Answer:
Probability that the sample will have a mean that is greater than $52,000 is 0.0057.
Step-by-step explanation:
We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.
We select a random sample of 1,000 people.
Let [tex]\bar X[/tex] = sample mean
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = $50,000
[tex]\sigma[/tex] = population standard deviation = $25,000
n = sample of people = 1,000
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample will have a mean that is greater than $52,000 is given by = P([tex]\bar X[/tex] > $52,000)
P([tex]\bar X[/tex] > $52,000) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } }[/tex] ) = P(Z > 2.53) = 1 - P(Z [tex]\leq[/tex] 2.53)
= 1 - 0.9943 = 0.0057
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.
Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.
The probability that a sample of 1,000 people will have an average income greater than $52,000 is approximately 0.57%, calculated using the standard error and the z-score in a normal distribution.
To calculate the probability that a sample will have a mean that is greater than $52,000, we would use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, even if the population distribution itself is not normal. Since we have a large sample size of 1,000 in this case, we can assume that the sampling distribution of the sample mean is approximately normal.
The first step is to determine the standard error of the mean, which is calculated as the population standard deviation divided by the square root of the sample size. In this case:
Standard Error = 25,000 / √(1,000) = 25,000 / 31.62 ≈ 790.57
Next, we calculate the z-score for the sample mean of $52,000:
Z = (Sample Mean - Population Mean) / Standard Error
Z = (52,000 - 50,000) / 790.57 ≈ 2.5262
Using the z-score value, we find the corresponding probability in a standard normal distribution table or use a calculator with a normal distribution function to find the probability that Z is greater than 2.5262. The area to the right of this z-score represents the probability we're seeking.
Since in standard normal tables we typically find the area to the left, we subtract this value from 1:
P(Z > 2.5262) = 1 - P(Z < 2.5262)
If we assume P(Z < 2.5262) = 0.9943 (from standard normal tables), then:
P(Z > 2.5262) = 1 - 0.9943 = 0.0057
Thus, the probability that the sample mean is greater than $52,000 is approximately 0.57%.
The area of a rectangle is 45.5 square inches. The base of the rectangle is 7 inches. What is the height of the rectangle in inches?
The height of the rectangle in inches is 6.5 inches.
The area of a rectangle = lw
where
l = length
w = width
Therefore,
area = 45.5 in²
length = 7 inches
The height of the rectangle can be found below:
45.5 = 7h
divide both sides by 7
45.5 / 7 = h
h = 6.5 inches
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Based on the information given the height of the rectangle in inches is 6.5 inches.
Using this formula
Area of a rectangle = Length× Width
Where:
Area = 45.5 in²
Length = 7 inches
Hence,
Let solve for Length
45.5 = 7h
Divide both sides by 7
h=45.5 / 7
h = 6.5 inches
Inconclusion the height of the rectangle in inches is 6.5 inches.
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g The tangent plane to z=f(x,y) at the point (1,2) is z=5x+2y−10. (a) Find fx(1,2) and fy(1,2). fx(1,2)= Number fy(1,2)= Number (b) What is f(1,2)? f(1,2)= Number (c) Approximate f(1.1,1.9). f(1.1,1.9)= Number
Answer:
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Approximation at points (1.1,1.9) is 0.7
Step-by-step explanation:
Given:
Tangent plane to a surface z=5x+2y-10 as the function at point (1,2)
To find :
f(x,y) at (1,2)
partial derivatives of function w.r.t. (x and y) and value of that function at given points.
Solution:(refer the attachment also)
Now we know that
the equation of tangent plane at given points to the surface is given by,
f(x1,y1,z1) and z=f(x,y)
z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)
here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.
now
taking partial derivative w.r.t. x we get
Fx(x1`,y1)=[tex]\frac{d}{dx} (5x+2y-10)[/tex]
=5.
Then w.r.t y we get
Fy(x1,y1)=
[tex]\frac{d}{dy}(5x+2y-10)[/tex]
=2.
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Using the Linearization or linear approximation we get
L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)
=-1+5(x-1)+2(y-2)
=5x+2y-10
Approximation at F(1.1,1.9)
=5(1.1)+2(1.9)-10
=5.5+3.8-10
=0.7
Approximation at points (1.1,1.9) is 0.7
Final answer:
The partial derivatives of f(x, y) at (1, 2) are fx(1,2) = 5 and fy(1,2) = 2. The function value f(1,2) is 0. An approximation for f(1.1, 1.9) using the tangent plane is 0.5.
Explanation:
The question concerns the computation of partial derivatives and the evaluation of a function f(x, y) given its tangent plane at a specific point. Given the tangent plane to z=f(x,y) at the point (1, 2), which is z=5x+2y−10, we have:
fx(1,2) is the partial derivative of z with respect to x at the point (1,2), equivalent to the coefficient of x in the tangent plane equation, which is 5.
fy(1,2) is the partial derivative of z with respect to y at the point (1,2), equivalent to the coefficient of y in the tangent plane equation, which is 2.
To find f(1,2), we substitute x=1 and y=2 into the tangent plane equation to get z = 5(1) + 2(2) − 10 = 0.
The value f(1.1,1.9) can be approximated by using the tangent plane equation. By plugging x=1.1 and y=1.9 into the equation, we obtain z = 5(1.1) + 2(1.9) - 10 = 0.5, for an approximate value of f(1.1, 1.9).
Summary of Answers:
fx(1,2) = 5
fy(1,2) = 2
f(1,2) = 0
f(1.1,1.9) ≈ 0.5
Mar’s, In. claims that its M&M candies are distributed with the color percentages of 20% brown, 20% yellow, 30% red, 10% orange, 10 % green, and 10% blue. A classroom exercise involving a random sample of 460 M&M’s resulted in the observed frequencies were: 90 brown, 94 yellow, 99 red, 64 orange, 51 green, and 62 blue. Test the claim that the color distribution is as claimed by Mars, Inc (α= 0.05). What can you conclude if the test statistic is greater than the critical value?
Answer:
Null hypothesis is rejected. There is no or little evidence to support the claim made by Mars.In
Step-by-step explanation:
Solution:-
- A claim is made by Mars.In that the M&M candies in a packet are distributed by color percentage given below.
- A random sample of N = 460 M&M's was taken and the frequencies of different colors were observed as given below.
- We are to test a claim made by the Mars.In regarding the color distribution of M&Ms at significance level α = 0.05.
- Compute the expected frequency of distribution for color as per Mars.In claim. Use the following formula for expected outcome:
Expected = N*pi
Where, pi : The percentages for each color.
- The table for expected and observed frequencies for each color is tabulated below.
Colors Percentage Expected Observed
Brown 20% 460*0.2 = 92 90
Yellow 20% 460*0.2 = 92 94
Red 30% 460*0.3 = 138 99
Orange 10% 460*0.1 = 46 64
Green 10% 460*0.1 = 46 51
Blue 10% 460*0.1 = 46 62
- To test the claim for color distribution of M&Ms using X^2 - test. We will state the Null and Alternate hypothesis as follows:
Null Hypothesis: The distribution is colors is as its claimed by the company
Alternate Hypothesis: The distribution is colors is not its claimed by the company
- We will first determine the X^2 statistics value using the following relation:
[tex]X^2-test = Sum [ \frac{(Oi- Ei)^2}{Ei} ]\\\\X^2-test = \frac{(90- 92)^2}{92} + \frac{(94- 92)^2}{92} + \frac{(99- 138)^2}{138} + \frac{(64- 46)^2}{46} + \frac{(51- 46)^2}{46} + \frac{(62- 46)^2}{46} \\\\X^2-test = \frac{4}{92} + \frac{4}{92} + \frac{1521}{138} + \frac{324}{46} + \frac{25}{46} + \frac{256}{46} \\\\X^2-test = 0.04347 + 0.04347 + 11.0217 + 7.04348 + 0.54348 + 5.56522\\\\X^2-test = 24.2608[/tex]
- The rejection region is defined by the significance level ( α ) = 0.05 and degree of freedom. The bound ( critical value ), X^2-critical is determined using the look-up table:
degree of freedom = number of observation category - 1 = 6 - 1 = 5
P ( X < X^2 - critical ) = 0.025
X^2 - critical = 12.8
- All the test values of X^2 > X^2-critical lie in the rejection region.
24.2608 > 12.8
X^-test > X^2-critical
Hence, Null hypothesis is rejected.
Conclusion: As per Chi-square test the claim made by the Mars.In has little or no evidence to be true; hence, the color distribution of M&M is not what is claimed.
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled, and the average error from the industry standard is measured in millimeters. The results are presented here. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. This example is what type of test
The question relates to a two-sample t-test in statistics, which compares the means of two processes. It involves calculating a t-score using sample data, and comparing this score to a critical value to determine if there is a significant difference between the two processes.
Explanation:This question pertains to the field of statistics within mathematics. Specifically, it involves the use of a two-sample t-test to compare the means of two different processes. The two-sample t-test is used when the population standard deviations are unknown but assumed to be equal, which is the case here.
The process involves computing a t-score using the observed data (including sample mean, standard deviation, and sample size) and then comparing this score to a critical value from the t-distribution. If the observed t-score exceeds the critical value, there is evidence to suggest that there is a significant difference between the two processes.
In this case, you would calculate the t-score for Processes A and B using their respective sample means, standard deviations, and sample sizes. If the observed t-score is greater than the critical t-value at the chosen significance level (typically 0.05 or 0.01), we reject the null hypothesis that there is no difference between the two processes.
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For a certain population of men, 8 percent carry a certain genetic trait. For a certain population of women, 0.5 percent carry the same genetic trait. Let pˆ1 represent the sample proportion of randomly selected men from the population who carry the trait, and let pˆ2 represent the sample proportion of women from the population who carry the trait. For which of the following sample sizes will the sampling distribution of pˆ1−pˆ2 be approximately normal?
Answer:
D
Step-by-step explanation:
200 men and 2,000 women
i dont know how but that was just the answer
The sampling distribution of ā-Ă will be approximately normal when both populations satisfy the conditions for np > 5 and nq > 5. The sample sizes must ensure these inequalities are met using the proportions 0.08 for men and 0.005 for women.
Explanation:The sampling distribution of ā - Ă will be approximately normal when the sample sizes are large enough to satisfy the condition np > 5 and nq > 5 for both populations. Given that in the population of men, 8 percent carry the genetic trait (p1 = 0.08), and in the population of women, 0.5 percent carry the trait (p2 = 0.005), we need to find appropriate sample sizes for each population.
For the men's population:
n1p1 > 5 and n1(1 - p1) > 5.
For the women's population:
n2p2 > 5 and n2(1 - p2) > 5.
The sample sizes should be selected in a way that these inequalities are met for both populations to ensure that the sampling distribution of ā-Ă is approximately normal.
The population of a community was 200 people 10 yrs ago. Today the population is 550 people. Using an exponential growth function when will the population be 1000?
Answer:
in 6 years
Step-by-step explanation:
Using t=10 to represent today, we can write the exponential growth function as ...
p(t) = 200(550/200)^(t/10)
Then we can set p(t) = 1000 and solve for t:
1000 = 200(11/4)^(t/10) . . . . simplifying the growth factor
1000/200 = (11/4)^(t/10) . . . . divide by 200
log(5) = (t/10)log(11/4) . . . . . . take logs
t = 10·log(5)/log(11/4) ≈ 15.91
That is, about 16 years from 10 years ago, the population will reach 1000.
The population will reach 1000 in about 6 years.
The circular track at your school has a radius of 64 meters. How far would you travel
if you ran one full lap around the circular track at your school?
Answer:
402.12 meters
Step-by-step explanation:
to measure the circumference,
C = 2πr
2π(64) =
to run 1 full lap around the track would be 402.12 meters
i hope this helps!
:)
To find the distance of a full lap around a circular track, calculate the circumference using the formula C = 2π r. With a radius of 64 meters, the distance is approximately 402.12 meters.
To calculate the distance traveled on a full lap around a circular track, you need to find the circumference of the circle. The circumference of a circle is given by the formula C = 2π r, where π (Pi) is approximately 3.14159 and r is the radius of the circle.
Given that the radius of the track is 64 meters, we can substitute this value into the formula to find the circumference.
C = 2π(64 meters)
C = 128π meters
C = approx. 128 × 3.14159 meters
C = approx. 402.1232 meters
Therefore, if you ran one full lap around the circular track, you would travel approximately 402.12 meters.
For what value(s) of k is k-3/2k+5 undefined?
Answer:
The expression is undefined where the denominator equals
0 , the argument of an even indexed radical is less than
0 , or the argument of a logarithm is less than or equal to 0 . k = − 2 , k = 0 , k = 2 , k = 6
Step-by-step explanation:
I'm not rocket scientist but I hope this helps in anyway, if not i'm so sorry i tried. :)
The slope of a pipe with a 1/4 inch of drop has a run of 1 foot. What is the run of a pipe that has a 3/4 inch drop?
Answer:3 foot
Step-by-step explanation:
PLEASE HELP !!!!!!
If the blueprint is drawn on the coordinate plane with vertices (1, 5) and (11, 15) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning. (4 points—2 points for finding the length of the diagonal; 2 points for explanation)
Answer:
[tex]50\sqrt{2} feet[/tex]
Step-by-step explanation:
Given the vertices (1, 5) and (11, 15) for the corners labeled with red stars, the diagonal of the square C will be the length of the line joining the two vertices.
Using the Distance Formula:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex](x_1,y_1)=(1, 5) \:and\: (x_2,y_2)=(11, 15)[/tex]
[tex]Distance=\sqrt{(11-1)^2+(15-5)^2}\\=\sqrt{10^2+10^2}\\=\sqrt{200}\\=10\sqrt{2}[/tex]
Since 1 Square Unit = 25 Square Feet
1 Unit =5 feet
Therefore, the length of the diagonal
[tex]=5*10\sqrt{2} \\=50\sqrt{2} \:feet[/tex]
Answer:
50 with 2 squared
Step-by-step explanation:
Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?
Answer:
The probability that Susan's average score for the week is between 220 and 228 is 0.7594.
Step-by-step explanation:
Average score of Susan = u = 225
Standard deviation = [tex]\sigma[/tex] = 13
Score of Susan follow a Normal Distribution and we have the population standard deviation, as this standard deviation is of her scores of previous 14 years.
In a given week, Susan bowls 16 games. This means, our sample size is 16. So,
n = 16
We have to find the probability that her average score of the week is between 220 and 228. Since the distribution is normal and value of population standard deviation is known, we will use the concept of z-score and z-distribution to find the desired probability.
First we will convert the given numbers to their equivalent z-scores. The formula to calculate the z-scores is:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
x = 220 converted to z-score will be:
[tex]z=\frac{220-225}{\frac{13}{\sqrt{16}}}=-1.54[/tex]
x = 228 converted to z-score will be:
[tex]z=\frac{228-225}{\frac{13}{\sqrt{16}}}=0.92[/tex]
So, probability that Susan's score is between 220 and 228 is equivalent to probability of z score being in between - 1.54 and 0.92
i.e.
P (220 < X < 228) = P( -1.54 < z < 0.92)
From the z-table we can find the following values:
P( -1.54 < z < 0.92) = P(x < 0.92) - P(x<-1.54)
P( -1.54 < z < 0.92) = 0.8212 - 0.0618
P( -1.54 < z < 0.92) = 0.7594
Since, P (220 < X < 228) is equivalent to P( -1.54 < z < 0.92), we can conclude that the probability that Susan's average score for the week is between 220 and 228 is 0.7594.
Using the Central Limit Theorem and Z-scores, we calculate the probability that Susan's average weekly score will be between 220 and 228 from the standard normal distribution table.
Explanation:This question revolves around the concept of standard deviation and probability in a normal distribution. Standard deviation measures the dispersion or variation of a set of values. In this case, her average score per week is a random variable, so Central Limit Theorem (CLT) applies because she plays a large number of games (16) every week. CLT states that the sum of a large number of independent and identically-distributed random variables has an approximately normal distribution.
We can calculate the mean (μ) and standard deviation (σ) of the weekly average:
μ = expected individual game score = 225σ = standard deviation of individual game score / sqrt (games per week) = 13 / sqrt (16) = 13 / 4 = 3.25To calculate the Z-scores for 220 and 228:
Z₁ = (220 - μ) / σ = (220 - 225) / 3.25 = -1.54Z₂ = (228 - μ) / σ = (228 - 225) / 3.25 = 0.92Finally, we need to find the probability P(Z₁ < Z < Z₂), which involves looking up these Z-scores in a Z-table or using statistical software or online resource that gives the values for a normal distribution.
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The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers revealed an average age of 28 years with a standard deviation of 10 years. Determine a 95% confidence interval for the average all of all his customers. Specifically provide the lower limit and upper limit of the confidence interval to one decimal.
Answer:
[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]
[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]
So on this case the 95% confidence interval would be given by (23.9;32.1)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
[tex]\bar X=28[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=10 represent the sample standard deviation
n=25 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=25-1=24[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that [tex]t_{\alpha/2}=2.064[/tex]
Now we have everything in order to replace into formula (1):
[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]
[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]
So on this case the 95% confidence interval would be given by (23.9;32.1)
The 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years, calculated using the sample mean of 28 years, a standard deviation of 10 years, and a sample size of 25.
To calculate a 95% confidence interval for the average age of all customers in the boutique, we will use the sample mean, standard deviation, and the size of the sample along with the z-score corresponding to a 95% confidence level.
The formula for a confidence interval when the population standard deviation is known is:
Confidence interval = {x} (Z {Σ}/√{n}})
In this case, we have:
Sample mean ({x}): 28 years
Standard deviation (Σ): 10 years
Sample size (n): 25
Z-score for 95% confidence: 1.96 (from z-tables)
First, we calculate the margin of error:
The margin of error = Z{Σ}/{√{n}} = 1.96 {10}/{√{25}} = 1.96 × 2 = 3.92
Then, the confidence interval is:
Lower limit = {x} - Margin of error = 28 - 3.92 = 24.08
Upper limit = {x} + Margin of error = 28 + 3.92 = 31.92
Therefore, the 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years.
Please help!
All parabolas have the same domain
True or False
Answer:
Step-by-step explanation:
false
Yes, All the parabolas have the same domain.
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
The statement is,
''All parabolas have the same domain.''
Now,
Since, The domain of the parabola will be (- ∞, ∞).
Hence, All the parabolas have the same domain.
Thus, All the parabolas have the same domain.
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A toy rocket is shot vertically into the air from a launching pad 8 feet above the ground with an initial velocity of 80 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h left parenthesis t right parenthesis equals negative 16 t squared plus 80 t plus 8. How long will it take the rocket to reach its maximum height? What is the maximum height?
The toy rocket will take 2.5 seconds to reach its maximum height, which is 108 feet above the ground.
Explanation:The question asks about the time it takes for a toy rocket to reach its maximum height and what that maximum height is, given the equation of its height h(t) = -16t2 + 80t + 8. This is a quadratic equation representing the height of the toy rocket as a function of time, which is a typical problem in physics or mathematics dealing with projectile motion. To solve for the time when the rocket reaches its maximum height, we need to find the vertex of the parabola shaped by the quadratic equation where the coefficient of t2 is negative indicating that the parabola opens downwards.
The formula to calculate the time to reach maximum height in a quadratic equation like this is t = -b/(2a), where a is the coefficient of t2 (-16) and b is the coefficient of t (80). Thus, t = -80/(2*(-16)) = 2.5 seconds. To find the maximum height, we plug this time into the height equation: h(2.5) = -16*(2.5)2 + 80*(2.5) + 8 = 108 feet.
Use the table. Which inference can you make by comparing the measures of center?
Finish Times of 30 Runners
in the 100-meter Dash
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Answer: the average speed of the runners increased since last year.
Step-by-step explanation:
The table is:
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Looking at this table we can see that this year, the mean time is smaller than the one from last year, so the runners are faster in average.
The mean absolute deviation is bigger, but the change in the mean is bigger.
difference of the mean 16.2 - 14.7 = 1.5
difference of the MAD 1.9 - 1.2 = 0.7
This means that the average speed of the runners increased since last year, and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike like last year.
Answer:
this guy above me is a genuies it correct
Step-by-step explanation:
what is the axis of symmetry for the graph of a quadratic function whose zeros or -2 and 4?
Answer:
x = 1
Step-by-step explanation:
As you might guess, the zeros are symmetrical about the axis of symmetry. That is, the axis of symmetry is midway between the zeros, so will be their average value:
x = (-2 +4)/2 = 1
The axis of symmetry is x = 1.
-2/3p + 1/5 -1 + 5/6p
Hey there!
All you have to COMBINE YOUR LIKE TERMS and you have your answer!
-2/3p + 1/5 - 1 + 5/6p
(-2/3p + 5/6p) + (1/5 - 1)
-2/3p + 5/6p = 1/6p
1/5 - 1 = -4/5
Answer: 1/6p + (- 4/5) ✅
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the sample points in the event A ∪ B.
The sample points in the event A ∪ B are 1, 2, 3, 4, 5, 6, 8, and 10, which is determined by the union.
To identify the sample points in event A ∪ B (the union of events A and B), we need to determine the numbers that satisfy either event A or event B or both.
Event A: The number is even.
Sample points in event A are: {2, 4, 6, 8, 10}.
Event B: The number is less than 7.
Sample points in event B are: {1, 2, 3, 4, 5, 6}.
To find the sample points in the union of events A and B (A ∪ B), we combine the sample points from both events without duplication.
Thus, the sample points in A ∪ B are: {1, 2, 3, 4, 5, 6, 8, 10}.
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The sample points in the event A ∪ B, which include numbers that are either even or less than 7, are {1, 2, 3, 4, 5, 6, 8, 10}.
Explanation:To find the sample points in the event A ∪ B, where event A: {The number is even} and event B: {The number is less than 7}, we first identify the numbers between 1 and 10 that satisfy each event. For event A, the even numbers between 1 and 10 are 2, 4, 6, 8, and 10. For event B, the numbers less than 7 are 1, 2, 3, 4, 5, and 6.
The union of two events, A ∪ B, includes all sample points that are in event A, event B, or in both A and B. Therefore, the union of A ∪ B includes the even numbers (2, 4, 6, 8, 10) and the numbers less than 7 (1, 2, 3, 4, 5, 6), without listing any number more than once.
Thus, the sample points in the event A ∪ B are {1, 2, 3, 4, 5, 6, 8, 10}.
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 4 days? How long is it until there are 10,000 mosquitoes?
Answer: 3,917 days
Step-by-step explanation:
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.5
pounds/square inch (psi). Assume the population variance is 0.64. The engineer designed the valve such that it would produce a mean pressure of 6.6 psi. It is believed
that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal
places
Answer:
The value of the test statistic is [tex]t = -2.09[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 6.6[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 6.6[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation(square roof of the variance) and n is the size of the sample.
In this problem, we have that:
[tex]X = 6.5, \mu = 6.6, \sigma = \sqrt{0.64} = 0.8, n = 280[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.5 - 6.6}{\frac{0.8}{\sqrt{280}}}[/tex]
[tex]t = -2.09[/tex]
The value of the test statistic is [tex]t = -2.09[/tex]
what's the least common denominator of 4 and 16
Answer:16
Step-by-step explanation:
The lcm of 4 and 16 is 16.
16
the lcm of 4 and 16 is 16
39% of what is 118.9?
Answer:
39% of 118.9=46.371
Step-by-step explanation:
Final answer:
To find out what 39% of a certain amount is equal to 118.9, we can set up an equation and solve for x. To solve "39% of what is 118.9?", we use the equation 0.39x = 118.9 and find that x, which represents the original number, is equal to 305.
Explanation:
To find 39% of a certain number that equals 118.9, we set up the equation where 0.39 (which is 39% as a decimal) times the unknown number (let's call it x) equals 118.9:
0.39x = 118.9
To find the value of x, we divide both sides of the equation by 0.39:
x = 118.9 / 0.39
x = 305
Therefore, 39% of 305 is equal to 118.9.
A tanker that ran aground is leaking oil that forms a circular slick about 0.2 foot thick. To estimate the rate dV/dt (in cubic feet per minute) at which oil is leaking from the tanker, it was found that the radius of the slick was increasing at 0.31 foot per minute (dR/dtequals0.31) when the radius R was 400 feet. Find dV/dt, using pi almost equals 3.14 .
Answer:
[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]
Step-by-step explanation:
Since it is circular slick, it's volume can be modeled as,
[tex]V = \pi R^{2}h[/tex]
Where R is the radius in feet and h is the thickness of slick.
taking derivative of the above equation with respect to time yields,
[tex]\frac{dV}{dt} = \pi 2Rh \frac{dR}{dt}[/tex]
Where the rate of change of radius of the slick (dR/dt) is given,
[tex]\frac{dV}{dt} = \pi 2(400)(0.2)(0.31)[/tex]
[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]
Therefore, the rate of change of volume is 155.82 cubic feet per minute.
The value of dV/dt using pi almost equal to 3.14 gives; dV/dt = 155.82 ft³/min
dV/dt = 155.82 ft³/min
We are given;
Radius; R = 400 ft
Height; h = 0.2 ft
Rate of Increase of radius; dr/dt = 0.31 ft/min
Formula for Volume of a cylinder is;
V = πr²h
Differentiation of both sides of V and r with respect to t gives;
dV/dt = 2πrh(dr/dt)
Plugging in the relevant values gives;
dV/dt = 2π × 400 × 0.2 × 0.31
dV/dt = 155.82 ft³/min
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put these numbers in order 55, 52, 46, 52, 46, 43, 49, 56, 42
Answer: 55
Step-by-step explanation:
Answer:
42,43,46,46,49,52,52,55,56
Step-by-step explanation:
64= 4^3 in logarithmic form
A researcher compared the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year. At the end of the year, the researcher found that the children who had used brand X has significantly fewer cavities than the children who had used brand Y. The difference was significant at the .05 level. What is the null hypothesis
Answer: the null hypothesis states that there is no difference between the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year.
Step-by-step explanation:
The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.
Looking at the given situation,
The difference was significant at the .05 level. This means that there was enough evidence to reject null hypothesis. Since the null hypothesis contradicts the alternative hypothesis, then the null hypothesis would state that there is no difference between the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year.
If you had $500 to put into a savings account with 8% interest , how would you know which bank to choose, if you plan to withdraw everything after 10 years—one that pays simple interest or compound interest? Explain.
Answer:
Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.
Step-by-step explanation:
Simple interest formula:
The simple interest formula is given by:
[tex]E = P*r*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), r is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex].
Compound interest formula:
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this problem:
[tex]P = 500, r = 0.08, t = 10[/tex]
So
Simple interest:
[tex]E = P*r*t = 500*0.08*10 = 400[/tex]
In total:
[tex]T = E + P = 500 + 400 = 900[/tex]
Using simple interest, you would withdraw an amount of $900.
Compound interest
We use n = 1
[tex]A = P(1 + \frac{r}{n})^{nt} = 500(1 + \frac{0.08}{1})^{10} = 1079.46[/tex]
You would withdraw $1079.86. Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.
The solution of the equation 2^x-1 - 7 = 9
IS X =
Answer:
x = log∨2 (17)
Explanation:
Calculate the difference
Move the constant to the right
Add the numbers
Then take the logarithm of both sides of the equation
Answer:
5
Step-by-step explanation:
Parallelogram ABCD has vertices at A(-2,3), B(4,3), C(-1,1). What is the length of side AB? Answer choices ;
A) 2 units
B) 3 units
C) 4 units
D) 6 units
Answer:
D)6 units
Step-by-step explanation:
the answer is D because since side AB have the same y coordinate then you would have to either subtract or add the x. if one point on x is negative and the other is positive then you would add. but if they were both positive or both negative then you would subtract the x.
A group of high school seniors took a scholastic aptitude test. The resulting math scores had a mean 504.7 with a standard deviation of 191.4, verbal scores had a mean 491.5 with a standard deviation of 168.9, and the correlation between verbal and math scores was r 0.824. Answer the questions below a) What is the correlation?b) Write the equation of the line of regression predicting verbal scores from math scores (Round to three decimal places as needed) d) A person tells you her math score was 387. Predict her verbal score.
The correlation is 0.824. The equation of the regression line is Y = -12.6 + 0.722X. The estimated verbal score for a math score of 387 can be calculated by inputting 387 in place of X in the regression equation.
Explanation:The subject of this question is regression analysis, which is a type of statistical modeling technique.
A) The correlation, as given in the question, is 0.824. This number tells us the degree to which the math and verbal scores vary together.
B) The regression equation predicting verbal scores from math scores can be calculated as follows:
Regression line equation is Y = a + bX. 'a' is Y intercept, 'b' is the slope, 'X' is the value of the independent variable (in this case math scores), and 'Y' is the predicted value of the dependent variable (in this case, verbal scores). We calculate the slope 'b' using the formula b = r*(Sy/Sx), where r is the correlation coefficient, Sy is the standard deviation of Y (verbal scores) and Sx is the standard deviation of X (math scores).
Inserting our values in gets us: b = 0.824 * (168.9/191.4) = 0.722 (rounded to three decimal places). And a = My - b*Mx = 491.5 - 0.722*504.7 should give us our Y intercept. Plugging in your calculator should give you a roughly around -12.6.
The equation of the regression line would then be Y = -12.6 + 0.722X.
D) To predict the verbal score from a math score of 387, we substitute X = 387 into the regression equation: Y = -12.6 + 0.722 * 387, giving us a predicted verbal score when calculated.
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