Answer:
1982.0 ft³
Step-by-step explanation:
The composite figure can be decomposed into a cube and a square pyramid. The volume is the sum of the volumes of these.
__
pyramidThe square base of the pyramid is 12 ft on each side, so the diagonal of the base is 12√2 feet. (The diagonal of a square is √2 times the side length.) Then the distance from a corner to the center of the base is half that, or 6√2 feet.
That distance and the height of the pyramid form a right triangle whose hypotenuse is the given 10 ft measure of the length of the edge of a face of the pyramid. Then the height can be found using the Pythagorean theorem:
h² +(6√2)² = 10²
h² = 100 -72 = 28
h = 2√7 ≈ 5.291503 . . . ft
The volume of the pyramid is ...
V = 1/3Bh = 1/3s²h
V = 1/3(12 ft)²(5.2910503 ft) ≈ 253.992 ft³
__
cubeThe volume of a cube is given by ...
V = s³
V = (12 ft)³ = 1728 ft³
__
total volumeThe total volume of the figure is the sum of the pyramid volume and the cube volume:
total volume = 253.992 ft³ +1728 ft³ = 1981.992 ft³
The volume of the figure is about 1982.0 ft³.
_____
Additional comment
Your figure for the volume seems to assume the height of the pyramid is 8 feet. That length is the slant height of one face of the pyramid. It would be the hypotenuse of a right triangle whose other legs are 6 ft and the height of the pyramid. Then we would have ...
h² +6² = 8²
h² = 64 -36 = 28 . . . . as above
The pyramid height is the perpendicular distance from the plane of the base to the peak. It is measured through the middle of the volume, not along one face.
Stephanie has $42,750 in student loans at a 6% compound interest
rate. If she decides to defer payment on the loan for two years, how
much additional interest will be added to the loan at the end of the
two-year deferment?
Answer:
You first take the annual interest rate on your loan and divide it by 365 to determine the amount of interest that accrues on a daily basis. Say you owe $10,000 on a loan with 5% annual interest. You'd divide that rate by 365 (0.05 ÷ 365) to arrive at a daily interest rate of 0.000137.
Brianna has $620 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $261.04.
She buys 3 bicycle reflectors for $13.07 each and a pair of bike gloves for $13.57.
She plans to spend some or all of the money she has left to buy new biking outfits for $51.03 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Brianna can purchase while staying within her budget.
Answer: 6 outfits
Step-by-step explanation:
$620 should be greater than the price of the new bicycle + 3 * bicycle reflectors + a pair of bike gloves + unknown number of biking outfits
Therefore, the inequality will be:
620 ≥ 261.04 + 3 × 13.07 + 13.57 + 51.03x
620 ≥ 313.82 + 51.03x
[tex]\text{Solving \ for \ x}[/tex]
[tex]620\ge \:313.82+51.03x[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]313.82+51.03x\le \:620[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]
[tex]313.82\cdot \:100+51.03x\cdot \:100\le \:620\cdot \:100[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]31382+5103x\le \:62000[/tex]
[tex]\mathrm{Subtract\:}31382\mathrm{\:from\:both\:sides}[/tex]
[tex]31382+5103x-31382\le \:62000-31382[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]5103x\le \:30618[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5103[/tex]
[tex]\frac{5103x}{5103}\le \frac{30618}{5103}[/tex]
[tex]\text{Simplify}[/tex]
[tex]{x\le \:6}[/tex]
Therefore, Brianna can buy 6 or fewer outfits while staying within her budget
the simple form of this is....
[tex] {2}^{3 } \div {2}^{ - 5} [/tex]
Answer: [tex]2^8 = 256[/tex]
Explanation:
The rule to use is
[tex]a^b \div a^c = a^{b-c}[/tex]
We subtract the exponents.
So in this case,
[tex]2^3 \div 2^{-5} = 2^{3-(-5)} = \boldsymbol{2^8} = \boldsymbol{256}[/tex]
I need help on this question
~Denki Kaminari here~
Answer:
5t\sqrt(6su) (THE SECOND ONE)
Step-by-step explanation:
simplify the radical by breaking it up into known factors, assuming positive real numbers.
hope this helps :D
On a coordinate plane, 2 lines are parallel to each other. This system of equations has
Answer:
no solution
Step-by-step explanation:
This is because they never intersect so there is no solution.
Answer:
no solution
Step-by-step explanation:
1) For x2 + 35x - 36 = (x + 2)(x + _), the operation signs of the factors are:
Step-by-step explanation:
please make it a little bit clear
Use a fraction or mixed number to represent the time on a number line. Let 0 represent noon.
8:30 A.M.
The time 8:30AM is 3 and half hours before noon.
The fraction that represents 8:30AM is -3 1/2
How to represent the time as fraction?The time is given as:
Time = 8:30 A.M
Given that Noon is represented by 0.
It means that time before noon would be represented with negative value
8:30AM is 3 and half hours before noon.
So, we have:
8:30AM = -3 1/2
Hence, the fraction that represents 8:30AM is -3 1/2
Read more about fractions at:
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Yes I wanted to know what is the answer
Answer:
14 flats
5 plants
Step-by-step explanation:
First you would do 89/6 but since that doesn’t divide nicely you can do 90/6 to get 15 then subtract 1 since the original number was 89 and you would get 14
The 14 times 6 would get you 84
Then subtract 84 from 89 and you get 5 plants left over ^^
Someone help. I do not understand.
Step-by-step explanation:
SinP = sin30° = 1/2
sinQ = sin60° = root3/2
cosR = cos90° = 0
cosQ = cos60° = 1/2
sinR = sin90° = 1
I work 4.5 hours I made $90.00 what did I make hourly
[tex]hourly-pay = \frac{total-money-paid}{number-of-hours} =\frac{90}{4.5} =20[/tex]
Thus you made $20 per hour
Hope that helps!
Find the solution set for the equation
|4x - 9| + 3 = 8
The solution set for the equation |4x - 9| + 3 = 8 are its true values
The solution set is x = 3.5 or x = 1
How to determine the solution set?The equation is given as:
|4x - 9| + 3 = 8
Subtract 3 from both sides
|4x - 9| = 5
Remove the absolute bracket
4x - 9 = 5 or 4x - 9 = -5
Add 9 to both sides
4x = 14 or 4x = 4
Divide both sides by 4
x = 3.5 or x = 1
Hence, the solution set is x = 3.5 or x = 1
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I WILL GIVE BRAINLEST
find the area of the composite figure (round to the nearest hundredth) A) 35.26. B) 41.70. C) 41.86. D) 48.46
Answer:
41.86 is the right answer
Step-by-step explanation:
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
Slope-intercept Form: y = 3/4*x -2
Step-by-step explanation:
From looking at the graph we can get out slopes which is rise/run and y-intercept.
m = 3/4 and b = -2
Slope-intercept Form: y = 3/4*x -2
If the teacher wants to show work you would have to use a point-slope form using those two points to solve m. Then using a point and slope plug that into the point-slope form and make it into slope-intercept form.
which statement correctly compares the shapes?
Answer:
I believe D should be the correct answer
what is the GCF of the terms 5x2 -15x
Answer:
it would be 5x
Step-by-step explanation:
5x^2-15x
would be 5x because dividing by 5x you would get 5x(x-3)
but if its 5*2-15x, I don't know
If the annual interest rate 4%, how long does it tke for you investment of $10,000 to grow to $15,000
If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years. Hope this helps ! Have a good day! :)
Find a root of the Equation, x2 − 4x −10 = 0 using bisection method.
Using the bisection method, a root of the equation, is: x = -1.74 or x = 5.74.
What is the Bisection Method?The bisection method is a method employed to approximately find the roots of an equation through repeated dividison of an interval until a relatively small interval is arrived at.
Given the equation:
x² - 4x - 10 = 0.
Applying the bisection method, we would have the following:
x² - 4x + (2²) - (2²) - 10 = 0
(x - 2)² - 14 = 0
Add 14 to both sides
(x - 2)² = 14
Take the square root of both sides
x - 2 = ±√14
x = 2 ± √14
x = 2 - √14 = -1.74
or x = 2 + √14 = 5.74
Therefore, using the bisection method, a root of the equation, is: x = -1.74 or x = 5.74.
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The graph of g(x) contains the points (3, -13) and (-3, 17).
Which statement is true?
OA. The graphs of f(x) and g(x) have the same steepness with negative slopes.
OB. The graph of g(x) is steeper than the graph of f(x).
OC. The graphs of f(x) and g(x) have the same steepness with positive slopes.
OD. The graph of g(x) is less steep than the graph of f(x).
Answer:
Step-by-step explanation:
Sorry if I got you the wrong answer but I think it's, OB
Please answer .....
there are 5 blue, 4 red, 1 yellow and 2 green bead in a bag.
A) Find the probability that a bead chosen at random from the bag is blue?
B) Find the probability that a bead chosen at random from the bag is red or yellow?
C) Find the probability that a bead chosen at random from the bag is white?
D) Find the probability that a bead chosen at random from the bag is NOT yellow?
Q4) A fruit bowl contains 4 apples, 3 oranges, and 8 bananas, find the probability of
a) Randomly selected orange
b) Randomly selected apples
c) Randomly selected apple or banana
d) Randomly selected orange ,replace it then select banana
Q5) a number cube labeled by the numbers (3,3,3,3,5,5),what is the probability of
a) The number cube shows a 5
b) The number cube shows a 3
c) Having 5 and then 5 when the number cube rolled twice
d) Having 5 and then 3 when the number cube rolled twice
Answer:
A) 5/12
B) 5/12
C) 0/12
D) 11/12
-------------
Q4.
A) 3/15
B) 4/15
C) 12/15
D) 8/15
-----------------
Q5.
A) 2/6 or 1/3
B) 4/6 or 2/3
C)
D)
Step-by-step explanation:
20. A centimeter is 1/100t of a meter, while a kilo-
meter is equal to 1000 meters?
a. True
b. False
Answer:
I think it true?
I is correct?
my brainlist answer please. <:(
Christian traveled 45.5 miles in 3.25 hours How many feet did Christian travel (1 mile = 5,280 feet)
Answer:
280,280
Step-by-step explanation:
i believe you just multiply 45.5 times 5280
Step-by-step explanation:
[tex]1mile = 5280feet[/tex]
[tex]45.5miles = x[/tex]
[tex] \frac{45.5}{1} \times 5280[/tex]
[tex]x = 240240feet[/tex]
What is the perimeter of a 6-inch square? 20 inches 24 inches 18 inches 14 inches
Answer:
24 inches
Step-by-step explanation:
the perimeter of a square with a side measurement of 6 inches is equal to 24 inches.
Find the decimal expansion for 5/12
Answer:
Answer would be 0.4166666667
Step-by-step explanation:
find the value of X.
(√32)²= (X+2)²+x
Answer:
Answer:x=−6.274917217635375,1.2749172176353745
Step-by-step explanation:
(3(2))2=(x+2)2+x12=x2+5x+4
Step 1: Subtract x^2+5x+4 from both sides.12−(x2+5x+4)=x2+5x+4−(x2+5x+4)−x2−5x+8=0
For this equation: a=-1, b=-5, c=7.999999999999998−1x2+−5x+8=0Step 2: Use quadratic formula with a=-1, b=-5, c=7.999999999999998.x=−b±b2−4ac2ax=−(−5)±(−5)2−4(−1)(8)2(−1)x=5±57−2x=−6.274917217635375,1.2749172176353745
please show me how you also got the answer as well, thanks a bunch!!
Answer:
Step-by-step explanation:
Solve for kkk.
8(10-k)=2k8(10−k)=2k
Answer:
k = 8
Step-by-step explanation:
We know that 8(10-k) = 2k so:
8(10−k)=2k
Simplify both sides of the equation:
8(10−k)=2k
(8)(10)+(8)(−k)=2k
80+−8k=2k
−8k+80=2k
Subtract 2k from both sides:
−8k+80−2k=2k−2k
−10k+80=0
Subtract 80 from both sides:
−10k+80−80=0−80
−10k=−80
Divide both sides by -10:
[tex]\frac{-10k}{-10} =\frac{-80}{-10}[/tex]
k = 8
Having a hard figuring this one out
If these two shapes are
similar, find X
Answer:
4
Step-by-step explanation:
If the shapes are similar we can use the side length proportion to find the value of x:
7/91 = x/52 cross multiply expressions
91x = 364 divide both sides by 91
x = 4
Triangles ABC and DEF are
A. Similar triangles
B. Not similar triangles
Answer:
A. Similar triangles
Step-by-step explanation:
Triangle ABC
35° + 90° + x = 180°
125° + x = 180°
x = 180° - 125°
x = 55°
They are similar due to the occurrence in angles
A box has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy. (Each candy falls into only one of these categories.) Laura wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are taffy?
The probability that the two candies selected by Laura from the box are taffy which has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy is 0.230.
What is the conditional probability?The conditional probability is the happening of an event, when the probability of occurring of other event is given.
A box has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy. (Each candy falls into only one of these categories.)
Let A is the event of selecting taffy in first attempt. Thus, the probability of it is,
[tex]P(A)=\dfrac{4}{14}[/tex]
Now 13 candies remain, in which 3 taffy candies are present. Let B is the event of selecting taffy in again. Thus, the probability of it is,
[tex]P(B)=\dfrac{3}{13}[/tex]
The probability of happening both event is,
[tex]P(A\cap B)=\dfrac{4}{14}\times\dfrac{3}{13}\\P(A\cap B)=\dfrac{12}{182}[/tex]
The probability that the two candies selected by Laura from the box are taffy is,
[tex]P(B| A)=\dfrac{\dfrac{12}{182}}{\dfrac{4}{14}}\\P(B| A)=0.230[/tex]
Thus, the probability that the two candies selected by Laura from the box are taffy which has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy is 0.230.
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