The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form.
(Please see attached picture)
8 square units
20 square units
24 square units
28 square units
Answers
We have then:
Rectangle 1:
[tex]A1 = (2) * (1) A1 = 2[/tex]
Rectangle 2:
[tex]A2 = (2) * (4) A2 = 8[/tex]
Rectangle 3:
[tex]A3 = (4) * (1) A3 = 4[/tex]
Then, the prism area is given by:
[tex]A = 2A1 + 2A2 + 2A3 [/tex]
Substituting values:
[tex]A = 2 (2) + 2 (8) + 2 (4) A = 4 + 16 + 8 A = 28[/tex]
Answer:
the surface area of the prism is:
28 square units
Related Questions
Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20. If she plans for them in 12 equal payments, what’s her monthly cost?
Answers
The monthly cost will be $62.88 if Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20.
What is debt?It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
We know the formula for the monthly payment:
[tex]\rm Monthly \ Payment \:=\:\dfrac{\left A\left(i\right)\left(1+i\right)^{n}\right}{\left(1+i\right)^{n}-1}[/tex]
It is given that:
Cathy is purchasing a DVD player and tv at the local electronic store.
The DVD player costs $49.36 and the tv cost $705.20.
If she plans for them in 12 equal payments,
Total cost(combining the cost of the DVD player and TV cost):
= $49.36 + $705.20
= $754.56
Per month payment = $754.56/12
Per month payment = $62.88
Thus, the monthly cost will be $62.88 if Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20.
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If the sample size gets smaller, how does that affect the shape of the smapling distribution of sample means
Answers
I'm a little confused on how to solve this, can anybody help?
Solve the following system of equations and show all work.
y = x^2 + 3
y = x + 5
Answers
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2 or x = -1
(x - 2)(x + 1) = 0
x = 2 or x = -1
Mr. Calloway has a rectangular yard that is 120 feet wide and 80 feet deep. To keep his dogs on his property, he needs to build a fence. How much fencing does he need
Answers
To find the amount of fencing needed, we calculate the perimeter of the yard. The formula is 2*(length + width), equating to 2*(120 feet + 80 feet), which equals 400 feet.
Explanation:The area needed to be fenced is the perimeter of the rectangular yard. We can find the perimeter of a rectangle by using the formula: Perimeter = 2*(length + width). In this case, the length of the yard is 120 feet and the width is 80 feet. So, the perimeter of the yard would be: Perimeter = 2*(120 feet + 80 feet) = 2*200 feet = 400 feet. Therefore, Mr. Calloway will need 400 feet of fencing to surround his yard.
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Becky is 18 and would like to buy a house when she is 36. What is the discount factor for today's prices if the housing values increase 6% per year?
Answers
Yearly increase of house value (i) = 6% = 0.06
After 18 years,
The house value = (1+i)^n = (1+0.06)^18 = 2.85 the current value.
Additionally,
Increase in rate = (2.85-1)/2.85 = 0.6491 ≈ 0.65 = 65%. This is the discount rate for today's price. In other words, if the house is bought today, it will be paid for 65% less the price after 18 years.
Answer: 35.0%
Step-by-step explanation:
Find the point on the line 4x+4y+5=0 which is closest to the point (−2,−3).
Answers
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) will be located on the line perpendicular to the given line and will go through the given point
step 1
the slopes of two perpendicular lines
are
m1*m2=-1
given line
4x+4y+5=0------> 4y=-4x-5----> y=-x-1.25
m1=-1
so
m2=1
step 2
find the equation of the line with m2=1 and point (−2,−3)
y-y1=m*(x-x1)-----> y+3=(1)*(x+2)----> y=x+2-3-----> y=x-1
step 3
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) is the intersection of the line y=-x-1.25 and the line y=x-1
using a graph tool
see the attached figure
the solution is the point (-0.125,-1.125)
A bird seed feeder has the approximate shape of a cone with a diameter of 12 centimeters and a height of 25.5 centimeters. What is the best approximation for the volume of the bird seed feeder? 320.44 cm³ 961.33 cm³ 2883.98 cm³ 3845.31 cm³
Answers
[tex]V= \frac{1}{3} \pi r^{2} h [/tex]
where V = volume of the cone, r = radius of the circular base, and h = height of the cone.
You are told that the height, h = 25.5 cm. You are also told that the diameter is 12 centimeters. Remember that the diameter of a circle is just twice the radius. Divide 12 by 2 to get the radius: r =12/2 = 6 cm.
Since you know h = 25.5 cm and r = 6 cm, plug these values into your equation for volume of a cone and solve for V, volume:
[tex]V= \frac{1}{3} \pi r^{2} h\\ V= \frac{1}{3} \pi (6) ^{2} (25.5)\\ V \approx 961.33[/tex]
------
Answer: B) 961.33 cm³
Answer: Volume of the bird seed feeder = 961.33 cm³
Step-by-step explanation:
Given shape of bird seed feeder of a cone
Diameter =12cm
So Radius =D/2 =12/2
=6cm
Height = 25.5cm
Volume of cone = [tex]\frac{1}{3 }\times \pi r^{2}h[/tex]
Volume = [tex]\frac{1}{3}\times\pi6^{2}\times25.5[/tex]
Volume =[tex]\frac{1}{3}\times \frac{22}{7}\times36\times25.5[/tex]
Volume = [tex]\frac{20196}{21}[/tex]
Volume = 961.33 cm³(approx)
So the volume of bird seed feeder is 961.33 cm³
A box has a volume of 135 feet3. The length is same as the height, and the width is 5 times the length. What are the dimensions of the box?
Answers
thus the volume will be:
volume=length*width*height
thus
135=x×x×5x
135=5x³
solving for x we get:
27=x³
getting the cube root of both sides:
∛27=x³
x=3 ft
thus
length=3 ft, height=3ft, width=3×5=15 ft
The dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.
Explanation:This is a classic problem of volume where we need to consider the volume formula of a box, which is length × width × height. The question states that the box has a volume of 135 cubic feet, with the length being the same as the height, and the width being 5 times the length.
To find the dimensions of the box, we can set up the equation: length × 5 ×length × length = 135. Simplifying, we get that the length is the cube root of 135/5, which equals to 3. Thus, the dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.
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The number of nails of a given length is normally distributed with a mean length of 5.00 in. and a standard deviation of 0.03 in. Find the number of nails in a bag of 120 that are less than 4.94 in. long.
Answers
P(x<4.94)=P(z<Z)
Z=(x-μ)/σ
where:
x=4.94 in
μ=5 in
σ=0.03
thus
Z=(4.94-5)/0.03
Z=-2
thus
P(x<4.94)=P(z<-2)=0.0228
Thus the number of nails that are less than 4.94 will be:
0.0228×200=4.56~5 nails
About 3 nails is correct on grad point
49a = 245.....................................................
Answers
a= 5
Short answer: 5
Why?
So, we have the equation 49 * a = 245, we have to find what 'a' is to make the equation true. To find this, divide the two known numbers, which are 245 and 49. 245 / 49 ==> 5
Hope this helped you! ♥
The amount of money in Nadia’s savings account is represented by the recursive formula mc010-1.jpg. If mc010-2.jpg, what are the first two numbers in the sequence? $25.36, $75.99 $50.00, $101.25 $101.25, $153.78 $75.99, $127.89
Answers
Answer:
a is correct
Step-by-step explanation:
An ice cream cone has a diameter of 2 inches and a height of 5 inches. What is the volume of the ice cream cone? Round your answer to the nearest hundredth. (Use 3.14 for π.) 10.47 in.3 20.93 in.3 5.23 in.3 15.7 in.3
Answers
to find the volume, you multiply radius squared by pi. the result of that is multiplied by the height divided by 3. [tex]V= 3.14* r^{2} \frac{h}{3} [/tex]
Answer:
The answer 5.23
Step-by-step explanation:
How much more would $1,000 earn in 5 years in an account compounded continuously than an account compounded quarterly if the interest rate on both accounts is $3.7%
Answers
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$1000\\ r=rate\to 3.7\%\to \frac{3.7}{100}\to &0.037\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &5 \end{cases} \\\\\\ A=1000\left(1+\frac{0.037}{4}\right)^{4\cdot 5}\implies A=1000(1.00925)^{20}\\\\\\ A \approx 1202.195676[/tex]
get the difference of the amounts.
Answer: There is a difference of $ 1.0228.
Explanation: Given, initial amount or principal = $ 1000,
Time= 5 years and given compound rate of interest = $3.7%
Now, Since the amount in compound continuously,
[tex]A= Pe^{rt}[/tex] , where, r is the rate of compound interest, P is the principal amount and t is the time.
Here, P=$ 1000, t=5 years and r= $3.7%,
Thus, amount in compound continuously , [tex]A=1000e^{3.7\times5/100}[/tex]
⇒[tex]A=1000e^{18.5}=1000\times 1.20321844013=1203.21844013[/tex]
Therefore, interest in this compound continuously rate =1203.21844013-1000=203.21844013
now, Since the amount in compound quarterly,
[tex]A=P(1+\frac{r/4}{100} )^{4t}[/tex], where, r is the rate of compound interest, P is the principal amount and t is the time.
Thus, amount in compound quarterly, [tex]A=1000(1+\frac{3.7/4}{100} )^{4\times5}[/tex]
⇒[tex]A=1000(1+\frac{3.7}{400} )^{20}[/tex]
⇒[tex]A=1000(1+\frac{3.7}{400} )^{20}[/tex]
⇒[tex]A= 1202.19567617[/tex]
Therefore, interest in this compound quarterly rate=1202.19567617-1000=202.19567617
So, the difference in these interests=203.21844013-202.19567617=1.02276396 ≈1.0228
A recipe for cookies calls for 2⁄3 of a cup of chocolate chips and 4 cups of flour. If you want to make a bigger batch, using 6 cups of flour, how many cups of chocolate chips will you need?
Answers
how many cups of chocolate if using 6 cups of flour
= (6 x 2/3) / 4
= 4/4
=1
answer
1 cup of chocolate if using 6 cups of flour
how to tell if the histogram is is right skewed
Answers
A histogram is right skewed if the tail extends to the right, with most data clustering on the left, and the mode, median, and mean increase in that order. This indicates that the higher values are more spread out.
Explanation:To determine if a histogram is right skewed, observe where the majority of the data points lie and the direction in which the tail extends. A right-skewed histogram, also known as a positively skewed histogram, will have a tail that extends to the right. In other words, the greater values are more spread out, and the bulk of the data clusters to the left, with fewer, higher-value outliers pulling the mean to the right.
The characteristics of a right-skewed distribution often include a mode that is less than the median, which in turn is less than the mean. Therefore, by calculating these three statistics, you can gain insights into the skewness of the data. Graphically, if the left side of the graph appears more compact and the right side looks stretched or 'pulled out', then the data are skewed to the right.
For example, if you have a dataset with the values 6, 7, 7, 7, 7, 8, 8, 8, 9, 10, you'll likely find that the mode is 7, while the median and mean are greater than 7, pointing towards a right-skewed distribution.
Which situation involves descriptive statistics?
A. The survey shows that 1 in 3 moviegoers would attend a midnight showing.
B. A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.
C. A reporter surveys some commuters in a city to estimate what percent of city’s commuters spend 45 minutes or more getting to work.
D. Eighty percent of the recipes in a cookbook require salt.
Answers
All options involve descriptive statistics, but option B is a classic example as it involves computation of a median, an important tool in descriptive statistics.
Explanation:Descriptive statistics is used to describe, show or summarize data in a meaningful way. All the options given indicate the use of descriptive statistics because they all describe a given population or set of data using numerical measures. However, the most classical use of descriptive statistics is found in option B: 'A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.' This situation involves the computation of a median, a common measure in descriptive statistics, to summarize property price data.
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Which expression is equivalent to (2x^5+7x^3)-(5x^2-4x^3)
Answers
Answer:
2x^5+11x^3−5x^2
Step-by-step explanation:
Math Papa
help needed please.
Answers
The explanation is shown below:
1. To solve the exercise you must apply the following proccedure:
2. You have that He wants it to be 2 parts compost to 10 parts potting soil and he wants to end up with 10 grams of mix. Therefore:
=(2/12)x12 kilograms
=0.166x12 kilograms
=2 kilograms
The sum of three consecutive integers is 162. what is the smallest og these integers?
Answers
The coefficient of the term 76x2 is:
(2 is the exponent of 76x)
Answers
Kylie drew a circle with a diameter of 8 cm. Paige drew a circle with a radius of 3 cm. Approximately how much larger is the area of Kylie’s circle than the area of Paige’s circle? Use 3.14 for mc022-1.jpg and round to the nearest whole number.
Answers
Answer: Approximately 21.98cm larger.
Step-by-step explanation: The area of a circle is A = π·r², where r is the radius of the circle.
Kyle's circle has a diameter of 8cm, which means it has a radius of 4cm.
Calculating the area, it is:
A1 = 3.14.4² = 50.24
Paige's circle has a radius of 3cm, so the area will be:
A2 = 3.14·3² = 28.26
To see how much larger:
50.24 - 28.26 = 21.98cm
So Kyle's circle is 21.98 cm larger.
How do you factor the expression #2x^2+ 5x + 3#?
Answers
a = 2; b = 5; c = 3.
-5 plus or minus sqrt( 25-4(2)(3) )
Then x = ----------------------------------------------
2(2)
-5 plus or minus sqrt (1) -5 plus or minus 1
= -------------------------------------- = --------------------------
4 4
-1 is one root, so x+1 is one factor. Can you find the other root and factor?
In FGH, mF = 65, mG = 55, and mH = 60. Which side of FGH is the shortest?
Answers
FH is the shortest side
Explanation:
In any triangle, the length of any side is proportional to the measure of its opposite interior angle.
This means that:
The shortest side is the side opposite to the smallest interior angle in the triangle
The longest side is the side opposite to the largest interior angle in the triangle
Now, in the given triangle we have:
measure angle F = 65°
measure angle G = 55°
measure angle H = 60°
We can note that angle G is the smallest angle.
Based on the above, the shortest side would be the one opposite to angle G which is side FH.
Hope this helps :)
Answer: Fh is the shortest
Please help me I'm so dumb
Answers
r=8cm and h = 3
plug and chug
A= 552.92
is what i calculated
The perimeter of a rectangular field is 242 yards if the width of the field is 54 yards what is the lenght
Answers
242 = 2 (L +W)
121= L+W
121= L + 54
L = 121-54
L= 67 Yards
Can someone help with number 3
Answers
201 , 218, 242, 257, 265, 275 , 301
find the midpoint ( there are 7 numbers so the mid point would be the middle number 257)
look at the numbers below the mid point ( 201, 218, 242)
the first quartile is the mid point of those numbers: 218
answer is 218
A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (A=lw), how long is the rectangle? a. 21 inches b. 340 inches c. 20 inches d. 15 inches
Answers
The rectangle that has an area of 357 square inches(a=357) is 17 inches wide(w=17). You are asked how long the length of the rectangle is. Then, you just need to put the number into the equation provided.
a=lw
area= length * width
357=length * 17
length= 357/17=21 inches
Answer:
a - 21 inches
Step-by-step explanation:
Following the formula [tex]Area = l*w[/tex], we can find the length of the rectangle by plugging in values into the formula, then solving for [tex]l[/tex].
[tex]357=l*17[/tex]
[tex]\frac{357}{17} =\frac{l*17}{17} \\\\21=l\\l=21[/tex]
What is the length of chord JK?
Answers
So, chord JK = LM
3p + 2 = 7p -2
4p = 4
So, p = 1
Since p = 1 then chord JK = 3p +2
JK = 3*1 + 2
JK = 5
Answer is "C"
(09.01 LC) Look at the figure below: A circle is shown with the center O. OP is a segment joining center O to a point P on the circle. MN is a line touching the cir Which is the tangent to the circle? (6 points) Segment OP Line ST Line MN Segment QR
Answers
Answer:
Line MN is the answer
Step-by-step explanation:
The rectangle shown has a perimeter of 62 cm and the given area. its length is 4 more than twice its width. write and solve a system of equations to find the dimensions of the rectangle.
Answers
taking the length to be 2x+4 and the width to be x,
[tex]62 = 2(2x + 4 + x)[/tex]
hence,
[tex]6x = 54[/tex]
and thus
[tex]x = 9[/tex]
that means the width is 9.
since we established that the length is (2x+4), we can substitute x=9 into the equation. hence,
[tex]2x + 4 = 2(9) + 4 = 22[/tex]
therefore the length is 22
use the area to check your answer!
Final answer:
By setting up a system of equations using the perimeter formula and the relationship between the rectangle's length and width, we determine that the width of the rectangle is 9 cm and the length is 22 cm.
Explanation:
To solve the problem, we must set up a system of equations based on the information provided about the perimeter and the given ratio between the length and width of the rectangle. The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. According to the problem, the perimeter is 62 cm, and the length l is equal to 4 more than twice the width, which we can write as l = 2w + 4.
Using these two equations, we can create the following system to solve for the dimensions of the rectangle:
2l + 2w = 62 (perimeter equation)l = 2w + 4 (length is 4 more than twice the width)Substitute the second equation into the first to get:
2(2w + 4) + 2w = 624w + 8 + 2w = 626w + 8 = 626w = 54w = 9 cm (width of the rectangle)Now substitute w back into the second equation:
l = 2(9) + 4l = 22 cm (length of the rectangle)Thus, the dimensions of the rectangle are a width of 9 cm and a length of 22 cm.