Answer:
a)
0.3632 = 36.32% approximate probability that 15 or fewer turn right.
0.369 = 36.9% exact probability that 15 or fewer turn right.
b)
0.4801 = 48.01% approximate probability that at least two-thirds of those in the sample turn.
0.4868 = 48.68% exact probability that at least two-thirds of those in the sample turn.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Vehicles entering an intersection from the east are equally likely to turn left, turn right, or proceed straight ahead.
This means that [tex]p = \frac{1}{3}[/tex]
50 vehicles
This means that [tex]n = 50[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 50\frac{1}{3} = 16.67[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50\frac{1}{3}\frac{2}{3}} = 3.33[/tex]
a. 15 or fewer turn right.
Using continuity correction, this is [tex]P(X \leq 15 + 0.5) = P(X \leq 15.5)[/tex], which is the pvalue of Z when X = 15.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.5 - 16.67}{3.33}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a pvalue of 0.3632
0.3632= 36.32% approximate probability that 15 or fewer turn right.
Using a binomial probability calculator, to find the exact probability, we get a 0.369 = 36.9% exact probability that 15 or fewer turn right.
b. at least two-thirds of those in the sample turn.
Turn either left or right, so:
[tex]p = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}[/tex]
The standard deviation remains the same, while the mean will be:
[tex]\mu = E(X) = np = 50\frac{2}{3} = 33.33[/tex]
Two thirds of the sample is 33.33, so at least 34 turning, which, using continuity correction, is [tex]P(X \geq 34 - 0.5) = P(X \geq 33.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 33.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.5 - 33.33}{3.33}[/tex]
[tex]Z = 0.05[/tex]
[tex]Z = 0.05[/tex] has a pvalue of 0.5199
1 - 0.5199 = 0.4801
0.4801 = 48.01% approximate probability that at least two-thirds of those in the sample turn.
Using a binomial probability calculator, we find a 0.4868 = 48.68% exact probability that at least two-thirds of those in the sample turn.
Anwita and her sister have $230 in total. Anwita has x dollars and her sister has 20
less than quadruple what Anwita has. How much more money does Anwita need to
have the same amount as her sister?
Answer:
$130
Step-by-step explanation:
x (the $ Anwita has) + y (the $ her sister has) = 230
y = 4x - 20
=> x+y=230 => x + 4x - 20 = 230
=> 5x - 20 = 230 => 5x = 250
=> x = 50
=> y = 180
the difference between 180 and 50 (180 - 50) is 130.
so, Anwita needs $130 more to have the same amount as her sister.
What is the growth factor of the following example? Assume time is measured in the units given.
A diamond mine is depleted by 1% per day.
a. 1.01 per day c. 0.99 per day
b. 0.01 per day d. 99 per day
Please select the best answer from the choices provided.
Answer:
C. 0.99 per day
Step-by-step explanation:
I calculated it logically
In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=71°, and RS = 2.5 feet. Find the length of SQ to the nearest tenth of a foot.
9514 1404 393
Answer:
0.9 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(71°) = (2.5 ft)/SQ . . . . . . . . fill in the given values
SQ = (2.5 ft)/tan(71°) ≈ 0.8608 ft
The length of SQ is about 0.9 feet.
Give an example of a polynomial that is a perfect square. How do you know that it is a perfect square? Give its factored form.
Answer:
Step-by-step explanation:
A polynomial is a perfect square if has the form:
[tex]a^2+2ab+b^2[/tex]
Its factored form is [tex](a+b)^2[/tex].
We can obtain examples by taking any value of a and b.
For example:
[tex]a=x[/tex] anb [tex]b=2y[/tex].
Thus we obtain a polynomial that is a perfect square:
[tex]x^2+2(x)(2y)+(2y)^2=x^2+4xy+4y^2[/tex]
i am a 5 digit number,my ones place digit is of no use as i, i still remain same without it . my ten's and hundreds place digits are mirror images. my thousand place digit are half of 2nd, my 10thousand digit is 3 more than my ones place , who am i ?
Answer:
I think 34880.
Step-by-step explanation:
34880 I AM NOT SURE
Combine the like terms
-n + (-4) - (-4n) + 6
the simplest form of the given expression is 3n+2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
-n + (-4) - (-4n) + 6
= -n + (-4) + 4n + 6
= 3n -4 +6
= 3n+2
Hence the simplest form of the given expression is 3n+2.
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What about this one
Answer:
$9,167
Step-by-step explanation:
renee spent 1/8 of the day landscaping around the house. she spent 1/2 of that time pulling weeds. what fractions of the day did renee spend pulling the weed? PLS HELP IM HAVING A UNIT TEST ON MONDAY
Answer:
Renee spent 1/2 of the time she spent landscaping pulling weeds, which is 1/2 * 1/8 = 1/16 of the day. Therefore, Renee spent 1/16 of the day pulling weeds.
how many positive 10 digit numbers can you make using seven ones and three zeros
The number of positive 10 digit numbers that can be made using seven ones and three zeros is; 28
How to solve probability combinations?We want to find the number of positive 10 digit numbers that can be made using seven ones and three zeros.
Now, the leftmost position digit cannot be 0 and as such it is 1, due to the fact that there are no other possibilities.
The rightmost position therefore must be 0 in order to fill the need for an even number.
Thus, we have 8 remaining positions that we need to fill with six ones and two zeros using an arbitrary manner.
This means that we can place two digits of zero among 8 positions by using combination formula as;
⁸C₂ = 8!/(2! * 6*)
= 28 different ways
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Mean of 8, 3,5
and mean of 44,89,23
Answer:
mean of 8,3,5 = 5.333 or 16/3
mean of 44,89,23 = 52
Step-by-step explanation:
Answers and step-by-step explanations:
To find the mean, first, we are going to add all of the numbers, and divide by how many numbers there were. The first data set is:
8, 3, 5
Add them all up:
8 + 3 + 5 = 16
Then, since there were three numbers, we divide 16 by 3.
16/3 = 5.33
Therefore, the mean of 8, 3 and 5 is around 5.33.
The second data set is:
44, 89, 23
Add them up:
44 + 89 + 23 = 156
Then, divide it by how many numbers there were, which is 3.
156/3 = 52
Therefore, the mean of 44, 89 and 23 is 52. Hope this helps!
XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
Answer:
To calculate XYZ Company's total assets minus liabilities, you would need to add up all of the assets listed on the balance sheet and then subtract the sum of all the liabilities.
In this case, the total assets would be $45,000 + $41,000 + $134,000 = $220,000. The total liabilities would be $55,000 + $56,000 + $50,000 = $161,000.
So, the total assets minus liabilities would be $220,000 - $161,000 = $59,000.
Step-by-step explanation:
Can someone Help me please
Answer:
Lower quartile= 4
Middle quartile= 6
Upper quartile=8
WILL MARK BRAINLIEST
M
Answer:
∠BEC = 119°
Step-by-step explanation:
∠BAC = 47° because it is an alternate interior angle to 47°
∠BEA = 180 - 47 - 72 = 61°
∠DEC = ∠BEA because they are vertical angles
∠BEC = ∠DEA because they are vertical angles
∠BEC + ∠DEA + ∠BEA + ∠DEC = 360°
∠BEC + ∠DEA + 61 + 61 = 360°
∠BEC + ∠DEA = 238°
since ∠BEC = ∠DEA, then ∠BEC = 238/2 = 119°
someone please help me
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Solve for B. Enter the number that goes under the radical Symbol
The number that goes beneath the radical is 7
What is the Pythagoras theorem?The Pythagoras theorem is used to find side or angle of a right angled triangle.
If you are dealing with any right triangle with given sides, using the Pythagorean Theorem, as shown below, makes things relatively simple.
Note that the Pythagorean Theorem: is a²+b²=c²
a and b are both the smaller sides of the triangle, while c is the hypotenuse (the longest side of the triangle).
This impies in this case, that we have 4 equivalent right triangles with given sides and for the hypotenuse, so let's see what we need to solve for by writing down what we know in a form following the Pythagorean Theorem.
The Pythagoras Equation is a²+b²=c²
Where a=3, b =? c=4
Isolate the unknown value without plugging in our known values yet. This step is unnecessary, but can help if you have trouble with making mistakes with your algebra.
a²+b²=c²
⇒b²=c²-a²
a=√(c²-a²)
Plug in our given values and solve for .
a=√(4²-3²)
a=√(16-9)
a=√7
Conclusively, the radical number that goes beneath 7
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Complete question :
The complete question is found on the attachment
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.77. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 21 specimens from the seam was 4.85. (Round your answers to two decimal places.)
Answer:
The 95% CI for the true average porosity of a certain seam is (4.52, 5.18).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.77}{\sqrt{21}} = 0.33[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.33 = 4.52.
The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.33 = 5.18
The 95% CI for the true average porosity of a certain seam is (4.52, 5.18).
When working with piping offsets, which are based on right triangles. Which of the following angle measurements will you see as a standard elbow angle? a. 22.5, b. 60, c. 70. d.45
Answer:
d. 45°
Step-by-step explanation:
You want to know which from your list is a standard elbow angle.
ElbowAn elbow is a pipe fitting that is used to change the direction of piping. Elbows can be used together to produce an offset and/or a change in the plane of the piping.
Standard elbow angles commonly are 90°, 45°, and, less commonly, 22.5°. The greater the angle, and/or the smaller the bend radius, the more resistance to flow it has.
The best choice of answer here is 45°.
__
Additional comment
The typical elbow has the same kind of threads on both sides. A "street elbow" has male threads on one side and female threads on the other side.
Elbow joints are not necessarily threaded. They may also be soldered, welded, or compression joints.
How many pairs of potential clients can be randomly chosen from pool or eight candidates
There are 34 ways by which pairs of potential clients can be randomly chosen from pool or eight candidates.
What is combination?We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.
As such we would have the use of the formula for combination as follows;
C = n!/r!( n - r)!
C = 8!/2!(8 - 2)!
C = 8 * 7 * 6!/2! 61
C = 8 * 7/ 2 * 1
C = 28
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Write an equation for the graph above
Answer:
y = 1/2x + 0
Step-by-step explanation:
Determine the lateral area and the surface area of a right rectangular prism that has rectangular bases measuring 2"x4" and a height of 8".
Answer:
112 in^2
Step-by-step explanation:
Given data
Length =2in
Width= 4in
Height=8 in
The expression for the total surface area is
SA=2lw+2lh+2hw
SA= 2*2*4+2*2*8+ 2* 4*8
SA= 16+ 32+ 64
SA= 112 in^2
Hence the surface area is 112 in^2
The Lateral area or the total surface area of the prism is 112 [tex]in^{2}[/tex].
The lateral surface area of a rectangular object is the sum of the surface areas of all the sides, which is its total surface area.
According to the question, let us assume,
width w = 2 in
length l = 4 in
height h = 8 in
The lateral surface area is
S = 2lw + 2lh + 2hw since the opposite faces have same dimensions
S = 2×4×2 + 2×4×8 +2×2×8
S = 112 [tex]in^{2}[/tex]
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Find the surface area of the give cube.
28 in
Answer:
4704 in²
Step-by-step explanation:
We are given that,
Edge of the cube = 6 inWe are asked to to find the surface area of the cube.
Surface area generally refers to total surface area .
[tex]\bigstar \: \boxed{\sf {Surface \; Area_{(Cube)} = 6a^2 }} \\ [/tex]
a denotes edge of the cube.→ Surface area of cube = 6 × (28)² in²
→ Surface area of cube = 6 × 784 in²
→ Surface area of cube = 4704 in²
[tex] \therefore [/tex] Surface area of cube is 4704 in².
Write the following number in correct scientific notation: 0.003538
Ski
Answer:
[tex] = 3.538 \times {10}^{ - 3} [/tex]
Which choice is equivalent to the expression below?
810
O A. 92
O B. 1
O C. 81
O D.O
Answer:
B) 1
Step-by-step explanation:
any number (except zero) raised to the zero power is equal to 1
FIRST PERSON TO GET CORRECT GETS BRAINLIEST!!!!!!!
PLZ HELP!!!!!!!!!!!
Answer:
9-14-21 this one do not support the statement
Step-by-step explanation:
When Bashir commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 32 minutes and a standard deviation of 3 minutes. What percentage of his commutes will be shorter than 32 minutes, to the nearest 10th?
A percentage of his commute that would be shorter than 32 minutes, to the nearest 10th is equal to 50%.
How to determine the required percentage?Mathematically, the z-score of a given sample size or data set can be calculated by using this formula:
Z-score, z = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.Substituting the parameters into the z-score formula, we have;
Z-score, z = (32 - 32)/3
Z-score, z = 0/3
Z-score, z = 0
Since a commute of 32 minutes on a test corresponds to a z-score of 0, the percentage of the commute will be shorter than 32 minutes is given by:
P(x > 32) = P(z > 0)
P(z > 0) = 0.5
P(z > 0) = 50%.
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Is it possible to scan a screenshot?
To be honest i dont know but u can try to find something like that to help u ?
According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met? Yes, the conditions for inference are met. No, the 10% condition is not met. No, the Large Counts Condition is not met. No, the randomness condition is not met.
Answer: The conditions for inference are met in this scenario.
In order to use inference to determine if the true proportion of American adults who work more than one job differs from 12%, the following conditions must be met:
The sample must be randomly selected from the population.
The sample size must be large enough (usually at least 30).
The sample must be representative of the population.
In this case, it is stated that a random sample of 100 American adults was selected, which meets the first condition.
The sample size of 100 is also large enough, which meets the second condition.
There is no information given about whether the sample is representative of the population, but this is not necessary for the conditions for inference to be met.
Therefore, the conditions for inference are met in this scenario.
Step-by-step explanation:
the driving distance fom pongola to piey retief alongN2is 105km if a taxi driver at an average speed of 80KM /H calculate the time per minutes
Answer:
78.75min
Step-by-step explanation:
t=S/v
105km/80km/hr
=1.3125hr
1.3125hr =78.75min
Pls help me, if you get it right I will give you Brainlist!
Answer:
38.5
Step-by-step explanation:
The formula for the area of the circle is [tex]\pi rx^{2} \\[/tex].
Since you have the diameter and you're told to use 3.14 as pi, all you need to do is to substitute.
The diameter is also 2 times the size of the radius so you divide 7 by 2.
So [tex](3.14)(3.5)^{2} = 38.5[/tex]
Solve: -19<3x-4<5
(Graphs are in the image)
Answer: B (−5 < x < 3)
Steps
−19 < 3x − 4 < 5
−19 < 3x − 4 and 3x − 4 < 5
x > −5 and x < 3
−5 < x < 3
Number Line
−19 < 3x − 4 < 5 : Solution: − 5 < x < 3
[ Interval Notation: (−5, 3)]
If a < u < b then a < u and u < b
−19 < 3x − 4 : x > −5
3x − 4 < 5 : x < 3
Combine the intervals
Merge Overlapping Intervals
And that equals=
−5 < x < 3