Answer:
1. 4π/3 in³
2. 2.6 ounces
3. 1081.5 ft³
Step-by-step explanation:
1. A soap manufacturing company changes the design of their soap from a cone to a sphere shape. The cone had a height of 4 inches and radius of 3 inches. The sphere has a diameter of 4 inches. In cubic inches, how much less soap is in the new design than the old design? Leave answer in terms of π and as a simplified fraction.
We find the volume of the cone and sphere to know the quantity of soap in each of them.
Volume of cone of soap, V = πr²h/3 where r = radius of cone = 3 inches and h = height of cone = 4 inches
So, V = πr²h/3
= π(3 in)² × 4 in/3
= 9π in² × 4 in/3
= 3π in² × 4 in
= 12π in³
We now find the volume of the sphere, V' = 4πR³/3 where R = radius of sphere = d/2 where d = diameter of sphere = 4 inches. So. R = d/2 = 4 in/2 = 2 in.
So, V = 4πR³/3
= 4π(2 in)³/3
= 4π × 8 in³/3
= 32π in³/3
So the amount of soap less used in the new design than the old design is the old volume - new volume = V - V' = 12π in³ - 32π in³/3 = (36π in³ - 32π in³)/3 = 4π/3 in³
2. Austin uses a mold to make cone shaped cupcakes. The diameter of the mold is 3 inches, and the height of the mold is 2 inches. If 1 cubic inch is about 0.55 ounce, how many ounces will ten cupcakes weigh? Use 3.14 for pi. Round to the nearest tenth of an ounce.
Since the cake is a cone, we find its volume to know its quantity.
So, Volume of cone of cupcakes, V = πr²h/3 where r = radius of cone = d/2 where d = diameter = 3 inches. So r = d/2 = 3/2 = 1.5 in and h = height of cone = 2 inches
So, V = πr²h/3
= π(1.5 in)² × 2 in/3
= 2.25π in² × 2 in/3
= 4.5π in³/3
= 4.5(3.14) in³/3
= 14.13 in³/3
= 4.71 in³
Now since 1 cubic inch = 0.55 ounces,
4.71 in³ = 4.71 × 1 in³
= 4.71 × 0.55 ounces
= 2.591 ounces
≅ 2.6 ounces to the nearest tenth of an ounce.
3. Walden is planning to install an above ground pool in he backyard. The pool has a diameter of 18 feet and depth of 5 feet. He is going to fill it to 85% capacity. How much water will be in the pool when he is finished?
We need to find the volume of the empty pool, V.
Since the pool has a diameter, d = 18 feet, it has a circular cross-section whose area, A = πd²/4.
Since the depth of the pool, h = 5 feet, the volume of the pool is V = Ah = πd²h/4.
So, V = πd²h/4
= π(18 ft)² × 5 ft/4
= 324π ft² × 5 ft/4
= 81π ft² × 5 ft
= 405π ft³
= 1272.35 ft³
Since Walden fills the pool to 85 % capacity, the volume of water would thus be V' = 85% of V
= 0.85V
= 0.85 × 1272.35 ft³
= 1081.5 ft³
Could I get some help with this question?
Answer:
But where is the question???
write the product in standard form: (x+4)(x-4)
Answer:
x² - 16
Step-by-step explanation:
Use the FOIL method here where
F = first
O = outer
I = inner
L = last
F = x * x = x²
O = -4 * x = -4x
I = 4 * x = 4x
L = -4 * 4 = -16
Combine the terms to get x² - 16.
Which decimal number is 17/22 equal to?
OA 0.7727
OB. 0.7727
C. 0.7722
OD
0.772
1/3 is equal to x/216 find x
Answer:
72
Step-by-step explanation:
proportions
Answer:
x = 72
Step-by-step explanation:
1/3 = x/216
cross multiply
216/3 = x
x = 72
is -13.1 + (-19) rational or irrational
Answer:
rational
Step-by-step explanation:
Answer:
Rational
Step-by-step explanation:
Rational numbers are numbers you can use in a ratio, basically things like negative/regular numbers, and fractions, decimals! Since you have a decimal negative number, it would be rational. It can't be Irrational because only numbers that are complicated
{ π, √10, and 1,271971910...)
can someone please tell me what angle x is
Answer:
it's an angle X duh he he he be
HELP ANSWER QUICKLY PLS!!!!
Answer:
G
Step-by-step explanation:
this should be right
the sides of a whiteboard are 12 inches by 4 inches. How many 2 inch by 2 inch Post-it notes will be needed to cover the entire whiteboard?
I NEED ANSWER ASAP
Answer:
12
Step-by-step explanation:
12 times 4 = 48
2 times 2 = 4
divide those both and you get 12.
12 post it notes will be needed to cover entire board.
have a nice Day!!
Find the product or type
"impossible"
[2 8 1 ][0 1 -2]
[0 5 -2][8 2 4]
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}2&8&1\\0&5&-2\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}0&1&-2\\8&2&4\end{array}\right][/tex] = "impossible"
The number of columns in the first matrix should be equal to the number of rows in the second.
Which of the following lines bets fits the data shown in the scatter plot?
Help I need this done by today
Answer:
the total gradius is equal to 90 0n this angle the answer is 28
Step-by-step explanation:
90-52=28 plz the brainliest!
What is the domain of F(x)=9-x??
F F(x) >9
G All real numbers
H-3
1 x59
The faces of a fair 6 - sided cube are numbered 1 through 6. What is the probability that a 2 will land face up on the next roll? Give your answer as a fraction in simplest form and the percent.
Answer:
You will have a 1/6 probability of getting a 2 that will land face up on the next roll.
Step-by-step explanation:
There is only one two on the cube, which means you will have 1 chance out of 6 of getting a 2.
Find the perimeter of the composite shape. Round to the nearest hundredth.
Answer:
36 is ur perimeter
Step-by-step explanation:
Answer: 47.31
Step-by-step explanation: I just took the unit test
An arrow is shot so that it hits the target above. Which of the following describes the method for calculating the
probability of hitting the red region?
A area of white circle / (area of blue circle - area of yellow circle)
B. (area of blue circle - area of yellow circle) / area of white circle
C area of white circle / (area of red circle - area of yellow circle)
D. (area of red circle - area of yellow circle) / area of white circle
Answer:It is c i think
Step-by-step explanation:
Rotate an isosceles right triangle around a line that contains the triangle's hypotenuse
Answer:
See attachment 2 for the rotation
Step-by-step explanation:
The question has a missing figure
See attachment 1 for the missing figure of the isosceles right-triangle
Required
Rotate around the hypotenuse
From the attachment, the hypotenuse is along the blue vertical line along the y-axis.
So, when the isosceles triangle is rotated around the hypotenuse, the result of the rotation we get a composite figure that has two congruent solids.
Which is a cone of radius and height equal to half of the hypotenuse
See attachment 2 for the rotation
James made 130 water
balloons for a party. He
has invited 15 friends. If
all 15 friends come, how
many balloons would
each guest receive?
Answer:
8
Step-by-step explanation:
130/15=8 and remainder 10
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 3 units. Which conclusion can be made from the given information?
The volume of the prism is half the volume of the cylinder.
The volume of the prism is twice the volume of the cylinder.
The volume of the prism is equal to the volume of the cylinder.
The volume of the prism is not equal to the volume of the cylinder.
The volume of the prism is not equal to the volume of the cylinder.
Volume of triangular prism and right cylinder
The volume of a triangular prism and right cylinder is given by the following formula;
V = Ah
where;
A is the base area of the objectsh is the height of the objectsV(prism) = 5A
V(cylinder) = 3A
Thus, the correct conclusion is, the volume of the prism is not equal to the volume of the cylinder.
Learn more about volume here: https://brainly.com/question/1972490
#SPJ2
Answer:
D. The volume of the prism is not equal to the volume of the cylinder.
Step-by-step explanation:
YES OR NO QUESTION PLS HELP
Can you make another triangle with the same angles that is not congruent to your original triangle? Can you create any pair of triangles with the same three angle measures that are not congruent?
Answer:
NO
Step-by-step explanation:
Which is a possible congruence statement for the following figures?
A BCD ≅ GHIF
B ABCD ≅FGHI
C BCDA ≅ FGHI
Answer:
it should be b
Step-by-step explanation:
As a builder you provide fences for the new houses. The cost per linear
foot of fence $30 per linear foot which includes installation.
20 Alex and Chris share sweets in the ratio Alex : Chris = 7:3.
Alex receives 20 more sweets than Chris.
Work out the number of sweets Chris receives.
Answer:
Alex:Chris 35:15
Step-by-step explanation:
7-3 (ratios)= 4
20 sweets= 4:1
20÷4= 5
5×7= 35 (how many sweets Alex got)
5×3= 15 (how many sweets Chris got)
Alex got 20 more sweets than Chris
(sorry if you didn't understand how I explained it)
1. Predict the height ( in cm) of boy
who is 30 months old.
2. Predict the age of a boy who is approximately 115 cm tall.
Use the linear model equation y=0.58x+72.27.
Answer:
Step-by-step explanation:
It'd be wise to say what is represented by each x and y. I will assume that x represents the age of the child in months and y the height in cm.
Then, if the height is 115 cm, 115 cm = 0.58x + 72.27. Must solve this for x:
115 cm - 72.27 cm
x = ---------------------------- = 73.7 cm (about 29 inches, which is reasonable)
0.58
If the child is 30 months old, x = 30 and y (the height) is
0.58(30) + 72.27 cm = 89.7 cm (about 35.3 cm, also reasonable)
I need some help finding the volume of a sphere with a diameter of 18.6cm. The website says the answer I got from my calculator was wrong! Help would be greatly appreciated!
Answer:
Volume, V = 3367.6 cm³
Step-by-step explanation:
Given the following data;
Diameter = 18.6 cm
Radius = diameter/2 = 18.6/2 = 9.3 cm
Pie, π = 3.14
To find the volume of the sphere;
Mathematically, the volume of a sphere is given by the formula;
[tex] Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} [/tex]
Where;
r is the radius of the sphere.
Substituting into the formula, we have;
[tex] V = \frac {4}{3} * 3.14 * 9.3^{3} [/tex]
[tex] V = 4.186666667 * 804.357 [/tex]
Volume, V = 3367.6 cm³
The following are the temperatures of 10 days in winter in °C. 5, 4, 4, -1, 4, 10, 9, 8, 6, 4 Work out the mean temperature.
Answer:
Answer is 5 °C.
Step-by-step explanation:
5 is answer
Answer:
The mean temperature is 5.3 degree Celsius
Step-by-step explanation:
5+4+4-1+4+10+9+8+6+4
= 53
So,
53/10
= 5.3
mark me brainliest plss :))
The table shows a function.
n
2
4
6
00
10
8(n)
3
6
9
12
15
What is the range of the function?
Answer:
All real numbers greater than 2
Find the mean, median, mode, and range of the gievn data below? Label each answer (ex: mean = 3, mode = ...) Online Purchases ($) 46. 50. 52. 52. 53, 58, 60, 61, 64, 65, 74, 75, 77.80.88
Answer:
median
46+50+52+52+53+58+60+61+64+65+74+75+77+80+88= 955÷15=63.66
round of =6
median 61
mode 52
range=88-46
=42
Una caja de carton se ha disenado para qu contenga 184cm cubicos. Si su altura es de 10cm, cual es el area de la base?
Answer:
18.4 cm²
Step-by-step explanation:
Una caja de carton se ha disenado para qu contenga 184cm cubicos. Si su altura es de 10cm, cual es el area de la base?
Volumen = Área de la base × Altura
Área de la base = Volumen / Altura
= 184 cm³ / 10 cm
Área de la base = 18.4 cm²
Por lo tanto, el área de la base es de 18.4 cm².
the radius is a circle is 17m. Find it’s circumference in terms of π.
C= ________m
Answer:
C= 106.81m
Step-by-step explanation:
PLEASE HELP
Write an expression in terms of x that could be used to determine the surface area of a cube with a side length of x inches.
Answer:
A=6x²
Step-by-step explanation:
A cube is an object which is three-dimensional. A cube has six square faces.
If the side length = x inches
The area of a square = x²
Therefore, the expression for the surface area of a cube(with 6 square faces) with a side length of x is given as:
A=6x²