Answer:
Step-by-step explanation:
A) The equation for the volume of a sphere is [tex]V=\frac{4}{3} \pi r^{3}[/tex]
As the diameter of each ball is 3 inches, that would mean that the radius of each is 1.5 inches.
Now we can plug our value into the equation
[tex]V=\frac{4}{3} \pi (1.5)^{3}[/tex]
This would simplify to
V = 14.12716694 [tex] in^{3}[/tex]
B) The equation for the volume of a cylinder is [tex]V=d\pi h[/tex]
As there are 3 balls in a container and the diameter of each is 3, that would mean that the height is 9 inches
Now we can plug in our values into the equation
[tex]V = (3)(9)\pi[/tex]
This would mean that this equation would simplify to
[tex]V = [/tex] 27\pi [tex]in^{3}[/tex]
C) To find the empty space, we must take the total volume, the volume of the cylinder, and subtract the volume of the tennis balls
This would mean that the equation would look like this
[tex](27\pi)-(3(\frac{4}{3} \pi (1.5)^{3})) [/tex]
This would simplify to
42.41150082 [tex]in^{3}[/tex] of empty space.
Answer:
The volume of each tennis vall is 14.13 cubic inches, approximately.The volume of each can is 63.59 cubic inches, approximately.There are 49.46 cubic inches of empty space between the tennis balls and the cans.Step-by-step explanation:
Givens
The diameter of each ball is 3 inches long.They are sold in cans of three, that is, each can contains 3 tennis balls.Each can has cylinder form.First, we find the volum of each tennis ball.
Notice that they have spherical form, so their volume is defined by
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Where [tex]r=\frac{d}{2}=\frac{3 in }{2}=1.5in[/tex]
Replacing the radius and using [tex]\pi \approx 3.14[/tex], we have
[tex]V=\frac{4}{3}(3.14)(1.5in)^{3}=14.13 \ in^{3}[/tex]
Therefore, the volume of each tennis vall is 14.13 cubic inches, approximately.
Assuming that the diameter of each ball is congruent with the diameter of the can, we have the volume of a cylinder defined by
[tex]V=\pi r^{2}h[/tex]
Where, [tex]r=1.5in[/tex] and [tex]h= 3(3in)=9in[/tex], because each can has three balls, and the height is the sum of all three diameters.
Replacing, we have
[tex]V=3.14(1.5in)^{2} (9in)=63.59 in^{3}[/tex]
Therefore, the volume of each can is 63.59 cubic inches, approximately.
Now, notice that between the can and the tennis balls thereis empty space, because balls are spherical and cans are cylindric.
Let's find the difference between their volumes:
[tex]V_{empy}=63.59-14.13= 49.46 in^{3}[/tex]
Therefore, there are 49.46 cubic inches of empty space between the tennis balls and the cans.
Which number can each term of the equation be multiplied by to eliminate the decimals before solving? –m + 0.02 + 2.1m = –1.45 – 4.81m
Answer:
100
Step-by-step explanation:
The given equation is;
–m + 0.02 + 2.1m = –1.45 – 4.81m
The highest decimal places is 2.
This implies that, we must multiply each term of the equation by [tex]10^2=100[/tex] before solving in order to eliminate the decimal.
In that case the equation becomes;
–100m + 2 + 210m = –145 – 481m
Hence the number is 100
Answer:
easy answer 100
Step-by-step explanation:
in a triangle there is three angles..one is 32° other is 116° what is the third one?
Answer:32 degrees
Step-by-step explanation:a triangle total is 180 degrees. So subtract 116 and 32 by 180 to get 32
Answer: 32°
Step-by-step explanation: Hello There! The Answer is 32°. This is because when we add up 116° and 32° we get 148° to get the Answer we subtract 148° from 180° and we get a difference of 32°.
Given that -5 < -3, which statement is not true?
-5 is to the left of -3 on the number line.
-3 is less than -5,
-3 > -5
-3 is to the right of -5 on the number line.
Answer:
- 3 is less than - 5 is not true
Step-by-step explanation:
Numbers to the right of numbers on the number line are greater.
Numbers to the left of numbers on the number line are less
- 3 is to the right of -5 on the number line and is greater than - 5
Which of the following are right triangles? A) Triangle ABC: AB=76 BC=357 AC=365
B) Triangle ABC: AB=123 BC=836 AC=845
ANSWER
AB=76 BC=357 AC=365 This triangle is a right triangle.
EXPLANATION
We use the Pythagoras Theorem to determine whether the triangles are right triangles.
According to this theorem, the square of the hypotebuse is equal to the sum of the squares of the two shorter legs.
We have:
AB=76 BC=357 AC=365
[tex] {365}^{2} = {76}^{2} + {357}^{2} [/tex]
133225=5776+127449
133225=133225
For the second triangle, we have;
B) Triangle ABC: AB=123 BC=836 AC=845
845²=123²+826²
714025=15129+682276
714025≠697405
The first triangle is a right triangle
Answer:
the firsst one
Step-by-step explanation:
The area of the trapezoid
The area of that trapeziod is 28 inches.
Answer:
Step-by-step explanation:
The area is a+b/2
so the answer is 28
Assessment 1
4. Use the recipe shown in the table to answer the questions below.
Use pictures, tables or number
sentences to solve the task.
Grandma's Recipe for Su
ecipe for Sugar Cookies
1% cups butter
2 cups sugar.
4 eggs
4 teaspoon baking powder
1 YA cups flour
14 teaspoon salt
a) How many cups of sugar are needed for each egg? How do you know?
a)Each egg requires 0.5 cups of sugar in Grandma's recipe.
b)The ratio of baking powder to salt is 3:1.
a) The recipe uses 2 cups of sugar and 4 eggs. To find out how many cups of sugar are needed per egg, we divide the total cups of sugar by the number of eggs:
2 cups of sugar / 4 eggs = 0.5 cups of sugar per egg
So, 0.5 cups of sugar are needed for each egg.
b) Ratio of baking powder to salt
The recipe calls for 3/4 teaspoon of baking powder and 1/4 teaspoon of salt. To find the ratio of baking powder to salt, we divide the amount of baking powder by the amount of salt:
(3/4) teaspoon of baking powder / (1/4) teaspoon of salt = 3
Thus, the ratio of baking powder to salt is 3:1. This means there is three times as much baking powder as salt in the recipe, which aligns with your sister's observation.
The complete question is:
Use the recipe shown in the table to answer the questions below. Use pictures, tables or number sentences to solve the task. Grandma's Recipe for Sugar Cookies 1/2 cups butter 2 cups sugar 4 eggs 34 teaspoon baking powder 1 % cups flour 14 teaspoon salt a) How many cups of sugar are needed for each egg? How do you know? Your sister notices that she needs three times as much baking powder as salt in this recipe. b)What is the ratio of baking powder to salt? Explain your reasoning in words.
here are the ingredients for making a trifle for four people. 120g strawberry jelly,8 sponge fingers, 420ml custard and 180g tinned fruit. Kevin is going to make a trifle for 3 people. work how much of each ingredients he needs
Answer:
For 3 people Kevin would need 90g of strawberry jelly, 6 sponge fingers, 315ml of custard and 135g of tinned fruit.
Step-by-step explanation:
To work this out you would need to work out how many ingredients would be needed for 1 person, so you would need to divide each ingredient amounts by 4. (For example for the strawberry jelly you would do 120÷4 which is 30).
Then, to work out how many ingredients would be needed for 3 people you would need to multiply the ingredient amounts by 3. (Like 30×3 is 90).
Find the exact value of sec 120°.
For this case we have that by definition:
[tex]Sec (a) = \frac {1} {cos (a)}[/tex]
Then, we can rewrite the expression as:
[tex]Sec (120) = \frac {1} {cos (120)}[/tex]
[tex]cos (120) = cos (180-60) = - cos (60) = - \frac {1} {2}[/tex]
So:
[tex]Sec (120) = \frac {1} {- \frac {1} {2}}\\Sec (120) = - 2[/tex]
Answer:
-2
The exact value of sec 120° is -2 as secant function is the reciprocal of the cosine function,
The secant function is the reciprocal of the cosine function, so we can find sec 120° by finding the reciprocal of cos 120°.
First, let's determine the value of cos 120°.
We know that cos 120° is negative in the unit circle, so we need to find the cosine of the reference angle, which is 60°.
In the unit circle, at 60°, the cosine value is 1/2.
Since cos 120° is negative, the value is -1/2.
Now, we can find the exact value of sec 120° by taking the reciprocal of -1/2:
sec 120° = 1 / (cos 120°) = 1 / (-1/2) = -2.
Therefore, the exact value of sec 120° is -2.
To learn more on Exact value click:
https://brainly.com/question/30754075
#SPJ6
F(x) = x^2. What is g(x)?
Answer:
The correct answer is C. g(x) = 1/4x^2
Step-by-step explanation:
In order to determine if the graph fits, take the point that is given on the parabola and see if it fits the equation. To do that we plug it in and see if it gives a true statement.
(2, 1)
g(x) = 1/4x^2
1 = 1/4(2)^2
1 = 1/4(4)
1 = 1 (TRUE)
Which expresión is equivalent to -3x - (x-1) + 3/2 (3x + 3)?
A. 1/2x + 11/2
B. 1/2x + 7/2
C. 5/2x + 11/2
D. 5/2x + 7/2
Answer:
[tex]\large\boxed{A.\ \dfrac{1}{2}x+\dfrac{11}{2}}[/tex]
Step-by-step explanation:
[tex]-3x-(x-1)+\dfrac{3}{2}(3x+3)\qquad\text{use the distributive property}\\\\=-3x-x-(-1)+\left(\dfrac{3}{2}\right)(3x)+\left(\dfrac{3}{2}\right)(3)\\\\=-3x-x+1+\dfrac{9}{2}x+\dfrac{9}{2}\qquad\text{combine like terms}\\\\=\bigg(-3x-x+\dfrac{9}{2}x\bigg)+\bigg(1+\dfrac{9}{2}\bigg)\\\\=\bigg(\dfrac{-6}{2}x-\dfrac{2}{2}x+\dfrac{9}{2}x\bigg)+\bigg(\dfrac{2}{2}+\dfrac{9}{2}\bigg)\\\\=\dfrac{-6-2+9}{2}x+\dfrac{2+9}{2}=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]
What are the numbers???
Answer:
In: 5, 4, 2, 3, 1, and 10.
Out: 40, 32, 16, 24, 8, and 80
Step-by-step explanation:
The first step you should do is to take notice of the pairs that have their "in" and "out" both answered.
The second step is to find out what you must multiply the "in" by to get the "out". In this answer, you must multiply the "in" by 8 to get the "out".
The third step is to do the same thing for all of the values until the chart is completely filled with values.
The fourth step is to check your work!
If you have any questions, please let me know!
The rule is 8
Bc 5 times 8 is 40
32/8 is 4
Either divide or multiply when needed
The cylinders are similar. The volume of the larger cylinder is 40,635 cubic centimeters. What is the volume of the smaller cylinder?
Answer:
1505 cubic centimeters
Step-by-step explanation:
Lengths are related by scale factor "k"
Volumes are related by scale factor "k^3"
From large to small:
What multiplied by 18, gives us 6? We can write:
18(k)=6
k = 6/18 = 1/3
So scale factor is 1/3
Now in terms of volume, the larger is given as 40, 635, so we can set up:
40,635 * k^3 = smaller volume
we know k = 1/3, so
40,635 * (1/3)^3 = smaller volume
Thus, smaller volume = 40,635 * (1/3)^3 = 1505
simplify the expression
(2b/3)^4
Answer:
2b/3 * 2b/3 * 2b/3 * 2b/3
Good luck!!
Answer:
16b^4/81
Step-by-step explanation:
Kyle fills the candle
mold with liquid candle wax. If the
candle has a volume of 99 cubic
inches, what is the width of the
mold?
1*3=3
99/3= 33
1*3*33=99
Answer:33in
What would be the dimensions for the poster at 1/4 times it’s current size
Answer:
D. Length = 9 cm; width = 6 cm
Step-by-step explanation:
Find 1/4 of the length and 1/4 of the width.
1/4 * 36 cm = 9 cm
1/4 * 24 cm = 6 cm
Answer: D. Length = 9 cm; width = 6 cm
Evaluate the expression and enter your answer in the box below |0|
Answer:
0
Step-by-step explanation:
When put in between these lines || a negative number becomes positive and a positive number stays the same.
In the formula d=/(x2-x1)^2+(y2-y1)^2 , how does each subtraction expression relate to the Pythagorean theorem?
Answer:
A
Step-by-step explanation:
I don't think you need this
Answer:
option A
Step-by-stevvp explanation:
In the formula [tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
The formula is used to find the distance between two points
(x2-x1) gives the length of one leg
(y2-y1) gives the length of another leg
In a right angle triangle , Pythagorean theorem is [tex]c=\sqrt{a^2 + b^2}[/tex]
where a and b represents the sides of the triangle
Each subtraction expression in the formula represents the leg of the right angle triangle with the hypotenuse of length d
Gisela cuts an apple into 8 pieces of the same size. What is the angle measure of each piece?
Answer:
45°
Step-by-step explanation:
Imagine a waistband stretched around the middle of an apple, horizontally.
The waistband could be represented by the circumference of the apple, with a central angle of 360°.
Divide this central angle by 8, obtaining 45°. Each piece of apple is measured by a central angle of 45°.
To find the angle measure of each of the 8 pieces of the apple, divide the total degrees in a circle by 8, resulting in each piece having an angle measure of 45 degrees.
To find the angle measure of each piece, we divide the circle into 8 equal slices.
Each slice corresponds to an angle of 360 degrees (the total degrees in a circle) divided by 8, which equals 45 degrees for each piece.
Therefore, the angle measure of each piece of the apple is 45 degrees.
Does anyone know this
Answer:
a2+1)-(4+2a2)
Step-by-step explanation:
to solve this, we need to get rid of the brackets as follow:
3a2+1-4-2a2
ading the common terms we have:
a2 - 3
that is all.
Plz mark me brainlist!!!
asap here plz I'm lost at this equation
Answer:
I believe the answer is C
Hope This Helps! Have A Nice Day!!
Answer:
y= 2
Step-by-step explanation:
Factor this expression 2
Answer:
Step-by-step explanation:
16x^4+56x^2+49
(4x^2+7)^2
The ratio to boys to girls in Ms.chunningham's class is 2 to 3. There are 18 girls in the class.What is the total number of students in ms.chunningham's class?
A. 12
B. 30
C.45
D.27
Answer:
B.30
Step-by-step explanation:
This was picked because if u divide 18 by 3. You get 6 and if u multiply it by 2. You get 12 plus the 18 equals 30.
the difference between a number and 2
Answer:
n-2
Step-by-step explanation:
Difference means subtraction
n-2
Can anyone help me with this
Answer:
ice cream = 3.80$
cup cake = 4.25$
donuts = 2.5$
Step-by-step explanation:
a=ice cream
b = cup cake
c = donuts
we can write the following equations given from the picture:
a+b+b=12.30$ equation 1
b+c+a=10.55$ equation 2
b+c+c =9.25$ equation 3
using equation 1 we have:
2b+a=12.30
a=12.30-2b
using equation 3 we have:
2c+b=9.25
c=(9.25-b)/2
using equation 2 we have:
b+((9.25-b)/2)+12.30-2b=10.55
((2b+9.25-b)/2) - 2b = 10.55-12.30
((2b+9.25-b-4b)/2) =-1.75
-3b+9.25=2*(-1.75)
-3b= -3.5-9.25
-3b=-12.75
b=12.75/3
so we have b= 4.25$ = cup cake
we have:
c=(9.25-b)/2= (9.25-4.25)/2
c=2.5$= donuts
a= 12.30-2b= 12.30-2*(4.25)
a= 12.30-8.5 = 3.8$ = ice cream
What is the range of the function y=cot(x)?
A) all real numbers
B) all real numbers except pi/2+n pi, where n is any integer
C) all real numbers except n pi/2, where n is any integer
D) all real numbers except n pi, where n is any integer
Answer:
A. all real numbers
Step-by-step explanation:
The range of the function y=cot(x) is (A) all real numbers.
Evaluate the sum
A. 306
B. 240
C. 360
D. 272
Answer:
Option D. [tex]272[/tex]
Step-by-step explanation:
we know that
To evaluate the sum , use the formula
[tex]S=\frac{1}{2}(a1+an)n[/tex]
where
a1 is the first term
an is the last term
n is the number of terms
In this problem
For n=1 ------> a1=2(1)=2
For n=16 ------> an=2(16)=32
n=16 terms
substitute in the formula
[tex]S=\frac{1}{2}(2+32)16[/tex]
[tex]S=272[/tex]
Multiply the polynomials (8x^2+6x+8)(6x-5) Apex
Answer:
[tex]48x^3+76x^2+78x+40[/tex]
Step-by-step explanation:
[tex](8x^2+6x+8)(6x+5)\\\\48x^3+36x^2+48x+40x^2+30x+40[/tex]
Now that we have distributed the values, we must now combine like terms
[tex]48x^3+36x^2+48x+40x^2+30x+40\\\\48x^3+(36x^2+40x^2)+(48x+30x)+40\\\\48x^3+76x^2+78x+40[/tex]
Answer: 48x^3 -4x^2 + 18x -40
Step-by-step explanation: multiply 8x^2 by 6x and -5 ➡ 48x^3 - 40x^2
multiply 6x by 6x and -5 ➡ 36x^2 -30x
multiply 8 by 6x and -5 ➡ 48x -40
now add the like terms
48x^3 - 40x^2 + 36x^2 -30x + 48x -40 ➡48x^3 -4x^2 + 18x -40
Brooke is using shiny rocks to make necklaces. Each necklace has 5 shiny rocks. Make a table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces
Answer:
10 necklaces = 50 rocks
15 necklaces = 75 rocks
20 necklaces = 100 rocks
25 necklaces = 125 rocks
Step-by-step explanation:
A table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces:
| Number of necklaces | Number of shiny rocks used |
| 10 | 50 |
| 15 | 75 |
| 20 | 100 |
| 25 | 125 |
To calculate the number of shiny rocks used, we simply multiply the number of necklaces by the number of shiny rocks per necklace. For example, to calculate the number of shiny rocks used for 10 necklaces, we multiply 10 by 5:
10 necklaces * 5 shiny rocks/necklace = 50 shiny rocks
We can do the same calculation for 15, 20, and 25 necklaces to get the following results:
15 necklaces * 5 shiny rocks/necklace = 75 shiny rocks
20 necklaces * 5 shiny rocks/necklace = 100 shiny rocks
25 necklaces * 5 shiny rocks/necklace = 125 shiny rocks
Therefore, the table above shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces.
For such more question on number
https://brainly.com/question/30752681
#SPJ12
The population of mice in a vacant building is 200. The population of mice grows according to the model: M(t)=200(1.2)^t where t is the time in days. Assuming none of the mice die, how many mice will be in the building at the end of 30 days
7200. Because 1.2 *30 *200=7200
To estimate the mouse population after 30 days using the given model, M(t)=200(1.2)^t, evaluate the expression with t=30, which results in approximately 47,475 mice.
The student is asking how many mice will be in the building after 30 days according to the exponential growth model M(t) = 200(1.2)^t, where t is the time in days and M(t) is the population of mice at time t. To find the answer, we simply plug the value of 30 days into the model to get M(30) = 200(1.2)^30.
Calculating the expression:
First, calculate 1.2 raised to the power of 30, which gives us approximately 237.3769.
Then, multiply that by the initial population of 200 mice, yielding a result of approximately 47,475.38.
Therefore, after 30 days, assuming no mice die, there will be approximately 47,475 mice in the building.
Find the Value of X.
Answer: 5
Step-by-step explanation: The dot in the middle of the circle is the center point of the circle. This means that it bisects every point from one edge to the other cutting through the middle. The two vertical red lines in the middle of the circle indicate they are the same measure. knowing this and that the angle interiors are 90 degrees, we can conclude that x is the same length as the 5 diagonal from it.
Answe is 5..
The (.) is the center of the circle..
The (|) mesns these lines are equal..
The angles also are right angles and equal..
Means the length ofvthis line also equals the other line = 5