[tex] \frac{13}{(x + 2)} = \frac{8}{(x - 1)} [/tex]
By cross - multiplication
[tex] \implies13 \times (x - 1) = 8 \times (x + 2)[/tex]
[tex] \implies13x - 13 = 8x + 16[/tex]
[tex] \implies13x - 8x = 16 + 13[/tex]
[tex] \implies5x = 29[/tex]
[tex] \implies \: x = \frac{29}{5} [/tex]
[tex] \implies \: x = 5.8[/tex]
Which distribution is used to test the claim that women have a higher mean resting heart rate than men?
This question is incomplete, the complete question is;
Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?
A.t
B.F
C.Normal
D. Chi-square
Answer:
A) t test
Step-by-step explanation:
A t-test uses sample information to assess how plausible it is for the population means μ1 and μ2 to be equal.
The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.
If the variances are assumed to be not equal,
he formula is:
t = (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )
If the variances are assumed to be equal, the formula is:
t = (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)
it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.
hence option A is correct. t test
Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 − 5x y2 = 0
Answer: Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]
Step-by-step explanation:
Thiis is quite straightforward, so I will be gudiding you through the process.
we have that;
y1 = x² -5x
and y² = 0
Taking Limits:
y1 = x² -5x, y2 = 0
x² - 5x = 0;
so x(x - 5) = 0
this gives x = 0 and x = 5
∴ 0≤x≤5
This is to say that the graph intersets at x = 0 and x = 5 and y2 is the upper most function.
Let us take the formula:
Area = ∫b-a (upper curve - lower curve)
where a here represents 0 and b represents 5
the upper curve y2 = 0
whereas the lower curve y1 = x² - 5x
Area = ∫5-0 [ 0 - (x² - 5x) ] dx
This becomes the Area.
Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]
cheers i hope this helped !!!
Use the quadratic formula to solve the equation: 0 = x2 + x - 20
Answer:
(x-4)*(x+5) : x =4,-5
Step-by-step explanation:
a= 1
b= 1
c= -20
x1,2 = (-1+-(1 - (4*1*-20))^0.5)/2
x1,2 = (-1+-(1+80)^0.5)/2
x1,2 = (-1+-(81^0.5))/2
x1,2 =(-1+-9)/2
x1 = 8/2 = 4 x2 = -10/2 = -5
Find the partial derivative of the function f(x,y)=Integral of cos(-7t^2-6t-1)dt. Find fx(x,y) and fy(x,y)
Answer:
[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]
[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]
Step-by-step explanation:
Given that :
[tex]f(x,y) = \int ^x_y cos (-7t^2 -6t-1) dt[/tex]
Using the Leibnitz rule of differentiation,
[tex]\dfrac{d}{dt} \int ^{b(t)}_{a(t)} f(x,t) dt= f(b(t),t) *b'(t) -f(a(t),t) * a' (t) + \int^{b(t)}_{a(t)} \dfrac{\partial f}{\partial t} \ dt[/tex]
To find: fx(x,y)
[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial }{\partial x} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]
[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial x}{\partial x} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial x} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial x} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]
[tex]\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1) -0+0[/tex]
[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]
To find: fy(x,y)
[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial }{\partial y} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]
[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial x}{\partial y} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial y} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial y} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]
[tex]\dfrac{\partial f}{\partial y}= 0 - cos ( -7y^2 -6y-1)+0[/tex]
[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]
I=prt,for p please show step by step for this variable
Answer:
[tex] p = \dfrac{I}{rt} [/tex]
Step-by-step explanation:
I = prt
Switch sides.
prt = I
We are solving for p. We want p alone on the left side. p is being multiplied by r and t, so we divide both sides by r and t.
[tex] \dfrac{prt}{rt} = \dfrac{I}{rt} [/tex]
[tex] p = \dfrac{I}{rt} [/tex]
Find the area of the shaded region.
Round to the nearest tenth.
Answer:
Area shaded blue = 294.5 m^2 (to the nearest tenth)
Step-by-step explanation:
Refer to the attached figure.
Consider sector patterned in orange
radius = 11.1 m
angle of sector = 360-130 = 230 degrees
area of sector = (angle / 360) * area of complete circle
A1 = (230/360)*pi * 11.1^2
= 78.7175 pi
= 247.298 m^2
Area of right triangle with hypotenuse, L, and one of the angles, x, known
= (Lsin(x))*L(cos(x)/2
= L^2 sin(2x)/4
A2 = 2* (11.1^2 sin(130/2)/4)
= 11.1^2 * sin(65) / 2
= 47.192 m^2
Area shaded blue
= A1+A2
= 247.298 + 47.192
= 294.49 m^2
The digit \greenD88start color #1fab54, 8, end color #1fab54 in which number represents a value of 888 thousandths?
Question:
The digit 8 in which number represents a value of 8 thousandths?
Answer:
See Explanation
Step-by-step explanation:
The question requires options and the options are missing.
However, the following explanation will guide you
Start by representing 8 thousandths as a digit
[tex]\frac{8}{1000} = 0.008[/tex]
i.e.
8 thousandths implies 0.008
Next;
Replace the 0s with dashes
_ . _ _8
Note that there are two dashes after the decimal point and before 8
PS: The dashes are used to represent digits
This implies that thousandths is the 3rd digit after the decimal point
Typical examples to back up this explanation are:
17.008, 1.1489, 0.008 and so on...
como dividir ? ? . . .. . . .. . . .. . .. . . .. .
Answer:
What
Step-by-step explanation:
What Do You Mean Bro
Question 1 of 4
A statistics test was taken in Mrs. Everett's class. Some of the students were surveyed for their
scores and here are the results of that survey:
25 30 35 40 40 45 45 50 50 50
55 55 55 60 60 65 65 70 75 80
✓ What is the average score of the student surveyed? a. 55.5
b. 52.5
What is the median of the student's surveyed?
c. 20.0
d. 60.5
How many students were surveyed?
Answer:
1) What is the average score of the student surveyed?
b. 52.5
2) What is the median of the student's surveyed?
52.5
3) How many students were surveyed?
20 students
Step-by-step explanation:
1) What is the average score of the student surveyed?
Average score of the student's been surveyed means we should calculate the mean of the above scores
The formula for Mean = Sum of the number of terms/ Number of terms
Number of terms = 20
Average(Mean score) =
25 + 30 + 35 + 40 + 40 + 45 + 45 + 50 + 50 + 50 + 55 + 55 + 55 + 60 + 60 + 65 + 65 + 70 + 75 + 80/20
= 1050/20
= 52.5
2) What is the median of the student's surveyed?
25, 30, 35, 40, 40, 45, 45, 50, 50, 50, 55, 55, 55, 60, 60, 65, 65, 70, 75, 80
From the above data, we can see that 20 students were surveyed. To find the Median, we find the sum of the 10th value and the 11th value and we divide by 2
Hence,
25, 30, 35, 40, 40, 45, 45, 50, 50,) 50, 55, (55, 55, 60, 60, 65, 65, 70, 75, 80
10th value = 50
11th value = 55
Median = 50 + 55/2
= 105/2
= 52.5
3) How many students were surveyed?
Counting the results of the survey, the number of students that were surveyed = 20 students
[tex]f(x) = {x}^{2} + 4x - 5[/tex]
when [tex]x > - 2[/tex]
find[tex] \frac{d {f}^{ - 1} }{dx} at \: x = 16[/tex]
Answer:
[tex] \dfrac{df^{1}(16)}{dx} = \pm \dfrac{1}{10} [/tex]
Step-by-step explanation:
[tex] f(x) = x^2 + 4x - 5 [/tex]
First we find the inverse function.
[tex] y = x^2 + 4x - 5 [/tex]
[tex] x = y^2 + 4y - 5 [/tex]
[tex] y^2 + 4y - 5 = x [/tex]
[tex] y^2 + 4y = x + 5 [/tex]
[tex] y^2 + 4y + 4 = x + 5 + 4 [/tex]
[tex] (y + 2)^2 = x + 9 [/tex]
[tex] y + 2 = \pm\sqrt{x + 9} [/tex]
[tex] y = -2 \pm\sqrt{x + 9} [/tex]
[tex]f^{-1}(x) = -2 \pm\sqrt{x + 9}[/tex]
[tex]f^{-1}(x) = -2 \pm (x + 9)^{\frac{1}{2}}[/tex]
Now we find the derivative of the inverse function.
[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2}(x + 9)^{-\frac{1}{2}}[/tex]
[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2\sqrt{x + 9}}[/tex]
Now we evaluate the derivative of the inverse function at x = 16.
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{16 + 9}}[/tex]
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{25}}[/tex]
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2 \times 5 }[/tex]
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{10}[/tex]
The shape of the distribution of the time required to get an oil change at a 10 minute oil change facility is unknown. However, records indicate that the mean time is 11.4 minutes and the standard deviation is 4.5 minutes.
a) To compute the probabilities regarding the sample mean using the normal model, what size sample would be required?
b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time of less than 10 minutes?
1) Choose the required sample size:
i) Sample size need to be greater than 30
ii) The normal model cannot be used if the shape of the distribution is unknown
iii) Any sample size could be used.
iv) Sample size needs to be less than 30
2) The probability is approximately ___________. (round to 4 decimal places as needed)
Answer:
a) Sample size need to be greater than 30
b) The probability is approximately 0.0571
Step-by-step explanation:
a) For a normal distribution, the sample size has to be greater than 30. A sample size greater than 30 makes it to be an approximate normal distribution.
b) Given that:
μ = 11.2 minutes, σ = 4.5 minutes, n = 35
The z score determines how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x < 10 minutes
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.5/\sqrt{35} }= -1.58[/tex]
Therefore from the normal distribution table, P(x < 10) = P(z < -1.58) = 0.0571
The probability is approximately 0.0571
A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)
Answer: 82 sq. units .
Step-by-step explanation:
Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.
Then we plot them on graph ( as provided in attachment)
Length = AB [tex]=\sqrt{(9+1)^2+(-1-7)^2}[/tex] units [By distance formula : [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]]
[tex]=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}[/tex] units
Width = BC = [tex]\sqrt{(-1+5)^2+(7-2)^2}[/tex] units
[tex]=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}[/tex]
Area = length x width
= [tex]2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}[/tex]
Hence, the area of the rectangle is 82 sq. units .
(b-(a-a)) ÷ 3; use a = 6, and b = 3
Answer:
The answer is 1Step-by-step explanation:
(b-(a-a)) ÷ 3
a = 6 , b = 3
Substitute the values into the above formula
That's
[tex](3 - (6 - 6)) \div 3[/tex]
Using PEDMAS solve the terms in the bracket first
That's
[tex](3 - 0) \div 3[/tex]
We have
3 ÷ 3
The final answer is 1Hope this helps you
A jar contains 100 ounces of lemonade. A spout at the bottom of the jar is opened and the lemonade pours out at a rate of 10 ounces per second. Which graph below represents the amount of lemonade in the jar for the first 15 seconds after the spout was opened?
Answer:
100 ounces(hope it help)
Step-by-step explanation:
because there is only 100 ounces in the jar.
Edward walks at a pace 2 1/4 miles in 2/3 hour. How many miles does Edward walk per hour
Divide distance walked by time:
2 1/4 miles / 2/3 hours = 3 3/8 miles per hour
If 3/4 +1/6 =p then the value of p is what?
Answer: 11/12
Step-by-step explanation:
Addition of fractions
#1 Change to the same denominator
- LCM (Least common multiple) of 4 and 6 is 12
- 9/12+2/12
#2 Add the numerator as usual
9/12+2/12
=(9+2)/12
=11/12
-------------------------------------------------
p=3/4+1/6
p=11/12
NEED THIS AND HOW U GOT THE ANSWER find the value of X given that M is greater than PQS equals 119°
Answer:
4.7 =x
Step-by-step explanation:
PQS = PQR + RQS
119 = 72+ 10x
Subtract 72 from each side
119 - 72 = 72+10x -72
47 = 10x
Divide by 10
47/10 = 10x/10
4.7 =x
Help please urgent !!!!The students of a certain college were asked to choose which of six movie genres was their favorite. The pie chart below shows the distribution of the students’ answers. If there are 18,500 students at the college, how many chose Drama , Other, or Comedy ?
Answer:
12,950
Step-by-step explanation:
drama: 23%
other: 27%
comedy: 20%
23% + 27% + 20% = 70%
70% of 18,500 =
= 0.7 * 18,500
= 12,950
Please help fast :) I really need the help thanks !!
Step-by-step explanation:
6 x 1/7 is Less than 1 since 6 x 1/7 is equal to 6/7 in decimal form is 0.8571429.
4 x 4/9 is greater than 1 since 4 x 4/9 is equal to 1 7/9 in decimal form is 1.777...
8 x 1/8 is equal to 1 since 8 x 1/8 is equal to 1.
7 x 1/5 is greater than 1 since 7 x 1/5 is equal to 1 2/5 in decimal form is 1.4
3 x 1/2 is greater than 1 since 3 x 12 is equal to 1 1/2 in decimal form is 1.5
1 x 3/4 is is less than 1 since 1 x 3/4 is equal to 3/4 in decimal form is 0.75
Find the points of intersection of the graphs of the equations. r = 1 + cos θ r = 1 − sin θ r ≥ 0, 0 ≤ θ < 2π
This question is based on the point of intersection.Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
Given:
Equations: r = 1 + cos θ ...(1)
r = 1 − sin θ ...(2)
Where, r ≥ 0, 0 ≤ θ < 2π
We need to determined the point of intersection of the graphs of the equations.
To obtain the points of intersection, Equate the two equations above as follows;
r = 1 + cos θ = 1 - sin θ
=> 1 + cos θ = 1 - sin θ
Solve further for θ. We get,
1 + cos θ = 1 - sinθ
cos θ = - sinθ
Now dividing both sides by - cos θ and solve it further,
[tex]\dfrac{cos\;\theta}{-cos\;\theta} =\dfrac{-sin\;\theta}{-cos\;\theta}\\\\tan\;\theta=-1\\\\\theta=tan^{-1}(1)\\\\\theta=45^{0}=\dfrac{-\pi }{4}[/tex]
To get the 2nd quadrant value of θ, add π ( = 180°) to the value of θ. i.e
[tex]\dfrac{-\pi }{4} +\pi =\dfrac{3\pi }{4} \\[/tex]
Similarly, to get the fourth quadrant value of θ, add 2π ( = 360° ) to the value of θ. i.e
[tex]\dfrac{-\pi }{4} +2\pi =\dfrac{7\pi }{4} \\[/tex]
Therefore, the values of θ are 3π / 4 and 7π / 4.
Now substitute these values into equations (i) and (ii) as follows;
[tex]When \;\theta=\dfrac{3\pi }{4},[/tex]
[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{3\pi }{4} =1+\dfrac{-\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]
[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{3\pi }{4} =1-\dfrac{\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]
[tex]When\; \theta=\dfrac{7\pi }{4}[/tex]
[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{7\pi }{4} =1+\dfrac{\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]
[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{7\pi }{4} =1-\dfrac{-\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]
Represent the results above in polar coordinates of the form (r, θ). i.e
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
Therefore, at the pole where r = 0, is also one of the points of intersection.
Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
For further details, please prefer this link:
https://brainly.com/question/13373561
______ income is gross income minus taxes and deductions. fill in the blank
Answer:
Net
Step-by-step explanation:
The definition of "Net Income" is a person's income after deductions and taxes. Hence it is also sometimes know as the "Take-Home" income. i.e the amount of money that you actually take home.
The following list is of 4 measurements.
There are four levels of measurement – nominal, ordinal, and interval/ratio – with nominal being the least precise and informative and interval/ratio variable being most precise and informative.
solve from here by understanding what i have write
Can someone please help me !❤️❤️
In a triangle ABC, AB=AC and ˂A=70°, find the angles,˂B and ˂C
please help !!!!!!!!!!!!!
Answer:
Then angles [tex]\angle B[/tex] and [tex]\angle C[/tex] both measure [tex]55^o[/tex]
Step-by-step explanation:
Notice that if sides AB and AC are equal, then the angles opposed to them (that is angle [tex]\angle C[/tex] and angle [tex]\angle B[/tex] respectively) have to be equal since equal sides oppose equal angles in a triangle.
So you also know that the addition of the three angles in a triangle must equal [tex]180^o[/tex], then:
[tex]\angle A + \angle B+\angle C= 180^o\\70^o+\angle B + \angle B = 180^o\\2\,\angle B = 180^o-70^o\\2 \angle B=110^o\\\angle B=55^o\\\angle C = 55^o[/tex]
Zev read 15% of his 56-page book. Kelly read 12% of her 64-page book. Marneisha read 14% of his 68-page book Aleisha read 10% of her 72-page book. what the grastest
Answer:
Marneisha with 9.52 pages.
Step-by-step explanation:
Zev: 56×0.15 = 8.4
Kelly: 64×0.12 = 7.68
Marneisha: 68×0.14 - 9.52
Aleisha: 72×0.10 = 7.2
In the diagram of O, m∠JOK = 60° and OJ = 6 in. What is the exact area of the shaded region?
Answer: 6π
Step-by-step explanation:
Area of a circle is π r².
Area of a section of a circle is π r² × the section of the circle.
[tex]A=\pi r^2\bigg(\dfrac{\theta}{360^o}\bigg)[/tex]
Given: r = 6, Ф = 60°
[tex]A=\pi (6)^2\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =\pi (6)^2\bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =6\pi[/tex]
Tim and Nikko bought new computers. Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer. The total amount that Tim and Nikko spent for their computers was $2,870. How much did Nikko spend for his computer?
A. $1,181.00
B. $1,407.50
C. $1,689.00
D. $1,755.00
Answer:
C. $1,689.00Step-by-step explanation:
Let the amount spent by Tim be x and the amount spent by Nikko be y
If Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer, then amount spent by Tim will be x = 55+2/3 y
Since the total amount that Tim and Nikko spent for their computers was $2,870 then;
x+y = $2,870
Substituting x = 55+2/3y into the equation above, we will have;
55+2y/3 + y = 2,870
(165 + 2y)/3 + y = 2,870
(165 + 2y+3y)/3 = 2,870
cross multiply
165 + 2y+3y = 3*2870
165+5y = 8610
5y = 8610-165
5y = 8445
y = 8445/5
y = 1689
Hence Nikko spent a sum of $1,689.00 on his computer.
Johnny has 6 apples,12 bananas, and 14 strawberries. Write the ratio of apples:bananas: strawberries in its simplest form.
Please help
Answer:
apples:bananas: strawberries
3 : 6 : 7
Step-by-step explanation:
apples:bananas: strawberries
6 12 14
Divide each by 2
6/2 12/2 14/2
3 6 7
The ratio is
3 : 6 : 7
Answer:
3:6:7
Step-by-step explanation
The answer is 3:6:7 because if you divide the numbers by 2, you will get a answer of 3, 6, and 7, the simplest form of the ratio.
Hope this helped!
~Emilie Greene
Find the horizontal asymptote (Show your work)
Answer:
[tex] y = 0 [/tex]
Step-by-step explanation:
To find the given asymptote of the given function, [tex] f(x) = \frac{x^2 - 2x + 1}{x^3 + x - 7} [/tex], first, compare the degrees of the lead term of the polynomial of the numerator and that of the denominator.
The numerator has a 2nd degree polynomial (x²).
The denominator has a 3rd degree polynomial (x³).
The polynomial of the numerator has a lower degree compared to the denominator, therefore, the horizontal asymptote is y = 0.
Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.
Answer:
The error was made in step 4, [tex]\pi[/tex] should have also been cancelled making the correct answer as 9 cm.
Step-by-step explanation:
Given that:
Volume of cylinder, [tex]V = 576 \pi\ cm^3[/tex]
Radius of cylinder, r = 8 cm
To find:
The error in calculating the height of cylinder by Sandra ?
Solution:
We know that volume of a cylinder is given as:
[tex]V = B h[/tex]
Where B is the area of circular base and
h is the height of cylinder.
Area of a circle is given as, [tex]B = \pi r^2[/tex]
Let us put it in the formula of volume:
[tex]V = \pi r^2 h[/tex]
Step 1:
Putting the values of V and r:
[tex]576\pi = \pi 8^2 h[/tex]
So, it is correct.
Step 2:
Solving square of 8:
[tex]576\pi = \pi \times 64\times h[/tex]
So, step 2 is also correct.
Step 3:
[tex]h=\dfrac{576\pi}{64 \pi} = \dfrac{64 \pi \times 9}{64\pi}[/tex]
Step 4:
Cancelling 64 [tex]\times \pi[/tex],
h = 9 cm
So, the error was made in step 4, [tex]\pi[/tex] should have also been cancelled making the correct answer as 9 cm.
Answer:
(C) In step 4, the pi should have canceled, making the correct answer 9 cm.