The relationship between the volume of a sphere and the volume of a cylinder is: the volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.
In this question we need to describe the relationship of the volume between the volume of a sphere and the volume of a cylinder.
Consider a cylinder with radius r and height h.
we know that the formula for the volume of cylinder is,
V1 = π * r² * h
Consider a sphere with radius r1.
We know that the formula for the volume of sphere is,
V2 = 4/3 * π * r1³
If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r1 = r and h = 2r
V2 = 4/3 * π * r³
And V1 = π * r² * (2r)
V1 = 2 * π * r³
V1 = 2 * 3/4 * V2
V1 = 3/2 * V2
volume of cylinder = 3/2 * volume of sphere
Therefore, the volume of a sphere = 2/3 * the volume of a cylinder
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Re-write the quadratic function below in Standard Form
y= -9(x - 1)2 – 6
I need to know the vertex of this parabola can someone help me ASAP
Use the graph of the function f(x) = (x + 1)² + 2. Identify the vertex and
the axis of symmetry.
Hey! Please answer this fast, it’s due soon. It’s fractions
Answer:
3/12 - 8/12= 5/12
10/12 - 5/12= 5/12
Gllberto invests $10,000 in a savings account that pays 4.75% simple interest. If Gilberto
makes no withdrawals or deposits to the account, how much will be in the account after 7
years?
Answer:
$13,325
Step-by-step explanation:
A rocket is launched from a tower. The height of the rocket, y in feet, is
related to the time after launch, x in seconds, by the given equation. Using
this equation, find the maximum height reached by the rocket, to the nearest
tenth of a foot.
y = -16x2 + 212x + 139
Answer:
y = 841.25 feet
Step-by-step explanation:
Given that,
The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation as follows:
[tex]y = -16x^2 + 212x + 139[/tex] ....(1)
We need to find the maximum height reached by the rocket.
For maximum height, put dy/dx = 0
So,
[tex]\dfrac{d(-16x^2 + 212x + 139)}{dx}=0\\\\-32x+212=0\\\\x=\dfrac{212}{32}\\\\x=6.625\ s[/tex]
Pu x = 6.625 in equation (1).
[tex]y = -16(6.625)^2 + 212(6.625) + 139\\\\y=841.25\ feet[/tex]
So, the maximum height reached by the rocket is equal to 841.25 feet.
help fast pls .. Find the equation for g(x) by substituting the known point (1, 4) and solving for k.
Answer:
6=k×2
k=3
g(x)=k f(x)
g(x)=3 |x|
Find the second base of a trapezoid with an area of 96 inches, a height of 8 inches, and a 1st base measuring 11 inches.
Answer:
13
Step-by-step explanation:
11+x=y
yx8=z
z/2=96
96x2=192
192/8=24
24-11=13
x=13
Which of the following could be used to estimate 75 -32?
A. 80 - 30
B. 70 - 30
C. 80-40
D. 70 - 40
Answer:
b
Step-by-step explanation:
the answer when not rounded is 43.
hello please help thanks
Answer:
D
Step-by-step explanation:
it states that the snikholes are from underneath when the soil it lose
A store gives reward points for every dollar
spent. The number of reward points varies
directly with the total amount spent.
Sofia spends $300 and receives 15 reward
points.
Juan spends $900. He receives reward points
at the same rate as Sofia.
How many more reward points will Juan
receive than Sofia?
Please help me I give u 14 points please only correct answers ,!!!
SOMEONE PLEASEEEE HELPPPP!?!!?!?!!?!?!
Answer:
3/35, 12/35, 16/35, 4/35
Step-by-step explanation:
The box has a total of 35 squares.
The pink fills 3 squares so the pink section is: 3/35
The dark blue section covers 12 squares
So 12/35 is another fraction.
The light blue area covers 16 squares so another fraction is 16/35
The white covers 4 squares
So the last possible fraction is 4/35.
Subtracting fractions with unlike denominators
Answer:
Answer is 9/8
Step-by-step explanation:
18/8-9/8=9/8
Answer:
9/8
Step-by-step explanation:
9/4 - 9/8
9/4 x 2 = 18/8 to match denominators
18/8 - 9/8
= 9/8
Failing please please
Answer:
A = 102m squared (Brainiest?)
Equation = b x h / 2
Step-by-step explanation:
A = (12 x 17) / 2
A = 204 / 2
A = 102m squared
Simplify completely the quantity 5 times x to the third power plus 10 times x to the 2nd power plus 15 times x all over 5 times x
Answer:
x²+2x+3
Step-by-step explanation:
We are to simplify the expression;
5x³+10x²+15x/5x
Factor out 5x from the numerator
= 5x(x²+2x+3)/5x
5x will cancel out both at the top and bottom to have;
x²+2x+3
Factorize
x²+2x+3
Hence the simplified form is x²+2x+3
Three friends are sharing 4 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
Answer:
3/4 of a cup or .75 of a cup
Step-by-step explanation:
What is the area of the parallelogram?
3
2
The cost of a small salad at the deli was marked up 30% after a recent drought destroyed most of the lettuce crop. Determine the new cost if the price prior to the drought was $1.80. Then find the sales tax of the new price if the tax rate is 6%.
Answer:
The new cost is $ 2.34 and sales tax is .14. Total cost is $2.48
Step-by-step explanation:
1.80 x 1.3 = 2.34
2.34 x .06 = .14
Add the two together for the total
A parabola has a vertex (-3, -2) and contains the point (-5, 6). Write the equation for this parabola in vertex form.
Answer:
[tex]y = 2(x +3)^2 -2[/tex]
Step-by-step explanation:
Given
[tex](h,k) = (-3,-2)[/tex] --- vertex
[tex](x,y) = (-5,6)[/tex] --- point
Required
Determine the equation
The general form is:
[tex]y = a(x - h)^2 + k[/tex]
First, we solve for a:
Substitute [tex](h,k) = (-3,-2)[/tex] and [tex](x,y) = (-5,6)[/tex] in [tex]y = a(x - h)^2 + k[/tex]
[tex]6 = a(-5 - (-3))^2 - 2[/tex]
[tex]6 = a(-2)^2 - 2[/tex]
[tex]6 = 4a - 2[/tex]
Solve for a
[tex]4a = 6 + 2[/tex]
[tex]4a = 8[/tex]
[tex]a = 2[/tex]
So:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = 2(x - (-3))^2 -2[/tex]
[tex]y = 2(x +3)^2 -2[/tex]
A cube is 0.5 cm on all sides, what is the surface area of the prism?
Answer:
[tex]0.5^{3}[/tex]=0.125
Step-by-step explanation:
.5*.5*.5
Number 1 help please
Answer:
D
Step-by-step explanation:
the figure is in the origin therefore no reflection will affect the shape
an average speed of 57 km/h and the remaining 55 km at an average speed of 110 km/h. Find the average speed of the car for its entire journey.
Answer:
83.5km/h
Step-by-step explanation:
To find average you have to add up all the numbers in a given set then divide it by the amount of numbers in that set
Which of these does NOT represent the distance a car travels when going 55 miles per hour?
Answer:
the first one
Step-by-step explanation:
just trust me
Find the slope between the two points:
(3,-2) and (-5, 2)
Answer:
the slope is -2
Step-by-step explanation:
please help me if you do not know do not answerr
Answer:
Quadratic
Step-by-step explanation:
Example of linear is 2x + 3
Example of quadratic is x² + 2x + 3
Example of cubic is x³ + 2x² + 3x + 4
Example of quartic is x⁴ + 2x³ + 3x² + 4x + 5
A gardener can increase the number of dahlia plants in an annual garden by either buying new bulbs each year or dividing the existing to create new plants. The table below shows the expected number of bulbs for each method.
Need Part A-C
Answer:
Step-by-step explanation:
Part A
If the gardener increases the number of dahlia plants by buying the new bulbs,
Let the equation representing year (x) and number of bulbs purchased (y) is,
y = mx + b
Here, m = Number of plants purchased each year
b = Initial numbers of plants
For x = 0, and y = 6,
6 = m(0) + b
b = 6
For x = 1, y = 56,
56 = m(1) + 6
m = 50
Therefore, equation for this method of increasing the numbers of plants will be,
y = 50x+ 6
Let the equation for the second method of increasing the number of plants is represented by the equation,
y = a(b)ˣ
From the data given in the table,
For x = 0, y = 6
6 = a(b)⁰
a = 6
For x = 1, y = 12
12 = 6(b)¹
b = 2
Therefore, equation representing the second method (By diving the existing bulbs) will be,
y = 6(2)ˣ
Part B
By substituting the value of x = 10 years,
Method - 1
y = 50(10) + 6
y = 506 plants
Method - 2
y = 6(2)¹⁰
y = 6144 plants
Part C
After 5 years number of plants by method - 1,
y = 50(5) + 6
= 256
After 5 years number of plants by method - 2,
y = 6(2)⁵
y = 192
Similarly, After 10 years number of plants by method - 1,
y = 50(10) + 6
= 506
By method - 2,
y = 6(2)¹⁰
y = 6144
Since, number of plants after 5 years are less by the second method as compared to method 1
But after 10 years second method results the number of plants more than method-1,
Therefore, gardener should adopt method 2 for increasing the numbers of plants.
Functions are used to represent tables and equations.
(a) The equation of the functions
The function of "Buy New Bulbs" is a linear function with an initial value of 6, and a rate of 50 (i.e. 56 - 6)
So, the equation is:
[tex]y = 6 + 50x[/tex]
The function of "Divide Existing Bulbs" is an exponential function with an initial value of 6, and a rate of 2 (i.e. 12/6)
So, the equation is:
[tex]y = 6(2)^x[/tex]
Hence, the equations of the functions are [tex]y = 6 + 50x[/tex] and [tex]y = 6(2)^x[/tex]
The expected number of bulbs in 10 years
This means that x = 10.
So, we have:
[tex]y = 6 + 50x =6 + 50*10 = 506[/tex]
[tex]y = 6(2)^x =6 *2^{10} = 6144[/tex]
Hence, the expected number of bulbs in 10 years for both functions are 506 and 6144, respectively
Compare the expected number of bulbs in 5 and 10 years
When x = 5.
We have:
[tex]y = 6 + 50x =6 + 50*5 = 256[/tex]
[tex]y = 6(2)^x =6 *2^5 = 192[/tex]
When x = 15
We have:
[tex]y = 6 + 50x =6 + 50*15 = 756[/tex]
[tex]y = 6(2)^x =6 *2^{15} = 196608[/tex]
By comparison;
In 5 years, the expected number of bulbs for the function of "Buy New Bulbs" is greater than the function of "Divide Existing Bulbs", however the expected number of bulbs for the function of "Buy New Bulbs" is less than the function of "Divide Existing Bulbs" in 15 years
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A company that recently changed it slogan is hosting an optional big company picnic.Some members of the marketing team are eating together at the picnic and sharing their thoughts on the new slogan. they find that 80% of them like the new slogan. for which population is 80% a legitimate estimate of the percent of employees who like the new slogan?
Answer:
Only those members of the marketing team eating together at the picnic
Step-by-step explanation:
The members of the marketing team eating together at the picnic weren't randomly selected from a larger population. They may not be representative of employees (marketing team or not) beyond their group.
Only members of the marketing team eating together depicts a 80 percent legitimate estimate of the percent of employees who like the new slogan.
What is an Estimate?This can be defined as the approximate calculation of a set of data or values.
The members of the marketing team eating together will represent 80 percent legitimate estimate because they weren't randomly selected from a larger population.
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What are the domain and
range
of an exponential parent function?
A. The domain is positive real numbers (x > 0), and the range is all
real numbers.
B. The domain is all real numbers, and the range is nonnegative real
numbers (y≥ 0).
C. The domain is nonnegative real numbers (x≥ 0), and the range is
all real numbers.
D. The domain is all real numbers, and the range is positive real
numbers (y > 0).
Answer: it’s D
Step-by-step explanation:
The domain and the range of an exponential parent function mean that the domain is all real numbers and the range signifies positive real numbers y > 0.
What is an exponential parent function?The simplest parent function of an exponential function takes the form:
[tex]\mathbf{f(x) = p^x}[/tex], where p refers to the base.
So, if we have a number such that x = 3 and the base is 2
f(3) = 2³f(3) = 6Therefore, we can conclude that the domain of an exponential parent function is all real numbers, and the range is positive real numbers (y > 0).
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The probability that is will rain today is 65%, and the probability that it will rain tomorrow is 25%.
The probability that it will rain both days is 35%.
What is the probability that is will rain today or tomorrow?
Answer:
65%
Step-by-step explanation:
Amanda, Boris, and Jose sent a total of 124 text messages during the weekend. Amanda sent 8 fewer messages than Jose
Boris sent 4 times as many messages as Jose. How many messages did they each send?
Answer:
Amanda= 14
Boris = 88
Jose= 22
Step-by-step explanation:
Amanda= jose-8
Boris = 4×jose
Jose= Jose
total all = 124
(jose-8)+(jose×4)+(jose)= 124
so we substitute jose with X .
(X-8)+(4X)+(X)=124
6X-8= 124.
6X=124+8
X=132/6
X= 22.
so that total jose is 22, minus 8 we get Amanda, times 4 we get Boris.