Answer:
313.3084 in3
Step-by-step explanation:
To find the final volume of the finished ball, we need to find the volume of the whole sphere and then decrease it by the volume of the three holes.
The volume of the sphere is given by this formula:
V = (4/3)*pi*r^3
Where r is the radius. In our case, the radius is 8.5 / 2 = 4.25 in, so the volume is:
V1 = (4/3)*pi*4.25^3 = 321.5551 in3
The volume of each cilindrical hole can be calculated as:
V = pi*r^2*h
Where r is the radius and h is the height. We have that the radius is 1/2 = 0.5 inches and the height is 3.5 inches, so:
V2 = pi*0.5^2*3.5 = 2.7489 in3
So the final volume is:
V = V1 - 3*V2 = 321.5551 - 3*2.7489 = 313.3084 in3
Answer:
313.313inches³
Step-by-step explanation:
A bowling ball is spherical in shape hence,
The Formula used to calculate the volume of sphere is
= 4/3 πr³
For the question, we were given diameter.
Diameter of the bowling ball = 8.5 inches
Radius = Diameter ÷ 2
Radius = 8.5 inches ÷ 2
Radius = 4.25 inches
Hence,
Volume of a Sphere =
4/3πr³
= 4/3 × π ÷ 4.25
= 321.55509806inches³
Approximately = 321.56inches³
From the question we can see that the bowling ball has 3 cylindrical holes in it
With a diameter of 1 inch and a depth of 3.5inches
Hence we find the volume of these holes
Volume of a cylinder = πr²h
Diameter = 1 inch,
Radius = Diameter /2 = 1/2 inches
Height(Depth) = 3.5 inches
Volume of the cylindrical holes = π ×(1/2) ² × 3.5
Volumes = 2.749inches³
Since we have 3 holes ,
Volumes of the 3 holes = 2.749inches³ × 3
= 8.247inches³
The Volume of the total Spherical bowling ball
= Volume of the total bowling ball without holes - Volume of the cylindrical holes on the bowling ball
= 321.56inches³ - 8.247inches³
= 313.313inches³
Hence, the best estimate of the volume of resin in the finished ball = 313.313inches³
The sum of two numbers is 7. The larger number is 16 more than 2 times the smaller number. What are the numbers? *
Answer:
-3, 10
Step-by-step explanation:
Let s represent the smaller number. Then 7-s is the larger one.
7-s = 16 +2s
-9 = 3s . . . . . . . add s-16
-3 = s
7-s = 10
The smaller number is -3, the larger one is +10.
5(3x+2)=8(2x-4) solve for x
Answer:
x = 42 i hope this helps! :)
Step-by-step explanation:
given 5(3x + 2) = 8(2x - 4)
distribute the 5 to both the 3x and the 2 15x + 10 = 8(2x - 4)
now distribute the 8 to both the 2x and the -4 15x + 10= 16x - 32
subtract 15x from both sides 10 = x - 32
add 32 to both sides 42 = x
flip the equation around so the x is first x = 42
answer x = 42
Jayden’s family took a road trip to the Grand Canyon. Jayden fell asleep 15% of the way through the trip if the total length of the trip was 1000 miles, how many miles had they travelled when Jayden fell asleep?
Answer:
150 miles
Step-by-step explanation:
0.15x1000=150
How do you find the arc length in a circle given any angle?
You find the circumference and multiply it by the central angle. If the central angle is in degrees, you divide that by 360. If the central angle is in radians, you divide by 2pi.
If f(x) = -x^2 – 1, and
g(x) = x + 5, then
g(f (x)) = [? ]x^2+[ ]x + [ ]
Answer:
g(f(x)) = - x² + 4
Step-by-step explanation:
To evaluate g(f(x)), substitute x = f(x) into g(x), that is
g(f(x))
= g(- x² - 1)
= - x² - 1 + 5
= - x² + 4
Which function has an initial value of 0.2?
Group of answer choices
Function Three
Function Four
Function Two
Function One
PICTURE IS BELOW
Answer:
Function 4
Step-by-step explanation:
How do i solve -1=-3r +2r
To solve this, you need to isolate/get the variable "r" by itself in the equation:
-1 = -3r + 2r Combine like terms(terms that have the same variable and power/exponent.) The only like terms you can combine are -3r and 2r
-1 = -r Divide -1 on both sides to get "r" by itself
[tex]\frac{-1}{-1} =\frac{-r}{-1}[/tex] (two negative signs cancel each other out and become positive)
1 = r or r = 1
Answer:R=-1
Step-by-step explanation: You would have to first do the math for the equation, then you would have to work in the "R" and given the answer is smaller than the equation itself we can tell that the "R" is a negative. So, if we add the -3 and the 2 we get 1,so we can say that the "R" are both equal to -1 then we put it in the equation. We get -1=1 we add the "R's" then get -1
4. *Each pair of polygons is similar. Find the value of x.
Step-by-step explanation:
since both objects and sides are similar, you can set each side equal, then you cross multiply, and do subtraction, then find x.
Final answer:
To find the value of x in similar polygons, justify the similarity, write an equation relating the sides, algebraically solve for x, calculate, and then check that the result is reasonable.
Explanation:
The subject of this question is Mathematics, and it is likely at the high school level, as it involves finding a missing length in similar polygons, which requires knowledge of ratios and properties of similar figures, often covered in high school geometry courses.
Steps to find the value of x:
Justify that the triangles are similar: This can typically be done by verifying that the triangles meet the criteria of similarity, such as having identical angles or corresponding sides in proportion.
Write an equation that relates the sides of the triangles: Utilize the properties of similar triangles to write ratios that compare the lengths of corresponding sides.
Algebraically isolate the unknown quantity x.
Plug in numbers and calculate the answer.
Check the answer to ensure it seems reasonable.
It's also important to remember that if two triangles are similar, their corresponding lengths are proportional, which you can express algebraically with a statement such as AB/CD = EF/GH where AB, CD, EF, and GH are corresponding sides of the similar triangles.
18. Ms. Acosta works in the lab at a pharmaceutical company. She needs to make 21 liters of a 32% acid solution to
test a new product. Her supplier only ships a 28% and a 35% solution. Ms. Acosta decides to make the
32% solution by mixing the 28% solution with the 35% solution. How much of the 28% solution will Ms. Acosta
need to use?
A. 6L
B. 9L
C. 12L
D. 21L
Answer:
vbighughyuogytifvyigguhui
Step-by-step explanation:
A regulation baseball can weigh no more than 149 grams. A factory produces baseballs with weights that are normally distributed with a mean of 146 grams and a standard deviation of 2.3 grams.
Answer:
0.9032
Step-by-step explanation:
Given that:
mean (μ) = 146 grams and standard deviation (σ) = 2.3 grams
The z score is a measurement used in statistics to calculate how far a value is from the mean in a normal distribution. The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For the baseball not to weigh more than 149 grams i.e x = 149 g
[tex]z=\frac{x-\mu}{\sigma}=\frac{149-146}{2.3} =1.30[/tex]
From the probability distribution table, P(x < 149) = P(z < 1.30) = 0.9032 = 90.32%
What value of x is a solution to x3 = 216?
Answer:
X=72
Step-by-step explanation:
216/3= 72
Scott runs 4 sprints of 20 yards each. If he continues his routine, how many practices will it take for Scott to have sprinted a total of 2 miles combined?
Answer:
It will take 44 practices for Scott to have sprinted a total of 2 miles combined
Step-by-step explanation:
This question can be solved using rules of three.
First step:
Scott practice is measured in yards.
We want to know how many practices it will take for him to have sprinted 2 miles.
So we pass 2 miles to yards
Each mile has 1760 yards.
So 2 miles is 1760*2 = 3520 yards.
A practice:
4 sprints of 20 yards each.
So 4*20 = 80 yards.
A practice is 80 yards. How many practices for 3520 yards?
1 practice - 80 yards
x practices - 3520 yards
80x = 3520
x = 3520/80
x = 44
It will take 44 practices for Scott to have sprinted a total of 2 miles combined
A truck rental company charges a weekend rate of $50.75 plus $8.25 for each hour a truck is rented.You have at most $125.00 to spend on a truck rental.Let x represent the number of hours you rent a truck.Which inequality describes the number of hours you can rent a truck?
Answer:
Step-by-step explanation:
Let x represent the number of hours for which you can rent the truck.
truck rental company charges a weekend rate of $50.75 plus $8.25 for each hour a truck is rented. It means that the cost of renting the truck for x hours would be expressed as
50.75 + 8.25x
You have at most $125.00 to spend on a truck rental. Therefore, the inequality that describes the number of hours you can rent the truck is
50.75 + 8.25x ≤ 125
Use the law of cosines to find each missing side. Round to the nearest tenth.
(I'm doing each individual question)
Answer:
x = 9.3
Step-by-step explanation:
The Law of Cosines
[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]
[tex] x^2 = 15^2 + 13^2 - 2(15)(13) \cos 38^\circ [/tex]
[tex] x^2 = 225 + 169 - 2(15)(13) \cos 38^\circ [/tex]
[tex] x^2 = 394 - 390(0.7880) [/tex]
[tex] x^2 = 86.6758 [/tex]
[tex] x = \sqrt{86.6758} [/tex]
[tex] x = 9.3 [/tex]
find the volume of a cylinder with a height of 2 and a radius of 3. Use terms of pi
Answer:
56.55
Step-by-step explanation:
The formula to find the volume of a cylinder is V=πr2h so you would just need to plug the numbers in to get 56.55.
If (− 4, −8) and (−10, −12) are the endpoints of a diameter of a circle, what is the equation of the circle?
A) (x + 7)^2 + (y + 10)^2 = 13
B) (x + 7)^2 + (y − 10)^2 = 12
C) (x − 7)^2 + (y − 10)^2 = 169
D) (x − 13)^2 + (y − 10)^2 = 13
Answer:
Correct option: A
(x + 7)^2 + (y + 10)^2 = 13
Step-by-step explanation:
First we need to find the center of the circle. We can find it calculating the midpoint of the diameter.
the x-coordinates of the diameter are -4 and -10, so the midpoint is:
(-4 -10)/2 = -7
the y-coordinates of the diameter are --8 and -12, so the midpoint is:
(-8 -12)/2 = -10
Now we need to find the radius of the circle, so we find the diameter and then find half of it.
The lenght of the diameter is the distance of the endpoints:
D = sqrt((-4+10)^2 + (-8+12)^2) = 7.21
radius = 7.21/2 = 3.605
The generic equation of the circle is:
(x - xc)^2 + (y - yc)^2 = r^2
So we have:
(x + 7)^2 + (y + 10)^2 = 13
Correct option: A
The triangular prism has
lateral faces.
square
The triangular prism has a lateral area of
inches.
Answer: 3 and 240
Step-by-step explanation:
Edg 2020
Answer:
The triangular prism has
✔ 3
lateral faces.
The triangular prism has a lateral area of
✔ 240
square inches.
Step-by-step explanation:
study it and got it rightThe Lopez family took a taxi to there next destination. The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled.When they arrived the total cost 37 dollars how far did they go in the taxi
Answer: 8.3
Step-by-step explanation: 37 divided by=12.3 then 12.3 - 4
Answer: the taxi travelled 11 miles
Step-by-step explanation:
Let x represent the number of miles that the taxi traveled.
The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled. It means that the total cost of renting and driving the taxi over x miles is
4 + 3x
The Lopez rented the taxi and when they arrived at their destination, the total cost 37 dollars. It means that
4 + 3x = 37
3x = 37 - 4
3x = 33
x = 33/3
x = 11 miles
Find an equation for the line that passes through the points (-3,-2) and (1,4)
Answer:
y=2/3x
Step-by-step explanation:
First, we have to find the slope, which is [tex]\frac{(y_{1} -y_{2})}{(x_{1}-x_{2}}[/tex]
(-3-1)/(-2-4)
-4/-6
2/3 is slope.
y=2/3x+-___
substitute in -3 from first point
y=-2+__=-2
y=2/3x+0
y=2/3x
Answer:
y + 2 = (3/2) (x+3) (point slope form)
Step-by-step explanation:
(see attached for reference)
Given
(x₁, y₁) = (-3,-2)
(x₂, y₂) = (1,4)
Since we are given 2 points, it would be easiest to express the equation of the line in point-slope form (see attached)
(y - y₁) = m (x - x₁)
we already have the values for x₁ and y₁, hence we only need to find the slope m (see 2nd attached graphic)
m = (y₂-y₁) / (x₂ - x₁)
= [4 - (-2) ] / [1 - (-3)]
= (4+2) / (1+3)
= 6/4
= 3/2
substituting the value for m and the values for x₁ and y₁:
(y - y₁) = m (x - x₁)
[y - (-2)] = (3/2) [x - (-3)]
y + 2 = (3/2) (x+3)
Sara and her family went to eat at Pappasito's for dinner. The total cost of the meal is $76.50. Sara left a 10% tip.
Determine their total cost, including the tip.
Answer:
The answer to your question is $84.15
Step-by-step explanation:
Data
cost of the meal = $76.50
tip 10%
total cost = ?
Process
1.- Calculate the 10% of $76.50 using proportions and cross multiplication.
$76.50 --------------- 100%
x ----------------- 10%
x = (10 x 76.5) / 100
x = 765/100
x = 7.65
2.- Calculate the total cost
Total cost = cost of the meal + tip
-Substitution
Total cost = $76.50 + $7.65
-Result
Total cost = $84.15
Sandra biked 7 kilometers on Wednesday. She biked 3 times as many kilometers on Thursday. How many total
meters did she bike?
What do you know? What do you need to find?
What question do you need to answer first?
How many meters did Sandra bike in all?
Which of the following sentences do you know? Select all that apply.
DA. Sandra biked 7 kilometers on Wednesday
OB. She biked 3 times as many kilometers on Thursday.
OC. How many total meters did she bike?
Answer:
A and B
Step-by-step explanation:
From what we know, Sandra biked 7 kilometers on Wednesday because of the statement, followed by how she biked 3x as many miles on Thursday. We do not know how many total meters she biked because it does not give us that information. Hope this helps!
what is an example of constant terms
A constant term is the whole number in an expression!
They are always easy to identify
5x + 14 ....
14 is the constant term!
80y - 2
-2 is the constant term!
I hope I helped :)
[tex]\huge\boxed{\sf{Hello\;there! :)}}[/tex]
A constant term is a number in an algebraic expression or equation.
A constant doesn't have any variables next to it.
For example, in the equation
4x²-2x=24, 24 is the constant.
[tex]\huge\boxed{\text{Hope\;it\;helps\;you!}}[/tex]
[tex]\huge\bold{\underline{\underline{Good\;luck!}}}[/tex]
[tex]\huge\rm{StillEnjoyingLife :)[/tex]
Erika is making cookies the recipe she has makes 20 cookies but she wants to make 60 cookies if she needs 2 cups of flour for 20 cookies how many cups of flour will she need for 60 cookies?
Answer:
The answer is 6 cups.
Step-by-step explanation:
If 20 cookies are 2 cups, that means that 10 cookies are 1 cup. If you see the pattern, the answer would easily be 6 cups.
A Pontiac Grand am I Pinterest so will Roger turn pike traveling at 50 mph. Once half an hour later a ford Mustangs enter the turnpike at the same location and travel in the same distance at 80 mph. How long would it take for the mustang to catch up to the grand am ?When it catch up how far will the two cars have traveled on the turnpike
Answer:
It will take 0.8333h for the mustang to catch up to the grand am.
The two cars will have traveled 66.664 miles on the turnpike
Step-by-step explanation:
The position for each car can be modeled by equations in the following format:
[tex]S(t) = S(0) + vt[/tex]
In which S(t) is the position t hours after the last car(the Ford Mustang) has left, S(0) is the position of each car when the Ford Mustang left and v is the speed of each car, in miles per hour.
Pontiac
Traveling at 50 mph, which means that [tex]v = 50[/tex].
The Ford Mustang leaves half an hour after the Pontiac. The Pontiac travels at 50 mph, which means that in this interval, the Pontiac will have traveled 0.5*50 = 25 mph. This means that S(0) = 25. So
[tex]S_{P}(t) = 25 + 50t[/tex]
Ford Mustang
Leaves from position 0, so S(0) = 0.
Travel in the same distance at 80 mph, so [tex]v = 80[/tex]. So
[tex]S_{M}(t) = 80t[/tex]
How long would it take for the mustang to catch up to the grand am ?
This is t when
[tex]S_{M}(t) = S_{P}(t)[/tex]
[tex]80t = 25 + 50t[/tex]
[tex]30t = 25[/tex]
[tex]t = \frac{25}{30}[/tex]
[tex]t = 0.8333[/tex]
It will take 0.8333h for the mustang to catch up to the grand am.
When it catch up how far will the two cars have traveled on the turnpike
This is either [tex]S_{M}(0.8333)[/tex] or [tex]S_{P}(0.8333)[/tex], since they will be in the same position. So
[tex]S_{M}(t) = 80t[/tex]
[tex]S_{M}(0.8333) = 80*0.8333 = 66.664[/tex]
The two cars will have traveled 66.664 miles on the turnpike
The Ford Mustang will catch up to the Pontiac Grand Am in 18.75 minutes and they will have traveled a total of 25 miles on the turnpike.
Explanation:To find out how long it takes for the Ford Mustang to catch up to the Pontiac Grand Am, we need to determine the time it takes for the Mustang to cover the same distance that the Grand Am has already traveled. The Grand Am has a head start of half an hour at a speed of 50 mph, so it has covered a distance of:
Distance = Speed x Time = 50 mph x 0.5 hr = 25 miles
Now, we can calculate the time it takes for the Mustang to cover this distance:
Time = Distance / Speed = 25 miles / 80 mph = 0.3125 hr = 18.75 minutes
Therefore, it will take the Mustang 18.75 minutes to catch up to the Grand Am.
When the two cars catch up, they will have traveled a total distance of 25 miles, which is the distance covered by the Grand Am in the half-hour head start.
Estimate the solution to the system of Equations
Answer:
Answer letter D
Step-by-step explanation:
-3x + 3y = 9
2x - 7y = -14
Let's start by simplifying both equations:
-3x + 3y = 9 (divide everything by 3)
2x - 7y = -14 (divide everything by 2)
We will then have:
-x + y = 3
x - [tex]\frac{7}{2}[/tex]y = - 7
Then we sum both equations, eliminating x and isolating y to find its value!
y + (- [tex]\frac{7}{2}[/tex]y) = 3 + (- 7)
[tex]\frac{2}{2}[/tex]y + (- [tex]\frac{7}{2}[/tex]y) = - 4
Summing the fractions of y we have
- [tex]\frac{5}{2}[/tex] y = - 4 .: y = [tex]\frac{8}{5\\}[/tex] .: y = 1 [tex]\frac{3}{5}[/tex](we found y!)
Now we substitute y in one of the previous equations to find x:
-3x + 3 × ( [tex]\frac{8}{5\\}[/tex] ) = 9
-3x + [tex]\frac{24}{5\\}[/tex] = 9
-3x = 9 - [tex]\frac{24}{5}[/tex]
-3x = [tex]\frac{45}{5}[/tex] - [tex]\frac{24}{5}[/tex]
-3x = [tex]\frac{21}{5}[/tex]
x = [tex]\frac{21}{5}[/tex] ÷ -3 (this is tricky, but it's the same as [tex]\frac{21}{5}[/tex] × -[tex]\frac{1}{3}[/tex] )
x = - [tex]\frac{7}{5}[/tex] .: x = - 1 [tex]\frac{2}{5}[/tex](finally found x!)
Bringing everything together we have:
x = - 1 [tex]\frac{2}{5}[/tex]
y = 1 [tex]\frac{3}{5}[/tex]
I hope it helps :)
Leila, Charlie, and Joe have a total of $144 in their wallets. Joe has 4 times what Leila has. Charlie has $6 more than Leila. How much does each have?
Answer:
The amounts of money each has are:
Joe = $92
Charlie = $29
Leila = $23
Step-by-step explanation:
To solve this, we will convert the statements into an equation, and use that to solve for the unknowns, as follows:
total amount = $144
Let Leila's share be S
Joe's share = 4 times Leila's = 4S
Charlie's share = $6 + Leila's share = 6 + S
Joe's share + Charlie's Share + Leila's Share = $144
4S + (6 + S) + S = 144
4S + 6 + S + S = 144
4S + 2S + 6 = 144
6S + 6 = 144
6S = 144 - 6 = 138
S = 138 ÷ 6 = $23
Therefore Leila's share 'S' = $23
Joe share= 4S = 4 × 23 = $92
Charlie's share = 6 + 23 = $29
Solve for x: x - 4 = -10
Answer:
x = -6
Step-by-step explanation:
x - 4 = -10
x = -6
Can I get brainliest
Answer:
x = -6
Step-by-step explanation:
you just add 4 to the other side in order to isolate the x
check
-6 - 4 = -10
A bag contains white marbles and green marbles, 64 in total. The number of white marbles is 4 less than 3 times the number of green marbles. How many white marbles are there?
Answer:
NOTE THIS IS AN EXAMPLE:
Step-by-step explanation:
Let W = # white marbles and Y = # yellow marbles
W + Y = 44
W = 3Y - 8
W - 3Y = -8
Subtract
4Y = 52
Y = 13
W =31
Antoine wants to get a subscription to a local library. There are two libraries, each of which charges a monthly subscription free plus a fee for each book instead
Answer:
b then a
Step-by-step explanation:
Answer:
Step-by-step explanation:
Use formulas to find the lateral area and surface area of the given prism. Round
your answer to the nearest whole number.
4 m
13 m
Not drawn to scale
208 m²: 240 m2
136 m²: 240 m2
136 m²: 188 m²
208 m²: 188m²
The lateral area of the rectangular prism is calculated to be 208m² using the formula for lateral area of a prism. Assuming the width is the same as the length, the surface area is calculated to be 240m² using the formula for surface area of rectangular prism.
Explanation:In mathematics, the lateral area and surface area of a rectangular prism can calculated using specific formulas. To calculate the lateral area of a rectangular prism, which is the area excluding the base and the top, you use the formula: Lateral area = Perimeter of the base x Height. Given the base length is 4m, and the height is 13m, the perimeter of the base is 4 x 4m = 16m. So, the lateral area = 16m x 13m = 208m².
The surface area of a rectangular prism is calculated using the formula: Surface area = 2lw + 2lh + 2wh. where l is the length, w is the width, and h is the height. In this case, the width is not given. Assuming it's the same as the length (since it's also 4m in the given figure), the surface area = 2*(4m*4m) + 2*(4m*13m) + 2*(4m*13m) = 32m² + 104m² + 104m² = 240m².
Learn more about Lateral and Surface Area of Prism here:https://brainly.com/question/31353385
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