The result will be the probability that 17 or fewer out of the 50 sampled students are bilingual.
To determine the probability that 17 or fewer out of 50 sampled students are bilingual, we can use the binomial probability formula. Let's calculate it step by step:
First, we need to determine the probability of an individual student being bilingual. We can do this by dividing the number of bilingual students by the total number of students:
P(bilingual) = 466 / 1320
Next, we'll use this probability to calculate the probability of having 17 or fewer bilingual students out of a sample of 50. We'll sum up the probabilities for having 0, 1, 2, ..., 17 bilingual students using the binomial probability formula:
P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)
Where:
P(X = k) = (nCk) * (P(bilingual))^k * (1 - P(bilingual))^(n - k)
n = Sample size = 50
k = Number of bilingual students (0, 1, 2, ..., 17)
Now, let's use a calculator to compute these probabilities. Assuming you have access to a scientific calculator, you can follow these steps:
Convert the probability of an individual being bilingual to decimal form: P(bilingual) = 466 / 1320 = 0.353
Calculate the cumulative probabilities for having 0 to 17 bilingual students:
P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)
Using the binomial probability formula, we'll substitute the values:
P(X ≤ 17) = (50C0) * (0.353)^0 * (1 - 0.353)^(50 - 0) + (50C1) * (0.353)^1 * (1 - 0.353)^(50 - 1) + ... + (50C17) * (0.353)^17 * (1 - 0.353)^(50 - 17)
Evaluate this expression using your calculator to get the final probability. Make sure to use the combination (nCr) function on your calculator to calculate the binomial coefficients.
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Using the central limit theorem, the probability that 17 or fewer of them are bilingual.
The following information is given in the question:
Population size N = 1320
Number of bilingual students = 466
Sample size n = 50
number of bilingual students in the sample = 17
Population proportion:
[tex]P =\frac{466}{1320}[/tex]
P =0.3530
Q= 1-3530
Q = 0.647
Sample proportion:
[tex]p = \frac{17}{50}[/tex]
p = 0.34
q = 1-0.34
q = 0.66
Since,
[tex]X \sim B(n, p)[/tex]
E(x) = np and var(x) = npq
Here, the sample size (50) is large and the probability p is small.
So we can use the central limit theorem, which says that for large n and small p :
[tex]X \sim (nP, nPQ)[/tex]
Where, P =0.3530
nP = 50 x 0.3530 = 17.65
and nPQ = 50x0.3530x0.647 = 11.41
Now, we want to calculate P(X≤17)
[tex]P(X\leq 17) = P(\frac{x-nP}{\sqrt{nPQ}}\leq \frac{17-17.65}{\sqrt{11.41}})[/tex]
[tex]P(X\leq 17) = P(z}\leq \frac{-0.65}{3.78}})[/tex]
[tex]P(X\leq 17) = P(z}\leq -0.172)[/tex]
[tex]P(X\leq 17) = P(z}\geq 0.172)[/tex]
[tex]P(X\leq 17) =1- P(z}\leq 0.172)[/tex]
[tex]P(X\leq 17) =1-0.56[/tex]
[tex]P(X\leq 17) =0.44[/tex]
Hence, the probability that 17 or fewer of the students are bilingual is 0.44.
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According to a Pew Research Center, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses: H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82.1. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).2. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.068).3. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.966).4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034)
Answer:
Step-by-step explanation:
For the null hypothesis,
p = 0.35
For the alternative hypothesis,
P > 0.35
Since the z score is given as z = 1.82, we would find the probability value by determining the area above the z score from the normal distribution table. The required probability value is
1 - 0.966 = 0.034
Assuming alpha = 0.05,
Since alpha, 0.05 > than the p value, 0.034, then we would reject the null hypothesis. Therefore, the correct option is
At significance level of 5%,
There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Diego planted a 8 inch tall magical beanstalk. The height of the beanstalk increases by 16% each day.Write a function ff that determines the height of the beanstalk in inches in terms of the number of days tt since Diego planted the beanstalk f(t)=f(1)/f(0)=f(2)/f(1)=f(5.28)/f(4.28)=For any value of x, what is the value of f(x+1)/f(x)?
Answer:
The expression for the height of the plant is: f(x) = 8*(1.16)^x;
The value of f(x+1)/f(x) is 1.16.
Step-by-step explanation:
Since Diego's beanstalk grows at an exponential rate of 16% per day, then the expression that represents the height of the plant, "f", in function of days, "x", can be found as shown below:
Initially the height of the plant was:
[tex]f(0) = 8[/tex]
After the first day however it was:
f(1) = 8*(1 + \frac{16}{100}) = 8*(1.16)
While after the second day:
f(2) = f(1)*(1.16) = 8*(1.16)*(1.16) = 8*(1.16)²
And so on, therefore the expression is:
f(x) = 8*(1.16)^x
The value of f(x + 1)/f(x) is:
[8*(1.16)^(x + 1)]/[8*(1.16)^x]
[8*(1.16)*(1.16)^(x)]/[8*(1.16)^x] = 1.16
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
problem decoded dude
first follow meh and then thank me
My name is Jerry
iven two dependent random samples with the following results: Population 1 70 60 72 55 69 50 55 74 Population 2 72 56 81 50 79 60 50 78 Can it be concluded, from this data, that there is a significant difference between the two population means? Let d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.1 for the test. Assume that both populations are normally distributed. Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.
Answer:
The value of the test statistic is:
t = -1.112
Step-by-step explanation:
In this case a paired difference test is to be performed.
The hypothesis can be defined as follows:
H₀: There is no difference between the two population means, i.e. d = 0.
Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.
The significance level of the test is, α = 0.10.
Use MS-Excel to perform the analysis.
Consider the output attached below.
The value of the test statistic is:
t = -1.112
The p-value of the two-tailed test is:
p-value = 0.303.
Decision rule:
Reject the null hypothesis if the p-value is less than the significance level.
p-value = 0.303 > α = 0.10.
The null hypothesis was failed to be rejected at 10% level of significance.
Conclusion:
There is not enough evidence to support the claim that there is a difference between the two population means.
anyone have free time to answer
Answer:
A.34
Do it in this order
PEDMAS
Parentheses
Exponents
division or multiplication (whichever is further left)
addition or subtraction (whichever is further to the left goes first)
3 x 8 = 24
2 x 5 = 10
24 + 10 = 34
A. = 34
For B. we do the addition first because they are inside the parentheses
8+2=10
10 x 3 = 30
30 x 5 = 150
B. = 150
Hope this helps
Step-by-step explanation:
Answer:
the answer is 34.
Step-by-step explanation:
a.3×8+2×5
=24+10
=34
b.3×(8+2)×5
=3×10×5
=30×5
=150
hope this help you!!!!!
HURRY TIMEDD!!!!!
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has? The discriminant is −4, so the equation has 2 real solutions. The discriminant is −4, so the equation has no real solutions. The discriminant is 35, so the equation has 2 real solutions. The discriminant is 35, so the equation has no real solutions.
Answer:
Second option is the correct choice.
Step-by-step explanation:
"The discriminant is −4, so the equation has no real solutions."
[tex]x^2-4x+5=0\\\\a=1,\:b=-4,\:c=5:\\\\b^2-4ac=\left(-4\right)^2-4\cdot \:1\cdot \:5=-4[/tex]
Best Regards!
Answer: B
The discriminant is −4, so the equation has no real solutions.
Step-by-step explanation:
Just took quiz EDG2021
Mark Brainliest
how to simplify 2x^2 - 18 =0
Answer:
X=3 or x= -3
Step-by-step explanation:
2x^2 - 18 =0
Take a common factor
2(x^2 - 9) = 0
2(x-3)(x+3)=0
X-3=0 or x+3=0
X=3 x=-3
Hope this helps!
Step-by-step explanation:
Hope this is correct
HAVE A GOOD DAY!
What is the additive inverse of the complex number 9-412
-9-41
-9 +41
9 - 41
9 + 41
Additive inverse means the sum should be 0
so all you gotta do is multiply the complex number by -1
(the question isn't clear so I can't state the option)
A laptop computer is purchased for $2300. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Answer:
after the 1st year
Step-by-step explanation:
$2300 × 75% = $1725.00
$2300-$1725= $575
"An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particular city for 1 year. The fire department is concerned that many houses remain without detectors. Let p= the true proportion of such houses having detectors, and suppose that a random sample of 25 homes is inspected. If the sample strongly indicates that fewer than 80% of all houses have a detector, the fire department will campaign for a mandatory inspection program. Because of the costliness of the program, the department prefers not to call for such inspections unless sample evidence strongly argues for their necessity. Let X denote the number of homes with detectors among the 25 sampled. Consider rejecting the claim that p>= 0.8 if x<= 15.
a. What is the probability that the claim is rejected when the actual value of p is 0.8?
b. What is the probability of not rejecting the claim when p= 0.7? when p= 0.6?
c. How do the "error probabilities" of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14?
Answer:
a) Probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 15) = 0.0173
b) Probability of not rejecting the claim when p = 0.7, P(X > 15) = 0.8106
when p = 0.6, P(X > 15) = 0.4246
c) Check Explanation
The error probabilities are evidently lower when 15 is replaced with 14 in the calculations.
Step-by-step explanation:
p is the true proportion of houses with smoke detectors and p = 0.80
The claim that 80% of houses have smoke detectors is rejected if in a sample of 25 houses, not more than 15 houses have smoke detectors.
If X is the number of homes with detectors among the 25 sampled
a) Probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 15)
This is a binomial distribution problem
A binomial experiment is one in which the probability of success doesn't change with every run or number of trials (probability that each house has a detector is 0.80)
It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure (we are sampling 25 houses with each of them either having or not having a detector)
The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 25 houses sampled
x = Number of successes required = less than or equal to 15
p = probability of success = probability that a house has smoke detectors = 0.80
q = probability of failure = probability that a house does NOT have smoke detectors = 1 - p = 1 - 0.80 = 0.20
P(X ≤ 15) = Sum of probabilities from P(X = 0) to P(X = 15) = 0.01733186954 = 0.01733
b) Probability of not rejecting the claim when p= 0.7 when p= 0.6
For us not to reject the claim, we need more than 15 houses with detectors, hence, th is probability = P(X > 15), but p = 0.7 and 0.6 respectively for this question.
n = total number of sample spaces = 25 houses sampled
x = Number of successes required = more than 15
p = probability that a house has smoke detectors = 0.70, then 0.60
q = probability of failure = probability that a house does NOT have smoke detectors = 1 - p = 1 - 0.70 = 0.30
And 1 - 0.60 = 0.40
P(X > 15) = sum of probabilities from P(X = 15) to P(X = 25)
When p = 0.70, P(X > 15) = 0.8105639765 = 0.8106
When p = 0.60, P(X > 15) = 0.42461701767 = 0.4246
c) How do the "error probabilities" of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14.
The error probabilities include the probability of the claim being false.
When X = 15
(Error probability when p = 0.80) = 0.0173
when p = 0.70, error probability = P(X ≤ 15) = 1 - P(X > 15) = 1 - 0.8106 = 0.1894
when p = 0.60, error probability = 1 - 0.4246 = 0.5754
When X = 14
(Error probability when p = 0.80) = P(X ≤ 14) = 0.00555
when p = 0.70, error probability = P(X ≤ 14) = 0.0978
when p = 0.60, error probability = P(X ≤ 14) = 0.4142
The error probabilities are evidently lower when 15 is replaced with 14 in the calculations.
Hope this Helps!!!
Square root of a-3 plus 5 = a
Answer:
1.41421356237
Step-by-step explanation:
-3 + 5 = 2
square root of 2 = 1.41421356237
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.10, he will reject the shipment. He will test the hypotheses H0: p = 0.10, Ha: p < 0.10. He selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. The P-value of this test is:
Answer:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89[/tex]
And the p value would be given by:
[tex]p_v =P(z<-1.89)=0.0294[/tex]
Step-by-step explanation:
Information given
n=200 represent the random sample taken
X=12 represent the potatoes with major defects
[tex]\hat p=\frac{12}{200}=0.06[/tex] estimated proportion of potatoes with major defects
[tex]p_o=0.10[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true proportion is less than 0.10 so then the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.1[/tex]
Alternative hypothesis:[tex]p < 0.10[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89[/tex]
And the p value would be given by:
[tex]p_v =P(z<-1.89)=0.0294[/tex]
Considering the hypothesis tested, the p-value is of 0.0294.
The null hypothesis is:
[tex]H_0: p = 0.1[/tex]
The alternative hypothesis is:
[tex]H_a: p < 0.1[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are:
[tex]p = 0.1, n = 200, \overline{p} = \frac{12}{200} = 0.06[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.06 - 0.1}{\sqrt{\frac{0.1(0.9)}{200}}}[/tex]
[tex]z = -1.89[/tex]
The p-value for this test is the probability of finding a sample proportion of 0.06 or below, which is the p-value of z = -1.89.
Looking at the z-table, z = -1.89 has a p-value of 0.0294.A similar problem is given at https://brainly.com/question/24166849
Please answer this correctly
problem decoded dude
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Answer:
50%
Step-by-step explanation:
There are 6 sides on a die, three Of Which are even and 3 odd.
the even ones are 2,4 and 6 and the odds are 1, 3 and 5
since there are 3 evens, u divide it by the total number of outcomes 6 which is 1/2 or 50percent
It is estimated that 17% of the vehicles entering Canada from the United States carry undeclared goods. Use the normal approximation to calculate the probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.
Answer:
The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.
P( x > 175) = 0.0256
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 900
The estimated proportion 'p' = 0.17
Mean of the binomial distribution
μ = n p = 900 × 0.17 = 153
Standard deviation of the binomial distribution
σ = [tex]\sqrt{npq} = \sqrt{900 X 0.17 X 0.83} = 11.26[/tex]
Step(ii):-
Let 'X' be the random variable of normal distribution
mean μ= 153 and σ = 11.26
Given X = 175
[tex]Z = \frac{175-153}{11.268} = 1.95[/tex]
The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.
P( x > 175) = P( Z> 1.95)
= 1- P( Z < 1.95)
= 1 - ( 0.5 +A( 1.95))
= 0.5 - A( 1.95)
= 0.5 - 0.4744
= 0.0256
Conclusion:-
The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.
P( x > 175) = 0.0256
The sum of the 3rd term and 4th term of an arithmetic sequence is 18. The 7th term exceeds the 5th term by 14. Find the first term and common difference.
Answer:
First term = -8.5.
Common difference = 7.
Step-by-step explanation:
The third term = a1 + 2d where a1 = first term and d is the common difference so we have
a1 + 2d + a1 + 3d = 18
2a1 + 5d = 18............(1)
Also:
7th term - 5th term = 14 giving
a1 + 6d - ( a1 + 4d) = 14
2d = 14
d = 7.
So the common difference is 7 and substituting for d in (1) we have:
2a1 + 5*7 = 18
2a1 = 18-35 = -17
a1 = -8.5.
The first term and the common difference of the sequence are -8.5 and 7 respectively.
The sum of the 3rd term and 4th term of an arithmetic sequence is 18.
Using Arithmetic progression formula,
aₙ = a + (n- 1)d
where
n = nth term
a = first term
d = common difference
a₃ = a + 2d
a₄ = a + 3d
Therefore,
a + 3d + (a + 2d) = 18
2a + 5d = 18
The 7th term exceeds the 5th term by 14. Therefore,
a₅ = a + 4d
a₆ = a + 6d
a + 6d - (a + 4d) = 14
a + 6d - a - 4d = 14
2d = 14
d = 14 / 2
d = 7
2a + 5d = 18
2a + 5(7) = 18
2a + 35 = 18
2a = 18 - 35
2a = -17
a = -17 / 2
a = -8.5
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Troy starts to construct a triangle congruent to right
isosceles triangle ABC. He begins by constructing a
perpendicular through a point not on a line, as shown.
D
Use the drop-down menus to complete the additional
steps needed to finish the congruent triangle
construction.
Place the compass center at C and set the radius to
the length of CB. Because
he needs to
set the compass radius only once.
Keeping the compass width the same, move the
compass center to F and draw arcs to intersect
segments
The points where the arcs intersect the segments are
the of the triangle. Construct segments to
form the remaining sides of the triangle.
А
F
E
с
B
H
Answer:
CB=CA
FD and FG
Verticies
Step-by-step explanation:
Answer:
B,A,C
Step-by-step explanation:
because Place the compass center at C and set the radius to
the length of CB. Because
he needs to
set the compass radius only once.
Keeping the compass width the same, move the
compass center to F and draw arcs to intersect
segments
The points where the arcs intersect the segments are
the of the triangle. Construct segments to
form the remaining sides of the triangle
Phil has $20,000, part of which he invests at 8% interest and the rest at 6%. If the total income from the two investments was $1460, how much did he invest at 6%?
Answer: 7000
Step-by-step explanation:
Let the amount invested in 8% account be P1 and the amount invested in 6% account be P2
. If the total amount invested is $20,000 then:
P1+P2=20,000. (Eq. 1)
The interest earned in one year from the 8% account is:
I1=0.08P1
and the interest earned in one year from the 6% account is:
I2=0.06P2
If the total interest earned is $1460, then:
I1+I2=1460
0.08P1+0.06P2=1460
(Eq. 2) From Eq. 1 :
P1=20000−P2
Substituting this into Eq. 2:
0.08 (20000−P2) + 0.06P2 = 1460
1600 − 0.08P2 + 0.06P2 = 1460
0.02P2 = 140
P2 = 140 / 0.02
P2 = 7000
Hence, he invested $7000 at the rate of 6%.
Gas prices are up 30% since last year when they were $4.35, how much is gas now?
Answer:
given;
previous year price of gas= $4.35
price of gas has been increased by 30%
now,price of gas in present year=?
we have;
price of gas in present year=priceof
previous year+30%of price of previous year.
so ,price of gas in present year=4.35+30%of4.35
=$4.35+30/100×4.35
=$4.35+1.305
= $5.655. ans....
therefore, the price of gas in present year is ;$5.655.
A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds. How long will it take the rock to hit the ground? Round your answers to the nearest three decimal places.
Answer:
3.189 seconds
Step-by-step explanation:
You want f(t) = 0, so ...
0 = -16t^2 +13.4t +120
0 = t^2 -0.8375t -7.5 . . . . divide by -16
0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*
0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square
√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root
t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875
It will take the rock about 3.189 seconds to hit the ground.
_____
* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...
(t^2 -2at +a^2) = (t -a)^2
Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.
_____
Comment on the question
We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...
Identify three misconception each of any five topic's in mathematics
62 = 12.
7 x 0 = 7.
Four hundred and eight is written as 4008.
0.10 = point ten.
0.5 x 10 = 0.50.
6 -:- ½ = 3.
- 5 + 3 = -8.
4% is 0.4 as a decimal.
help me please please
Answer:
3.88 nm
Step-by-step explanation:
The angle at Port Latta between the actual direction of travel and the destination at Lookout Point is 90° -75° = 15°. The sine function relates the angle, the side opposite, and the hypotenuse of a right triangle, so you have ...
sin(15°) = (distance to Lookout Point)/(15 nm)
Solving for the desired distance, we have ...
distance to Lookout Point = (15 nm)sin(15°) = 3.88 nm
The yacht is 3.88 nautical miles from Lookout Point.
A tire manufacturer is measuring the margin of error in the thickness of their tires to make sure it is within safety limits. Overall, the tires' thickness is normally distributed with a mean of 0.45 inches and a standard deviation of 0.05 inches. What thickness separates the lowest 5% of the means from the highest 95% in a sample size of 65 tires
Answer:
Z = -1.65
[tex]\bar x \approx 0.44 \ inches[/tex]
Step-by-step explanation:
The main objective is to compute the data for the Z value and determine the [tex]\bar x[/tex] of the sample distribution
Given that;
the tires' thickness is normally distributed with a mean μ = 0.45 in
standard deviation σ = 0.05 in
sample size = 65 tires
Also; we are being told that the thickness separates the lowest 5% of the means from the highest 95%
∴
P(Z < Z) =0.05
From the Z- table
P(Z < -1.645) = 0.05
Z = -1.65
Similarly;
Let consider [tex]\bar x[/tex] to be the sample mean;
Then:
mean [tex](\mu_{\bar x}) = \mu = 0.45[/tex]
standard deviation[tex](\sigma_{\bar x} ) = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=\dfrac{0.05}{\sqrt{65}}[/tex]
= 0.00620174
By applying the Z-score formula:
x = μ + ( Z × σ )
[tex]\bar x = \mu _{\bar x} +(Z * \sigma _{\bar x})[/tex]
[tex]\bar x = 0.45 + (-1.65 *0.00620174)[/tex]
[tex]\bar x= 0.439767129[/tex]
[tex]\bar x \approx 0.44 \ inches[/tex]
What is the sampling method used in the following scenario? The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
Answer:
Step-by-step explanation:
The method applied in this scenario is called simple random sampling. A sample of 100 customers is chosen from a larger population of customers and each customer has the same chance of being selected for the survey at any given time. Also, the chance of selecting 100 customers from each store is the same during the sampling process. The order of sampling at each store does not follow a certain order, thus, It is different from systematic random sampling.
thanks for the help!
Answer:
I. and II. are correct
Step-by-step explanation:
The line y=0 is a horizontal asymptote in both directions, so ...
[tex]\lim\limits_{x\to -\infty}{f(x)}=\lim\limits_{x\to\infty}{f(x)}=0[/tex]
The function value f(0) is 0, so the limit is the same from either direction:
[tex]\lim\limits_{x\to 0^-}{f(x)}=\lim\limits_{x\to 0^+}{f(x)}=0[/tex]
__
The expression for statement III can be simplified:
[tex]\dfrac{f(x)-\dfrac{1}{2}}{x-1}=\dfrac{\dfrac{x}{1+x^2}-\dfrac{1}{2}}{x-1}=\dfrac{2x-(1+x^2)}{2(1+x^2)(x-1)}=\dfrac{-(x-1)^2}{2(x-1)(x^2+1)}\\\\=\dfrac{1-x}{2(x^2+1)}[/tex]
The limit of this is 0 from either direction, so the limit does exist at x=1.
_____
We consider that ...
both statements I. and II. are correct.
The function f(x)= 200/X+ 10 models the cost per student of a field trip when x students go on the trip. How is the parent function
f(x) = 1/x transformed to create the function f(x)= 200/x + 10
O It is vertically stretched by a factor of 200.
O It is vertically stretched by a factor of 200 and shifted 10 units leftt
O It is vertically stretched by a factor of 200 and shifted 10 units up.
O It is vertically stretched by a factor of 200 and shifted 10 units right
Answer:
It is vertically stretched by a factor of 200 and shifted 10 units right
Step-by-step explanation:
Suppose we have a function f(x).
a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.
f(x - a) is shifting f(x) a units to the right.
f(x + a) is shifting f(x) a units to the left.
In this question:
Initially: [tex]f(x) = \frac{1}{x}[/tex]
Then, first we shift, end up with:
[tex]f(x+10) = \frac{1}{x + 10}[/tex]
f was shifted 10 units to the left.
Finally,
[tex]200f(x+10) = \frac{200}{x + 100}[/tex]
It was vertically stretched by a factor of 200.
So the correct answer is:
It is vertically stretched by a factor of 200 and shifted 10 units right
Answer:
the answer is D
Step-by-step explanation:
If the radius of a circle is 31.2 cm, what is the approximate area if you use 3.14 for pi and the area is rounded to the nearest tenth?
Answer:
3056.6 cm^2
Step-by-step explanation:
A = (pi)r^2 = 3.14 * 31.2 cm * 31.2 cm = 3056.6 cm^2
Answer: 3056.60 sq. cm.
Step-by-step explanation:
Area of a circle = π x r^2
= 3.14 x 31.2^2
= 3056.60
six more than the product of nine and a number Evaluate when q = 6
Answer:
60
Step-by-step explanation:
Let's name "a number" "q."
The expression we can set up is 6+9q
Plug 6 in for q.
6+9(6)
6+54
60
If a square with a width of 30 feet a length of 72 feet, and the diagonal is 78 feet, would the square have right angles. Yes or No answer please explain
Please answer this correctly
Answer:
6 pizzas
Step-by-step explanation:
At least 10 and fewer than 20 makes it 10-19
So,
10-19 => 6 pizzas
6 pizzas have at least 10 pieces of pepperoni but fewer than 20 pieces of pepperoni.
Find the fifth term of an=(-1)^n/2n-1
a.-1/7 b.-1/9 c.1/9 d.1/7
Answer:
b) -1/9
Step-by-step explanation:
Given
[tex]a_{n} = \frac{(-1)^{n} }{2n-1}[/tex]
First term
[tex]a_{1} = \frac{(-1)^{1} }{2(1)-1} = -1[/tex]
second term
[tex]a_{2} = \frac{(-1)^{2} }{2(2)-1} = \frac{1}{3}[/tex]
Third term
[tex]a_{3} = \frac{(-1)^{3} }{2(3)-1} = \frac{-1}{5}[/tex]
Fourth term
[tex]a_{4} = \frac{(-1)^{4} }{2(4)-1} = \frac{1}{7}[/tex]
Fifth term
[tex]a_{5} = \frac{(-1)^{5} }{2(5)-1} = \frac{-1}{9}[/tex]
Answer:
B
Step-by-step explanation:
right on edge 2021
