The new area of the figure after the dilation with a scale factor of 4 will be 400 units²
We have,
When a figure is dilated by a scale factor of k, its area is multiplied by k².
So,
If the original area of the figure = 25 units²
Dilated by a scale factor = 4
The new area.
= (4²)(25 units²)
= 16(25 units²)
= 400 units²
Therefore,
The new area of the figure after the dilation with a scale factor of 4 will be 400 units².
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A motorboat travels 234 miles in 6 hours going upstream. It travels 342 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current
The boat is moving at 48 mph while the current is moving at 9 mph in still water.
To solve this problemLet's use the letters "B" for the boat's speed in still water and "C" for the current's speed.
The boat's effective speed upstream is B - C because it is moving against the current.
Since the boat is moving downstream against the tide, its effective speed is equal to B plus C.
Based on the supplied data, we can construct the following two equations:
234 = 6(B - C)
342 = 6(B + C)
Making these equations simpler:
39 = B - C
57 = B + C
Now that we have added the two equations, we may solve for B and C:
39 + 57 = 2B
96 = 2B
B = 48
Therefore, the boat's speed in calm water is 48 mph.
To find C, we can rewrite one of the initial equations with this value as a substitute:
39 = 48 - C C = 9
Thus, the current is moving at a 9 mph velocity.
Therefore, the boat is moving at 48 mph while the current is moving at 9 mph in still water.
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Work out and simplify where possible. A) 3/4 + 5/6. B) 4/7 - 1/3
What are the coordinates of the vertex of the graph of:
f(x) = 2 lx - 3l
Enter your answer in the boxes.
( ), ( )
Answer:
(3, 0)
Step-by-step explanation:
It might be first helpful to think about the function [tex]|x-3|[/tex], we will call this [tex]g(x)[/tex]. So, [tex]g(x)=|x-3|[/tex].
The modulus (absolute value) function reflects any points on a graph that go below the x-axis up into the positive x region.
We know that the graph of [tex]y=x-3[/tex], will cross the x-axis at (3,0). We can work this out by setting y to 0 and rearranging for x. At the x-axis, y = 0.
Therefore, when the modulus comes in, a vertex will be created at (3,0).
But that is the vertex of [tex]g(x)[/tex].
Using basic algebra we can derive from previous working that [tex]f(x)=2g(x)[/tex].
Graphically, the multiplier of 2 on the outside of [tex]g(x)[/tex] stretches the graph in y-axis, and does so by the scale factor of 2.
With our vertex (3,0), the y value is 0. And if you multiply 0 and 2 together, 0 is produced. The x value will remain unchanged as a result of this transformation.
Therefore, the vertex of [tex]f(x)[/tex] is (3,0).
When Emilia looked at her cell phone bill for the month, she saw that she had spent 1/12 of her minutes talking to her mother and 5/12 of her minutes talking to her best friend. What fraction of the minutes did Emilia spend talking to either her mom or her best friend?
Answer:
The answer to your problem is, She spend more talking to her friend then her mother
Step-by-step explanation:
The question asking:
What fraction of the minutes did Emilia spend talking to either her mom or her best friend?
So we can see that she talks to her friend instead of her mother shown;
[tex]\frac{1}{12} < \frac{5}{12}[/tex]
The total equals to [tex]\frac{6}{12} or\frac{1}{2}[/tex]
So, She spend more talking to her friend then her mother
Thus the answer to your problem is, She spend more talking to her friend then her mother
A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
A house is infested with mice and to combat this the householder acquired four cats cyd, Greg, Ken, and Rom, The householder observes that only half of the creatures caught are mice. A fifth are voles and the rest are birds. 20% of the catches are made by Cyd, 45% by Greg, 10% by Ken and 25% by rom. a) What is the probability of a randomly selected catch being a mouse caught by Cyd? b) Bird not caught by Cyd? c) Greg's catches are equally likely to be a mouse, a bird or a vole. What is the probability of a randomly selected d) The probability of a randomly selected catch being a mouse caught by Ken is 0.05 . What is the probablity that a catch being a mouse caught by Greg? e) Given that the probability of a randomly selected catch is a mouse caught by Rom is 0.2 verify that the catch made by Ken is a mouse? probability of a randomly selected catch being a mouse is 0.5 . f) What is the probability that a catch which is a mouse was made by Cyd?
Note that the probabilities are given below.
a) the probability of a randomly selected catch being a mouse caught by Cyd
p(Catching a mount) x p(Cyd made the catch)
= 0.5x .2
= 0.1
b) the probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.
Thus
P(that a catch is a bird) x p(the Cyd didn't make the catch)
= 0.3 x 0.8
=0.24
c) The probability of a randomly selected catch being caught by Greg is 0.45
To calculate, we say
(0.5 x0.45) + (0.3 x 0.45) + (0.2 x .45)
= 0.45.
d)
P (mouse caught by Greg) = (0.45 x 0.5) / 1
= 0.225.
e) P(catch is a mouse caught by Ken and catch is a mouse)
= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)
= 0.05 x 0.1
= 0.005
f)
P (catch made by Cyd | catch is a mouse)
= 0.1 x 0.2 / 0.5
= 0.04
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What has no solutions in common with 6x+2y=12
Answer:
-6x - 2y = 12
Step-by-step explanation:
3. Olivia is constructing a monument to honor the heroes in her community. It will be in
the shape of a regular pentagonal prism and stand 10 feet tall. She will need 5,119.5
cubic feet of concrete to fill the prism. Olivia will run lights across the top of the
monument from the center to the midpoint of one side.
17.25 ft
SCRATCHPAD
10 ft
The height will be 61.8 ft
How to solve for the heightFind the volume of prism
Volume = Base Area × Height
since height = 10 feet
5,119.5 ft³ / 10 ft
= 511.95 ft²
formula for the area of a regular polygon is:
Area = (Perimeter × Apothem) / 2
ide length of the pentagon as 's' and the apothem as 'a'
511.95 ft² = (5s × a) / 2
angle at the center of the pentagon is 360° / 5 = 72°
72 / 2 = 36 degrees
tan(36°) = (s/2) / 17.25
solve for the value of s
s = 2 × 17.25 × tan(36°)
= 12.36 ft
5 s =
5 x 12.36 ft
= 61.8 ft
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Filipe practiced 12 fewer hours than Bianca. If Filipe practiced for 16 hours, how long did Bianca practice?
Bianca practiced for
____
hours.
Answer:
28 hours
Step-by-step explanation:
Let's use "B" to represent the number of hours Bianca practiced.
From the problem, we know that Filipe practiced 12 fewer hours than Bianca, which means:
Filipe's practice time = Bianca's practice time - 12
We are also told that Filipe practiced for 16 hours, so we can substitute that into the equation:
16 = B - 12
To solve for B, we can add 12 to both sides:
16 + 12 = B
So, Bianca practiced for a total of 28 hours.
Mr Greenwood paid $11 for 5 buns and 2 sausages last week. His wife bought 8 such buns and 4 such sausages for $19.60 this week.
(a)
How much was each bun?
(b) How much was each sausages?
Answer:
Step-by-step explanation:
mark me brainliest
So I still don’t understand.
An equation for the height of the rocket after t seconds is h(t) = -16t² + 352t.
The time it takes for the rocket to reach a height of 0 is 22 seconds.
The time it takes to reach the top of its trajectory is 11 seconds.
The maximum height is 1,936 feet.
The time it takes to reach a height of 968 feet is 18.8 or 3.2 seconds.
How to determine the time when the rocket would hit the ground?Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the ground is related to time by the following quadratic function:
h(t) = -16t² + Vit
When the initial velocity is 352 feet per seconds, the height function becomes;
h(t) = -16t² + 352t
Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:
0 = -16t² + 352t
352t = 16t²
Time, t = 352/16
Time, t = 22 seconds.
Next, we would determine the maximum height of this rocket by taking the first derivate in order to determine the time (t) it takes;
h(t) = -16t² + 352t
h'(t) = -32t + 352
352 = 32t
t = 352/32 = 11 seconds.
h(11) = -16(11)² + 352(11)
h(11) = 1,936 feet.
At a height of 968 feet, the time is given by;
968 = -16t² + 352t
16t² - 352t + 968 = 0
t² - 22t + 60.5 = 0
Time, t = 18.8 or 3.2 seconds.
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(06.06 MC)
The table below shows the amount of money, in cents, Celine had in her savings account after different
number of years:
Years 251463
Money in
36 112 12 85 150 60
cents
Approximately, what will be the amount of money, in cents, that Celine will save in 12 years?
250
300
400
200
Approximately, the amount of money, in cents, that Celine will save in 12 years is: B. 300
How to determine the equation of line of best fit?In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the money (in cents) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the years and the money (in cents), an equation for the line of best fit is given by
y = 26.9x - 18.5
when x = 12, the amount of money, in cents, that Celine will save in 12 years is given by;
y = 26.9(12) - 18.5
y ≈ 300 cents.
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For the given rectangular equation give its equivalent polar equation
Answer:
The last option
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
Step-by-step explanation:
Given equation is 6x - y = 14
To convert an equation in rectangular(cartesian) form, f(x, y) to polar f(r, θ) we use the following information
x = rcosθ
y = rsinθ
Substituting for x and y in the original rectangular equation 6x - y = 14,
6(rcosθ) - rsinθ = 14
Factoring out r on the left side,
r(6cosθ - sinθ) = 14
which gives
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
That would be choice 4
The insurance premium of a new bus is GH¢93.30 plus 15% of the insured value. What is the insurance premium of a bus whose insured value is GH¢250.00?
The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.
Let's first calculate 15% of¢250.00:
15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50
Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:
GH¢93.30 + GH¢37.50 = GH¢130.80
Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
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The coordinate of the points below represents the vertices of a rectangle what is the perimeter in units of the rectangles WXYZ
The perimeter of the rectangle is P = 18 units
Given data ,
Let the rectangle be represented as ΔWXYZ
Now , the coordinates of the triangle are
W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )
The perimeter of the rectangle = 2 ( length + width )
The width of the rectangle W = ( 7 - 3 ) = 4 units
The length of the rectangle L = ( ( 8 - 3 ) = 5 units
So , P = 2 ( 4 + 5 )
P = 2 x 9
P = 18 units
Hence , the perimeter is 18 units
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A marketing research company desires to know the mean consumption of milk per week among people over age 30 . They believe that the milk consumption has a mean of 3.5 liters, and want to construct a 85% confidence interval with a maximum error of 0.07 liters. Assuming a standard deviation of 1.4 liters, what is the minimum number of people over age 30 they must include in their sample? Round your answer up to the next integer.
The minimum number of people over age 30 they must include in their sample is: 829 people
How to calculate the standard error?The formula for calculating the standard error is:
SE = μ ± Z(σ/√N)
Where:
σ = the standard deviation,
N = the sample size,
Z = the Z value for the percent confidence level desired.
We must find the Z value, at the 85% confidence level from a Cumulative Standardized Normal table for the 99% confidence level. This gives us the value of Z = 1.44
σ = 1.4 liters
N = 0.07
Thus:
0.07 = 1.44(1.4/√N)
0.07/1.44 = 1.4/√N
1.4/√N = 0.04861
√N = 1.4/0.04861
N = (1.4/0.04861)²
N = 829 people
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What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
The correct answer is option B:
⇒ Y decreases and X increases.
Given that;
the y value starts to decrease and the x value remains the same over time.
Now, We know that;
the slope remains constant, but the y value decreases as you move along the slope in the negative y direction, while the x value increases.
Hence,
If the y value starts to decrease while the x value remains the same over time on a consistent slope,
Thus, The correct answer is option B:
⇒ Y decreases and X increases.
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Give me the domain and range
Tell me if the graph is a function or not
The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the x values to be
x = -2 to 5
On the graph, we have the y values to be
y = -6 to 2
This means that domain = [-2, 5] and range is [-6, 2]
If the graph is a function or notThe graph is the graph of a circle
A circle does not represent a function
Hence, the graph is not a function
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Consider the sequence 4,323,313,3
The explicit rule for the sequence 4, 3 2/3, 3 1/3, 3.... is f(n) = 4 - 1/3(n - 1)
Finding the explicit rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
4, 3 2/3, 3 1/3, 3....
In the above sequence, we can see that 1/2 is subtracted from the previous term to get the new term
Take for instance
2nd = 4 - 1/3 = 3 2/3
3rd = 3 2/3 - 1/3 = 3 1/3
4th = 3 1/3 - 1/3 = 3
And so on
This means that
First term, a = 4Common difference, d = -1/3So, the explicit rule is
f(n) = a + (n - 1)d
This gives
f(n) = 4 - 1/3(n - 1)
Hence, the explicit formula is f(n) = 4 - 1/3(n - 1)
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Complete question
Consider the sequence 4,3 2/3,3 1/3, 3....
What is the explicit rule for this sequence
10. Bond A is zero-coupon bond paying $100 one year from now. Bond B is a zero-coupon bond paying
$100 two years from now. Bond C is a 10% coupon bond that pays $10 one year from now and $10 plus the $100 principal two years from now. The yield to maturity on bond A is 10%, and the price of bond B is $84.18. Assuming annual
compounding, what is the yield to maturity on Bond B?
*Make sure to input all percentage answers as numeric values without symbols,
0.0600.
The yield to maturity on Bond B is 9%
How to calculate the yield to maturityWe know that Zero Coupon Bond Value= F/(1+r)^t
F= Face Value =100
r= Rate of interest
t= time to maturity =2Yrs
Price= F/(1+r)^t
84.18 = 100/(1+r)^t
(1+r)^t=100/84.18
(1+r)^2=1.18793
1+r=(1.18793)^(1/2)
r = 1.089922 - 1
r = 8.9922%
r = 9% (Approx)
In conclusion, the yield to maturity on Bond B is 9%
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The circumference of a circle is 43.96 m. What is the approximate area of this circle? Use 3.14 for TT.
O 153.86 m²
O 164.32 m²
O 138.03 m²
O 615.44 m²
Answer:
43.96 = 2πr
r = 21.98/π
A = π(21.98/π)^2 = 483.1204/π = 153.78 square meters
A = 483.1204/3.14 = 153.86 square meters
(Please help in image)
Answer:
[tex] {x}^{2} + 11x + 18 = [/tex]
[tex](x + 2)(x + 9)[/tex]
The two numbers are 2 and 9.
2 + 9 = 11, and 2 × 9 = 18.
Find the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
A. (x - 2)2 + (y - 5)2 = 169
B. (x - 2)2 + (y - 5)2 = 25
C. (x + 3)2 + (y + 7)2 = 169
D. (x + 3)2 + (y + 7)2 = 25
(x+3)²+(y+7)²=169 is the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
The equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
The radius of the circle is 13
The equation of circle in standard form is (x-h)²+(y-k)²=r²
(h, k) is centre of circle
(-3, -7) is centre
(x+3)²+(y+7)²=13²
(x+3)²+(y+7)²=169
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Is it 65 and 5 bag variability????
The estimate of the population mean is 80 and the variability in the distribution is 120
The estimate of the population meanHere, we have
The dot plots
From the dot plots, we can see that the data are normally distributed
This means that the mean, the median and the mode are equal
From the distribution of the random variable, we have the following readings
mean = 80Hence, the estimate of the population mean is 80
The variability in the distributionHere, we use the range
So, we have
Variability = Highest - Least
This gives
Variability = 140 - 20
Variability = 120
So, the variability in the distribution is 120
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PLEASE HELP ASAP WILL GOVE BRAINLIEST NEED THIS AWNSERED IN 15 MINUTES
The segment lengths on the right triangle are given as follows:
JL = 13.[tex]KL = 13\sqrt{3}[/tex]What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.The sum of the internal angle measures of a triangle is of 180º, hence the missing angle is given as follows:
m < L = 180 - (30 + 60)
m < L = 90º.
Hence the segment JL represents the hypotenuse of the figure.
JL is opposite to the angle K, hence it's length is obtained as follows:
sin(30º) = JL/26
1/2 = JL/26
2JL = 26
JL = 13.
Segment KL is adjacent to the angle of 30º, hence it's length is obtained as follows:
cos(30º) = KL/26
[tex]\frac{\sqrt{3}}{2} = \frac{KL}{26}[/tex]
[tex]2KL = 26\sqrt{3}[/tex]
[tex]KL = 13\sqrt{3}[/tex]
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10. Find the surface area of the
polyhedron that can be
assembled from this net. Show
your reasoning.
The surface area of the polyhedron is calculated be equal to 224 square inches.
How to evaluate for the area of the polyhedronThe polyhedron can be observed to have a large rectangle between two identical triangles by the sides
area of rectangle = length × width
The large rectangle have;
length = (12 + 10 + 10) in = 32 in
width = 4 in
area of large rectangle the = 32 in × 4 in = 128 in²
area of one identical triangles = 1/2 × 12 in × 8 in = 48 in²
area of 2 identical triangles = 2 × 48 in² = 96 in²
Surface area of the polyhedron = 128 in² + 96 in²
Surface area of the polyhedron = 224 in²
Therefore, the surface area of the polyhedron is calculated be equal to 224 square inches.
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find the inverse of the function f(x)=-1/25x^2, x<0
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex] the inverse function is:
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
What is an inverse function ?If the inverse function of f is the function g, then x = f(x) gives x = g(y). We just need to reverse the function.
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
We have to find the inverse of the function.
The inverse, interchange the variables solve for y,
Now,
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
[tex]f^-^x(x)=\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
So, [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Hence,
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
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I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
Answer:The algebraic steps you have taken are incorrect, leading to an invalid conclusion. Let's go through each step and see where the mistake is made:
X = 1 (given)
X+X = 1+X (adding X to both sides)
2X = 1+X (combining like terms)
2X = X+1 (rearranging terms)
2X-2 = X+1-2 (subtracting 2 from both sides)
2X-2 = X-1 (simplifying)
2(x-1)/(x-1) = (x-1)/(x-1) (dividing both sides by x-1, note that x cannot be 1 as it would result in division by 0)
2 = 1 (canceling out the (x-1)/(x-1) on both sides)
The error lies in dividing both sides by (x-1) in step 7. Although (x-1) appears on both sides of the equation, it is not equal to zero as x cannot be 1 due to division by zero. Dividing by (x-1) effectively cancels it out, leading to the incorrect result of 2=1.
Step-by-step explanation:
If x and y vary directly and y is 2 when x is 3, what is why when x is 2
Step-by-step explanation:
Direct variation means y = k x
when y = 2 x= 3
2 = k *3
2/3 = k
so the variation becomes y = 2/3 x
when x = 2
y = 2/3 (2)= 4/3
gingerbread house is shaped like the image below. How many square centimeters of frosting will take to cover the outside?
(NEED HELP!!!)
There are 32 cm² of frosting will take to cover the outside.
Given that;
Base of house = 2 cm
And, Height of house = 3 cm
Since, The shape of house is like a prism.
We know that;
Area of Prism is,
SA = 2B + ph,
where B, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.
Hence, We get;
SA = 2 × (2 × 2) + 2 (2 + 2) × 3
SA = 8 + 24
SA = 32 cm²
Hence, There are 32 cm² of frosting will take to cover the outside.
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