Considering a linear function for the radius, we have that:
The volume of the sphere is modeled by [tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex].After 300 seconds, it is of 775,735 in³.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, radius r increases at the rate of 0.03 inches per second and that r=48, hence it is represented by the following linear function:
[tex]r(t) = 0.03t + 48[/tex]
Thus, the volume of the sphere is given by:
[tex]V = \frac{4\pi r(t)^3}{3}[/tex]
[tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex]
After 300 seconds, the volume in cubic inches is given by:
[tex]V(300) = \frac{4\pi(0.03(300) + 48)^3}{3} = 775735[/tex]
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2. When an adult is physically active, suppose the amount of water they will consume is normally distributed with an average of 20 ounces of water with a standard deviation of 7 ounces. If 10 adults are physically active, what is the probability that the average water consumed by them is less than 18 ounces? (note that we are working with a sampling distribution in this question). Report to 5 decimal positions
Using the normal distribution and the central limit theorem, it is found that there is a 0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For the population, the mean and the standard deviation are, respectively, given by [tex]\mu = 20, \sigma = 7[/tex].
For samples of n = 10, the standard error is given by:
[tex]s = \frac{7}{\sqrt{10}} = 2.2136[/tex]
The probability that the average water consumed by them is less than 18 ounces is the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 20}{2.2136}[/tex]
Z = -0.9.
Z = -0.9 has a p-value of 0.18406.
0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
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What is the product?
48+ 2 K-2
24 2+1
4
O2k+1
2
K-2
2
2641
2
R+2
Answer:
[tex]\frac{2}{k+2}[/tex]
Step-by-step explanation:
Simplify the expression and you will get this.
hope this helps
Choose the correct graph of the function y=√x-3
Answer:
C. where the start point is on (3,0) and goes up and to the right
Step-by-step explanation:
y= √x−3
Swap sides so that all variable terms are on the left hand side.
√x−3 =y
Square both sides of the equation.
x−3=y^2
Add 3 to both sides of the equation.
x−3−(−3)=y^2 −(−3)
Subtracting −3 from itself leaves 0.
x=y^2 −(−3)
Subtract −3 from y^2.
x=y^2 +3
A relief worker needs to divide 1350 bottles of water and 144 cans of food into boxes that each contain the same number of items. Also, each box must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put in each box?
The largest number of relief supplies that can be put in each box is 75 bottles and 8 cans of food respectively.
How to find highest common factorThe factors of:
1350 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675 and 1350.
144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
The highest common factor of 1350 and 144 is 181350 bottles / 18
= 75 bottles per box
144 cans of food / 18
= 8 cans of food per box
So, there 18 boxes of items, each containing 75 bottles and 8 cans of food respectively.
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The length is :____meters and the width is____meters.
Answer:
Length = 42, Width = 14
Step-by-step explanation:
Say width = x
3x + x = 56
4x = 56
x = 14
14 x 3 = 42.
Answer:
width = 7
length = 21
Step-by-step explanation:
x + 3x = 56/2
4x = 28
x = 7
A car dealership sold 212 cars in 4 months. At what rate did the dealership sell cars in cars per month?
Answer: 59 cars per month
Step-by-step explanation:
For each pair of real numbers show that the first number is a factor of the second number?
Need help ASAP!!
Answer:
[tex]\red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}}[/tex]
Answer:
Putanginaaaaaaaaaaaaaaaaaaaaa
How do I solve it the problem completely
Answer:
42 in²
Step-by-step explanation:
Total: Shape 1 + Shape 2
Area of a square: l x w, where l is the length and w is the width.
= 6 x 5
= 30
Area of a triangle: 1/2 x b x h, where b is the base and h is the height.
= 1/2 x 4 x 6
= 1/2 x 24
= 12
Total = 30 + 12
= 42 in²
Answer:
Step-by-step explanation:
This figure is trapezium
a and b are the parallel lines.
a = 5 +4 = 9 in & b = 5 in and h = 6 in
[tex]\boxed{\text{Area of trapezium =$\dfrac{(a+b)*h}{2}$}}[/tex]
[tex]\sf = \dfrac{(9+5)*6}{2}\\\\=\dfrac{14*6}{2}\\\\= 7*6\\\\= 42 \ in^{2}[/tex]
A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?
I need the answer to this quick pls
Answer:
Option A
Step-by-step explanation:
The median of the trapezoid is the line connecting the midpoints of the legs.The median of the trapezoid can be caculated by the fromula,
[tex]\bf Median = \dfrac{a +b}{2}[/tex]
Here, a and b are the base (parallel sides)
a = 13 inches & b = 19 inches
[tex]\bf Median = \dfrac{13+19}{2}[/tex]
[tex]= \dfrac{32}{2}\\\\\\= 16 \ inches[/tex]
Express √12+√27 in the form n√3, where n is an integer.
Answer:
5sqroot3
Step-by-step explanation:
see image.
An integer is just a whole positive or negative (positive in this case) number that's not a fraction or decimal or mixed number. In the answer that is the 5.
To simplify a radical, look for a factor that is a perfect square. Radicals and multiplying are very friendly to each other and you can separate the "radicand" (the inside number) into factors inside the radical also into separate radicals to simplify. See image
The volume of a right cone is 252pi units^3. If its height is 21 units, find its radius.
Based on the calculations, the radius of this right cone is equal to 6 units.
Given the following data:
Volume of cone = [tex]252\pi \;units^3[/tex]Height of cone = 21 units.How to calculate the volume of a cone.Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where:
h is the height.r is the radius.Making r the subject of formula, we have:
[tex]r=\sqrt{\frac{3V}{\pi h} } \\\\[/tex]
Substituting the given parameters into the formula, we have;
[tex]r=\sqrt{\frac{3\times 252\pi}{\pi \times 21} } \\\\r=\sqrt{\frac{756}{21} }\\\\r=\sqrt{36}[/tex]
r = 6 units.
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Consider the rectangle with width 4 ft and length 18 ft, write a ratio of the length to the width.
Answer: 18:4
Step-by-step explanation:
Ez
Answer:
9 : 2
Step-by-step explanation:
length : Width = 18 : 4
[tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]
= 9 : 2
Solve for the b 4 ( b + 5 )- 2b = 100
4 ( b + 5 )- 2b = 100
____________________
B = 40
Answer:
[tex]\tt b=40[/tex]
Step-by-step explanation:
[tex]\tt 4 ( b + 5 )- 2b = 100[/tex]
[tex]\bf Expand\; (Apply\; Distributions\; Law) :-[/tex]
[tex]\tt 2b+20=100[/tex]
[tex]\tt 2b+20-20=100-20\;\; (Subtract \;20\; from\; both \;sides)[/tex]
[tex]\tt 2b=80[/tex] [tex]\tt (Simplify)[/tex]
[tex]\tt \cfrac{2b}{2}=\cfrac{80}{2}\;\;( Divide\; both \;sides\: by\; 2)[/tex]
[tex]\tt b=40[/tex]
~
how many one third cup servings are in 16 cups
Gabrielle’s age is two time Mikhaïl’s age. The sum of their ages is 27. What is Mikhail’s age?
Mikhail is 9
Step-by-step explanation:
Divide 27 by 3 because G is 2 times than Mik. So G=2 Mik=1. and 27 divided 3 is 9
These numbers are multiples of __________.
4, 8, 16, 24
A) 3
B) 4
C) 5
D) 6
Answer:
4
Step-by-step explanation:
All these numbers multiply by 4
Answer:
The answer is B.
Step-by-step explanation:
4÷4=1
8÷4=2
16÷4=4
24÷4=6
Jessica sells 50.5 ounces of lemonade for a total of 20.20.
Find the unit price in dollars per ounce.
If necessary, round your answer to the nearest cent.
Answer:
2.5
Step-by-step explanation:
Answer: 2.5
Step-by-step explanation: do it yourself jk lol first you add then divide by 6.5
If 10% of your paycheck was withheld for federal income taxes and another 6% for state income taxes, how much would your net (or take-home) pay be?
Your net income/take-home would be 84.6 percent of the gross amount.
What is net income?Your net income is the amount of money left after payroll deductions in the form of taxes and other charges on the gross amount of your paycheck.
If we deduct federal and state taxes, 10 percent and 6 percent respectively, we would charge 10 percent and 6 percent of 100 and have 84.6 percent of your original(gross) income left.
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[tex] \rm \int_{0}^2 \left( \sqrt[3]{ {x}^{2} + 2x} + \sqrt{1 + {x}^3 } \right )dx \\ [/tex]
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
[tex]\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx[/tex]
Let [tex]f(x) = \sqrt{1 + x^3}[/tex]. Compute the inverse:
[tex]f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}[/tex]
and we immediately notice that [tex]f^{-1}(x+1)=\sqrt[3]{x^2+2x}[/tex].
So, we can write the given integral as
[tex]\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx[/tex]
Splitting up terms and replacing [tex]x \to x-1[/tex] in the first integral, we get
[tex]\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}[/tex]
in the figure d||m. what is the value of x?
Step-by-step explanation:
2X - 20 =86 ( Alternate angles are equal)
2X = 86 - 20
2X = 66
X = 33
Is ABSE- ATES? If so, identify the similarity postulate or theorem that
applies.
What does using the degrees of freedom in a sample correct for? possible bias between the alternative and null hypotheses possible bias between the sample and the population possible bias between the standard deviation and variance possible bias between the standard deviation and the mean
In Statistics and mathematics, the degrees of freedom in a sample are used to correct: A. possible bias between the alternative and null hypotheses.
What is a null hypothesis?A null hypothesis ([tex]H_0[/tex]) can be defined as the opposite of an alternate hypothesis ([tex]H_a[/tex]), and it asserts that two (2) possibilities are the same.
In In Statistics and mathematics, the test statistics of a given sample is calculated with this formula:
[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the sample size.Also, the degrees of freedom in a sample are used to correct a possible bias that exists between the alternative and null hypotheses.
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Find the greatest possible number of consecutive zeros at the end of the product of three positive integers if the sum of these three integers equals 939.
Answer:
I think its 5 consecutive zeros.
Step-by-step explanation:
This would be a guess but I think you would need two numbers in the hundreds that also have 2 parts of which have a product of a number ending in 0, like 4 and 5.
So my guess would be
400 * 500 * 39
= 7800000
The coldest temperature recorded on the surface of a planet was - 248 Celsius is the warmest temperature recorded on the surface of the planet was 108 Celsius what are the correspondence temperatures in degrees Fahrenheit
Answer:
-414.4 F° and 226.4 F°
hope it helps
* PLEASE HELP ME SOLVE THIS PROBLEM I WILL GIVE BRAINIEST*
2. Change from dog/cat to tails/heads.
DDC = ________
CDC= _________
DCD = ________
CCD = _________
DDD = _________
CCC = _________
DCC = _________
CDD = _________
please help :))
Answer:
Tails Tails Heads
Heads Tails Heads
Tails Heads Tails
Heads Heads Tails
Tails Tails Tails
Heads Heads Heads
Tails Tails heads
Heads Tails Tails
------------------------------------------------——------------------------------------------------------
Thanks!
Always keep more than 2 smiles so that you can share it to someone who doesn't have one. You happy! Me happy! EVERYONE HAPPY!!!!
Have a great day!
:D
Find the value of the expression 1/2x+3 if x=12
Answer:
The answer is 9.
Step-by-step explanation:
1/2 * 12 = 6
6+3=9
Answer:
9
Step-by-step explanation:
x = 12
1/2 · 12 = 6
6 + 3 = 9
Please help me i need help!!!
Answer:
sorry cant help with that
Step-by-step explanation:
Which is the inverse of the function f(x) = 4x − 9?
Step-by-step explanation:
x and y trade places.
f(x) = y = 4x - 9
y + 9 = 4x
x = (y + 9)/4
and to make it a true function notation, we need to rename x to y and vice versa and get
y = (x + 9)/4
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
A 34
B 47.5
C 68
D 95
Answer:
A
Step-by-step explanation:
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?