Answer:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Step-by-step explanation:
For this problem we have the following dataset given:
44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7
We can find the mean and sample deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex]\bar X= 51.278[/tex]
[tex] s= 22.979[/tex]
The confidence interval for the mean is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The degrees of freedom are:
[tex] df=n-1= 9-1=8[/tex]
The confidence would be 0.98 and the significance [tex]\alpha=0.02[/tex] then the critical value would be:
[tex] t_{\alpha/2}= 2.896[/tex]
Ad replacing we got:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
A superintendent of a school district conducted a survey to find out the level of job satisfaction among teachers. Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.
z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction
The superintendent wishes to construct a significance test for her data. She find that the proportion of satisfied teachers nationally is 18.4%.
What is the z-statistic for this data? Answer choices are rounded to the hundredths place.
a. 2.90
b. 1.15
c. 1.24
d. 0.61
Answer:
b. 1.15
Step-by-step explanation:
The z statistics is given by:
[tex]Z = \frac{X - p}{s}[/tex]
In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.
This means that [tex]X = \frac{13}{53} = 0.2453[/tex]
She find that the proportion of satisfied teachers nationally is 18.4%.
This means that [tex]p = 0.184[/tex]
Standard error:
p = 0.184, n = 53.
So
[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]
Z-statistic:
[tex]Z = \frac{X - p}{s}[/tex]
[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]
[tex]Z = 1.15[/tex]
The correct answer is:
b. 1.15
Let x=−1−5i and y=5−i. Find x⋅y.
Answer:
-10 -24i
Step-by-step explanation:
Note : i=√-1 (imaginary number)
i² = -1
xy
= (−1−5i)(5−i)
= -5 +i -25i +5i²
=-5 +i -25i + 5(-1)
= -5 +i -25i -5
= -5 -5 +i -25i
= -10 -24i
A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit. The value of x·y is (−10 −24i).
What is a complex number?A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit, and satisfies the equation i² = -1; every complex number may be represented as a + bi, where a and b are real numbers.
Given that x=−1−5i and y=5−i. Therefore, the value of x·y is,
x·y = (−1 −5i)(5-i)
= −5 + i −25i +5i²
= −5 −24i − 5
= −10 −24i
Hence, the value of x·y is (−10 −24i).
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Yvette exercises 14 days out of 30 in one month. What is the ratio of the number of days she exercises to the number of days in the month? Simplify the ratio.
Answer:
7 to 15, 7:15, 7/15
Step-by-step explanation:
Ratios can be written as:
a to b
a:b
a/b
We want to find the ratio of exercise days to days in the month. She exercises 14 days out of 30 days in the month. Therefore,
a= 14
b= 30
14 to 30
14:30
14/30
The ratios can be simplified. Both numbers can be evenly divided by 2.
(14/2) to (30/2)
7 to 15
(14/2) : (30/2)
7:15
(14/2) / (30/2)
7/15
Answer:
divide both numbers by 14.. the ans is 1: 2
Anna spends $4.65 each weekday (20 weekdays/month) on coffee and buys a bag of coffee for $8.99 that lasts 6 months. Her monthly income is $2,350. What percent of her monthly income does she spend on coffee? 1) 0.58% 2)4.34% 3) 4.02% 4) 4.65%
Answer:
C. 4.02%
Step-by-step explanation:
Anna spends $4.65 each weekday (20 weekdays/month) on coffee and buys a bag of coffee for $8.99 that lasts 6 months. Her monthly income is $2,350. What percent of her monthly income does she spend on coffee? 1) 0.58% 2)4.34% 3) 4.02% 4) 4.65%
She spends $4.65/weekday, and there are 20 weekdays/month
In 1 month, she spends:
$4.65/weekday * 20 weekdays/month = $93/month
In 6 months, she spends 6 * $93 = $558
She buys a bag of coffee for $8.99 that lasts 6 months.
The total cost of all coffee in 6 months is:
$558 + $8.99 = $566.99
Her income in 1 month is $2,350
Her income in 6 months is 6 * $2,350 = $14,100
The percent is:
566.99/14,100 * 100% = 4.02%
Answer: 3) 4.02%
Solve the inequality and enter your solution as an inequality in the box below,
using "<=" for sor">=" for 2 if necessary.
-2(5x + 1) > 48
Answer here
Answer:
x < -5
Step-by-step explanation:
-2(5x + 1) > 48
Divide by -2, remembering to flip the inequality
-2/ -2(5x + 1) < 48/-2
5x +1 < -24
Subtract 1 from each side
5x+1-1 < -24-1
5x < -25
Divide by 5
5x/5 < -25/5
x < -5
if jonny has 3 × 6 amounts of dish soap, how much dish soap does he have?!
a(I dont know)
b(18)
c(12)
d(6)
look up a skit called what's 6×3 before answering.
Answer: 18 (b)
Step-by-step explanation:
3x6=18
Answer:
18
Step-by-step explanation:
you can use a visual for a short answer or organize 3 dots in six groups, count in total
The area of a gymnasium floor is 264 square yards. the floor is 11 yards wide. How long is the floor?
Answer:
24 yards long
Step-by-step explanation:
if A=l*w then it's 264=l*11
if you divide 264 (area) by 11 (width) then the answer is 24 which is the length
Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2?
Each side of the square would have to be 6 cm to have an area of 36 cm^2. However, as a side can never be 0, and you never gave a starting size for the square, the question is unanswerable.
a dense fog advisory means visibility is less than 1/8 of a mile
-true
-false
What is the complete factorization of x^2+4x-45?
Answer:(x-5)(x+9)
Step-by-step explanation:
You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.
Answer: (x - 5)(x + 9)
If you have to solve, x=5 or x= -9
Step-by-step explanation: You need two numbers that multiply to be 45.
(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.
9 - 5 =4, so use those. -45 has a negative sign, so one of the factors must be + and the other - Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.
So (x -5)(x + 9) are your factors. You can FOIL to be sure
x × x += x² . x × 9 = 9x . -5 × x = -5x . -5 × 9 = -45 .
Combine the x terms: 9x -5x = +4x
The two triangles are similar. What is the value of x? Enter your answer in the box. x =
Answer:
the value of x=12
Step-by-step explanation:
d) the answer is d on edg.
I got the answer but I really don’t know if it’s correct or not, please help this is due today
PLEASE HELP. FINAL TEST QUESTION!!!!
Devon is having difficulty determining if the relation given in an input-output table is a function. Explain why he is correct or incorrect.
Step-by-step explanation:
input x , output y
if x= x1 then y=y1 and y1 is the only value then it is a function
if we get multiple values of y then it is not a function
if p+4/p-4, what is the value of p
Answer:
p = 2
Step-by-step explanation:
p + 4/p - 4
multiplying through by p,
p×p + 4/p ×p - 4×p
p² + 4 - 4p = 0
p² - 4p + 4 = 0
factorizing,
p(p - 2) -2(p - 2) =0
(p -2)(p -2) =0
p-2 =0
p=2
An election ballot asks voters to select six city commissioners from a group of 24 candidates in how many ways can this be done? Six city commissioners can be selected from a group of 24 candidates in blank different ways
Answer:
134,596 diffrent ways.
Step-by-step explanation:
Combination has to do with selection. When n object is to be selected from n objects, this can be achieved using the combination formula as shown; \
nCr = n!/(n-r)!r!
If an election ballot asks voters to select six city commissioners from a group of 24 candidates, then the selection can be done in 24C6 different ways.
Applying the formula above:
24C6 = 24!/(24-6)!6!
24C6 = 24!/18!6!
24C6 = 24*23*22*21*20*19*18!/18!*6*5*4*3*2
24C6 = 24*23*22*21*20*19/24*30
24C6 = 23*22*21*20*19/30
24C6 = 134,596 different ways.
Hence, Six city commissioners can be selected from a group of 24 candidates in 134,596 different ways
HELP PLEASE!!What method can you use to find the area of the composite figure. Check ALL that apply.
Answer:
C
Step-by-step explanation:
The reason we can use this method is because we are given a composite figure with a house shape with one triangle on top. We can use the guidance of the dotted lines to make out that a rectangle can be used to find the figure. We can see that apart from the figure, there are two congruent triangles. To find the area we would do -
First find the missing height of the smaller triangles. We would use the pythagorean theorem to find that the missing height is√5
We could do 8(4) = 32 to find the area of the rectangle.
Then, we could do 2√5/2 to find one missing triangle. We could then add the triangles to find the measures of the combined triangles as 2√5. Then, we could do 32 - 2√5 to find the area as 27.5.
Hope this helps :)
Answer:
it is A,B,D
Step-by-step explanation:
i got it right on edge
simpifly (-5x2 - 3x - 7) + (-2x3 + 6x2 - 8)
Answer:
-2x³ + x² - 3x - 15
Step-by-step explanation:
Simply combine like terms together:
-5x² - 3x - 7 - 2x³ + 6x² - 8
-2x³ + (-5x² + 6x²) - 3x + (-7 - 8)
-2x³ + x² - 3x + (-7 - 8)
-2x³ + x² - 3x - 15
Answer: -2x^3+x^2-3x-15
Step-by-step explanation:
As there is only addition and subtraction here, and the two groups of parenthesis are added, you can ignore the parenthesis.
Thus, simply combine like terms to get.
-2x^3+x^2-3x-15
Hope it helps <3
Which of the following is an even function? (A) g(x)=5x+2 (B) g(x)=x (C) g(x)= x 2 (D) g(x)=x3 (E) g(x)=−|x|
Answer:
(C) g(x) = x² and (E) g(x) = -|x|Step-by-step explanation:
If f(x) is an even function, then f(-x) = f(x).
(A)
g(x) = 5x + 2
g(-x) = 5(-x) + 2 = -5x + 2
g(-x) ≠ g(x)
(B)
g(x) = g(x) = x
g(-x) = -x
g(-x) ≠ g(x)
(C)
g(x) = x²
g(-x) = (-x)² = (-1x)² = (-1)²(x)² = x²
g(-x) = g(x)
(D)
g(x) = x³
g(-x) = (-x)³ = (-1x)³ = (-1)³(x)³ = -1x³ = -x³
g(-x) ≠ g(x)
(E)
g(x) = -|x|
g(-x) = -|-x| = -|-1x| = -(|-1|)(|x|) = -1|x| = -|x|
g(-x) = g(x)
According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.
(a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.)
H0:
Ha:
(b) Using the sample from the 60 bottles, what is the test statistic? (Round your answer to three decimal places.)
Using the sample from the 60 bottles, what is the p-value? (Round your answer to four decimal places.)
p-value =
(c) At α = 0.05, what is your conclusion?
Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
(d) Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
Ha:
Find the value of the test statistic. (Round your answer to three decimal places.)
State the critical values for the rejection rule. Use
α = 0.05.
(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic ≤
test statistic ≥
State your conclusion.
Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Answer:
a) Null and alternative hypothesis
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
b) Test statistic t=-1.565
P-value = 0.0612
NOTE: the sample size is n=65.
c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
d) Null and alternative hypothesis
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
Test statistic t=-1.565
Critical value tc=-1.669
t>tc --> Do not reject H0
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
The significance level is 0.05.
The sample has a size n=65.
The sample mean is M=30.15.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=65-1=64[/tex]
This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.565)=0.0612[/tex]
As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Critical value approach
At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.
As the test statistic is greater than the critical value, it falls in the acceptance region.
The null hypothesis failed to be rejected.
If a baseball player has a batting average of 0.375, what is the probability that the player will get the following number of hits in the next four times at bat?
A. Exactly 2 hits(Round to 3 decimal places as needed)
B. At least 2 hits (Round to 3 decimal places as needed)
Answer:
a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.375)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
Part b
[tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
What is the solution to the system of equations x+y=10 and x+2y=4 using the linear combination method?
Answer:
The solution:
X = 16 and Y = -6
Step-by-step explanation:
The equations to be solved are:
x+y = 10 ------- equation 1
x+2y = 4 ----------- equation 2
we can multiply equation 1 by -1 to make the value of x and y negative.
This will give us
-x- y = - 10 ------- equation 3
x+2y = 4 ----------- equation 2
We will now add equations 3 and 2 together so that x will cancel itself out.
this will give us
y = -10 +4 = -6
hence, we have the value of y as -6.
To get the value of x, we can put this value of y into any of the equations above. (I will use equation 1)
x - 6 = 10
from this, we have that x = 4
Therefore, we have our answer as
X = 16 and Y = -6
when should homeowners ask their lenders for mortgage modification
Homeowners may consider asking their lenders for mortgage modification in the following situations listed below:
When should homeowners ask their lenders for mortgage modification?1. Financial hardship: If a homeowner is facing financial hardship as a result of a large decrease in income, unanticipated medical expenditures, or other unforeseen events
2. Changes in interest rates: If interest rates have fallen significantly after the homeowner obtained their mortgage, they may be able to negotiate a lower interest rate through mortgage modification.
3. Default: If a homeowner has fallen behind on their mortgage payments and is facing foreclosure, mortgage modification may be an option for bringing the loan up to date and avoiding foreclosure.
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Answer:
When they know they can't afford it & before the next payment
Step-by-step explanation:
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard deviation 1.3 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible
a. What is the distribution of X?
b. What is the distribution of a?
c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
e. For part d), is the assumption that the distribution is normal necessary?
f. Find the IQR for the average of 38 cities.
Q1=__________ ppm
Q3 =_________ ppm
IQR=_________ ppm
We assume that question b is asking for the distribution of [tex] \\ \overline{x}[/tex], that is, the distribution for the average amount of pollutants.
Answer:
a. The distribution of X is a normal distribution [tex] \\ X \sim N(8.6, 1.3)[/tex].
b. The distribution for the average amount of pollutants is [tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].
c. [tex] \\ P(z>-0.08) = 0.5319[/tex].
d. [tex] \\ P(z>-0.47) = 0.6808[/tex].
e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution.
f. [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.
Step-by-step explanation:
First, we have all this information from the question:
The random variable here, X, is the number of pollutants that are found in waterways near large cities.This variable is normally distributed, with parameters:[tex] \\ \mu = 8.6[/tex] ppm.[tex] \\ \sigma = 1.3[/tex] ppm.There is a sample of size, [tex] \\ n = 38[/tex] taken from this normal distribution.a. What is the distribution of X?
The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with [tex] \\ \mu = 8.6[/tex] ppm and [tex] \\ \sigma =1.3[/tex] ppm or [tex] \\ X \sim N(8.6, 1.3)[/tex].
b. What is the distribution of [tex] \\ \overline{x}[/tex]?
The distribution for [tex] \\ \overline{x}[/tex] is [tex] \\ N(\mu, \frac{\sigma}{\sqrt{n}})[/tex], i.e., the distribution for the sampling distribution of the means follows a normal distribution:
[tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].
c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
Notice that the question is asking for the random variable X (and not [tex] \\ \overline{x}[/tex]). Then, we can use a standardized value or z-score so that we can consult the standard normal table.
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
x = 8.5 ppm and the question is about [tex] \\ P(x>8.5)[/tex]=?
Using [1]
[tex] \\ z = \frac{8.5 - 8.6}{1.3}[/tex]
[tex] \\ z = \frac{-0.1}{1.3}[/tex]
[tex] \\ z = -0.07692 \approx -0.08[/tex] (standard normal table has entries for two decimals places for z).
For [tex] \\ z = -0.08[/tex], is [tex] \\ P(z<-0.08) = 0.46812 \approx 0.4681[/tex].
But, we are asked for [tex] \\ P(z>-0.08) \approx P(x>8.5)[/tex].
[tex] \\ P(z<-0.08) + P(z>-0.08) = 1[/tex]
[tex] \\ P(z>-0.08) = 1 - P(z<-0.08)[/tex]
[tex] \\ P(z>-0.08) = 0.5319[/tex]
Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is [tex] \\ P(z>-0.08) = 0.5319[/tex].
d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
Or [tex] \\ P(\overline{x} > 8.5)[/tex]ppm?
This random variable follows a standardized random variable normally distributed, i.e. [tex] \\ Z \sim N(0, 1)[/tex]:
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
[tex] \\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ z = \frac{-0.1}{0.21088}[/tex]
[tex] \\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47[/tex]
[tex] \\ P(z<-0.47) = 0.31918 \approx 0.3192[/tex]
Again, we are asked for [tex] \\ P(z>-0.47)[/tex], then
[tex] \\ P(z>-0.47) = 1 - P(z<-0.47)[/tex]
[tex] \\ P(z>-0.47) = 1 - 0.3192[/tex]
[tex] \\ P(z>-0.47) = 0.6808[/tex]
Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is [tex] \\ P(z>-0.47) = 0.6808[/tex].
e. For part d), is the assumption that the distribution is normal necessary?
For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.
f. Find the IQR for the average of 38 cities.
We must find the first quartile (25th percentile), and the third quartile (75th percentile). For [tex]\\ P(z<0.25)[/tex], [tex] \\ z \approx -0.68[/tex], then, using [2]:
[tex] \\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ (-0.68 *0.21088) + 8.6 = \overline{X}[/tex]
[tex] \\ \overline{x} =8.4566[/tex]
[tex] \\ Q1 = 8.4566[/tex] ppm.
For Q3
[tex] \\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ (0.68 *0.21088) + 8.6 = \overline{X}[/tex]
[tex] \\ \overline{x} =8.7434[/tex]
[tex] \\ Q3 = 8.7434[/tex] ppm.
[tex] \\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868[/tex] ppm
Therefore, the IQR for the average of 38 cities is [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.
20% of city employees ride the bus to work. This is up 10% from last year. What percent of employees rode the bus to work last year?
Answer:
18.18% of employees rode the bus to work last year
Step-by-step explanation:
This question can be solved using a rule of three.
Last year, a proportion of x employees riding the bus was 100% = 1.
This year, 20% = 0.2 ride the bus, which is 100 + 10 = 110% = 1.1 of last year.
So
0.2 - 1.1
x - 1
[tex]1.1x = 0.2[/tex]
[tex]x = \frac{0.2}{1.1}[/tex]
[tex]x = 0.1818[/tex]
0.1818*100 = 18.18%
18.18% of employees rode the bus to work last year
Evaluate the expression.........
Answer:
9
Step-by-step explanation:
p^2 -4p +4
Let p = -1
(-1)^1 -4(-1) +4
1 +4+4
9
help help help pls pls
Answer:
C. {2.4, 4.8, 6.3, 8.8}
Step-by-step explanation:
You only need to find the first domain value to make the appropriate answer selection.
14.1 = 7x -2.7
16.8 = 7x . . . . . . add 2.7
2.4 = x . . . . . . . . divide by 7
The appropriate choice is ...
C. {2.4, 4.8, 6.3, 8.8}
_____
In the attachment, we have applied the same "solve for x" steps to each of the range values, confirming our answer choice.
Find the domain of the graphed function.
10
-10
10
10
O A. -45x39
B. -43x8
C. X2-4
0
D. x is all real numbers.
Currently patrons at the library speak at an average of 64 decibels. Will this average decline after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 47 people speaking at the library. Their average decibel level was 63.2 and their standard deviation was 5. What can be concluded at the the α α = 0.05 level of significance?
Answer:
The conclusion is that the average level of decibel at the library has changed since the installation of a new computer plug
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 64[/tex]
The sample size is [tex]n = 47[/tex]
The sample mean is [tex]\= x = 63.2[/tex]
The sample standard deviation is [tex]\sigma = 5[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The Null Hypothesis is
[tex]H_o : \mu = 64[/tex]
The Alternative Hypothesis is
[tex]H_a : \mu \ne 64[/tex]
The test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{63.1 - 64 }{\frac{5 }{\sqrt{47} } }[/tex]
[tex]t = -1.234[/tex]
The negative sign show that this is a left-tail test
Now the critical value of the level of significance obtained from the critical values table is
[tex]z_{0.05} = 1.645[/tex]
Now comparing the critical value of the [tex]\alpha[/tex] and the test statistics we see that critical value is greater than the test statistic which implies that the null hypothesis is rejected.
The conclusion is that the average level of decibel at the library has changed since the installation of a new computer plug
Which of the following represents a coefficient from the expression given?
9x – 20 + x2
Answer:
1 or 9.
Step-by-step explanation:
A coefficient is "a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy)".
So, in this case, the coefficient of 9x would be 9.
The coefficient of x^2 would be 1.
Hope this helps!
In the given quadratic expression 9x - 20 + x, 1, 9, and -20 are the coefficients.
What are coefficients in a quadratic expression?In a quadratic expression of the standard form ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
How to solve the given question?In the question, we are asked to identify the coefficients from the given quadratic expression 9x - 20 + x².
First, we try to express the given quadratic expression, 9x - 20 + x², in the standard form of a quadratic expression, ax² + bx + c.
Therefore, 9x - 20 + x² = x² + 9x - 20.
Comparing the expression x² + 9x - 20 with the standard form of a quadratic expression ax² + bx + c, we get a = 1, b = 9, c = -20.
We know that in a quadratic expression ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
Thus, we can say that in the given quadratic expression 9x - 20 + x², 1, 9, and -20 are the coefficients.
Learn more about quadratic expressions at
https://brainly.com/question/1214333
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PLEASE HELP ITS DUE SOON ALL HELP NEEDED!!
Answer:
12345678901234567890
Answer:
[tex]95ft^2[/tex]
Step-by-step explanation:
First, note the surfaces we have. We have four triangles and one square base. Thus, we can find the surface area of each of them and them add them all up.
First, recall the area of a triangle is [tex]\frac{1}{2} bh[/tex]. We have four of them so:
[tex]4(\frac{1}{2} bh)=2bh[/tex]
The base is 5 while the height is 7. Thus, the total surface area of the four triangles are:
[tex]2(7)(5)=70 ft^2[/tex]
We have one more square base. The area of a square is [tex]b^2[/tex]. The base is 5 so the area is [tex]25ft^2[/tex].
The total surface area is 70+25=95.