Answer:
The answer is "Option C."
Step-by-step explanation:
[tex]y=6x, \ \ y=x, \ \ , y=24,\\[/tex]
In this we calculate two points that are (0,4) and(4,24)
on[0,4]
shell radius=x
height = 6x-x
=5x
on[4,24]
shell radius=x
height = 24x-x
6x=24
x=4
Calculating shell volume by shell method:
[tex]v=\int\limits^b_a {2\pi(radius) \cdot(height)} \, dx \\[/tex]
[tex]=\int\limits^4_0 {2\pi(x) \cdot(5x)} \, dx +\int\limits^{24}_4 {2\pi(x) \cdot(24-x)} \, dx \\\\=\int\limits^4_0 {10\pi(x^2) dx +\int\limits^{24}_4 {2\pi x(24-x)} \, dx[/tex]
That's why the answer is "Option C".
verify:
cos(2A)=(cotA-tanA)/cscAsecA
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
cot A = [tex]\frac{cosA}{sinA}[/tex], tanA = [tex]\frac{sinA}{cosA}[/tex], cscA = [tex]\frac{1}{sinA}[/tex], secA = [tex]\frac{1}{cosA}[/tex]
Consider the right side
[tex]\frac{cotA-tanA}{cscAsecA}[/tex]
= [tex]\frac{\frac{cosA}{sinA}-\frac{sinA}{cosA} }{\frac{1}{sinA}.\frac{1}{cosA} }[/tex]
= [tex]\frac{\frac{cos^2A-sin^2A}{sinAcosA} }{\frac{1}{sinAcosA} }[/tex]
= [tex]\frac{cos^2A-sin^2A}{sinAcosA}[/tex] × sinAcosA ( cancel sinAcosA )
= cos²A - sin²A
= cos2A
= left side ⇒ verified
In order to estimate the difference between the average Miles per Gallon of two different models of automobiles, samples are taken, and the following information is collected. Model A Model B Sample Size 50 55 Sample Mean 32 35 Sample Variance 9 10 a) At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon for the two models. b) Is there conclusive evidence to indicate that one model gets a higher MPG than the other
Answer:
At 95% confidence limits for the true difference between the average Miles per Gallon for the two models is -1.8210 to 4.1789
Yes 95 % confidence means that there's conclusive evidence to indicate that one model gets a higher MPG than the other.
Step-by-step explanation:
Model A Model B
Sample Size 50 55
Sample Mean x` 32 35
Sample Variance s² 9 10
At 95 % confidence limits are given by
x1`-x2` ± 1.96 [tex]\sqrt{\frac{s^{2} }{n1} +\frac{s^{2}}{n2} }[/tex]
Putting the values
32-35 ± 1.96 [tex]\sqrt\frac{9}{50}+\frac{10}{55}[/tex] ( the variance is the square of standard deviation)
-3 ± 1.96 [tex]\sqrt{ \frac{495+500}{2750}[/tex]
-3 ± 1.96( 0.6015)
-3 ± 1.17896
-1.8210; 4.1789
Thus the 95% confidence limits for the true difference between the average Miles per Gallon for the two models is -1.8210 to 4.1789.
Yes 95 % confidence means that there's conclusive evidence to indicate that one model gets a higher MPG than the other.
The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. What is the sum of the lengths of the two remaining sides?
Answer:
9
Step-by-step explanation:
Extend every other side of the hexagon so that a triangle is formed. Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.
The length of the sides of the overall triangle is 7 + 2 + 4 = 13.
Therefore, the other two sides of the hexagon are 5 and 4.
The sum is 5 + 4 = 9.
A large sample of men, aged 48 was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men 90% were alive at 65%. Is this a sample or population?
given sin theta=3/5 and 180°<theta<270°, find the following: a. cos(2theta) b. sin(2theta) c. tan(2theta)
I hope this will help uh.....
The cost of a renting premises is 90% of the total costs of a company. The rental price was reduced 6 times, ceteris parabus. What percentage does the rental cost constitute in the total costs of the company?
Answer:
60%
Step-by-step explanation:
Reducing the rental cost by a factor of 6 makes it be 90%/6 = 15% of the original costs of the company. The non-rental costs are 100% -90% = 10% of the original costs of running the company.
Now, the rental costs are 15%/(15%+10%) = 3/5 of the present costs of the company.
Rental cost constitutes 60% in the total costs of the company.
In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age It was also reported that interviews were conducted on 1, 018 American adults, and that the margin of error was 3% using a 95% confidence level.
a. Verify the margin of error reported by The Marist Poll.
b. Based on a 95% confidence interval, docs the poll provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65?
Answer:
a
The Margin of error is correct
b
No the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 66[/tex]% = 0.66
The sample size is n = 1018
The margin of error is MOE = 3 % = 0.03
The confidence level is C = 95%
Given that the confidence level is 95% , then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level ([tex]1-\alpha[/tex]) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which what we required to calculate the margin of error
Generally the margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{p (1-p )}{n} }[/tex]
substituting values
[tex]MOE = 1.96 * \sqrt{\frac{0.66 (1-66 )}{1018} }[/tex]
[tex]MOE = 0.03[/tex]
[tex]MOE = 3[/tex]%
The 95% is mathematically represented as
[tex]p - MOE < p < p +MOE[/tex]
substituting values
[tex]0.66 -0.03 < p < 0.66 +0.03[/tex]
[tex]0.63 < p < 0.69[/tex]
Looking at the confidence level interval we see that the population proportion is between
63% and 69%
shown that the population proportion is less than 70%
Which means that the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
Help which of the following sets of ordered pairs represent a function?
Answer:
B
Step-by-step explanation:
B is the only set of ordered pairs to represent a function because it is the only one that has no repeating x values while the others do.
A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90. its price-earnings ratio equals:
Answer: Price-earnings ratio= 22.0
Step-by-step explanation:
Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90
To find: price-earnings ratio
Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]
Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]
⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]
Hence, the price-earnings ratio= 22.0
factorize 3x square+5x
Answer:
x(3x+5)
Step-by-step explanation:
3x^2+5x
take out common factor x
= x(3x+5)
Answer:
[tex]x(3x + 5)[/tex]Step-by-step explanation:
3x² + 5x
Factor out X from the expression
= x ( 3x + 5 )
Hope this helps...
Best regards!!
5(x + 3) – 12 = 43 solve
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
We can solve this equation by isolating the variable x.
First let’s apply the distributive property:
[tex]5(x+3)-12=43\\5\cdot x + 5\cdot3 - 12=43\\5x + 15 - 12 = 43[/tex]
Combine like terms:
[tex]5x + 3 = 43[/tex]
Now we can subtract 3 from both sides:
[tex]5x + 3 - 3 = 43-3\\5x = 40[/tex]
Divide both sides by 5:
[tex]5x\div5 = 40\div5\\x = 8[/tex]
So [tex]x=8[/tex].
Hope this helped!
Answer:
x = 8
Step-by-step explanation:
5(x + 3) – 12 = 43
Add 12 to each side
5(x + 3) – 12+12 = 43+12
5(x+3) =45
Divide each side by 5
5(x+3)/5 = 55/5
x+3 = 11
Subtract 3 from each side
x+3-3 = 11-3
x = 8
A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is feet. What is the net change in elevation going from the floor of the underground level to the ceiling of the fourth level above ground? Assume the floor at ground level is at an elevation of zero feet.
Answer:
72.5 feet
Step-by-step explanation:
The height of each level from floor to ceiling is 14 1/2 feet.
We want to find the net change in elevation going from the floor of the underground level to the ceiling of the 4th level above ground.
In other words, the change in elevation in going 5 floors up.
Each level has a height of 14 1/2 feet (29/2 feet).
Therefore, the height of the fourth level above ground from the underground level will be 5 times the height of one level:
h = 5 * 29/2 = 72.5 feet
The net change in elevation from the floor of the underground level to the 4th level above ground is:
ΔE = [tex]h_4 - h_0[/tex]
[tex]h_0 = 0 feet\\\\h_4 = 72.5 feet[/tex]
Therefore:
ΔE = 72.5 - 0 = 72.5 feet
Answer:
72.5
Step-by-step explanation:
Sung Lee invests $10,000 at age 18. He hopes the investment will be worth $30,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
r=17%
Step-by-step explanation:
P is the investment
A is the targeted amount
t= time (25-18=7 years)
A=P(1+r)^t
30000=10000(1+r)^7
(1+r)^7=30000/10000
r=\root(7)(3)-1
r=0.16993 ≅0.17= 17%
check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
An account is opened with an initial deposit of $100 and earns 3.0% interest compounded monthly. What will the account be worth in 25 years? Round your answer to the nearest dollar.
Answer:
A = $211.50
A = P + I where
P (principal) = $100.00
I (interest) = $111.50
Step-by-step explanation:
$209.37 will the account be worth in 25 years.
What is compound interest?Compound Interest is defined as interest earn on interest.
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
P= $100
r = 3%
t=25 years
substitute the values in formula,
[tex]A = 100(1 + \frac{3}{100})^{25}[/tex]
[tex]A = 100(1 + 0.03)^{25}[/tex]
[tex]A = 100(1.03)^{25}[/tex]
[tex]A=100(2.0937)[/tex]
[tex]A=209.37[/tex]
Hence, $209.37 will the account be worth in 25 years.
Learn more about Compound Interest
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3)
Rick says he has
two miles already.
Which form of the verb best completes the sentence?
A)
ran
B)
run
C)
running
D)
runs
Step-by-step explanation:
Because the sentence is speaking that he has done already so we will use the past verb ran
Rick says he has ran two miles already
Answer:
b. run
Step-by-step explanation:
Rick says he has run two miles already
It will be "ran" if the sentence had said, "Rick 'ran' two miles already."
BRAINLIST PLS!
A pretzel company calculated that there is a mean of 75.4 broken pretzels in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that there will be fewer than 66 broken pretzels in a run.
Answer:
P [ Z < 66 ] = 35,15 %
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 75,4
Standard deviation σ = 5,2
Then:
P [ Z < 66 ] = ( 66 - 75,4 ) / 5,2
P [ Z < 66 ] = - 9,4 / 5,2
P [ Z < 66 ] = - 1,81
In z-table we look for the reciprocate area for that z score and find
P [ Z < 66 ] = 0,3515
P [ Z < 66 ] = 35,15 %
PLZ CHECK MY ANSWER. Round your answer to the nearest tenth.
I chose D.
A: 72.56 cm^2
B: 80.29 cm^2
C: 60.66 cm^2
D: 70.32 cm^2
Answer:
D. [tex]70.34 cm^2[/tex]
Step-by-step explanation:
Area of sector of a circle is given as θ/360*πr²
Where,
r = radius = 12 cm
θ = 56°
Use 3.14 as π
Plug in the values into the formula and solve
[tex] area = \frac{56}{360}*3.14*12^2 [/tex]
[tex] area = 70.34 [/tex]
Area of the sector ABC = [tex] 70.34 cm^2 [/tex]
The answer is D
Derek is building a deck. The sum of the interior angles is 10800 and each interior angle is 1350. How many sides does his deck have
sum of angles = 10800
measurement of a single angle= 1350
Therefore,
No. of sides = sum of angles / single angle
No of sides = 10800 / 1350
No of sides = 8
Answer:
8 sides.
Step-by-step explanation:
If the sum of the angles is 10,800 degrees, and each angle is 1,350 degrees, the deck will have the number of sides of the sum of the angle measurements divided by each angle's measurements.
10,800 / 1,350 = 1,080 / 135 = 8 sides.
Hope this helps!
select the decimal that is equivalent to the fraction 57 over 100
Answer:
0.57.
Step-by-step explanation:
57 / 100
We divide 57 by 100:
= 0.57
The area of each square below is 1 square unit. How can we calculate the area of the striped region? A: 7/5 x 1/2 B: 6/12 x 2/10 C: 7/5 x 2/10
Answer:
wrong thing
Step-by-step explanation:
13 arent shaded of the 20 units
7/20 are shaded, 7X1=7, 2X5=10
Question 12 of 20 :
Select the best answer for the question.
12. If a number is divisible by both 2 and 3 then we can say the number is divisible by
O A.2.
OB.4.
O C.5.
OD.6.
Mark for review (Will be highlighted on the review page)
<< Previous Question
Next Question >>
Answer:
The number must be divisible by 6
Step-by-step explanation:
Being divisible by 2 means that 2 is a factor of the number. Same with being divisible by 3, so that means the number has 2 and 3 as factors, therefore, 6 is also a factor, and the number will be divisible by it.
A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.
Answer:
first number(x) = 2 second number(y)= 6
Step-by-step explanation:
This is an example of a simultaneous equation.
First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".
x + 2y = 14 (equation 1)
2x + y = 10 (equation 2)
This is solved using the elimination method.
We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.
2x + y = 10 MULTIPLY BY 2
4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)
Now subtract equation 1 from equation 2.
4x - x + 2y - 2y = 20 - 14 (2y cancels out here)
3x = 6
x = 2
Now we substitute our x value into equation 1 to find the value of y.
2 + 2y = 14
2y = 12
y = 6
Hope this has answered your question.
Answer:
6 and 2
Step-by-step explanation:
Let the first number =a
Let the second number =b
A first number plus twice a second number is 14.
a+2b=14Twice the first number plus the second totals 10.
2a+b=10We solve the two equations simultaneously
[tex]a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6[/tex]
Recall:
a=14-2b
=14-2(6)
=14-12
a=2
The two numbers are 6 and 2.
Which of the following best describes an unpredictable event?
Answer:
B. The weather on a particular day a year from now
Step-by-step explanation:
We can only predict the weather in the near future, not long term or all time. The rest of the answer choices are predictable. We will always know the age of a person 10 years from now, we can predict the rating of the movie if we preview and watch it, and if a student studies enough/not enough we can predict the type of grade they will get on a test.
I believe the answer is B since to find the age of a person ten years from now, just add their age by ten. You can predict the rating of an upcoming movie by watching the trailer and seeing if it is good or bad. You can predict the grade a student gets on a test if you know that person is smart or not. You can’t predict weather from a year in the future because anything could happen in a year. This is why I think the answer is B.
905,238 In a word form
Answer:
nine hundred five thousand two hundred thirty-eight
The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v).
Estimate the values of fT(−15, 50) and fv(−15, 50).
V 20 30 40 50 60 70
T
−10 −18 −20 −21 −22 −23 −23
−15 −25 −26 −27 −29 −30 −30
−20 −30 −33 −34 −35 −36 −37
−25 −37 −39 −41 −42 −43 −44
Answer:
value of Ft(-15,50) = 1.3
Value of Fv(-15,50) = -0.15
Step-by-step explanation:
W = perceived temperature
T = actual temperature
W = f( T,V)
Estimate the values of ft ( -15,50) and fv(-15,50)
calculate the Linear approximation of f at(-15,50)
[tex]f_{t}[/tex] (-15,50) = [tex]\lim_{h \to \o}[/tex] [tex]\frac{f(-15+h,40)-f(-15,40)}{h}[/tex]
from the table take h = 5, -5
[tex]f_{t}(-15,40) = \frac{f(-10,40)-f(-15,40)}{5}[/tex] = [tex]\frac{-21+27}{5} = 1.2[/tex]
[tex]f_{t} = \frac{f(-20,40)-f(-15,40)}{-5}[/tex] = 1.4
therefore the average value of [tex]f_{t} (-15,40) = 1.3[/tex]
This means that when the Temperature is -15⁰c and the 40 km/h the value of Ft (-15,40) = 1.3
calculate the linear approximation of
[tex]f_{v} (-15,40) = \lim_{h \to \o} \frac{f(-15,40+h)-f(-15,40)}{h}[/tex]
from the table take h = 10, -10
[tex]f_{v}(-15,40) = \frac{f(-15,50)-f(-15,40)}{10}[/tex] = [tex]\frac{-29+27}{10} = -0.2[/tex]
[tex]f_{v} (-15,40) = \frac{f(-15,30)-f(-15,40)}{-10}[/tex] = [tex]\frac{-26+27}{-10}[/tex] = -0.1
therefore the average value of [tex]f_{v} (-15,40) = -0.15[/tex]
This means that when the temperature = -15⁰c and the wind speed is 40 km/h the temperature will decrease by 0.15⁰c
w = f(T,v)
= -27 + 1.3(T+15) - 0.15(v-40)
= -27 + 1.3T + 19.5 - 0.15v + 6
= 1.3T - 0.15v -1.5
calculate the linear approximation
[tex]\lim_{v \to \infty}[/tex][tex]\frac{dw}{dv} = \lim_{v \to \infty} \frac{d(1.3T-0.15v-1.5)}{dv}[/tex] = -0.15
jogged the track 5/9 miles long and jogged around it 4 times
Answer:
The answer is 2 1/5 miles.
Step-by-step explanation:
You have to multiply 5/9 with 4 since you are going around 4 times. You could also use addition which is 5/9 + 5/9 + 5/9 + 5/9.
Answer:
Hey there!
The person jogged a total of 20/9 miles.
Hope this helps :)
A jewel box is to be constructed of materials that costs K1 per square inch for the bottom, K2 per square inch for the sides, and K5 per square inch for the top. If the total volume is to be 96 inch cubic, advise Mr Lukonde on what dimensions will minimize the total cost of construction. Show all the calculations.
Answer:
x= 5,77 *∛ K₂ / ( K₁ + K₅ ) the side f the square bottom-top
h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]² heigh of the box
Step-by-step explanation:
Data from problem statement only gives one relation between dimensions of the box, we need two, in order to express surface area as a function of just one variable. In such a case we must assume the box is of square bottom and top.
Then
Area of the bottom A(b) = x² ⇒ C(b) = K₁*x²
Area of the top A(t) = x² ⇒ C(t) = K₅*x²
Total lateral area ( 4 sides) A(l) = 4*x*h ⇒ C(l) = 4*K₂*x*h
V(bx) = 96 in³
V(bx) = x²*h = 96
h = 96/x²
Then total cost as a function of x
C(x) = K₁*x² + K₅*x² + 4*K₂*(96)/x
Taking derivatives on both sides of the equation
C´(x) = 2*K₁*x + 2*K₅*x - 384*K₂/x²
C´(x) = 0 ⇒ 2*K₁*x + 2*K₅*x - 384*K₂/x² = 0
2*K₁*x³ + 2*K₅*x³ = 384*K₂ or K₁*x³ + k₅*x³ = 192*K₂
x³ ( K₁ + K₅ ) = 192*K₂
x = ∛192*K₂ / ( K₁ + K₅ )
x= 5,77 *∛ K₂ / ( K₁ + K₅ )
If we obtain the second derivative
C´´(x) = 2*K₁ + 2*K₅ - (-2*x)*384*K₂/x⁴
C´´(x) = 2*K₁ + 2*K₅ + 768*K₂/x³
As x can not be negative the expression C´´ wil be C´´> 0
then we have a minimum for the function for x = 5,77 *∛ K₂ / ( K₁ + K₅ )
and h = 96 / [ 5,77 *∛ K₂ / ( K₁ + K₅ )]²
h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]²
PLEASE HELP QUICK!!!! What is the solution to the equation Two-thirds x + 1 = one-sixth x minus 7? x = negative 16 x = negative 4 x = 4 x = 16
Answer:
-16
Step-by-step explanation:
I solved it out.
Answer:
its d 16
Step-by-step explanation:
i did the test
12+[(15-5)]+(9-3)] what is the answer
Answer:
28
Step-by-step explanation:
12+[(15-5)]+(9-3)]
PEMDAS
Parentheses first
12+[(10)]+(6)]
Then add
12+10+6
Answer: 28
Step-by-step explanation: