Answer:
π/10
Step-by-step explanation:
α=-19π/10=-19π/10+2π=(-19π+20π)/10=π/10
Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-12x^2+2160x-59000 To maximize the monthly rental profit, how many units should be rented out? units What is the maximum monthly profit realizable?
Answer:
To maximize the monthly rental profit, 90 units should be rented out.
The maximum monthly profit realizable is $38,200.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]
To maximize the monthly rental profit, how many units should be rented out?
This is the x-value of the vertex, so:
[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]
To maximize the monthly rental profit, 90 units should be rented out.
What is the maximum monthly profit realizable?
This is p(90). So
[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]
The maximum monthly profit realizable is $38,200.
Find the Antilog of 547.840
Answer:
It's impossible because the figure is greater than 10
Step-by-step explanation:
[tex]{ \boxed{ \bf{antilog \: of \: x = \frac{x}{ log} = {10}^{x} }}}[/tex]
Therefore:
[tex]{ \sf{anti(547.840) = {10}^{547.840} }} \\ { \tt{ \red{math \: error \: !}}}[/tex]
What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?
A. 9 miles
B. 16 miles
C. 38 miles
D. 48 miles
Can you post an image of the map?
Answer:
i believe that the answer is 38 please trust me
Write a simple algorithm to add two numbers
Answer:
Write an algorithm to add two numbers entered by user. Step 2: Declare variables num1, num2 and sum. Step 3: Read values num1 and num2. Step 4: Add num1 and num2 and assign the result to sum.
find x
please help!!
Answer: [tex]9\sqrt{3}[/tex]
==========================================================
Explanation:
For any 30-60-90 triangle, the short leg is always half the hypotenuse.
This makes the short leg to be 18/2 = 9 units long.
We then multiply this by [tex]\sqrt{3}[/tex] to get the length of the long leg.
[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\text{long leg} =9\sqrt{3}[/tex]
Or you could use the pythagorean theorem to solve [tex]x^2+9^2 = 18^2[/tex] and you should get [tex]x = \sqrt{243} = 9\sqrt{3}[/tex]
Solve this pleaseeeeeeeeeee
Answer:
10d
Step-by-step explanation:
5d on 1 side, double it to get 10d cuz from Point O to Point D, y increases from 0 to 5d and since the triangles are congruent, we can add another 5d (or in total 10d).
*20 points*
how do you get the weighted average from this table?
Answer:
it is
[(2+3+4+6)-2*4]:4=1.75
I THINK
Step-by-step explanation:
You are offered two stocks. The beta of A is 1.4 while the beta of B is 0.8. The growth rates of earnings and dividends are 10% and 5%, respectively. The dividend yields are 5% and 7%, respectively.
Since A offers higher potential growth, should it be purchased?
Investments- Individual Work 2 Page 3
Since B offers a higher dividend yield, should it be purchased?
If the risk-free rate of return were 7% and the return on the market is expected to be 14%, which of these stocks should be bought?
Answer:
a) Yes , Cause The Expected Returns of stock A is Higher than that of B
b) No, Cause The Expected Returns of stock B is Lower than that of A
Step-by-step explanation:
From the question we are told that:
Beta A \beta A=1.4
Beta B \beta B=0.8
Stock 1 Growth rates of earnings and dividends G_1=10\%
Stock 2 Growth rates of earnings and dividends G_2=5\%
Stock 1 Dividend yields D_1=5\%
Stock 2 Dividend yields D_2=7\%
Generally the equation for Expected Returns is mathematically given by
Expected Returns =Growth rates+Dividend yields
For Stock 1
Expected\ Returns =G_1+D_1
Expected\ Returns =5%+10%
Expected\ Returns =15%
For Stock 2
Expected\ Returns =G_2+D_2
Expected\ Returns =7%+5%
Expected\ Returns =12%
Therefore
a) Yes , Cause The Expected Returns of stock A is Higher than that of B
b) No, Cause The Expected Returns of stock B is Lower than that of A
Hi,there,can you solve this equation.
4x*sqrt(2x-x²)=2x-1
Answer:
Step-by-step explanation:
4x*sqrt(2x-x²)=2x-1
sqrt(2x-x²)=(2x-1)/4x
2x-x² = 4x^2 -4x + 1 /(16x^2)
32x^3 - 16x^4 = 4x^2 -4x + 1
[tex]-16x^4+32x^3-4x^2+4x-1=0\\[/tex]
[tex]x = 1.92887[/tex]
A newsletter publisher believes that less than 61% of their readers own a laptop. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer: See explanation
Step-by-step explanation:
From the information given in the question, we are informed that a newsletter publisher believes that less than 61% of their readers own a laptop.
The null hypothesis will be: H0: p ≥ 0.61
The alternative hypothesis will be: Ha: p < 0.61.
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.
Answer:
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Step-by-step explanation:
There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.
At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just
[tex]\frac{4}{52}[/tex]
After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is
[tex]\frac{4}{51}[/tex]
Now to get the total probability we need to multiply the two probabilities together
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
What would be an appropriate domain if the function hin) gives the number
of man-hours it takes to assemble n engines in a factory in a day, subject to a
maximum of 300 engines?
Answer:
assuming that you are NOT allowed to build 1/2 of an engine or that you dont destroy any of them in the process of building them ...
"all positive integers less than or equal to 300"
Step-by-step explanation:
An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the proportion of scanners that can be expected to fail within plus or minus 6 months of the mean. (Enter your answer as a percentage without the percent sign; keep 2 decimal places)
Answer:
The answer is "36.14%"
Step-by-step explanation:
The complete question is given in the attached file please find it.
[tex]\mu =41\\\\\sigma= 4\\\\P(42<\bar{x}<48)= p(\bar{x}<48)-p(\bar{x}<42)\\\\Z =\frac{(42-41)}{4} = \frac{1}{4} =0.25\\\\Z =\frac{(48-41)}{4} = \frac{7}{4} = 1.75\\\\[/tex]
Using z-table to find the value.
[tex]\to P(41<\bar{x}<48) = 0.9599- 0.5987 = 0.3614\times 100= 36.14\%[/tex]
This means that between 42 and 48 months, 36.14 % of scanners could be predicted will break down.
Write the equation of the line in fully simplified slope-intercept form.
Nancy left a bin outside in her garden to collect rain water. She notices the 1/2 gallon fills 2/3 of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.
Here we want to solve a question involving fractions, we will find that:
3/4 gallon fils the complete bin.
Ok, so we know that 1/2 gallon of water, fills 2/3 of the bin.
We want to find the total amount of water that would fill the entire bin.
So we could write an equation like:
amount of water = amount of the bin that it fills.
Then, using the above information, we have:
1/2 gal = 2/3 of a bin
Now we want to get at 1 on the right side, this would mean "1 bin"
Then we multiply both sides by (3/2)
(3/2)*(1/2) gal = (3/2)*(2/3) of a bin
3/4 gal = 1 bin
From this, we can conclude that (3/4) gallons of water would fill the complete bin.
If you want to learn more about algebra, you can read:
https://brainly.com/question/4837080
x = 0,75 gallons or x = 3/4 gallons The volume of the bin
The volume of the bin is: In terms of a fraction
1 = 3/3 or any unitary fraction 5/5 7/7 9/9
We will take 3/3 since we have the information that 2/3 of the volume of the bin was filled with 2/3 of a gallon
If 2/3 of the volume of the bin was filled with 1/2 gallon then we make a rule of three according to:
If 0,5 gal. fill 2/3 of the volume of the bin then
x gal fill 3/3 ( the volume of the bin)
solving
0,5 (gal) * 3/3 = (2/3)*x ( The equation)
0,5*3 = 2*x
x = (0,5*3)/2
x = 0,75 gallons or x = 3/4 gallons
Max needs to paint a wall that is shaped like a square. He knows that the area of the wall is 75 ft2 . He needs to find the height of the wall. Find the height of the wall to the nearest tenth of a foot.
Answer:
8.7 feet
Step-by-step explanation:
Use the square area formula, a = s², where s is the side length of the square.
Plug in the area and solve for s:
a = s²
75 = s²
√75 = s
8.7 = s
So, to the nearest tenth of a foot, the height is 8.7 feet
Use the compound interest formula to find the annual interest rate, r, if in 2 years an investment of 4,000 grows to 4410 The rate is %.
Answer:
5%
Step-by-step explanation:
Bank amount=PA*(1+r/100)^t
4410=4000*(1+x/100)^2
1.05=(1+x/100), x=5%
A biologist was interested in determining whether sunflower seedlings treated with and an extract from Vinca minor roots resulted in a lower average height of sunflower seedlings that the standard height of 15.7 cm. The biologist treated a random sample of 33 seedlings with the extract and subsequently measured the height of those seedlings. At the 0.01 significance level, is there evidence that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm?
Height
15.5
15.8
15.7
15.1
15.1
15.5
15.2
15.7
15.8
15.4
16.2
15.5
16.2
15.5
15.4
16.3
14.9
15.3
15.1
16.1
15.3
15.4
15.1
15.3
14.6
15.1
15.0
15.3
15.8
15.5
14.8
15.2
14.8
a. State the null and alternative hypotheses.
b. Report the value of the test statistic. Round answer to 2 decimal places. (Either calculate or use software such as minitab)
c. Using the p-value, do you reject the null hypothesis or fail to reject the null hypothesis? Explain your decision.
d. Based on your decision in part (c), write a conclusion within the context of the problem.
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : μ = 15.7
H1 : μ < 15.7
This is a one sample t test :
Test statistic = (xbar - μ) ÷ (s/√(n))
n = sample size = 33
Using calculator :
The sample mean, xbar = 15.41
The sample standard deviation, s = 0.419
Test statistic = (15.41 - 15.70) ÷ (0.419/√(33))
Test statistic = - 3.976
Using the Pvalue calculator :
Degree of freedom, df = n - 1 ; 33 - 1 = 32
Pvalue(-3.976, 32) = 0.000187
Decison region :
Reject H0 if Pvalue < α
Since Pvalue < α ; we reject H0
There is significant evidence to conclude that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm.
which lines are parallel?
Answer:
Lines 'p' and 'q' are parallel I believe!
Step-by-step explanation:
They are the only two lines relating to angles 8 and 11 of the three listed pairs.
Answer:
p and q are parallel
Step-by-step explanation:
Catherine Chao, Director of Marketing Research, needs a sample of households to participate in the testing of a new toothpaste package. She chooses thirty-six of her closest friends. Catherine's sample is a _____________.
Answer:
Convenience sampling.
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Random sampling.
2. Systematic sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Quota sampling.
6. Convenience (opportunity) sampling.
Convenience sample can be defined as a sampling technique in which the representatives to be used are easily accessible. For example, a researcher using a social media poll such as Twitter polls.
In this scenario, Catherine Chao, Director of Marketing Research, chooses thirty-six of her closest friends to participate in the testing of a new toothpaste package. Thus, Catherine's sample is a convenience sampling.
A sailor on a trans-Pacific solo voyage notices one day that if he puts 625.mL of fresh water into a plastic cup weighing 25.0g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly the same level as the seawater outside the cup (see sketch at right).
Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits.
You'll need to know that the density of fresh water at the temperature of the sea around the sailor is 0.999/gcm3. You'll also want to remember Archimedes' Principle, that objects float when they displace a mass of water equal to their own mass.
Answer:
can you say again please
Which number line shows the solution for n + 3 < 12?
Answer:
None of them
Step-by-step explanation:
n+3<12
(Subtract 3 from both sides)
n<9
(n is less than 9, so n is everything left of 9)
(the inequality symbols: > and < are an open dot)
(none of the choices display n<9 with an open dot, so none of the options are correct)
(if you meant < with a line underneath it, then the dot would be filled, and the answer would be D)
Which of the following theorems verifies that abc wxy
Answer:
C. AA
Step-by-step explanation:
Since m<Y = 27°, then m<W = 27°.
We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).
Answer: C. AA
Which of the following is equivalent to the expression below
Answer:
Could you add a picture or answer choices so we know what to choose from?
Please help!!
Find BD
Answer: [tex]8\sqrt{2}[/tex]
==========================================================
Work Shown:
Focus entirely on triangle ABD (or on triangle BCD; both are identical)
The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.
Apply the pythagorean theorem.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
So that's why the diagonal BD is exactly [tex]8\sqrt{2}\\\\[/tex] units long
Side note: [tex]8\sqrt{2} \approx 11.3137[/tex]
Scores on a national English test are Normally distributed, with a mean score of 510 and a standard deviation of 75. Sixty-eight percent of English tests were less than which score, rounded to the nearest whole number?
A) 475
B) 529
C) 545
D) 561
Answer:
Should be (C). Can't verify.
545
ED2021
Derive the explicit rule for the pattern: 3, 0, - 3, - 6, - 9, ...
Answer:
Step-by-step explanation:
a1 = 3
d = -3
an = a1 + (n - 1)*d
an = a1 + (n - 1)*-3
Try it
Let n = 5
a5 = 3 + (5 - 1)*-3
a5 = 3 + 4*-3
a5 = 3 - 12
a5 = - 9 which is exactly what it should be.
The interesting one to try is n = 2
a2 = a1 + (2 - 1)*-3
a3 = 3 + 1(-3)
a3 = 3 - 3
a3 =0
Which is exactly what the second term is. It's interesting because you would never guess that 0 is what you get.
The value of 4√(10) -2 is
Answer:
8√2
Step-by-step explanation:
4√(10) -2
= 4√8
=4√4×2
=4×2√2
=8√2
A data set is made up of the values 2, 3, 7, 8, 9, and 13.
The table shows the distance between each value and the mean of 7.
Data value Distance between
value and mean
2 5
3 4
7 0
8 1
9 2
13 6
Sum of distances 18
What is the mean absolute deviation (MAD) of the data set?
help please
Answer:
3
Step-by-step explanation:
Given the data :
2, 3, 7, 8, 9, 13
2 5
3 4
7 0
8 1
9 2
13 6
The mean, = Σx / n ; n = sample size
Mean = 42 / 6 = 7
The mean absolute deviation = Σ|x - mean| / n
The mean absolute deviation is Hence,
(5 + 4 + 0 + 1 + 2 + 6) / 6
Mean absolute deviation = 18 / 6
Mean absolute deviation = 3
Which correlation best describes the data below. no correlation weak positive weak negative strong positive
