Answer:
The z score when x =72 is:
[tex] z = \frac{72-58}{11}= 1.273[/tex]
The mean is 58
This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.
Step-by-step explanation:
Assuming the following info for the question: Suppose John's words per minute on a typing test are normally distributed. Let X -the number of words per minute on a typing test. Then X N(58, 11) If necessary, round to three decimal places.
Provide your answer below rds per minute in a typing test on Sunday. The z score when x =72 is
For this case we know that the variable of interest is modelled with the normal distribution:
[tex]X \sim N (\mu= 58, \sigma=11)[/tex]
And the z score is given by:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z = \frac{72-58}{11}= 1.273[/tex]
The mean is 58
This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.
9. ABCD is a square and ABK is an equilateral triangle outside the square,
Find measurment of angle DKC
Answer:
< DKC = [tex]60^{0}[/tex]
Step-by-step explanation:
A square is a quadrilateral that has equal length of side. While an equilateral triangle is one with equal length of sides and equal values of angles.
Given square ABCD and that equilateral triangle ABK is outside the square, both figures share side AB. This shows that the length of the sides of the triangle is the same as the length of the side of the square.
i.e /AD/ = /CD/ = /BC/ = /AB/ = /AK/ = /KB/
Thus, < DKC = [tex]60^{0}[/tex] (property of angles in an equilateral triangle)
A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per minute, compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Answer: ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 80.6 words per minute
Standard deviation r = 7.2
Number of samples n = 18
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
80.6+/-1.96(7.2/√18)
80.6+/-1.96(1.697056274847)
80.6 +/- 3.33
= ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function F(x) = 0, x< 0, 1 − e−8x, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.
Answer:
(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Step-by-step explanation:
The cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:
[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]
(a)
Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:
[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]
The probability is:
[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]
[tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b)
The probability density function of X is:
[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]
Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:
[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]
[tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Please answer this correctly
Answer: 1/4
Step-by-step explanation:
The cheesiest recipe would be 1 cup and the least cheesy recipe would be 3/4 cups
1 - 3/4 = 1/4
Answer:
[tex]\frac{1}{4}[/tex] cup of cheese
Step-by-step explanation:
The least cheesiest recipe uses [tex]\frac{3}{4}[/tex] cup of cheese while the most cheesiest uses 1 cup of cheese.
[tex]1-\frac{3}{4} =\\\\\frac{1}{4}[/tex]
The most cheesiest uses [tex]\frac{1}{4}[/tex] cup more cheese than the least cheesiest.
What’s the correct answer for this question?
Answer:
B) (1,2,3,4,5,6,7,8)
Step-by-step explanation:
The answer is B because the union of a set represents everything thing that is within the sets.
Simplify 6r · s · 4rt. this is the question
Answer=6 . S/R . 4T
This is the answer because u have to simplify so to do this u have to divide all of this by R
The relationship between the number of pencil sharpener a company can sell each week and the price of each sharpener p is given by the equation x = 2300 − 100 p At what price should the sharpeners be sold if the weekly revenue is to be $ 12000
Answer:
The price p could be any of $8 or $15 .
Step-by-step explanation:
The equation is a relationship between the numbers of pencil sharpener x can sell each week and the price of each sharpener p.
x = 2300 - 100p
xp = 12000
therefore,
x = 12000/p
insert the value of x in the equation
x = 2300 - 100p
12000/p = 2300 - 100p
12000/p + 100p - 2300 = 0
multiply through by p
12000 + 100p² - 2300p = 0
100p² - 2300p + 12000 = 0
divide through by 100
p² - 23 + 120 = 0
Find the number that we can multiply to give 120 and add to give - 23. The number are -15 and - 8.
p² - 8p - 15p + 120 = 0
p(p - 8) - 15(p - 8) = 0
(p - 8)(p - 15)
p = 8 or 15
x = 2300 - 100p
x = 2300 - 100(8)
x = 2300 - 800
x = 1500 pencil sharpener sold
or
x = 2300 - 100(15)
x = 2300 - 1500
x = 800 pencil sharpener sold
The price could be any of $8 or $15 .
A laundry basket has 24 shirts in it for our Navy 12 arete and the remaining our way what is the probability of selecting a red shirt
Answer:
[tex]P(selecting a red t-shirt)=1/2[/tex]
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW;
A laundry basket has 24 t-shirts in it. Four are Navy, 12 are red, and the rest is white. What is the probability of randomly selecting a red t-shirt
EXPLANATION
Total number of the t-shirt in the laundry basket = 24
Number of Navy t-shirt = 4
Number of red t- shirt = 12
The number of white t- shirt in the laundry basket can be calculated as follow;
Total number of t- shirt - (Number of Navy t-shirt + Number of red t- shirt)
Number of white t- shirt = 24 -(4+12)
Number of white t- shirt = 8
The probability of randomly selecting a red t-shirt = [tex]Number of red t- shirt/Total number of the t-shirt[/tex]
[tex]P(selecting a red t-shirt)=12/24[/tex]
[tex]P(selecting a red t-shirt)=1/2[/tex]
Noah has a t-shirt collection. Three-eighths of the t-shirts are blue. Of the blue t-shirts,two-ninths of them have a pocket. What fraction represents the numbers of t-shirts that are blue and have a pocket?
Answer:
1/12
Step-by-step explanation:
blue = (3/8)collection
blue&pocket = (2/9)blue = (2/9)(3/8)collection
blue&pocket = (6/72)collection = (1/12)collection
1/12 of Noah's collection is blue and has a pocket.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. F(x) = 2(x-3)^2 + 3
Step-by-step explanation:
We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)
We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.
The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.
Our two equations left are:
B. F(x) = 2(x+3)^2 + 3
D. F(x) = 2(x-3)^2 + 3
Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.
y = 2(3+3)^2 + 3 =
2(6)^2 + 3 =
2·36 + 3 =
72 + 3 =
75
That one didn't give us a y value of 3.
y = 2(3-3)^2 + 3 =
2(0)^2 + 3 =
2·0 + 3 =
0 + 3 =
3
This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:
D. F(x) = 2(x-3)^2 + 3
Hopefully this helps you to understand parabolas better.
Question 1 Muit Choice Worth 1 points)
(08.01 LC)
The school principal wants to know whether the students in the entire school prefer football or basketball. The principal draws a random sample from the following groups:
• All school teachers
. All girls in each grade
. All students in each grade
• All students on the basketball team
Which of the following groups best represents the population she should take a random sample from to get the best results for her survey?
All school teachers
All girls in each grade
All students in each grade
All students on the basketball team
Answer:
I think its C. All students in each grade
Step-by-step explanation:
because it should be the students choice.
Banking fees have received much attention during the recent economic recession as banks look for ways to recover from the crisis. A sample of 41 customers paid an average fee of $12.22 per month on their interest-bearing checking accounts. Assume the population standard deviation is $1.86. Complete parts a and b below.
a. Construct a 95% confidence interval to estimate the average fee for the population.
b. What is the margin of error for this interval?
Answer:
a) The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79
b) $0.57
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1.86}{\sqrt{41}} = 0.57[/tex]
So the answer for b) is $0.57.
The lower end of the interval is the sample mean subtracted by M. So it is 12.22 - 0.57 = $11.65
The upper end of the interval is the sample mean added to M. So it is 12.22 + 0.57 = $12.79
The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79
Grandmother bought enough cat food for her four cats to last for 12 days. On her way home she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the cat food last
Answer:
The number of days the cat food will last is 8 days.
Step-by-step explanation:
In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.
Assume that each cat consumes x portions of food each day.
Then the four cats will consume, 4x portions of food each day.
Then in 12 days the amount of food consumed by the 4 cats will be:
Total amount of cat food = 12 × 4x
= 48x.
Now, it is provided that she on her way home she brought back two stray cats.
Then the six cats will consume, 6x portions of food each day.
Compute the number of days the cat food will last as follows:
[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]
[tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]
Thus, the number of days the cat food will last is 8 days.
How many degrees was ABCD rotated?
the answer is 180°
Step-by-step explanation:
because it rotated 2x and 90+90 is 180
To test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.
Answer:
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].
And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]
And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]
Step-by-step explanation:
We need to take in count that we are conducting a regression model with just one dependent variable and 3 independent variables
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].
And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]
And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]
Solve the equation.
3(x + 1)-1=3x+2
Answer:
0=0
Step-by-step explanation:Let's solve your equation step-by-step.
3(x+1)−1=3x+2
Step 1: Simplify both sides of the equation.
3(x+1)−1=3x+2
(3)(x)+(3)(1)+−1=3x+2(Distribute)
3x+3+−1=3x+2
(3x)+(3+−1)=3x+2(Combine Like Terms)
3x+2=3x+2
3x+2=3x+2
Step 2: Subtract 3x from both sides.
3x+2−3x=3x+2−3x
2=2
Step 3: Subtract 2 from both sides.
2−2=2−2
0=0
mp
The probability of drawing a pearl bead out of a bag of mixed beads is 2/3. What is the probability of drawing a bead which is not a pearl?
Answer:
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
Step-by-step explanation:
For each bead that you draw, there are only two possible outcomes. Either it is a pearl bead, or it is not. The sum of these probabilities = 100% = 1.
So
2/3 probability of drawing a pearl bead.
p probability of drawing a non pearl bead.
What is the probability of drawing a bead which is not a pearl?
[tex]p + \frac{2}{3} = 1[/tex]
[tex]p = 1 - \frac{2}{3}[/tex]
[tex]p = \frac{3*1 - 2}{3}[/tex]
[tex]p = \frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
Help please!!! Everything is in the picture.
Answer:
3u-2v = [tex]\sqrt{505\\}[/tex]
5u-v = [tex]\sqrt{1,157}[/tex]
2u-3v = [tex]\sqrt{1,300}[/tex]
u+4v = [tex]\sqrt{4,505}[/tex]
Step-by-step explanation:
I just started by doing the results for each of the operations given.
3u-2v:
3u = (-9, 24) 2v = (-28, 12)
Do the operation of 3u-2v and you get a resultant vector of (19, 12).
You calculate this by doing the square root of 19^2 + 12^2, which is the square root of 505.
5u-v:
5u = (-15, 40) v = (-14, 6)
Do the operation of 5u-v and you get a resultant vector of (-1, 34).
You calculate this by doing the square root of (-1)^2 + 34^2, which is the square root of 1,157.
2u-3v:
2u = (-6, 16) 3v = (-42, 18)
Do the operation of 2u-3v and you get a resultant vector of (36, -2).
You calculate this by doing the square root of 36^2 + (-2)^2, which is the square root of 1,300.
3u+2v:
3u = (-9, 24) 2v = (-28, 12)
Do the operation of 3u+2v and you get a resultant vector of (-37, 36).
You calculate this by doing the square root of (-37)^2 + 36^2, which is the square root of 2,665. This is not a given tile, so we can just ignore this one.
u+4v:
u = (-3, 8) 4v = (-56, 24)
Do the operation of u+4v and you get a resultant vector of (-59, 32).
You calculate this by doing the square root of (-59)^2 + 32^2, which is the square root of 4,505.
Since this is a given tile, I didn't do 7u-2v, but you would use the same methodology.
Simplify the number into simplest radical form.
Answer:
4 sqrt(6)
Step-by-step explanation:
sqrt(96)
We know sqrt(ab) =sqrt(a) sqrt(b)
sqrt(16*6)
sqrt(16) sqrt(6)
4 sqrt(6)
Suppose a company's revenue function is given by R(q) = - q^3 + 220q^2 and its cost function is given by C(q) = 500 + 13q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)
MP(q) =
B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)
Answer:
A) MP(q) = -3q² + 440q - 13
B) 146.64 units.
Step-by-step explanation:
The profit function is given by the revenue minus the cost function:
[tex]P(q) = R(q) - C(q)\\P(q) = -q^3+220q^2-500-13q[/tex]
A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:
[tex]P(q) = -q^3+220q^2-500-13q\\MP(q) = \frac{dP(q)}{dq} \\MP(q)=-3q^2+440q-13[/tex]
B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:
[tex]MP(q)=0=-3q^2+440q-13\\q=\frac{-440\pm \sqrt{440^2-(4*(-3)*(-13))} }{-6}\\q'=146.64\\q'' = - 0.03[/tex]
Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.
which is the domain of f(x) = 4^x
will give brainlist!
Answer:
all real numbers
Step-by-step explanation:
The domain is the input values
All values for x are valid as inputs to the function
A bread machine produces 159 loaves of bread per hour. The machine operates 10 hours per day. How many loaves of bread does it produce per day? _____ loaves
Answer:
It can produce 1590 loaves of bread per day.
Step-by-step explanation:
Given that the bread machine operates only 10 hours per day. So in order to calculate how many loaves can be produce a day, you have to multiply it by 10 :
[tex]1hour = 159loaves[/tex]
[tex]10hours = 159 \times 10[/tex]
[tex]10hours = 1590loaves[/tex]
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
The percent, X, of shrinkage on drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2. est at 5% level of significance whether the true average shrinkage percentage : is greater than 17.5 and write your conclusion. Report the p-value.
Answer:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.
Match each linear equation with the name of its form.
y=-x+8
slope-intercept form
2x - 5y = 9
standard form
y + 6 = -3(x - 1)
point-slope form
Answer:
y + 6 = -3(x - 1) - Point Slope
y=-x+8 - Slope Intercept
2x - 5y = 9 - Standard
Step-by-step explanation:
Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]
y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.
Slope-intercept form is: [tex]y=mx+b[/tex]
y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.
This only leaves 2x - 5y = 9, which is in standard form.
All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
All the expressions are,
1) y = -x + 8
2) 2x - 5y = 9
3) y + 6 = -3(x - 1)
Now, All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
A circular garden has a diameter of 12 feet. About how much trim is needed to surround the garden by placing trim on the garden's circumference? 38 ft or 48 ft or 144 ft or 432 ft
Answer:
About 38 feet
Step-by-step explanation:
The formula for a circle's circumference is 2 times pi times r, which is the radius.
Since the diameter is 12, the radius is half the diameter, so the radius is 6.
2 times pi times 6 is about 37.7 feet, or 38 feet.
Hope this helped.
In a college of exactly 2800 students, exactly 55 % are male. What is the number of female students? Express your answer as an integer.
Chocolate chip cookies have a distribution that is approximately normal with a mean of 23.1 chocolate chips per cookie and a standard deviation of 2.9 chocolate chips per cookie. Find Upper P 10 and Upper P 90. How might those values be helpful to the producer of the chocolate chip cookies?
Answer:
[tex]z=-1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 -1.28*2.9=19.388[/tex]
And for the 90 percentile we can do this:
[tex]z=1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 +1.28*2.9=26.812[/tex]
The P10 would be 19.388 and the P90 26.812
Step-by-step explanation:
Let X the random variable that represent the chocolate chip cookies of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(23.1,2.9)[/tex]
Where [tex]\mu=23.1[/tex] and [tex]\sigma=2.9[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.90[/tex] (a)
[tex]P(X<a)=0.10[/tex] (b)
We can find a z score value who that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28.
Using this value we can do this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]
And we can solve for the value of interest
[tex]z=-1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 -1.28*2.9=19.388[/tex]
And for the 90 percentile we can do this:
[tex]z=1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 +1.28*2.9=26.812[/tex]
The P10 would be 19.388 and the P90 26.812
If log10y=2, what does y equal?
Answer:
[tex]y=100[/tex]
Step-by-step explanation:
I don't know if by the 10 you mean the base is 10 or it's being logged with the y, but I'm assuming the base is 10. If that's not right, message me and I'll fix my answer. If,
[tex]log_an=x\\a^x=n[/tex]
Then,
[tex]log_1_0y=2\\10^2=y\\100=y[/tex]
What is 9/8 squaredto the power of 2 ?
Answer:
81/64
Step-by-step explanation:
(9/8)²=9²/8²=81/64
