A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is
Answers
Answer:
Step-by-step explanation:
Hello!
*Full text*
A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is
weight = b + width * m
This model was fit to the data using the method of the least squares. The following results were obtained from statistical software.
(See attachment for output)
R2 = 0.423
A.) What is the regression equation for this example?
The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963
In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:
^Y= 2.3013 + 0.7963Xi
B.) What is the explanatory, or predictor, variable in this study?
The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:
X: Width of a horseshoe crab (cm)
C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.
To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.
The hypotheses are:
H₀: β=0
H₁: β≠0
α: 0.05
[tex]t= \frac{m-\beta }{S_m} ~t_{n-2}[/tex]
[tex]t_{H_0}= \frac{0.7963-0}{0.0939}= 8.48[/tex]
The value of the statistic under the null hypothesis is t= 8.48
D.) What can we say about the p-value?
This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:
P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001
E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?
As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:
Critical values ±[tex]t_{n-2;1-\alpha /2}[/tex] = ± [tex]t_{98; 0.975}[/tex] = ± 1.984
This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-
F.) Find the confidence interval for the slope.
Using a 95% confidence level, the interval for the slope is:
[m ± [tex]t_{n-2;1-\alpha /2}[/tex] Sm]
[0.7963 ± 1.984 * 0.0939]
[0.61; 0.98]
G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.
Yes, there is a significant relationship between the width and weight of the horseshoe crabs.
Using the critical value approach:
The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.
If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.
I hope this helps!
Related Questions
Any polygon can be the base of a prism. A. True B. False
Answers
Answer:
true
Step-by-step explanation:
A prism is a solid with parallelogram sides (usually rectangles) and a polygon for the 2 bases. Any polygon can be the base.
Answer:
Hello!
__________________
Your answer would be (A) True.
Step-by-step explanation: Hope this helped you!
Any polygon can be the base of a prism so the answer is true.
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answers
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function Interval f(x) = 7 − 2x [1, 2]
Answers
Answer:
-2n
Step-by-step explanation:
f(x)=7-2x {1,2}
f(1)=7-2(1)=5
f(2)=7-2(2)=3
Slope (m)=3/5
{7-2(1)}-{7-2(2)}=3-5=-2
In terms of n=-2n
The upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3]
Given the function of the graph bounded by the inteval [1, 2] expressed as
f(x) = 7 - 2x
The upper limit of the function is the point where the domain of the function x is 2. Substitute x = 2 into the function, we will have:
f(2) = 7 - 2(2)
f(2) = 7 - 4
f(2) = 3
For the lower limit, the domain of the function is at x = 2:
f(1) = 7 - 2(1)
f(1) = 7 - 2
f(1) = 5
Hence the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3].
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The amount of time it takes a bat to eat a frog was recorded for each bat in a random sample of 12 bats. The resulting sample mean and standard deviation were 21.9 minutes and 7.7 minutes, respectively. Assuming it is reasonable to believe that the population distribution of bat mealtimes of frogs is approximately normal, a. Construct a 95% confidence interval for the mean time for a bat to eat a frog. b. Construct a 95% confidence interval for the variance of the time for a bat to eat a frog.
Answers
Answer: a. CI for the mean: 17.327 < μ < 26.473
b. CI for variance: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093
Step-by-step explanation:
a. To construct a 95% confidence interval for the mean:
The given data are:
mean = 21.9
s = 7.7
n = 12
df = 12 - 1 = 11
1 - α = 0.05
[tex]\frac{\alpha}{2}[/tex] = 0.025
t-score = [tex]t_{0.025,11}[/tex] = 2.2001
Note: since the sample population is less than 30, it is used a t-score.
The formula for interval:
mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]
Substituing values:
21.9 ± 2.200.[tex]\frac{7.7}{\sqrt{12} }[/tex]
21.9 ± 4.573
The interval is: 17.327 < μ < 26.473
b. A 95% confidence interval for the variance:
The given values are:
[tex]s^{2}[/tex] = [tex]7.7^{2}[/tex]
[tex]s^{2}[/tex] = 59.29
α = 0.05
[tex]\frac{\alpha}{2}[/tex] = 0.025
[tex]1-\frac{\alpha}{2}[/tex] = 0.975
[tex]\chi^{2}_{0.025,11}[/tex] = 21.92
[tex]\chi^{2}_{0.975,11}[/tex] = 3.816
Note: To find the values for [tex]\chi^{2}_{\alpha/2,n-1}[/tex] and [tex]\chi^{2}_{1-\alpha/2,n-1}[/tex], look for them at the chi-square table
The formula to calculate interval:
([tex]\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}}[/tex])
are the lower and upper limits, respectively.
Substituing values:
([tex]\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816}[/tex])
(29.7532, 170.9093)
The interval for variance is: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093
Decide whether the sets are equivalent {d: d is a month of the year} and {g : g is a state in the United States}
Answers
Answer:
Non equivalentStep-by-step explanation:
The equivalent between sets is determined by the number of elements. If two sets have the same number of elements, then they are equivalent sets.
In this case, a year has 12 months, and the US has 50 states. So, one month is not equal to 1 state because they have different natures and they represent a different proportion. A month represents 1/12 of a year and a state represents 1/50 of the total number of states.
Clara writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:
Answers
Answer:
CPCTC
Step-by-step explanation:
Statements 3 and 4 show the top and bottom triangles are congruent, and the left and right triangles are congruent. Statement 5 is making use of these facts to claim that the alternate interior angles are congruent. This claim is valid because ...
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Which of the following is represented by MN?
Answers
Answer: MN represents the radius of the circle.
Step-by-step explanation:
The radius is the distance from the center to the outside of the circle.
ten percent of 140,000 = ?
Answers
Answer:
14000
Step-by-step explanation:
Of means multiply
10% * 140000
Change to decimal form
.10 * 140000
14000
Answer:
[tex]14000[/tex]
Step-by-step explanation:
[tex]10\% \times 140000[/tex]
[tex]\mathrm{Apply} \: a\% = \frac{a}{100}[/tex]
[tex]\frac{10}{100} \times 140000[/tex]
[tex]\mathrm{Apply} \: \frac{a}{100} \times b = \frac{ab}{100}[/tex]
[tex]\frac{1400000}{100}[/tex]
[tex]\mathrm{Simplify.}[/tex]
[tex]\frac{14000}{1} =14000[/tex]
I'm having a hard time with this. A new housing development extends 4 miles in one direction, makes a right turn, and then con- tinues for 3 miles. A new road runs between the beginning and ending points of the development. What is the perimeter of the triangle formed by the homes and the road? What is the area of the housing development?
Answers
Answer:
perimeter = 12 miles
area = 6 square miles
Step-by-step explanation:
Since it makes a right triangle, use the Pythagorean Formula.
3^2+4^2=c^2
9+16=c^2
25=c^2
5=c, so the hypotenuse of the right triangle is 5.
Perimeter = 3+4+5 = 12 miles
area = 1/2bh (1/2 base times height)
=1/2x3x4
=6
Area = 6 square miles
Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answers
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables a. More than 61 pounds
Answers
Answer:
0.007
Step-by-step explanation:
We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage
Step 1
We would have to find the sample standard deviation.
We use the formula = σ/√n
σ = 12.2 pounds
n = number of house holds = 51
= 12.2/√51
Sample Standard deviation = 1.7083417025.
Step 2
We find the z score for when the sample mean is more than 61
z-score formula is z = (x-μ)/σ
where:
x = raw score = 61 pounds
μ = the population mean = 56.8 pounds
σ = the sample standard deviation = 1.7083417025
z = (x-μ)/σ
z = (61 - 56.8)/ 1.7083417025
z = 2.45852
Finding the Probability using the z score table
P(z = 2.45852) = 0.99302
P(x>61) = 1 - P(z = 2.45852) = 0.0069755
≈ 0.007
Therefore,the probability that the sample mean will be more than 61 pounds is 0.007
Consider circle T with radius 24 in. and θ = StartFraction 5 pi Over 6 EndFraction radians. Circle T is shown. Line segments S T and V T are radii with lengths of 24 inches. Angle S T V is theta. What is the length of minor arc SV?
Answers
Answer:
20π inStep-by-step explanation:
Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;
[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]
The length of the minor arc SV is expressed as:
[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]
Hence, The length of the arc SV is 20π in
Answer:
20 pi
Step-by-step explanation:
Please help! V^2 = 25/81
Answers
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
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heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode
Answers
median=order them and find the middle=6
mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4
range= the difference between the smallest and largest number=9-3=6
mode= the one that appears the most= 7
The median, mean, range and mode will be 6, 5.4, 9 and 7.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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Which expression is equivalent to -3(2m - 1) - n? 6m - n - 3 6m - n + 3 -6m - n - 3 -6m - n +3
Answers
Answer:
-6m+3
Step-by-step explanation:
Answer:
An equivalent value is -6m -n +3
Step-by-step explanation:
Given
-3(2m-1)-n expand
=-6m+3-n
(also equals -6m -n +3 by commutativity)
Irvin buys a car for $21 comma 804. It depreciates 25% each year that he owns it. What is the depreciated value of the car after 1 yr? after 2 yr? The depreciated value of the car after 1 yr is $? The depreciated value of the car after 2 yr is $?
Answers
Answer:
The depreciated value of the car after 1 yr is $16,353
The depreciated value of the car after 2 yr is $12,264.75
Step-by-step explanation:
Given
purchase amount P= $21,804
rate of depreciation R= 25%
applying the formula for the car deprecation we have
[tex]A= P*(1-\frac{R}{100} )^n[/tex]
Where,
A is the value of the car after n years,
P is the purchase amount,
R is the percentage rate of depreciation per annum,
n is the number of years after the purchase.
1. The depreciated value of the car after 1 yr is
n=1
[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]
The depreciated value of the car after 1 yr is $16,353
2. The depreciated value of the car after 2 yr is
n=2
[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]
The depreciated value of the car after 2 yr is $12,264.75
The Beer Institute reported that monthly consumption of beer in is 1.7 gallons per person. A random sample of 36 adults was selected. Using a population standard deviation of 0.5 gallons per month per person, what is the probability that the sample mean was between 1.6 and 1.8 gallons per month per person?
Answers
Answer:
.7698
Step-by-step explanation:
Convert into the following unit into 30 cm into miter
Answers
Answer:
it we'll be 0.3
Step-by-step explanation:
trust me man I like to explain but it's long
Answer:
0.3 meter or 3/10 meter
Step-by-step explanation:
As there are 100cm in 1 meter and you want to find 30cm in terms of meters.
It will be as
100cm = 1 meter (rule/lax)
100/100 cm = 1/100 meter (divide both sides of equation with 100)
1 cm = 1/100 meter
1 *30 cm = (1/100)*30 meter (multiply both sides with 30)
30 cm = 30/100 meter
30/100 more shortly can be written as 3/10 meter or in decimals 0.3 meter.
Find the area of a circle with a diameter of 8yards. Use 3.14. The area of the circle is approximate
Answers
Answer:
50.24 yd²
Step-by-step explanation:
pi r² = (3.14)(4)² = 50.24
The length of a rectangular garden is 3 yards greater
than the width of the garden. If the garden measures
15 yards diagonally, what is its length?
Answers
Answer:
12
Step-by-step explanation:
Let's call the width x and the length x + 3. Using the Pythagorean Theorem we can write:
(x + 3)² + x² = 15²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
2(x² + 3x - 108) = 0
2(x + 12)(x - 9) = 0
x + 12 = 0 or x - 9 = 0
x = -12 or x = 9
x cannot be -12 because length/width can't be negative so x = 9 which means that the length is 9 + 3 = 12.
An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answers
Answer:
[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]
The p value would be given by:
[tex]p_v =2*P(z<-2.23)=0.0257[/tex]
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
Step-by-step explanation:
Information given
[tex]\bar X=46.5[/tex] represent the mean
[tex]\sigma=1.1[/tex] represent the population standard deviation
[tex]n=150[/tex] sample size
[tex]\mu_o =46.7[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean for this case is 46.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 46.7[/tex]
Alternative hypothesis:[tex]\mu \neq 46.7[/tex]
Since we know the population deviation the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]
The p value would be given by:
[tex]p_v =2*P(z<-2.23)=0.0257[/tex]
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
What is 1 standard deviation on a
normal curve?
A. Another name for the mean.
B. Another name for the inflection point.
C. The distance from the mean to the bottom of the
curve.
D. The distance from the mean to an inflection point.
Answers
Answer:
D. The distance from the mean to an inflection point
Step-by-step explanation:
We rarely encounter the actual formula for the normal PDF. It is ...
[tex]p(x)=\dfrac{1}{\sqrt{2\pi}}e^{-\dfrac{x^2}{2}}[/tex]
In fact, the inflection points are at x = ±1, where the curve changes from being concave downward to concave upward.
So, one standard deviation is the distance from the mean to an inflection point.
A fair die is rolled repeatedly. Calculate to at least two decimal places:__________
a) the chance that the first 6 appears before the tenth roll
b) the chance that the third 6 appears on the tenth roll
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
d) the expected number of rolls until six 6's appear
e) the expected number of rolls until all six faces appear
Answers
Answer:
a. 0.34885
b. 0.04651
c. 0.02404
d. 36
e. 14.7, say 15 trials
Step-by-step explanation:
Q17070205
Note:
1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.
2. use R to find the probability values from the respective distributions.
a) the chance that the first 6 appears before the tenth roll
This means that a six appears exactly once between the first and the nineth roll.
Using binomial distribution, p=1/6, n=9, x=1
dbinom(1,9,1/6) = 0.34885
b) the chance that the third 6 appears on the tenth roll
This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.
Again, we have a binomial distribution of p=1/6, n=9, x=2
p1 = dbinom(2,9,1/6) = 0.27908
The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.
Thus the probability of both happening, by the multiplication rule, assuming independence
P(third on the tenth roll) = p1*p2 = 0.04651
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
Again, using binomial distribution, probability of 3-6's in the first 10 rolls,
p1 = dbinom(3,10,1/6) = 0.15504
Probability of 3-6's in the NEXT 10 rolls
p1 = dbinom(3,10,1/6) = 0.15504
Probability of both happening (multiplication rule, assuming both events are independent)
= p1 * p1 = 0.02404
d) the expected number of rolls until six 6's appear
Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6
= n(1-p)/p
Total number of rolls by adding n
= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36
e) the expected number of rolls until all six faces appear
P1 = 6/6 because the firs trial (roll) can be any face with probability 1
P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials
P3 = 6/4 ...
P4 = 6/3
P5 = 6/2
P6 = 6/1
So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials
write the equation of a circle with the center (6,4) that passes through the coordinate (2,1) in your final answer include all of your calculations
Answers
Step-by-step explanation:
define define equation we need the value of the radius and
which figure has the same order of rotational symmetry as a rectangle
Answers
Answer:
rhombus
Step-by-step explanation:
on edge
What is 3 1/2 times 4?
Answers
Answer:
14
Step-by-step explanation:
3 1/2 × 4
Convert 3 1/2 to an improper fraction.
7/2 × 4
7/2 × 4/1
Multiply.
(7× 4) / (2 × 1)
28 / 2
= 14
Answer: 14
Step-by-step explanation: To multiply a mixed number times a whole number, first write each of them as an improper fraction.
So we can rewrite 3 and 1/2 as the improper fraction 7/2
and we can write 4 as the improper fraction 4/1.
If you've forgotten how to write a mixed number as an improper fraction, feel free to ask me below and I will review this with you.
So now we have 7/2 × 4/1.
When we're multiplying fractions, we want to
cross-cancel first whenever possible.
So here, notice that we can cross-cancel 2 and 4 to 1 and 2.
So we have 7/1 × 2/1.
Now we just multiply across the numerators and multiply across the denominators and we have our answer, 14/1 or just 14.
What is the equation of a circle with center (−8, 3) and radius 8?
Answers
Answer:
(x + 8)² + (y - 3)² = 64
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (- 8, 3) and r = 8 , thus
(x - (- 8))² + (y - 3)² = 8² , that is
(x + 8)² + (y - 3)² = 64
Answer:
See below.
Step-by-step explanation:
The equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius.
Plug in what we know. (-8,3) for (h,k) respectively and 8 for the radius:
[tex](x-(-8))^2+(y-(3))^2=(8)^2[/tex]
[tex](x+8)^2+(y-3)^2=64[/tex]
f(x)=1/3x g(x)= 1/3x f(g(x))= Are they inverses? Please explain.
Answers
Answer:
no
Step-by-step explanation:
f(g(x))= x if they are inverses
(x)=1/3x
g(x)= 1/3x
f(g(x)) = 1/3 (g(x) = 1/3 (1/3x) = 1/9x
This is not x so they are not inverse functions
Refer to the accompanying data set and construct a 90​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.
Male/Females
81 82
77 94
53 60
59 66
53 53
60 81
54 78
76 83
52 87
64 53
73 34
57 64
65 83
78 74
79 81
66 66
69 65
94 76
45 61
89 64
71 82
66 80
70 71
74 77
52 88
68 90
56 87
79 91
75 89
62 93
66 68
96 87
60 83
65 81
55 74
57 56
70 101
70 71
83 74
57 77
Answers
The required 90% confidence interval for adult males is
[tex]\text {CI} = (64.2, \: 70.6)\\\\[/tex]
The required 90% confidence interval for adult females is
[tex]\text {CI} = (72, \: 79.2)\\\\[/tex]
The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.
Step-by-step explanation:
We are given the pulse rates of adult females and adult males and we have to construct the 90% confidence interval of the mean pulse rate for males and females.
Let us first compute the mean and standard deviation of the given pulse rates data.
Using Excel,
=AVERAGE(number1, number2,....)
The mean pulse rate of adult males is found to be
[tex]\bar{x}_{male} = 67.4[/tex]
The mean pulse rate of adult females is found to be
[tex]\bar{x}_{female} = 75.6[/tex]
Using Excel,
=STDEV(number1, number2,....)
The standard deviation for adult male pulse rate is found to be
[tex]s_{male} = 11.9[/tex]
The standard deviation for adult female pulse rate is found to be
[tex]s_{female} = 13.5[/tex]
The confidence interval is given by
[tex]$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean, n is the sample size, s is the sample standard deviation and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 90% confidence level.
The t-score corresponding to a 90% confidence level is
Significance level = α = 1 - 0.90 = 0.10/2 = 0.05
Degree of freedom = n - 1 = 40 - 1 = 39
From the t-table at α = 0.05 and DoF = 39
t-score = 1.685
The required 90% confidence interval for adult males is
[tex]\text {CI} = 67.4 \pm 1.685\cdot \frac{11.9}{\sqrt{40} } \\\\\text {CI} = 67.4 \pm 1.685\cdot 1.882\\\\\text {CI} = 67.4 \pm 3.17\\\\\text {CI} = 67.4 - 3.17, \: 67.4 + 3.17\\\\\text {CI} = (64.2, \: 70.6)\\\\[/tex]
Therefore, we are 90% confident that the actual mean pulse rate of adult male is within the range of 64.2 to 70.6 bpm
The required 90% confidence interval for adult females is
[tex]\text {CI} = 75.6 \pm 1.685\cdot \frac{13.5}{\sqrt{40} } \\\\\text {CI} = 75.6 \pm 1.685\cdot 2.1345\\\\\text {CI} = 75.6 \pm 3.60\\\\\text {CI} = 75.6 - 3.60, \: 75.6 + 3.60\\\\\text {CI} = (72, \: 79.2)\\\\[/tex]
Therefore, we are 90% confident that the actual mean pulse rate of adult female is within the range of 72 to 79.2 bpm
Comparison:
The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.
What is the value of x in the equation 0.7 x - 1.4 = -3.5
Answers
Answer:
x=12.5
Step-by-step explanation:
0.7x times (-1.4)=-3.5
-0.28x=-3.5 (divide both sides)
Ans:12.5