Answer:
10 2/3π or 33.51
Step-by-step explanation:
the volume of a sphere is 4/3πr^3
if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51
Answer:
32π/3 cubic cm
Step-by-step explanation:
Tasha wants to take money out of the ATM for a taxi fare. She wants to do a quick estimate to see if taking $120 out of her bank account will overdraw it. She knows she had $325 in the account this morning when she checked her balance. Today she bought lunch for $19, a dress for $76, a pair of shoes for $53, and a necklace for $23. She also saw a movie with a friend for $12. Rounding each of her expenses to the nearest tens place, estimate how much money Tasha has left in her account before she goes to the ATM. Do not include the $ in your answer.
Answer:145
Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145
Let the sample space be
S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Suppose the outcomes are equally likely. Compute the probability of the event E = 1, 2.
Answer:
probability of the event E = 1/5
Step-by-step explanation:
We are given;
Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
Number of terms in sample S is;
n(S) = 10
We are given the event; E = {1, 2}
Thus, number of terms in event E is;
n(E) = 2
Now, Probability = favorable outcomes/total outcomes
Thus, the probability of the event E is;
P(E) = n(E)/n(S)
P(E) = 2/10
P(E) = 1/5
Teresa's parents are getting phones that each and 64 GB of storage how many bits of storage come with each phone answer both in scientific in standard notation
Answer:
5.12 x 10¹¹ bit
Step-by-step explanation:
1GB = 8 x 10⁹ bits
so 64gb = 64 x 8 x 10⁹
= 512 x 10⁹
= 5.12 x 10¹¹ bits
scientific notation = 5.12 x 10¹¹ bits
standard Notation = 512 ,000,000,000 bits.
Given a normal distribution with (mean) μ= 50 and (standard deviation) σ = 4, what is the probability that:__________.
a) x>43
b) x<42
c) x>57.5
d) 42
e) x<40 or x>55
f) 5% of the values are less than what X value?
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
h) 85% of the values will be above what X value?
Answer:
a) P(x > 43) = 0.9599
b) P(x < 42) = 0.0228
c) P(x > 57.5) = 0.03
d) P(x = 42) = 0.
e) P(x<40 or x>55) = 0.1118
f) 43.42
g) Between 46.64 and 53.36.
h) Above 45.852.
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 = 50, \sigma = 4[/tex]
a) x>43
This is 1 subtracted by the pvalue of Z when X = 43. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{43 - 50}{4}[/tex]
[tex]Z = -1.75[/tex]
[tex]Z = -1.75[/tex] has a pvalue of 0.0401
1 - 0.0401 = 0.9599
P(x > 43) = 0.9599
b) x<42
This is the pvalue of Z when X = 42.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42 - 50}{4}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
P(x < 42) = 0.0228
c) x>57.5
This is 1 subtracted by the pvalue of Z when X = 57.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{57.5 - 50}{4}[/tex]
[tex]Z = 1.88[/tex]
[tex]Z = 1.88[/tex] has a pvalue of 0.97
1 - 0.97 = 0.03
P(x > 57.5) = 0.03
d) P(x = 42)
In the normal distribution, the probability of an exact value is 0. So
P(x = 42) = 0.
e) x<40 or x>55
x < 40 is the pvalue of Z when X = 40. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 50}{4}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
x > 55 is 1 subtracted by the pvalue of Z when X = 55. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 50}{4}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944
1 - 0.8944 = 0.1056
0.0062 + 0.1056 = 0.1118
P(x<40 or x>55) = 0.1118
f) 5% of the values are less than what X value?
X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -1.645*4[/tex]
[tex]X = 43.42[/tex]
43.42 is the answer.
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.
20th percentile:
X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -0.84*4[/tex]
[tex]X = 46.64[/tex]
80th percentile:
X when Z has a pvalue of 0.8. So X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = 0.84*4[/tex]
[tex]X = 53.36[/tex]
Between 46.64 and 53.36.
h) 85% of the values will be above what X value?
Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -1.037*4[/tex]
[tex]X = 45.852[/tex]
Above 45.852.
Write the Algebraic expression for each of the following.
1. Sum of 35 and 65
2. Take away 14 from y
3. Subtract 3 from the product of 6 and s
4. 10 times the sum of x and 8 5. Take away p from 6
Step-by-step explanation:
1. 35 + 65
2. y - 14
3. (6 x s) - 3
4. 10(x+8.5).. 6-p
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly se
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?
Answer:
P( X' ∩ Y' ) = 0.205
Step-by-step explanation:
Let X is the event that the customer insures more than one car.
Let X' is the event that the customer insures exactly one car.
Let Y is the event that customer insures a sport car.
Let Y' is the event that customer insures not a sport car.
From the given information we have
70% of customers insure more than one car.
P(X) = 0.70
20% of customers insure a sports car.
P(Y) = 0.20
Of those customers who insure more than one car, 15% insure a sports car.
P(Y | X) = 0.15
We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
P( X' ∩ Y' ) = ?
Which can be found by
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
From the rules of probability we know that,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y ) (Additive Law)
First, we have to find out P( X ∩ Y )
From the rules of probability we know that,
P( X ∩ Y ) = P(Y | X) × P(X) (Multiplicative law)
P( X ∩ Y ) = 0.15 × 0.70
P( X ∩ Y ) = 0.105
So,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )
P( X ∪ Y ) = 0.70 + 0.20 - 0.105
P( X ∪ Y ) = 0.795
Finally,
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
P( X' ∩ Y' ) = 1 - 0.795
P( X' ∩ Y' ) = 0.205
Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.
y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05
A) Compute E(Y).
B) Suppose an individual with Y violations incurs a surcharge of $110Y2. Calculate the expected amount of the surcharg.
Answer:
A. The E(Y) is 0.80
B. The expected amount of the surcharges is $165
Step-by-step explanation:
A. In order to calculate the E(Y), we would have to calculate the following formula:
E(Y)=∑yp(y)
E(Y)=(0*0.5)+(1*0.25)+(2*0.20)+(3*0.05)
E(Y)=0+0.25+0.40+0.15
E(Y)=0.80
B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:
E($110Y∧2)=110E(Y∧2)
=110∑y∧2p(y)
=110((0∧2*0.5)+(1∧2*0.25)+(2∧2*0.20)+(3∧2*0.05))
110(0+0.25+0.80+0.45)
=$165
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
A. 91.68
Answer:
B) 92.03 < μ < 97.97
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Step-by-step explanation:
Step(i):-
Given sample mean (x⁻) = 95
standard deviation of the sample (s) = 6.6
Random sample size 'n' = 30
99% confidence interval for the mean score of all students.
[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]
step(ii):-
Degrees of freedom
ν = n-1 = 30-1 =29
[tex]t_{0.01} = 2.462[/tex]
99% confidence interval for the mean score of all students.
[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]
( 95 - 2.966 , 95 + 2.966)
(92.03 , 97.97)
Final answer:-
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample
Question:
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.
Answer:
61.03
Step-by-step explanation:
Given:
Standard deviation = 18
Sample estimate = 5
Confidence level = 97%
Required:
Find sample size, n.
First find the Z value. Using zscore table
Z-value at a confidence level of 97% = 2.17
To find the sample size, use the formula below:
[tex] n = (Z * \frac{\sigma}{E})^2[/tex]
[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]
[tex] n = (2.17 * 3.6)^2 [/tex]
[tex] n = (7.812)^2 [/tex]
[tex] n = 61.03 [/tex]
Sample size = 61.03
In an office complex of 1110 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 77% chance that she will be at work tomorrow, and if the employee is absent today, there is a 54% chance that she will be absent tomorrow. Suppose that today there are 899 employees at work.
Required:
a. Find the transition matrix for this scenario.
b. Predict the number that will be at work five days from now.
c. Find the steady-state vector.
Answer:
B
Step-by-step explanation:
Given z = 4x – 6y, solve for y.
Answer:
Step-by-step explanation:
-6y+4x=z
-6y=z-4x
y=(z-4x)/-6
Answer:
[tex]y=\frac{z-4x}{-6}[/tex]
Step-by-step explanation:
combine like terms to create an equivalent expression -1/2(-3y+10)
Answer:
3/2y - 5
Step-by-step explanation:
-1/2(-3y+10)
Expand the brackets.
-1/2(-3y) -1/2(10)
Multiply.
3/2y - 5
Answer:
[tex]= \frac{ 3y}{2} - 5 \\ [/tex]
Step-by-step explanation:
we know that,
[tex]( - ) \times ( - ) = ( + ) \\ ( - ) \times ( + ) = ( - )[/tex]
Let's solve now,
[tex] - \frac{1}{2} ( - 3y + 10) \\ \frac{3y}{2} - \frac{10}{2} \\ = \frac{ 3y}{2} - 5[/tex]
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
38 units
Step-by-step explanation:
We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.
Thus, see attachment below for the number of units of each length of the figure that we have counted.
The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38
Perimeter of the shaded figure = 38 units
what 826,497 in standard form answer
Answer:8.2 x 10^5
Step-by-step explanation:
Please help me find Jebel dhanna in UAE map.
Answer:
The full name of the place is the "Danat Jebel Dhanna". The Jebel Dhanna is currently located in the Abu Dhabi. It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.
hope this helps ;)
best regards,
`FL°°F~` (floof)
AC =
Round your answer to the nearest hundredth.
с
6
B
40°
А
Answer:
5.03
Step-by-step explanation:
Answer:
5.03 = AC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 40 = AC /6
6 tan 40 = AC
5.034597787 = AC
To the nearest hundredth
5.03 = AC
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
What is the solution of √1-3x = x+3 ?
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
A ladder leans against the side of a house. The angle of elevation of the ladder is 66 degrees, and the top of the ladder is 15 ft above the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.
Answer:
x ≈ 6.7 ft
Step-by-step explanation:
We are going to use tan∅ to find our answer:
tan66° = 15/x
xtan66° = 15
x = 15/tan66°
x = 6.67843 ft
Which of the following is the graph of y = negative StartRoot x EndRoot + 1?
Answer:
see below
Step-by-step explanation:
y = -sqrt(x) +1
We know that the domain is from 0 to infinity
The range is from 1 to negative infinity
Answer:
b
Step-by-step explanation:
e2020
Find the equation of the line.
Use exact numbers.
y=
Answer:
y = 2x+4
Step-by-step explanation:
First we need to find the slope using two points
(-2,0) and (0,4)
m = (y2-y1)/(x2-x1)
m = (4-0)/(0--2)
= 4/+2
= 2
we have the y intercept which is 4
Using the slope intercept form of the line
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
Write the expression in simplest form 3(5x) + 8(2x)
Answer:
31x[tex]solution \\ 3(5x) + 8(2x) \\ = 3 \times 5x + 8 \times 2x \\ = 15x + 16x \\ = 31x[/tex]
hope this helps...
Good luck on your assignment...
The expression [tex]3(5x) + 8(2x)[/tex] in simplest form is 31x.
To simplify the expression [tex]3(5x) + 8(2x)[/tex], we can apply the distributive property:
[tex]3(5x) + 8(2x)[/tex]
[tex]= 15x + 16x[/tex]
Combining like terms, we have:
[tex]15x + 16x = 31x[/tex]
Therefore, the expression [tex]3(5x) + 8(2x)[/tex] simplifies to [tex]31x.[/tex]
To learn more on Expressions click:
https://brainly.com/question/14083225
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An economist at Vanderbilt University devised a study to compare different types of online auctions. In one experiment he compared a Dutch auction to a first-place sealed bid auction. In the Dutch auction the item for sale starts at a very high price and is lowered gradually until someone finds the price low enough to buy. In the first-price sealed bid auction each bidder submits a single sealed bid before a particular deadline. After the deadline, the person with the highest bid wins. The researcher auctioned off collectible trading cards from the game Magic: The Gathering. He placed pairs of identical cards up for auction; one would go into Dutch auction and the other to the first-price sealed bid auction. He then looked at the difference in the prices he received on the pair. He repeated this for a total of 88 pairs.
[a] Explained why the data should be analyzed using paired samples as opposed to two independent samples.
[b] What makes a pair?
[c] What is the explanatory variable? Is it categorical or quantitative?
[d] What is the response variable? Is it categorical or quantitative?
[e] State the relevant hypotheses in words:
Null hypothesis:
Alternative hypothesis:
[f] Define the parameter of interest and give the symbol that should be assigned to it.
[g] State the relevant hypotheses in symbols (using a parameter):
Null hypothesis:
Alternative hypothesis:
[h] Assume the p-value is 0.17 (write a conclusion).
Answer:
Step-by-step explanation:
a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.
b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.
c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.
d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.
e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.
Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.
f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.
g. Null hypothesis: p(dutch) = p(first-price sealed auction)
Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)
h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.
Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:
1. Flip the coin.
2. Flip the coin again.
3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.
(a) Show that the result is equally likely to be either heads or tails.
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
Answer:
Step-by-step explanation:
Given that;
the following procedure for accomplishing our task are:
1. Flip the coin.
2. Flip the coin again.
From here will know that the coin is first flipped twice
3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails
But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.
Let the probability of head = p
so P(head) = p
the probability of tail be = (1 - p)
This kind of probability follows a conditional distribution and the probability of getting heads is :
[tex]P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}[/tex]
[tex]=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}[/tex]
[tex]=\dfrac{(1-p)*p}{2(1-p)*p}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Thus; the probability of getting heads is [tex]\dfrac{1}{2}[/tex] which typically implies that the coin is fair
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.
The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.
Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of p.
In essence, NO, procedure (b) does not give a fair coin flip outcome.
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 404 grams. Assume the population standard deviation is known to be 24. A level of significance of 0.01 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
Step-by-step explanation:
Information given
[tex]\bar X=404[/tex] represent the sample mean
[tex]\sigma=24[/tex] represent the population standard deviation
[tex]n=42[/tex] sample size
[tex]\mu_o =409[/tex] represent the value to verify
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is less than 409, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 409[/tex]
Alternative hypothesis:[tex]\mu < 409[/tex]
The statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. 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.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
A triangular window has an area of 594 square meters. The base is 54 meters. What is the height?
Answer:
22 m
Step-by-step explanation:
Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.
A = (1/2)bh
594 m^2 = (1/2)(54 m)h
h = (594 m^2)/(27 m) = 22 m
The height of the window is 22 meters.
Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x
3x^2
x^2 + 2x
x^2 - 10x
3x^2 + 2x
Answer:
x^2 - 10x
Step-by-step explanation:
2x^2 - 4x - x^2 +6x
You subtract x^2 from 2x^2 and you get x^2
Then you add 6x and 4x together and get 10x
So then you have x^2 - 10x
(plus I took the test and this was the correct answer.)