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Reasoning A cone with radius 6 and height 9 has its radius quadrupled. How many times greater is the
volume of the larger cone than the smaller cone?l
Answers
Let's see
For initial cone
r=6h=9Volume
1/3πr²h1/3π(6)²(9)3(36)π108π units³For new cone
r=4(6)=24h=9Volume
1/3π(24)²(9)3(576)π1728πSo
1728π/108π16timesAnswer:
16 times
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h[/tex]
Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.
ProofGiven:
radius = 6height = 9Substituting the given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units[/tex]
If the radius is quadrupled:
radius = 6 × 4 = 24height = 9Substituting the new given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units[/tex]
To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:
[tex]\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16[/tex]
So the volume of the larger cone is 16 times greater than the volume of the smaller cone.
f(x) = x g(x) = 1
What is the domain of ( g/f ) (x)?
Answers
Answer:
Step-by-step explanation:
First one- x=0
Second=All real numbers
2/3 - 5/4 + 7/3 whats the4 answer pls
Answers
Answer:
7/4Step-by-step explanation:
2/3 - 5/4 + 7/3
=8/12 - 15/12 + 28/12 (LCM=12)
(8 - 15 + 28)/12
=21/12
=7/4
B
5 in.
a.
(6.257 25) in.
-
b. (6.25π – 12.5√2)in.²
d.
Find the value of x and y rounded to the nearest tenth.
C.
(6.25π- 12.5) in.2
none of these
Answers
Answer:
Step-by-step explanation:
5 in.
a.
(6.257 25) in.
-
b. (6.25π – 12.5√2)in.²
d.
Find the value of x and y rounded to the nearest tenth.
C.
(6.25π- 12.5) in.2
Ida's ice-cream stand has increasing profits each week during the hot summer months. Ida finds that each week during the summer her profits increase by 15% over what they were the previous week. In her first week of business, her profits were $600.How much money will she make in all over 5 weeks
Answers
Answer:
4045.43
Step-by-step explanation:
A rental car company charges $77.50 per day to rent a car and $0.10 for every mile driven. Sydney wants to rent a car, knowing that:
She plans to drive 275 miles.
She has at most $260 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Sydney can afford to rent while staying within her budget.
Answers
The number of days that Sydney can afford to rent while staying within her budget is 3 days.
How many days can Sydney afford to rent?Total budget ≤ (total number of days x cost per day) + (cost per mile x total mile)
$260 ≤ $77.50xx + ($0.10 x 275)
$260 ≤ $77.50xx + 27.50
$260 - 27.50 ≤ $77.50xx
232.50 ≤ $77.50xx
xx ≤ 232.50 / $77.50
xx ≤ 3
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The table shows the solution to the equation |2x - 3| -1 = 2:
Step 1
|2x - 3|= 2 + 1
Step 2
|2x - 3|= 3
Step 3
2x - 3= 3 or 2x + 3 = 3
Step 4
2x = 6 or 2x = 0
Step 5
x = 3 or x = 0
Which is the first incorrect step?
Answers
The first incorrect step is step 2 because this step did not take the two signs positive and negative.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in a mod function;
|2x - 3| - 1 = 2
Step 1:
|2x - 3| = 3
Step 2:
2x - 3 = 3 or 2x - 3 = -3
(after removing mod, we get two same values but opposite in sign)
The first incorrect step is step 2 in which did not take the two sign,
2x - 3= 3 or 2x + 3 = 3 (wrong)
Thus, the first incorrect step is step 2 because this step did not take the two signs positive and negative.
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Determine the marginal distribution of Gender. In paragraph form, how you calculated the marginal distribution. Include your calculations in your explanation.
Answers
The marginal distribution for gender tells you the probability that a randomly selected person taken from this sample is either male or female, regardless of their blood type.
In this case, we have total sample size of 714 people. Of these, 379 are male and 335 are female. Then the marginal probability mass function would be
[tex]\mathrm{Pr}[G = g] = \begin{cases} \dfrac{379}{714} \approx 0.5308 & \text{if }g = \text{male} \\\\ \dfrac{335}{714} \approx 0.4692 & \text{if } g = \text{female} \\\\ 0 & \text{otherwise} \end{cases}[/tex]
where G is a random variable taking on one of two values (male or female).
Which statement best describes the polynomial?
-24x7-12x²-9x+6
OIt is in standard form because the exponents are in order from highest to lowest.
OIt is in standard form because the coefficients are in order from highest to lowest.
OIt is not in standard form because the constant should be the first term.
OIt is not in standard form because it can be further simplified.
Answers
It is in standard form because the exponents are in order from highest to lowest.
The given polynomial is [tex]-24x^{7} -12x^{2} -9x+6[/tex].
We need to determine from the given statements, which statement best describes the given polynomial.
What is the standard form of the polynomial?The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form. The standard form of the polynomial is [tex]f(x)=a_{n} x^{n} +a_{n-1} x^{n-1}+a_{n-2} x^{n-2} +........a_{1}x+a_{0}[/tex].
So, in the given polynomial [tex]-24x^{7} -12x^{2} -9x+6[/tex], the exponents of the variable are in decreasing order.
Therefore, it is in standard form because the exponents are in order from highest to lowest.
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Which is the solution set of the compound inequality 3.5 x minus 10 greater-than negative 3 and 8 x minus 9 less-than 39 negative 2 less-than x less-than 3 and three-quarters negative 2 less-than x less-than 6 2 less-than x less-than 6 2 less-than x less-than 3 and three-quarters
Answers
Answer:
The solution for the compound inequality is x \in(2,6)
Step-by-step explanation:
To find the solution set for these compound inequalities, we need to solve the inequality.
First, we shall solve the inequality
Adding both sides of the equation by 10, we have,
Dividing both sides by 3.5, we get,
Now, we shall solve the inequality ,
Adding both sides of the equation by 9, we have,
Dividing both sides by 8, we get,
The solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.
What is the general equation of a Straight line inequality?
The general equation of a straight line inequalities are -
[y] < [m]x + [c]
[y] > [m]x + [c]
[y] ≥ [m]x + [c]
[y] ≤ [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the following compound inequality -
3.5x - 10 > - 3
8x - 9 < 39
We have -
3.5x - 10 > - 3
8x - 9 < 39
3.5x - 10 > - 3
3.5x > 7
x > 2
AND
8x - 9 < 39
8x < 48
x < 6
Solution inequality -
2 < x < 6
Therefore, the solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.
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Which of the following situations can be defined using an exponential function?
A The value of the stocks decreased by $100 last year.
B The number of bacteria decreases by 7% each hour.
C The number of bacteria increases by 700 each hours.
D The value of the stocks increases by $10 every year you own them.
Answers
The situation which can be defined using an exponential function is "The number of bacteria decreases by 7% each hour".
What is an exponential function?An exponential function is used to represent a situation in which values of an event do not increase at a constant or linear rate.
From the above,
The value of the stocks decreased by $100 last year is a linear function.The number of bacteria increases by 700 each hour is a linear function.The value of the stocks increases by $10 every year you own them is a linear function.Learn more about exponential function:
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Select all the correct answers.
Which expressions represent a quadratic expression in factored form?
x²-x-72
(x+3)(x-7)
-8(x + 56)
(x + 1)(x - 2)
(x-2) + (x + 3)
Answers
Answer:
(x + 3)(x - 7)
(x + 1)(x - 2)
Step-by-step explanation:
The general form of factored equations :
y = (x + a)(x + b) [it can be ±, so don't worry about that part]
===============================================================
Hence, the expressions which are in factored form :
⇒ (x + 3)(x - 7)
⇒ (x + 1)(x - 2)
Anton is drawing a flag of switzerland, which has a square shape, for a school project. if he wants the flag to have sides that are 16 inches long, what will be the area of the completed flag? 64 inches squared 128 inches squared 256 inches squared 512 inches squared
Answers
Considering the side length, the area of the complete square flag will be of 256 inches squared.
What is the area of a square?The area of a square of side length l is given by l squared, that is:
A(l) = l².
In this problem, we have that l = 16 inches, hence the area in square inches is given by:
A(16) = 16² = 256.
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If a is real and the product of (a+6i)(5-3i) is a real number, the find a.
PLS HELP ASAP WILL MARK BRAINLIEST
Answers
Answer:
5a−3ai+30i+18
Step-by-step explanation:
i just did this
Find the value of x.
Answers
Answer:
125 minus 81 will give me 34°
Answer:
x = 44°
Step-by-step explanation:
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Part a
describe the process you could use to find the probability that jake will earn at least 30 points on a throw, given that he hits the target? note: assume that it is equally likely that he will hit any region in the target.
Answers
The probability that Jake will earn at least 30 points on a throw is 0.335
How to describe the process?The attached image represents the missing part of the question.
From the attached image, we can see that:
For Jake to earn at least point, he must hit the three circles (starting from the inner circle)
The radius of the yellow circle is:
Radius = 3
While the width of the other circles is:
Width = 4
The total area of the sections that give a point of at least 30 is:
A₁ = π * (3 + 4 + 4)² = 121π
The total area of all the sections is:
A₂ = π * (3 + 4 + 4 + 4 + 4)² = 361π
The probability of getting at least 30 points is:
P(At least 30) = 121π/361π
Evaluate
P(At least 30) = 0.335
Hence, the probability that Jake will earn at least 30 points on a throw is 0.335
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The scatter plot below shows the number of enrollments, N, in a sports club, t years after the year 2005.
The equation of the line of best fit is
N = 62t + 35.
What does the why intercept of the line of best fit represent?
A. The number of enrollments in the year 2006 were 97
B. The number of enrollments in the year 2005 were 35
C. Each year the number of enrollments increases by 35
D. Each year the number of enrollments increases by 62
Answers
I did this on my test
pls answer asap, thanks!!
Answers
Since the amount is compounded monthly, the amount would triple after 26 months
Since the money is compounded monthly, we use the compound interest formula
How to calculate compound interestThe amount obtained on compound interest is given by A = P(1 + r)ⁿ where
P = present value, r = interest rate and n = timeNow, since you deposit an amount of $1000 at an interest rate of 3.15 % per year compounded monthly and an extra $75 added monthly after n month, the amount is A = A' the amount compounded monthly + the extra amount monthly A"
Amount compounded monthly
Since A' = P(1 + r)ⁿ where
P = initial amount = $1000, r = interest rate = 3.15 %/12 (since it is compounded monthly) = 0.002625 and n = number of monthsSo, A' = P(1 + r)ⁿ
= 1000(1 + 0.002625)ⁿ
= 1000(1.002625)ⁿ
Extra amount added monthly
Also, since $75 is added monthly, after n months, A" = 75n
Total amount after n months
So, the total amount added is A = A' + A"
= 1000(1.002625)ⁿ + 75n
Time for amount to tripleSince we require the time when the initial amount would triple, so, A = 3A'
= 3 × 1000
= 3000.
So,
A = 1000(1.002625)ⁿ + 75n
3000 = 1000(1.002625)ⁿ + 75n
3000 - 75n = 1000(1.002625)ⁿ
The solution of the above equation is obtained graphically. Find the graph in the attachment. They intersect at (25.736, 1069.797)
So, n = 25.736
≅ 26 months
So, the amount would triple after 26 months
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Solve 2x+6 ≤ 10 or 2x + 8 > 20.
A. x ≤2 or x>6
OB. x < 1 or x > 2
OC. x ≤ 1 or x > 6
OD.
2 and x > 2
Answers
Answer:
A. x ≤2 or x>6Step-by-step explanation:
2x+6 ≤ 10 or 2x + 8 > 20
⇔ 2x ≤ 4 or 2x > 12
⇔ x ≤ 2 or x > 6
how many Years are in 1,000
Answers
The number of years in 1000 days is = 2 . 74 years .
How many Years are in 1,000 day?Division is the arithmetic operation that is used to determine the quotient of a number. Division parts a number into equal parts with another number.
Number of years in 100 days = 1000 / 365
= 2 . 74 years
Here is the complete question:
how many Years are in 1,000 days
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Indicate the most appropriate if-then statement that the english sentence represents: people 18 or older can vote in a federal election
Answers
The most appropriate if-then statement that the english sentence represents is: B. If a person is 18 years old or older, then the person can vote in Federal elections.
What is Federal Election?
Federal election can be defined as the way in which a person vote for a preferred.
For a person to be eligible to vote during election, such person must be 18 years old or older.
The if -then statement is: If a person is 18 years old or older, then the person can vote in Federal elections.
Therefore the correct option is B.
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Which equation is represented by the graph below?
Answers
Answer:
1
Step-by-step explanation:
this is becasue the slope is positive
A cylinder has a height of 4 meters and a radius of 1.5 meters. What is the approximate radius of a sphere that has the same surface area
as the cylinder?
OA. 2.0m
OB. 4.1 m
O c. 1.7m
OD. 2.9 m
Answers
If the surface area of the cylinder is 12π square meters. Then the radius of the sphere will be 1.7 meters.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a height of 4 meters and a radius of 1.5 meters.
Then the approximate radius of a sphere that has the same surface area as the cylinder.
We know that the Surface area of the cylinder will be is given as
Surface area = 2πrh
Surface area = 2 x π x 1.5 x 4
Surface area = 12π square meters
Then we have
Surface area of sphere = surface area of cylinder
4πr² = 12π
r² = 3
r = 1.7 meters
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Answer:
2.0 m
Step-by-step explanation:
A. 2.0 m
O is the center of the regular octagon below. Find its area. Round to the nearest tenth
if necessary.
Answers
Answer:229.1
Step-by-step explanation: to much work I thought to hard that’s the answer your welcome buddy
A family purchases a Light sphere to be used out on their patio. The diameter of the sphere is 20 inches. What is the volume of the light sphere? Use 3.14 for pi. Enter your answer as a decimal and round only your final answer to the nearest hundredth.
Two people had different answers but had 5 stars. So can someone explain how to solve this question correctly. Thank you in advance
Answers
Answer:
The answer is 4188.79 ft^3.
Step-by-step explanation:
The formula is V=4/3πr^3. The radius is 10, turning that into V=4/3π10^3. 10^3 is 1000, and 1000 times 4/3 is 1333.33. 1333.33 times 3.14 (or π) is equal to 4188.79 ft ^3 rounded to the nearest 100th. I hope this helps! :)
if 7544644555- x is 45000 whats the value of x
Answers
Answer:
Step-by-step explanation:
45000+7544644555=x
x=7544689555
Answer:
x = 7544599555
Step-by-step explanation:
First let's make an equation :
7544644555 - x = 45000
Now to make x the subject and positive :
We add x to both sides :
7544644555 = 45000 + x
Now we subtract 45000 from both sides :
7544644555 - 45000 = x
x = 7544599555
Hope this helped and brainliest please
The speed of light is roughly 186,000 miles per second. How many minutes does it take for light to arrive from the sun, which is 93,000,000 miles away?
Answers
Answer:
8.3 minutes
Step-by-step explanation:
93,000,000 m/186,000 m/s = 500 s
500/60 = 8.333333
−6×(−8)= what is the answers
Answers
Answer:
48
Step-by-step explanation:
when you multiply a negative times a negative (or divide a negative by a negative), it equals a positive!
-6 times -8 will equal 48!
let me know if you have any questions :)
Pls help I literally have no clue what this means
Find the missing number based on the description
below:
“12 less than 7 times a number is the same as 32 less than the product of -3 and the number”
A.-5
B.10
C.-2
D.-1
Answers
Answer:
I think the answer is c -2
Step-by-step explanation:
but don't quote me on that and if it's wrong i truly am sorry
Answer:
Step-by-step explanation:
Question:
A circular frame has a diameter of 10 inches. Identify the area of the mirror that the frame
can hold. Use 3.14 for TT.
Answers
The frame can hold a mirror with an area of 78.5 in².
How to find the area?
The area for a circle of diameter D is given by the formula:
[tex]A = pi*(D/2)^2[/tex]
Where pi = 3.14
Here we know that the diameter is 10 inches, replacing that in the area equation we can get:
[tex]A = 3.14*(10in/2)^2 = 3.14(5in)^2 = 78.5 in^2[/tex]
So the frame can hold a mirror with an area of 78.5 in².
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