Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height [tex]= \frac{10}{4}[/tex]
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
[tex]A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}[/tex]
For, A to be greatest ,
[tex]\frac{dA}{dh} =0 = 10h-4h^{3}[/tex]
⇒ [tex]h[10-4h^{2} ]=0[/tex]
⇒ [tex]h^{2} =\frac{10}{4} {Since, h≠ 0}[/tex]
⇒ [tex]h = ±\frac{\sqrt{10} }{2}[/tex]
Therefore, from equation (3), k = 5 - h²
⇒ [tex]k=5-\frac{10}{4} =\frac{10}{4}[/tex]
Hence,
Width = 2h =√10 and
Height = [tex]k =\frac{10}{4}.[/tex]
In order to get promoted to the next grade, a student is required to score above 55 in the final test. Assume the scores to be normally distributed with a mean of 60 and a standard deviation of 5.5. Calculate the percentage of students who will be promoted to the next grade.
Answer:
[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]
And we can find this probability with the complement rule:
[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]
And we can use excel or the normal standard table and we got:
[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]
So then we expect about 81.8% of students that will be promoted
Step-by-step explanation:
Let X the random variable that represent the scores of promotion of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(60,5.5)[/tex]
Where [tex]\mu=60[/tex] and [tex]\sigma=5.5[/tex]
We want to find the following probability:
[tex]P(X>55)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the z score formula we got:
[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]
And we can find this probability with the complement rule:
[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]
And we can use excel or the normal standard table and we got:
[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]
So then we expect about 81.8% of students that will be promoted
At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time?
Step-by-step explanation:
The probability of success = 8/(8 + 17) = 8/25 = 0.32.
Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.
Hence, X ~ Bin(4, 0.32).
Thus, P(X = 1) = [tex]4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3[/tex]
The probability the individual will win a prize exactly one time is
C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.
The probability of success
P = 8/(8 + 17)
P = 8/25
P = 0.32
Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.
So,
X ~ Bin(4, 0.32).
Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹
= C(4, 1)(0.32)¹ (0.68)³
Thus, the probability the individual will win a prize exactly one time is
C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.
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What is the surface area of the figure shown?
Answer:
90 square feet.
Step-by-step explanation:
Let's set up an equation!
SA= 2(xy)+2(xz)+2(yz).
Lets say that x=3 y=6 and z=3
We plug it in.
2(18)+2(9)+2(18)= SA
36+18+36=SA
72+18=SA
90=SA
90 square feet = Surface area.
factorise fully 24x+16
Answer:
8(3x + 2)
Step-by-step explanation:
→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.
→The GCF is 8:
8(3x + 2)
Answer:
8(3x+2)
Step-by-step explanation:
24x+16
8*3*x + 8*2
Factor out an 8
8(3x+2)
The sum of a number and its reciprocal is 41/20. Find the number. smaller value larger value
Step-by-step explanation:
Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :
[tex]x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0[/tex]
It is a quadratic equation. The values of x are :
[tex]20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}[/tex]
The smaller number is 4/5 and the larger number is 5/4.
Find the angle of least positive measure that is coterminal with 541 degrees
Answer: 181 degrees.
Step-by-step explanation:
If we have an angle A, between, then the angle B is coterminal to A if:
B = A + n*360°
where n can be any whole number (if n = 0, we have B = A)
Then, if we take our angle as A = 541°
we can take n = -1 and get:
B = 541° - 1*360° = 181°
Now, if we subtract again 360°, we will end with an angle of negative measure, so 181° is the least positive measure angle that is coterminal with 541°
The domain of the function is all
The range of the function is all
The domain of a function is the set of all the x terms of the function and the range of a function is the set of all the y terms of a function.
For example, take a look below.
The domain is the set of all x terms in each ordered pair and the
range will be the set of all the y terms in each ordered pair.
Find cos angle∠ C
A. 5/13
B. 12/13
C. 12/5
D. 13/5
Answer:
The answer is A.
Step-by-step explanation:
Recall SohCahToa, which tells us that cosine is the ratio of the adjacent side to the hypotenuse. In other words:
[tex]\displaystyle \cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side to ∠C is 10 and the hypotenuse is 26.
Therefore:
[tex]\displaystyle \cos(C)=\frac{10}{26}=\frac{5}{13}[/tex]
Our answer is A.
3. Barbara was asked to create a set of numbers that contained only integers. Which of the sets does
NOT contain only integers?
А
12
B
-3, -4,600,
9, 100, - 4, 12, -6, 5
5. 3, -6, -14, 3.5, 7
с
24
12
D 22, -12.0, 9, -14, 28, 4
Answer:
C (5.3, -6, -14, 3.5, 7)
Step-by-step explanation:
Integers are the sets of positive and negative whole numbers including zero.
In set notation, we denote the set of integers using the letter [tex]\mattbb{Z}[/tex].
From the given options:
In Option C (5. 3, -6, -14, 3.5, 7), we have the number 3.5 and 5.3 which are not whole numbers. Therefore 3.5 and 5.3 are not integers.
Option C is the set which does not contain only integers.
What is this answer?
Answer:
1
Step-by-step explanation:
coz 1 x 1 x 1=1
How many edges dose the following shape have?
Which symbol should go into the box to make the statement true?
|17| ? 17.
A.< B.> C.equal sign with a line through it D. =
Answer:
the 3rd option is the right one
Terry, Edin and Gordon are hygiene inspectors. Three takeaways, kebab, fish and chips and pizza. It is decided to share the work so that all inspectors will visit one takeaway each, chosen at random. List all the possible different ways they could share the work. (TK-EF-GP,
Answer: There are 6 different ways in which they can share the work.
Step-by-step explanation:
Suppose that Terry selects first the place where he goes, in the selection he has 3 options at random to chose.
Then Edin selects, Edin has two options (because one is already taken)
Then Gordon selects, he has only one options.
The number of combinations is equal to the product of the number of options for each selection, this is:
Combinations = 3*2*1 = 6
There are 6 different ways in which they can share the work.
At 5:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 38520 ft and is descending at the rate of 750 ft/min. Airplane #2 has an elevation of 9400 ft and is climbing at the rate of 550 ft/min. (1) Let t represent the time in minutes since 5:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t . plane #1: E ( t ) = plane #2: E ( t ) =
Answer:
Plane 1
[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]
Plane 2
[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]
Step-by-step explanation:
As each plane is travelling at constant speed, each equation can be modelled after this expression:
[tex]y = y_{o} + \dot y \cdot t[/tex]
Where:
[tex]y_{o}[/tex] - Intial elevation of the airplane, measured in feet.
[tex]\dot y[/tex] - Climbing/Descending rate of the airplane, measured in feet per minute. (Positive - Climbing, Negative - Descending)
[tex]t[/tex] - Time, measured in minutes.
Equations are described below:
Plane 1
[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]
Plane 2
[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]
rewrite the following without an exponent (-7)-1
Answer:
Step-by-step explanation:
-7-1=-8
What is the value of X?
Answer:
the answer to the problem is 35.
Answer:
he horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"
Step-by-step explanation:
Question 20 (5 points)
In a jet engine, what purpose does the afterburner serve?
A,) It reheats the gas from the fuel and releases it more rapidly.
B.) It burns fuel once the plane reaches its maximum altitude.
C.) After the plane lands, it burns off excess fuel that wasn't used in flight.
D.) It provides a way to slow the plane down by cooling the exhaust gas.
It reheats the gas from the fuel and releases it more rapidly.
The answer is option A.
How long can a jet fly on an afterburner?In full afterburner at low altitudes, the F-16 can burn in excess of 64,000 pounds an hour. At full throttle, a U.S.-variant F-16 with maximum external fuel stores has about 20 minutes until it's on emergency reserves (which would only last an extra minute or so at full afterburner).
Does afterburner increase thermal efficiency?Since the exhaust gas already has a reduced oxygen content, owing to the previous combustion, and since the fuel is not burning in a highly compressed air column, the afterburner is generally inefficient in comparison to the main combustion process.
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What’s the correct answer for this question?
Answer:
D.
Step-by-step explanation:
For independent events
P(A and B) = P(A) × P(B)
FINDING P(B)
P(B) = P(A and B) /P(A)
P(B) = 0.6/0.8
P(B) = 0.75
A password for a website must have 4 different digits. What is the probability a password chosen at random is 7654?
Please show work thanks
The 1st digit is 1 out of 10 numbers
The 2nd digit is 1 out of 9 numbers
The 3rd digit is 1 out of 8 numbers
The 4th digit is 1 out of 1 numbers.
Total combinations are 10 x 9 x 8 x 7 = 5040
Since the combination 7654 is one out of the total the probability would be 1/5040
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
- 8b³+5ab²+7a²b
Step-by-step explanation:
(32ab³ - 20a²b² - 28a³b)/(-4a)= - 8b³+5ab²+7a²b
The required return on equity is:
A) It has nothing to do with market risk premium
B) generally less than post-tax debt costs.
C) A debt/capital ratio of 0.5 is smaller than WACC.
D) is directly related to the risk of the company's assets.
E) It is generally the reciprocal of inflation.
Answer:
D) is directly related to the risk of the company's assets.
Step-by-step explanation:
Equity which may be defined as what the difference between what your business worth minus what you owe in it.
It can also be put in a way as the remaining value of an owners interest in a particular company after all debt might have been cleared.
Equity= assets - liability
So equity has a lot to do in the risk management of a business or a particular company.
Given the data shown below, which of the following is the best prediction for
the number of years it will take for the population to reach 200,000?
Year
Population
11,920
2
16,800
3
23,300
4
33,000
5
45,750
6
64,000
O A. 9.41
O B. 12.45
O C. 15.82
O D. 18.14
Answer:
The best prediction for the number of years it will take for the population to reach 200,000 is 9.41
Step-by-step explanation:
Year Population
1 11,920
2 16,800
3 23,300
4 33,000
5 45,750
6 64,000
[tex]y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)[/tex]
Substitute the values
[tex]11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2[/tex]
Divide 1 and 2
[tex]\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238[/tex]
The exponential function that passes through the points (1, 11920) and (2, 16800) is[tex]y=8457.5238 e^{0.3432t}[/tex]
Now we are supposed to find the best prediction for the number of years it will take for the population to reach 200,000
[tex]200000=8457.5238 e^{0.3432t}[/tex]
[tex]\frac{200000}{8457.5238}=e^{0.3432t}[/tex]
[tex]ln(\frac{200000}{8457.5238})=0.3432t[/tex]
t = 9.41
Hence the best prediction for the number of years it will take for the population to reach 200,000 is 9.41
Amy's car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas she needs, in liters, to fill the gas tank.
Answer:
37.8541 litres.
Step-by-step explanation:
To find the amount of gas that she needs to fill her gas tank is 19 -9. She needs 10 gallons to fill her tank.
It says to state in litres, so convert.
1 gallon is about 3.78541 liters, so 10 gallons is 37.8541 litres
Hope that helped : )
I keep gettin this wrong please help!!!
Answer:
Slow = 30
Fast = 50
Step-by-step explanation:
So make variables for the speed.
Slow wanderer = x
Faster wanderer = x + 20
The time it took was 2.5 hours.
2.5x + 2.5x + 50 = 200
5x + 50 = 200
x = 30
I am just confused can someone help please...
What is the completely factored form of polynomial 5X cubed +20 X squared plus 2X +8
Step-by-step explanation:
5x3 + 20x2 + 2x + 8
5x2 (x + 4) + 2(x + 4)
(5x2 + 2) (x + 4)
A standard card deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled deck, without replacement. Complete parts a through c below. a. Determine whether the following statement is true or false. The probability of being dealt three black cards is one half times one half times one half equals one eighth . If true, explain why. If false, show how to get the correct probability.
Answer:
6 / 51
Step-by-step explanation:
It is false.
Reason:
The probability of picking a black card at first is:
26 / 52 = 1/2
There are now 25 black cards and 51 cards in total.
The probability of picking another black card, if there's no replacement is now:
25 / 51
Now, there are 24 black cards and 50 cards left in total.
The probability of picking a black card without replacement now becomes:
24 / 50 = 12 / 25
Hence, the probability of picking three black cards without replacement is:
1/2 * 25/51 * 12 / 25 = 300 / 2550
In simplest form, it is 6 / 51
Keep getting this wrong please help!!!
Answer:
14.13 in³
Step-by-step explanation:
Volume of a ball (sphere) is:
V = ⁴/₃ π r³
Circumference of a ball (circle) is:
C = 2π r
Use the circumference to find the radius.
9.42 in = 2π r
r = 1.50 in
Use the radius to find the volume:
V = ⁴/₃ π (1.50 in)³
V = 14.13 in³
Directions:
Write and solve a proportion to answer the question.
1/5 is 40% of what number?
Answer:
20/40
Step-by-step explanation:
1/5=40/100*x
x=1/5*100/40
x=20/40 or 10/20 or 0.5
Y is directly proportional to (x+2)2 when x=8 y = 250 find y when x=4
Answer: 150
Step-by-step explanation: K is constant
250= K (8+2)2
250= K (10)2
250= K (20)
250= K20
divide both sides by 20
250/20= K
12.5= K
THEREFORE
Y= K (4+2)2
Y= 12.5 (6)2
Y= 12.5 × 12
Y= 150
At x = 4 the value of the variable y will be 90 as per the proportionality given.
What is proportionality?The property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, Y is directly proportional to (x+2)2 when x=8 y = 250
Since Y ∝ (x + 2)²
Y = k (x + 2)²
Where k is constant
For x = 8 y = 250
Substituting the values
250 = k(8 + 2)²
k = 2.5
Thus for x= 4
y = 2.5 (4 + 2)²
y = 90
therefore, According to the proportionality, the variable y will have a value of 90 at x = 4.
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