Answers
9514 1404 393
Answer:
a) 300 square units
b) 260 square units
c) 264 square units
Step-by-step explanation:
The total surface area of a triangular prism is the sum of the areas of its 5 faces. Two of those are triangles (the bases), and three are rectangles. The area of an individual triangle is A = 1/2bh, but the area of the two of them together will be simply A = bh.
The area of the three rectangular faces is the sum of the products of the height of the prism and the edge length of each face. Then the sum of these products can be computed as the product of the height and the perimeter of the base.
These repetitive calculations are nicely done by a spreadsheet loaded with the appropriate formulas. Areas are all in "square units." (For problem 3, the units are centimeters.)
Example: (2a)
Base area = 5×12 = 60 . . . . combined area of both bases
Lateral area = (5 +12 +13)(8) = 30×8 = 240
Total surface area = 60 + 240 = 300 . . . . square units
Answer:
2. a. 300 units²
b. 260 units²
c. 264 units²
Step-by-step explanation:
2. a. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 12
h = 5
s1 = 13
s2 = 12
s3 = 5
H = 8
Plug in the values into the formula
Surface area of triangular prism = 12*5 + (13 + 12 + 5)*8
= 60 + (30)*8
= 60 + 240
Surface area = 300 units²
b. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 11
h = 3
s1 = 11
s2 = 5
s3 = 6.7
H = 10
Plug in the values into the formula
Surface area of triangular prism = 11*3 + (11 + 5 + 6.7)*10
= 33 + (22.7)*10
= 33 + 227
Surface area = 260 units²
c. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 6
h = 8
s1 = 10
s2 = 6
s3 = 8
H = 9
Plug in the values into the formula
Surface area of triangular prism = 6*8 + (10 + 6 + 8)*9
= 48 + (24)*9
= 48 + 216
Surface area = 264 units²
Related Questions
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answers
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
The ratio of the number of boys to that of girls in a school is 4:3. If the number of girls in the school is 162, find the number of boys in it. Then find the ratio of the number of girls to the total number of students in the school.
Answers
Answer:
total number of boys in skool is 216
And
ratio of girls to boys is a 3:4
Step-by-step explanation:
let total no. of boys be X
ACCORDING TO QUESTION
ratio of boys to girls = 4:3
total number of girls = 162
now
4/3=X/162
or, 4×162= 3x
or, 4×162/3= X
hence
X = 216
therefore total number of boys is 216
and
ratio of girls to boys is =162/216
=3/4
=3:4
what is 3/16 of 200 written as a percentage?
Answers
Answer:
Step-by-step explanation:
3/16 = 0.1875
As a % this is 18.75%
18.75/100 * 200 = 37.5
I'm not sure from the question, exactly what you want. 18.75% of 200 is one possibility.
3/16 of 200 as a percentage is 3750%
The question can be represented as:
[tex]\frac{3}{16} * 200[/tex]
Rewrite as:
[tex]\frac{3}{16} * 200 =\frac{3* 200}{16}[/tex]
Multiply the numerator
[tex]\frac{3}{16} * 200 =\frac{600}{16}[/tex]
[tex]\frac{3}{16} * 200 =37.5[/tex]
Multiply by 100% to represent it as a percentage
[tex]\frac{3}{16} * 200 =37.5 * 100\%[/tex]
[tex]\frac{3}{16} * 200 =3750\%[/tex]
Read more at:
https://brainly.com/question/19994306
a car drives at 45 km/h for 75 minutes how far does the car travel
Answers
Answer:
56.25km
Step-by-step explanation:
75min = 5/4 h
distance = speed * time = 45 * 5/4 = 56.25
Instructions: Solve the following equation for the variable given.
on
1/4 (4x - 4) = -2(6x + 7)
Solving Linear Equation
Answers
Answer:
x = -1
Step-by-step explanation:
1/4 (4x - 4) = -2(6x + 7)
1x - 1 = -12x - 14
13x = -13
x = -1
Becca tried to evaluate the expression
45−(8×3+15
Answers
Answer:
Step-by-step explanation:
45 - (8 x 3 + 15)
45 - (24 + 15) ---> do parentheses first
45 - ( 39 )
45 - 39
6
The value of the expression Becca should get after simplification is 6.
Given is an expression 45 - (8 × 3 + 15), Becca is trying to solve the same,
To evaluate the expression 45 - (8 × 3 + 15), Becca should follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
First, calculate the value inside the parentheses: 8 × 3 + 15
= 24 + 15
= 39.
Now, substitute this value back into the original expression: 45 - 39.
Finally, perform the subtraction: 45 - 39 = 6.
So, the value of the expression is 6.
Learn more about expression click;
https://brainly.com/question/34132400
#SPJ3
Regression and Correlation are two of the most often used and abused tools in research.
a. True
b. False
Answers
A.True
Answer:
it is true
Step-by-step explanation:
Rewrite the polynomial in the form ax+by+c and then identify the values of a, b, and c.
x -- 1 -- 2y
Answers
Answer:
a=1, b=-2,c=-1
Step-by-step explanation:
1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1
D. Rom has just given an insurance company $35,000. In return, he will receive an annuity of $3,700 for 20 years. At what
rate of return must the insurance company invest this $35,000 in order to make the annual payments?
Answers
Answer:
0.53%
Step-by-step explanation:
hope it is well understood
The formula for finding the area of a square that has a side length, s, is A= 52. If a square has an area of 40 square
units, what is the length of a side?
20
10/
2 /10
Answers
Answer:
2√10
Step-by-step explanation:
Given the following data;
Area of square = 40
Mathematically, the area of a square is calculated by using the formula;
Area, A = s²
Where;
s is the length of sides of a square.
Substituting into the formula, we have;
40 = s²
s = √40
s = √4 * √10
s = 2 * √10
s = 2√10
WILL MARK BRAINLIEST PLEASE SHOW WORK!
Answers
Step-by-step explanation:
4. the area of semi circle R =
3²/5² × 75π = 9/25 × 75π = 27π cm²
5. the ratio of their areas = 1²:7² = 1:49
what is symmetrical line
Answers
Answer:
assuming youre asking for line of symmetry, it's a line that cuts a shape exactly in half.
for example, a square has 4 lines of symmetry
11. Find the 5th term of the sequence defined by the given rule. (1/2 point)
f(n) = 6n + 4
Answers
Answer:
34
Step-by-step explanation:
n = 5
f(5) = 6(5)+4
f(5)=34
The fifth term of the sequence is equal to 34.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,
n = 5
f(5) = 6(5)+4
f(5)=34
Therefore, the fifth term of the sequence is equal to 34.
To know more about arithmetic progression follow
https://brainly.com/question/6561461
#SPJ2
Hi I need help with part c please and thank you so much if you can do so
Answers
For the hole in one pythagores theorem would work because a right angled triangle eill be formed and hole in one would be the hypotenuse which can be found using the theorem.
b²+p² = h²
Answered by Gauthmath must click thanks and mark brainliest
Cons on the main shown on the graph over which interval is the value of the exponential function greater than
the value of the quale Action?
2513
113
O 038
Se
Answers
9514 1404 393
Answer:
-0.58 < x ≤ 2
Step-by-step explanation:
The exponential function is greater on the interval of approximately (-0.58, 1).
about -0.58 < x < 1
Find the length of AC again
Answers
Answer:
B
Step-by-step explanation:
side Ac is the opposite of angle B, therefore use the sin ratio to find ac since the hypotenuse is also given
sin B=opposite/hypotenuse
sin 27=ac/15
ac=sin27×15
=6.81
I hope this helps
Answer:
AC = 6.81
Step-by-step explanation:
∠BAC = 90° - 27° = 63°
Cos 63° =[tex]\frac{AC}{AB}[/tex] = 0.454
AC = cos 63° * AB = 0,454 * 15 = 6.81
Bridgette bought 1 pack of white T-shirts and 5 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 2, and the blue T-shirts come in packs of 6. How many T-shirts did Bridgette buy in all?
Answers
Work Shown:
1 pack of white = 2 shirts = A
1 pack of blue = 6 shirts
5 packs of blue = 5*6 = 30 shirts = B
A+B = 2 white shirts + 30 blue shirts = 32 shirts total
Answer:
32 T-shirts in total
Step-by-step explanation:
1 white has 2
1 blue has 6
1*2=2 white T
5*6=30 blue T
30+2=32
Do this please helpppp
Answers
Answer:
y = [tex]\frac{20}{9}[/tex]
Step-by-step explanation:
Since the figures are similar then the corresponding sides are in proportion, that is
[tex]\frac{JH}{PQ}[/tex] = [tex]\frac{FM}{ST}[/tex] , substitute values
[tex]\frac{6}{4}[/tex] = [tex]\frac{7}{3y-2}[/tex] ( cross- multiply )
6(3y - 2) = 28
18y - 12 = 28 ( add 12 to both sides )
18y = 40 ( divide both sides by 18 )
y = [tex]\frac{40}{18}[/tex] = [tex]\frac{20}{9}[/tex]
Answer:
20/9
Step-by-step explanation:
since the 2 are similar,
JH/PQ = FM/ST
6/4 = 7/(3y-2)
6(3y-2) = 7*4
18y-12=28
18y = 40
y = 40/18 = 20/9 = 2 2/9
Bryce grew 3 1/2 inches each year for the past 4 years. How many inches total has Bryce grown in the past 4 years?
Answers
Answer:
14
Step-by-step explanation:
3 1/2 multiply by 4 equals 14
Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!
Answers
Answer: [tex]\dfrac{11}{9}I[/tex]
Step-by-step explanation:
Given
There is [tex]l[/tex] liter of pure alcohol
Suppose [tex]x[/tex] liters of water is added
After addition of water, alcohol becomes 45% in concentration
[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]
Thus, [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.
Need it done ASAP please help
Answers
Answer:
[tex]M_{st} = (\frac{-2+4}{2}, \frac{-4+6}{2})[/tex]
[tex]M_{st}=(\frac{2}{2}, \frac{2}{2} )[/tex]
[tex]M_{st}=(1, 1)[/tex]
[tex]M_{cd}=(\frac{-6+4}{2} , \frac{10-8}{2} )[/tex]
[tex]M_{cd}=(\frac{-2}{2} , \frac{2}{2} )[/tex]
[tex]M_{cd}=(-1, 1)[/tex]
The graph is that of a fourth-degree polynomial function. Which of the following correctly shows three factors of the function? Image included, please help!
Answers
C.
Observe that the roots of polynomial are [tex]-3,2,5[/tex]
We have a polynomial in a factored form,
[tex](x+3)(x-2)(x-5)[/tex]
If you substitute x for any of [tex]-3,2,5[/tex] the product will always equal to zero that is these numbers are roots of polynomial.
Hope this helps :)
Find the value of z.
54°
X
2049
(32+1)°
A. 25.25
OB. 129
Answers
Answer:
Step-by-step explanation:
(z)° + (3z + 1)° = 360° - ( 54° + 204° )
z + 3z + 1 = 360 - 258
4z = 101
z = 25.25
The total amount of time university students in the United States spend sleeping grooming, eating and drinking, and traveling is about Average weekday time use for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.19% 3.3% 4.2% Grooming 13.8% 5.8% Eating and drinking Educational activities 10.0% 9.696 Traveling Other Work and related activities
Answers
Answer:
yes
Step-by-step explanation:
The total amount of time university students in the United States spend sleeping, eating and drinking, and doing leisure and sports is about: Average weekday time used for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.1% 3.3% Grooming 4.2% Eating and drinking 13.8% 5.8% Educational activities 9.6% Traveling 10.0% Other Work and related activities A A 1/3 of their total time 3/5 of their total time C) 1/2 of their total time 3/4 of their total time
How many hours of sleep does a typical college student get on a weekday?"Our data was consistent with what researchers have found in academic studies — that students are in bed, on average, seven to eight hours per weeknight," says Brian Wilt, Jawbone's head of data science and analytics.
How much time does the average college student spend sleeping?On average, college students get a whopping six hours of sleep a night according to a study by the University of Georgia. Lack of sleep can take a toll on your mental health, cause a reduction in cognitive performance and affect your memory capacity!
Learn more about the average college student spend sleeping at
https://brainly.com/question/14448167
#SPJ2
Help please!!!! Im really stuck.
Answers
Answer: 275 adults and 130 children
Step-by-step explanation:
First, find the value of one variable by rearranging a equation:
[tex]a+c=405\\c=405-a[/tex]
Substitute it into the other equation and solve for a:
[tex]12a+5c=3950\\12a+5(405-a)=3950\\12a+2025-5a=3950\\12a-5a=3950-2025\\7a=1925\\a=\frac{1925}{7} =275[/tex]
Use the a-value to find b by substituting it into the rearranged equation:
[tex]c=405-a=405-275=130[/tex]
Therefore, the answer would be:
[tex]\left \{ {{a=275} \atop {c=130}} \right.[/tex]
need help asap
what is the value of f(3) in the function below
Answers
Answer:
Step-by-step explanation:
The given function is :
Here , x= independent variable where we place the input value and f(x) = dependent variable where we get the output value.
Now , when we put x= 3 , we get
That means , the value of f(3) in the given function is 8.
Hence, the correct answer is B=8.
2*2*2=8
8 is the answer
What is the distance between (-6, 8) and (-3, 9)?
Answers
Answer:
√10
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[-3 - (-6)] + (9 - 8)²
√(3)² + (1)²
√9 + 1
√10
which data is represented by this plot?
a)2,4,0,4,6,3,1,7,8,1,1
b)0,1,2,3,4,5,6,7,8,0,1
c)0,2,3,0,2,4,4,5,7,8,7
d)1,2,6,4,7,7,2,2,0,1
Answers
a)
Step-by-step explanation:
Data represented by the plot: 0, 1, 1, 1, 2, 3, 4, 4, 6, 7 & 8
B) & C) Can’t be answers cuz of 2 0’s
So it’s between A) & D)
Well D is missing one more 1 in the data plot so the answer is A
A parallelogram is made up of a rectangle with a base of 12 centimeters (cm) and a height of 5 cm, and two triangles, each with a base of 2 cm and height of 5 cm. Jeremy calculates the area of the parallelogram by multiplying the base and height of the rectangle to get 60 cm2.
Is Jeremy's answer correct? Why or why not?
Select the option that correctly answers both questions.
No, he forgot to multiply by 12 when calculating the area of the rectangle.
Yes, he correctly calculated the area of the parallelogram as b⋅h.
No, he forgot to add the area of the triangles to the area of the rectangle.
Yes, he correctly calculated the area of the parallelogram as 12bh.
Answers
It is said that Jeremy thought he solved for the area of the whole parallelogram correctly by multiplying the base and height of the rectangle, which is just a part of the whole parallelogram.
Jeremy’s answer is incomplete, he only calculated the area of the triangle as the answer.
This is because one way of finding an area of a parallelogram is dividing the shape into a rectangle with a triangle on each side.
The real area of the parallelogram is 70 cm^2
(with areas of each triangles added)
With that being said, the formula of a parallelogram that is said is:
A = bh
Which means a height perpendicular to the base of the whole paralleogram.
Fiona invested $1000 at 7% compounded continuously. At the same time, Maria invested $1100 at 7% compounded daily. How long will it take for their investments to be equal in value? Assume there are 365 days in every year.
Answers
9514 1404 393
Answer:
14,201 years
Step-by-step explanation:
The two compound interest formulas are ...
A = P·e^(rt) . . . . . continuous compounding at rate r for t years
A = P·(1 +r/365)^(365t) . . . . . daily compounding at rate r for t years
We went the amounts to be equal:
1000·e^(0.07t) = 1100·(1+0.07/365)^(365t)
Dividing by 1000(1 +0.07/365)^(365t), we have ...
((e^0.07)/(1+0.07/365)^365)^t = 1.1
The base of the exponential on the left is ...
( e^0.07)/(1+0.07/365)^365 ≈ 1.00000671149321522
Taking logs, we have ...
t×ln(1.00000671149321522) = ln(1.1)
t = ln(1.1)/ln(1.00000671149321522) ≈ 0.09531018/(6.7114704·10^-6)
t ≈ 14,201.09 . . . . . years
It will take about 14,201 years for the investments to be equal.
_____
Additional comment
The investment value at that time will be about $5.269·10^434. (That's a larger number than anything countable in the known universe, including energy quanta.)
These calculations are beyond the ability of many calculators, so might need to be carefully rewritten if the calculator only keeps 10 significant digits, or only manages exponents less than 100.
This shows that daily compounding is very close in effect to continuous compounding. It would take almost 150 years to make a difference of 0.1% in value.
