Find the volume of the composite solid. Round your answer to the nearest hundredth.
The volume is about _____ cubic meters.
(5.1)
Answer:
97.92 m³ (nearest hundredth)
Step-by-step explanation:
The composite solid is a cube with a cone cut out.
Therefore, to find the volume of the solid, subtract the volume of the cone from the volume of the cube.
Volume of Cube[tex]\textsf{Volume of a cube}=\sf s^3 \quad\textsf{(where s is the side length)}[/tex]
Given:
s = 5.1 mSubstitute given value into the formula:
[tex]\begin{aligned}\implies \sf V_{cube} & = \sf 5.1^3\\& = \sf 132.651\: m^3\end{aligned}[/tex]
Volume of Cone[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
[tex]\sf r=\dfrac{1}{2}(5.1)=2.55\:m[/tex][tex]\sf h = 5.1\:m[/tex]Substitute given values into the formula:
[tex]\begin{aligned}\sf \implies V_{cone} & = \sf \dfrac{1}{3} \pi (2.55^2)(5.1)\\& = \sf 11.05425 \pi \: m^3\end{aligned}[/tex]
Volume of Composite Solid[tex]\begin{aligned}\sf V_{solid} & = \sf V_{cube}-V_{cone}\\& = \sf 132.651-11.05425 \pi \\& = \sf 97.92304941...\\& = \sf 97.92 \: m^3 \: (nearest\:hundredth)\end{aligned}[/tex]
Volume of the cube
Side³(5.1)³132.65m³For the cone
Radius of base=r=5.1/2=2.55mHeight=h=5.1mVolume
1/3πr²h1/3(π)(2.55)²(5.1)34.71m³Total volume of the figure
132.65-34.7197.94m³In the diagram, Find y.
a bookstore carries 50 magazines. 34% of the magazines are womens magazines. how many woman’s magazines does the bookstore carry?
Answer:
50 * 34%
50 * 34/100
34 / 2 = 17
Given f(x)=x^2, write the equation of the transformed function if g(x)=f(x-1)
Answer:
1. g(x) = (x - 1)²; translation of 1 unit to the right.
2. g(x) = 3^(x + 1) - 2; translation to the left of 1 unit and translation of 2 units down.
Step-by-step explanation:
1.
f(x) = x²
g(x) = f(x - 1)
g(x) = (x - 1)²
Since x was replaced by x - 1, g(x) is similar to f(x) with a translation of 1 unit to the right.
2.
f(x) = 3^x
g(x) = f(x + 1) - 2
g(x) = 3^(x + 1) - 2
Since x was replaced by x + 1, which is the same as x - (-1), there is a translation to the left of 1 unit. In addition, the -2 causes a translation of 2 units down.
solve the equation 6=5x+2
Hi Student!
Looking at this problem, it is pretty straight forward and we don't need to do much information gathering to help answer our question. The main point is that we just need to solve the equation also known as solving for the unknown variable.
Subtract 2 from both sides
[tex]6= 5x + 2[/tex][tex]6 - 2 = 5x + 2 - 2[/tex][tex]4 = 5x[/tex]Divide both sides by 5
[tex]\frac{4}{5} = \frac{5x}{5}[/tex][tex]\frac{4}{5} = x[/tex]Therefore, our final solution to this problem is that x is equal to 4/5 or we can convert this to a decimal to which we will then get 0.8.
A grocery store has advertised a sale on ice cream. Each carton of any flavor of ice cream costs $5.25
A. If Millie buys one carton of strawberry ice cream and one carton of chocolate ice cream, write a
algebraic expression that represents the total cost of buying the ice cream.
B. Write an equivalent expression for your answer in part (a).
C. Explain how the expressions are equivalent.
Each carton of any flavour costs same
THE COST IS $5.25so
Total cartons:-
One strawberry+One chocolate2Total cost
2(5.25)$10.56. Clark wants to transform a shape on the
coordinate plane by using a rigid transformation.
Of the choices below, list any that Clark can use.
I.
Dilation
II. Rotation
III. Translation
IV. Reflection
A mass attached to a spring is pulled toward the floor so that its height above the floor is 10 mm (millimeters). The mass is then released and starts moving up and down reaching maximum and minimum heights of 20 and 10 mm , respectively, with a cycle of 0.8 seconds.
a) Assume that the height h(t) of the mass is a sinusoidal function, where t is the time in seconds, sketch a graph of h from t = 0 to t = 0.8 seconds. t = 0 is the time at which the mass is released.
b) Find a sinusoidal function for the height h(t).
c) For how many seconds is the height of the mass above 17 mm over one cycle?
(would anyone like to talk not to be weird or anything lol)
PPPPPLLLSSS HELP THIS IS LEGITEWWFAE I ONLY HAVE 20 MINSW
Answer:
56 units^2
Step-by-step explanation:
Area of a parallelogram = base length times height length
Base = 7 units
Height = 8 units
A = BH
A = 7x8
A = 56 units^2
For her 16th birthday party Patriot got a birthday cake with a radius of 10 centimeters. her dad cut her a slice of cake with a central angle of 20 degrees.
A. convert the angle measure of Patty's slice to radians.
B. find the area of Patty's slice of cake Leave your answer interms of pie.
C. Find the perimeter of Patty's slice of cake.
Answer:
Part A
To convert degrees to radians, multiply the given value by π/180°.
[tex]\begin{aligned}\implies 20^{\circ} & =20^{\circ} \times \dfrac{\pi}{180^{\circ}} \: \sf rad\\ & =\dfrac{1}{9} \pi \: \sf rad\end{aligned}[/tex]
Part B
Given:
r = 10 cm[tex]\theta=\dfrac{1}{9} \pi[/tex][tex]\begin{aligned}\textsf{Area of a sector of a circle} & =\dfrac12 r^2 \theta\\\\\implies \textsf{Area of slice of cake} & =\dfrac{1}{2} \cdot 10^2 \cdot \dfrac{1}{9} \pi\\\\& = \dfrac{50}{9} \pi \: \sf cm^2\end{aligned}[/tex]
Part C
Given:
r = 10 cm[tex]\theta=\dfrac{1}{9} \pi[/tex][tex]\begin{aligned}\textsf{Perimeter} & = 2r + \textsf{arc length}\\& = 2r + r \theta \\& = 2(10)+10\left(\dfrac{1}{9} \pi \right) \\& = 20 + \dfrac{10}{9} \pi \\& = 23.4906585\\& = 23.5\: \sf cm \:(1 \:dp)\end{aligned}[/tex]
HELP ASAP
Which of the following equations are linear functions?
I. 3x + 4y = -6
II. y = -4x + 7
III. 5x2 + 3y = 12
Choose one answer.
A. I
B. II and III
C. I, II, and III
D. I and II
Answer:
I and II
Step-by-step explanation:
In a 'linear function,' the exponents of x and y are both 1.
This characteristic is found in both I and II but not in III (which is a quadratic function).
Line segment SU is dilated to create S'U' using point Q as the center of dilation.
The scale factor of the dilation is:
If a point divides any line segment into two equal parts, then the point is the mid-point of that line. The ratio of the whole line segment and the distance from mid-point to any end point of the line segment is always 2:1, hence the scale factor of the dilation is 2.
To find the scale factor of the dilation, we need to find the ratio from initial point of the line segment to the distance from the point that is lie on that line segment.
Following points can be concluded from the given conditions.
It is shown in the figure that the distance from Q to S is 4 unit, and the distance from Q to S' is 8 unit.The distance from Q to U is 5 unit and the distance from Q to U' is 10 unit.U and S both are the mid-points of the line segment QU' and QS' respectively.The ratio of the whole line segment and the distance from mid-point to any end point of the line segment is always 2:1, hence the scale factor of the dilation is 2.
To know more about the scale factor, please refer to the link:
https://brainly.com/question/20449840
Ali is 5 years older than salifu, If Salifu is y years.
how find Ali's age. Write answer in an equation
If 7a+3b=20 and 3a+7b=10, what is a+b?
Answer:
3
Step-by-step explanation:
7a+3b=20
3a+7b=10
Substitution:
[tex]\begin{bmatrix}3\cdot \frac{20-3b}{7}+7b=10\end{bmatrix}[/tex]
[tex]a=\frac{20-3\cdot \frac{1}{4}}{7}[/tex]
[tex]a=\frac{11}{4},\:b=\frac{1}{4}[/tex]
11=4 + 1=4 = 12/4
12/4 = 3
how many times greater is 8.5x10^8 than 42x10^7 in scientific notation
Step-by-step explanation:
first, let's bring them to the same exponent of 10.
8.5 × 10⁸ is already scientific notation
42 × 10⁷ = 4.2 × 10⁸ (this is now scientific notation AND it is using the same exponent of 10)
so, how many times is the first one greater ?
(8.5 × 10⁸) / (4.2 × 10⁸) = 8.5 / 4.2 = 2.023809524...
so, the first number is 2.023809524... times greater than the second number.
maybe you made a typo ?
maybe the second number was actually 42.5 × 10⁷ ?
because then
42.5 × 10⁷ = 4.25 × 10⁸
and
8.5 / 4.25 = 2
so,
8.5 × 10⁸ is 2 times greater than 42.5 × 10⁷ or 4.25 × 10⁸.
With the metal detector we find 70 Roman coins underground,30 are Etruscan,15 are Greek. What is the probability ,that I draw a Greek coin?
Answer:
30*100/70= 42.85% chances that you will draw a Etruscan coin and same way 42.85-100= 57%
Answer:
3/23
Step-by-step explanation:
Probability (Greek) :
Number of Greek coins / Total coins15 / 70 + 30 + 1515/1153/23Find the mass of a thin triangular plate bounded by the coordinate axes and the line if
The mass of a thin triangular plate bounded by the coordinate axes is 3 3/4.
How to calculate the mass?It should be noted that mass simply means a quantity of matter that's in a body. It's the meaure of the inertia in the body.
In this case, from the complete question, the mass will be:
= 3/1000[1/24x⁴ - 25x² + 1000/3x]
= 15/4
= 3 3/4
Learn more about mass on:
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The following dot plot shows how many pets each customer own before entering Jeremy‘s pet store today each that represents one customer based on this data what is a reasonable estimate for four of the probability that the next customer to enter Jeremy‘s pet store has exactly 3 pets
Answer:
0.23
Step-by-step explanation:
Was the answer on khan academy
The volume of a cylinder is 1,600pie cubic centimeters.the height is 16 centimeters.what is the radius of the cylinder?
Answer:
Radius = 10
Step-by-step explanation:
Volume of a cylinder=πr^2h
1600πcm^3=πxr^2x16
π cancels out
1600=r^2x16
1600/16=r^2
100=r^2
√100=r
r=10
David currently earns $25.00 per hour. He receives a 5% raise each year. He
wants to know how many years it will be until he is earning more than $30.00
per hour.
Answer:
4 years
Step-by-step explanation:
30 = 25 ( 1.05)^n
1.2 = 1.05^n
log 1.2 / log 1.05 = n years = 3.73 ~ 4 years
DIRECTIONS: Use the numbers 0 through 9 (once and only once) in each blank space. Your goal is to form a way to say the target number.
The answers are 9, 6, 7, 0, 2, 5, 7, 1, 7, and 2 which makes the target value by putting in the blank box.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
The target number is 54
= 9×6 = 54
= 8×7 - 02
= 5×7 + 19
= 27×2 = 54
Thus, the answers are 9, 6, 7, 0, 2, 5, 7, 1, 7, and 2 which makes the target value by putting in the blank box.
Learn more about the arithmetic operation here:
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Giving brainlyest to the person with the correct answer :)
Answer:
He will need a total of 168.8 total gallons of oil.
He will need 34.4 gallons of oil for machine A.
He will need 134.4 gallons of oil for machine B.
Please Vote Me Brainliest. Thank You.
can someone help me with this?
Answer:
45
Step-by-step explanation:
We know that B is 90 because its a right angle, and in that triangle it has to add up to 180
So 180 - 90 = 90
90 ÷ 2 = 45
And thats a right angled triangle so it has a right angle and two equal angles.
Hope it helps :))
What is the slope of the line passing through (9,-6) and (5, 10)?
Answer:
-4
Step-by-step explanation:
m=y2-y1/x2-x1
m=10+6/5-9
m=16/-4
m=-4
Answer: 4/-4
Step-by-step explanation:
Slope Formula= (y2-y1/x2-x1)
10-6/5-9
4/-4
Unit test
Complete the point-slope equation of the line through (2, 3) and (7, 4).
Use exact numbers.
y
Answer:
y - 4 = 1/5(x-7)
Step-by-step explanation:
Find slope:
4-3 / 7-2
1 / 5
y - y1 = m(x-x1)
y - 4 = 1/5(x-7)
mark brainliest pls
36.4 divided by 109 1/5
Answer:
0.33
Step-by-step explanation:
36.4 divided by 109 1/5 is 0.33.
Olive plots (4,−3π2)on the polar plane.
How does she proceed?
What you need to write in each blank is:
1) positive x-axis.
2) negative x-axis.
3) positive y-axis.
How to plot the point on the polar plane?
To plot a point (R, θ) on the polar plane. First, if R is positive the angle is measured from the positive x-axis, if R is negative, the angle is measured from the negative x-axis.
Because here R is 4, positive, the point will lie on the x-axis. Then, she needs to move it clockwise by an angle of (3/2)pi (a total of 3 quadrants) This means that the point will end up in the positive y-axis.
So what you need to write in each blank is:
1) positive x-axis.
2) negative x-axis.
3) positive y-axis.
If you want to learn more about polar coordinates:
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To put money into a savings account, CDs, and stocks is to
A. be risk-adverse
B. invest
OC. secure assets
OD. diversity
pleaseeeee i need help
Answer:
110687192.78951, 6488.47368421, 4214, 0.0464, 0.03626
SIMPLIFIED WAY OF SAYING IT:
Last One to First Box
3rd One to 2nd Box
1st one to 3rd box
2nd one to 4th box
4th one to 5th box
Step-by-step explanation:
(4.3*10^(6))*(9.8*10^(-4)) = 4,214
(2.9*10^7)*(1.6*10^-9) = 0.0464
(4.7*10^3)*(8.6*10^-7)/(3.8*10^-4)*(6.1*10^2) = 6488.47368421
(4.9*10^3)*(7.4*10^-6) = 0.03626
Last one = 110687192.78951
Find the surface area of the rectangular prism
Answer:
82 inches squared
Step-by-step explanation:
7*3*2 = 42
7*2*2 = 28
3*2*2 = 12
42 + 28 + 12 = 82