The probability that Eli's playlist will still be playing at 11 p.m. is approximately 0, indicating it's very unlikely for the playlist to be still playing at that time.
To find the probability that Eli's playlist will still be playing at 11 p.m., we need to calculate the cumulative probability up to 11 p.m. based on the average length and standard deviation of the songs.
First, let's convert the given time into minutes for easier calculation. 11 p.m. is 60 minutes after 9:50 p.m., so it corresponds to 70 minutes.
Next, we need to calculate the mean (average) length of a song in minutes. The average length in seconds is given as 197 seconds, so we divide it by 60 to get the average length in minutes:
Mean (μ) = 197 seconds / 60 = 3.28 minutes
The standard deviation (σ) is given as 33 seconds, which also needs to be converted to minutes:
Standard Deviation (σ) = 33 seconds / 60 = 0.55 minutes
Now, we can use these values to calculate the probability using the Normal distribution.
We want to find P(X > 70), where X represents the length of a song.
Using the Z-score formula:
Z = (X - μ) / σ
where Z is the standard score or Z-score, X is the value we're interested in, μ is the mean, and σ is the standard deviation.
Plugging in the values:
Z = (70 - 3.28) / 0.55 ≈ 126.87
To find the probability, we need to calculate the area under the curve to the right of the Z-score. We can use a Z-table or a calculator to find this value.
Assuming a standard normal distribution, the probability can be calculated as follows:
P(Z > 126.87) = 1 - P(Z < 126.87)
Using a Z-table or a calculator, we can find that P(Z < 126.87) is virtually 1 (it's extremely close to 1), so:
P(Z > 126.87) ≈ 1 - 1 ≈ 0
Therefore, the probability that Eli's playlist will still be playing at 11 p.m. is approximately 0, indicating it's very unlikely for the playlist to be still playing at that time.
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Can you show me how to answer this question?
Answer:
Rollerskates: 9 miles/hr
Bike: 17.5 miles/hr
Step-by-step explanation:
How fast→ referring to speed
Speed= distance/ time
Rollerskates:
Distance= ¾ mile
Time= 5 mins
Since the question wants the speed to be in miles per hour, convert the time from minutes to hours.
60 mins= 1 hr
1 min= 1/60 hr
Time= 5/60 hr
Speed
[tex] = \frac{3}{4} \div \frac{5}{60} \\ = \frac{3}{4} \times \frac{60}{5} \\ = 9 \: miles/hr[/tex]
Bike:
Distance= 3.5 miles
Time
= 12 mins
= 12/60 hr
= ⅕ hr
Speed
= distance ÷ time
= 3.5 ÷ ⅕
= 3.5 ×5
= 17.5 miles/hr
If f(x)=3x+2, find the following value:
f(4)=?
Answer:
f(4)=14
Step-by-step explanation:
f(x)=3x+2
f(4)=3x+2
f(4)=3*4+2
f(4)=12+2
f(4)=14
Hope this helps!
I need help ASAP please!!!!!!
Answer:
1. d
2. c
3. b
4. a
Step-by-step explanation:
Answers:
1. d
2. c
3. b
4. a
================================================
Explanation:
For problem 1, subtracting a negative is the same as adding a positive. The two negatives cancel out
In problem 2, we can add a negative to mean we're subtracting. One way to think of it is like adding on debt to your bank balance.
Problem 3 is similar to problem 2. The first term -17 isn't changed.
Problem 4 is similar to problem 1. The only difference is that the 17 is negative this time around.
A flashlight shines straight up into the sky, 9 ft to the right of a tent located at the origin. For which values of A, B, and C will Ax+By=C represent the beam of light?
please say the answer as a= b= c=
Answer:
The right answer is "a = 1, b = 0, c = 9"
Step-by-step explanation:
As the direction would have to be vertical, this same direction should therefore seem to have a consistent or constant x-coordinate.
∴ The equation a line is:
⇒ [tex]x=9[/tex]
On comparing it with:
⇒ [tex]Ax+By=C[/tex]
We get,
[tex]A=1\\[/tex]
[tex]B=0[/tex]
[tex]C=9[/tex]
u got snap and wanna ft breanna_8406
Answer:
hiiiii
Step-by-step explanation:
Answer:
-.-_-.- rlly dont use this just to find friends
Step-by-step explanation:
Learning Task 3. Solve for the variable of the following quadratic equations
A. by extracting square roots.
1. x2 = 169
4. (x - 2)2 = 16
2. 9b2 = 25
5. 2(t - 3)2 - 72 = 0
3. (3y - 1)2 = 0
B. by factoring
1. x2 + 7x = 0
3. x2 + 5x - 14 = 0
2. m2 + 8m = -16
4. 2y2 +8y - 10= 0
C. by completing the square.
1. x2 + 5x + 6= 0
2. x2 + 2x = 8
3. 2x2 + 2x = 24
D. using quadratic formula.
1. x2 + 5x = 14
2. 2x2 +8x - 10= 0
3. 2x2 + 3x = 27
Answer:
A. By extracting square roots
1. x = 13
4. x = 6
2. b = 5/3
5. t = 9
3. y = 1/3
B. By factoring
1. x = -7
3. x = -7 or x = 2
2. m = -8 or m = -2
4. y = -5 or y = 1
C. By completing the square
1. x = 2 or x = 3
2. x = 10 or x = -8
3. x = 3 or x = -4
D. Using the quadratic formula
1. x = 2 or x = -7
2. x = 1 or x = -5
3. x = 3 or x = -4.5.
Step-by-step explanation:
A. By extracting square roots
1. x² = 169
Extracting square roots from both sides of the equation gives;
√(x²) = x and √169 = 13
∴ √(x²) = √169 = 13
x = 13
4. (x - 2)² = 16
Extracting square roots from both sides of the equation gives;
√(x - 2)²= √16 = 4
However;
√(x - 2)² = x - 2
∴ x - 2 = √16 = 4
x - 2 = 4
x = 4 + 2 = 6
x = 6
2. 9·b² = 25
√(9·b²) = √25 = 5
√(9·b²) = √9 × √(b²) = 3·b
∴ 3·b = √25 = 5
3·b = 5
b = 5/3
5. 2·(t - 3)² - 72 = 0
2·(t - 3)² = 72
(t - 3)² = 72/2 = 36
t - 3 = √36 = 6
t = 6 + 3 = 9
t = 9
3. (3·y - 1)² = 0
√(3·y - 1)² = √0
∴ 3·y - 1 = 0
3·y = 0 + 1 = 1
y = 1/3
B. By factoring
1. x² + 7·x = 0
By factoring, we have;
x·(x + 7) = 0
(x + 7) = 0/x = 0
x + 7 = 0
x = 0 - 7 = -7
x = -7
3. x² + 5·x - 14 = 0
Noting that 7 × (-2) = -14 and 7 + (-2) = 5, we get;
x² + 5·x - 14 = (x + 7)·(x - 2) = 0
∴ x = -7 or x = 2
2. m² + 8·m = -16
m² + 8·m + 16 = 0
Which gives;
m² + 8·m + 16 = (m + 8) × (m + 2) = 0
m = -8 or m = -2
4. 2·y² + 8·y - 10 = 0
Which gives;
2·(y² + 4·y - 5) = 0
y² + 4·y - 5 = 0/2 = 0
y² + 4·y - 5 = (y + 5) × (y - 1) = 0
y = -5 or y = 1
C. By completing the square
1. x² + 5·x + 6 = 0
x² + 5·x = -6
Adding (5/2)² to both sides of the equation gives;
x² + 5·x + (5/2)² = -6 + (5/2)²
Which gives;
(x + 5/2)² = -6 + (5/2)² = 1/4
x + 5/2 = ±√(-6 + (5/2)²) = ±√(1/4)
x + 5/2 = ±1/2
x = 5/2 - 1/2 or x = 5/2 + 1/2
∴ x = 2 or x = 3
2. x² + 2·x = 8
x² + 2·x + (2/2)² = 8 + (2/2)²
2/2 = 1 and (2/2)² = 1² = 1
∴ x² + 2·x + (2/2)² = 8 + (2/2)² gives;
x² + 2·x + 1 = 8 + 1 = 9
(x + 1)² = 9
x + 1 = ±√9
x = 1 + 9 or x = 1 - 9
x = 10 or x = -8
3. 2·x² + 2·x = 24
2·(x² + x) = 24
x² + x = 24/2 = 12
x² + x = 12
x² + x + (1/2)² = 12 + (1/2)²
(x + 1/2)² = 12 + (1/2)² = 49/4
√(x + 1/2)² = √(49/4) = ±7/2 = ± 3.5
x + 1/2 = ±3.5
x = -1/2 + 3.5 or x = -1/2 - 7/2
x = -0.5 + 3.5 or x = -0.5 - 3.5
x = 3 or x = -4
D. Using the quadratic formula
1. x² + 5·x = 14
Simplifying, gives;
x² + 5·x - 14 = 0
The quadratic formula for the equation, a·x² + b·x + c = 0, is given as follows;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
Comparing with the equation in the question, we get;
[tex]x = \dfrac{-5\pm \sqrt{5^{2}-4\times 1\times(-14)}}{2\times 1} = \dfrac{-5\pm \sqrt{81}}{2} = \dfrac{-5\pm 9}{2} = \dfrac{-5+ 9}{2} \ or \dfrac{-5 - 9}{2}[/tex]
x = 4/2 or x = -14/2
x = 2 or x = -7
2. 2·x² + 8·x - 10 = 0
quest
2. 2·x² + 8·x - 10 = 0
[tex]x = \dfrac{-8\pm \sqrt{8^{2}-4\times 2\times(-10)}}{2\times 2} = \dfrac{-8\pm \sqrt{144}}{4} =\dfrac{-8+ 12}{4} \ or \dfrac{-8 - 12}{4}[/tex]
x = 4/4 or x = -20/4
x = 1 or x = -5
3. 2·x² + 3·x = 27
Rewriting the above equation in the form a·x² + b·x + c = 0, we get;
2·x² + 3·x - 27 = 0
Which gives;
[tex]x = \dfrac{-3\pm \sqrt{3^{2}-4\times 2\times(-27)}}{2\times 2} = \dfrac{-3\pm \sqrt{225}}{4} =\dfrac{-3+ 15}{4} \ or \dfrac{-3 - 15}{4}[/tex]
x = 12/4 = 3 or x = -18/4 = -4.5
x = 3 or x = -4.5.
7) In 2019, Skylar sold an apartment building for $144,000 cash and a $1,440,000 note due in two years. Skylar's cost of the property was $1,152,000, and he had deducted depreciation of $691,200, $276,480 of which was in excess of what the straight-line amount would have been. a. Under the installment sales method, what is Skylar's total realized gain? b. In 2019, how much § 1250 gain does Skylar recognize? How much § 1231 gain does he recognize?
Answer:
(a) he total realized gain is $1,123,200.
(b) § 1250 gain realized in 2019 is, $276,480.
(c) The § 1231 gain realized in 2019 is, $77040.
Step-by-step explanation:
(a)
Compute Skylar's total realized gain under the installment sales method as follows:
Cash Received = $144,000
Note Receivable = $1,440,000
Total Selling Price = Cash Received + Note Receivable
= $144,000 + $1,440,000
= $1,584,000
Cost of Property = $1,152,000
Deducted Depreciation = $691,200
Adjusted Bias = Cost of Property - Deducted Depreciation
= $1,152,000 - $691,200
= $460,800
Total Realized Gain = Total Selling Price - Adjusted Bias
= $1,584,000 - $460,800
= $1,123,200
Thus, the total realized gain is $1,123,200.
(b)
§ 1250 gain will be same as the amount of depreciation that was in excess of the straight-line amount.
Thus, § 1250 gain realized in 2019 is, $276,480.
(c)
Total Realized Gain = $1,123,200
§ 1250 gain realized in 2019 = $276,480
§ 1231 gain = Total Realized Gain - § 1250 gain realized in 2019
= $1,123,200 - $276,480
= $846,720
The total selling price was, $1,584,000.
Compute the percentage of § 1231 gain of the selling price as follows:
§ [tex]\text{ 1231 gain}\%=\frac{846,720}{1,584,000}\times 100=53.45455\%\approx 53.5\%[/tex]
Thus, 53.5% of the cash received will be the § 1231 gain.
§ 1231 gain realized in 2019 = $144,000 × 53.5% = $77,040.
Thus, the § 1231 gain realized in 2019 is, $77040.
Find the value of X.
3(4x + 8) = - 35+23
Answer:
x = -3
Step-by-step explanation:
3(4x + 8) = - 35+23
Combine like terms
3(4x + 8) =-12
Divide by 3
3/3(4x + 8) = -12/3
4x+8 = -4
Subtract 8 from each side
4x+8-8 = -4-8
4x = -12
Divide by 4
4x/4 = -12/4
x = -3
Answer:
x= -3
Step-by-step explanation:
first distribute 3 into the parenthesis
than it will result in 12x+24=-35+23. Than add -35+23
Than it will result in 12x+24=-12. Than subtract 24 from each sides.
This will result in 12x=-36. Than divide 12/-36 than you get -3 for x
Identify the type of function represented by the equation y = – 3.
a
absolute value
b
quadratic
c
constant
I think the answer of this question is number b. quadratic
if you have a slope of 1/3,what would you do on a graph?
A.go up 1 and right 3
B.go up 3 and 1 right
Answer:
A, go up 1 and right 3
Step-by-step explanation:
when looking at fractions as slope, the numerator is how far up you go, and the denominator is how far over you go.
What value of x makes this equation true?
0.5x - 10 = 0.3x + 20
Answer:
[tex]x[/tex] = 150
0.5[tex]x[/tex] - 10 - 0.3[tex]x[/tex] + 20 = 0.3[tex]x[/tex]
0.2[tex]x[/tex] - 10 = 20
0.2[tex]x[/tex] - 10 + 10 = 20 + 10
0.2[tex]x[/tex] = 30
[tex]\frac{0.2x}{0.2}[/tex] = [tex]\frac{30}{0.2}[/tex]
Answer = 150
Answer: x = 150
Step-by-step explanation: Since our two decimals in this problem, .5 and .3 are both taken to tenths place, we can get rid of the decimals by multiplying both sides of the equation by 10.
This moves the decimals over 1 place to
the right and we have 5x - 100 = 3x + 200.
Next we simply solve from here by subtracting
3x from both sides to get 2x - 100 = 200.
Then adding 100 to both sides to get 2x = 300.
Now divide both sides by 2 and we have x = 150.
Which equation has non-real solutions
Answer: bro u need to give us the answer choices not just the answer
Step-by-step explanation:
Please help, I'm doing graphs and it wont explain what an interval is.
Answer:
Step-by-step explanation:
In mathematics, a interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.
Solve the quadratic equation using square roots method.Leave the answer in irrational form. 15-6x-2x^2=0 HELP
Answer:
The answer is
[tex]x_1 = \frac{ - 3 + \sqrt{39} }{2} \: \:, \: \: \: \: x _2 = \frac{ - 3 - \sqrt{39} }{2} \\ [/tex]
Step-by-step explanation:
15 - 6x - 2x² = 0
Rewriting it we have
2x² + 6x - 15 = 0
Using the quadratic formula that's
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ [/tex]
From the question
a = 2 , b = 6 , c = - 15
So we have
[tex]x = \frac{ - 6 \pm \sqrt{ {6}^{2} - 4(2)( - 15) } }{2(2)} \\ = \frac{ - 6\pm \sqrt{36 + 120} }{4} \\ = \frac{ - 6\pm \sqrt{156} }{4} \: \: \: \: \: \: \: \: \: \: \\ = \frac{ - 6\pm2 \sqrt{39} }{4} \: \: \: \: \: \: \: \: \: \\ = - \frac{6}{4} \pm \frac{2 \sqrt{39} }{4} \: \: \: \: \: \: \: \: \\ = - \frac{3}{2} \pm \frac{ \sqrt{39} }{2} \: \: \: \: \: \: \: \: \: \: \\ = \frac{ - 3\pm \sqrt{39} }{2} \: \: \: \: \: \: \: \: \: \: \: [/tex]
Separate the solutions
We have the final answer as
[tex]x_1 = \frac{ - 3 + \sqrt{39} }{2} \: \: \: \: \: \: x _2 = \frac{ - 3 - \sqrt{39} }{2} \\ [/tex]
Hope this helps you
The ages (years) of three government officials when they died in office were 56, 46, and 60. Complete parts (a) through () a. Assuming that 2 of the ages are randomly selected with replacement, list the difflerent possible samples O A. (56,56), (56,46),(56,60),(46,46),(46,60),(60,60) ○ B. (56,46),(56,60),(46,56),(46.60)·(00,56),(60A6) O C. (56,46),(56,60),(46,60) O D. (56,56), (56,46)(56,60),(46,56),(46,46),(46,60),(60,56),(60,46),(60,60) b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution Sample Range Probability Type an integer or a fraction.) c. Compare the population range to the mean of the sample ranges Choose the correct answer below
a) The different possible samples, assuming 2 ages are randomly selected with replacement, are:
A. (56, 56), (56, 46), (56, 60), (46, 46), (46, 60), (60, 60)
B. (56, 46), (56, 60), (46, 56), (46, 60)
C. (56, 46), (56, 60), (46, 60)
D. (56, 56), (56, 46), (56, 60), (46, 56), (46, 46), (46, 60), (60, 56), (60, 46), (60, 60)
b) To find the range of each sample, we subtract the minimum age from the maximum age. The sampling distribution of the ranges can be summarized in the following table representing the probability distribution:
Sample Range Probability
2 2/9
10 3/9
14 3/9
c) To compare the population range to the mean of the sample ranges, we need the population range. Since the given information only provides the ages of the government officials when they died, the population range cannot be determined. Therefore, we cannot compare the population range to the mean of the sample ranges.
Note: The actual range of the population would depend on the complete set of ages of government officials, which is not provided in the given information.
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The parking lot charges $2 for the first hour plus 50¢ for each additional half hour or part thereof. What is the total charge for parking a car in the lot from 11:30 a.m. until 2:15 p.m.?
Carl, Deb and Ellen formed an equal general partnership.
They contributed the following assets:
Carl: Asset Basis FMV Equipment (all Sec. 1245 gain) $1,000 $3,000 Goodwill 0 5,000 Accounts receivable 0 1,000
Deb: Asset Basis FMV Cash $ 3,000 $3,000 Whiteacre 10,000 4,000 Installment Note 500 2,000
Ellen: Asset Basis FMV Cash $7,000 $7,000 Greenacre 1,000 2,000
Carl had held the equipment for two years and generated the goodwill in his sole proprietorship business, which he had been operating for ten years. Deb had held Whiteacre for five years prior to contribution and had held it for investment purposes. Her installment note was from the sale of land she had held for investment for five years prior to sale. Ellen had held Greenacre for two years prior to contribution and had held it for investment purposes.
a) What are the tax consequences to each of Carl, Deb and Ellen?
b) What are the tax consequences to the partnership?
c) Construct a balance sheet to reflect the situation of the partners and partnership at the time of formation.
Carl, Deb, and Ellen created an equal general partnership by pooling their assets. Because the assets were contributed to the partnership in exchange for ownership interests, there was no gain or loss recognition for Carl, Deb, or Ellen.
The partners will maintain their own capital accounts to reflect the amount and composition of their initial investment in the partnership. The partnership received Carl's equipment, which had a $1,000 basis but a $3,000 fair market value, as well as his goodwill, which had a $0 basis but a $5,000 fair market value. Section 1245 of the Internal Revenue Code applies to depreciable personal property (such as equipment), which means that the difference between basis and fair market value (in this case, $2,000) is taxable as ordinary income. Because the property has been kept for two years, it is a long-term capital gain and is taxed at a lower rate.
The partnership received Deb's cash ($3,000 basis and $3,000 fair market value), Whiteacre (a piece of real estate that Deb has owned for five years and is worth $4,000, despite a $10,000 basis), and an installment note (with a $500 basis and a $2,000 fair market value). Deb does not realize any gain or loss on the cash because the basis equals the fair market value, but she realizes a loss on the installment note because the fair market value ($2,000) is less than the basis ($500). Because Whiteacre was used for investment purposes, it is considered a capital asset. As a result, the difference between the basis and the fair market value ($6,000) is a long-term capital loss that can offset any capital gains that the partnership may recognize later.Ellen contributed cash ($7,000 basis and $7,000 fair market value) and Greenacre (a piece of real estate that Ellen has owned for two years and is worth $2,000, despite a $1,000 basis). Ellen does not realize any gain or loss on the cash because the basis equals the fair market value. The difference between the basis and the fair market value of Greenacre ($1,000) is a short-term capital gain that is taxed at ordinary income rates. The tax consequences for the partnership are as follows:Whiteacre's $6,000 capital loss offsets the $2,000 short-term capital gain on Greenacre, resulting in a net capital loss of $4,000 for the partnership. The partnership will be able to use $3,000 of this loss to offset other capital gains, with the remaining $1,000 carrying forward to future years.
At the time of formation, the balance sheet for the partners and the partnership is given below:Carl: Goodwill $5,000 Equipment $3,000 Account receivable $1,000 Total assets $9,000Deb: Cash $3,000 Whiteacre $4,000 Installment note $2,000 Total assets $9,000Ellen: Cash $7,000 Greenacre $2,000 Total assets $9,000Partnership: Cash $10,000 Whiteacre $4,000 Greenacre $2,000 Total assets $16,000
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Ben fills a glass with orange juice and lemonade in the ratio 1:4 by volume.
He mixes the liquid that is in the glass.
Ben drinks 1/4
of this liquid.
He then fills the glass using orange juice.
Work out the ratio of orange juice to lemonade, by volume, that is now in the glass.
Give
your ratio in its simplest form.
O = Orange, L = Lemonade
1/4 O + 3/4 L = x
Drink 1/4 of x, ratio of O and L doesn't change
1/4 O + 3/4 L = 3x/4
Fill up by adding 1/4 O
So it becomes 1/4 O + 1/4 O + 3/4 L = x
1/2 O + 3/4 L = x
Ratio of O to L = 1/2 divided by 3/4
= 1/2 * 4/3
Ratio of orange to Lemonade is 2:3
The ratio of orange juice to lemonade, by volume, is now in the glass 2/3.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Suppose the volume of orange is O while Lemonade is L.
Total volume V = 1/4 O + 3/4 L
Drink 1/4 of V, the ratio of O and L will not go to change
(3/4)V = 1/4 O + 3/4 L
Adding (1/4)O
(1/4)O + (1/4)O + (3/4)L = V
V = (1/2)O + (3/4)L
The ratio of O to L = (1/2)/(3/4)
⇒ (1/2)(4/3) = 4/6 = 2/3
Hence "The ratio of orange juice to lemonade, by volume, is now in the glass 2/3".
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Select the correct answer.
Answer:
The correct answer is the third option
C. 84x10
Please help With this one will give a lot of points
Answer:
not really sure can’t see the problem to good but C?
Step-by-step explanation:
hope this helped tho. cross multiple (btw if you search it on google it will help you)
who can answer all my math questions right?
Answer:
I can
Step-by-step explanation:
i can
The length of a rectangle is 2 less than twice the width. If the perimeteris 11m, find the length and width.
Answer:
Length: 3, Width: 5/2
Step-by-step explanation:
The width would be w, so the length would be 2w-2. set the equation to equal 11, and set the problem so its 2w-2+2w-2+w+w, or 6w-4=11. w=5/2, then plug in to get your dimensions
The radius of a cylinder is 4 inches and the height is 5 inches. Which statements are correct? Check all that apply.The area of the two bases is 16π in2.The area of the two bases is 32π in2.The lateral area is 40π in2.The lateral area is 72π in2.The total surface area is 72π in2.The Correct Answer is: 2,3,5
The radius of a cylinder is 4 inches and the height is 5 inches. The surface area is equal to the sum of the areas of all the faces of a solid.
A cylinder has two circular bases, and each circular base has an area of πr² square units, where r is the radius of the base. The lateral area of a cylinder is the area of the cylinder's curved surface, which is the height of the cylinder multiplied by the cylinder's base perimeter. It is given by the formula: 2πrh. The surface area of the cylinder is obtained by summing the lateral area and two times the area of the base. Hence, we have:
Surface area = 2πrh + 2πr²
Let us calculate the area of the two bases by plugging the given values into the formula.
Area of one base = πr²= π (4)²= 16π square inches
Therefore, the area of the two bases is 2 × 16π = 32π square inches. Thus, statement 2 is correct
Lateral area of a cylinderLateral area = 2πrh= 2 × π × 4 × 5= 40π square inches.
Thus, statement 3 is correct.
The total surface area of the cylinderTotal surface area = Lateral area + 2 × Area of base= 2πrh + 2 × πr²= 2πr(h + r)= 2π × 4(5 + 4)= 72π square inches.
Therefore, statement 5 is correct.
Therefore, the following statements are correct:Statement 2: The area of the two bases is 32π square inches.Statement 3: The lateral area is 40π square inches.Statement 5: The total surface area is 72π square inches are true.Therefore, the correct statements are 2, 3, and 5.
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Brianna bought 134 pounds of cheese that cost $3.00 per pound. What is the total cost of the cheese?
Answer:
402.00$
Step-by-step explanation:
Just multiply the amount by the cost?
Answer:
$402
Step-by-step explanation:
Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $150 and for each table is $750. At the optimal solution, how many tables should be produced? What is the maximum profit?
Maximize: Profit = 150C + 750T
Subject to:
5C + 3T ≤ 240 (Labor constraint)
4C + 20T ≤ 700 (Material constraint)
C ≥ 0
T ≥ 0
To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.
Let's define the decision variables:
Let C represent the number of chairs produced.
Let T represent the number of tables produced.
Objective function:
The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:
Profit = 150C + 750T
Constraints:
Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:
5C + 3T ≤ 240
Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:
4C + 20T ≤ 700
Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:
C ≥ 0
T ≥ 0
Now, we can solve the linear programming problem to find the optimal solution:
Maximize: Profit = 150C + 750T
Subject to:
5C + 3T ≤ 240 (Labor constraint)
4C + 20T ≤ 700 (Material constraint)
C ≥ 0
T ≥ 0
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What is the slope of y = -4?
Answer:
The slope is 0
Step-by-step explanation:
y = -4 is a horizontal line
Horizontal lines have a slope of zero
What’s the equation for
3/9 + 2/3
Answer:
1
Step-by-step explanation:
3/9 + 2/3
Simplify the first fraction by dividing the top and bottom by 3
1/3 + 2/3
Since the denominators are the same, add the numerators
3/3
1
what is 10 + x = 23 please help me
Answer:
x = 13
Step-by-step explanation:
x=23−10
x=13
Answer:
x=13
Step-by-step explanation:
subtract 10 from both sides
x = 13
that's ur answer
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. 's car had5.4 gallons in the 12-gallon tank on the coldest day of the year. Filled the tank with gas that cost $3.60 per gallon. How much did spend on gas?
Answer:
$19.44
Step-by-step explanation:
5.4 gallons in the 12-gallon tank on the coldest day of the year.
1 gallon = $3.60
5.4 gallons = x
Cross Multiply
x = 5.4 gallons × $3.60 /1 gallon
x = $19.44
Therefore, you spent $19.44 on gas
Find the midpoint of the segment with the following endpoints.
(-2,3) and (5, -6)
Answer:
The midpoint is ( 1.5, -1.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -2+5)/2 = 3/2 =1.5
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
( 3-6)/2 = -3/2 =-1.5
The midpoint is ( 1.5, -1.5)
