The surface area of a triangular prism can be found by adding the areas of all faces. The triangular faces are calculated using the formula for the area of a triangle, and the rectangular faces are calculated using the given dimensions of the sides of the triangles. The total surface area is the sum of these areas.
Explanation:The question is asking for the surface area of a triangular prism. In order to find this, you need to add the areas of all the faces. A triangular prism has 5 faces, 2 are triangles, and 3 are rectangles.
For the triangular faces, we use the formula for the area of a triangle which is 1/2ab, where a and b are the provided dimensions. Thus, the triangle's area is 1/2 * 20 cm * 25 cm = 250 cm². Since there are two of these, the total area is 500 cm².
The rectangular faces are more challenging since it seems like we don't have enough information. The rectangle is made up of the sides of the triangles, so one side is 20 cm. However, we don't know the length (C) of the triangle which would be the other side of the rectangle. Assuming C is given, multiply each corresponding side to get the area of each rectangle, and add all together.
The final step is to add the area of the triangles and rectangles together to find the total surface area of the prism.
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Situation A
Maria opened a new savings
account with an initial deposit of
$100. She deposits $75 into this
savings account every
two-weeks. What equation can
be used to represent Maria's
account balance, a, after she has
completed d deposits?
The equation a = 100 + 75d represents Maria's account balance.
Step-by-step explanation:
Given that,
Maria opened a new savings account with an initial deposit of $100.She deposits $75 into this savings account every two-weeks.You need to find the equation to represent Maria's account balance, a after she has completed d deposits.
Let 'd' be the number of deposits Maria made after the initial deposit.Let 'a' be the total account balance after 'd' deposits.Therefore, the equation for the total account balance can be framed as the sum of the initial deposit and amount deposited after that.
To find the amount that was deposited after the initial deposit :
⇒ $75 × number of times Maria deposited.
⇒ 75 × d
The equation is written as,
⇒ a = 100 + 75d
Hence the equation a = 100 + 75d represents Maria's account balance.
what is the value of w
Answer: 126 degrees
Formula number of sides -2 times 180 = total degrees for polygon
5-2=3x180= 540
Add the 78+132+137+67=414
540-414= 126
Step-by-step explanation:
A model for consumers' response to advertising is given by the equation N(a)=2000+500 ln (a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.
How many units are sold when $1000 is spent on advertising?
Answer:
Therefore 2000 units are sold when $1000 is spent on advertising.
Step-by-step explanation:
Given that,
The equation of a model for consumer's response to advertising is
N(a)=2000+500 ln(a)
where a is the amount spent on advertising, in thousand of dollars and a≥1,N(a) is the amount of units sold.
$1000 is spent on advertising.
Since a is in thousand of dollars.
∴a=1
Now plug a=1 in the given model
N(a)=2000+500 ln(1)
⇒N(a)=2000+500×0 [ ∵ln(1)=0 ]
⇒N(a) = 2000
Therefore 2000 units are sold when $1000 is spent on advertising.
Work out the percentage change when a price of £65 is decreased to £39.
Answer:
40% decrease
Step-by-step explanation:
Say the percent decrease is x%. Then, we can write the equation:
65 - x% * 65 = 39
Notice that 65 is a common factor of both terms on the left, so factor that out:
65 * (1 - x%) = 39
Divide by 65 on both sides:
1 - x% = 0.6
Subtract 0.6 from and add x% to both sides:
x% = 0.4
Remember that % simply means "out of 100", so x% = x/100:
x/100 = 0.4
Multiply by 100:
x = 40
So the percentage decrease is 40%, or the percent increase is -40% (whichever way the question asks).
Hope this helps!
Answer:
p = 40%
Step-by-step explanation:
65 - p%65 = 39
65 - 65p/100 = 39
6500 - 65p = 3900
6500 - 3900 = 65p
65p = 2600
p = 2600 : 65
p = 40%
A line passes through the points (1,4) and (3,-4). Which is the equation of the line
Answer: y=-4x+8
Step-by-step explanation:
Please help me with this I will mark you as brainliest!
Answer:
21, 42, 63, 84
Step-by-step explanation:
Numbers that have a star and a circle on them are all multiples of 3 and 7. As there are less multiples of 7 between 1-100 we should list the multiples of 7 and then check if they are also multiples of 3.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
A quick way of calculating if a number is a multiple of 3 is to see if its digital root is either 3, 6, or 9
7 is not as 7 is not a multiple of 3
14 is not as 1+4 = 5 is not a multiple of 3
21 is, as 2+1 = 3 is a multiple of 3
28 is not, as 2+8 = 10 is not a multiple of 3
35 not, 3+5=8
42 is, 4+2=6
49 is not, 4+9=13
56 is not , 5+6=11
63 is, 6+3=9
70 is not, 7+0=7
77 is not, 7+7=14, 1+4=5
84 is, 8+4=12, 1+2=3
91 is not, 9+1=10 1+0 = 1
98 is not, 9+8=17, 1+7=8
Alberts sixth grade class will have five test for social studies they already have two of Alberts grades for these two tests are shown below. If Albert wants the mean of his five tests to be 90 what could be his last three grades. Test 1 was an 85 Test two was a 100
Solve for x
Your answer must be simplified.
x/-6 ≥−20
Answer: x ≤ 120
Step-by-step explanation: To get x by itself in this inequality, since it's being divided by -6, we must multiply both sides by -6 just like we would if we were solving an equation.
But here is the trick you have to
watch out for with inequalities.
When you multiply or divide both sides of an inequality by a
negative, you must switch the direction of the inequality sign.
So our second step in this problem reads x ≤ 120.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when multiplying or dividing both sides of an inequality by a negative.
what is the third step when calculating mean absolute deveation
Answer:
Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points.
Step-by-step explanation:
The garden bed has a width of 1.5 meters and an area of 6 square meters . Which Equation and Solution correctly represent x , the length , in meters , of the rectangular garden bed
Answer: The answer is 4!
6/1.5= 4
I need help with this ASAP
Answer:
60 degrees
Step-by-step explanation:
These two shapes are similar, which means that their corresponding angles are congruent.
Angle L corresponds to angle X. We know that <L = 60, which means that <X is also equal to 60.
Thus, the answer is 60 degrees.
Hope this helps!
Answer:
60°
Step-by-step explanation:
The two figures are similar and they have the same distribution of angles.
Angle X corresponds to Angle L = 60°
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Key: 2|5 means 25
A stem-and-leaf plot with a stem value of 1 with a leaf value of 2, 3, 5, a stem value of 2 with a leaf value of 8 and 8, a stem value of 3 with a leaf value of 0, and a stem value of 4 with a leaf value of 2.
Answer:
mean = 24
Step-by-step explanation:
In a stem-and-leaf plot, each leaf represents a number or piece of data.
Each the leaf will only show the last digit of the number, and the stem will have the rest.
Examples:
stem value of 1 with a leaf value of 2 = 12
a stem value of 3 with a leaf value of 0 = 30
So, this is your plot:
Stems| Leaves
1 | 2 3 5
2 | 8 8
3 | 0
4 | 2
Your data is 12, 13, 15, 28, 28, 30, 42.
Add up all these numbers and divide by the number of leaves.
Sum of data = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
Number of leaves = 7
168 ÷ 7 = 24
∴ The mean is the values in the stem-and-leaf plot is 24.
Which equation represents:
"An unknown integer, multiplied by the unknown integer minus a different unknown integer, equals 100."
A) x2 + xy + 100 = 0
B) x2 + xy − 100 = 0
C) x2 − xy + 100 = 0
D) x2 − xy − 100 = 0
Answer:
D) x² − xy − 100 = 0
Step-by-step explanation:
You want an expression for "An unknown integer, multiplied by the unknown integer minus a different unknown integer, equals 100."
SetupLet x represent the unknown integer, and y represent the different unknown integer. Their difference will be (x -y). When that is multiplied by x and the result equal to 100, we have ...
x(x -y) = 100
SimplifyEliminating parentheses using the distributive property, we have ...
x·x -x·y = 100
x² -xy = 100
Subtracting 100 gives an expression equal to zero:
x² -xy -100 = 0 . . . . . . . matches choice D
What is the slope of y=-x+7
Answer:
The slope is -1
Step-by-step explanation:
y=mx+b where m is the slope
y =-x+7 can be also be written as y=-1x +7
So therefore the number infront of x is considered the slope
-1
Answer:
Slope m = − 1
Y-intercept = 7
A bag contains 4 red marbles and 1 yellow marble. What is the probability of drawing a red marble, then replacing that marble, then drawing a red marble again on the second pick?
Answer:
16/25
Step-by-step explanation:
We have 4 red marbles and a total of 4 + 1 = 5 marbles.
Probability is simply (# times a specific event can occur) / (# times any event can occur).
Here, the probability of drawing a red marble is: 4/5 (because there are 4 red marbles to choose from and a total of 5 marbles to choose from).
We replace the marble afterward, so the probability that the second pick is also red would still be 4/5.
Then, multiply the two fractions together: (4/5) * (4/5) = 16/25.
Hope this helps!
Roscoe traced around the bottom of a can to draw a circle. tell whether each statement about Roscoe 's circle is true. use 3.14 for pie
Answer with Step-by-step explanation:
a.If the circle has circumference of [tex]6\pi[/tex] in,then it has a diameter of 3 in.
Circumference of circle=[tex]6\pi[/tex]in
We know that
Circumference of circle=[tex]2\pi r[/tex]
Using the formula
[tex]6\pi=2\pi r[/tex]
[tex]r=\frac{6\pi}{2\pi}=3[/tex]in
Diameter of circle=[tex]2\times 3=6[/tex]in
It is false.
b.f the circle has diameter of 2 inches,then it has a circumference of 6.28 in.
Diameter,d=2 in
Circumference of circle=[tex]\pi d=3.14 \times 2=6.28[/tex]in
It is true.
c.If the circle has a circumference of [tex]2\pi[/tex]in then it has an area [tex]\pi[/tex] square inches.
Circumference=[tex]2\pi[/tex]in
[tex]2\pi r=2\pi[/tex]
[tex]r=\frac{2\pi}{2\pi}=1[/tex]in
Area of circle=[tex]\pi r^2=\pi(1)^2=\pi in^2[/tex]
It is true.
d.If the circle has a circumference of [tex]\pi[/tex]in then it has an area [tex]0.5\pi[/tex] square inches.
Circumference=[tex]\pi[/tex]in
[tex]2\pi r=\pi[/tex]
[tex]r=\frac{\pi}{2\pi}=\frac{1}{2}in[/tex]
Area of circle=[tex]\pi(\frac{1}{2})^2=0.25\pi in^2[/tex]
It is not true.
e.If the circle has a radius of 1.5 inches,then it has an area of 7.065 square inches.
Radius,r=1.5 in
Area of circle=[tex]3.14\times (1.5)^2=7.065in^2[/tex]
It is true.
A textbook store sold a combined total of 448 physics and biology textbooks in a week. The number of biology textbooks sold was 66 less than the number of physics textbooks sold. How many textbooks of each type were sold?
Answer:
Step-by-step explanation:
448 - 66 = 382
448 physics books and 382 biology books
In which step did Cyrus make an error?
7 7 (x - 1)² = 12
(x - 1)2 = 36 Step 1
I-1= 6
Step 2
I=7
Step 3
Answer:
In step 2 Cyrus make an error.
Step-by-step explanation:
Given : Expression [tex]\frac{1}{3}(x-1)^2=12[/tex]
To find : In which step did Cyrus make an error?
Solution :
Expression [tex]\frac{1}{3}(x-1)^2=12[/tex]
Step 1 - [tex](x-1)^2=36[/tex]
Step 2 - [tex]x-1=6[/tex]
Step 3 - [tex]x=7[/tex]
There is a mistake in step 2,
As we are taking root both side so RHS value is +6 and -6.
So that there are two solutions of the equation.
Correct steps are,
Step 2 - [tex]x-1=6,-6[/tex]
Step 3 - [tex]x=7,-5[/tex]
Therefore, In step 2 Cyrus make an error.
Answer is step 2
Step-by-step explanation:
Mark owns a cattle ranch near Hugo, Oklahoma. Mark is currently producing beef at an output level where marginal revenue exceeds marginal cost. In order to
maximize his profit, Mark should
O A. decrease his output.
OB. shut down his ranch.
O c. not change his output.
OD. increase his output.
O E. probably change his output, but more information is needed to determine if he should increase, decrease, or not change it.
Answer:
Answer is D. Increase his output.
Refer below.
Step-by-step explanation:
Mark owns a cattle ranch near Hugo, Oklahoma. Mark is currently producing beef at an output level where marginal revenue exceeds marginal cost. In order to
maximize his profit, Mark should increase his output.
Find all constants α such that the vectors (α, 4) and (α, 5) are parallel.
Answer:
[tex]\alpha_{2} = \frac{5}{4}\cdot \alpha_{1}[/tex], for all [tex]\alpha_{1} \in \mathbb{R}[/tex]
Step-by-step explanation:
Vectors are parallel to each other if:
[tex]\vec u = \beta \cdot \vec v[/tex]
[tex](\alpha_{2}, 5) = (\beta\cdot \alpha_{1}, \beta \cdot 4)[/tex]
The value of [tex]\beta[/tex] is:
[tex]\beta = \frac{5}{4}[/tex]
Then, the following relationship is found:
[tex]\alpha_{2} = \frac{5}{4}\cdot \alpha_{1}[/tex], for all [tex]\alpha_{1} \in \mathbb{R}[/tex]
What is the domain of this exponential function?
Answer:
Domain = x E R
Step-by-step explanation:
Since an exponential function has no restriction on the "x" value, its domain can range from anywhere on the plane of "x."
Any help? Will mark you as brainliest for the correct answer
Answer:
see explanation
Step-by-step explanation:
Given that 40 people liked cats, that is 20 women and 20 men
Then the dual bar representing 20 is made up of 4 frequency bars
Then each frequency bar represents 20 ÷ 4 = 5 people
Thus
dogs = 25 (men) + 30 (women) = 55
hamster = 15 ( men) + 5(women) = 20
other = 10(men) + 15(women) = 25
Favourite pet frequency table
favourite pet frequency
cat 40
dog 55
hamster 20
other 25
A total of 40 + 55 + 20 + 25 = 140
It takes Carol 45 minutes to drive to work using two roads. She drives 24 mph on a small road for hour. Then she drives 56 mph on a highway for hour. How far does Carol travel to work?
Answer:
She travels 30 miles for work.
Given,
Total time = 45 minutes
Speed on small world = 32mph
Time on small world = 1/2 hour
Distance = Speed * time =
Distance on small world = 16 miles
Speed on small road = 56mph
Time on small road = 1/4 hour
Distance on small road =
Distance on small road = 14 miles
Total distance = Distance on small world + Distance on small road
Total distance = 16+14= 30 miles
She travels 30 miles for work.
Keywords: Distance, speed
Step-by-step explanation:
Final answer:
Carol travels 12 miles on the small road and 28 miles on the highway, totaling 40 miles to get to work.
Explanation:
The question asks us to calculate the total distance Carol travels to work using two different speeds on two different roads. To solve this problem, we use the formula d = vt, where d represents distance, v is velocity (or speed), and t is time.
On the small road, Carol drives at 24 miles per hour for half an hour (0.5 hours). Therefore, the distance traveled on the small road is:
d = (24 miles/hour)(0.5 hours) = 12 miles
On the highway, she drives at 56 miles per hour for half an hour (0.5 hours) as well. The distance traveled on the highway is:
d = (56 miles/hour)(0.5 hours) = 28 miles
To find the total distance, we add the distances from both roads:
Small road: 12 milesHighway: 28 milesTotal distance = 12 miles + 28 miles = 40 miles
Carol travels a total of 40 miles to get to work.
Please help !!!!!
I need it asap
Answer:
just do your homework
Step-by-step explanation:
Answer:
answer is the page is to blurry for my windows 95 can you make it into a better picture so i can help
Step-by-step explanation:
A construction company purchased seven house lots of the following sizes:
1 ⅜ acres, 2 ⅛ acres, l ⅛ acres, l ¾ acres, and 2 ¼ acres. What is the range of these
lot sizes?_
Answer:
between 1 1/8 acres and 2 1/4 acres
Step-by-step explanation:
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,980 was collected on the sale of 1,236 tickets. How many of each type of ticket were sold?
Answer:
750 adult tickets
486 student tickets
Step-by-step explanation:
5 x 150=750 adult tickets
486 student tickets
Plz give brainliest need 1 more
what is the radius of the cone ? I need help
Answer:
4
Step-by-step explanation:
pi*r^2
just put each number where r is to find out the answer
Please help me with this one!
Answer: 184
Step-by-step explanation: i looked
Daniel’s school is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 8 senior citizen tickets and 8 child tickets for a total of $136. The school took in $138 on the second day by selling 9 senior citizen tickets and 4 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Answer:
the answer is 17
Step-by-step explanation:
You divide 8 and 136 and get 17, you multiply 17 and 8 to double check your answer, Hope this helps :P!
Evaluate the geometric series. Please help me out!!!
Answer:
- 1364
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
4[tex](-2)^{n-1}[/tex] ← is an n th term
with a = 4 and r = - 2
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex], thus
[tex]S_{10}[/tex] = [tex]\frac{4((-2)^{10}-1) }{-2-1}[/tex]
= [tex]\frac{4(1024-1)}{-2-1}[/tex]
= [tex]\frac{4(1023)}{-3}[/tex]
= [tex]\frac{4092}{-3}[/tex]
= - 1364