Answer:
a)From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard error for the mean would be:
[tex]\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14[/tex]
b) We want this probability:
[tex] P(\bar X >120) [/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143[/tex]
And we can find this probability with the complement rule and the normal standard deviation or excel and we got:
[tex] P( z>2.143) = 1-P(Z<2.143) = 1-0.984 = 0.016[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
Part a
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard error for the mean would be:
[tex]\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14[/tex]
Part b
We want this probability:
[tex] P(\bar X >120) [/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143[/tex]
And we can find this probability with the complement rule and the normal standard deviation or excel and we got:
[tex] P( z>2.143) = 1-P(Z<2.143) = 1-0.984 = 0.016[/tex]
8. A well-balanced stock market portfolio will often experience an exponential growth. A
particular investor with a well-balanced stock market portfolio records the portfolio balance
every month, in thousands of dollars, from the date of investment. The roughly exponential
growth can be transformed to a linear model by plotting the natural log of the balances
versus time, in months, where t - 0 represents the date the money was invested. The linear
regression equation for the transformed data is
In (balance)-5.550 + 0.052t.
Using this equation, what is the predicted balance of the portfolio after 2 years (24 months)?
(A) $5,654
(B) $6,798
(C) $285,431
(D) $896,053
(E) $948,464
Answer:
D) $896,053
Step-by-step explanation:
I swear they got me doing algebra in 8th grade i wanna refund please help me... again
Answer: C represents a function
Step-by-step explanation: It represents a function because there is exactly one range for each domain, and only one. In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power.
A particular sale involves four items randomly selected from a large lot that is known to contain 9% defectives. Let X denote the number of defectives among the four sold. The purchaser of the items will return the defectives for repair, and the repair cost is given by 2 C X X = + + 3 2 1. Find the expected repair cost
Answer:
The expected repair cost is $3.73.
Step-by-step explanation:
The random variable X is defined as the number of defectives among the 4 items sold.
The probability of a large lot of items containing defectives is, p = 0.09.
An item is defective irrespective of the others.
The random variable X follows a Binomial distribution with parameters n = 9 and p = 0.09.
The repair cost of the item is given by:
[tex]C=3X^{2}+X+2[/tex]
Compute the expected cost of repair as follows:
[tex]E(C)=E(3X^{2}+X+2)[/tex]
[tex]=3E(X^{2})+E(X)+2[/tex]
Compute the expected value of X as follows:
[tex]E(X)=np[/tex]
[tex]=4\times 0.09\\=0.36[/tex]
The expected value of X is 0.36.
Compute the variance of X as follows:
[tex]V(X)=np(1-p)[/tex]
[tex]=4\times 0.09\times 0.91\\=0.3276\\[/tex]
The variance of X is 0.3276.
The variance can also be computed using the formula:
[tex]V(X)=E(Y^{2})-(E(Y))^{2}[/tex]
Then the formula of [tex]E(Y^{2})[/tex] is:
[tex]E(Y^{2})=V(X)+(E(Y))^{2}[/tex]
Compute the value of [tex]E(Y^{2})[/tex] as follows:
[tex]E(Y^{2})=V(X)+(E(Y))^{2}[/tex]
[tex]=0.3276+(0.36)^{2}\\=0.4572[/tex]
The expected repair cost is:
[tex]E(C)=3E(X^{2})+E(X)+2[/tex]
[tex]=(3\times 0.4572)+0.36+2\\=3.7316\\\approx 3.73[/tex]
Thus, the expected repair cost is $3.73.
g Exercise 6. Let X be a Gaussian random variable with X ∼ N (0, σ2 ) and let U be a Bernoulli random variable with U ∼ Bern(?) independent of X. Define V as V = XU. (a) Find the characteristic function of V , ϕV = E(e jsV ) = RfV (v)e jsv. Hint: use iterated expectation. (b) Find the mean and variance of V .
Answer:
Step-by-step explanation
question solved below
4 identical taps can fill a tank in 70 minutes. Find the time taken for 7 such taps to fill the same tank.
Answer:
4 taps take 70 minutes
2 taps would take 140 minutes
8 taps would take 35 minutes
time = (4 / # of taps) * 70
time = (4 / 7) * 70 = 40 minutes
Step-by-step explanation:
The demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.
p = −0.01x2 − 0.1x + 32
Determine the consumers' surplus if the market price is set at $2/cartridge. (Round your answer to two decimal places.)
Demand function: p = -0.01x^2-0.2x+13 (1).
The equation (2) is: CS = ∫ D(p) dp, where D is the demand curve expressed in terms of the price. The bottom limit of the integrand is the market price given as $5 and the top limit is $13 found by setting x = 0 in (1) above. Equation (2) above requires we solve the original equation, (1) above, for x in terms of p. The first step is (a) to multiply both sides of equation by -100 to clear decimals, then (b) place equation in standard quadratic form, namely, x^2 + 20x + 100p – 1300 = 0. Step (c): Solve for x by applying quadratic formula, namely, x = (-b +- √(b^2 – 4ac)) / 2a to solve for x. Use a = 1, b = 20, c = 100p – 1300. The new demand equation is: x = -10 + 10√(14 – p). Now calculate ∫ (-10 + 10(14 – p)^(1/2)) dp and evaluate at 5 and 13. This gives: -10(13 – 5) – (2/3) (10) ((14 - 13)^(3/2) – (14 – 5)^(3/2)) . This evaluates to: -80 – (20/3) + 180. So, CS = $93.33.
The consumer surplus demanded will be 50 per week if the market price is set at $2/cartridge.
What do you mean by domain and range of a function?For any function y = f(x), Domain is the set of all possible values of [x] for which [y] exists. Range is the set of all values of [y] that exists for the given domain.
Given is the demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where [p] is the unit price in dollars and [x] is the quantity demanded each week, measured in units of a thousand.
The demand function is -
p = − 0.01x² − 0.1x + 32
For p = 2, we can write -
− 0.01x² − 0.1x + 32 = 2
− 0.01x² − 0.1x + 30 = 0
Graph the equation and note the [x] intercepts. Taking the positive value of [x] intercept, we get 50.
Hence, the consumer surplus demanded will be 50 per week if the market price is set at $2/cartridge.
To solve more questions on functions, visit the link below -
brainly.com/question/1632425
#SPJ2
the four-digit numeral 3AA1 is divisible by 9. What digit does A represent?
Answer:
7
Step-by-step explanation:
Trial and error. Start with 1 and go to 9
The digit A in the numeral 3AA1, which is divisible by 9, represents the number 7. This is deduced by the rule that a number is divisible by 9 if the sum of its digits is also divisible by 9.
To find the digit that A represents in the four-digit numeral 3AA1 that is divisible by 9, we must remember that a number is divisible by 9 if the sum of its digits is divisible by 9. Let's denote A as a single digit, and since we know that 3 and 1 are already part of the sum, the equation we need to solve is:
3 + A + A + 1 = 3 + 2A + 1
Simplifying further:
2A + 4 must be divisible by 9. Since A is a digit, it can only be one of the following numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. We can now test these values:
For A = 0, the sum is 4 (not divisible by 9)
For A = 1, the sum is 6 (not divisible by 9)
For A = 2, the sum is 8 (not divisible by 9)
For A = 3, the sum is 10 (not divisible by 9)
For A = 4, the sum is 12 (not divisible by 9)
For A = 5, the sum is 14 (not divisible by 9)
For A = 6, the sum is 16 (not divisible by 9)
For A = 7, the sum is 18 (divisible by 9)
For A = 8, the sum is 20 (not divisible by 9)
For A = 9, the sum is 22 (not divisible by 9)
The only value for A that makes the sum divisible by 9 is 7. Therefore, A represents the digit 7.
14.) Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds. Ayrshire cows average 47 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 43 pounds, with a standard deviation of 5 pounds. Assume that Normal models describe milk production for these breeds.
Answer:
69.50%
Step-by-step explanation:
Given:
Ayrshire cows:
E(X) =μ = 47
SD(X) = σ = 6 Var (X) = 6^2 = 36
Jersey cows:
E(Y) = μ = 43
SD(Y) = σ = 5 Var(Y) = 52 = 25
Properties mean, variance and standard deviation:
E(X +Y) = E(X) E(Y)
V ar(X +Y) = Var(X) + Var(Y)
SD(X +Y) = √Var(X)+Var(Y)
X — Y represents the difference between Ayrshire and Jersey cows.
E(X — Y) = E(X) — E(Y). 47 — 43 = 4
SD(X — Y) = √Var(X)+ Var(Y) =√36+ 25 = √61 = 7.8102
The z-score is the value decreased by the mean, divided by the standard deviation:
z = x-μ /σ = 0-4/ 7.8102 = -0.51
Determine the corresponding probability using table Z in appendix F.
P(X—Y [tex]\geq[/tex] 0) = P(Z > —0.51) = 1—P(Z < —0.51) = 1-0.3050 = 0.6950 = 69.50%
A pair of snow boots at an equipment store in Big Bear that originally cost $60 is on sale for 40% off. Then, you have a coupon for 10% off. What is the final cost?
Answer:
$30 i think
Step-by-step explanation:
because %40+%10=%50
and %50 is half of %100 so 60-(60×(50%)=30
sorry is its wrong
the difference of two numbers is 1. their sum is 19. find the numbers.
Answer:
x = 10
y = 9
Step-by-step explanation:
First, you need to write two equations that represent the information given. I'm going to set the two numbers and x and y.
x - y = 1
x + y = 19
This turns it into a systems of equations. When you add the two equations, keeping everything on each side, you eliminate a variable, and solve for the other.
2x = 20
x = 10
Now, you'd plug x into either original equation.
(10) - y = 1
-y = -9
x = 10
I hope this helped!
Answer:
The numbers are 9 and 10. Add to get a sum of 19, but subtract to get a difference of 1.
Step-by-step explanation:
Is 26, 31, 36, 41, 46 an arithmetic sequence?
Answer:
Yes, it is arithmetic sequence.
Step-by-step explanation:
31-26=5
36-31=5
41-36=5
46-41=5
Difference between consecutive numbers is the same, so we have arithmetic sequence.
Answer:
Yes it is an arithmetic sequence
26+5=31
31+5=36
36+5=41
41+5=46
The plot shows the temperatures (in ºF) for a group of children who visited a doctor’s office. A plot shows the temperature of children at a doctor's office. 1 child had a temperature of 96 degrees; 2, 97 degrees; 5, 98 degrees; 2, 99 degrees; 1, 100 degrees. What conclusions can be drawn from the data set? Check all that apply.
Answer:
See below.
Step-by-step explanation:
1) the measure of center are the same
3) there is little variability in the data
4) the average temperature is 98
5) the data is clustered around the mean
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 86 students in the school. There are 38 in the Spanish class, 27 in the French class, and 16 in the German class. There are 14 students that in both Spanish and French, 6 are in both Spanish and German, and 5 are in both French and German. In addition, there are 2 students taking all 3 classes. If one student is chosen randomly, what is the probability that he or she is taking at least one language class
Answer: The required probability is 0.674.
Step-by-step explanation:
Since we have given that
Number of students in the Spanish class = 38
Number of students in the French class = 27
Number of students in the German class = 16
Number of students in both spanish and French = 14
Number of students in both Spanish and German = 6
Number of students in both French and German = 5
Number of students in all three class = 2
So, it becomes:
[tex]n(S\cup F\cup G)=n(S)+n(F)+n(G)-n(S\cap F)-n(G\cap F)-n(S\cap G)+n(S\cap F\cap G)\\\\n(S\cup F\cup G)=38+27+16-14-5-6+2=58[/tex]
So, Probability that he or she is taking at least one language class is given by
[tex]\dfrac{58}{86}=0.674[/tex]
Hence, the required probability is 0.674.
The exact numbers of each color of Umbrella Corporation's most popular candy, W&Ws, naturally vary from bag to bag, but the company wants to make sure that the process as a whole is producing the fve colors in equal proportions. Which of the following would represent the alternative hypothesis in a chi squared goodness-of-fost conducted to determine if the five colors of W&Ws occur in equal proportions? My: Al of the proportions are different from 0.20 MP1 P2 =3 =p4 P5 - 0.20 0 Hy: At least two of the mean number of colors differ from one another He the number of candies per bag and candy color are dependent Hy: At least one proportion is not equal to 0 20 5.5556
Question in order:
The exact numbers of each color of Umbrella Corporation's most popular candy, W&Ws, naturally vary from bag to bag, but the company wants to make sure that the process as a whole is producing the five colors in equal proportions. Which of the following would represent the alternative hypothesis in a chi-squared goodness-of-fit test conducted to determine if the five colors of W&Ws occur in equal proportions?
a. H1: All of the proportions are different from 0.20
b. HI: p1 = P2 = p3 =P4=p5 = 0.20
c. H1: At least one proportion is not equal to 0.20
d. H1: At least two of the mean number of colors differ from one another.
e. HI: the number of candies per bag and candy color are dependent
Answer:
option C
Step-by-step explanation:
H1: At least one proportion is not equal to 0.20
What percentage of the data values falls between the values of 27 and 45 in the data set shown?
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
25%
50%
75%
100%
Answer:
the answer is 75% hope that helps
Step-by-step explanation:
i did the test and i got it right
The required percentage of the data values falls between the values of 27 and 45 in the data set shown is 75%.
What is a box plot?A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value. Horizontal lines on both sides of the rectangle show the lower and upper quartiles.
Based on the box-and-whisker plot, we can see that the majority of the data values fall between the values of 32 and 45, and the median value is 36.
To find the percentage of data values that fall between 27 and 45, we can estimate by visually analyzing the plot. Since the whiskers go from 27 to 48, we can assume that all data values between 27 and 48 are included. Then, we need to estimate how much of the data falls between 32 and 45, which is the range of the box.
Since the box takes up most of the range of values between 32 and 45, we can estimate that around 75% of the data values fall within this range. Therefore, the percentage of data values that fall between 27 and 45 can be estimated as around 75%.
Learn more about box plots here:
brainly.com/question/1523909
#SPJ6
What is 3 to the 3rd power
Answer:
27
Step-by-step explanation:
3 x 3 x 3=27
Answer:
27
Step-by-step explanation:
you can just do 3x3x3 or 3^3 to figure it out.. 3x3=9 and 9x3= 27.. hope this helped..
A B C or D? I need help
Answer:
The answer is (A)
Answer:
The answer is A.
Step-by-step explanation:
This is because the plus sign after the first mixed number gets multiplied to the second mixed number. When a plus sign gets multiplied to something that is negative already, then the answer is negative, so the equation will still stay the same and be -3 1/8 - 2 1/2.
if this answer helped u, please mark as brainliest!
The point (-3,1) is on the terminal side of the angle in standard position. What is tanθ
Answer:
[tex] \tan \theta = - \frac{1}{3}[/tex]
Step-by-step explanation:
Since, point (-3, 1) is on the terminal side of the angle in standard position.
[tex] \therefore \: ( - 3, \: 1) = (x, \: y) \\ \therefore \:x = - 3 \: \: and \: \: y = 1 \\ \because \tan \theta = \frac{y}{x} \\ \therefore \:\tan \theta = \frac{1}{ - 3} \\ \\ \huge \red{ \boxed{\therefore \:\tan \theta = - \frac{1}{3} }}[/tex]
Suppose samples of size 100 are drawn randomly from a population that has a mean of 20 and a standard deviation of 5. What are the values of the mean and the standard deviation of the distribution of the sample means
Answer:
a) The mean of the sampling distribution of means μₓ = μ = 20
b) The standard deviation of the sample σₓ⁻ = 0.5
Step-by-step explanation:
Explanation:-
Given sample size 'n' =100
Given mean of the Population 'μ' = 20
Given standard deviation of population 'σ' = 5
a) The mean of the sampling distribution of means μₓ = μ
μₓ = 20
b) The standard deviation of the sample σₓ⁻ = [tex]\frac{S.D}{\sqrt{n} }[/tex]
Given standard deviation of population 'σ' = 5
= [tex]\frac{5}{\sqrt{100} } = 0.5[/tex]
Final answer:
The mean of the distribution of the sample means drawn from a population with a mean of 20 and a standard deviation of 5, using samples of size 100, is 20. The standard deviation of this distribution, also known as the standard error, is 0.5.
Explanation:
The question involves understanding the concept of the distribution of sample means, also known as the sampling distribution. When samples of size 100 are drawn from a population with a mean (μ) of 20 and a standard deviation (σ) of 5, the mean of the distribution of the sample means will be the same as the population mean, which is 20. However, the standard deviation of the distribution of sample means, known as the standard error (SE), will be the population standard deviation divided by the square root of the sample size (√n), which in this case is 5/√100 = 0.5.
Therefore, the mean of the distribution of the sample means is 20 and the standard deviation (standard error) of this distribution is 0.5. This is based on the central limit theorem which states that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the population’s distribution, with these exact parameters of mean and standard deviation.
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 29 tires surveyed, the mean lifespan was 45,800 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≥ 50000
For the alternative hypothesis,
µ < 50000
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = lifetime of the tyres
µ = mean lifetime
σ = standard deviation
n = number of samples
From the information given,
µ = 50000 miles
x = 45800 miles
σ = 8000
n = 29
z = (50000 - 45800)/(8000/√29) = - 2.83
Looking at the normal distribution table, the probability corresponding to the z score is 0.9977
Since alpha, 0.05 < than the p value, 0.9977, then we would accept the null hypothesis. Therefore, At a 5% level of significance, the data is not highly consistent with the claim.
The U.S. Department of Agriculture claims that the mean cost of raising a child from birth to age 2 by husband-wife families in the United States is $13,120. A random sample of 500 children (age 2) has a mean cost of $12,925 with a standard deviation of $1745. At α=.10, is there enough evidence to reject the claim? (Adapted from U.S. Department of Agriculture Center for Nutrition Policy and Promotion).
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 13120
For the alternative hypothesis,
µ ≠ 13120
This is a 2 tailed test
Since the population standard deviation is not given, the t test would be used to determine the test statistic. The formula is
t = (x - µ)/(s/√n)
Where
s = sample standard deviation
x = sample mean
µ = population mean
n = number of samples
From the information given,
µ = $13120
x = $12925
n = 500
s = $1745
t = (12925 - 13120)/(1745/√500) = - 2.5
Degree of freedom = n - 1 = 500 - 1 = 499
Using the t score calculator to find the probability value,
p = 0.012
Since α = 0.10 > p = 0.012, it means that there is enough evidence to reject the claim
Ali is riding his bicycle. He rides at a Speed of 12.8 kilometers per hour for 2 hours how many kilometers did he ride
Answer:
25.6 kilometers
Step-by-step explanation:
12.8 km in an hour
he is riding for 2 hours
12.8 x 2 = 25.6
Using the formula 'Distance equals Speed times Time', we find that Ali rode a distance of 25.6 kilometers given that he rode his bicycle at a speed of 12.8 kilometers per hour for 2 hours.
Explanation:To answer this question, you can use the formula to calculate distance, which is Speed multiplied by Time. In Ali's case, he's riding his bicycle at a speed of 12.8 kilometers per hour and for 2 hours. Using the formula, you'll multiply 12.8(km/h) by 2(h). Thus, Ali's distance covered would be 25.6 kilometers.
Here's how it works in a step-by step format:
Use the formula: Distance = Speed x TimePlug in the given values: Distance = 12.8 km/h x 2 hCompute: Distance = 25.6 kmTherefore, Ali rode his bicycle for a distance of 25.6 kilometers.
Learn more about Distance Calculation here:https://brainly.com/question/34212393
#SPJ3
you just bought 4 bags of chips and 3 cans of soda and paid $9.75. As it is being bagged, you notice one bag of chips has expired. Instead of choosing replacements, you decide to get a refund. You get $2.75 back. How much does one bag of chips cost? How much does one can of soda cost?
Answer:
50 cents or 0.5
Step-by-step explanation:
Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal.
1. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute).
weight, X 25 35 50 75 500 1000
Galloping speed, Y 191.5 184.7 175.8 162.2 124.9 113.2
Answer:
Galloping speed Y=179.984-0.076 weight X
Step-by-step explanation:
The required equation is
y=a+bx
where y is galloping speed and x is weight of animal.
We have to estimate intercept a and slope b.
x y xy x²
25 191.5 4787.5 625
35 184.7 6464.5 1225
50 175.8 8790 2500
75 162.2 12165 5625
500 124.9 62450 250000
1000 113.2 113200 1000000
sumx=1685
sumy=952.3
sumxy=207857
sumx²=1259975
[tex]slope=b=\frac{n(sumxy)-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }[/tex]
[tex]slope=b=\frac{6(207857)-(1685)(952.3)}{6*(1259975)-(1685)^{2} }[/tex]
[tex]slope=b=\frac{-357483.5}{4720625}[/tex]
slope=b=-0.07573.
intercept=a=ybar-b*xbar
[tex]ybar=\frac{sumy}{n}[/tex]
[tex]ybar=\frac{952.3}{6}[/tex]
ybar=158.7167
[tex]xbar=\frac{sumx}{n}[/tex]
[tex]xbar=\frac{1685}{6}[/tex]
xbar=280.8333
intercept=a=ybar-b*xbar
intercept=a=158.7167-(-0.07573)*280.8333
intercept=a=158.7167+21.2675
intercept=a=179.9842
rounding intercept and slope to 3 decimal places
intercept=179.984.
slope=-0.076
The required equation is
Galloping speed Y=179.984-0.076 weight X
The required equation is galloping speed Y = 179.984 - 0.076 weight X.
Given that,
Four-legged animals run with two different types of motion: trotting and galloping.
The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal.
We have to determine,
An equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute).
According to the question,
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
The required linear equation is,
y = a + bx
Where y is galloping speed and x is weight of animal.
To estimate intercept a and slope b from the table showing below.
x y x.y x²
25 191.5 4787.5 625
35 184.7 6464.5 1225
50 175.8 8790 2500
75 162.2 12165 5625
500 124.9 62450 250000
1000 113.2 113200 1000000
Then,
sum of x = 1685 , sum of y = 952.3 , sum of xy = 207857 , sum of x² = 1259975.
Therefore, Slope of b is given by the formula;
[tex]b = \dfrac{(sum\ of \ xy )- (sumx).(sumy)}{n(sumx^{2})- (sumx)^{2} }\\\\b = \dfrac{6(207857)-1685(952.3)}{6(1259975)-(1685)^{2} }\\\\b = \dfrac{-357483.5}{4720625}\\\\b = -0.7573[/tex]
Then,
[tex]Y_b_a_r = \dfrac{sumx}{n} = \dfrac{952.3}{6} = 158.71\\\\X_b_a_r = \dfrac{sumy}{n} = \dfrac{1685}{6} = 280.83[/tex]
Therefore, The intercept is given by,
[tex]intercept = a = Y_b_a_r-b\times X_b_a_r\\\\intercept = a = 158.7167 - (-0.07573)\times 280.8333\\\\intercept = a = 158.7167 + 21.2675\\\\intercept = a = 179.984[/tex]
On rounding intercept and slope to 3 decimal places,
intercept = 179.984.
slope = -0.076
Hence, The required equation is galloping speed Y = 179.984 - 0.076 weight X.
To know more about Linear equation click the link given below.
https://brainly.com/question/14824234
A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school. (7 points) What is the proportion of semester students returning to summer school
Answer:
The proportion of semester students returning to summer school
p = 0.35
Step-by-step explanation:
Explanation:-
Given data A university planner is interested in determining the percentage of spring semester students who will attend summer school.
She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school
Given the sample size 'n' = 160
let 'x' = 56
Sample proportion of semester students returning to summer school
[tex]p = \frac{x}{n} = \frac{56}{160}[/tex]
p = 0.35
Find the average temperature on that part of the plane 2x + 5y +z = 9 over the square |x| <= 1, y <= 1, where the temperature is given by T(x,y,z) = e^-z. The average value is :_______
Answer:
This question answer is attached in the attachment,
Step-by-step explanation:
A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 per foot, while the remaining two sides will use standard fencing costing $2 per foot. The budget that will be entirely used for fencing is $6000. In order to maximize the area of the plot, how many feet of standard fencing should be purchased for the project?
So, the required length of the sides that have standard fencing is 1500 ft.
Area of the rectangle:The area of rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a type of quadrilateral, a 2d shape that has four sides and four vertices.
Let [tex]x[/tex] ft be the length of the sides that duty fencing and [tex]y[/tex] ft be the length of the sides that have standard fencing.
So, the area will be calculated by the above formula we get,
[tex]Area=xy[/tex]...(1)
Now, the cost of fencing is,
[tex]3x+2y=6000\\y=3000-\frac{3x}{2}[/tex]...(2)
Now, substituting equation (2) in equation (1) we get,
[tex]A=3000x-\frac{3x^2}{2}[/tex]
Now, differentiating the above equation we get,
[tex]\frac{dA}{dx} =3000-3x=0\\x=1000[/tex]
Substituting [tex]x=1000 ft[/tex] in equation (2) we get,
[tex]y=3000-\frac{3\times 1000}{2}\\=1500 ft[/tex]
Learn more about the topic area of the rectangle:
https://brainly.com/question/18251225
The question pertains to maximizing the area of a rectangular land plot within a fence budget. We derive a mathematical equation to fit the budget involving both types of fences and then maximize the equation to find the solution. It involves applications of maximization and differentiation.
Explanation:The subject of this question is Mathematics, specifically problems involving equations and budgets. This problem can be solved by using the concept of maximization of areas in rectangle and budget calculations.
We know the total budget which is $6000, and costs of the two types of fencing. Let's denote the lengths of the heavy-duty fenced sides as H and the lengths of the standard fenced sides as S. The equation that describes the budget is 3H + 2S = 6000.
If we're maximizing area, we want to maximize S*H. Remember that the area of a rectangle is the product of its dimensions (length times width). Since H and S are lengths of sides of a rectangular plot, H*S will give us the area.
Replacing H from the budget equation we get H = (6000 - 2S) / 3. You can plug this into the area equation to get Area = S * (6000 - 2S) / 3. To find the maximum of this function, take its derivative and set it to zero, solve for S.
Doing this results in the required amount of standard fencing for the project, making it a solution to the question asked.
Learn more about Maximization here:https://brainly.com/question/36610486
#SPJ3
Josh wants to download music online. He must buy a membership for $14.
Then he can download songs for 99 cents each. Josh has $20. How many
songs can Josh buy without spending more money than he has?
Answer:
6 songs
Step-by-step explanation:
It's best to start by setting up an equation equal to $20.
$14 + $.99s = $20
s being songs in this case.
First we add like terms by subtracting $14 from both sides.
$.99s = $6
Now we solve for s by dividing both sides by $.99
s = $6.06
Therefore, Josh can by 6 songs.
Final answer:
Josh can buy 6 songs with his remaining $6 after purchasing a $14 membership, since each song costs 99 cents.
Explanation:
Josh wants to download music online. With $20 to spend, he first needs to buy a membership for $14, leaving him with $6 to spend on songs. Each song costs 99 cents, so to determine how many songs Josh can purchase without exceeding his budget, we have to divide the remaining money by the cost per song.
Step 1: Calculate the remaining budget after membership: $20 - $14 = $6.
Step 2: Divide the remaining budget by the cost per song: $6 \(\div\) $0.99 ≈ 6 songs.
Thus, Josh can buy 6 songs without spending more than he has.
Find the output, k, when the input, t, is 3.
k = 13t – 2
k=
Answer:
k= 13*3-2
k= 39-2
k=37 is the required answer
Answer:
k = 37
Step-by-step explanation:
[tex]k = 13t - 2 \\ \therefore \: k = 13 \times 3 - 2 \\ \therefore \: k = 39 - 2 \\ \huge \red{ \boxed{ \therefore \: k = 37}}[/tex]
100 POINTS.
PLEASE PROVIDE STEP BY STEP ANSWER
THANK YOU.
Step-by-step explanation:
W(x) = (10x⁴ − 8) (30x + 25)^0.5
A) Take log of both sides.
ln(W) = ln[(10x⁴ − 8) (30x + 25)^0.5]
ln(W) = ln(10x⁴ − 8) + ln[(30x + 25)^0.5]
ln(W) = ln(10x⁴ − 8) + 0.5 ln(30x + 25)
Take derivative.
W' / W = 40x³ / (10x⁴ − 8) + 0.5 (30) / (30x + 25)
W' / W = 20x³ / (5x⁴ − 4) + 3 / (6x + 5)
W' = W [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]
W'(x) = (10x⁴ − 8) (30x + 25)^0.5 [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]
B) Evaluate at x = 0.
W'(0) = (0 − 8) (0 + 25)^0.5 [0 / (0 − 4) + 3 / (0 + 5)]
W'(0) = (-8) (5) (0 + 3/5)
W'(0) = -24
Answer:
[tex]\textsf{A)}\quad W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
[tex]\textsf{B)}\quad W'(0)=-24[/tex]
Step-by-step explanation:
Part AGiven function:
[tex]W(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5}[/tex]
Take the natural logarithm of both sides:
[tex]\ln \left(W(x)\right) = \ln \left( (10x^4 - 8) \cdot (30x + 25)^{0.5} \right)[/tex]
Use properties of logarithms to simplify:
[tex]\ln \left(W(x)\right) = \ln (10x^4 - 8) +\ln(30x + 25)^{0.5} \\\\\\ \ln \left(W(x)\right) = \ln (10x^4 - 8) +0.5 \ln(30x + 25)[/tex]
Differentiate both sides with respect to x:
[tex]\dfrac{d}{dx} \ln \left(W(x)\right) = \dfrac{d}{dx} \left( \ln (10x^4 - 8) + 0.5 \ln (30x + 25) \right)[/tex]
Apply the chain rule on the right-hand side:
[tex]\dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot \dfrac{d}{dx} (10x^4 - 8) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot \dfrac{d}{dx} (30x + 25) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot (40x^3) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot (30) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{40x^3}{10x^4 - 8} + \dfrac{15}{30x + 25} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{2(20x^3)}{2(5x^4 - 4)} + \dfrac{5(3)}{5(6x + 5)} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5}[/tex]
Multiply both sides by W(x) to solve for W'(x):
[tex]W'(x) = W(x) \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
Substitute W(x) back in:
[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
Therefore, the derivative W'(x) is:
[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
[tex]\dotfill[/tex]
Part BTo find W'(0), substitute x = 0 into W'(x):
[tex]W'(0) = (10(0)^4 - 8) \cdot (30(0) + 25)^{0.5} \left(\dfrac{20(0)^3}{5(0)^4 - 4} + \dfrac{3}{6(0) + 5} \right) \\\\\\ W'(0) = (0 - 8) \cdot (0 + 25)^{0.5} \left(\dfrac{0}{0 - 4} + \dfrac{3}{0 + 5} \right) \\\\\\ W'(0) = (- 8) \cdot (25)^{0.5} \cdot \left( \dfrac{3}{5} \right) \\\\\\ W'(0) = (- 8) \cdot 5 \cdot \dfrac{3}{5} \\\\\\ W'(0)=-24[/tex]
Therefore, the value of W'(0) is -24.