Answers
Related Questions
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
Answers
The dimensions of the Norman window that admit the greatest possible amount of light are approximately:
Width (w) ≈ 11.72 ft
Height (h) ≈ 2.91 ft
To find the dimensions of the Norman window that admit the greatest possible amount of light, we need to maximize the area of the window. The window consists of a rectangle and a semicircle, so the area is the sum of the areas of both shapes.
Let's assume the width of the rectangle is "w" and the radius of the semicircle is "r".
Since the diameter of the semicircle is equal to the width of the rectangle, the radius "r" is half of "w".
Area of the rectangle = w * h, where h is the height of the rectangle.
Area of the semicircle = (1/2) * π * r²
The perimeter of the window is given as 30 ft, which can be written as:
Perimeter = 2 * (w + h) + π * r + w
Since r = w/2, we can rewrite the perimeter equation as:
Perimeter = 2 * (w + h) + (π/2) * w + w
Perimeter = 2w + 2h + (π/2 + 1) * w
Given that the perimeter is 30 ft, we have:
30 = 2w + 2h + (π/2 + 1) * w
Now, we can express "h" in terms of "w" using the perimeter equation:
h = (30 - 2w - (π/2 + 1) * w) / 2
Next, let's express the area "A" of the window in terms of "w" using the formulas for the area of the rectangle and the semicircle:
Area (A) = Area of rectangle + Area of semicircle
A = w * h + (1/2) * π * r²
A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w/2)²
A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w² / 4)
Now, we want to maximize the area "A."
To find the maximum value, we take the derivative of "A" with respect to "w" and set it equal to zero:
dA/dw = (30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0
Solving for "w":
(30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0
(30 - 2w - (π/2 + 1) * w) + (π/2) * w = 0
(30 - (2 + π/2) * w) + (π/2) * w = 0
30 - (2 + π/2) * w + (π/2) * w = 0
(30 - 2w) + (π/2 - π/4) * w = 0
30 - 2w + (π/4) * w = 0
(π/4) * w - 2w = -30
w ((π/4) - 2) = -30
w = -30 / ((π/4) - 2)
w ≈ 11.72 ft
Now that we have the value of "w," we can find the value of "h" using the perimeter equation:
Perimeter = 2w + 2h + (π/2 + 1) * w
30 = 2(11.72) + 2h + (π/2 + 1) * (11.72)
30 = 23.44 + 2h + (π/2 + 1) * 11.72
2h = 30 - 23.44 - (π/2 + 1) * 11.72
2h = 6.56 - (π/2 + 1) * 11.72
h = (6.56 - (π/2 + 1) * 11.72) / 2
h ≈ 2.91 ft
So, the dimensions of the Norman window that admit the greatest possible amount of light are approximately:
Width (w) ≈ 11.72 ft
Height (h) ≈ 2.91 ft.
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The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis
Foundation. This foundation was created to help ease the pain of HIV/AIDS in Africa Lewis, a Canadian
works for the United Nations trying to determine ways to stop the spread of this deadly disease from crippling
an entire continent
a. Choose a variable to represent the money earned during fundraising activities and the revenue generated
for the foundation
b. Use these variables to create an equation that will determine the amount of money the foundation will
receive
c. In their latest bake sale, the club raised $72. Calculate the amount the foundation will receive
d. At the end of the year, the World Issues Club mailed a cheque to the foundation for $850. How much
money did they fundraise in total?
Answers
Answer:
a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.
b. [tex]M =0.60x[/tex]
c. $43.2
d. $1416.67
Step-by-step explanation:
Given that:
The World Issues club donates 60% of the total of their fundraising activities.
Answer a.
Let us choose the variable [tex]x[/tex] to represent the money earned during fundraising activities and [tex]M[/tex] for the revenue generated for foundation.
Answer b.
Foundation will receive 60% of the total of the fundraising activities.
Equation to determine the money that will be received by foundation:
[tex]M = 60\%\ of\ x\\OR\\M = 0.6x[/tex]
Answer c.
Given that x = $72, M = ?
Putting the value of x in the equation above:
[tex]M = 0.6 \times 72\\\Rightarrow \$43.2[/tex]
Answer d.
Given that M = $850, x = ?
Putting the value of M in the equation above to find x:
[tex]850= 0.6 \times x\\\Rightarrow x = \dfrac{850}{0.6}\\\Rightarrow x = \$ 1416.67[/tex]
So, the answers are:
a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.
b. [tex]M =0.60x[/tex]
c. $43.2
d. $1416.67
Given that IG is perpendicular to FT, which of the following statements is true?
Answers
Answer:
B ). IF = IT
Step-by-step explanation:
IG is perpendicular to FT, means that the line IG divides the line FT into two equal parts without remainder.
Line IG does not only divide line FT, it also bisect the arc FT into two equally parts also.
It also divide the segment of the circle FIT into two equal parts.
So to the correct answer to the question, IF = IT
Emily and George had a farm with a new barn.
True
False
Answers
Answer:
true
Step-by-step explanation:
it is so because they are brother and sister
And in the chapter there is that they had farm with a new barn
if in your book lesson there is that they had no farm with a new barn then there will be false
Now did you understood?
Answer:
True
Step-by-step explanation:
two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability of choosing a diamond and then without replacement another diamond? express your answer as a fraction or decimal number rounded to four decimal places.
Answers
Answer:
1/17
Step-by-step explanation:
There are 13 diamond cards in a standard 52-card deck.
First drawing:
13 diamonds
52 total cards
After the first drawing you already took a diamond, so there are 12 diamonds left out of 51 total cards.
p(diamond and diamond) = 13/52 * 12/51 = 1/4 * 4/17 = 1/17
The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.6 sine (3520 pi t). What is the frequency of the tuning fork?
Answers
Answer:
The frequency of the tuning fork is 1760 Hz.
Step-by-step explanation:
Suppose we have a sine function in the following format:
[tex]y = A\sin{Bx + C}[/tex]
The period is:
[tex]T = \frac{2\pi}{B}{/tex]
The frequency, in Hz, is:
[tex]F = \frac{1}{T}[/tex]
In this question:
[tex]d = 0.6\sin{3520\pi t}[/tex]
So
[tex]B = 3520\pi, T = \frac{2\pi}{3520} = \frac{2}{3520}, F = \frac{1}{T} = \frac{1}{\frac{2}{3520}} = \frac{3520}{2} = 1760[/tex]
The frequency of the tuning fork is 1760 Hz.
Answer:
its C. 1760 Hz
on edge2020
What is the greatest common factor of the polynomial below 12x^2-9x
Answers
Answer:
the greatest common factor of this is 3
The prize in a raffle is a flat-screen TV valued at $350, and 1,000 tickets are sold for a dollar each. Let’s find the expected value if you buy 1 ticket. Find the expected value. Round your answer to two decimal places. Remember a gain would be posit
Answers
Answer:
the expected value EV = −$0.65
Step-by-step explanation:
Expected value EV = expected gain - expected loss
Given;
Cost of a ticket L = $1
Probability of losing the ticket P(L)= 999/1000 = 0.999
Cost of a flat screen TV = $350
Expected gain G = $350 - $1 = $349
Probability of winning the TV P(G) = 1/1000 = 0.001
EV = G × P(G) - L × P(L)
Substituting the values;
EV = $349 × 0.001 - $1 × 0.999
EV = −$0.65
the expected value EV = −$0.65
The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.Private Colleges 52.8 30.6 43.2 45.8 45.0 37.8 33.3 50.5 44.0 42.0 Public Colleges 20.3 22.8 22.0 25.8 28.2 18.5 15.6 25.6 24.1 14.4 28.5 21.8 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places.
S1 =
S2 =
b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place.
Interpret this value in terms of the annual cost of attending private and public colleges.$
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges.
Answers
Answer:
Step-by-step explanation:
a) For private colleges,
Mean = (52.8 + 30.6 + 43.2 + 45.8 + 45.0 + 37.8 + 33.3 + 50.5 + 44.0 + 42.0)/10 = 42.5
x1 = 42.5 × 1000 = 42500
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (52.8 - 42.5)^2 + (30.6 - 42.5)^2 + (43.2 - 42.5)^2 + (45.8 - 42.5)^2 + (45.0 - 52.5)^2 + (37.8 - 42.5)^2 + (33.3 - 42.5)^2 + (50.5 - 42.5)^2 + (44.0 - 42.5)^2 + (42.0 - 52.5)^2 = 598.56
standard deviation = √(598.56/10 = 7.74
s1 = 7.74 × 1000 = 7740
For public colleges,
Mean = (20.3 + 22.8 + 22.0 + 25.8 + 28.2 + 18.5 + 15.6 + 25.6 + 24.1 + 14.4 28.5 + 21.8)/12 = 22.3
x2 = 22.3 × 1000 = 22300
n2 = 12
Summation(x - mean)² = (20.3 - 22.3)^2 + (22.8 - 22.3)^2 + (22 - 22.3)^2 + (25.8 - 22.3)^2 + (28.2 - 22.3)^2 + (18.5 - 22.3)^2 + (15.6 - 22.3)^2 + (25.6 - 22.3)^2 + (24.1 - 22.3)^2 + (14.4 - 22.3)^2 + (28.5 - 22.3)^2 + (21.8 - 22.3)^2 = 225.96
standard deviation = √(225.96/12 = 4.34
s2 = 4.34 × 1000 = 4340
b) The point estimate is the difference between the sample means
Point estimate = 42500 - 22300 = 20200
The best guess for the difference in population mean annual cost of attending private and public colleges is $20200. The range of the value is determined by the margin of error.
c) Confidence interval = point estimate ± margin of error
Margin of error = z√(s²/n1 + s2²/n2)
Where z is the test score for 95% confidence level from the t distribution table. To find the test score, we would first find degree of freedom, df
df = (n1 - 1) + (n2 - 1) = (10 - 1) + (12 - 1) = 20
From the t distribution table,
z = 2.086
Margin of error = 2.086√(7.74²/10 + 4.34²/12) = 4.84
4.84 × 1000 = 4840
Confidence interval = 20200 ± 4840
what is Divide −240 by 8
Answers
-30
Explanation:
1. A negative divided by a positive = a negative
2. 8•-30=-240
I hope this helps you!!
The division -240 by 8 gives the quotient is -30.
What is Division?The division is one of the four introductory fine operations, the other three being addition, deduction, and addition. In simple words, division can be defined as the splitting of a large group into lower groups similar that every group will have an equal number of particulars. It's an operation used for equal grouping and equal sharing in calculation.
We have to divide -240 by 8.
So, the division is
8 | -240 | 30
24
____
00
Thus, the quotient is -30.
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Which graph represents the function?
Answers
the answer is the bottom left option
Please answer this correctly
Answers
Answer:
9/49
Step-by-step explanation:
The probability of landing on an even number is 3/7.
Because there are only 3 numbers even out of 7 total numbers.
[tex]3/7 \times 3/7[/tex]
[tex]= 9/49[/tex]
What is the circumference of the circle below? (Round your answer to the nearest tenth.)
Answers
Hey there! :)
Answer:
75.4 cm.
Step-by-step explanation:
Formula for the circumference of a circle:
C = 2rπ
Given:
r = 12 cm
Plug this value of r into the equation:
C = 2(12)π
C = 24π
Multiply by π (3.14)
24 × 3.14 = 75.36 cm
Round to nearest tenth:
75.36 ≈ 75.4 cm.
Answer: B
Step-by Step: C=2n
r= 2•n•12= 75.39822
You round it to the nearest tenth, it would be 75.4
At an international conference, flags from 8 different countries will be displayed. Of these flags, 4 are from the continent of Africa and 4 flags are from the continent of Europe. The flags will be displayed in a row, alternating between continents. A flag from Africa will be in the first position. In how many ways can the flags be displayed?
Answers
Answer:
96 ways
Step-by-step explanation:
Let´s call flags of countries from Africa as A₁, A₂, A₃, A₄, and from Europe as E₁, E₂, E₃ and E₄
We have to display the flags always beginning with one flag from Africa let´s take A₁
For that flag, we have 4! possibilities Then 4! is:
4*3*2*1 = 24
As we have 4 different Flags from Africa, we will have
4*24 = 96 possibilities
Of the following points, name all that lie on the same horizontal line? (7,-1) (2,-1) (-3,9) (-3,-1)
Answers
Hey there!
If everything is on the same horizontal level, it is at the same elevation, or height. On a graph, the elevation is the y-value. So, if we want the points to on the same horizontal line, they have to have the same y-value.
The points that all share the y-value of -1 are (7,-1), (2,-1), and (-3,-1). Since (-3,9) is at a different y-value it is not on the horizontal line of y=-1.
Have a wonderful day!
Answer:
A (7,-1)
B (2,-1)
D (-3,-1)
Step-by-step explanation:
Well lets plot the following points on a graph first,
A (7,-1)
B (2,-1)
C (-3,9)
D (-3,-1)
Look at the image below ↓
By looking at the graph we can tell that points,
A, B, and D lie on the same horizontal line.
Thus,
points A, B, and D lie on the same horizontal line.
Hope this helps :)
Priya was busy studying this week and ran 7 fewer miles than last week. She ran 3 times as far as Elena ran this week. Elena only had time to run 4 miles this week. How many miles did Priya run last week?
Answers
Answer:Priya ran 19 miles last week
Step-by-step explanation:
4 x 3 = 12
12 + 7 = 19
Someone help me please pls pls pls
Answers
Answer:
There is 9 on each pace and 3 on a row
Step-by-step explanation:
54/6=9
if there is 9 on each side and the same on each side, then it has to be 3 in each row and column. Also, this is a Rubix cube
Please give me brainliest, it really helps! :)
Have a good day!
John multiplied 400,000 by 7,800 on his calculator. He got the result shown on his calculator display. What is this number in standard form? A calculator screen that shows 3 point 1 2 E 9. A 0.00000000312 B 0.000000312 C 312,000,000 D 3,120,000,000
Answers
Answer:
D
Step-by-step explanation:
jtrsytexjgfcgvhjbkjnhgfdsasdfghjhgrertyu
Answer:
Correct answer is D
Step-by-step explanation:
How long will it take 3800 to grow into 5700 if it’s invested at 6% interest compounded continuously?
Answers
Answer:
1234567891234567890
Answer: 25 years
Step-by-step explanation:
t = I / Pr
t = 5700 / ( 3800 × 0.06 ) = 25
t = 25 years
Consider the following hypothesis test:
H0:
≤ 50
Ha: > 50
A sample of 55 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05.
a. With = 52.5, what is the value of the test statistic (to 2 decimals)?
Can it be concluded that the population mean is greater than 50?
Yes or No
b. With = 51, what is the value of the test statistic (to 2 decimals)?
Can it be concluded that the population mean is greater than 50?
Yes or No
c. With = 51.8, what is the value of the test statistic (to 2 decimals)?
Can it be concluded that the population mean is greater than 50?
Yes or No
Answers
Answer:
a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.
b. z=1.24. No, it can not be concluded that the population mean is greater than 50.
c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.
Step-by-step explanation:
We have a hypothesis test for the mean, with the hypothesis:
[tex]H_0: \mu\leq50\\\\H_a:\mu> 50[/tex]
The sample size is n=55 and the population standard deviation is 6.
The significance level is 0.05.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{55}}=0.809[/tex]
For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.
a. If the sample mean is M=52.5, the test statistic is:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{52.5-50}{0.809}=\dfrac{2.5}{0.809}=3.09[/tex]
The null hypothesis is rejected, as z>zc and falls in the rejection region.
b. If the sample mean is M=51, the test statistic is:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51-50}{0.809}=\dfrac{1}{0.809}=1.24[/tex]
The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.
c. If the sample mean is M=51.8, the test statistic is:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51.8-50}{0.809}=\dfrac{1.8}{0.809}=2.22[/tex]
The null hypothesis is rejected, as z>zc and falls in the rejection region.
Given an objective function value of 150 and a shadow price for resource 1 of 5, if 10 more units of resource 1 are added (assuming the allowable increase is greater than 10), what is the impact on the objective function value?
Answers
Answer:
The impact on the objective function is that it is increased by 50.
Step-by-step explanation:
In this case we have that the value of the objective function is 150, and they tell us that 10 more units of resource one are added, but they tell us that the shadow price ranges from 1 to 5, therefore:
10 * 5 = 50
Which means that the impact on the objective function is that it is increased by 50.
In 1968, vehicle emission standards allowed
6.3 hydrocarbons released per mile driven. By 1980, the
standards allowed only 0.41 hydrocarbons per mile driven.
What was the rate of change from 1968 to 1980?
Answers
Answer:
Step-by-step explanation:
In 1968, vehicle emission standards allowed 6.3 hydrocarbons released per mile driven and by 1980, the
standards allowed only 0.41 hydrocarbons per mile driven. This means that the change in the amount of hydrocarbons released per mile driven as allowed by the vehicle emission standards between 1968 and 1980 is
6.3 - 0.41 = 5.89
Therefore, the percentage rate of change in the amount of hydrocarbons released per mile driven as allowed by the vehicle emission standards between 1968 and 1980 would be
5.89/6.3 × 100 = 93.49%
(1 point) A vendor sells ice cream from a cart on the boardwalk. He offers vanilla, chocolate, strawberry, blueberry, and pistachio ice cream, served on either a waffle, sugar, or plain cone. How many different single-scoop ice-cream cones can you buy from this vendor
Answers
Answer:
six single scoops icecream cones
a bag contains 6 cherry 3 orange and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability of all lemons
Answers
Answer:
0.181818
Step-by-step explanation:
There are total 11 candies. The possibility of combinations is 165 which is found by using computation technique 11C3. It is assumed that order does not matter. There are 3 pieces of candy are selected at random. There are 6C2 which is 15 different ways to select cherry and lemon. There are 30 ways to choose 2 cherry and a lemon combination. The probability is [tex]\frac{30}{165}[/tex] = 0.181818
If you can help with the explanation I will mark brainpower
Answers
Answer:
It is 90º
Step-by-step explanation:
Looking at the picture, we realize that the angle direcly beside it, EGD, is 90º. Now, both angles form a straight line, which equals 180º. 180-90= 90º.
Answer: A 40 B 50 C 90 D 130
where they go: B goes under A, D goes under the whole thing, just like E (although that doesn't want to be answered) and C goes under B
hope this helped
What is the solution of the system? {2x+y=15x−y=3 Enter your answer in the boxes. ( , )
Answers
Step-by-step explanation:
2x+y=15x-y=3
then u group like terms
2x-15x= -y+y=3
then ur answer
13x=3
Find the value of x. Please help! Thanks.
Answers
Answer:
[tex]\huge\boxed{x=\sqrt{30}}[/tex]
Step-by-step explanation:
ΔABC and ΔBDC are similar (AAA).
Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]
substitute
[tex]AC=7+3=10\\{BC}=x\\CD=3[/tex]
[tex]\dfrac{10}{x}=\dfrac{x}{3}[/tex] cross multiply
[tex](10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}[/tex]
Manueala scored -4 \dfrac12−4 2 1 minus, 4, start fraction, 1, divided by, 2, end fraction points relative to her season average against the China Dragons. She scored 1 \dfrac121 2 1 1, start fraction, 1, divided by, 2, end fraction points relative to her season average against the Canada Moose. Drag the white cards onto the gray rectangle to write an inequality that correctly compares Manueala's relative numbers of points. Which one of the following descriptions is correct? Choose 1 answer: Choose 1 answer: (Choice A) A Manueala scored more points against the China Dragons than against the Canada Moose. (Choice B) B Manueala scored more points against the Canada Moose than against the China Dragons.
Answers
Answer:
1 1/2 > - 4 1/2 and Manuela scored more points against the Canada Moose than against the China Dragons.
Please help me!!!!!!!!
Answers
Step-by-step explanation:
might be option c is a correct answer of your given question
In a random sample of 964 young adults aged 18-29, it was found that 196 of them were married. Construct a 99% confidence interval for the proportion of married young adults aged 18-29.
Answers
Answer:
99% confidence interval for the proportion of married young adults aged 18-29.
(0.1779 , 0.2287)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 964
Given data a random sample of 964 young adults aged 18-29, it was found that 196 of them were married
sample proportion
[tex]p^{-} = \frac{196}{964} = 0.2033[/tex]
Step(ii):-
99% confidence interval for the proportion of married young adults aged 18-29.
[tex](p^{-} - Z_{0.05} \sqrt{\frac{p^{-}(1-p^{-} ) }{n} } ,p^{-} +Z_{0.05} \sqrt{\frac{p^{-}(1-p^{-} ) }{n} })[/tex]
[tex](0.2033 -1.96 \sqrt{\frac{0.2033(1-0.2033 ) }{964} } ,0.2033 +1.96\sqrt{\frac{0.2033(1-0.2033 ) }{964} })[/tex]
(0.2033 - 0.02540 , 0.2033 +0.02540)
(0.1779 , 0.2287)
Conclusion:-
99% confidence interval for the proportion of married young adults aged 18-29.
(0.1779 , 0.2287)