Marco is carrying two cylinder-shaped cans. Each can has the same height
and cross-sectional area as the other. Which of the following best describes
the relationship between the cans according to Cavalieri's principle?
Answers
Answer:
Choice D
Step-by-step explanation:
The Cavalieri's principle states that if two or more solids have identical cross-sectional area as well as height, then the solids will have equal volume.
Therefore, the volumes of the cylinders are the same
Answer:
The volumes of the cylinders are the same.
Step-by-step explanation:
Related Questions
Daniel looks at the prices of 5 guitars. The prices are $137, $159, $127, $188 and $680. These prices contain one extreme value ($680). Which measure of center should Daniel use to describe the prices?
A. Median
B. Range
C. Mean
D. Mean absolute deviation
Answers
Answer:
A. Median
Step-by-step explanation:
Mean and median both are used to measure the central tendency of a given data while range gives us the spread of the data roughly.
Mean is even affected by a single extreme value in the data while median gives us the central value of data even when there are extreme values.
The given set of five prices has one extreme value which will affect the mean. While median is a better option to measure the central tendency of data.
So Daniel will use median to measure the central tendency to describe the prices..
Step-by-step explanation:
Answer is A. Median by jesse
i need help im stuck on this
Answers
Hello There!
Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.
First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.
Next, we multiply pi*radius^2 * height because a cylinder has a height too.
HOW TO SOLVE
First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.
Once we multiply, we get a product of 471.
Our final answer is 471.units^3
Factor by grouping: x^3 + 3x^2 - 25x -75 Which of the following is one of the factors?
Answers
Answer:
Final factor is [tex](x + 3)(x+5)(x-5)[/tex].
Step-by-step explanation:
Given expression is [tex]x^3 + 3x^2 - 25x -75[/tex]
Now we need to factor that expression [tex]x^3 + 3x^2 - 25x -75[/tex] by grouping. So let's make group of first two terms and group of last two terms.
[tex]x^3 + 3x^2 - 25x -75[/tex]
[tex]=(x^3 + 3x^2)+( - 25x -75)[/tex]
factor each group
[tex]=x^2(x + 3)-25(x +3)[/tex]
[tex]=(x + 3)(x^2-25)[/tex]
[tex]=(x + 3)(x+5)(x-5)[/tex]
Hence final factor is [tex](x + 3)(x+5)(x-5)[/tex].
I got the Same answer
Find the distance between the points ( - 16, - 9) and ( - 16, - 18).
Answers
notice, the x-coordinate is the same for both points, thus is a vertical line.
Check the picture below.
To find the distance between the points (-16, -9) and (-16, -18), subtract the y-coordinates, which gives us a distance of 9 units.
To find the distance between the points (-16, -9) and (-16, -18), we can use the distance formula for two points in a Cartesian coordinate system. However, because the x-coordinates of the two points are the same, this means that the line connecting these two points is vertical, and we can simply subtract the y-coordinates to find the distance.
The distance formula in a two-dimensional Cartesian coordinate system is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Since the x-coordinates are identical, the formula simplifies to:
d = |y₂ - y₁|
Applying this to the points given:
d = |-18 - (-9)|
d = |-18 + 9|
d = |-9|
Therefore, the distance is 9 units.
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)
Answers
Answer:
C
Step-by-step explanation:
x(x2 + 5) – 9(x2 + 5)
= x³ + 5x - 9x² - 45
(try to expand one by one of the answer given)
Answer:
x(x2 + 5) – 9(x2 + 5)
Step-by-step explanation:
Question 30
Find the length of the long leg. Leave answer in simplest radical form.
Help plz
Answers
Use SOHCAHTOA. You must use sine or cosine since the hypotenuse is involved, but since you are given both angles, it does not matter which one of them you choose. We'll use sine:
sinx=O/H
sin60=O/14
√3/2=O/14
*Cross multiply*
(14√3)=2O
*Divide both sides by 2*
7√3=O
Hope this helps!!
Answer:
B
Step-by-step explanation:
Since the triangle is right we can use the sine ratio to find TI along with
the exact value of sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{TI}{TR}[/tex] = [tex]\frac{TI}{14}[/tex]
Multiply both sides by 14
TI = 14 × sin60° = 14 ×[tex]\frac{\sqrt{3} }{2}[/tex] = 7[tex]\sqrt{3}[/tex]
Which of these numbers is between 7 and 9?
A. √8
B. √79
C. 3√64
Answers
Answer: It has to be A. 8
Step-by-step explanation:
On Friday, a local hamburger shop sold a combined total of 420 hamburgers and cheeseburgers. The number of cheeseburger sold was three times tge number of hamburgers sold. How many hamburgers were sold on Friday?
Answers
Answer:
315 hamburgers
Step-by-step explanation:
Because 3 times the amount of hamburgers were sold than the cheeseburgers, it is fair to say that 420 burgers is 4 times the amount of cheeseburgers sold.
That means that 420/4 = 105 cheeseburgers were sold.
That means that 105 * 3 = 315 hamburgers were sold.
The total number of hamburgers sold on Friday is 105
How to find the number of hamburgers sold on Friday?Number of Hamburgers sold = h
Number of Cheeseburgers sold = c
h + c = 420
c = 3*h
substitute the value of c in ( h + c = 420 )
h + 3h = 420
4h = 420
h = [tex]\frac{420}{4}[/tex]
h = 105
The number of hamburgers sold is 105
To learn more about solving an equation using the substitution method, refer to:
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Evaluate C(8, 8).
0
1
n
8
Answers
Answer: Second Option
C(8,8)=1
Step-by-step explanation:
We must calculate a combination
The combination [tex]C (n, r) =\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of elements that you can combine and you choose "r" from them.
So
C (8, 8) is the combination of 8 in 8.
Therefore
[tex]n = 8\\r=8[/tex]
[tex]C(8,8)= \frac{8!}{8!(8-8)!}\\\\C(8,8)=\frac{8!}{8!(0)!}\\\\C(8,8)=\frac{1}{1*1}\\\\C(8,8)=1[/tex]
The answer is the second option
The value of [tex]\( C(8, 8) \)[/tex] is 1 because choosing all 8 items from 8 yields only 1 combination.
The expression [tex]\( C(8, 8) \)[/tex] represents choosing 8 items from a set of 8 items without regard to order, which is also known as a combination. Here's how we can evaluate it step by step:
Step 1: Recall the formula for combinations.
The formula for combinations is [tex]\( C(n, k) = \frac{n!}{k!(n - k)!} \),[/tex] where [tex]\( n \)[/tex] is the total number of items and [tex]\( k \)[/tex] is the number of items to choose.
Step 2: Substitute the values into the combination formula.
In this case, [tex]\( n = 8 \) and \( k = 8 \),[/tex] so the expression becomes:
[tex]\[ C(8, 8) = \frac{8!}{8!(8 - 8)!} \][/tex]
Step 3:
Simplify the expression.
[tex]\[ C(8, 8) = \frac{8!}{8!0!} \][/tex]
Step 4:
Recall that [tex]\( n! = n \times (n - 1) \times (n - 2) \times \ldots \times 1 \)[/tex] and [tex]\( 0! = 1 \).[/tex]
[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 1} \][/tex]
Step 5:
Cancel out the common terms.
[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ C(8, 8) = 1 \][/tex]
So, [tex]\( C(8, 8) = 1 \).[/tex]
which equation can be used to solve for b?
Answers
Answer:
First option
b = (8) * Tan (30)
Step-by-step explanation:
Tan (B) = Oppo. / Adj.
Tan (B) = AC/BC
Tan (30) = b / 8
b = (8) * Tan (30)
Answer
First option
b = (8) * Tan (30)
a boat took 4 hours to make a trip downstream with a current of 6 kilometers/hour. The return trip against the same current took 10 hours. How far did the boat travel?
Answers
The boat traveled a distance of 80 km during the whole trip.
This question involves determining the distance a boat traveled based on its travel times with and against a current. Let's denote the speed of the boat in still water as b km/h.
Step-by-step solution:
Given data: Current speed = 6 km/h, Time downstream (with current) = 4 hours, Time upstream (against current) = 10 hours.Speed downstream = (b + 6) km/h.Speed upstream = (b - 6) km/h.The distance (d) traveled downstream is the same as upstream, so:Downstream, distance d = speed × time = (b + 6) × 4
Upstream, distance d = speed × time = (b - 6) × 10
Since the distances are equal:
(b + 6) × 4 = (b - 6) × 10
Expanding and simplifying:
4b + 24 = 10b - 60
84 = 6b
b = 14 km/h
Now, using the downstream speed to find the distance:
Distance, d = (b + 6) × 4 = (14 + 6) × 4 = 20 × 4 = 80 km.
Thus, the boat traveled a distance of 80 km.
The boat traveled 80 kilometers.
To determine how far the boat traveled, let's denote the speed of the boat in still water as B km/h. The current speed is given as 6 km/h.
When traveling downstream, the effective speed of the boat is (B + 6) km/h.When traveling upstream, the effective speed of the boat is (B - 6) km/h.Using the formula speed = distance/time, we get:
Downstream: (B + 6) = D/4Upstream: (B - 6) = D/10We now have two equations:
4(B + 6) = D10(B - 6) = DSetting the right-hand sides of these equations equal to each other:
4(B + 6) = 10(B - 6)
Simplifying this equation:
4B + 24 = 10B - 60
Bringing like terms together:
84 = 6B
Solving for B:
B = 14
Substituting B back into either distance equation, we use D = 4(B + 6):
D = 4(14 + 6) = 4(20) = 80
Therefore, the boat traveled 80 kilometers.
You ask a friend to think of a
number from four to twelve. What
is the probability that his number
will be 8?
Answers
The answer is 1/9 or about 11%.
Answer:8
Step-by-step explanation: it’s right
HELP!!!!!!!!!!!!!
Triangle PQR has vertices P(3,5), Q(-2,6) and R(8,-1). Give the coordinates of the vertices after the translation (x,y)——> (x+4,y - 5)
1. P’(_,_)
2.Q’ (_,_)
3.R’ (_,_)
Answers
Answer:
P'(7,0)Q'(2,1) R'(12,-6)
Step-by-step explanation:
P(3,5)------>P'(3+4,5-5)
P'(7,0)
Q(-2,6)----->Q'(-2+4,6-5)
Q'(2,1)
R(8,-1)------>R'(8+4,-1-5)
R'(12,-6)
Answer:
i think it is the third one c plz give me brainliest
Step-by-step explanation:
Find the volume of the cone in terms of pi.
Answers
Answer:
how to find pi you have to add a lot of math and for a volume for the cone is V=πr2h 3
Step-by-step explanation:
i had did this all in my head.
Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars. After leaving an 18% tip, the amount Jake pays at the restaurant is represented by the following expression in this expression, what does the term 0.18m represent?
m+0.18m
Answers
Answer:
It means meal cost plus the 18% tip
Step-by-step explanation:
Answer:
[tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.
Step-by-step explanation:
We have been given that Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars.
Jake left an 18% tip. The amount Jake pays at the restaurant is represented by the following expression in this expression [tex]m+0.18m[/tex].
We know that Jake's total amount will be equal to cost of his meal plus 18% of the cost of meal.
[tex]\text{Total cost of dinner}=m+(\frac{18}{100}\times m)[/tex]
[tex]\text{Total cost of dinner}=m+0.18m[/tex]
Therefore, the term [tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.
kate has 567 cars she put 77 on each table how many cars does she have left
Answers
Answer:
well how many tables are there?
Step-by-step explanation:
The price of a gallon of unleaded gas was $2.83 yesterday. Today, the price rose to $2.88 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
The percentage increase from yesterday's gas price to today's price is 1.8%.
Explanation:To find the percentage increase from yesterday's price to today's price, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100.
The difference between $2.88 and $2.83 is $0.05. Dividing $0.05 by $2.83 gives us 0.0176. Multiplying by 100 gives us 1.76%. Rounding to the nearest tenth of a percent, the percentage increase is 1.8%.
What is the real part of the complex number 18 - 6i?
• i
• -6i
• 18
•-6
Answers
18 is the real part of the complex number
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
18
Step-by-step explanation:
Given a complex number z = a + bi
where a is the real part the imaginary part is b
Given
18 - 6i then 18 is the real part
In the triangles, and . Which statement correctly compares the angles? Angle G is congruent to angle P. Angle G is smaller than angle P. Angle G is larger than angle P. Angle G is congruent to angle N.
Answers
Answer:
B) Angle G is smaller than angle P.
Step-by-step explanation:
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
I know that's a mouthful and probably sounds really weird but just trust me.
Would appreciate brainliest, new to brainly! good luck!
The correct option is, (B) Angle G is smaller than angle P.
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
What is called triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.A triangle is also a polygon.Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.What is triangle and its types?Triangles are shapes with three sides.There are different names for the types of triangles.A triangle's type depends on the length of its sides and the size of its angles (corners).There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene.
What is triangle shape?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.This property is called angle sum property of triangle.
Learn more about triangle here:
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The graph below is correct for the linear equation y=-3.
True
False
Answers
Answer:
False.
Step-by-step explanation:
The graph that is shown is correct for the equation x= -3. The graph for y= -3 would run vertically, not horizontally.
Answer:
True
Step-by-step explanation:flip it and reverse it its esrever dna ti pilf
SOMEONE PLEASE HELP ME ANSWER THIS
Answers
Answer: 84
Step-by-step explanation:
7 x 3 x 4 = 84
It would be 84.
Hope this helps!
Pls tell me if it is inncorrect and i will revise my answer.
7•3•4=84
There are 20 cups of flour in package of flour, how many muffins can i make from a package of flour if it take 1/4 cup?
Answers
Answer:
80 Muffins.
Step-by-step explanation:
There are 20 cups of flour in package
It takes [tex]\frac{1}{4}[/tex] cup to make one muffin
From a package of 20 cups of flour, you can make:
20 × 1 ÷ [tex]\frac{1}{4}[/tex] = 20 × 4 = 80 muffins
Kevin says that lines p and m will eventually intersect.
Is Kevin correct?
Answers
Answer:
no because they are parallel
Step-by-step explanation:
Find the sum of the measures of the interior angles of each convex polygon decagon
Answers
Answer:
Nvm about those questions the answer is 1440 degrees
Step-by-step explanation:
Select the correct answer. A coin is tossed 5 times in a row. What is the size of the sample space of this experiment? A. 5 B. 7 C. 10 D. 32
Answers
Answer:
32
Step-by-step explanation:
Number of times a coin is tossed up = 5
Number of possible outcomes in a toss of a coin = 2 ( Head or a Tail)
The sample space can be calculated by calculating total number of possible outcomes in 5 tosses of the coin.
Number of outcomes in 1 toss of a coin = 2
Number of outcomes in 2 tosses of a coin = 2 × 2
Number of outcomes in 3 tosses of a coin = 2 × 2 × 2
Number of outcomes in 4 tosses of a coin = 2 × 2 × 2 × 2
Number of outcomes in 5 tosses of a coin = 2 × 2 × 2 × 2 × 2
⇒ Total number of outcomes = 32
Therefore, Size of the sample space = 32
Answer:
I did the calculations and I also got 32.
Step-by-step explanation:
hope this helps!!
Find the value of x
A.
38
B.
62
C.
102
D.
150
Answers
Answer:
x=62
Step-by-step explanation:
You set the two angles equal to each other and solve. See work attached for more.
Answer:
A. 38
Step-by-step explanation:
From the diagram, [tex]s=(2x+26)\degree[/tex] because corresponding angles are equal.
[tex]s+(3x-36)\degree=180\degree[/tex]. the sum of interior angles of a triangle.
By substitution, we obtain;
[tex](2x+26)\degree+(3x-36)\degree=180\degree[/tex]
Group similar terms;
[tex]2x+3x=180+36-26[/tex]
[tex]5x=190[/tex]
Divide both sides by 5.
[tex]x=38[/tex]
Please help I'm very confused
Answers
30 ≥ g [keyword - "no more than"
4 ≤ i [keyword - "at least"]
Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.
log2 11
Answers
Answer:
3.4594
Step-by-step explanation:
To change the base of a logarithm
• [tex]log_{b}[/tex] x = [tex]\frac{log_{c}x }{log_{c}b }[/tex]
where c represents the new base
Changing the base from 2 to 10
[tex]log_{2}[/tex] 11 = [tex]\frac{log_{10}11 }{log_{10}2 }[/tex] ≈ 3.4594
What is the 6th term of this sequence? 8,-12,18-27
Answers
Answer:
-60.75
Step-by-step explanation:
-12 / 8 = -3/2
18 / -12 = -3/2
-27 / 18 = -3/2
This is a geometric sequence with a common ratio of -3/2.
an = 8 (-3/2)^(n-1)
The sixth term is:
a₆ = 8 (-3/2)^(6-1)
a₆ = 8 (-3/2)^5
a₆ = -60.75
Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?
10 hours
5.5 hours
8.5 hours
55 hours
Answers
It will take Steve's friend 6.5 hours to catch up to Steve.
The correct answer is:
e) 6.5 hours.
To calculate this, let's first determine the time it takes for Steve's friend to catch up to him after he starts driving.
Steve's speed = 55 mph
Steve's friend's speed = 65 mph
Relative speed = Speed of Steve's friend - Speed of Steve
Relative speed = 65 mph - 55 mph = 10 mph
Now, since Steve's friend starts one hour later, Steve has already traveled for one hour at 55 mph before his friend starts.
Distance traveled by Steve in one hour = Speed × Time
Distance = 55 mph × 1 hour = 55 miles
Now, when Steve's friend starts driving, he needs to catch up this initial distance of 55 miles.
Time = Distance / Relative speed
Time = 55 miles / 10 mph = 5.5 hours
But we must remember that Steve's friend started driving one hour later than Steve. So, we add this one hour to the time calculated above to find the total time it takes for Steve's friend to catch up to Steve.
Total time = 5.5 hours + 1 hour = 6.5 hours
Therefore, it will take Steve's friend 6.5 hours to catch up to Steve.
Steve travels for one hour at 55 mph before his friend starts driving. By then, Steve's friend needs to catch up the initial distance of 55 miles at a relative speed of 10 mph. This gives us a time of 5.5 hours. However, since Steve's friend started one hour later, we add this one hour to the calculated time, resulting in a total time of 6.5 hours. Therefore, the correct answer is 6.5 hours.
Complete question:
Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?
a.10 hours
b.5.5 hours
c.8.5 hours
d.55 hours
e. 6.5 hours.