Answer:
north and south sides are 38 8/9 ft longeast and west sides are 17.5 ft longStep-by-step explanation:
Short answer: area is maximized when half the cost is spent in each of the orthogonal directions. This means the east and west sides will total $350 at $20 per foot, so will be 17.5 feet. The north and south sides will total $350 at $9 per foot, so will be 38 8/9 feet.
The dimensions that maximize the area are 17.5 ft in the north-south direction by 38 8/9 ft in the east-west direction.
__
Long answer: If x represents the length of the north and south sides, and y represents the length of the east and west sides, then the total cost is ...
10y +10y +2x +7x = 700
9x +20y = 700
y = (700 -9x)/20
We want to maximize the area:
A = xy = x(700 -9x)/20
We can do this by differentiating and setting the derivative to zero:
dA/dx = 700/20 -9x/10 = 0
350 -9x = 0 . . . . multiply by 10
x = 350/9 = 38 8/9
y = (700 -9(350/9))/20 = 350/20 = 17.5
The north and south sides are 38 8/9 ft long; the east and west sides are 17.5 ft long to maximize the area for the given cost.
Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article "Forces on the Hand in the Tennis One-Handed Backhand" (Int. J. of Sport Biomechanics (1991) reported the force (N) on the hand just after impact on a one- handed backhand drive for six advanced players and for eight intermediate players.
Advanced 44.70 26.31 55.75 28.54 46.99 39.46
Intermediate 15.58 19.16 24.13 10.56 32.88 21.47 14.32 33.09
1. Do the data shown above indicate that the mean force after impact is greater for advanced tennis players than it is for intermediate players?
2. Do a hypothesis test at .05 confidence level.
Answer:
Step-by-step explanation:
Hello!
The objective is to study whether there is a greater force after impacting on one- handed backhand drive in advanced tennis players than in intermediate tennis players.
Sample 1: Advanced tennis players
X₁: Force (N) on the hand just after impact on a one- handed backhand drive for an advanced tennis player.
n₁= 6
X[bar]₁= 40.29 N
S₁= 11.29
Sample 2: Intermediate players
X₂: Force (N) on the hand just after impact on a one- handed backhand drive for an intermediate tennis player.
n₂= 8
X[bar]₂= 21.40
S₂= 8.30
Assuming that both variables have a normal distribution and both population variances are equal, to compare these two populations is best to do so trough their population means using a t-test for independent samples.
If the force is greater for the advanced players than for the intermediate players, then you'd expect the population mean for the advanced players to be greater than the population mean for the intermediate players:
H₀: μ₁ ≤ μ₂
H₁: μ₁ > μ₂
α: 0.05
[tex]t= \frac{(X_[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{5*127.51+7*68.92}{6+8-2} }= 9.66[/tex]
[tex]t_{H_0}= \frac{(40.29-21.40)-0}{9.66\sqrt{\frac{1}{6} +\frac{1}{8} } } = 3.62[/tex]
Using the p-value approach, the decision rule is
If p-value ≤ α, reject the null hypothesis
If p-value > α, do not reject the null hypothesis
The p-value for this test is 0.00024, it is less than the level of significance, so the decision is to reject the null hypothesis.
This means that at a 5% significance level you can conclude that the average force experienced on the hand after a one-handed backhand drive for advanced players is greater than the average force experienced on the hand after a one-handed backhand drive for intermediate players.
I hope this helps!
Element X decays radioactively with a half life of 8 minutes. If there are 980 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 43 grams?
y=a(.5)^t/h
Answer:
[tex]t \approx 36.1\,min[/tex]
Step-by-step explanation:
The time constant for the isotope decay is:
[tex]\tau = \frac{8\min}{\ln 2}[/tex]
[tex]\tau \approx 11.542\,min[/tex]
Now, the decay of the isotope is modelled after the following expression:
[tex]m (t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
The time is now cleared with some algebraic handling:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
Finally, the time need for the element X to decay to 43 grams is:
[tex]t = - (11.542\,min)\cdot \ln\left(\frac{43\,g}{980\,g} \right)[/tex]
[tex]t \approx 36.1\,min[/tex]
Academic Advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Since then, a local California community college that participated in the survey hired several new academic counselors and focused on outreach efforts to increase student awareness of available services. The counseling office staff then conducted a survey of 500 randomly selected students at the college, and 26% of those students said that they rarely or never use academic advising services. Campus administrators want to know whether the hiring and outreach efforts increased student use of academic advising. Which alternative hypothesis is appropriate?
Answer:
The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.
Ha: p < 0.32
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
Let p represent the proportion of the students surveyed that rarely or never use academic advising services.
The null hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is equal to 32% or 0.32.
H0: p = 0.32
The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.
Ha: p < 0.32
4. Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister
Liz starts from the same location driving at 50 miles per hour. How long after Liz
leaves home will she catch up to Candice?
A 9 hours
B 4 hours
C 8 hours
D 7 hours
Answer: B. 4 hours
Step-by-step explanation:
Answer with Explanation please! Thank you!
Answer:
B)
Step-by-step explanation:
Slope = -3
Y-intercept = 3
So
Equation is
y = mx+b
Where m is slope and b is y-intercept
y = -3x+3
A group of scientists wants to investigate if they can predict the life expectancy
Step-by-step explanation:
There is no question asked here, bit of course it is possible to predict the life expectancies of a lot of things. This takes patience, resistance, and persistence, because working on something that takes time without persistence would result in a painful waste of time.
To predict the life expectancy of an effect is to predict how long it is going to take before it goes extinct, or seize from existence.
Apply the distributive property to create an equivalent expression. 4(3+1/4c-1/2d)??
Answer:16/16c-4/8d
Step-by-step explanation:
find the complete factored form of the polynomial 48m^5+8n^2
Answer:
8 ( 6 m 5^ + n 2^ )
Answer:
8( 6m^5 + n^2)
Step-by-step explanation:
48m^5+8n^2
Factor out 8
8* 6m^5 + 8 * n^2
8( 6m^5 + n^2)
Solve the system by elimination: 4x+7y=-1 8x-4z=36 6y-4z=-22
What’s the correct answer for this question?
Answer:
21/100
Step-by-step explanation:
By looking at the table, we can find the box that has information on people who have dogs but do not walk. The number is 21. The total number of people is 100. To find probability, divide 21 by 100.
21/100
This fraction is in its simplest form and cannot be simplified any further.
An urn contains 78 slips of paper. Each slip bears a number from 1 to 26. Each number appears on 3 different slips. A child selects two slips of paper at random and without replacement. Find the probability that the drawn slips have the same number. Write your answer as a reduced fraction.
Answer:
2 / 77
Step-by-step explanation:
Each number appears 3 times in the urn.
After picking any number, the number picked will appear only two more times in the urn, and the total slips of paper will be 77.
So for any first number we pick, the probability of the second number picked being the same number as the first pick is the number of times the same number appears in the urn (2) over the total number of slips in the urn (77):
Probability = 2 / 77
An analogy: For this set of questions, choose between two cars that we will call "A" and "B." Car A is a two-door coupe. It gets 60 miles per gallon and has a 10-gallon tank. Car B is an SUV. It gets 2 miles per gallon and has a 60-gallon tank. Suppose both cars embark on a very long journey together, side by side, each with a full tank of gas. Which car holds more fuel?
Car B, the SUV, obviously holds more fuel after 0 driven miles, 60 gallons, while car A holds 10 gallons after 0 miles.
let's speak about miles with the abbreviation x.
sk at x=0 Car B got more fuel.
Car A gets 60 Miles per gallon, it's consuming 1/60 gallon per mile. The amount of fuel decreases by 1/60 per mile
After each mile, or each x-step, Car A has
This can be expressed mathematically:
A(x) = -1/60*x + 10
The -1/60x is, again, the consumption per mile, the +10 is the full tank at the start.
A(0)= -1/60*0 + 10
=10
For Car B the consumption is 1/2 gallons per mile and the tank holds 60 gallons of fuel, wich ammount is decreases with traveled distance.
B(x) = -1/2*x + 60
See that we could draw these two functions as lines in a coordinate system. (I did it with desmos btw). This step is just to help understand.
After some distance/ amount x of miles, Car A will hold more fuel than car B, because it drives more efficiently.
In the picture we can see that this is after about 100 miles and we could guess the amount of fuel, but I won't. Let's calculate it and then answer the question precisely.
We get the intersection of the two lines by setting them equal, a(x)=b(x)
-1/60x + 10 = -1/2x + 60
Exactly one point lies, equally, on both lines
So let's solve for x
Further on the right, each step is explained. we have to do the same operation on both sides of the equation, just to not break it.
-1/60x + 10 = -1/2x + 60 | -10
-1/60x = -1/2x + 50 | + 1/2x
-1/60x + 1/2x = 50 | *60
-1x + 30x = 3000
29x = 3000 | /29
x = 103.448275862
so after about 103.45 miles, Car B holds less fuel than Car A (and Car A more than Car B), until both are empty. Car B could therefore drive more miles
We can also ask how much fuel is left in both tanks at the intersection point by plugging the x-value we got into one of the equations (doesn't matter which one, since the point is the same)
a(103.4482) = -1/60 * 103.4482 + 10 = 8.28
If you want it to be precise, stay with fractions
a(3000/29) = -1/60 * 3000/29 + 10
= -50/29 +10
= 9 -21/29
= 8 + 8/29
Finding out how far each car could travel would be achieved by setting their fuel-equation equal to 0, because that's the value of it when they run of of fuel. For example 0 = -1/60x+10, then you (just) solve for x.
I did overshoot the given problem to offer offer you understanding that's spans more of the topic you are dealing with
(would really appreciate the brainliest)
A company is planning a four-year project, with an initial cost of $1.67 million. This investment cost is amortised to zero over four years on a straight-line basis. However, the asset could be disposed of for $435,000 in four years. The project requires $198,000 in working capital initially and is fully recoverable after the project is completed. The project generates $1,850,000 in sales and $1,038,000 in costs each year. If the tax rate is 21% and the required return rate is 16.4%, what is NPV?
Answer:
The Net Present Value = $451180.733
Step-by-step explanation:
Given that:
the initial cost of the project is $1670000
the initial increase in working capital is $198000
The total investment will be ; initial cost of the project + initial increase in working capital
The total investment = $1670000 + $198000
The total investment = $1868000
So, This investment cost is amortised to zero over four years; This implies that the project will depreciate in four years;
Now; lets determine the rate of the annual depreciation
The annual depreciation = [tex]\dfrac{Initial \ cost \ of \ project }{life \ of \ project}[/tex]
The annual depreciation = [tex]\dfrac{1670000}{4}[/tex]
The annual depreciation = $417500
Over to the annual operating cash flow; the annual operating cash flow can be calculated as follows:
annual operating cash flow = (sales - cost) × (1 - tax rate )+ (annual depreciation × tax rate )
Given that the tax rate = 21% = 0.21
annual operating cash flow = (1850000 -1038000)×(1-0.21)+(417500× 0.21)
annual operating cash flow = 812000 × 0.79 + 87675
annual operating cash flow = 641480 + 87675
annual operating cash flow = $729155
So; let's calculate the after tax salvage value for the project
We know that the sales values for the project in four years is $435,000 (i.e the disposal rate of the asset after four years)
Thus; the book value is zero
The after tax salvage value for the project can now be determined by the relation:
after tax salvage value = sale value - tax (sale value - book value)
after tax salvage value = 435000 - 0.21 (435,000 -0)
after tax salvage value = 435000 - 91350
after tax salvage value = $343650
Similarly; given that the recovering rate of the project is $198000;
The cash flow in year 4 will be: annual operating cash flow + after tax salvage + recovery working capital
cash flow in year 4 = $(729155 + 343650 + 198000)
cash flow in year 4 = $ 1270805
This implies that the cash flow from year one to three is : 729155
the cash flow in year four is : 1270805
Given that the Required return rate = 16.4% = 0.164
We can therefore determine the Present cash inflows by using the relation:
[tex]Present \ Value = \dfrac{c_1}{(1+r)^1}+ \dfrac{c_2}{(1+r)^2}+ \dfrac{c_3}{(1+r)^3}+ \dfrac{c_4}{(1+r)^4}[/tex]
[tex]Present \ Value = \dfrac{729155}{(1+0.164)^1}+ \dfrac{729155}{(1+0.164)^2}+ \dfrac{729155}{(1+0.164)^3}+ \dfrac{1270805}{(1+0.164)^4}[/tex]
[tex]Present \ Value = \dfrac{729155}{1.164^1}+ \dfrac{729155}{1.164^2}+ \dfrac{729155}{1.164^3}+ \dfrac{1270805}{1.164^4}[/tex]
Present Value = $(626421.8213 + 538163.0767 + 462339.413+692256.4225)
Present Value = $2319180.733
Finally, The net present value = Present Value - Total Investment
Net Present Value = $(2319180.733 - 1868000)
Net Present Value = $451180.733
Therefore; The Net Present Value = $451180.733
omar has 5 liters of water he divides the water evenly between 4 buckets. how many milliters does omar pour in each bucket
Answer:
1250 milliliters
Step-by-step explanation:
Omar has 5 liters of water. He divides evenly between 4 buckets.
5/4 = 1.25
He pours 1.25 liters in each bucket.
Convert 1.25 liters into milliters.
1.25 × 1000
1250 milliliters.
Omar pours 1250 milliliters in each bucket.
HELP PLEASE!!!
For what value of x does 4^x= (1/8)^x+5
answers:
-15 - 3 3 15
HELP PLEASE!!!
Answer:
Create equivalent expressions in the equation that all have equal bases, then solve for
x
.
Exact Form:
5/3
Decimal Form:
x
=
1.6
Mixed Number Form:
x
=
1 2/3
Answer:-3
Step-by-step explanation:
Please Help I will mark as brainliest
Answer:
A. True
B. True
C. False
D. True
Step-by-step explanation:
A) To find the probability of the letters spelling CAT go to the letter C, then A, and finally T. there is only one sequence that does this, so the numerator will be 1. There are 6 outcomes overall, so the denominator will be 6. The probability of the letters spelling CAT would be 1/6. The answer is true.
B) To find the probability of T being the first letter go to the letter T. All sequences after the letter T will all be included in the answer. TAC and TCA are both possible solutions, this means there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of T being the first letter is 2/6, which is equal to 1/3. The answer is true.
C) To find the probability of A being the first letter go to the letter A. All sequences after the letter A will all be included in the answer. ACT and ATC are both possible solutions, this mean there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of A being the first letter is 2/6. The answer is false.
D) To find how many total outcomes are possible go to the tree diagram and look to the far right. Go down each of the rows to find all of the outcomes, there is T,C,T,A,C, and A. That means there are six possible outcomes. The answer is true.
2.34−1.7*0.2 = I am very confused
Answer:
2.34-1.7*0.2=2
Step-by-step explanation:
Well to solve this, we need to use PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication comes first before subtraction. You can do long multiplication for this and multiply 1.7 and 0.2 together. Once done that, the product of those 2 numbers are 0.34.
Now 2.34-0.34=2.00
Our answer is 2.
Answer:
2
Step-by-step explanation
1.7 x 0.2 = 0.34
2.34-0.34=2
Carrie rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 9
Answer:
Probability of a sum of 9 = 0.111111
OR
Probability of a sum of 9 = 1/9
Step-by-step explanation:
Carrie rolls 2 fair dice and adds the results from each.
The total sample space = 36
Gotten from 6²= 36
The probability of getting a total of 9
Now let's look at the possible sum to give us a 9 (3 and 6, 4 and 5) twice.
So we gave number of occurrence of 9 to be four.
Probability of a sum of 9 = 4/36
Probability of a sum of 9 =1/9
Probability of a sum of 9 = 0.111111
The probability of getting a total of 9 is 0.111111 and this can be determined by using the concept of probability.
Given :
Carrie rolls 2 fair dice and adds the results from each.
The sample space is equal to [tex]6^2[/tex] that is 36. The numbers require on both the dices to get the sum equal to 9 are 4 and 5 or 6 and 3.
So, there is a total of 4 numbers in 36 sample size in order to get the sum of 9.
Now, the probability of getting a total of 9 is given by:
[tex]\rm P=\dfrac{4}{36}[/tex]
Further, simplify the above expression.
[tex]\rm P = \dfrac{1}{9}[/tex]
P = 0.111111
So, the probability of getting a total of 9 is 0.111111.
For more information, refer to the link given below:
https://brainly.com/question/23017717
Please help me out:/
Answer:
Step-by-step explanation:
find the y intercept!
Answer:
-23
Step-by-step explanation:
We note that as x increases by 36 from -72 to 36, y decreases by 24 from 25 to 1.
Increasing x from -36 by another 36 to zero will correspond to a decrease in y by another 24 from 1 to -23.
The y-intercept is -23.
_____
You could go to the trouble to use these observations to compute the slope as -24/36 = -2/3. Then you could pick one of the points and write the equation in point-slope form as ...
y = -2/3(x +36) +1 . . . point-slope form with m=-2/3, (h, k) = (-36, 1)
y = -2/3x -24 +1 . . . . . eliminate parentheses
y = -2/3x -23 . . . . . . . y-intercept is -23
Which sequence of transformations on the red triangle will map it onto the missing portion of the square?
Answer:
A 90° counterclockwise rotation about the origin and then a translation 16 units right and 16 units up
Solution -Rotating the triangle 90° counterclockwise will take the triangle to 3rd quadrant and then further moving it 16 steps right will take it to 4th quadrant and followed by 16 steps upward will take it to the desired position which is in 1st quadrant.
which best describes the triangle?
a) isosceles
b) acute
c) scalene
d) equilateral
Answer:
[tex]scalene \: triangle[/tex]
Step-by-step explanation:
The above given triangle represents the unequal lengths of three sides properties of scalene triangle
hence, it's a scalene triangle♥Hope this helps you out!!!
Please answer this correctly
Answer:
5 cm
Step-by-step explanation:
Use lenght times wight times height
So, you need to do 4 times 4 times ________ is 80
A notebook costs £1.30, a pen costs 38p , a pencil costs 21p and a sharpener costs 84p.
Remi buys 2 pencils, 3 pens, 2 sharpeners and some notebooks.
He pays with £10 and receives 26p change.
How many notebooks did he buy?
Answer:5
Step-by-step explanation:
The diagram shows the scores given by the panel of judges
during a dancing competition.
a) Which score was the mode?
8
7
6
b)
Frequency
There were 5 judges.
They each gave one score in each
round of the competition.
3
2
How many rounds were there?
+
o
0 1 2 3 4 5
Score
Note: Please make sure your final answer says ... rounds.
Answer:
a) 4b) 6 roundsA clown has a silly string that is a 52cm long and magic scarf that is 28cm long.
How long are the clown's silly string and magic scarf combined?
Answer:
you asked about Telugu movies I see Telugu moviesI am from India telangana
A random sample of 100 college students is taken from the student body of a large university Assume that, in fact, a population mean of 20 hours and a standard deviation of 15 hours describe the weekly study estimates for the entire student body. Therefore, the sampling distribution of the mean has a mean that:________.
a) approximates 20 hours.
b) equals 20 hours.
c) lies within a couple of hours of 20.
d) equals the one observed sample mean.
Answer:
b) equals 20 hours.
Step-by-step explanation:
The sampling distribution of means refers to the distribution of all the possible sample means, with a certain sample size (in this case, n=100) extracted from the population.
The sampling distribution of the means is equal to the population mean. That does not mean that every sample will result in a mean equal to the population, but that the population of sample means will have an average of 20 hours.
Find the value of MP! Need help!
Answer:
c) 118°
Step-by-step explanation:
PN is the diameter of the given circle.
[tex] \purple {\bold {\therefore m(\widehat{PMN}) = 180°}}.... (1)\\[/tex]
Now, by inscribed angle theorem:
[tex] m\widehat {MN} = 2\times m\angle MPN\\
\therefore m\widehat {MN} = 2\times 31°\\
\red{\bold {\therefore m(\widehat {MN}) = 62°}}....(2) \\\\[/tex]
Now,
[tex] \because m(\widehat{MP}) + m(\widehat{MN}) =m(\widehat{PMN})\\
\therefore m(\widehat{MP}) + 62° =180°\\
\therefore m(\widehat{MP}) =180°-62°\\
\huge \orange {\boxed {\therefore m(\widehat{MP}) =118°}} \\[/tex]
6 times a number plus 22 is greater than 7
Answer: A
Step-by-step explanation: A is the correct answer because once you do the math (6*5/2+22) it gives you the correct amount. You also need to pay attention to the greater then and less than signs so that you don’t get confused.
If you found this answer helpful, give it a five star rating and a thanks!
(Even a brainliest if you want ;D)
Answer:a
Step-by-step explanation:
Luke invested $69,000 in an account paying an interest rate of 5.1% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 19 years?
Answer:
A = $ 181,824 rounded
Step-by-step explanation:
A = $ 181,823.93
A = P + I where
P (principal) = $ 69,000.00
I (interest) = $ 112,823.93
