Question 1
Here is the base of a prism.
a. If the height of the prism is 5 cm, what is its surface area? What is its volume?
b. If the height of the prism is 10 cm, what is its surface area? What is its volume?
c. When the height doubled, what was the percent increase for the surface area? For the volume?
Answer:
A). Surface area = 222 cm²
Volume = 180 cm³
B). Surface area = 375 cm²
Volume = 360 cm³
C). % increase in surface area = 67.57%
% increase in volume = 100%
Step-by-step explanation:
In the figure attached base of a prism has been given.
A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)
Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8
= 30
Area of the base = 8×5 - 2×2 = 36 cm²
Surface area of the prism = 30×5 + 2×(36)= 222 cm²
Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off
= 8×5×5 - 2×2×5
= 200 - 20
= 180 cm³
B). Surface area of the prism if it's height is 10 cm,
Surface area = 30×10 + 2×(36) = 372 cm²
Volume of the prism = 8×5×10 - 2×2×10
= 400 - 40
= 360 cm³
C). Increase in surface area = 372 - 222 = 150 cm²
% increase in the surface area = [tex]\frac{150}{222}\times 100[/tex] = 67.57%
Increase in volume = 360 - 180 = 180 cm³
% increase in volume = [tex]\frac{180}{180}\times 100[/tex] = 100%
Select the ordered pairs that satisfy the equation y=1/5x.Check all that apply.
Answer: C, E, F
Step-by-step explanation:
Plug in the "x" and "y" values from the ordered pairs into the equation.For A: 3 = [tex]\frac{1(5)}{5}[/tex] → 3 ≠ 1 → A is eliminated.For B: 5 = [tex]\frac{1(1)}{5}[/tex] → 5 ≠ [tex]\frac{1}{5}[/tex] → B is eliminated.For C: 2 = [tex]\frac{1(10)}{5}[/tex] → 2 = 2 → C satisfies the equation.For D: 10 = [tex]\frac{1(4)}{5}[/tex]→ 10 ≠ [tex]\frac{4}{5}[/tex] → D is eliminated.For E: -1 = [tex]\frac{1(-5)}{5}[/tex]→ -1 = -1 → E satisfies the equation.For F: 3 = [tex]\frac{1(15)}{5}[/tex]→ 3 = 3 → F satisfies the equation.Therefore, C, E, and F are the answers.Answer:
C, E, and F
Step-by-step explanation:
Substitute each pair in for the variables and see which pairs are true.
5(2-y)+y=-6 Please the yr is almost over
Answer:
4
Step-by-step explanation:
5(2-y)+y=-610-5y+y= -610-4y= -64y=10+64y=16y=16/4y=4Answer: 4
Step-by-step explanation:
16 - 4y =-4 • (y - 4)
-4 • (y - 4) = 0
y-4 = 0
y = 4
Match the rate - - .08 -- with corresponding time of year.
A. Three Months, 1/4 =
B. Six Months, 6/12 =
C. Nine Months, 9/12 =
D. 1 Month, 1/12 =
Answer: D. 1 Month, 1/12 =1÷12 = 0.08
Step-by-step explanation:
Hi, to answer this question we have to convert the fraction into decimals and compare:
A. Three Months, 1/4 = 1÷4 = 0.25
B. Six Months, 6/12 = 6÷12 =0.5
C. Nine Months, 9/12 = 9÷12 = 0.75
D. 1 Month, 1/12 =1÷12 = 0.08
The option that matchs the rate 0.08 is D.
Feel free to ask for more if needed or if you did not understand something.
Simplify the expression below.
13y + x - 7y
[tex]\text{Simplify:}\\\\13y + x - 7y\\\\\text{Combine like terms}\\\\13y + x - 7y\\\\6x+y\\\\\text{Since you can't combine anything else, that will be your answer}\\\\\boxed{6y+x}[/tex]
What is the slope of the line that contains the points (-1, 8) and (5,-4)?
O A. 2
O B -1/2
O c. 1/2
O D. -2
Answer:
-2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ;)
Please find the SURFACE AREA of this figure... Write the formula and plug in the values... Write your answer with units and box your answer
Answer:
124(cm)^2
Step-by-step explanation:
total surface area of a cuboid=[tex]2(LB+BH+HL)[/tex]
length=7cm
Breadth=5cm
Height=4cm
2{(2*7)+(5*4)+(4*7)}
2{14+20+28}
2*62
124(cm)^2
The segment shown below could form a triangle. 6, 5, 8
AC 6 , CB 5, BA 8
Answer:
Yes
Step-by-step explanation:
In order to form a triangle sum of the lengths of any two sides must always be greater than the length of the third side.
Here,
6 + 5 = 11 > 8
5 + 8 = 13 > 6
8 + 6 = 14 > 5
Given side lengths satisfy above condition. Hence the given segment can form a triangle.
* this is pretty difficult for me , provide details if necessary * // ANSWER ASAP //
Answer:
A.
Step-by-step explanation:
1 radian = 180/π
So
Multiplying both sides by 25π/18
We'll get,
25π/18 (r) = (180/π)×(25π/18)
= (180×25)/18
= 10×25
= 250 degrees
Are extraneous solution always negative numbers
Answer: i would say no there not always negative
Answer:
Step-by-step explanation:
Help me with this I dont get it.
Answer:
(-infinity, 1)
Step-by-step explanation:
What is the interquartile range of the box and whisker plot
Answer:
(IQR) interquartile range = 5
Step-by-step explanation:
Lower quartile: 48
Upper quartile: 53
Median: 52
Lowest value: 46
Highest value: 55
(IQR) interquartile range: Upper quartile - Lower quartile = final answer
(IQR) interquartile range: 53 - 48 = 5
For the graph, what is a reasonable constraint so that the function is at least 200? graph of y equals minus 2 times the square of x plus 30 times x plus 200 −5 ≤ x ≤ 20 0 ≤ x ≤ 15 x ≥ 0 All real numbers
Answer:
The correct constraint is:
0 ≤ x ≤ 15
Step-by-step explanation:
The function given to us in the question is:
y = -2x² + 30x + 200
It is given that the function is at least 200, we can write is as:
-2x² + 30x + 200 ≥ 200 ⇒ Equation (i)
To find the constraint, replace ≥ sign with = sign and solve for x:
-2x² + 30x + 200 = 200
-2x² + 30x = 0
x(-2x + 30) =0
x = 0 , -2x + 30 = 0
x = 0 , -2x = -30
x = 0 , x = -30/-2
x = 0 , x = 15
So the end values of constraint are 0 and 15.
Take any value between 0 and 15 and substitute in equation (i) to see whether it satisfies the equation or not.
-2x² + 30x + 200 ≥ 200
Substitute x = 5 in the equation:
-2(5)² + 30(5) +200 ≥ 200
-50 + 120 +200 ≥ 200
270 ≥ 200
As the equation satisfies. it means that the solution lies between 0 and 15, including the end values.
Hence.
0 ≤ x ≤ 15
Answer:
0 ≤ x ≤ 15
Step-by-step explanation:
got it right on flvs
After entering the table values in his calculator, Cory used the LinReg button
to get the results shown. Identify the correlation coefficient and the type of
correlation.
Answer:
Strong positive correlation, 0.9663
Step-by-step explanation:
The value of the correlation coefficient will be; -0.2985, and the relation between x and y is a weak negative.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
The value of the correlation coefficient can be found as;
r = -0.2984713607
After rounding off we get;
r = -0.2985
As the value of r is not close to the -1 therefore, the relation between x and y is weak negative.
Hence, the value of the correlation coefficient will be; -0.2985, and the relation between x and y is a weak negative.
Learn more about the correlation here:
brainly.com/question/11705632
#SPJ5
brainlist and thanks
question is the screen shot
thank you :)
Answer:
x=5
Step-by-step explanation:
2(x-4)+3x=17
You distribute
2x-8+3x=17
Simplify
5x-8=17
add 8 to both sides
5x=25
x=5
Boom. :0
PIck from smallest to largest Smallest 8.008 8.018 8.088 8.88 8.808 Largest
Answer:
8.880,8.808,8.018,8.008
The numbers 8.008, 8.018, 8.088, 8.88, and 8.808 are in ascending order will be 8.008, 8.018, 8.088, 8.808, and 8.88.
What is ascending order?It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.
The numbers are given
8.008, 8.018, 8.088, 8.88, and 8.808.
Then we are arranging in ascending order, then we have
8.008, 8.018, 8.088, 8.808, and 8.88.
More about the ascending order link is given below.
https://brainly.com/question/320500
PLEASE HELP ME PLEASEEEEE
Our first step is to get rid of the fraction by multiplying both sides by 3.
So in our second step we have x - 4 > -36.
Now add 4 to both sides to get x > -32.
Since x is greater than -32, the values that would
make this inequality true are -31 and 31.
Option 3
Option 4
A tree house is 10 feet up in a tree. A ladder that leans against the tree and
leads to the tree house door is 12 feet long. How far away from the base of
the tree is the bottom of the ladder? Draw a picture and solve. Round your
answer to the nearest tenth.
Answer:
6.63 ft
Step-by-step explanation:
In this case we use pythagora's theorem which is
[tex]hyp^{2}[/tex] = [tex]adj^{2}[/tex] + [tex]opp^{2}[/tex]
in this case, the hypotenuse (hyp) is the length of the ladder, the opposite (opp) is the height of the tree house and, the adjacent (adj) is the distance of the ladder's bottom to the base of the tree.
hpy = 12 ft
opp = 10 ft
adj = ?
substituting into the equation above, we have
[tex]12^{2}[/tex] = [tex]adj^{2}[/tex] + [tex]10^{2}[/tex]
144 = [tex]adj^{2}[/tex] + 100
144 - 100 = 44 = [tex]adj^{2}[/tex]
the image is shown below
adj = [tex]\sqrt{44}[/tex] = 6.63 ft
What is the value of the angle marked with I?
3.2
87°
3.2)
3.2
C
3.2
What difference is in cosine than sine
Answer:
One of the most important differences between the sine and cosine functions is that sine is an odd function (i.e. while cosine is an even function (i.e. . Sine and cosine are periodic functions; that is, the above is repeated for preceding and following intervals with length .
Step-by-step explanation:
Hope that helps
Solve #10 asap please.
Answer:
x=1
Step-by-step explanation:
1. add 7/3x and 1/3x
2. subtract 5/3x because its the lowest number with a variable and you'll get 3/3x = 1
3. divide 3/3 from both sides (3/3) equals 1, so its 1/1 which is 1
4. x=1
Which equation represents the graphed function?
(0,3)
(1,1)
y = -2x + 3
y = 2x + 3
y= 1/2x + 3
y=-1/2x+ 3
you know that (0,3) is a point and (1,1) is another point.
so now you have to replace them in the follow equations.
i did that and the right answer is the first equation => y=-2x+3
Answer:
a
Step-by-step explanation:
i did the question
Help on an input question?
Answer:
The input is the letter in the parentheses.
Step-by-step explanation:
f(h) is h
g(f) is f
h(g) is g
A blue die and a white die are tossed. Find n
Answer: Then the sample space is 36.
Step-by-step explanation:
n is the number of possible combinations.
Now, as the die are of different colors, the case where:
white = 1 blue = 2, sum = 1+ 2 = 3
white = 2 blue = 1, sum = 2 + 1 = 3
are different.
So the number of possible combinations is:
6 options for the white dice and 6 options for the blue dice, so we have:
6*6 = 36 different combinations.
Then the sample space is 36.
At the end of a year, the gross debt of a country stood at about $24 trillion. Express this amount in dollars per person, assuming that the population of the country is about 298 million
Answer: $80536.9
Step-by-step explanation:
From the question, at the end of a year, the total debt of a country stood at about $24 trillion and the country has a population of 298 million.
To calculate the amount in dollars per person, we divide the gross debt by the population. This will be:
= 24 trillion ÷ 298 million
= 24,000,000,000,000 ÷ 298 000 000
= 80536.9
The amount in dollar per person will be $80536.9
(FAST ANSWER, 20 POINTS!) The heights of a group of boys and girls at a local middle school are shown on the dot plots below. When comparing the shapes of the two sets of data, what conclusion can someone draw?
A. The shortest boy is taller than the shortest girl.
B. The range for the girls is greater than the range for the boys.
C. There is an outlier in the data for the boys, but not for the girls.
D. The girls are generally taller than the boys.
Answer:
The answer is D) The girls are generally taller than the boys.
Step-by-step explanation:
The heights of a group of boys and girls at a local middle school are shown on the dot plots. When comparing the shapes of the two sets of data, the girls are generally taller than the boys.
I hope I helped, please correct me if I'm wrong!
Kevin is buying water for his camping trip. He knows he needs at least 20 gallons of water for the trip. He already has five and a half gallons. The water comes in 32-fluid ounce (quarter-gallon) containers. Which algebraic inequality represents this situation? One-fourth x + 5 and one-half greater-than-or-equal-to 20 One-fourth x + 5 and one-half less-than-or-equal-to 20 One-fourth x + 5 and one-half greater-than 20 One-fourth x minus 5 and one-half greater-than 20
Answer:
Kevin is buying water for his camping trip. He knows he needs at least 20 gallons of water for the trip. He already has five and a half gallons. The water comes in 32-fluid ounce (quarter-gallon) containers.
Which algebraic inequality represents this situation?
(correct) One-fourth x + 5 and one-half greater-than-or-equal-to 20
One-fourth x + 5 and one-half less-than-or-equal-to 20
One-fourth x + 5 and one-half greater-than 20
One-fourth x minus 5 and one-half greater-than 20
Step-by-step explanation:
The first one is correct.
Answer:
it's A :P
One-fourth x + 5 and one-half greater-than-or-equal-to 20
Step-by-step explanation:
Which point on the number line best represents V10?
Answer:
F
Step-by-step explanation:
The square root of 10 is 3.16. Point F is between 3.1 and 3.2.
The point on the number line best represents √10 is point F.
The following information should be considered:
The square root of 10 is 3.16. As attached in the figure we can see that Point F is lies between 3.1 and 3.2.Learn more:
https://brainly.com/question/4626564?referrer=searchResults
The circumference of a redwood tree trunk is 16 ft, and it is 100 ft tall. What is the approximate volume of the redwood tree trunk?
O2,560rt ft
O 640 ft
O 25,600r ft
O 6,400rt ft
Answer:
O 25,600r ft
Step-by-step explanation:
Volume =πr2h
= π×82×100
= 6400π
= 20106.192982975 feet ^3
Answer:
6,400π ft3
Step-by-step explanation:
took test and got it right
CAN SOMEONE PLS HELP ME 10 POINTS PLS
a. Which of these could be the area of Circle B? *
About 100 in ^2
About 300 in^2
About 900 in^2
About 2,700 in^2
b. Explain your reasoning for part a. Use the approximation of about 3 for pi. *
Answer:
D) About 2,700 in^2
Step-by-step explanation:
Equation for area of a circle is A=3r² (it would usually be A=πr² but we are using the approximation)
The diameter is 60, we want to find the radius for the equation. We can use the equation d=2r to find the radius of the circle.
60=2r
30=r
Put radius into the area equation.
A=3(30)²
A=3(900)
A=2700
Answer:
2,700 in^2 ; Option D
Step-by-step explanation:
If it is known that the diameter of Circle B ⇒ 60 inches,
[tex]Diameter - 60 inches,\\\\Radius - 60 / 2 = 30 inches,\\\\Area of Circle B ( \pi stands for 3 ) - \pi * ( r )^2 = ( 3 ) * ( 30 )^2 = ( About ) 2,700 square inches\\\\Solution; 2,700 square inches[/tex]
( About ) 2,700 square inches; Option D
