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A rectangular prism is completely packed with 90 cubes of edge length 1/2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism?
A: 11 unit cubes and 1 smaller cube of volume 1/8 cubic inch
B: 22 unit cubes and 4 smaller cubes of volume 1/8 cubic inch each
C: 11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each
D: 22 unit cubes and two smaller cubes of volume 1/8 cubic inch each
Answer:
C. (11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each.)
Step-by-step explanation:
90 cubes * 1/8 inch = 11 1/8 inch.
what is the sum of the finite arithmetic series ? 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)
[tex]\text{Consider the sum of the finite arithmatic series}\\ \\ 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)\\ \\ \text{We know that the sum of the finite arithmatic series }\\ \\ a_1,a_2, a_3, ..., a_n \text{ is given by the formula}\\ \\ S_n=\frac{n}{2}\left ( a_1+a_n \right )\\ \\ \text{here in the given series, we can see that }a_1=7.6, \ a_n=-1.5 \text{ and}\\ \text{the number of terms is, }n=8. \text{ so using above formula, we get}[/tex]
[tex]S_8=\frac{8}{2}\left ( 7.6+(-1.5) \right )\\ \\ =4\left ( 7.6-1.5 \right )\\ \\ =4\left ( 6.1 \right )\\ \\ =24.4[/tex]
Hence the sum of the finite Arithmetic series is: 24.4
Which explanation justifies how the area of a sector of a circle is derived?
- Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by the area of the circle .
- Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
- Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle.
- Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.
The statement that justifies how the area of a sector of a circle is derived is:
Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.What is an area?This refers to the quantity that expresses the extent of a region on the plane such as on a curved surface.
Furthermore, the area of sector of a circle is talking about the amount of space enclosed within the boundary of the sector.
Generally, it is explained in step that we first calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
Therefore, the Option B is correct.
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Which ratio can be used to convert meters to kilometers
Martha and steve have 95 colored pencils. If Martha has 4 times as many as steve, how many does Steve have
Answer:
Steve has 19 pencils
Step-by-step explanation:
4 times of 19 is 76
So, Martha has 76 and Steve has 19
76+19=95
hope this helps!
solve the problem 22=4+8e-2e
The smaller rectangle was scaled by a factor of 4 to produce the larger figure.
Use the drop-down menus to show the missing dimensions of the scaled figure.
Answer:
Step-by-step explanation: so the problem is asking for the missing dimensions of the rectangle. The smaller rectangle has a length of 12 inches, a width of 8 inches, and an area of 96 inches. To clarify, 8x12 is 96 so when looking at the bigger rectangle, it says that it was scaled by a factor of 4.
The Answer-
Length:48
Width:32
Area:1,536
Use 3.14 for and round your final answer
You charged $65 dollars on a credit card and you returned a item hat was pitched with the card and it cost $24? Then u bought an item with he card that cost $24 dollars
what was sal finding when he plugged t=10 into the expression 5t+3?
a. The cost of 10 tickets
b. The cost of 53 tickets
c. The number of tickets that would cost 10 dollars
d. The number of tickets that would cost 53 dollars
Answer:
a. The cost of 10 tickets
Step-by-step explanation:
We don't know what the expression is supposed represent, but the answer choices suggest that ...
c = 5t +3
represents the cost of t tickets. Then, when t=10, c = 53 will represent the cost of 10 tickets.
What’s 5/9 rounded to the nearest half
The round off to nearest half is 1/2.
What is Round off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
The fraction = 5/9.
Now, rounded to the nearest half is 1/2
we know 9 halved value is 4.5 which is much closer to 5.
So, we can write it as 5/10 = 1/2.
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Four friends share 3 apples equally. what fraction of an apple does each friend get
HELP! Multiplying radicals. Questions on photo.
Determine whether the following expressions are equivalent to 3(4+2b) . Expressions Yes - Yes No - No 24b 6(b+2) (12b+2b) 6b+12
Find the distance between (6,-3) & (-1, 7) on the CCS
Answer:
9 or (5,4)
Step-by-step explanation:
Just subtract it on each side :)
Answer the manager one
a triangle has interior angles measuring 36° and 112° which triangles are similar to this triangle select true or false for each triangle
Answer:
Triangle with interior angles measuring 36° and 32°
Triangle with interior angles measuring 32° and 112°
Step-by-step explanation:
we know that
If two triangles are similar, then its corresponding angles are congruent
If two triangles have two equal internal angles, then the triangles are similar by AA Similarity Postulate
step 1
Calculate the measure of the third internal angle
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
Let
x------> the measure of the third internal angle
[tex]x\°+36\°+112\°=180\°\\ \\x=180\°-148\°\\ \\x=32\°[/tex]
step 2
Verify each triangle
case A) Triangle with interior angles measuring 36° and 32°
Is true -----> by AA Similarity Postulate
case B) Triangle with interior angles measuring 36° and 148°
Is false -----> Is not a triangle because the sum of its internal angles is greater than 180 degrees
case C) Triangle with interior angles measuring 32° and 112°
Is true -----> by AA Similarity Postulate
case D) Triangle with interior angles measuring 112° and 148°
Is false -----> Is not a triangle because the sum of its internal angles is greater than 180 degrees
Answer:
agree
Step-by-step explanation:
What is the slope of the line that passes through the points (2, 3) and (–2, 6)?
solomon has read 1/3 of his book. He finishes the book by reading the same amount eat night for 5 nights what fraction of the book does he read each of the 5 nights?
Final answer:
Solomon has 2/3 of the book left to read. To finish it over 5 nights, he needs to read 2/15 of the book each night.
Explanation:
Solomon has read 1/3 of his book already. To finish the remaining 2/3 of the book in 5 nights, we need to calculate the fraction of the book he should read each night. Since he has to evenly distribute the remaining portion over 5 nights, we will divide 2/3 by 5.
Here's the calculation step-by-step:
First, represent the remaining part of the book as a fraction, which is 2/3.
To divide this fraction by 5, we multiply the denominator by 5. This gives us (2/3) × (1/5).
Multiplying these fractions, we get (2 × 1) / (3 × 5), which simplifies to 2/15.
Thus, Solomon reads 2/15 of the book each night for the next 5 nights.
Audrey is buying a nee car for $32,998. She plans to make a down payment of $4,200. If she's to make a monthly payments of $525 for the next five years, what APT has she paid?
What is the slope of the line passing through the point (-3,-1) and the origin?
Describe the differences between vertical and adjacent angles
irrational number of 5
2 × 7/8 as a model how do I draw it as a model
What is the following product? 4 square root 7
"4√7" means four times the square root of 7, approximately equal to 10.582, an irrational number with decimal expansion.
The expression "4√7" represents the square root of 7, multiplied by 4. Let's break it down step by step:
1. Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Similarly, the square root of 25 is 5 because 5 × 5 = 25.
2. √7: This symbol (√), called the radical symbol, represents the square root. So, √7 represents the square root of 7, which is an irrational number, meaning it cannot be expressed as a simple fraction and has decimal places that go on indefinitely without repeating.
3. 4√7: This means you're taking the square root of 7 and then multiplying it by 4. So, if you calculate it, it's like doing 4 times the square root of 7.
To give a numerical example, if we want to find the value of 4√7:
4 × √7 ≈ 4 × 2.6457513110645905905016157536393... (approximately)
Thus, 4√7 is approximately equal to 10.582, depending on how many decimal places you round to.
In summary, "4√7" represents four times the square root of 7, which is an irrational number, approximately equal to 10.582.
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1. ABC undergoes a dilation, with a scale factor of 8, to form A'B'C'.
Side A'B' is 8 times the length of side AB.
What is the area of A'B'C', compared to the area of ABC?
A. The area of A'B'C' is 1/8 of the area of ABC
B. The area of A'B'C' is 1/64 of the area of ABC
C. The area of A'B'C' is 8 times the area of ABC
D. The area of A'B'C' is 64 times the area of ABC
2. DEF undergoes a dilation, with a scale factor of 4, to form D'E'F'.
Side D'E' is 8 times the length of side DE.
What is the area of D'E'F', compared to the area of DEF?
A. The area of D'E'F' is 1/4 of the area of DEF
B. The area of D'E'F' is 1/16 of the area of DEF
C. The area of D'E'F' is 4 times the area of DEF
D. The area of D'E'F' is 16 times the area of DEF
3. ABC undergoes a dilation, with a scale factor of 3, to form A'B'C'.
Side A'B' is 3 times the length of side AB.
What is the area of A'B'C', compared to the area of ABC?
A. The area of A'B'C' is 1/3 of the area of ABC
B. The area of A'B'C' is 1/9 of the area of ABC
C. The area of A'B'C' is 3 times the area of ABC
D. The area of A'B'C' is 9 times the area of ABC
area of triangle is = 1/2 * base * altitude
1- each side is made 8 times
so the net change in area is 64 times
The area of A'B'C' is 64 times the area of ABC
2- each side is made 4 times
so the net change in area is 16 times
The area of D'E'F' is 16 times the area of DEF
3- each side is made 3 times
so the net change in area is 9 times
The area of A'B'C' is 9 times the area of ABC
There are 56 trees in an apple orchard. They are arranged in equal rows. There are 8 trees in each row. How many rows of apple trees are there? Which equation can be used to solve this problem?
solve the compound inequality