Answer:
Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. ... If you are using a ruler with a centimeter (cm) scale, then your units are going to be in cm, and if you ... We have to do the same thing to volume like we did with the surface area.
:)
Answer:
Rectangular prism
I chose a box of cereal.
Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part 2).
Describe the shape of the cross-section when the box is cut parallel to the base.
The shape of the cross-section would be a rectangle in dimensions.
20 cm x 8 cm
Part 3)
What is the surface area of the box?
surface area=2*area of the base + perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is
2,112 cm²
Part 4)
What is the surface area of the box if it is scaled up by a factor of 10?
we know that
surface area of the larger box =[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is
211,200 cm²
Part 5)
What is the volume of the box?
volume of the box = L*W*H 20*8*32-5,120 cm³
the answer Part 5) is
5,120 cm³
Part 6)
What is the volume of the box if it is scaled down by a factor of 1/10?
we know that
the volume of the smaller box =[scale factor]³volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box =[1/10]³*5,120 5.12 cm³
the answer part 6) is
5.12 cm³
The length is 6 in., the width is 2 in., and the height is 16 in.
A scale drawing of Jimmy's living room is shown below:
If each 2 cm on the scale drawing equals 8 feet, what are the actual dimensions of the room?
Length = 8 feet, width = 6 feet
Length = 12 feet, width = 8 feet
Length = 18 feet, width = 16 feet
Length = 24 feet, width = 16 feet
Answer:
last option
Step-by-step explanation:
Basically, every 1 cm is 8 / 2 = 4 feet so the width is 4 * 4 = 16 and the length is 6 * 4 = 24.
Answer:
option D
Step-by-step explanation:
For what values of the following expressions are true: |a−5|=5−a
Answer:
Whenever a-5<0 or a<5
Step-by-step explanation:
So if you have an absolute value, that turns into two equations. The one we care about is -(a-5)=5-a. After distributing the negative through the left side of the equation, you'll get that 5-a=5-a, which is an identity. But you can only say that abs(a-5)=5-a when a-5<0. To see a visual representation of this, graph both sides of the equation in desmos.
Which system has no solution?
Check all that appy.
PLEASE HELP ASAP ON ALL THE PARTS!!! suppose there is a card game where you are dealt a hand of three cards. you have already learned that the total number of three card hands that can be dealt from a deck of 52 cards is:
Answer:
A. The total number of three-card hands (permutations) that can be made with two aces is 576
B. The actual number of two-ace hands (combinations) you can get from a deck of 52 cards is 288
C. The probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 0.0130
Step-by-step explanation:
A. In order to calculate the total number of three-card hands (permutations) that can be made with two aces we would have to make the following calculation:
total number of three-card hands (permutations) that can be made with two aces=4*3*52
total number of three-card hands (permutations) that can be made with two aces=576.
B. In order to calculate the actual number of two-ace hands (combinations) you can get from a deck of 52 cards we would have to make the following calculation:
actual number of two-ace hands (combinations) you can get from a deck of 52 cards=4C2*48
4C2=4!/2!2!
C2=6
Therefore, actual number of two-ace hands (combinations) you can get from a deck of 52 cards=6*48=288
C. In order to calculate the probability of drawing a three-card hand that includes two aces from a deck of 52 cards we would have to make the following calculation:
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=actual number of two-ace hands (combinations) you can get from a deck of 52 cards/52C3
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=288/22,100
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=0.0130
John has 14 boxes of apples. Each box holds 12 apples. If 6 of the boxes are full, and 8 of the boxes are half full, how many apples does John have?
Answer:
120
Step-by-step explanation:
12 x 6 = 72
8x(12/2)=48
72+48 =120
At a figure skating competition, the order of skaters is randomly selected. If
there are 20 skaters, what is the probability that Christie, Taylor, and Jona will
skate first, second, and third, respectively?
Answer: [tex]\dfrac{1}{6840}[/tex]
Step-by-step explanation:
According to the permutations:
The arrangement of n things in an order = n!
If we fix that the first, second, and third person for skating, then we to arrange only 17 of the skaters.
Number of ways to arrange rest of 17 skaters = 17!
Number of ways that Christie, Taylor, and Jona will skate first, second, and third, respectively = 1 x 17!=17!
Number of ways to arrange all 20 skaters = 20!
Now, the required probability = [tex]\dfrac{\text{favourable outcomes}}{\text{total ways}}[/tex]
[tex]=\dfrac{17!}{20!}\\\\=\dfrac{1}{20\times19\times18}\\\\=\dfrac{1}{6840}[/tex]
Hence, the required probability = [tex]\dfrac{1}{6840}[/tex]
is the folllowing shape a square? how do you know
Answer:If it has 4 equal sides
If the angles are 90°
Hope this may helps you
Answer:
A square is characterized by
4 equal sides.Each angle measures 90°Diagonals meet and bisect each other at 90°Opposite sides are parallel and equal.Diagonals are equal.Hope this helps ;) ❤❤❤
Which expressions are equivalent to -6n+(-12)+4n−6n+(−12)+4nminus, 6, n, plus, left parenthesis, minus, 12, right parenthesis, plus, 4, n ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 4(n-3) -6n4(n−3)−6n4, left parenthesis, n, minus, 3, right parenthesis, minus, 6, n (Choice B) B 2(2n-6)2(2n−6)2, left parenthesis, 2, n, minus, 6, right parenthesis (Choice C) C None of the above
Answer:
The correct option is;
Choice A 4·(n - 3) - 6·n
Step-by-step explanation:
The given expression is
Which gives;-6·n+(-12)+4·n
- 12 + 4·n-6·n = -2·n - 12 = - (2·n + 12)
The options given are Choice A and/or Choice B;
(Choice A) 4·(n - 3) - 6·n
Which can be simplified as follows;
4·(n - 3) - 6·n = 4·n - 12 - 6·n
Which gives;
4·n - 12 - 6·n = 4·n - 6·n- 12 = -2·n - 12 = -(2·n + 12)
Therefore, 4·(n - 3) - 6·n is equivalent to -6·n+(-12)+4·n
For choice B, we have;
2·(2·n - 6) which gives;
2·(2·n - 6) = 4·n - 12
Therefore, 2·(2·n - 6) is not equivalent to -6·n+(-12)+4·n
Which gives the correct option as Choice A.
4(n-3)-6n
Khan academy I got this right
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs
Answer:
1/5 or 20%
Step-by-step explanation:
This problem can be easily solved by finding the probability of her picking one matching pair to leave in the suitcase (which results in pulling out exactly two matching pairs)
For the first sock, it does not matter what sock she picks.
For the second sock, there is only 1 out of the 5 socks left that would match the first one picked. Therefore, the probability that she pulls out exactly two matching pairs is 1/5 or 20%
02.06A LC) Which number is not in scientific notation? 02.06A
the answer is (A) you cant have 11 it should be 1.1 x 10^22
Please help I’m being timed!! The computer rendering of a mural in a town’s square uses the function represented in the table to define the outline of a mountain in the town’s logo, where x is the distance in feet from the edge of the mural and f(x) is the distance from the ground in feet. How can the point (12, 16) be explained? A) The highest point of the mountain defined by the function is 12 feet. B) The highest point of the mountain defined by the function is 16 feet. C) The width of the base of the mountain defined by the function is 12 feet. D) The width of the base of the mountain defined by the function is 16 feet.
Answer:
The correct option is;
B) The highest point of the mountain defined by the function is 16
Step-by-step explanation:
From the given information, we have;
The distance in feet from the edge of the mountain is given as the independent variable, x
The distance in feet from the ground (which is the height) is given the as the dependent variable f(x)
Therefore, given that the point (12, 16) are the values of x and f(x) such that x = 12 and f(x) = 16 and 16 is the largest value of f(x) in the data, therefore, 16 represents the highest defined point of the mountain.
What is the function rule that describes the pattern in the table
Answer:
C
Step-by-step explanation:
As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:
f(x)=-14 cos(720(t-10))+14
Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?
Answer:
a) 28 units
b) 0.0262 seconds
c) Minimum height of the nail = 1.923 units
Step-by-step explanation:
a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)
Where:
d = The mid line
a = The amplitude
The period = 2π/b
c/b = The shift
Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28
b) Given that three revolution = 6×π, we have;
At t = 0
cos(720(t-10) = cos(720(0-10)) = cos(7200) = 1
Therefore, for three revolutions, we have
720(t - 10) = 720t - 7200
b = 720
The period = 2π/b = 6·π/720 = 0.0262 seconds
c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;
f(x) = -14×cos(720(t - 10)) + 14
At t = 0 gives;
f(x) = -14×cos(720(0 - 10)) + 14
Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923
Minimum height of the nail = 1.923
Beatrice threw a stone one and seven fourteenths yards. Tilly threw a stone nine fourteenths of a yard. What is a reasonable estimate of the difference between their two throws?
Answer:
The difference between the two throws is 6/7 yards
Step-by-step explanation:
Beatrice throw=1 7/14 yards
Tilly throw=9/14 yards
Difference between the two throws=Beatrice throw - Tilly throw
=1 7/14 - 9/14
=21/14 - 9/14
= 21-9/14
=12/14
=6/7 yards
The difference between the two throws is 6/7 yards
computer valued at $6500 in 2007 depreciates at the rate of 14.3% per year.
Answer:
Here,
initial price (p)=$6500
Time from 2007 to 2020 (t)= 13yrs.
rate (r)=14.3%
now,
[tex]present \: price \: (pt) = p(1 - \frac{r}{100} )[/tex]
or, pt = $6500(1-14.3/100)
by simplifying it we get,
The, present price is $5570.5.
now, if you are searching for depreciated amount only then,
depreciated amount =$6500-$5570.5
=$929.5.
Hope it helps...
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three eighths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television
Answer:
32 inches by 64 inches
Step-by-step explanation:
Since the generic television is [tex]\frac{3}{8}[/tex] the size of the brand name.
Then the brand name is [tex]\frac{8}{3}[/tex] the size of the generic, thus
[tex]\frac{8}{3}[/tex] × 12 = 32
[tex]\frac{8}{3}[/tex] × 24 = 64
Thus dimensions are 32 inches by 64 inches
Answer:
The dimensions are 32 inches by 64 inches
Is it possible to draw a triangle whose sides are as follows? 6 cm, 7 cm, 17 cm. Give reasons to support your answer.
Answer:
No
Step-by-step explanation:
The sum of two random sides of a triangle must be bigger than the third side and their differences must be smaller than the third side
For example
3 - 4 - 5 can be made into a triangle because 3 + 4 > 5 and 4 - 3 < 5
Give the digits in the tens place and the tenths place.
12.05
How does the graph of y = a(x – h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. The vertex of the graph moves to a point half as far from the x-axis. The vertex of the graph moves to a point half as far from the y-axis.
Answer:
The vertex of the graph moves to a point twice as far from the y-axis.
Step-by-step explanation:
How does the graph of y = a(x – h)2 + k change if the value of h is doubled?
The vertex of the graph moves to a point twice as far from the x-axis.
The vertex of the graph moves to a point twice as far from the y-axis.because the role of h is to indicate the distance of the vertex from the y-axis.
The vertex of the graph moves to a point half as far from the x-axis.
The vertex of the graph moves to a point half as far from the y-axis.
Transformation involves changing the position of a function.
When h is doubled in [tex]\mathbf{y = a(x - h)^2 + k}[/tex], the vertex of the graph moves to a point twice as far from the y-axis.
The function is given as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
When the value of h is doubled, the new function becomes:
[tex]\mathbf{y' = a(x - 2h)^2 + k}[/tex]
Rewrite as:
[tex]\mathbf{y' = a(x - h- h)^2 + k}[/tex]
The above equation means that:
Function y will be translated to the right by h units
Assume the vertex is:
[tex]\mathbf{Vertex = (2,5)}[/tex]
The new vertex will be:
[tex]\mathbf{Vertex = (4,5)}[/tex]
Comparing the vertices, it means that:
The new function will have its vertex twice as far from the y-axis
Hence, option (b) is correct.
Read more about transformation at:
https://brainly.com/question/13801312
If you know the value of sin(30°), which of the following can you calculate directly through using the half angle formula?
cos(30°)
sin(45°)
sin(15°)
sin(60°)
Answer:
cos(30)
Step-by-step explanation:
Answer:
sin(15)
Step-by-step explanation:
Please help it’s urgent
[tex]\bold{\text{Answer:}\quad \dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]
Step-by-step explanation:
[tex].\quad \dfrac{-5x}{8x+7}-\dfrac{6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}+\dfrac{-6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}\bigg(\dfrac{3x+1}{3x+1}\bigg)+\dfrac{-6x^3}{3x+1}\bigg(\dfrac{8x+7}{8x+7}\bigg)\\\\\\=\dfrac{-15x^2-5x}{(8x+7)(3x+1)}+\dfrac{-48x^4-42x^3}{(8x+7)(3x+1)}\\\\\\=\large\boxed{\dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]
How to do this question plz answer me step by step plzz plz
Answer:
x=10 cm
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
x^2 + ( sqrt(200) )^2 = (sqrt(300))^2
x^2 +200 = 300
Subtract 200 from each side
x^2 +200-200 = 300-200
x^2 = 100
Take the square root of each side
sqrt(x^2) = sqrt(100)
x = 10
Is anyone here good at geometry? please help
Answer:
Sin 24 = 0.4067366431 = 0.4
Cos 45 = [tex]\frac{\sqrt{2} }{2}[/tex] = 0.7071067812 = 0.7
Tan 88 = 28.63625328 = 28.6
At a birthday party, each child is given some chocolates. There are five 5-year-olds, five 6-year-olds and five 7-year-olds at the party. If each child receives three times as many chocolates as their age in years, how many chocolates are given out altogether?
Answer: 270 chocolates
Step-by-step explanation:
Given the following :
Number of 5-year Olds = 5
Number of 6-year Olds = 5
Number of 7-year Olds = 5
Number of chocolates received by each child = 3 times as many chocolate as their age.
Number of chocolates received by 5-year Olds = 3 × 5 = 15 chocolates
Number of chocolates received by 6-year Olds = 3 × 6 = 18 chocolates
Number of chocolates received by 7-year Olds = 3 × 7 = 21 chocolates
Total Number of chocolates received by 5-year Olds = 5 * 15 = 75 chocolates
Total Number of chocolates received by 6-year Olds = 5 * 18 = 90 chocolates
Total Number of chocolates received by 7-year Olds = 5 * 21 = 105 chocolates
Totak number of chocolates altogether :
(75 + 90 + 105) = 270 chocolates
help with pre algebra
Answer:
The y-axis.
Step-by-step explanation:
This is because it is mirroring across the y-axis, and the x-coordinate's sign is getting changed from positive to negative.
Answer:
Y-axis
Step-by-step explanation:
B is a reflection of point A across theY-axis. The vertical line is Y and the horizontal line is X.
What is the center of the circle with the equation (x-1)^2 + (y+3)^2= 9? a (1,3) b (-1,3) c (-1,-3) d (1,-3)
Answer:
The center is ( 1,-3) and the radius is 3
Step-by-step explanation:
The equation of a circle can be written in the form
( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x-1)^2 + (y+3)^2= 9
(x-1)^2 + (- -3)^2= 3^2
The center is ( 1,-3) and the radius is 3
Select the correct answer.
What is the justification for step 2 in the solution process?
10x − 25 − 3x = 4x − 1
Step 1: 7x − 25 = 4x − 1
Step 2: 7x = 4x + 24
A.
the multiplication property of equality
B.
the division property of equality
C.
the addition property of equality
D.
the subtraction property of equality
Answer:
The answer is C addition property of equality.
Step-by-step explanation:
In step 1, 7x − 25 = 4x − 1 there are the numbers -25 and -1
In step 2, 7x = 4x + 24 The -25 is removed and -1 is replaced with 24
Meaning that in step 2 25 was added to those numbers meaning the answer C addition property of equality.
Answer:
C
Step-by-step explanation:
Sekkrit!!! Find the inverse of f(x) = 3x-5
Answer:
1/3(x+5)
Step-by-step explanation:
f(x) = 3x-5
y = 3x-5
Exchange x and y
x = 3y-5
Solve for y
Add 5 to each side
x+5 = 3y
Divide each side by 3
1/3 ( x+5) = 3y/3
1/3 ( x+5) = y
The inverse is 1/3(x+5)
Answer:
[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]
Step-by-step explanation:
[tex]f(x)=3x-5[/tex]
[tex]\mathrm{We \: need \: to \: find \: the \: inverse \: of \: the \: function.} \\ \mathrm{The \: inverse \: of \: a \: function \: reverses \: the \: original \: function.}[/tex]
[tex]\mathrm{Plug \: f(x) \: as \: y.}[/tex]
[tex]y=3x-5[/tex]
[tex]\mathrm{Solve \: for \: x.}[/tex]
[tex]\mathrm{Add \: 5 \: to \: both \: sides \: of \: the \: equation.}[/tex]
[tex]y+5=3x[/tex]
[tex]\mathrm{Divide \: both \: sides \: of \: the \: equation \: by \: 3.}[/tex]
[tex]\frac{y+5}{3} =x[/tex]
[tex]\mathrm{Switch \: variables.}[/tex]
[tex]\frac{x+5}{3} =y[/tex]
[tex]\mathrm{Plug \: y \: as \: f^{-1}(x).}[/tex]
[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]
please help me. I will love u forever if u do <333
Answer:
61% is a reasonable choice
Step-by-step explanation:
The probability of a strike is 79% or 0.79
=> Independently, the probability of 2 consecutive strikes:
P = 0.79 x 0.79 = 0.6241 ~ 61%
If a and b are rational numbers and 5 +2 root 3/7+4 root3=a-b root 3;then a and b=
Answer:
[tex]\bold{a=5\,,\quad b=-4\frac27}[/tex]
Step-by-step explanation:
[tex]5+\frac{2\sqrt3}7+4\sqrt3=5+\frac27\sqrt3+4\sqrt3=5+4\frac27\sqrt3=5-(-4\frac27)\sqrt3[/tex]
