Answer:
Step-by-step explanation:
8
Select the correct answer.
Which of these probability values fit the tree diagram?
O A.
PA) = 0.35, P(B) = 0.65, P{9 = 0.70, P(D) = 0.30, PC) = 0.30, PA) = 0.70
B.
P(A) = 0.35, PCB) = 0.65, PC = 0.70, PCD) = 0.30, PCE) = 0.70, RA= 0.30
O c.
PA) = 0.35, PCB) = 0.65, PC 9 = 0.30, PCD) = 0.70, PCE) = 0.70, PCA) = 0.30
OD. PCA) = 0.65, PCB) = 0.35, P = 0.70, PCD) = 0.30, PCE) = 0.30, PCA) = 0.70
Answer:
C. P(A) = 0.35, P(B) = 0.65, P(C) = 0.30, P(D) = 0.70, P(E) = 0.70, P(F) = 0.30
Step-by-step explanation: Plato / Edmentum
The probability values fit is:
P(A) = 0.35, P(B) = 0.65, P(C) = 0.70, P(D) = 0.30, P(E) = 0.70, P(F)= 0.30
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
The probability that an employee gets placed in a job that is suitable for the employee is 0.65.
The test has an accuracy rate of 70%.
So, P(A) = 0.35
Then, P(B) = 1 - P(A) = 1- 0.35 = 0.65
Now, P(C) = 70%= 0.70
P(D) = 1- 0.70 = 0.30
Now, P(E) = P( test for correct job) = 0.70
P(F) = 0.30
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Use PQR below to answer the question that follows:
Answer:
Angle P is congruent to itself due to the reflexive property.
Explanation:
Angle P must be congruent to angle S through corresponding angle theory.
Otherwise, it wouldn't prove ΔPQR is similar to ΔSTR.
Answer:
Angle P is congruent to itself due to the reflexive property.
Step-by-step explanation:
Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 49 cm2
Answer:
70cm/sStep-by-step explanation:
Area of a square with side of length L is expressed as A = L². The rate at which the area is increasing will be expressed as dA/dt.
dA/dt = dA/dL * dL/dt where
dL/dt is the rate at which each side of the square is increasing.
Since dA/dL = 2L, dA/dt = 2L dL/dt
Given dL/dt = 5cm/s and the Area of the square = 49 cm²
49 = L²
L = √49
L = 7cm
dA/dt = 2(7) * 5
dA/dt = 14*5
dA/dt = 70cm/s
The rate at which the area of the square is increasing is 70cm/s
Identify an equation in point slope form for the line parallel to y=1/2x-7 that passes through (-3,-2)
Answer:
Step-by-step explanation:
The point slope form of a straight line is expressed as
y - y1 = m(x - x1)
Where
m represents slope of the line
y1 represents the initial value of y
x1 represents the initial value of x
If two lines are parallel, it means that they have the same slope. From the equation of the given line, slope = 1/2
Therefore,
m = 1/2
x1 = - 3
y1 = - 2
Substituting into the point slope equation, it becomes
y - - 2 = 1/2(x - - 3)
y + 2 = 1/2(x + 3)
The equation is
y + 2 = 1/2(x + 3)
Answer: The point slope form of a straight line is expressed as y - y1 = m(x - x1)Wherem represents slope of the liney1 represents the initial value of yx1 represents the initial value of xIf two lines are parallel, it means that they have the same slope. From the equation of the given line, slope = 1/2Therefore,m = 1/2x1 = - 3y1 = - 2Substituting into the point slope equation, it becomesy - - 2 = 1/2(x - - 3)y + 2 = 1/2(x + 3)The equation is y + 2 = 1/2(x + 3)
Step-by-step explanation:
convert 3days to minutes
Answer:
4320 minutes
Step-by-step explanation:
Recall,
1 day ---> 24 hours
but each hour has 60 minutes, hence 1 day can also be expressed:
1 day -----> 24 x 60 = 1440 minutes
3 days -----> 1440 min/day x 3 days = 4320 minutes
Answer: 4,320 minutes
Step-by-step explanation: 1 day = 1440 days. 1440 * 3 = 4,320 minutes
Actividad 1.1
Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que
la función
definida a continuación sea diferenciable en t = 2, luego construya su gráfica.
at +b, sit < 2
f(t) = {2t2 – 1, si 2 st
1
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उपरोक्त लिंक पर क्लिक करें, निम्नलिखित प्रश्न का उत्तर दें, फिर, मैं आपके प्रश्न का उत्तर दूंगा। (यदि आप मदद की जरूरत है, यह टिप्पणी करने के लिए उत्तर दें।)
uparokt link par klik karen, nimnalikhit prashn ka uttar den, phir, main aapake prashn ka uttar doonga. (yadi aap madad kee jaroorat hai, yah tippanee karane ke lie uttar den.)
25 points Please help will mark brainleyest type the correct answer in each box use numerals instead of words if necessary use / for the fraction bars. the vertex of a parabola is (-2, -20) and its y-intercept is (0,-12) the equation of the parabola is y= ___ x^2+___x+___
Answer:
the three boxes should be filled with
2 8 -12
respectively
Step-by-step explanation:
The general equation of the parabola in this problem is
y = a(x-h)^2 + k
vertex is at (-2, -20), => k=-20, h = 2
so the equation is
y = a(x+2)^2 - 20
To have y-intercept = -12, we set x = 0
-12 = a(0+2)^2 - 20
a(2^2) = 8
a = 2
therefore the equation of the parabola is
y = 2 (x+2)^2 -20 = 2x^2 + 8x - 12
the three boxes should be filled with
2 8 -12
respectively
please assist me with the power of i(imaginary)
Let's raise i to various powers starting with 0,1,2,3...
i^0 = 1
i^1 = i
i^2 = ( sqrt(-1) )^2 = -1
i^3 = i^2*i = -1*i = -i
i^4 = (i^2)^2 = (-1)^2 = 1
i^5 = i^4*i = 1*i = i
i^6 = i^5*i = i*i = i^2 = -1
We see that the pattern repeats itself after 4 iterations. The four items to memorize are
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.
To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.
This means i^25 = i^1 = i
Likewise,
i^5689 = i^1 = i
because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely
You have different video games. How many different ways can you arrange the games side by side on a shelf? You can arrange the different video games in nothing different ways.
Answer:
See Explanation below
Step-by-step explanation:
This question has missing details because the number of video games is not stated;
However, you'll arrive at your answer if you follow the steps I'll highlight;
The question requests for the number of arrangement; That means we're dealing with permutation
Let's assume the number of video games is n;
To arrange n games, we make use of the following permutation formula;
[tex]^nP_n = \frac{n!}{(n-n)!}[/tex]
Simplify the denominator
[tex]^nP_n = \frac{n!}{0!}[/tex]
0! = 1; So, we have
[tex]^nP_n = \frac{n!}{1}[/tex]
[tex]^nP_n = n![/tex]
Now, let's assume there are 3 video games;
This means that n = 3
[tex]^3P_3 = 3![/tex]
[tex]^3P_3 = 3 * 2 * 1[/tex]
[tex]^3P_3 = 6\ ways[/tex]
So, whatever the number of video games is; all you have to do is; substitute this value for n;
The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 41 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 3.9 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 41?H0 : µ = 40
H1 : µ > 401. Compute the value of the test statistic. 2. What is your decision regarding H0?
Answer:
1. Test statistic t=1.581.
2. The null hypothesis H0 failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
NOTE: if the null hypothesis is µ = 40, there is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40 (test statistic t=3.161).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 41.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=41\\\\H_a:\mu> 41[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-41}{0.633}=\dfrac{1}{0.633}=1.581[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=1.581, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>1.581)=0.061[/tex]
As the P-value (0.061) is bigger than the significance level (0.025), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
For µ = 40:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 40.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=40\\\\H_a:\mu> 40[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-40}{0.633}=\dfrac{2}{0.633}=3.161[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=3.161, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.161)=0.002[/tex]
As the P-value (0.002) is smaller than the significance level (0.025), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40.
Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than 0.05 mm. What hypotheses should be tested, and why?The appropriate hypotheses areH0: σ0.05 mmversusHa: σ0.05 mm.With this formulation, the burden of proof is on the data to show that the requirementbeen met.In this context, what are the type I and type II errors?In this context, the type I error occurs if wea shipment that should have been . A type II error occurs if we a shipment that should have been.Need Help? Read It Talk to a Tutor
Answer:
Null and alternative hypothesis:
[tex]H_0: \mu=0.05\\\\H_a:\mu< 0.05[/tex]
The alternative hypothesis is the one that needs evidence to be supported, while the null hypothesis is the one that can be nullified (reject).
Only if there is enough evidence that thickness is less than 0.05 the null hypothesis will be rejected and the alternative hypothesis claim supported.
A Type I error happens when a true null hypothesis is rejected. In this case we will be purchase a order that is not fulfilling the thickness required.
A Type II error happens when a false null hypothesis is failed to be rejected. In this case, the order has a thickness significantly smaller than 0.05, but the sample gives no enough evidence and the order will not be purchased.
Step-by-step explanation:
A hypothesis test to see conclusive evidence that the true standard deviation of sheath thickness is less than 0.05 mm will have the following hypothesis:
[tex]H_0: \mu=0.05\\\\H_a:\mu< 0.05[/tex]
The alternative hypothesis Ha will state that the true mean is significantly smaller than 0.05, while the null hypothesis H0 will state the opposite: that the true mean is not significantly smaller than 0.05.
The alternative hypothesis is the one that needs evidence to be supported, while the null hypothesis is the one that can be nullified (reject).
Only if there is enough evidence that thickness is less than 0.05 the null hypothesis will be rejected and the alternative hypothesis claim supported.
Use the distributive property to find an expression equivalent to 6(s -7) -5 (4 - t)
Answer:
6s-62+5t
Step-by-step explanation:
6s-42-20+5t=6s-62+5t
C(n)=-6(-1/3) n-1 what’s the 2nd term in the sequence
Answer:
The second term is 3
Step-by-step explanation:
C(n)=-6(-1/3) n-1
The first term of the sequence
C(1) = -6(-1/3)1-1
C(1) = (2)-1
C(1) = 1
C(n)=-6(-1/3) n-1
The second term of the sequence
C(2) = -6(-1/3)2-1
C(2) = -6(-2/3)-1
C(2) = 4-1
C(2) = 3
Answer:
2
Step-by-step explanation:
C(2)= -6(-1/3)^2-1
=2
Sam has stamps from Malaysia, Thailand and New Zealand. The ratio of the number of stamps from Malaysia to the number of stamps from Thailand is 3:2.The ratio of the number of stamps from New Zealand to the number of stamps from Thailand is 6:5. What fraction of Sam's stamps is from Malaysia?
Answer:
21
Step-by-step explanation:
9 plus 10= 21
The ratio shows how many times one value is contained in another value.
The ratio of stamps from Malaysia, Thailand, and New Zealand is
15M : 10T : 12N
The fraction of stamps from Malaysia is 15/37.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of the number of stamps from Malaysia to the number of stamps from Thailand is 3:2.
This can be written as,
Number of stamps from Malaysia = 3M
Number of stamps from Thailand = 2T
Multiply both by 5.
Number of stamps from Malaysia = 15M ____(1)
Number of stamps from Thailand = 10T _____(2)
The ratio of the number of stamps from New Zealand to the number of stamps from Thailand is 6:5.
Number of stamps from New Zealand = 6N
Number of stamps from Thailand = 5T
Multiply both by 2.
Number of stamps from New Zealand = 12N _____(3)
Number of stamps from Thailand = 10T _____(4)
From (1), (2), (3), (4) we get,
15M : 10T : 12N
The fraction of stamps from Malaysia.
= 15/37
Thus,
The fraction of stamps from Malaysia is 15/37.
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You decide finance a $12,000 car at 3% compounded monthly for 4 years. What will your monthly payments be? How much interest will you pay over the life of the loan?
Answer:
Step-by-step explanation:
The cost of the car is $12,000
We would apply the periodic interest rate formula which is expressed as
P = a/[{(1+r)^n]-1}/{r(1+r)^n}]
Where
P represents the monthly payments.
a represents the cost of the car
r represents the interest rate
n represents number of monthly payments. Therefore
a = 12000
r = 3%/12 = 0.03/12 = 0.0025
n = 12 × 4 = 48
Therefore,
P = 12000/[{(1+0.0025)^48]-1}/{0.0025(1+0.0025)^48}]
12000/[{(1.0025)^48]-1}/{0.0025(1.0025)^48}]
P = 12000/{1.127 -1}/[0.0025(1.127)]
P = 12000/(0.127/0.0028175)
P = 12000/45.075
P = $266.22
The monthly payment is $266.22
The total amount that would be paid over the life of the loan is
266.22 × 48 = $12778.56
The amount of interest paid is
12778.56 - 12000 = $778.56
Please help will definitely say thanks
Answer:
[tex]\mathrm{Image \: below.}[/tex]
Explanation:
Ruby talks about a 3D shape, so sphere.
Shriya talks about the points that are equal in distance from the opposite points, the diameter, she is right.
Abhishek's definition is not shown completely in the photo, so by process of elimination, he is incorrect.
Solve (x – 3)2 = 5.
O A. X = 5+ 3
O B. X = 8 and x = -2
O C. X = 3 + 5
O D. X=-3+5
Step-by-step explanation:
(x - 3)2 = 5
2x - 6 = 5
2x = 5 +6
2x = 11
x = 11/2
x = 5.5
Answer: so what was the answer
Step-by-step explanation:
The scheduled commuting time on the MTA Marc train from BWI to DC is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be less than 70 minutes
Answer:
60% probability that the commuting time will be less than 70 minutes
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X < x) = \frac{x - a}{b-a}[/tex]
Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes.
This means that [tex]a = 64, b = 74[/tex]
What is the probability that the commuting time will be less than 70 minutes
[tex]P(X < 70) = \frac{70 - 64}{74 - 64} = 0.6[/tex]
60% probability that the commuting time will be less than 70 minutes
A U.S. dime has a diameter of about 18 millimeters. What is the area of one side of a dime to the nearest square millimeter? Use 3.14 as an approximation for pi. The area of one side of a U.S. dime is approximately _____ square millimeters.
Area of one side of a U.S. dime is approximately 254 square millimeters.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that U.S. dime has a diameter of about 18 millimeters.
We need to find the area of one side of a dime to the nearest square millimeter.
Diameter=18 millimeters
Diameter is two times of radius
D=2R
18=2R
Divide both sides by 2
Radius is 9 millimeters.
Area of dime=πr²
=3.14×(9)²
=3.14×81
=254 square millimeters.
Hence, area of one side of a U.S. dime is approximately 254 square millimeters.
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What are the intercepts?
Answer:
A, C, E, and F.
Step-by-step explanation:
To find the y-intercept, simply plug in 0 for x since y-intercepts are (0,y):
[tex]f(0)=\frac{(0-3)(0+4)(0-1)}{(0+2)(0-12)} =\frac{(-3)(4)(-1)}{(2)(-12)} =\frac{12}{2(-12)}=-1/2[/tex]
[tex](0,-1/2)[/tex]
To find the x-intercepts, plug in 0 for y since x-intercepts have the format (x,0):
[tex]0=\frac{(x-3)(x+4)(x-1)}{(x+2)(x-12)}[/tex]
[tex]0=(x-3)(x+4)(x-1)[/tex]
[tex]x=3, -4, 1[/tex]
[tex](-4,0), (1,0), (3,0)[/tex]
The correct choices are:
A, C, E, and F.
What is the most accurate statement about correlations? a. Apparent correlations between two or more variables can stimulate investigation and present possible solutions to be explored. b. Correlations prove cause-and-effect relationships. c. Correlations are not useful as statistical analysis tools. d. All of these choices
Answer:
a. Apparent correlations between two or more variables can stimulate investigation and present possible solutions to be explored.
Step-by-step explanation:
Correlation is a scenario, where an action X causes another action Y to occur, but one of the actions does not really need to affect the other's occurrence. Correlation occurs because of the tendency of people to seek the relationship between events. The fact that two events are happening at the same time does not necessarily imply a cause and effect relationship, although there might be a possibility of such.
Correlation is used in scientific studies to draw the relationship between two events, but it does not stop at that. Through investigation has to be made to confirm that there is indeed a correlation.
B.Imagine you are 1 of the people who left the luncheon with a contagious disease and interacted with an average of 9 different people each day. How many people could potentially be infected in 7 days
Answer:
5380839 infected
Step-by-step explanation:
Let's do the calculations day by day, we have:
Day 1
That person spread 9 people.
Day 2
Each of the nine people infect 9 others, plus that person infected 9 others, therefore it would be:
9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = (9 x 9) + 9 = 9 ^ 2 + 9 (assume this number as first term + second term)
Day 3
By the end of day 2, there were a total of 9 ^ 2 persons (first term) will infect 9 each, which makes this figure:
9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 = 9x9 ^ 2 = 9 ^ 2. The second term will now become 9 ^ 2, plus another 9 infected by the person who started it all. Therefore it would remain:
9 ^ 3 + 9 ^ 2 + 9
Following the sequence would be:
Day 4
9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9
Day 5
9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9
Day 6
9 ^ 6 + 9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9
Day 7
9 ^ 7 + 9 ^ 6 + 9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9 = 5380839
Which means that in total there would be 5380839 infected
Simplify.
In e =
In e 2x=
In 1 =
Answer:
ln e = 1
ln e 2x = 2x
ln 1 = 0
Step-by-step explanation:
ln e
ln(2.718282) = 1
In e 2x
ln(2.718282)(2)x = 2x
ln 1 = 0
Find all the missing side lengths for the following triangles.
Answer:
Step-by-step explanation:
A) u = 4 v = 4/(sqrt)3
B) b = 5 c = 10
C) b = 2(sqrt)2 a = 4
D) m and n are both 7(sqrt)2/2
The missing side lengths for the three triangles are 10√3, 12, and 8. The first triangle is a 30-60-90 triangle, the second triangle is a 45-45-90 triangle, and the third triangle is a right triangle. The missing side lengths were found using the properties of special triangles and the Pythagorean Theorem.
Here are the missing side lengths for the following triangles:
Triangle 1:
The missing side length is 15.
The triangle is a 30-60-90 triangle, so the ratio of the side lengths is 1:√3:2. The hypotenuse of the triangle is 20, so the shorter leg is 10 and the longer leg is 10√3. The missing side length is the longer leg, so it is 10√3.
Triangle 2:
The missing side length is 12.
The triangle is a 45-45-90 triangle, so the ratio of the side lengths is 1:1:√2. The hypotenuse of the triangle is 12√2, so each of the legs is 12. The missing side length is one of the legs, so it is 12.
Triangle 3:
The missing side length is 8.
We can use the Pythagorean Theorem to find the missing side length. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 10 and one of the other sides is 6. Let x be the missing side length.
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]
100 = 36 +[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 64
x = 8
Therefore, the missing side length is 8.
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Please answer this correctly
Answer:
50%
Step-by-step explanation:
The numbers that are not odd are 2, 4, and 6 on a dice.
3 numbers out of 6.
3/6 = 1/2 = 0.5
P(not odd)= 50%
Q3. Sixteen percent of Americans do not have health insurance. Suppose a simple random sample of 500 Americans is obtained. In a random sample of 500 Americans, what is the probability that more than 20% do not have health insurance?
Answer:
[tex]P(X > 100.5) = 0.0062 \\\\[/tex]
Therefore, there is 0.0062 probability that more than 20% of Americans do not have health insurance.
Step-by-step explanation:
Sixteen percent of Americans do not have health insurance. Suppose a simple random sample of 500.
From the above information,
p = 16% = 0.16
n = 500
The mean is given by
[tex]\mu = n \times p \\\\\mu = 500 \times 0.16 \\\\\mu = 80[/tex]
The standard deviation is given by
[tex]\sigma = \sqrt{n \times p(1-p)} \\\\\sigma = \sqrt{500 \times 0.16(1-0.16)} \\\\\sigma = 8.197[/tex]
What is the probability that more than 20% do not have health insurance?
We can use the Normal distribution as an approximation to the Binomial distribution since the following conditions are satisfied.
n×p ≥ 5 (satisfied)
n×(1 - p) ≥ 5 (satisfied)
So the probability is given by
500×0.20 = 100
[tex]P(X > 100) = 1 - P(X < 100)[/tex]
We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution) to approximate discrete probability distribution (Binomial distribution).
[tex]P(X > 100.5) = 1 - P(X < 100.5)\\\\P(X > 100.5) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 100.5) = 1 - P(Z < \frac{100.5 - 80}{8.197} )\\\\P(X > 100.5) = 1 - P(Z < \frac{20.5}{8.197} )\\\\P(X > 100.5) = 1 - P(Z < 2.50)\\\\[/tex]
The z-score corresponding to 2.50 is 0.9938
[tex]P(X > 100.5) = 1 - 0.9938\\\\P(X > 100.5) = 0.0062 \\\\P(X > 100.5) = 0.62\% \\\\[/tex]
Therefore, there is 0.0062 probability that more than 20% of Americans do not have health insurance.
The life in hours of a battery is known to be normally distributed, with a standard deviation of 1.25 hours. A random sample of 10 batteries has a mean life x = 40.5 hours.
a) Is there evidence to support the claim that battery life exceeds 40 hours? Use
α = 0.05.
b) What is the P-value for this test?
Answer:
a) Test statistic
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
b)
p- value = 0.8962
Step-by-step explanation:
Step(i):-
Given sample size 'n' =10
Mean of the sample x⁻ = 40.5 hours
Mean of of the Population μ = 40 hours
Standard deviation of the Population = 1.25 hours
Step(ii):-
Null Hypothesis:H₀: μ = 40 hours
Alternative Hypothesis :H₁ : μ < 40 hours
step(ii):-
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{40.5 -40}{\frac{1.25}{\sqrt{10} } }[/tex]
Z = 1.265
Level of significance = 0.05
Z₀.₀₅ = 1.96
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
Step(iii):-
P - value
P( Z < 1.265) = 0.5 + A( 1.265)
= 0.5 + 0.3962
= 0.8962
P( Z < 1.265) = 0.8962
i ) p- value = 0.8962 > 0.05
Accept H₀
There is no significant
The battery life is not exceeds 40 hours
What is cos A?
15
С
36
B
Enter your answer as a simplified fraction, in
the box
COS A
Answer:
[tex] cos A = \frac{5}{13} [/tex]
Step-by-step explanation:
The given triangle, ∆ABC is a right triangle.
To find cos A, we'd need to apply the trigonometric ratio formula, which is cos A = adjacent length/hypotenuse length
From the ∆ given,
AC = adjacent = 15,
BC = opposite = 36
We are not given the hypotenuse length AB.
==>Find the hypotenuse length AB, using the Pythagorean theorem formula:
c² = a² + b²
AB² = 15² + 36² = 225 + 1296 = 1521
AB = √1521
AB = 39
==>Find cos A:
cos A = adjacent/hypotenuse
[tex] cos A = \frac{adjacent}{hypotenuse} [/tex]
Adjacent = AC = 15
Hypotenuse = AB = 39
[tex] cos A = \frac{15}{39} [/tex]
[tex] cos A = \frac{5}{13} [/tex]
Determine whether the sequence converges or diverges. If it converges, find the limit (if an answer does not exist, enter DNE.)
{lnn/ln3}
limn→[infinity]{lnn/ln3n}=________
Answer:
The sequence converges. The limit DNE.
Step-by-step explanation:
Find the limit of n as n tends to infinity (in other words, positive infinity) in {Ln(n)/ Ln(3n)}
Positive infinity values for n start from 1,2,3,4,5,6,7,8,9,10,11,12,13,14,...,infinity
So I solved for values of n, up to n=20. All values are rounded up to 3 decimal places; for better accuracy.
When n is 1, the function is equal to 0.000
When n is 2, the function is = 0.387
When n is 3, the function = 0.500
When n is 4, the function = 0.558
When n is 5, the function = 0.594
When n is 6, the function = 0.619
When n is 7, the function = 0.639
When n is 8, the function = 0.654
When n is 9, the function = 0.667
When n is 10, the function = 0.677
When n is 11, the function = 0.686
When n is 12, the function = 0.693
When n is 13, the function = 0.700
When n is 14, the function = 0.706
When n is 15, the function = 0.711
When n is 16, the function = 0.716
When n is 17, the function = 0.721
When n is 18, the function = 0.725
When n is 19, the function = 0.728
When n is 20, the function = 0.732
We say there is a convergence because the space between the values of n gets smaller and smaller as n tends to infinity and there is no definite limit. Limit DNE.
The local news is conducting a poll of the residents’ opinions regarding a new traffic law that is being proposed. At the end of a news segment, viewers had the opportunity to dial in or use social media to choose whether they agree or disagree with the law. A large sample size was represented, and this poll was repeated again one week later with similar results. When working with this data, which of the following statements best applies?
a. The surveys are biased because people chose to respond or not.
b. Because of the large sample size, the results are most accurate of all members of the community.
c. The same sampling methods were used for both polls, demonstrating reliability.
Answer:
Option A is correct.
The surveys are biased because people chose to respond or not.
Step-by-step explanation:
When humans are given the choice whether to participate in a poll like in this question, most often than not, the poll is biased.
This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the poll. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.
Discontent is more visibly and strongly expressed in humans.
In order to remove this bias, people should have been chosen at random and their responses recorded.
The two other options are not absolutely correct, these are the reasons.
b. Because of the large sample size, the results are most accurate of all members of the community.
Like I expressed above, the base of the sample is flawed and biased as it will most likely favour a group of the population that don't agree with the law. So, no matter how large the sample is, that type of bias makes the poll unreliable.
c. The same sampling methods were used for both polls, demonstrating reliability.
The sampling method is biased, so, it doesn't matter if it is repeated for both polls. it most likely will not represent the correct general consensus about the new traffic law.
Hope this Helps!!!