What steps should be taken to calculate the volume of the right triangular prism? Select three options.
A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters.
A. Use the formula A = one-half b h to find the area of the base.
B. Use the formula A = b h to find the area of the base.
C. The area of the base, A, is One-half (7) (8) = 28 meters squared.
D. The area of the base, A, is One-half (8) (14) = 56 meters squared.
E. The volume of the prism, V is (56) (7) = 392 meters cubed.
Answer:
A D E
Step-by-step explanation:
A) The formula for the area of a triangle is [tex]\frac12 bh[/tex]
D) The base is 8 and the height is 14 so the area of the triangle is 56 meters squared.
E) Volume is [tex]56\times7=392[/tex] meters cubed.
Have a nice day :)
8.27 Any quarter has a face value of $0.25. An eccentric collector offers to buy state quarters for 600% of their face value. At that rate, how much will Larry receive for his collection of all 50 state quarters?
Answer:
$7.50
Step-by-step explanation:
First we find what is the value at which the eccentric collector offers to buy the quarters for. We know the value at which they will buy the quarter for is 600% of the face value - which is $0.25.
Now we do some math and find the value at which the person will buy the quarter for is $1.50.
Now we multiply the value by 50 since Larry would be giving 50 quarters.
$1.50*50 = 7.50
So, Larry will receive $7.50 for selling his 50 quarters to the eccentric collector.
Answer:
Larry will get $1.50.
Step-by-step explanation:
Given:
Any quarter has a face value of $0.25. An eccentric collector offers to buy state quarters for 600% of their face value.To find:
How much will Larry receive for his collection of all 50 state quarters.The formula used to calculate percentage is: (value/total value)×100%.
Step 1 of 1
An eccentric collector offers to buy state quarters for 600% of their face value which means [tex]$6 \times 100 \%$[/tex]. Therefore, 600% of a number is the same as 6 times that number.
50 state quarters is 0.25 dollars .
Larry will get [tex]$6 \times 0.25=1.50$[/tex] dollars.
an algebraic expression with square of the sum of two numbers is 49
(x+y)=7
Step-by-step explanation:
because the x plus y was squared,we find the square root of the 49 which is 7 and the answer remains (x+y)=7
−11−(−5)/2×3 is an example of
A. an algebraic expression
B. a numerical equation
C. a numerical expression
D. an algebraic equation
Answer:
C, numerical expression
Step-by-step explanation:
B and D mean equations, not expressions. Equations are when one side is equal to the other so we can rule those out. A algebraic expression has variables like X in it, but this doesn't have any variables, so C is your answer, a numerical expression.
19. Parkash had just enough money to buy 100 pencils. However, he bought only 70 pencils and had $4.50 left. What was the cost of each pencil?
Answer:
since the unknown amount can buy 100 pencils
he bought 70 pencils
therefore $4.50 can buy 30 pencils
so 1 pencils cost $4.50 /30=0.15
7.59. Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them, then how long total will it take to build the road?
Hint: Problems involving rates and work can often be solved by thinking about how much work is done per unit of time.
Hint: How long would it take one worker to build the whole road? What fraction of the road does one worker complete in one day?
Answer:
The number of days it takes to complete the work is 15 days.
Step-by-step explanation:
Given:
Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them
Find:
the numbers of days it takes to complete the work
Step 1 of 1
Because 5 workers can build a road in 20 days, each worker can build [tex]$\frac{1}{5}$[/tex] of a road in 20 days.
Therefore, each worker can build 1 road working alone in [tex]$20 \cdot 5=100$[/tex] days.
So, each worker builds [tex]$\frac{1}{100}$[/tex] road each day.
Therefore, three workers together build [tex]$\frac{3}{100}$[/tex] of a road each day, so in 10 days they build $10.
[tex]$\frac{3}{100}=\frac{3}{10}$[/tex] of a road.
At this point, they have [tex]$1-\frac{3}{10}=\frac{7}{10}$[/tex] of the road to the finish.
After the 11 extra workers join in, the 14 workers build [tex]$\frac{14}{100}$[/tex] of the road each day.
So, to finish the remaining [tex]$\frac{7}{10}$[/tex] of a road, the workers must work for
[tex]$$\begin{aligned}\frac{\frac{7}{10} \text { road }}{\frac{14}{100} \frac{\text { ruad }}{\text { day }}} &=\frac{7}{10} \cdot \frac{100}{14} \text { days } \\&=5 \text { days. }\end{aligned}$$[/tex]
Therefore, the road is built in 10+5=15 days
It will take 15 days to finish the road.
What is Proportion?Proportion is defined as where two or more ratios are set to be equal to each other.
If two quantities are directly proportional, if one increases or decreases, other also increases or decreases simultaneously.
If two quantities are inversely proportional, if one increases, other decreases and vice versa.
Here,
Number of days and number of workers are directly proportional to the road built.
Number of workers to build the road is inversely proportional to number of days to build the road.
Let R be the total road need to be built.
Five workers together can build a road in 20 days.
Road built by 5 workers in 20 days = R
Road built by 1 worker in 20 days = R/5
Road built by 1 worker in 1 day = (R/5) / 20
= R/100
Now, three workers work on the road for 10 days.
We have,
Road built by 1 worker in 1 day = R/100
Road built by 3 workers in 1 day = 3R/100
Road built by 3 workers in 10 days = (3R/100) × 10
= 30R/100
Remaining road to complete = R - (30R/100)
= 70R/100
= 7R/10
This is the time when eleven more workers joined.
That is, total number of workers = 3 + 11 = 14
We have,
Number of days taken by 5 workers to complete R = 20 days
Number of days taken by 1 worker to complete R = 20 × 5 = 100 days
Number of days taken by 1 worker to complete 7/10 of R = 100 × [tex]\frac{7}{10}[/tex]
= 70 days
Number of days taken by 14 workers to complete 7/10 of R = 70/14
= 5 days
Total number of days taken = 10 + 5 = 15 days
Hence if three workers work on the road for 10 days before eleven more workers join them, then it will take a total of 15 days to build the road.
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8.41 Compute 40% of 20% of 10% of 80,000.
Answer: 640
Step-by-step explanation:
In this case, we can substitute the word "of" with multiplication.
we have:
40% ×20%×10%×80000
solving this out, you get the answer!
(and yes, I recognize this problem from the aops textbook, if you want a different solution, check 8.21 in the solutions manual)
Answer:
The 40% of 20% of 10% of 80000 is 640.
Step-by-step explanation:
We are given with a number 80000We are asked to find the 40% of 20% of 10% of the numberWe can do this in one single stepStep 1: Computing the value
Step 1 of 1
We are asked to find the value 40% of 20% of 10% 80,000 40% of 20% of 10% of 80000
[tex]&=\frac{40}{100} \times \frac{20}{100} \times \frac{10}{100} \times 80000 \\&=\frac{40}{100} \times 1600 \\&=640\end{aligned}$$[/tex]
18. Ericka bought 5 palettes and 3 paint brushes for $22.40. She could have bought 14 palettes with the same amount of money. If she had bought 5 paint brushes and no palettes, how much more money would she have had to pay?
Step-by-step explanation:
since 14 palette can be bought for $22.40
then one pallet will be bought for $1.6
so 5 pallet = $8
the amount for 3 brushes = $22.40-$8 =$14.4
so the amount for one brush = 14.4/3=4.8
therefore the amount for 5 brushes =$24
therefore Ericka will extra ($24 -22.40)
=$1.6
Tell which number is greater.
11. 0.12, 1.2%
Answer: 11
Step-by-step explanation:
Out of the 3 choices, the last two both give decimals less than one, so we know they won't be greater than 11.
7.6.7. Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later, Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?
Answer:
When they finished, the number of potatoes had Christen peeled is 20 potatoes.
Step-by-step explanation:
Given:
Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute.
Four minutes later, Christen joined him and peeled at the rate of 5 potatoes per minute We have to find the number of potatoes Christen has peeled.
Step 1 of 1
Homer peels 3 potatoes a minute, so in the four minutes he works alone, he peels [tex]$3 \cdot 4=12$[/tex] potatoes.
This leaves 44-12=32 potatoes for them to peel together.
Together, they peel 3+5=8 potatoes per minute, so they need
[tex]$\frac{32 \text { potatoes }}{8 \frac{\text { potatuos }}{\text { minute }}}=4$[/tex]minutes
to peel the rest of the potatoes.
Christen peels 5 potatoes a minute for 4 minutes, so she peels [tex]$5 \cdot 4=20$[/tex] potatoes.
I REALLY NEED HELP: Greg uses an overhead projector to enlarge a rectangular drawing to a width of 300mm. The original drawing is 60 mm wide by 80mm high. What is the height of the projected image?
Answer:
height = 400mm high
Step-by-step explanation:
if 300/60=5
so 80x5=400.
If "a" is a negative integer and "b" is a positive integer, which of the following statements must be true?
I. b + a > 0
II. [tex]\frac{b-a}{a}[/tex] < 0
III. a^b < 0
A) I only
B) II only
C) III only
D) I and II only
Answer:
B
Step-by-step explanation:
I. Falae. Consider a = -3 and b = 2.
II. True. b-a must be positive, and a is negative.
III. False. Over the reals, exponential functions are positive.
8.28 Katie wants a fancy new music player that costs $300. Katie can buy it in her home state and pay 8% sales tax, or she can drive to a neighboring state and pay only 5% sales tax. How much does Katie save on the player if she drives to the neighboring state?
Answer:
Explanation
Given:- Katie wants a fancy new music player that costs $300
. Katie can buy it in her home state and pay 8% sales tax, or she can drive to a neighboring state and pay only 5% sales tax
To Find:- To determine the cost Katie saves on the player if she drives to the neighboring state
The difference between the sales tax of the home state and the neighboring state provides the percentage of sales tax . Then, multiplying the determined percentage of sales tax on the new music player would be the cost Katie saves on the player if she drives to the neighboring state.
Step-by-step explanation:
The sales tax in the home state is 8% and the sales tax in the neighboring state is 5%The percentage of sales tax saved when travelling from home state to neighboring state will be=8%-5%
=3%
Therefore, the cost Katie saves on the new music player which costs $300 if she drives to the neighboring state will be=300*3%
=300*(3/100)
=3*3
=$9
The amount Katie saves on the new music player if she drives to the neighboring state is $9
Answer:
Katie saves $9.
Step-by-step explanation:
Buy it in her home:
8% of $300 = $24
Buy it in neighbouring state:
5% of $300 = $15
How much she save's (Answer):
She saves $9 because 24 - 15 = 9.
Which ratio is leColleen compared the ratios 3:8 and One-half. Her work is shown below.
Write the ratios as fractions: Three-eighths and One-half
The common denominator is 8.
Write each fraction using the common denominator: Three-eighths and One-eighth
Compare the numerators: 3 > 1
Write the correct statement: Three-eighths > One-half
Where did Colleen make her first mistake?ss than 15/24 ?
Answer:
Step #3 is where Colleen messed up.Step-by-step explanation:
When Colleen was making a common denominator for the two fractions, she should have multiplied the numerator by 8/denominator.
For example,
1/2 with a denominator of 8 would be 4/8 since we must multiply the numerator by 4. (8/2 = 4)
So, her answer should have been 3/8 < 4/8 (which is also 3/8 < 1/2)
Answer:
Step 3 is where Colleen messed up.
Step-by-step explanation:
The Crawfords drove for 4000 miles. This was 1/3 the distance the Blake family drove. How many miles did the jones family drive.
How many arrangements of all eight letters in TRESPASS do not have S as the final letter?
Answer:
i think its 16
Step-by-step explanation:
Evaluate the following expression. -8 x (-10 + (-7))
please help!
Answer:
136
Step-by-step explanation:
Answer:136
Step-by-step explanation: 136
-10+-7 equals -17
-17x-8 equals 136
a negative times a negative equals a positive
What is angle A equal?
Thanks :)
I only need 1 more mark for this question but I don’t know what to write in order to get that mark. Can anyone help ?
Answer:
The difference between the lengths of two line segments AB and CD given in the following figure is
Step-by-step explanation:
PLEASE ANSWER ASAP: After moving to a new house the McGraths budgeted $250 for landscaping. On their visit to a local nursery they chose 8 sunflowers priced at $10.95 a piece and 12 roses priced at $11.95 each. By how much did they exceed their budget?
Answer:
They did not exceed their budget.
Step-by-step explanation:
8(10.95) + 12(11.95) = $231
250 - 231 = $19 savings
Answer: They didn't exceed the budget
Step-by-step explanation:
FACTS:
their budget is $250 dollars.
They buy:
8 sunflowers at 10.95 each
12 roses at 11.95 each.
How much did they exceed their budget? (in other words, by how much did they go over their spending limit?)
Step 1: Find the total amount of money spent on sunflowers.
We know they got 8 sunflowers, and each sunflower cost $10.95.
Total on sunflowers= 10.95x8= $87.60
Step 2: Find the total amount spent on roses
12 roses, each one costs 11.95.
total on roses= 11.95x12=$143.40
Step 3: Find how much was spent
143.4+87.6= 231
They didn't exceed their budget. In fact, they were $19 under their spending limit because 250-231= 19. I double checked my answer.
Circle the correct option: A, B, C, or D.
3. What is the value of 0.008 km in meters?
A 0.8
B 80
C 8
D 1.8
Answer:
Recall 1000m=1km
hence
0.008*1000=8
Ans 8m
how many more cartons are needed to hold 1500 books in cartons of 10 than in cartons of 15?
The cartoons of 10 be 150 and cartoons of 15 be 100.
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary MethodFirst, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
total books = 1500
So, cartoons of 10 needed
=1500 / 10
=150 cartoons
and, cartoons of 15 needed
=1500/15
=100 cartoons
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IM NEED HELPP: This year the elementary school had 175% the number of students they had last year. Last year, there were 300 students. How many are there this year?
Answer:
525
Step-by-step explanation:
Multiply 300 by 1.75. You get 525
send help 20 points added
Answer:
$6/$7
Step-by-step explanation:
150/175=
30/35=
6/7
Answer:
6/7 :)
Step-by-step explanation:
150/175 reduces to 6/7
help i dont know how to find the surface area. a step by step explanation would help me better.
Answer:
256
Step-by-step explanation:
so there is 4 rectangles, 1 square, and 4 triangles within the composite figure in the question.
so basically you find the area of each of those shapes and add them together and that's your answer.
the rectangles width is 4 and length is 12, to find the area of a rectangle you do length times width so 4 times 12 which is 48, you have 4 rectangles so 48 times 4, which is 192.
the squares sides are 4 so you multiple two of the sides so 4 times 4 which is 16.
now we have the triangles, the formula for the area of a triangle is A=[tex]\frac{hx_{b}b }{2}[/tex], so b is base, the base is 4, h is height, the height is 6, so you plug in those numbers in the formula and you get 12. you have 4 triangles so 12 times 4 which is 48.
so now you add them all together 192 + 16 + 48 = 256
400 ducks consume a reservoir of feed in 30 days, how long will it take 500 ducks
Answer:
24 days.
Step-by-step explanation:
First lets look at the facts.
400 ducks can eat a bunch of feed in 30 days.
That means that 200 ducks would take 60 days.
100 ducks would take 120 days.
Now, we must multiply 100 by 5 to get 500, the target amount of ducks, and divide 120 by 5 to get 24. So, 500 ducks can eat a reservoir of feed in 24 days.
Answer:
24 days
Step-by-step explanation:
It is an inverse proportion, the more ducks the less days the food lasts
400 ----- 30
500 ----- X
[tex]x=\frac{(400)(30)}{500} =\frac{12000}{500} =24[/tex]
Hope this helps
PLEASE ANSWER: 3 1/2 + (-7) x (2 2/3 + 1 1/2) = ?
Answer:
[tex]-\frac{77}{3}[/tex]
Step-by-step explanation:
So we have the equation: [tex]3\frac{1}{2} + (-7) * (2\frac{2}{3} + 1\frac{1}{2})[/tex]. and I'm assuming you meant to do mixed fractions and not actually multiplying. 2 * 2/3. So the first thing to do is follow PEMDAS which essentially says Parenthesis first, Exponents next, Multiplication or Division, and then Addition or Subtract. So let's start by evaluating the 2 2/3 and 1 1/2. The first step is to combine 2 into the 2/3 and the 1 into 1/2. This is done by multiplying the 2 by the denominator of 3, and adding it to the numerator so: [tex]2\frac{2}{3} = > \frac{(2*3)+2}{3} = > \frac{8}{3}[/tex]. And you do this for the 1/2 as well: [tex]1\frac{1}{2} = > \frac{(2*1)+1}{2}= > \frac{3}{2}[/tex].
Now when adding fractions, you can only add them when they have the same denominator, so we have the get 3/2 and 8/3 to have the same denominator. You can list the multiplies of 2 and 3 to try to find a LCM, but in this case, I'll just multiply 2 and 3, since they're really small numbers, also because 6 is the LCM. [tex]\frac{8}{3} * \frac{2}{2} = \frac{16}{6}[/tex]. And now do this to the 3/2 you get: [tex]\frac{3}{2} * \frac{3}{3} = \frac{9}{6}[/tex]. Now the inside of the parenthesis is: [tex]\frac{9}{6} + \frac{16}{6} = \frac{25}{6}[/tex]. So now we have the equation: [tex]3\frac{1}{2} -7 * \frac{25}{6}[/tex] . Also notice how I got ride of the plus sign and made it negative? Think of it as having a 1 in front and simply distributing that to the -7, 1*(-7) becomes -7.
Now to multiply the fraction by a whole number you simply multiply the denominator and numerator, and you can think of the denominator of a whole number as a 1. So this gives you: [tex]\frac{-7}{1} * \frac{25}{6} = \frac{-7 * 25}{1 * 6} = -\frac{175}{6}[/tex]. Now we have the equation: [tex]3\frac{1}{2} - \frac{175}{6}[/tex]. And to subtract these two numbers I'll make the 3 1/2 a fraction by multiplying the 3 by the denominator and adding it to the 1 which should become 7/2. And after that multiply both sides by 3/3 to get 21/6 so they have the same denominator. This gives you the equation: [tex]\frac{21}{6} - \frac{175}{6} = \frac{21-175}{6} = -\frac{154}{6}[/tex]. Which can simplify by dividing both sides by 2 to get: [tex]-\frac{77}{3}[/tex]
A lightbulb manufacturer must test
a
to ensure
sample of lightbulbs
that quality and safety standards are being met.
Which of these methods will produce the most representative sample
of the
population of lightbulbs made by this company?
O A. The manufacturer tests every lightbulb made on Monday.
O B. The manufacturer tests the last 100 lightbulbs produced each
month.
O C. The manufacturer tests the first lightbulb off the production line
each day.
manufacturer tests every 1000th lightbulb off the production
• D. The
line.
7. Find the sum of 67 tenths and 35 hundredths. Give your answer as a decimal.
Step-by-step explanation:
since the tenth for the 67 is 6
and the hundredth for 35 is 5
then the sum
6/10+5/100
0.6+0.05
= 0.65
Answer:
7.05
Step-by-step explanation:
67 tenths is 6.7
35 hundredths is 0.35
6.7 + 0.35 = 7.05
Which means the answer is 7.05.
The graph shows the relationship between the number of months different students practiced baseball and the number of games they won:
The title of the graph is Baseball Games. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Games Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 1 and 1, 3 and 2, 5 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 14 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 1.8 and 2, 5.6 and 4, 9.2 and 6, 13 and 8, 16.5 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent?
Answer:
Answer:
won: The title of the graph is Baseball Games. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Games Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 1 and 1, 3 and 2, 5 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 14 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 1.8 and 2, 5.6 and 4, 9.2 and 6, 13 and 8, 16.5 and 10, 20.5.
Step-by-step explanation:
Answer:
2nd one
Step-by-step explanation:
i think