What is the volume of the right triangular prism below? a 1600cm 800cm 400cm 160cm
Answers
The formula for determining the volume of a triangular prism is expressed as
Volume = area of triangular face * height of prism
The fotmula for finding the area of the triangular face is
Area = 1/2 * base * height
Looking at the diagram,
base = 8 cm
height = 10 cm
Area of triangular face = 1/2 * 8 * 10 = 40 cm^2
height of prism = 20 cm
Volume of prism = 40 * 20 = 800 cm^3
Option B is correct
Related Questions
What is the slope of a line that is perpendicular to the line whose equation is 3x+2y=6?A. −3/2B. −2/3C. 3/2D. 2/3
Answers
We would begin by determining the slope of the line given;
[tex]3x+2y=6[/tex]To determine the slope, we would have to express the equation of the line in slope-intercept form as follows;
[tex]y=mx+b[/tex]Therefore, we need to make y the subject of the equation as shown below;
[tex]\begin{gathered} 3x+2y=6 \\ \text{Subtract 3x from both sides of the equation} \\ 2y=6-3x \\ \text{Divide both sides by 2 } \\ \frac{2y}{2}=\frac{6-3x}{2} \\ y=\frac{6}{2}-\frac{3x}{2} \\ y=3-\frac{3}{2}x \end{gathered}[/tex]The equation in slope-intercept form appears as shown above. Note that the slope is given as the coefficient of x.
Note alo that the slope of a line perpendicular to this one would be a "negative inverse" of the one given.
If the slope of this line is
[tex]-\frac{3}{2}[/tex]Then, the inverse would be
[tex]-\frac{2}{3}[/tex]The negative of the inverse therefore is;
[tex]\begin{gathered} (-1)\times-\frac{2}{3} \\ =\frac{2}{3} \end{gathered}[/tex]The answer therefore is option D
what is 3 x 10 to the 4 in standard notation
Answers
Find the length of the arc. Use 3.14 for it.270°8 cm
Answers
The radius of circle is r = 8 cm.
The arc is of angle 270 degree.
The formula for the arc length is,
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]Determine the length of the arc.
[tex]\begin{gathered} l=2\cdot3.14\cdot8\cdot\frac{270}{360} \\ =37.68 \end{gathered}[/tex]So lenth of the arc is 37.68.
The point K lies on the segment JL. Find the coordinates of K so that the ratio of JK to KL is 5 to 4.J(-19,12)K(?,?)L(8,-6)
Answers
The Solution:
Step 1:
We shall find the distance between point J an
In a competition of 837 people, Jenny scored at the 77th percentile.
In what place did she finish?
Answers
Answer:
Jenny scored 644th place.
Step-by-step explanation:
To find out what place she finished, you need to write it out first like this:
77% of 837.
Now, to make the equation possible to solve, we can take the 77 and make it a decimal: 0.77.
The term "of" means multiplication.
So, in turn, we have the equation:
0.77 x 837 = 644.49
And, if you round it, your answer would be:
Jenny scored 644th place.
Answer:
See below
Step-by-step explanation:
77th percentile means she scored better than 77 per cent of the test takers...
So Jenny's place was .23 * 837 = ~ 193 rd Out of 837 people
CALCULATO 11 i You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth. 1 2 3 The probability of spinning blue, flipping heads, then spinning a 1 is
Answers
Let:
A = Spinning blue
B = flipping heads
C = Spinning a 1
The probality of spinning blue is given by:
[tex]P(A)=\frac{1}{3}[/tex]The probality of flipping heads is:
[tex]P(B)=\frac{1}{2}[/tex]The probality of spinning 1 is given by:
[tex]P(C)=\frac{1}{3}[/tex]Since they are independent events:
[tex]P(A\cap B\cap C)=P(A)\cdot P(B)\cdot P(C)=\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{3}=\frac{1}{18}[/tex]
Bill has these expenditures for his utilities: December,
$234.45; January, $281.23; February, $284.33. What is his
average monthly expense for utilities?
Answers
The average monthly expenses for Bill's utilities is $266.67.
It is given in the question that:-
Expenditure in December by Bill = $ 234.45
Expenditure in January by Bill = $ 281.23
Expenditure in February by Bill = $ 284.33
We have to find the average monthly expenses for Bill's utilities.
We know that,
Average monthly expense for utilities = (Expenditure in December + Expenditure in January + Expenditure in February)/3
Hence, using the data given in the question, we can write,
Average monthly expense for utilities = (234.45 + 281.23 + 284.33)/3
Average monthly expense for utilities = 800.01/3 = $266.67
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Add and subtract square roots that need simplification Number 186
Answers
Hello!
To solve this exercise, we must simplify these square roots until we have the same square root in both numbers (by the factorization process):
[tex]3\sqrt{98}-\sqrt{128}[/tex]First, let's factorize the square root of 98:
So, we know that:
[tex]\begin{gathered} 3\sqrt{98}=3\sqrt{7^2\times2}=3\sqrt[\cancel{2}]{7\cancel{^2}\times2}=3\times7\sqrt{2}=21\sqrt{2} \\ \\ 3\sqrt{98}=21\sqrt{2} \end{gathered}[/tex]Now, let's do the same with the square root of 128:
So:
[tex]\sqrt{128}=\sqrt{2^2\times2^2\times2^2\times2}^1[/tex]Notice that it also could be written as:
[tex]\begin{gathered} \sqrt{128}=\sqrt{2\times2\times2\times2\times2\times2\times2} \\ \text{ or also} \\ \sqrt{128}=\sqrt{2^7} \end{gathered}[/tex]As we are talking about square roots, it will be easier if we group them in pairs of powers of 2, as I did:
[tex]\sqrt[2]{128}=\sqrt[2]{2^2\times2^2\times2^2\times2^1}[/tex]Now, let's analyze it:If the number inside the root has exponent 2, we can cancel this exponent and remove the number inside the root. Then, we can write it outside of the root, look:
[tex]\begin{gathered} \sqrt[2]{128}=\sqrt[2]{2^{\cancel{2}}\times2^{\cancel{2}}\times2^{\cancel{2}}\times2^1} \\ \sqrt[2]{128}=2\times2\times2\sqrt[2]{2^1} \\ \sqrt[2]{128}=8\sqrt[2]{2} \end{gathered}[/tex]Now, let's go back to the exercise:[tex]\begin{gathered} 3\sqrt{98}-\sqrt{128}\text{ is the same as } \\ 21\sqrt{2}-8\sqrt{2} \end{gathered}[/tex]So, we just have to solve it now:
[tex]21\sqrt{2}-8\sqrt{2}=\boxed{13\sqrt{2}}[/tex]A cylinder whose height is 3 times its radius is inscribed in a cone whose height is 6 times its radius. What fraction of the cone's volume lies inside the cylinder? Express your answer as a common fraction.
Answers
The fraction of the cone's volume that lies inside the cylinder would be; V = 44/21 r^4
How to find the volume of a right circular cone?Suppose that the radius of the considered right circular cone is 'r' units.
And let its height be 'h' units. The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
Then, its volume is given :
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Let the radius of the cylinder is r
The height of the cylinder is h = 3r
The height of the cone is h = 6r
The fraction of the cone's volume that lies inside the cylinder would be;
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
[tex]V = \dfrac{1}{3} \times 3.14 \times r^3 \times 6r \: \rm unit^3[/tex]
V = 44/21 [tex]r^{4}[/tex]
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Answer:
4/9
Step-by-step explanation:
Please help with this practice question
Answers
Explanation below:
Jenna organizes the food in her pantry. She organizes 4 cereal boxes, 6 cans, t pieces of fruit, and 2 bags of rice. How many food items does Jenna organize?
Answers
Solution:
The number of food items is given by the following expression:
4 cereal boxes + 6 cans+ t pieces of fruit+ 2 bags of rice
that is, she organizes
4+6+t+2 meals
this is equivalent to
(4+6+2)+t
this is equivalent to say
12 + t meals.
So that the correct answer is:
12 + t
Graph the line y = 5x - 1, then name the slope and y-intercept by looking at the graph. What is m= and what is b= and how do I graph this what are the points ?
Answers
Answer:
Step-by-step explanation:
Slope-intercept form: y = mx + b
The 'm' in this formula means slope. The 'b' means the y-intercept.
y = 5x - 1
m = 5.
b = -1.
Now that we have identified the slope and the y-intercept, we can graph the equation.
When graphing these kinds of equations, always start at the y-intercept.
The y-intercept is -1, so we start from there and move up 5 and right 1 repeatedly.
Remember, slope = rise/run. We rise 5, and we run 1.
5 can also be represented as a fraction: [tex]\frac{5}{1}[/tex]
Let me know if you have any questions.
There are 4 options on the dessert menu at a restaurant. Bill and Laura like all of the choices equallyeach choose a dessert at random from the menu. What is the probability that Bill will choose apple pLaura will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessalyour answer to the nearest thousandth.0 0.938O 0.063O 0.25O 0.083
Answers
Solution
If we have 4 options and we want to find that Bill select one option and then Laura a different second option is:
1/2 * 1/2= 1/4= 0.25
Then the best answer is:
0.25
Please help me answer this correctly,
Answers
anywhere you see x, input the value in the brackets.
eg f(-2) = 2(-2)+8
= -4+8
=4
Answer:
if x= -2
then f(x) = 2×(-2)+8
= -4+8
= 4
if x=0
then f(x)=2×0+8
=0+8
=8
if x=5
then f(x)=2×5+8
=10+8
=18
what is the answer and how do i solve it?
Answers
EXPLANATION
Since we have the expression:
[tex]\frac{x}{x^2+x-6}-\frac{2}{x+3}[/tex]First, we need to find the least common multiplier as follows:
Least common multiplier of x^2 + x - 6, x+3: (x-2)(x+3)
Ajust fractions based on the LCM:
[tex]=\frac{x}{\left(x-2\right)\left(x+3\right)}-\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]\mathrm{Apply\: the\: fraction\: rule}\colon\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]=\frac{x-2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]Expand\text{ x-2(x-2)}[/tex][tex]=\frac{-x+4}{\left(x-2\right)\left(x+3\right)}[/tex]The final expression is as follows:
[tex]=\frac{-x+4}{(x-2)(x+3)}[/tex]
What is 5 5/7 divided by 1 3/5 divided by 4 2/3 in simplest form?
Answers
The simplest form of the given division is,[tex][tex]\frac{550}{13}[/tex][/tex].
What is division?
The opposite of multiplication is division. Dividing a sum of numbers into equal pieces. A number is divided in division, which is a straightforward procedure.
Given that: (55/7)/(13/5)/(42/3)
First to simplify:
[tex](13/5)/(42/3)[tex]\frac{(\frac{13}{5}) }{(\frac{42}{3}) } = \frac{(\frac{13}{5}) }{14} \\[/tex] [tex]= \frac{13}{(5)(14)} \\= \frac{13}{70}[/tex][/tex]
So, expression becomes,
[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )}[/tex][/tex]
Now to simplify this expression.
Using:[tex][tex]\frac{(\frac{a}{b} )}{(\frac{c}{d} )} = \frac{ad}{bc}[/tex][/tex]
Then,[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )} = \frac{(55)(70)}{(7)(13)} = \frac{3850}{91} = \frac{550}{13}[/tex][/tex]
Therefore, [tex][tex]\frac{550}{13}[/tex][/tex] is the simplest form of the given division.
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For each expression build a rectangle using all of tiles,....
Answers
a.
[tex]\begin{gathered} y^2+xy+2x+2y \\ Factor_{\text{ }}as\colon \\ (y+2)(x+y) \end{gathered}[/tex]i) Sketch each rectangle:
ii) Find its dimensions
iii)
[tex]\begin{gathered} y^2+xy+2y+2x \\ \text{grouping terms:} \\ (y^2+xy)+(2y+2x)=y(y+x)+2(y+x)=(y+x)(2+y) \end{gathered}[/tex]10 × 1/3
make sure the answer is a fraction and that u explain
Answers
multiply the top and bottom ----> 10*1 and 1*3
10/3 would be your answer
relation and functionFunction OperationComposition of functionsymmetryfunction Inversesrate of change scartterplots
Answers
The answer is
[tex]m\text{ }\ne\text{ 0}[/tex]So the first one is the answer.
Because if m = 0 then the function would be a constant function that does not have inverse. and we don't care if b= 0 or not because even if b= 0 or no we just need to know about m.
Select the correct answer. What are the zeros of the graphed function? у -6 -5 3 -2 2 3 6 2 3 OA O and 4 OB. 4,-2, and o OC. 0, 2, and 4 OD. -4 and o Reset Next
Answers
We have that the next x-intercepts 0,2 and 4, in the graph therefore the zeros of the graph are 0,2 and 4.
The correct choice is C.
find the product of 1/1728.
Answers
The answer is 12
Because 12x12x12 = 1728
can you help me please
Answers
Let f(x)= 1/x-2 and g(x)=5/x+2Find the following functions. Simplify your answers.F(g(x))=g(f(x))=
Answers
Given:
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{x\text{ - 2}} \\ g(x)\text{ = }\frac{5}{x}\text{ + 2} \end{gathered}[/tex]To find:
a) f(g(x)) b) g(f(x))
[tex]\begin{gathered} a)\text{ f\lparen g\lparen x\rparen\rparen: we will substitue x in f\lparen x\rparen with g\lparen x\rparen} \\ f(g(x))\text{ = }\frac{1}{(\frac{5}{x}+2)-2} \\ \\ f(g(x))\text{ = }\frac{1}{(\frac{5+2x}{x})-2} \\ \\ f(g(x))\text{ = }\frac{1}{(\frac{5+2x-2x}{x})}\text{ = }\frac{1}{\frac{5}{x}} \\ \\ f(g(x))\text{ = }\frac{x}{5} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ g\lparen f\lparen x\rparen\rparen: we will substitue x in g\lparen x\rparen with f\lparen x\rparen} \\ g(f(x))\text{ = }\frac{5}{\frac{1}{x-2}}+2 \\ \\ g(f(x))\text{ = }\frac{5(x\text{ -2\rparen}}{1}+2 \\ \\ g(f(x))\text{ = }5(x\text{ -2\rparen}+2\text{ = 5x - 10 + 2} \\ \\ g(f(x))\text{ = 5x - 8} \end{gathered}[/tex]the ratio of red candies to Blue candies is 5:4 in the bag if there are 20 blue candies in the bag how many rare candies are there
Answers
The ratio of Red candies to Blue candies is 5:4 in the bag.
10. (01.04 LC)
Your first six-month auto insurance premium was $658.00. Based on your driving record, your renewal premium is $756.70. What percent increase did you see in your premium? (1
12%
15%
28%
35%
Answers
There is 15% in the premium.
How take out percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
First six-month auto insurance = $658
Renewal premium = $756
Change in the insurance = $98
percentage of $98 from $658
= 15%
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If $5000 is invested at 9% annual simple interest, how long does it take to be worth $9050?
Answers
It takes 9 years to make $9050 from $5000 investment.
Given that, Principal = $5000, rate of interest = 9% and Amount = $9050.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, S.I. = Amount - Principal
= 9050-5000 = $4050
Now, 4050=(5000×9×T)/100
⇒ 4050/450 = T
⇒ T = 9 years
Therefore, it takes 9 years to make $9050 from $5000 investment.
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7. An antique dealer has a fund of $1,160 for investments. She spends 50%of the fund on a 1911 rocking chair. She then sells the chair for $710, all ofwhich she returns to the fund.a) What was the percent gain on the investment?b) What percent of the original value of the fund is the new value of the fund?
Answers
Given:
Total amount dealer has is $1160.
Spend 50% of the fund to buy a 1911 rocking chair and sells it for $710.
[tex]Fund\text{ she spends on chair=}1160\times\frac{50}{100}[/tex][tex]Fund\text{ she spends on chair= \$580}[/tex]a)
[tex]\text{Fund gain on selling the chair= 710-580}[/tex][tex]\text{Fund gain on selling the chair= \$}130[/tex][tex]\text{Percent gain on the investment=}\frac{130}{580}\times100[/tex][tex]\text{Percent gain on the investment=}22.41\text{ \%}[/tex]b)
[tex]\text{New value of the fund=1160+130}[/tex][tex]\text{New value of the fund= \$}1290[/tex][tex]\text{Percentage of original to the new value = }\frac{1290}{1160}\times100[/tex][tex]\text{Percentage of original to the new value =111.21 \%}[/tex]111.21% of the original value of the fund is the new value of the fund.
Use a calculator to find the values of X. Round sides to the nearest 10th and angles to the nearest whole number. Use sin or COS as appropriate.
Answers
Given the information about the triangle, we can use the cosine function on angle x to get the following:
[tex]\begin{gathered} \cos x=\frac{\text{adjacent side}}{hypotenuse}=\frac{7}{16} \\ \Rightarrow\cos x=\frac{7}{16} \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} \cos x=\frac{7}{16} \\ \Rightarrow x=\cos ^{-1}(\frac{7}{16})=64.1 \\ x=61.1\degree \end{gathered}[/tex]therefore, the value of x is 61.1
Help in writing an equation. I believe that it is supposed to be a linear equation
Answers
Since the information required us that the equation has to start in zero we can think of functions like the root of x but also we have to add a value of 1/3. In other words one equation with those characteristics is
[tex]y=\sqrt{x}+\frac{1}{3}[/tex]Point B is on line segment AC. Given BC = 10 and AB = 5, determine the lengthAC.Answer: AC= Anyone know how to solve these???
Answers
3
1) Let's sketch that, to better understand this:
2) Considering the Segment Addition Postulate, we can write that:
DF = DE + EF Plug into that the given values
9 = 6 + EF
9-6 = 6-6 + EF
3 = EF
EF =3
3) Hence, the line segment EF is 3 units long