Answer:
1, 3, 5.
Step-by-step explanation:
The members of the set are {1, 3, 5}.
Note 0 is an even integer so is not included in the set.
Also 0 is neither negative or positive.
the time taken by a student to the university has been shown to be normally distributed with mean of 16 minutes and standard deviation of 2.1 minutes. He walks in once a day during term time, 180 days per year, and leaves home 20 minutes before his first lecture. a. Find the probability that he is late for his first lecture. b. Find the number of days per year he is likely to be late for his first lecture.
Answer:
a) 2.84% probability that he is late for his first lecture.
b) 5.112 days
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 16, \sigma = 2.1[/tex]
a. Find the probability that he is late for his first lecture.
This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 16}{2.1}[/tex]
[tex]Z = 1.905[/tex]
[tex]Z = 1.905[/tex] has a pvalue of 0.9716
1 - 0.9716 = 0.0284
2.84% probability that he is late for his first lecture.
b. Find the number of days per year he is likely to be late for his first lecture.
Each day, 2.84% probability that he is late for his first lecture.
Out of 180
0.0284*180 = 5.112 days
g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. Let p represent the probability that the psychic correctly identified the symbols on the cards in a random trial. How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence?
Answer:
Step-by-step explanation:
Hello!
The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.
Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.
p the probability that the psychic identified the symbol on the cards correctly
You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01
The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:
p' ± [tex]Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]
Where [tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex] is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:
Every time the psychic has to identify a card he can make two choices:
"Success" he identifies the card correctly
"Failure" he does not identify the card correctly
If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25
Let's say, for example, that the card has the star symbol.
The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25
And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75
So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.
The value of Z will be [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
Now using the formula you have to clear the sample size:
[tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]
[tex]\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex](\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}[/tex]
[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')[/tex]
[tex]n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2[/tex]
[tex]n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203[/tex]
To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.
I hope this helps!
Answer:
The sample size should be 6157
Step-by-step explanation:
Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.
Let us assume that the guess p = 0.25 as the value of p.
α = 1 - C = 1 - 0.95 = 0.05
[tex]\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]
The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore [tex]Z_\frac{\alpha }{2}=Z_{0.025}=1.96[/tex]
To determine the sample size n, we use the formula:
[tex]Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157[/tex]
FIND P(NOT 6) WHEN YOU ROLL A STANDARD NUMBER CUBE THEN DESCRIBE THE LIKELIHOOD OF THE EVENT WRITE IMPOSSIBLE ,UNLIKELY , EQUALLY LIKELY , LIKLEY OR CERAIN
Answer: LIKLEY
Step-by-step explanation:
Formula : Probability [tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
A standard cube has six numbers on it (1,2,3,4,5 and 6).
P( NOT 6) =[tex]\dfrac{\text{Numbers that are not 6}}{\text{Total numbers}}[/tex]
[tex]=\dfrac{5}{6}=0.8333[/tex]
We know that when the probability of any event lies between 0.5 and 1then the event is said to be likely to happen.
Since , P(not 6)=0.8333 which lies between 0 and 0.5.
That means, it is likely to happen.
Note :
When probability of having A = 0 , we call A as uncertain event.
When probability of having A = 1 , we call A as certain event.
When probability of having A = 0.5 , we call A as equally likely event.
When probability of having A lies between 0 and 0.5 , we call A as unlikely event.
When probability of having A lies between 0.5 and 1 , we call A as likely event.
Skyler is out shopping and sees that striped shirts are on sale for
$19.00 each, and plaid pants are on sale for $19.50 each. He
buys 8 shirts and 6 pairs of pants. What is the total of his
purchase?
The total was $_______
Answer:
His total is $269
Step-by-step explanation:
8x19 = 152
6x19.50 = 117
152+117 = 269
Which ordered pair is the solution of the system of equations? 3x+2y=4, -2+2y=24
Answer:
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
y = 13
Step-by-step explanation:
→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):
-2 + 2y = 24
2y = 26
y = 13
→Then, plug in 13 for y into the other equation:
3x + 2y = 4
3x + 2(13) = 4
3x + 26 = 4
3x = -22
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
The volume of pyramid = 1/3 wlh
Where w = width, l = length and h = height
While,
The volume of rectangular prism = wlh
So,
The volume of pyramid = 1/3(the volume of prism)
Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication. At this rate of decay, how many bacteria will there be in 8 hours?
Answer:
There will be 66 bacteria in 8 hours.
Step-by-step explanation:
The number of bacteria after t hours is given by the following formula.
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initual number of bacteria and r is the decay rate.
Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.
This means that [tex]P(0) = 750000, P(48) = 250[/tex]
We use this to find r. So
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]250 = 750000(1-r)^{48}[/tex]
[tex](1-r)^{48} = \frac{250}{750000}[/tex]
[tex]\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}[/tex]
[tex]1-r = 0.84637[/tex]
So
[tex]P(t) = 750000(0.84637)^{t}[/tex]
How many bacteria will there be in 8 hours?
8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).
[tex]P(56) = 750000(0.84637)^{56} = 65.83[/tex]
Rounding to the nearest number
There will be 66 bacteria in 8 hours.
Answer:
197,488
Step-by-step explanation:
This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.
Identify the variables in the formula.
AA0ktA=250=750,000=?=48hours=A0ekt
Substitute the values in the formula.
250=750,000ek⋅48
Solve for k. Divide each side by 750,000.
13,000=e48k
Take the natural log of each side.
ln13,000=lne48k
Use the power property.
ln13,000=48klne
Simplify.
ln13,000=48k
Divide each side by 48.
ln13,00048=k
Approximate the answer.
k≈−0.167
We use this rate of growth to predict the number of bacteria there will be in 8 hours.
AA0ktA=?=750,000=ln13,00048=8hours=A0ekt
Substitute in the values.
A=750,000eln13,00048⋅8
Evaluate.
A≈197,488.16
At this rate of decay, researchers can expect 197,488 bacteria.
If 6 newborn babies are randomly selected, how many different gender sequences are possible?
Answer:
720
Step-by-step explanation:
6!
6x5x4x3x2x1=720
A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
H0: \mu \leq 5 days versus H1: \mu > 5 days. At \alpha = .05, choose the right option.
a) Reject H0 if tcalc < 1.7960
b) Reject H0 if tcalc >1.7960
Answer:
The degrees of freedom first given by:
[tex]df=n-1=12-1=11[/tex]
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
[tex] t_{\alpha}= 1.796[/tex]
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
Step-by-step explanation:
Information given
5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
System of hypothesis
We want to test if the true mean is higher than 5, the system of hypothesis are :
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The degrees of freedom first given by:
[tex]df=n-1=12-1=11[/tex]
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
[tex] t_{\alpha}= 1.796[/tex]
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
Find the amount to which $2,500 will grow if interest of 6.75% is compounded quarterly for 10
years.
Find the amount to which $2,500 will grow if interest of 6.75% is compounded daily for 10
years.
Answer:
Part a
For this case n = 4. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]
Part b
For this case n = 365. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]
Step-by-step explanation:
We can use the future vaue formula for compound interest given by:
[tex] A= P(1+ \frac{r}{n})^{nt}[/tex]
Where P represent the present value, r=0.0675 , n is the number of times that the interest is compounded in a year and t the number of years.
Part a
For this case n = 4. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]
Part b
For this case n = 365. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]
Find the area of the triangle
Answer:
Step-by-step explanation:
The formula for the area of a triangle is base*height divided by 2. Remember this because itll be important for everything you do in math relating to geometry and calculus. Assuming you go that far
[tex]\frac{base*height}{2} =\frac{14*8}{2} =\frac{112}{2} = 56 units^2[/tex]
Answer:
A =56 units^2
Step-by-step explanation:
The area of a triangle is given by
A =1/2 bh where 14 is the base and 8 is the height
A = 1/2 (14)8
A =56 units^2
In a particular region, for families with a combined income of $75,000 or more, 15% of these families have no children, 35% of the families have one child, 45% have two children, and 5% have three children. Use this information to construct the probability distribution for X, where x represents the number of children per family for this income group. Arrange x in increasing order and write the probabilities P(x) as decimals
Answer:
The probability distribution for x:"number of children per family for this income group" is:
[tex]\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\[/tex]
Step-by-step explanation:
With the information given we have the relative frequencies of each category.
We know:
[tex]\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\[/tex]
Which number is irrational
Answer:
Can you give the question. Can you post the picture. I can help solve. I will edit this answer once you have given the question/picture.
is 7.68 bigger than 7.680
Answer:
literally 7.68=7.680
Help asap giving branlist!!!
Answer:
D.
Step-by-step explanation:
So you know you have to have $62 as the base fee.
If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.
You get C = 62 + 30(g - 2)
Answer:
anwser is d because it is write.
Step-by-step explanation:
What is the missing side length?
Answer:
8 yds
Step-by-step explanation:
The sides have to have the same length
14 yd = 6yd + ?
Subtract 6 from each side
14-6 = 8
8 yds
The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. Is the process in control or out of control and why?
Answer:
Step-by-step explanation:
The mean of the reading points is
Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48
The process is out of control if the mean salt level of the readings is greater than 5.4
For the null hypothesis,
µ = 5.4
For the alternative hypothesis,
µ > 5.4
This is a right tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5.4
x = 5.48
σ = 0.3
n = 10
z = (5.48 - 5.4)/(0.3/√10) = 0.84
Looking at the normal distribution table, the probability corresponding to the z score is 0.7996
The probability value to the right of the z score is 1 - 0.7996 = 0.2
Assuming a significance level of 0.05
Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.
Please answer this correctly I have to finish this today as this is my deadline
Answer:
r = 1.499619733762 m There is no such thing a quarter radius!
C = 9.4223886775301 m
A = 7.065 m^2
Step-by-step explanation:
Calculate r and C | Given A
Given the area of a circle calculate the radius and circumference
r = √(A / π)
C = 2πr
Agenda:
r = radius
C = circumference
A = area
π = pi = 3.1415926535898
√ = square root
What is the volume of the rectangular prism?
Answer:
10ft[tex]{3}[/tex]
Step-by-step explanation:
One face has 15 blocks of 1/3 ft. You can clearly see 2 sets of blocks.
15 x 2 = 30
30 ÷ 3 or 30 x 1/3
= 10 ft cubed
In order to understand reasons why consumers visit their store, a local business conducts a survey by asking the next 100 people who visit their store to fill out a short survey. The business finds that 40 of the 100 people state that the main reason they visited the store was because the store is running a sale on coats that week. A confidence interval is constructed for the population proportion of consumers who would visit the store because of the coat sale. Which confidence interval would be the narrowest?
a. 90%
b. 99%
c. 95%
d. 85%
Answer:
d. 85%
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The higher the confidence level, the higher the value of z, which means that the margin of error will be higher and the interval will be wider,
Which confidence interval would be the narrowest?
The one with the lowest confidence level. So the answer is d.
Write an equation of a line that passes through (-6, 1), parallel to y = 2x – 6.
Answer:
y = -1/2x - 2
Step-by-step explanation:
If it's parallel, that means that the slope is the opposite of the one in the given equation, meaning that 2 would be flipped and turned negative into -1/2.
Then, fill in the x and y values to get the y-intercept.
1 = -1/2(-6) + b
1 = 3 + b
-2 = b
So your answer is y = -1/2x - 2
Please answer this correctly
Answer:
[tex]h=\sqrt{1.44}\\h = 1.2[/tex]
Step-by-step explanation:
Base of the triangle on the left = 0.5
Use pythagorean theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
Substitute
[tex]0.5^{2} + b^{2} = 1.3^{2}[/tex]
[tex]b^{2} = 1.3^2 - 0.5^2[/tex]
[tex]b^2 = 1.44[/tex]
[tex]b = \sqrt{1.44} \\[/tex]
[tex]b = 1.2[/tex]
in this case b is the height
so
[tex]h=\sqrt{1.44}\\h = 1.2[/tex]
The mean height of women in a country (ages 20minus29) is 64.2 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume sigmaequals2.84. The probability that the mean height for the sample is greater than 65 inches is nothing.
Answer:
[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]
And we can find the probability using the complement rule and with the normal standard table like this:
[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]
The probability that the mean height for the sample is greater than 65 inches is 0.007
Step-by-step explanation:
Let X the random variable that represent the women heights of a population, and we know the following parameters
[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]
We are interested on this probability
[tex]P(X>65)[/tex]
Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we find the z score for 65 inches we got:
[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]
And we can find the probability using the complement rule and with the normal standard table like this:
[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]
The probability that the mean height for the sample is greater than 65 inches is 0.007
80 81 82 83 84 85 86 87 88 89 90
Anika's test scores are shown below.
Anika's Test Scores
80 81 82 83 84 85 86 87 88 89 90
Which statement compares the shape of the two dot plots?
There is a gap in both plots.
There is a gap in Anika's scores, but not in Lorenzo's scores.
The data is widely spread across both plots.
The data is more widely spread for Lorenzo's scores than for Anika's.
Mark this and return
Save and Exit
Answer:
D :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Braily please
1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]
Hope this helps!
What is the difference of the polynomials? (–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)
Answer:
-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵
Step-by-step explanation:
(–2x³y² + 4x²y³ – 3xy⁴) – (6x⁴y – 5x²y³ – y⁵)=
–2x³y² + 4x²y³ – 3xy⁴ – 6x⁴y + 5x²y³ + y⁵=
-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵
Ralph is 3 times as old as Sara. In 4 years, Ralph will be only tice as old as Sara will be then.
If x represents Sara's age now, which of the following expressions represents Ralph's age in four years?
A. 3x
B. 2x+4
C. 3x+4
Answer:
In 6 years, Ralph will be only twice as old as Sara
Step-by-step explanation:
Answer:
The answer is C, 3x+4
Step-by-step explanation:
The “in four years” part translates to +4. The 3x translates to 3 times his current age. Hope this helped :)
An appliance repairman charges $25 plus $40 per hour for house calls. Write the rule as an equation that relates hours worked x and his fee y.
To get the total fee, you need to multiply the hourly rate by number of hours worked and add that to the flat fee of $25.
The equation would be y = 40x + 25
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer: f(x)=2-x^2
Step-by-step explanation:
The quadratic equation is
y=ax^2+bx+c
and c is equal to the y-intercept.
in the twi graphs shown both have the same shape but different y-intervepts.
c(the y-intercept) in the first graph is 5 and in the second graph(F) is 2.
On the graphing calculator it says that f(x)=2-x^2 is the correct answer therefore it is correct.
Which set of ordered pairs does NOT represent a function ?
Answer:
The answer is C.
Step-by-step explanation:
For a function, we do a vertical line test. If there is more than one point in one single x-position, it is not a function. Example, the ordered pairs (1, 1) and (1, 2) do NOT describe a function because there are more than one point on x=1.
