tana fills the prism shown (3 1/4 and 4 inch) with 110 1/2 in squared of liquid what is the height of the prism
Answers
4
(x)(3.25)= 27.625
3.25
x = 8.5
(8.5)(3.25)(4)= 110.5
Answer:
[tex]h=8\frac{1}{2}\text{ inch}[/tex]
Step-by-step explanation:
Let h represent height of prism.
We have been given that Tana fills the prism with base lengths [tex]3\frac{1}{4}[/tex] inch and [tex]4[/tex] inch with a [tex]110\frac{1}{2}\text{ inch}^3[/tex].
We know that volume of prism is area of base times height, so we can set an equation as:
[tex]\text{Volume of prism}=\text{Base length}\times\text{Base width}\times \text{Height of prism}[/tex]
[tex]110\frac{1}{2}\text{ inch}^3=3\frac{1}{4}\text{ inch}\times 4\text{ inch}\times h[/tex]
[tex]\frac{221}{2}\text{ inch}^3=\frac{13}{4}\text{ inch}\times 4\text{ inch}\times h[/tex]
[tex]\frac{221}{2}\text{ inch}^3=13\text{ inch}^2\times h[/tex]
[tex]\frac{221}{2*13\text{ inch}^2}\text{ inch}^3=\frac{13\text{ inch}^2\times h}{13\text{ inch}^2}[/tex]
[tex]\frac{221}{26}\text{ inch}=h[/tex]
[tex]8\frac{13}{26}\text{ inch}=h[/tex]
[tex]8\frac{1}{2}\text{ inch}=h[/tex]
Therefore, the height of the prism is [tex]8\frac{1}{2}\text{ inch}[/tex].
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Lena's guest house is 15 m long and 12 m wide. How long is the diagonal of the house?
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If a square with a side of six is cut into three congruent rectangles, what is the perimeter of one of those rectangles
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Square= a shape with four sides of equal length that meet to form four right angles.
Congruent rectangles = rectangles that are exactly the same in size and shape.
Perimeter = in this case, it is the sum of all the sides of the rectangle
The question asks you to divide a square with sides that are 6 units long into 3 congruent rectangles.
If it is hard to picture this in your head, I recommend that you draw a picture. I drew one for you so you can see how mine looks. In the picture, you can see I cut one side of the square into 3 equal pieces. So, we divide the total side length by the number of equal divisions to get the heights of the rectangles. I got height (h)= 2 units. To find the width of the rectangles, you can merely use the length of a side of the square. So, the width(w)=6 units. So, then to get the perimeter of a rectangle you add up all the sides. Perimeter= h+h+w+w= 2+2+6+6= 16 units. I got rectangle perimeter=16 units for my final answer. Hope this helped! Comment on this answer if you still have any questions or you think I messed up. :)
In the expression, 8.92 x (10 x 10 x 10), which number is the base?
a) 8.92
b) 10
c) 3
d) 8
Answers
What is 68127000000000000 in scientific notation
Answers
6.8127 *10^16
68127000000000000 can be written in scientific notation as 6.8127 × 10¹⁶
What is Scientific Notation?
Scientific Notation is a method used in mathematics to express large numbers in standard form so that they will be easier to calculate.
This standard form is written in decimal form multiplied by the power of the corresponding values after the first digit.
From the given information;
68127000000000000 can be written in scientific notation as:
= 6.8127 × 10¹⁶
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Anna buys groceries for her family.hamburger meat is $3.38 per pound sweet potatoes are$0.79. Each and hamburger rolls are $2.30a bag.if Anna buys 3 pounds of meat 5 sweet potatoes and 1 bag of hamburger rolls what will she pay in all for the groceries
Answers
3.38 x 3 = 10.14 for the hamburger meat
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To further explain this, and/or to find answers to similar problems like this, you take the amount per pound or whatever unit of measurement (let’s say this variable is Z) and then you take the amount that they are getting per said unit ( let’s say Y) thus an equation that can be used to find problems like this is Z x Y.
The total amount of money paid by Anna is [tex]\fbox{\bf \$16.39}[/tex].
Further explanation:
Given:
Anna buys 3 pounds of hamburger meat.
Anna buys 5 sweet potatoes.
Anna buys 1 bag of hamburger rolls.
The cost of hamburger meat is $3.38 per pound.
The cost of 1 sweet potato is $0.79.
The cost of 1 bag hamburger is $2.30.
Procedure:
1. First find the money spent on hamburger meat, sweet potatoes, and hamburger rolls.
2. Now add all the money to obtain the total money spent on the groceries.
Calculation:
The money spend by Anna on the hamburger meat is obtained as follows:
[tex]\boxed{3.38\times3=\$ 10.14}[/tex]
The money spend by Anna on the sweet potato is obtained as follows:
[tex]\boxed{0.79\times5=\$ 3.95}[/tex]
The money spend by Anna on the hamburger roll is obtained as follows:
[tex]\boxed{2.30\times1=\$ 2.30}[/tex]
Total money spent by Anna to buy all the groceries can be obtained by the sum of the amount of money spent on all the groceries.
Therefore the total money paid by Anna is obtained as,
\boxed{\$ \left( {10.14 + 3.95 + 2.30} \right) = \$ 16.39}.
Thus, the total amount of money paid by Anna is [tex]\fbox{\bf \$16.39}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expression
Keywords:
Anna, groceries, sweet potato, hamburger meat, hamburger rolls, bag, pounds, 3, $3.38, $0.79, family, total money, spend.
Sandra and her friend went to the candy store. Each of the purchased a bag of jelly beans. Sandra's bag weighed 1.25 pounds. Her friend's bag weighed 1.05 pounds. Who bought more candy?
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The area, a, of a trapezoid is calculated using the formula A= 1\2(b+c)h, where h is the height of the trapezoid and b and c are the base of the trapezoid. Rearrange the formula to solve for h
Answers
To rearrange the formula for the area of a trapezoid to solve for the height, divide both sides of the equation by (b+c)/2. The rearranged formula is h = 2A/(b+c).
Explanation:The formula for the area of a trapezoid is given by A= 1/2(b+c)h, where A is the area, h is the height, and b and c are the lengths of the two bases. To rearrange this formula to solve for h (the height), you need to isolate h on one side of the equation. The rearranged formula would look as follows: h = 2A/(b+c).
To obtain this, we divided both sides of the equation by (b+c)/2. This gives us a new formula to find the height of the trapezoid given the area and the lengths of the two bases.
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What number is 46% of 150
Answers
0.46(150) = 69 <==
So, lets workout this problem to find our [tex]answer[/tex]
Just remember the [tex]percentage [/tex] will be going out of [tex]100[/tex]
Now, [tex] \frac{46}{100} (150) [/tex]
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Good luck on your assignment and enjoy your day!
~[tex]MeIsKaitlyn :)[/tex]
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A rancher has a roll of fencing to enclose a rectangular area. The table shows how the area that the rancher can enclose with the fencing depends on the width of the rectangle.
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Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet?
A. A(w)= -w to the power of 2+200w
B. A(w)= -w to the power of 2+100w
C. A(w)= w to the power of 2+40w
D. A(w)= w to the power of 2+90w
Answers
and then the second one
B
Option A: [tex]A(w) = -w^2+200w[/tex]
Substitute w = 10 and check if we'd get 900 as the answer
[tex]A(10) = -(10)^2+200(10) = -100+2000 = 1900[/tex]
Option B: [tex]A(w) = -w^2+100w[/tex]
Substitute w = 10 and check if we'd get 900 as the answer
[tex]A(10)=-(10)^2+100(10)=-100+1000=900[/tex]
Option C: [tex]A(w)=w^2+40w[/tex]
Substitute w = 10 and check if we'd get 900 as the answer
[tex]A(10) = 10^2+40(10)=100+400=500[/tex]
Option D: [tex]A(w) = w^2+90w[/tex]
Substitue w = 10 and check if we'd get 900 as the answer
[tex]A(10)=10^2+90(10) = 100+900=1000[/tex]
Answer: Option B
3.6 divided by 24 equals what?
Answers
The value of the expression is 3/20.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
3.6 ÷ 24
= 3.6/24
= 36/240
= 9/60
= 3/20
Thus,
The value of the expression is 3/20.
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Angela ordered 2 glass paperweights. The volume of each paperweight is 5 cubic inches, and the density of the glass is 1.5 ounces per cubic inch. Angela can use the calculation below to find the total weight of her order.
2×(5×1.5)
How can Angela simplify the calculation using only the associative property of multiplication?
Answers
Answer:
(2 times 5) then times 1.5
Step-by-step explanation:
i took K12 test
at movies you order 3 boxes of popcorn and a bottle of water the cost of the bottle of water is $1.75 your total cost is 9.25 write and solve an equation to find the cost of one box of popcorn
Answers
9.25-1.75=7.50
7.50/3=2.50
$2.50
The sum of two numbers is 26. Four less than four times the smaller number is equal to the larger number x. Find the larger number.
Answers
This question just wants you to create an equation and solve. In this case, the larger number is equal to x. To find the smaller number, we would need to multiply x by 4 and subtract 4 from it. This means that the smaller number is equal to (4x – 4). You add the two numbers, x and (4x – 4), to get 26. Your final equation is:
x + (4x – 4) = 26
Now, just solve.
x + 4x – 4 = 26
(5x – 4) + 4 = (26) + 4
(5x) ÷ 5 = (30) ÷ 5
x = 6
Finally, just plug in 6 for both numbers to get your answer.
(6) + (4(6) – 4) = 26
6 + 20 = 26
Your two numbers are 6 and 20.
Hope this helped you out! :-)
Final answer:
To find the larger number, two equations were formed based on the given problem and solved sequentially. The smaller number was found to be 6, and using this value, the larger number was determined to be 20.
Explanation:
The sum of two numbers is given as 26. This information forms our first equation: s + l = 26, where s is the smaller number and l is the larger number.
We are also told that four less than four times the smaller number is equal to the larger number. This gives us our second equation: 4s - 4 = l.
Now, we can use substitution to solve for the larger number. First, rewrite the second equation in terms of s: l = 4s - 4. Then, substitute this expression for l into the first equation: s + (4s - 4) = 26.
Solving for s, we combine like terms: 5s - 4 = 26. Then, we add 4 to both sides to isolate the terms with s: 5s = 30. Dividing both sides by 5 gives us the smaller number: s = 6.
Finally, we find the larger number by substituting s back into the second equation: l = 4(6) - 4. This operation gives us the larger number l = 24 - 4, hence l = 20.
The larger number is 20.