Answer:
9.88% probability that fewer than 5 of them use their smartphones in meetings or classes.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they use their smartphone is meetings or classes, or they do not. The probability of an adult using their phones is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
56% use them in meetings or classes.
This means that [tex]p = 0.56[/tex]
12 adult smartphone users are randomly selected
This means that [tex]n = 12[/tex]
Probability that fewer than 5 of them use their smartphones in meetings or classes.
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.56)^{0}.(0.44)^{12} = 0.0001[/tex]
[tex]P(X = 1) = C_{12,1}.(0.56)^{1}.(0.44)^{11} = 0.0008[/tex]
[tex]P(X = 2) = C_{12,2}.(0.56)^{2}.(0.44)^{10} = 0.0056[/tex]
[tex]P(X = 3) = C_{12,3}.(0.56)^{3}.(0.44)^{9} = 0.0239[/tex]
[tex]P(X = 4) = C_{12,4}.(0.56)^{4}.(0.44)^{8} = 0.0684[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0001 + 0.0008 + 0.0056 + 0.0239 + 0.0684 = 0.0988[/tex]
9.88% probability that fewer than 5 of them use their smartphones in meetings or classes.
n a survey from 1998, 449 teenagers were surveyed about the music that they listen to. Of these teenagers, 129 of them said that their favorite genre of music is hip-hop. In a similar survey from 2008, 176 of 509 teenagers surveyed said that their favorite genre is hip-hop. Use a two-proportion hypothesis test to determine whether the proportion of teenagers whose favorite genre of music is hip-hop has changed from 1998 to 2008. Assume that the samples are random and independent. Use α=0.01. Let the sample from 1998 correspond to sample 1 and the other to sample 2. (a) Which answer choice shows the correct null and alternative hypotheses for this test?
Answer:
We accept H₀
Step-by-step explanation:
To compare two proportion:
proportion 1. 1998
n₁ = 449
p₁ = 129/449 p₁ = 0,2873
proportion 2. 2008
n₂ = 509
p₂ = 176/509 p₂ = 0,3457
Test hypothesis
Null Hypothesis H₀ p₂ - p₁ = 0
Alternative Hypothesis Hₐ p₂ > p₁
We have a one tail test ( to the right)
As α = 0,01 we find in z-table the z score z = 2,29 ( approximation for 0,011)
To calculate z(s),
z(s) = ( p₂ - p₁ ) /√ p*q ( 1/n₁ + 1/n₂)
p = ( x₁ + x₂ ) / n₁ + n₂
p = 129 + 176 / 449 +509
p = 0,3184 and q = 1 - p q = 0,6816
1/n₁ + 1/n₂ = 1/ 449 + 1 / 509 = 0,00222 + 0,001964
1/n₁ + 1/n₂ = 0,004184
z(s) = 0,0584/ √(0,3184*0,6816)*0,004184
z(s) = 0,0584/ 0,03013
z(s) = 1,938
z(s) < z(c) 1,938 < 2,29
z(s) is in the acceptance region we accept H₀ at α = 0,01
A farmer is enclosing a rectangular area for a pigpen. He wants the length of the pen to be 20 ft longer than the width. The farmer can use no more than 100 ft of fencing. What is the pen’s greatest possible length? Let w represent the width of the pen. What expression represents the length?
Answer:
Width is 15, length is 35.We can check our answer by multiplying the length by 2 and the width by two in order for the perimeter to be equal to 200.15 times 2 is 30 and 35 times two equals 70.70+30=100 so our solution satisfies our problem.
Step-by-step explanation:
Let the width be x.Then the length should be x+20.The farmer can’t use more than 100 ft of fencing and by mentioning enclosing a rectangle area for a pigpen, we can tell that 100 is the perimeter.So 2(x+20) + 2(x)=100.2x+ 40 + 2x=100.4x+40=100.4x=60.X is 15 which is the width so then the length is 35.
A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.
Rating (last year): 87 67 68 75 59 60 50 41 75 72
Rating (this year): 85 52 51 53 50 52 80 44 48 57
Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the rating from last year and x2 be the rating from this year and use the formula d=x2âx1 to calculate the paired differences. Round your answer to one decimal place.
Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.
Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 4 of 4: Construct the 90%90% confidence interval. Round your answers to one decimal place.
Answer:
Step 1 of 4
Point estimate for the population mean of the paired differences = -8.2
Step 2 of 4
Sample standard deviation of the paired differences = 16.116244
Step 3 of 4
Margin of Error = ±9.326419
Step 4 of 4
90% Confidence interval = (-17.5, 1.1)
Step-by-step explanation:
The ratings from last year and this year are given in table as
Rating (last year) | x1 | 87 67 68 75 59 60 50 41 75 72
Rating (this year) | x2| 85 52 51 53 50 52 80 44 48 57
Difference | x2 - x1 | -2 -15 -17 -22 -9 -8 30 3 -27 -15
Step 1 of 4
Mean = (Σx)/N = (-82/10) = -8.2 to 1 d.p.
Step 2 of 4
Standard deviation for the sample
= √{[Σ(x - xbar)²]/(N-1)} = 16.116244392951 = 16.116244 to 6 d.p.
Step 3 of 4
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = -8.2
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 10 - 1 = 9.
Significance level for 90% confidence interval
= (100% - 90%)/2 = 5% = 0.05
t (0.05, 9) = 1.83 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 16.116244
n = sample size = 10
σₓ = (16.116244/√10) = 5.0964038367
Margin of Error = (Critical value) × (standard Error of the mean) = 1.83 × 5.0964038367 = 9.3264190212 = 9.326419 to 6 d.p.
Step 4 of 4
90% Confidence Interval = (Sample mean) ± (Margin of Error)
CI = -8.2 ± (9.326419)
90% CI = (-17.5264190212, 1.1264190212)
90% Confidence interval = (-17.5, 1.1)
Hope this Helps!!!
A director of the library calculates that 10% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 899 books would be less than 11%? Round your answer to four decimal places.
Answer:
0.8413
Step-by-step explanation:
p = 0.10
σ = √(pq/n) = 0.01
z = (x − μ) / σ
z = (0.11 − 0.10) / 0.01
z = 1
P(Z < 1) = 0.8413
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
We have,
We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.
First, we need to calculate the mean and standard deviation of the binomial distribution:
Mean:
np = 899 × 0.1 = 89.9
Standard deviation:
√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427
Next, we need to standardize the sample proportion of 11% using the formula:
z = (x - μ) / σ
where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Substituting the values we have, we get:
z = (0.11 - 0.1) / 0.9427 = 0.1059
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.
Therefore,
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
Rounded to four decimal places, the answer is 0.5425.
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A number cubed is rolled. What is the probability that a one or six will be rolled
Answer: 1/3
Step-by-step explanation: Since there are six sides to a number cube, the total number of outcomes will be 6.
Since there are 2 favorable outcomes, rolling a 1 or a 6,
the probability of rolling a 1 or a 6 is 2/6 which reduces to 1/3.
Answer:
1/3
Step-by-step explanation:
A cube by default has 6 sides, and a number cube generally is tallied from 1 - 6 (being the numbers are 1, 2, 3, 4, 5, 6).
You are solving for the probability of the numbers 1 or 6 being rolled, which are 2 numbers of the given amount. Change into a fraction form by placing part over the total amount of numbers:
2/6
Most likely, you will be told to simplify. Divide common factors from both the numerator & denominator:
(2/6)/(2/2) = 1/3
1/3 is the probability that a 1 or a 6 is rolled in a standard number cube.
~
If you shifted y=3x+6 five units to the right, what would the linear equation be? (Hopefully it's challenging and easy at the same time.)
Answer:
[tex]3x + 6 = y \\ 3x = y - 6 \\ \frac{3x}{3} = \frac{y - 6}{3} \\ x = \frac{y - 6}{3} \\ x = \frac{y}{ 3 } - 2[/tex]
Answer:
y = 3x - 9
Step-by-step explanation:
y = 3x + 6 is a linear equation.
Shift the equation 5 units to the right.
The linear equation becomes:
y = 3x - 9
PLZ I need Help the Question is: 5+13·18+85÷17−11
Answer:
233
Step-by-step explanation:
Which statement explains if a dilation was applied? A dilation was applied to the fabric because the width of the fabric was preserved. A dilation was applied to the fabric because the angle measures were preserved. A dilation was not applied to the fabric because the angle measures are the same. A dilation was not applied to the fabric because the length was changed, not the width.
Answer:
A dilation was not applied to the fabric because the length was changed, not the width.
Step-by-step explanation: B was not the answer it was D.
Answer:
D.
Step-by-step explanation:
Edge 2022.
g Determine whether the statement is true or false. If fx(a, b) and fy(a, b) both exist, then f is differentiable at (a, b). True False Correct: Your answer is correct.
Answer:
False
Step-by-step explanation:
A function is said to be differentiable over a given region if the function is continuous and has only one value for each input.
Therefore in order to conclude that f is differentiable at (a, b), the partial derivatives must be continuous at (a, b).
It is true that the function has to be defined over a given region because without it, you cannot determine if a partial derivative is continuous or otherwise.
But the fact that the partial derivatives exist at a point is not a sufficient condition for continuity.
Find the circumference and the area of a circle with diameter 8 yd.
Use the value 3.14 for, and do not round your answers.
I need the area and circumference!!
Answers:
area = 50.24 square yards
circumference = 25.12 yards
values are approximate
================================================
Work Shown:
d = 8 is the diameter
r = 4 is the radius, half the diameter
pi = 3.14 approximately
C = 2*pi*r = circumference
C = 2*3.14*4
C = 25.12 yards is the circumference. The circumference is the distance around the circle, aka the perimeter
An alternative formula you can use is C = pi*d
-------------------
A = area of circle
A = pi*r^2
A = 3.14*4^2
A = 50.24 square yards is the area
Answer:
25.12 and 50.24
Step-by-step explanation:
8/2=4
4= radius
8= diameter
3.14*8=25.12
This would be the circumfrence (25.12)
3.14*4^2
3.14*16
50.24
This would be the area (50.24)
Hope this helps!
As a prize for winning a contest, the contestant is blindfolded and allowed to draw 3 dollar bills one at a time out of an urn. The urn contains forty $1 bills and ten $100 bills. The urn is churned before each selection so that the selection would be at random. What is the probability that none of the $100 bills are selected
Answer:
The probability that none of the $100 bills are selected is 79.6%.
Step-by-step explanation:
The urn contains forty $1 bills and ten $100 bills. This gives a total of 50 bills in the urn.
To draw 3 dollar bills one at a time out of an urn, the probability of not selecting a $100 bill, decreases with each selection.
And the probability of not selecting a $100 bill is the probability of selecting a $1 bill in the first selection = 80% (40/50 x 100).
The probability of selecting a $1 bill the second time = 79.6% (39/49).
The probability of selecting a $1 bill the third time = 79.2% (38/48).
The sum of the probabilities divided by 3 = 79.6% (238.8/3)
b) Probability arises when there is a chance that an event may occur from a set of events that could have occurred. It is based on an estimate that one event happens when all the events in the set are given no less equal chance.
Find the 10th term of the geometric sequence whose common ratio is 1/2 and whose 1st term is 2.
Answer:
[tex]\frac{1}{256}[/tex]
Step-by-step explanation:
Geometric sequence means there is a common ratio. All that means is term divided previous term is the same across your sequence.
ONE WAY:
So we are given here that:
[tex]\frac{f(2)}{f(1)}=\frac{1}{2}[/tex] and that the first term which is [tex]f(1)[/tex] is 2.
[tex]\frac{f(2)}{2}=\frac{1}{2}[/tex]
This implies [tex]f(2)=1[/tex] after multiplying both sides by 2 and getting that [tex]f(2)=\frac{1}{2}(2)=\frac{2}{2}=1[/tex].
So you have that
2,1,...
basically you can just multiply by 1/2 to keep generating more terms of the sequence.
Third term would be [tex]f(3)=1(\frac{1}{2})=\frac{1}{2}[/tex].
Fourth term would be [tex]f(4)=\frac{1}{2}(\frac{1}{2})=\frac{1}{4}[/tex].
...keep doing this til you get to the 10th term.
ANOTHER WAY:
Let's make a formula.
[tex]f(n)=ar^{n-1}[/tex]
[tex]a[/tex] is the first term.
[tex]r[/tex] is the common ratio.
And we want to figure out what happens at [tex]n=10[/tex].
Let's plug in our information we have
[tex]a=2[/tex]
[tex]r=\frac{1}{2}[/tex]:
[tex]f(10)=2(\frac{1}{2})^{10-1}[/tex]
Put into calculator or do by hand...
[tex]f(10)=2(\frac{1}{2})^9[/tex]
[tex]f(10)=2(\frac{1^9}{2^9})[/tex]
[tex]f(10)=2(\frac{1}{2^9})[/tex]
[tex]f(10)=\frac{2}{2^9}[/tex]
[tex]f(10)=\frac{2}{2(2^8)}[/tex]
[tex]f(10)=\frac{1}{2^8}[/tex]
Scratch work:
[tex]2^8=2^5 \cdot 2^3=32 \cdot 8=256[/tex].
End scratch work.
The answer is that the tenth term is [tex]\frac{1}{256}[/tex]
Answer:
For an nth term in a geometric sequence
[tex]U(n) = a ({r})^{n - 1} [/tex]
where n is the number of terms
r is the common ratio
a is the first term
From the question
a = 2
r = 1/2
n = 10
So the 10th term of the sequence is
[tex]U(10) = 2 ({ \frac{1}{2} })^{10 - 1} \\ \\ = 2 ({ \frac{1}{2} })^{9} \\ \\ \\ = \frac{1}{256} [/tex]
Hope this helps you
Find the missing side and round the answer to the nearest tenth. Thanks.
Answer:
22.2
Step-by-step explanation:
The missing side is x
cos19° = 21/x switch x and cos19° x = 21/cos 19°x = 22.21≈ 22.2
Lindsey made an error while solving this equation. 143.5 = 2 - (7(x+3). What line has the error?
(Refer to image)
A: Step 1
B: Step 2
C: Step 3
D: Step 4
Answer:
Step 1
Step-by-step explanation:
She didn't distribute the negative while she distributed 7. It should be -7x - 21, not 7x - 21.
Marvin and Ruby had the same number of stickers. After Marvin gave 12 stickers to Ruby, Ruby had 4 times as many as Marvin. How many stickers did Ruby have in the beginning?
Answer:
20 Tickets
Step-by-step explanation:
Given
Marvin and Ruby had the same number of stickers.
Let
no. of tickets with Ruby = No. of tickets with Marvin = x
condition
Marvin gave 12 ticket to Ruby
Now\
no. of tickets with Ruby = x+12
No. of tickets with Marvin = x-12
Ruby had 4 times as many as Marvin
Thus,
no. of tickets with Ruby = 4* No. of tickets with Marvin
x+12= 4(x-12) = 4x-48
x+12 = 4x-48
adding 48 both sides
x+12 +48= 4x-48+48
x+60 = 4x
subtracting 4 from both sides
x+60 -x= 4x -x
60 = 3x
dividing both side by 3
60/3 = 3x/3
x = 20
Thus, Ruby had 20 tickets in the beginning.
what is refraction of light
Answer:
Refraction is what happens when light passes through some medium and changes it's direction because of it. For instance, when light travels through a lens light is bent as it goes from air to glass and back to air again. :)
The table shown lists the atomic weight of the elements that begin with the letter c. What's the range of these
atomic weights?
Review My Answers
Save & EVE
No. Atomic Weight Name 48112411 2040078 98251000
Cadmium cd Calcium Ca Californium Cf Carbon Cerium Ce Cesium Cs Chlorine C Chromium Cr Cobalt Co Copper Cu Curium Cm
6 12.011 58140116 55132906 1735453 2451996 2758933 2963546 96 *247.00
A. 215.547
B. 238.989
C. 234.989
D. 134.589
The Answer is 2
34.989.I used a physics book
Write the equation of each line in slope intercept form (If possible please show work)
Hope it make sense now :)
If a carton contains 6 eggs, how many eggs are there in 13 cartons? would it be 6x13?? which is equal to 78 I'm not sure.
Answer:
78 eggs
Step-by-step explanation:
13 × 6 = 78 eggs
Hope this helps! :)
Answer:
Yes it would be 6x13=78
Step-by-step explanation:
cross multiplication and divide:
1 cartoon = 6 eggs
13 cartoons = x
7. Factor by grouping.
6p2 - 17p - 45
A (2p - 9)(3p + 5)
B (2p + 9)(3p + 5)
7096
Oc
C (2p - 9)(3p - 5)
90%
D (2p + 9)(3p - 5)
ping
Answer:
Step-by-step explanation: 4
The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname If more than one surname begins with a letter besides A and O, how may surnames begin with that letter?
Step-by-step explanation:
40children - 23 (with A, O) = 17left
26 letter in alphabet- ( A, O) = 24 letter left
24 letters left - 14 (not used for 1st letters) = 10
10 letters left to use/ 17 children left
10÷17 = 0.5882352941 x 10 =5.8 or as close to 6 I can get
There are six surnames that start with each letter other than A and O when more than one surname does.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, The surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A.
Since, 14, of the letters of the alphabet do not appear as the first letter of a surname
14 of the letters of the alphabet do not appear as the first letter of the surname
∴ the no. of letters that appeared = 26-14 = 12 alphabets
15 surnames begin with 10 letters beside O and A
∴ 6 surnames begin with a letter
Therefore, If more than one surname begins with a letter besides A and O, 6 surnames begin with that letter.
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A researcher wishes to see if the average number of sick days a worker takes per year is less than 5. A random sample of 30 workers at a large department store had a mean of 4.8. The standard deviation of the population is 1.2 days. Is there enough evidence to support the claim at alpha = 0.01?
Answer:
No. At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average number of sick days a worker takes per year is significantly less than 5.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]
The significance level is 0.01.
The sample has a size n=30.
The sample mean is M=4.8.
The standard deviation of the population is known and has a value of σ=1.2.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.2}{\sqrt{30}}=0.219[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{4.8-5}{0.219}=\dfrac{-0.2}{0.219}=-0.913[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-0.913)=0.181[/tex]
As the P-value (0.181) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.
Using the z-distribution, it is found that since the test statistic is greater then the critical value for the left-tailed test, this is not enough evidence to support the claim at [tex]\alpja = 0.01[/tex].
At the null hypothesis, it is tested if the number of sick days is of at least 5, that is:
[tex]H_0: \mu \geq 5[/tex]
At the alternative hypothesis, we test if it is less than 5, that is:
[tex]H_1: \mu < 5[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 4.8, \mu = 5, \sigma = 1.2, n = 30[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{4.8 - 5}{\frac{1.2}{\sqrt{30}}}[/tex]
[tex]z = -0.91[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.01 is of [tex]z^{-\ast} = -2.327[/tex].
Since the test statistic is greater then the critical value for the left-tailed test, this is not enough evidence to support the claim at [tex]\alpja = 0.01[/tex].
A similar problem is given at https://brainly.com/question/16194574
I NEED HELP PLEASE, THANKS! :)
Answer:
[tex]10e^{i\frac{7\pi}{4}}[/tex]
Step-by-step explanation:
The magnitude of the number is ...
[tex]|5\sqrt{2}-5i\sqrt{2}|=\sqrt{(5\sqrt{2})^2+(-5\sqrt{2})^2}=\sqrt{50+50}=10[/tex]
The angle of the number is in the 4th quadrant:
[tex]\arctan{\dfrac{-5\sqrt{2}}{5\sqrt{2}}}=\arctan{(-1)}=\dfrac{7\pi}{4}[/tex]
So, the exponential form of the number is ...
[tex]\boxed{10e^{i\frac{7\pi}{4}}}[/tex]
1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
divide by a fraction = multiply by reciprocal
1/4 * 8/3
2/3
Answer:
⅔
Step-by-step explanation:
= ¼ ÷ ⅜
= ¼ × ⁸/3
= ⅔
Have a great day !
PLEASE HELP!!(PIC INCLUDED)
Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 3 units right and 2 units down
B. shifted 4 units right and 2 units down
C. shifted 2 units right and 3 units down
D. shifted 3 units right and 1 unit down
Answer:
A. Shifted 3 unit right and 2 unit down
Step-by-step explanation:
Let's determine the reason for the answer.
We will use a reference point, only one point to determine the reason.
Because the both shape are identical.
Let's use point A
The position of A is 2 on the y axis and 1 on the x axis
While the position of A' is 0 on the y axis and 4 on the X asis
Let's know how many units where moved from the position.
A' -A
For X axis
4-1= 3
For y axis
0-2= 2(we need only the magnitude)
So its 2 units Down and 3 unit right
Given: a concave polygon Conjecture: It can be regular or irregular
Answer:
[tex]false[/tex]Step-by-step explanation:
A concave polygon can never be regular (all sides and angles must be congruent). Hope this helps..
I NEED HELP PLEASE, THANKS! :)
As you know, a parallelogram's area is calculated by multiplying the length of it's sides, so all we are being asked to do is find the product of u and v -
[tex]( - 4i - 9j + k )( - 6i + j + 5k ),\\[/tex]
You would apply cross products in order to determine u * v. Doing so, you would get a solution of -46i + 14j - 58k.
Now we can take the magnitude of this vector -
u * v = √( - 46 )^2 + ( 14 )^2 - ( 58 )^2,
u * v = ( About ) 75.3 square units,
Solution = Option A
If4.3 x 0.37 = 1.591, then 0.43 x 370 is 3. 4. 5.
Answer:
0.43 x 370= 159.1
Step-by-step explanation:
A simple random sample of size has mean and standard deviation.Construct a confidence interval for the population mean.The parameter is the population The correct method to find the confidence interval is the method.
ANSWER:
EXPLANATION:
A simple random sample of size has mean and standard deviation. Construct a confidence interval for the population mean. The parameter is the population The correct method to find the confidence interval is the method.
The sample size is not given. Mean and Standard Deviation are not given.
To construct a confidence interval for the population mean, first find out the margin of error of the sample mean. This is why you need a confidence interval. If you are 90% confident that the population mean lies somewhere around the sample mean then you construct a 90% confidence interval.
This is equivalent to an alpha level of 0.10
If you are 95% sure that the population mean lies somewhere around the sample mean, your alpha level will be 0.05
In summary, get the values for sample size (n), sample mean, and sample standard deviation.
Make use of a degrees of freedom of (n-1).
A random sample of adult drivers was obtained where 52% were men and 46% were women. Note that everyone is not classified as a man or a women. A survey showed that 65% of the drivers rely on GPS systems. 30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected.
a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places.b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.
Answer:
a) P(G | M) = 0.577
b) P(W | G) = 0.523
c) P(M and G') = 0.220
d) P(M or G) = 0.870
e) P(G') = 0.350
Step-by-step explanation:
A random sample of adult drivers was obtained where 52% were men and 46% were women.
P(M) = 0.52
P(W) = 0.46
A survey showed that 65% of the drivers rely on GPS systems.
P(G) = 0.65
30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS.
P(M and G) = 0.30
P(W and G) = 0.34
a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places
P(G | M) = ?
Recall that conditional probability is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(G | M) = P(M and G)/P(M)
P(G | M) = 0.30/0.52
P(G | M) = 0.577
b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.
P(W | G) = ?
Recall that conditional probability is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(W | G) = P(W and G)/P(G)
P(W | G) = 0.34/0.65
P(W | G) = 0.523
c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.
P(M and G') = ?
Where G' means does not rely on a GPS system
P(M and G') = P(M) - P(M and G)
P(M and G') = 0.52 - 0.30
P(M and G') = 0.220
d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.
P(M or G) = ?
Using the addition rule of probability,
∵ P(A or B) = P(A) + P(B) - P(A and B)
For the given case,
P(M or G) = P(M) + P(G) - P(M and G)
P(M or G) = 0.52 + 0.65 - 0.30
P(M or G) = 0.870
e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.
P(G') = ?
P(G') = 1 - P(G)
P(G') = 1 - 0.65
P(G') = 0.350