansion of ( 6x + 6y)^11
Answers
The 5 th term of the given expression is 330[tex](6x)^{7}( 6y)^{4}[/tex].
Step-by-step explanation:
Given,
[tex](6x+6y)^{11}[/tex]
To find the 5th term of the given expression.
Formula
In a binomial series [tex](a+b)^{n}[/tex], the r th term is = nC(r-1) [tex]a^{n-r-1} b^{r-1}[/tex], where,
nC(r-1) = [tex]\frac{n!}{(r-1)!(n-r+1)!}[/tex]
Now,
Putting, n=11, r = r, a=6x and b=6y we get,
5 th term = 11C4[tex](6x)^{7}( 6y)^{4}[/tex]
= [tex]\frac{11!}{4!7!}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]
= [tex]\frac{11X10X9X8X7!}{7!X4X3X2X1}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]
= 330[tex](6x)^{7}( 6y)^{4}[/tex]
Here is the answer.
PLEASE PLEASE HELP the question is below
Answers
Answer:
24
Step-by-step explanation:
First do parenthesis:
3*(9+1)-6 -> 3*(10)-6
Then do multiplication:
3*(10)-6 -> (30)-6
Then complete it with subtraction:
(30)-6 -> (24)
So your answer would be 24!
PEMDAS= Parenthesis, Exponents, Multiplication, Division, Add, Subtract.
3 x 10 - 6
30-6
24
Brian says that there is no such thing as an acute triangle that also has a 90 degree angle. Is this statement true? Yes or No?
Explain you reasoning about Brian's statement
Answers
Answer:
Brian is correct.
Step-by-step explanation:
An accute triangle has to have every angle being less then 90 degrees or else it is a right triangle
The diameter of a circle is 8 inches. What is the area?
8 pi inches squared
16 pi inches squared
32 pi inches squared
64 pi inches squared
Answers
Answer:
1 6 p i s q u a r e s i s m y f i n a l a n s w e r ! ! ! y o u r w e l c o m e
It’s not A can someone plz help me with this
Answers
Answer:
x = 4.92
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin 38 = x/8
Multiply each side by 8
8 sin 38 = x/8 *8
8 sin 38 = x
4.925291803 =x
The Cold Be Gone Company conducted a study where 100 participants were assigned to either receive a cold
medicine or not receive a cold medicine. The Cold Be Gone Company then recorded whether the participant's
cold lasted 7 days or longer. The Venn diagram below shows their data.
Complete the following two-way frequency table.
Received cold medicine
Did not receive cold medicine
Cold lasted longer than 7 days
Cold did not last longer than 7 days
Cold medicine
Cold longer than 7 days
27
23
20
30
Answers
Answer: Received cold medicine Did not receive cold medicine
Cold lasted longer than 7 days 23 20
Cold did not last longer than 7 days 27 30
Step-by-step explanation:
i hope it helps
To complete the two-way frequency table, calculate the values for each cell based on the given information.
Explanation:To complete the two-way frequency table, we need to fill in the missing values. Given that there are 100 participants in total, we can calculate the value for each cell. Starting with the top left cell, which represents participants who received the cold medicine and had their cold last longer than 7 days, the value would be 27. Similarly, we can calculate the values for the other cells in the table.
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a box contains 3 red marbles 6 blue marbles and 1 white marble. find the following probability. P(red and white and blue) without replacement
Answers
Answer:
3% unlikely
Step-by-step explanation:
if there are 10 marbles you can try to get 1 white, 1 blue, 1 red is't 3/10 = .3
Answer:
Blue 60%
Red 30%
White 10%
Which is better for value. I need the workings out too
600g of honey for £4.25 or 1kg of honey for £6.99
Can someone please help me and explain how you did it thank you very much! :)
Answers
Answer:
Buying the 1kg is a better value.
Step-by-step explanation:
okay so 1000g for every 1kg
so first we will find out how much the 600g would cost if it was 1kg
(ill be using $ instead of £)
600g/$4.25=1000g/? (finding the question mark which will be "x")
you cross multiply so 600x = 4.25×1000
600x = 4250
then cancel out the 600 so x is left, since the 600 is multiplying into the x, you would divide it out to cancel. so
600x=4250
_________ <(dividing)
600 600
so it would be
x= 7.08
which means it is $7.08 which is NOT better for value because it is 9 cents more than just buying the 1kg.