Answers
Answer : The correct option is, [(10 × 4 × 5) + (5 × 5 × 5)] cubic inches.
Step-by-step explanation :
As we know that,
Formula used for volume of cube is:
[tex]V=(a)^3[/tex]
or,
[tex]V=a\times a\times a[/tex]
where,
V = volume of cube
a = side of cube
Formula used for volume of cuboid is:
[tex]V=l\times b\times h[/tex]
where,
V = volume of cuboid
l = length of cuboid
b = breadth of cuboid
h = height of cuboid
The given figure is formed by the combination of two figure that is cube and cuboid.
Volume of cube = [tex](a)^3[/tex]
Given :
a = side of cube = 5 inch
Volume of cube = [tex]5\times 5\times 5[/tex] cubic inches
and,
Volume of cuboid = [tex]l\times b\times h[/tex]
Given :
l = length of cuboid = 10 inch
b = breadth of cuboid =5 inch
h = height of cuboid = 4 inch
Volume of cuboid = [tex]10\times 5\times 4[/tex] cubic inches
Total volume of figure = Volume of cuboid + Volume of cube
[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches
Thus, the correct volume of the figure will be,
[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches
Related Questions
The sun produces 3.9 x 10^33 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 3.25 x 10^3 seconds?
Answers
Answer:
1.2675 x 10^37
Step-by-step explanation:
you would have to first multiply 3.9 x 3.25 =12.675. It is not in scientific notation so you would have to change the decimal 1.2675 x 10^37
The ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]
The rate of energy is given as:
[tex]Rate = 3.9 * 10^{33}\[/tex] radiant energy per second
The time is given as:
[tex]Time = 3.25 * 10^3[/tex] seconds
The amount of radiant energy produced in this time is:
[tex]Energy = Rate * Time[/tex]
So, we have:
[tex]Energy = 3.9 * 10^{33} * 3.25 * 10^3[/tex]
Multiply
[tex]Energy = 12.675* 10^{36}[/tex]
Rewrite as:
[tex]Energy = 1.2675* 10^{37}[/tex]
Approximate
[tex]Energy = 1.3* 10^{37}[/tex]
Hence, the ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]
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Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?
Answers
I=prt
I interest earned 90
P amount invested?
R interest rate 0.04
T time 6/12
Solve the formula for p
P=I÷rt
P=90÷(0.04×(6÷12))
P=4,500 ....answer
Answer:
the answer is 4500 i got it right
Step-by-step explanation:
Evaluate the integral. (use c for the constant of integration.) sin^2(πx) cos^5(πx) dx
Answers
transform
integral of sin^2(πx)cos^5(πx)dx
=integral of sin^2(πx)[1-sin^2(πx)]^2 cos(πx)dx
=integral of [sin^2(πx)-2sin^4(πx)+sin^6(πx)]cos(πx)dx
using the substitution u=sin(πx), du=πcos(πx)dx
=integral of [u^2-2u^4+u^6] (du/π)
=1/π[u^3/3-(2/5)u^5+u^7/7] + C
back substitute u=sin(πx)
=1/π[sin(πx)^3/3-(2/5)sin(πx)^5+sin(πx)^7/7]
or
=sin(πx)^3/3π-2sin(πx)^5/5π+sin(πx)^7/7π
805 tens in standard form
Answers
To write 8,050 in standard form, we have
[tex]805\ tens=8,050=8.05\times10^3[/tex]
Balcony and orchestra tickets were sold for a Friday night concert last week. The balcony and orchestra tickets sold for $35 and $45, respectively. If 90 tickets were sold, and the total revenue was $3550 for the night, find the number of balcony and orchestra tickets sold.
Answers
x + y = 90....x = 90 - y
35x + 45y = 3550
35(90 - y) + 45y = 3550
3150 - 35y + 45y = 3550
-35y + 45y = 3550 - 3150
10y = 400
y = 400/10
y = 40 <== 40 orchestra tickets
x = 90 - y
x = 90 - 40
x = 50 <== 50 balcony tickets
What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =
Answers
For this case we have the following quadratic expression:
[tex] (5y + 6) ^ 2 = 24
[/tex]
From here, we must clear the value of y.
For this, we follow the following steps:
1) We clear the square term:
[tex] (5y + 6) =+/-\sqrt{24} [/tex]
[tex] (5y + 6) =+/-2\sqrt{6} [/tex]
2) Pass the value of 6 by subtracting:
[tex] 5y =-6+/-2\sqrt{6} [/tex]
3) Pass the value of 5 to divide:
[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]
Answer:
The solutions to the quadratic equation are:
[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]
[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]
The variable Z is directly proportional to X. When X is 5, Z has the value 55.
What is the value of Z when X = 12
Answers
z = k.x, with k is the coefficient of proportionality:
Let calculate k:
When x = 5, z = 55. Plug in:
55 = k.5 → k=55/5 ; k =11
The value of z when = 12 is : z= kx; z = 11(12) and z = 132
z=kx, we are given the point (5,55) so we can solve for the constant of variation
55=5k divide both sides by 5
11=k so our equation is:
z=11x, so when x=12
z=11(12)
z=132
How do you rename 5400
Answers
__________________________________________________
Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.
Answers
Answer:
Joint variation.
Step-by-step explanation:
There are four types of variation,
Direct variation : When a variable varies directly as another variable,
Example : y varies directly with x ⇒ y = kx,
Where, k is the constant of variation,
Inverse variation : When a variable varies inversely as another variable,
Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]
Joint variation : When a variable varies directly with two or more than two variables,
Example : y varies directly with both x and z ⇒ y = kxz
Combined variation : When a variable varies both directly and indirectly as another variables,
Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]
Now, here the given expression,
y = 4mt,
Where, y, m and t are variables and 4 is the constant of variation,
⇒ y varies directly as both m and t,
⇒ y = 4mt is an example of joint variation.
Nate rides his bike to school every day. From his home he rides 2.5 miles north, and then six miles west. If a straight line is drawn from Nate's house to the school, find the distance between these two locations.
Answers
use Pythagorean Theorem
2.5^2 + 6^2 = x^2
6.25 +36 = 42.25
x= sqrt(42.25) = 6.5 miles
h^2=x^2+y^2
h^2=6^2+2.5^2
h^2=36+6.25
h^2=42.25
h=√(42.25) miles
h=6.5 miles
Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?
Answers
The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.
Calculation of standard deviationFirst calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7
= 300/7
= 42.9
Then for each number, subtract the Mean and square the result.
(25 - 42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(35-42.9)² = -7.9² = 62.41
(25-42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(60-42.9)² = 17.1²= 292.41
(75-42.9)² = 32.1²= 1030.41
Then work out the mean of those squared differences. That is,
320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7
= 2042.89/7
= 291.8
Take the square root of 291.8 which is,
√291.8 = 17.08215443
= 17.1 to the nearest tenth.
Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1
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Answer:
17.1
Step-by-step explanation:
got it right
A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?
Answers
(Working with numbers is easier than working with percentages).
There are 27 students who passed both tests, and 51 who passed only the first test.
The 27 students who passed both tests are included in the 51 who passed the first test.
We are asked "What percent of those who passed the first test also passed the second test?"
so we are asked "what percent of 51 is 27?"
let 51 be 100%
then 27 is [tex] \frac{27*100}{51} [/tex]%=52.941%
Answer: 52.941%
There are 36 girls and 40 boys at a summer camp. The campers will be divided into equal-sized groups. Each group will have the same number of girls and the same number of boys. What is the greatest number of groups that can be formed?
Answers
Hope it helps.
This is called the prime factorization of a number:
Lets do this for 36 first, can it be diveded by the smallest prime? (2) Yes, 36/2=18 can 18 still be dived by 2? Yes, 18/2=9 . Can 9 be divided by 2? No, so we move up in primes. Can it be divieded by 3, yes 9/3=3 and 3 is a prime so we can stop.
What we concluded is that 36=2*2*3*3
Lets do this with 40 too, 40/2=20, 20/2=10, 10/2=5 and that is a prime so we can stop.
40=2*2*2*5
Now will you figure out how does this help you?
Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7
Answers
= 24 + 21
answer is
24 + 21
The slope of a vertical line is zero. true or false
Answers
The solution is False
The slope of a vertical line is given by the equation Slope m = undefined
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the line be represented as A
Now , the line A is a vertical line
So , the equation of line will be represented as y = mx + c
where m is the slope of the line
And , Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of a vertical line is infinite or undefined as it has no y-intercept
Because , the change is x is 0
So , the denominator of the fraction is 0 and division by 0 is undefined
Slope m = ( y₂ - y₁ ) / 0
Hence , the slope m is undefined
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Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.
Answers
the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship
The distance between the City and Lemont can be worked out using the Sin rule
[tex] \frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)} [/tex]
[tex]City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....[/tex]≈98.3
The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
[tex] \sqrt{57.8^{2}- 44.6^{2} } =36.765... [/tex]≈36.8
The distance between the ship and the Buoy is given:
[tex]98.3-36.8=61.5 [/tex] miles
Hours worked: 40 Rate: $3.85 Wages: ?
Answers
Answer: $154.00
Step-by-step explanation:
I am assuming you are looking for how much the person made.
Multiply 40 hours times $3.85
$154.00
A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)
Answers
so.. "p" is the distance from the vertex to either, the focus point or the directrix.
thus the focus is "p" units from the vertex.
now, if we set the parabola at the origin, like in the picture, and then use another point on the parabola, let's say we'll use (6,1), then
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{cases} h=0\\ k=0 \end{cases}\implies (x-0)^2=4p(y-0)\implies x^2=4py \\\\\\ \begin{cases} x=6\\ y=1 \end{cases}\implies (6)^2=4p(1)\implies \cfrac{6^2}{4}=p\implies \cfrac{36}{4}=p\implies 9=p[/tex]
For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.
Explanation:For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.
Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.
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The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse
Answers
you can pretty much get the values for "a" and "b" from the grid.
What is next number after 2 7 8 3 12 9
Answers
Which set of numbers does 8 2/3 belong to
Answers
Find the half-life of an element which decays by 3.411% each day. Hint: use y = ab^t.
Answers
a/2=a(0.96589)^t
0.5=0.96589^t
ln(0.5)=t(ln(0.96589))
t=ln(0.5)/ln(0.96589)
t≈19.97 days (to nearest hundredth of a day)
This is about half life of elements with exponential decay.
Half life = 20 years
We are given a decay rate of 3.411% per day.We are given;
y = ab^(t)
Where;
t is the half life
y = a/2 is the amount of substance remaining after decay
a is amount of substance initially
b = 100% - 3.411% = 96.589% = 0.96589
Thus;a/2 = a(0.96589)^(t)
a will cancel out to give;
0.5 = 0.96589^(t)
ln (0.5) = t(ln 0.96589)
t = ln(0.5)/ln(0.96589)
t = 19.968 days
This is approximately 20 days.
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0.063 written as fraction or a mixed number
Answers
Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?
Answers
subtract one- fifth from seven times w
Answers
7 times of w , we can write as = 7w
Now we have to subtract one fifth from seven times of w.
So we can write it in algebraic expression as
[tex]7w - \frac{1}{5} [/tex]
The excluded values of a rational expression are 2 and 5. Which of the following could be this expression?
Answers
An example that would work for your specific question is:
[tex] y = \frac{(x - 3)(x-1)}{(x-2)(x-5)} [/tex]
If you plug in either 2 or 5 into this equation the denominator will be zero causing the expression to undefined there, so the values 2 and 5 are excluded from the domain of the expression.
Answer: d on eng
Step-by-step explanation:
last year, Carmen opened an investment account with $7400. At the end of the year, the amount in the account had decrease buy 26.5%. How much is this decrease in dollars? How much money was in her account at the end of the year?
Answers
7,400×0.265=1,961
The account at the end of the year
7,400−1,961=5,439
The decrease in Carmen's account was $1961, which is 26.5% of her original investment of $7400. Hence, by subtracting this decrease from the original investment, we find that Carmen had $5439 left at the end of the year.
Explanation:The decrease in Carmen's account over the year is 26.5% of the original investment of $7400. In mathematical terms, we can calculate this value by multiplying the original investment by the percentage decrease, using the formula: Decrease = Original Amount * Percentage Decrease.
In Carmen's case, this would be $7400 * 0.265 (converted from 26.5%). Upon calculating, we find that the decrease is $1961.
Now, to find how much money Carmen had at the end of the year, we subtract this decrease from the original amount invested. Again, using the formula: Final Amount = Original Amount - Decrease, we plug in the numbers to get $7400 - $1961, which equals $5439. This is how much Carmen had left in her account at the end of the year after the decrease.
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On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answers
Final answer:
To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.
Explanation:
The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.
Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.
find the coefficient of x^6 in the binomial expression of (2x+3)^9
Answers
(a + b)^n = sum(k=0 to n) [C(n, k) * a^(n - k) * b^k].
By letting a = 2x, b = 3, and n = 9
(2x + 3)^9 = sum(k=0 to 9) [C(9, k) * (2x)^(9 - k) * 3^k].
As you can see, the power of x is 9 - k. Since we want the x^6 term:
9 - k = 6 ==> k = 3
Thus, letting k = 3 yields the term containing x^6 to be:
C(9, 6) * (2x)^(9 - 3) * 3^4 = 435456x^6.
.
in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation
Answers
[tex]\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad \qquad _6P_3=\cfrac{6!}{(6-3)!}[/tex]
Answer:
120 possible arrangements.
It is a permutation
Step-by-step explanation:
Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.
Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:
N= Total number possibilities:
[tex]N=6*5*4=120[/tex]
This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.
The permutation can be learnt by the formula:
[tex]N=\frac{p!}{(p-n)!}[/tex]
where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:
[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]