Answer:
Part 1)
The scale factor of the smaller prism to the larger prism is 3
or
The scale factor of the larger prism to the smaller prism is 1/3
Part 2) The surface area of the smaller prism is 66 square centimeters
Step-by-step explanation:
Part 1) What is the scale factor for the similar figures?
we know that
If two figures are similar, then the ratio of their volumes is equal to the scale factor raised to the cube
Let
z ----> the scale factor
x ---> volume of the larger prism
y ---> volume of the smaller prism
so
[tex]z^3=\frac{x}{y}[/tex]
we have
[tex]x=972\ cm^3\\y=36\ cm^3[/tex]
substitute
[tex]z^3=\frac{972}{36}[/tex]
Simplify
[tex]z^3=27\\z=3[/tex]
therefore
The scale factor of the smaller prism to the larger prism is 3
or
The scale factor of the larger prism to the smaller prism is 1/3
Part 2) What is the surface area of the smaller prism?
we know that
If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared
Let
z ----> the scale factor
x ---> surface area of the larger prism
y ---> surface area of the smaller prism
so
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]x=594\ cm^2[/tex]
[tex]z=3[/tex]
substitute
[tex]3^2=\frac{594}{y}[/tex]
solve for y
[tex]y=\frac{594}{9}=66\ cm^2[/tex]
therefore
The surface area of the smaller prism is 66 square centimeters
The steps Quentin took to evaluate the expression 3m - 3+3 when m = 8
are shown below.
3m - 3 + 3 when m=8
3 x 8 = 24
24 - 3 =21
21 + 3 = 7
What should Quentin have done differently in order to evaluate the
expression?
divided (24-3) by (24x3)
divided (24-3) by (24-3)
subtracted (3 + 3) from 24
subtracted 3 from (24 +3)
Quentin had properly substituted m with 8, but he mistakenly added 3 to 21 rather than subtracting. The right final calculation should provide 24, not 7.
Explanation:In order to correctly evaluate the expression 3m - 3 + 3 when m = 8, Quentin starts off correctly by replacing m with 8, resulting in 24. The mistake happens when Quentin incorrectly adds 3 to 21 instead of subtracting 3 from 21. The correct sequence of steps should be:
3m - 3 + 3 when m=8Replace m with 8. Therefore, 3 * 8 = 24Subtract 3 from 24. Therefore, 24 - 3 = 21Add 3 back to the result of 21 - 3. Therefore, 21 + 3 = 24Learn more about Math Expression Error Correction here:
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if one m&m is randomly selected from a dish containing 7 green, 4 red, 5 blue and 8 yellow m&ms, find the probability that a red is selected
Answer:
1/6 = 16.67%
Step-by-step explanation:
There are a total of 24 m&ms. The probability of picking an m&m that has a quantity of 4 is 4/24 = 1/6 = 16.67%
A 12 pack of cola costs $5.46. How much does one can of cola cost? In other words, find the unit rate of one can of cola.
Answer:
.45
Step-by-step explanation:
5.46 is a 12 pack
5.46/12 = .455
Answer:
$0.46
Explanation:
12 cans = $5.46
1 can = .455
Which dimensions will create an unlimited number of triangles?
angle 55°
angle 50°
angle 60°
angle 45°
angle 45°
angle 90°
side length of 6
side length of 8
side length of 10
side length of 5 in.
side length of 10 in.
side length of 12 in.
Answer:
B
Step-by-step explanation:
the answer to this question is
angle 45
angle 45
angle 90
The common difference ,d in an arithmetic sequence whose fourth term is 16 and whose seventh therm is 31
Answer: d=5
Step-by-step explanation:
Arithmetic progression
An=a1+d(n-1)
An= nth term
A1= first term
D= common difference
N= nth position
We are given the 4th and 7th terms
For 4th term,n=4
A4=a1+d(4-1)
A4= 16
16= a1+d(4-1)
16= a1+3d........equation 1
For the 7th term,n=7
A7=a1+d(7-1)
A7= 31
31=a1+6d......equation 2
Bring them together
16=a1+3d
31=a1+6d
Subtract equation 1 from 2
So we have
15=3d
D=15/3
D=5
Therefore, the common difference is 5
How many inches if wooden sticks will be required?
The required amount of wooden sticks would depend on specific measurements for different projects, such as making a Biltmore stick for tree height measurement or spacing vertical studs 16 inches apart, which is equal to 40.64 centimeters. Measurements and conversions would be necessary to determine the exact amount of material needed.
Explanation:The amount of wooden sticks required would depend on the specific project being undertaken. The details provided mention various projects, including constructing a Biltmore stick for measuring tree heights, vertical studs spaced 16 inches apart for lumber usage, and spacing between scaffolds that could be anywhere from 3 to 12 inches. For the Biltmore stick, you would need a stick long enough to reach from your eye level to the ground, as well as additional sticks or markers for the grading. For constructing vertical studs spaced 16 inches apart, you would convert that distance into centimeters, where 16 inches is equal to about 40.64 centimeters. Other examples require sticks of varying sizes, from the barrel of a plastic stick pen cut in half, which would be a few inches, to a list of materials needed for a pyramid structure that changes by 12 inches per level.
Estimate the perimeter of the figure to the nearest whole number.
Answer:
See Explanation Below
Step-by-step explanation:
The question is incomplete (because the figure to calculate the perimeter is missing).
However from the comment attached to your question, I understand that the figure looks like a plus sign.
The perimeter of a plane shape is calculated by adding the length of each side of the shape.
Take for instance;
A square of length 5cm.
We know that a square has 4 equal sides; meaning that the length of the other sides are also 5cm
So, the perimeter of the square will be calculated as 5cm + 5cm + 5cm + 5cm = 20cm
Similarly, the perimeter of a triangle whose sides are 4ft, 3ft and 5ft will be calculated by adding up the length of the three sides.
Perimeter of the triangle = 4ft + 3ft + 5ft
Perimeter = 12ft.
Having explained how the perimeter of a plane shape is calculated; take for example, the attachment below.
(The sides are measured in centimetres)
The plus sign has 12 sides; Its perimeter is calculated by adding up the length of the 12 sides.
Perimeter = 3 + 7 + 7 + 5 + 5 + 5 + 5 + 2 + 2 + 4 + 4 + 3
Perimeter = 52cm
Answer:
stop tryna cheat and figure it out
Step-by-step explanation:
Factor this expression completely.
39x − 52y + 13
Answer:
13(3x-4y+1)
Step-by-step explanation:
Rewrite 52 as (4)(13)
Rewrite 39 as (3)(13)
[tex]=(3*13)x+(4*13)y+13[/tex]
Then factor out the common term 13
[tex]13(3x-4y+1)[/tex]
That is your answer!
Have a nice day. Please vote brainliest!
Answer:
13(3x-4y+1)
Step-by-step explanation:
a rectangle has an are of 240 square centimeters. The height of the rectangle is 24 centimeters. What is length of its base?
Answer:
The length is 10 cm
Step-by-step explanation:
The area of a rectangle is found by
A = l*w
240 = 24*l
Divide each side by 24
240/24 = 24l/24
10 =l
The length is 10 cm
6. Y=...?
Find the equation using the graph and table of values.
Answer:
[tex]y=-1x+1[/tex]
Step-by-step explanation:
To find the equation, you have to know the equation 'format' which is [tex]y=mx+b[/tex]
mx is the slope
b is the y-intercept
The slope is -1 because it goes down 1 and right 1 [tex]\frac{rise}{run}[/tex]
The y-intercept is 1 because that is where the line touches the y-axis.
So, if we plug it in, it will look like:
y = -1x + 1 which can also be written as y = -x + 1
A pyramid-shaped roof has a slant height of 16 ft and its square base is 40 ft wide. How much roofing material is needed to
cover the roof?
Answer:
1280ft²
Step-by-step explanation:
To find the total surface area of a square pyramid, we find the area of the square base and add it to the area of the four triangular faces.
The area of the square base is
[tex] {40}^{2} = 1600 {ft}^{2} [/tex]
The area of the four triangular faces is
[tex] = 4 \times \frac{1}{2} \times 40 \times 16 = 1280 {ft}^{2} [/tex]
In the context of this problem , the base will not be roofed, therefore the 1280 ft² of material is needed to cover the roof
2 PONS
Factor the polynomial: x(3x + 5) - 4(3x+5)
O A. (3x+5)(x - 4)
O B. 4x(3x + 5)
O C. (3x+5)(x+4)
O D. -4x(3x + 5)
SUBMIT
The right answer is of option A.
Look at the attached picture⤴
Hope it will help you...
Round 6.82245628434 to 5 decimal places
The number after rounding off to 5 decimal places will be -
6.88246
We have the following number - 6.82245628434
We have to round it of to 5 decimal places.
What are Rounding numbers?Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. Foe example - 53 rounded to the nearest ten is 50.
According to the question, we have the following number -
6.82245628434
Rounding it off One by one until we get 5 digits after decimal -
R1 - 6.8224562843
R2 - 6.822456284
R3 - 6.82245628
R4 - 6.8224563
R5 - 6.822456
R6 - 6.82246
Hence, the number after rounding off to 5 decimal places will be -
6.88246
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The number 6.82245628434 rounded to 5 decimal places is 6.82245.
Explanation:To round the number 6.82245628434 to 5 decimal places, you should consider the 6th digit beyond the decimal point. In this case, the 6th digit is number 5, and the 5th digit is 2 that is even. Because the digit following the decimal place you are rounding to (5th place, the digit is 2) is exactly 5 and preceding digit is even, you don't round up the preceding digit. So, when you round 6.82245628434 to 5 decimal places, you get 6.82245.
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Need help on number 10!!
Answer:
looking for the leg
Step-by-step explanation:
use patharoum therom to solve
Answer:
Step-by-step explanation:
For the check one box it will be hypotenuse and the equation will be 36^2 and 34^2
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.
What is the probability of drawing a red marble out of the bag without looking?
Answer:
3/9
Step-by-step explanation:
Help me ASAP please
Answer: 120
Step-by-step explanation:
Answer:
The one on the left is 120.
The one on the right is 185
Step-by-step explanation:
It izz wat it izzzz!!!
How many solutions does the equation 5x=2 have
Answer:
one solution
Step-by-step explanation:
5x=2
Divide each side by 5
5x/5 = 2/5
x = 2/5
There is one solution
Started at 15 degrees and dropped 1/2 degrees each minute
Answer:
7.5 should be the answer sorry if its wrong i don't have all of the information
please...please help offering 20 points
Answer:
Option D 0.84
Step-by-step explanation:
Answer:
0.84
Step-by-step explanation:
i think thats it because i know it cant be a negative
What is the distance between (-6,4) and (-8, 6)?
Answer:
[tex]\sqrt{8}=2\sqrt{2}[/tex]
Step-by-step explanation:
by using well known formula, distance on XOY plane
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\=\sqrt{(-8-(-6))^2+(6-4)^2}
\\=\sqrt{(-2)^2+(2)^2}[/tex]
The distance between the points (-6,4) and (-8, 6) can be found using the distance formula derived from the Pythagorean Theorem. After substituting and simplifying, we find the distance to be sqrt[8] or about 2.83 when rounded to two decimal places.
To find the distance between two points, we use the distance formula derived from the Pythagorean Theorem: d = sqrt[(x2 - x1)² + (y2 - y1)²].
Here, we are trying to find the distance between points (-6,4) and (-8, 6). We assign (-6,4) to (x1, y1) and (-8,6) to (x2, y2).
So, substituting into our formula we get: d = sqrt[(-8 - (-6))² + (6 - 4)²] = sqrt[(2)^2 + (2)^2] = sqrt[4 + 4] = sqrt[8] or about 2.83 when rounded to two decimal places.
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Which of the following groups is NOT considered a sample of the US population?
A.) Women who live in the US
B.) People who are registered to vote in the US
C.) Europeans who vacation in the US
D.) Students who attend public schools in the US
The correct groups is NOT considered a sample of the US population is,
⇒ Europeans who vacation in the US.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
To find groups which is NOT considered a sample of the US population.
Now, By the given statements we get;
The correct groups is NOT considered a sample of the US population is,
⇒ Europeans who vacation in the US.
Thus, Option C is true.
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What did the Selective Service Act mean for American men
Answer: The Selective Service Act requires all men between the ages of 21 and 30 to register for military service.
Step-by-step explanation:
Answer:
they could be drafted into the army
Step-by-step explanation:
Ape x
What is the mean?
1 4 0 0 1 5 3 2 2
Answer:
Mean is 2
Step-by-step explanation:
what is the width of orion’s belt? That is, what is the distance between alnitak and mintaka
Answer:width-184.08 light year distance between alnitak and mintaka-60 light years
Step-by-step explanation:
2/3 of the students in the cafeteria are in sixth grade how many students are in the cafeteria if 42 of them are sixth graders
Answer:
28
Step-by-step explanation:
2/3 times 42
A windshield wiper blade turns through an angle of 135°. The bottom of the blade traces an arc with a 5-inch radius. The top of the blade traces an arc with a 22-inch radius. To the nearest inch, how much longer is the top arc than the bottom arc? Round to the nearest whole number.
The upper arc is longer than the lower arc by inches.
Step-by-step explanation:
Since both the arcs are made by the same wiper blade, hence the angle of the arc would be the same.
The radius of upper arc= 22 inch
The radius of the lower arc= 5 inch
Angle made by the arc= 135°
We know that length of the arc= (angle made/360)*2πr
Where r is the radius of the arc
The difference in the arc length has been due to the difference in radius of the arcs.
Hence, the difference in the radius would be equal to the difference in arc length.
Difference in wiper radius= 22-5= 17 inch
Putting the values together
arc length= (135/360)*2*3.14*17
arc length= 40.035
The difference in arc length=40 inches (rounded off to the nearest whole number)
Jonas and Marisol were the only candidates for sixth-grade class president. Jonas received 35 votes and Marisol received 75 votes.
Of the 75 votes cast for Marisol, 40% were girls. How many girls voted for Marisol?
****BRANLIEST OF 2
Answer:
30girls
Step-by-step explanation:
If out the 75 votes cast for Marisol, 40% were girls, the number of girls that votes for Marisol can be gotten by taking 40% of the total number of votes casted for Marisol as shown:
Number of girls = 40/100 × 75
Number of girls = 300/10
Number of girls that voted for Marisol = 30girls
Answer:
30 girls
Step-by-step explanation:
I just took the quiz and got thirty girls right. May I please have Brainliest?
Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
Answer:
2012
Step-by-step explanation:
Based on the graph, you can tell that private residence needed 6000 liters of cleaner in 2012 and only 2000 in 2016
Recess began at 11:12am. It ended at 11:44am. How long was recess?
Answer:
32 minutes
Step-by-step explanation:
44-12=32
Answer:
32 minutes
Step-by-step explanation:
Both times were at 11 am and some minutes. The difference is only in the minutes.
44 - 12 = 32
Answer: Recess was 32 minutes long.
Describe the likelihood of spinning an odd
number then an even number.