The Volume of the cone with base radius 5cm and Total Surface Area 907cm² is 1374.5cm³.
The Volume of the cone is denoted by
V = (1/3)*π*r²*h
where r = base radius
h = height of the cone
In the given question
the base radius r = 5cm
the total surface area of the cone = 907cm²
Total Surface Area of the cone is denoted by = πr(L+r)
where L is the slant height .
Step1: we first calculate Slant height "L"
Substituting the values in Total Surface Area formula we get
907 = π*5(L+5)
Simplifying further we get
L+5 = 907/5π
L = 907/5π - 5
L = 57.77 - 5
L = 52.77
Step2: Use L to find the height of cone
Using Pythagoras Theorem
L²=r²+h²
(52.77)² = (5)² + h²
Simplifying further we get
2784.67 = 25 + h²
h² = 2759.67
h = √2759.67
h = 52.53
Step 3: use h to find the Volume
Substituting the value of h and r in Volume formula we get ,
V = (1/3)*π*5²*52.53
= (1/3)*(3.14)*25*52.53
= 4123.605 / 3
= 1374.535
≅1374.5
Therefore , the volume of the cone is 1374.5cm³.
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A batting average is the ratio of hits to at bats batting averages are expressed as a decimal rounded to the nearest thousandth show two differnt ways if finding how much grater derek jeters batting average than jorge posadas batting average express as a percent
Derek Jeter average was 4.9%greater than Jorge Posada 4.9% expressed as a percent.
To express decimal as percent we need to multiply the decimal with 100 .
The average or mean is defined as the sum divided by the frequency.
Here we have four averages given in decimal
Derek Jeter average in percentage =0.334*100=33.4%
Alex Rodriguez average in percentage=0.286*100=28.6%
Jorge posada average in percentage =0.285*100=28.5%
Hideki Matsui average in percentage=0.274*100=27.4%
From the above percentages Derek Jeter average was 4.9%greater than Jorge Posada =33.4-28.5=4.9%
Or we can say it as Derek peter percentage was 14.68% greater than Jorge Posada on a scale of 100 percentage.
Hence Derek peter percentage was 14.68% greater than Jorge Posada on a scale of 100 percentage and Derek Jeter average was 4.9% greater than Jorge Posada 4.9%.
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(c) Using your knowledge and abilities show Andrew how to evaluate the expression correctly. State the
correct value.
The correct value of the expression is 9 and to evaluate correctly the multiplication of 2 and 0 that 2(0) must be written 0.
What is an expression?An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.
The constraint of expression is represented as = or <, >.
Given the expression,
x² - 2(x - 3) when x = 3
⇒ x² - 2(x - 3)
⇒ 3² - 2(3 - 3)
⇒ 3² - 2(0)
⇒ 9 - 0
⇒ 9.
Hence "The correct value of the expression is 9".
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The given question is an incomplete complete question shown below in the image ;
Calculate.
5*10^9/2*10^4
A parking area at a department store is shaped like a quarter circle with a radius of 123 meters. Due to the fact that the department store is to be rebuilt, the parking area must be temporarily reduced to 1/3 of its original area. What is the radius of the new parking area assuming it is still a quarter circle?
a. 91 m
b. 71 m
c. 77m
d. 82 m
The radius of the new parking area is 82 meters
How to determine the radius of the new parking area?The radius of the old parking area is given as
Radius, R = 123 meters
From the question, we understand that:
The parking area must be temporarily reduced to 1/3 of its original area
This means that
New Radius = Old radius - Old radius * 1/3
So, we have
New Radius = 123 meters - 123 meters * 1/3
Evaluate the product
So, we have
New Radius = 123 meters - 41 meters
Evaluate the difference
New Radius = 82 meters
Hence, the radius of the new parking area is 82 meters
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Simplify the following.
a)
3x y x 2x®
Answer:
Hi i think your question implies that
Step-by-step explanation:
3xy × 2x
=6x²y
pls rate as brainliest
Tyrone makes a scale drawing of his backyard. The scale from the backyard to the
drawing is 2 ft to 1 in. The width of the patio on the drawing is 8 in. What is the
width of Tyrone's actual patio? Show your work.
Answer:The width of the patio on the drawing is 8 in.
Step-by-step explanation:
Problem Solving
Use the table for Exercises
13-16 that shows the average
weights of popular dog breeds.
13. Complete the table.
14. Which weight(s) have a prime
factorization of exactly three
factors?
Breed
Cocker Spaniel
German Shepherd
Labrador Retriever
Beagle
Golden Retriever
Siberian Husky
Weight (lb)
20
81
67
25
70
50
Prime Factorization
Prime numbers are those numbers that are divisible only by the number itself and by 1. Such numbers are 2, 3, 5, and 7 etc.
Factorization is when we write a given mathematical term in product of its various factors. Suppose we are provided with a mathematical expression of:
x^2 + 3x + 2
We will undergo its Factorization and write the expression in its possible factors:
( x + 1 ) ( x + 2)
By multiplying these factors, we will get the actual expression x^2 + 3x + 2.
Prime Factorization is a method of identifying which prime numbers multiply together to give the original value/expression.
Suppose we have a number 60, then the prime factors of it will be:
60
6 x 10
2 x 3 2 x 5
In the problem statement above, we are provided with some popular dog breeds, and we are expected to find the prime factors of each of the given weights of the breed.
The weights that have a prime factorization of exactly three number are as follows:
Prime factors of 20 (Cocker Spaniel)
= 2 x 2 x 5
Prime factors of 50 (Siberian Husky)
= 2 x 5 x 5
Prime factors of 70 (Golden Retriever)
= 2 x 5 x 7
Weights that have the same number in their prime factorization are:
Prime factors of 81 (German Shepherd)
= 3 x 3 x 3 x 3
Prime factors of 25 (Beagle)
= 5 x 5
So, the prime factorization of the weights of the dog breeds are being found. While Labrador Retriever 67 is a prime number itself.
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Nick was scuba diving at -32 1/2 feet. If he descends another 8 3/5 feet, what is his location?
Answer:
-41.1 feet
Step-by-step explanation:
-32.5-8.6=-41.1
1/2=0.5
3/5=6/10=0.6
APR include:
the principle and the term on the loan
finance and interest charges on the loan
finance charges on the loan
the principle and the interest on the loan
Interest on the loan
APR include: Interest on the loan
What does APR mean?
The APR which means annual percentage rate, is the interest rate on the loan, it is expressed in annual terms which is normally compounded monthly, by monthly compounding I mean the interest is computed on monthly basis.
APR has does not have anything to do with the principle and term of the loan since the principle is the loan amount and the term is the number of periods that the borrower is allowed to make repayments until the loan is fully repaid
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three times the smaller of three consecutive even integers is four less than twice the larger
The required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.
Given:
The statement is three times the smaller of three consecutive even integers is four less than twice the larger
According to given question we have
Let the even integers be x and x + 2 .
Here, x is the smaller integer
(x + 2) the bigger integer.
By the equation is
3x =2(x + 2)-4
compare the like terms we get
x=4-4
x=0
The smaller integer=0
The bigger integer= 0+2=2
Therefore, the required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.
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Given g(x)=5x-3g(x)=5x−3, find g(-2)g(−2).
Reasoning Relation r has one element in its domain and two elements in its range. Is r a function? Is the inverse of r a function? Explain.
Relation r is not a function and Inverse function because a single
input gives several outputs.
What is the Reasoning Relation R?A subset of AB is a relation between two sets A and B. Consequently, an ordered pair (a,b) of a relation R is one where a=A and b=B. If (a,b)R, we say that it is connected to and write aRb.Sets are defined as a collection of well-defined objects. Relation refers to a relationship between the elements of 2 sets A and B. It is represented by R. We say that R is a relation from A to A, then R ⊆ A×A1. Identity Relation: In an identity relation, every element is related to itself. Its notation is I = (a, a), A.
2. Empty relation: In an empty relation, there will be no connection between the set's components. This is a subset of.
3. Reflexive relation: Each element is mapped to itself in a reflexive relation. If (a, a) R for all aR, a relation R in a set A is automatic.
4. An irreflexive relation exists when two elements are not related to one another.
5. Inverse relation: An inverse relation exists when a set contains elements that are inverse pairs of those in another set. For instance, R-1 = (q,p), (s,r) if A = (p,q), (r,s), etc.
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Which of the following functions are continuous for all real numbers?
f(x) = e²
g(x)=√x
Choose 1 answer:
f only
g only
Both f and g
Neither f nor g
These two triangles are similar .Find side lengths a and b .Note The two figures are not drawn to scale
Wayne charges a flat photography fee of $100 to take pictures. He also charges $35 per hour. If Wayne made $240 to take pictures at an event, how many hours did he spend taking pictures at the event?
Answer:
100 + 35x = 240
240 - 100 = 140 = 35x
140/35 = 4
Step-by-step explanation:
4 hours, not a bad pay o.o
Answer:
4 Hours
Step-by-step explanation:
Let y=money
Let x= Hours
y=mx+b
240=35x+100
minus 100
140=35x
divide 35
4=x
What is the image point of (-1,8)after a translation right 1 unit and up 2 units?
Answer:
so your first number in your plotted points is the x value and the next is the y value as shown here (x,y) so if it needs to go up 2 and right 1 what we do is increase the -1 to a 0 because you are moving right on the graph which makes it become a positive. now if you were to move up 2 that is your y coordinate because y controls up and down movement while x controls left and right movement so you would increase the 8 to 10 so you'll find no coordinates would end up being (0,10)
x
10
8
What is the value of x?
X =
your ans
Step-by-step explanation:
the value of x is 6
The value of x will be 6 for the given triangle.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that in the right-angle triangle, the hypotenuse is 10, the base is 8 and the perpendicular is x.
The value of x will be calculated as:-
x² = 10² - 8²
x² = 100 - 64
x² = 64
x = √36
x = 6
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There are two teams of customer service representatives at a call center for a software company. The call center manager wants to give a prize to the team who most consistently has customer service calls with the least total call times. The two graphs show the distributions of the total call times of the two different teams. Team A 0 3 4 5 1 2 Total Call Times (minutes) Team B 0 I 2 3 4 5 Total Call Times (minutes) Which of the following provides a correct argument in support of the team that should be awarded the prize?
The correct argument in support of the team that should be awarded the prize is; Team A because their distribution of total call times is skewed to the right, which shows the majority of total call times are less than the mean.
How to interpret Skewed Graphs?
A skewed distribution is a distribution which is non-symmetric and also it has no mirror-imaging.
One common characteristic of skewed distributions, is that one tail of the distribution will be quite longer or drawn out relative to the other tail.
A distribution is said to be skewed right when one of the tail is on the right side.
A distribution is said to be skewed left when one of the tail is on the left side.
Now, we want to find the correct argument in support of the team that should be awarded the prize.
Looking at the two graphs of team A and B, we see that team A has a distribution that is skewed to the right which means majority of total call times are less than the mean.
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Please help me please help me
Answer:
the third option I think it says (-1,4)
Step-by-step explanation:
So the directions are basically asking to turn in the paper 3 times ending up in the 1st quadrant. Because 90*3 equals 270 degrees. There would be only one point in the negative and there are 2 options. So, we would immediately know that the first option or the last option is wrong. I don't really know how to explain this without drawing so if you could try turning your paper 3 times then you'll see what I mean. Comment if you need any more help. Or if you have any questions. My explanation is pretty bad I apologize.
Please help is this true or false
Answer:
True
Step-by-step explanation:
Solve the equation using multiplication or division.
-7y=28
Oy=-4
Oy = 4
O y = 14
O y = 35
Answer:
y=-4
Step-by-step explanation:
-7y=28
DIVIDE BY -7
28/-7=-4
Answer=-4
Melvin ordered a cinnamon roll, 3 doughnuts, and 2 dozen doughnut holes. The sales tax was $0.72. He paid with a $20 bill. How much change should Melvin receive from a $20 bill? Responses A $9.66 B$10.34 C$11.78 D$11.06
The amount of change that Melvin would receive from a $20 bill is equal to: C. $11.78.
How to determine Melvin's change?In order to determine the amount of change that Melvin would receive from a $20 bill, we would first of all calculate the total cost before tax.
For the cinnamon roll, we have:
Cinnamon roll's cost = $2.59.
For three (3) doughnuts, we have:
Doughnut's cost = 0.95 × 3
Doughnut's cost = $2.85.
For two (2) dozen doughnut holes, we have:
Doughnut hole's cost = 1.75 × 2
Doughnut hole's cost = $3.5.
Total cost = $2.59 + $2.85 + $3.5
Total cost = $8.94
Next, we would determine the new cost after applying sales tax:
New cost = 8.94 - 0.72
New cost = $8.22.
Now, we can determine Melvin's change:
Change = Dollar bill - New cost
Change = $20 - $8.22.
Change = $11.78.
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Answer:
4 C$11.78
Step-by-step explanation:
3. An example of an irrational number is _____.
A. -17 square root
B. square root of 16
C, -9 square root
D. square root for 1
△LMN with vertices L(4, 8), M(4, 3), and N(8, 8) is rotated 270° clockwise about the origin.
What are the coordinates of L′?
The image of the triangle at point L is L' = (-8, 4)
How to determine the image of the triangle when rotated?The vertices of the triangle are given as:
L(4, 8), M(4, 3), and N(8, 8)
The transformation rule is given as
270 degrees rotation
The rule of 270 degrees rotation is
(x,y) = (-y , x)
When the above rule is applied to the vertices of the triangle, we have:
L' = (-8, 4)
Hence, the image of the triangle at point L is L' = (-8, 4)
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Find the highest common factor (HCF) of 90
I need help…………………..
Answer:
I believe its 3.5, 6
Step-by-step explanation:
the right arrow points to the last box and after 4 it goes to 5 then 6
the left arrow points at the 3 quarters between 4 and 2 so it's technically 3.5
hope it helps!
The density of a certain material is such that it weighs 430 kilograms per cubic foot
of volume. Express this density in grams per cup. Round your answer to the nearest
whole number.
Density ( in grams per cup )= 3593
Density( in kilograms per cubic foot )=430
1 kilogram per cubic foot = 8.36 grams per cup
Density ( in grams per cup )= 3593
The density of a material indicates the density of that material in a specific area. The density of a material is defined as its mass per unit volume. Density is a measurement of how closely matter is packed together. It is a distinct physical property of a specific object. Archimedes, a Greek scientist, discovered the density principle. If you know the formula and understand the units, calculating density is simple. Density is represented by the symbol, which can also be represented by the letter D.
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2+z×−1/3=3 please help
2 + z * −1/3 = 3
if that is how it is grouped, your answer is -3
Evaluate each logarithm.
log₇49
After evaluating the logarithm log ₇ 49, we get the result as 2.
The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.
For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output. The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.
We need to evaluate log ₇ 49
x = log₇ 49
We can also write it as:
7ˣ = 49
7ˣ = 7²
Comparing the bases, we get that:
x = 2
Therefore, after evaluating the logarithm log ₇ 49, we get the result as 2.
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Need an answer!! Please and thank you.
Answer: 110 degrees
Step-by-step explanation:
We know that all the angles of a triangle add to 180 degrees. Notice how there are already 60 and 50 degrees on the triangle. In order to find the last angle, we subtract 110 (60+5) from 180 to get 70.
Now, we know that the angle of a straight line is 180.
So, in order to find <BCD, take 70 and subtract it from 180.
Doing this, we find that m<BCD is 110 degrees