Answer:
The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
n = 200
X = 24
Confidence level = 90%
Compute the value of sample proportion as follows:
[tex]\hat p=\frac{X}{n}=\frac{24}{200}=0.12[/tex]
Compute the critical value of z for 90% confidence level as follows:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
Compute the 90% confidence interval for the population proportion of all train travelers who do not buy a ticket as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.12\pm 1.645\times\sqrt{\frac{0.12(1-0.12)}{200}}\\\\=0.12\pm0.038\\=(0.082, 0.158)\\\approx (0.08, 0.16)[/tex]
The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).
The 90% confidence interval (0.08, 0.16) for the population proportion of all train travelers who do not buy a ticket implies that there is a 0.90 probability that the true proportion lies in this interval.
Or if 100 such intervals are computed then 90 of those intervals will consist of the true proportion.
This table gives the dimensions for a scale drawing of a house. Every 2 inches on the scale drawing represents 1.5 feet of the original house. Use proportional reasoning to complete the table with the original lengths.
Answer:
A: 6
B: 9
Step-by-step explanation:
All you do is multiply 1.5 times 4. To get A
And for B you just multiply 1.5 times 6
Whenever Nicole rents a movie from iTunes, the probability that it will be a comedy is 52%. Of the next seven movies she rents, what is the probability that she rents NO MORE THAN two comedies?
The question pertains to cumulative probability in a binomial distribution, where the probability of Nicole renting no more than two comedies out of seven movies is calculated by adding the probabilities of renting 0, 1, or 2 comedy movies.
Explanation:The question is about calculating a cumulative probability, specifically the probability that Nicole rents no more than two comedy movies out of seven. Here the events are not mutually exclusive, and we use the concept of binomial distribution to solve it.
The binomial distribution describes the probability of having exactly k successes (defined as the desired outcome, in our case renting a comedy) in n independent Bernoulli trials (independent events with two possible outcomes - here, renting a comedy or not).
To calculate the binomial distribution, we would use the formula P(k; n, p) = C(n, k) * (p^k) * (1-p)^(n-k), where P(k; n, p) is the probability of k successes in n trials, C(n, k) is the combinations of n items taken k at a time, and p is the probability of a success on a single trial.
In this case, we want to find the cumulative probability, i.e., the probability that Nicole rents 0, 1, or 2 comedy movies. This can be calculated as P(0;7,0.52) + P(1;7,0.52) + P(2;7,0.52).
C(n, k) can be calculated using the formula n! / [(n-k)!k!], where n is the total number of trials and k is the number of successes and '!' denotes factorial.
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To determine the probability that Nicole rents no more than two comedies out of seven movies, we apply the binomial probability formula to calculate the cumulative probability of renting 0, 1, or 2 comedies, and summing those probabilities gives the final answer.
Explanation:The problem at hand requires calculating the probability of an event occurring a certain number of times given a fixed probability. In this case, we are interested in finding the probability that Nicole rents no more than two comedies out of the next seven movies from iTunes, with the probability of renting a comedy being 52%.
To solve this, we can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the number of trials, 'k' is the number of successes, and 'p' is the probability of success on any given trial. We are looking for P(X ≤ 2), which is the cumulative probability of renting 0, 1, or 2 comedies.
P(X = 0) = (7 choose 0) * 0.52^0 * 0.48^7P(X = 1) = (7 choose 1) * 0.52^1 * 0.48^6P(X = 2) = (7 choose 2) * 0.52^2 * 0.48^5Summing these probabilities will give us the final probability that Nicole rents no more than two comedies.
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A cat is stuck on the roof If the ladder is 16 feet long and must be placed six feet long and must be placed six feet away from the building How high can the ladder reach up the building to help save the cat?
14.8 feet
22 feet
37.9 feet
220 feet
How did it get on the roof?
Answer:
The answer is A. 14.8 feet.
Explanation:
We can use the Pythagorean theorem to solve this problem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder represents the hypotenuse, and the distance from the building and the height reached by the ladder represent the other two sides.
Let's denote:
- [tex]\( a \)[/tex] as the distance from the building to the base of the ladder (6 feet)
- [tex]\( b \)[/tex] as the height reached by the ladder up the building (what we need to find)
- [tex]\( c \)[/tex] as the length of the ladder (16 feet)
According to the Pythagorean theorem, we have:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Substituting the given values:
[tex]\[ 6^2 + b^2 = 16^2 \][/tex]
[tex]\[ 36 + b^2 = 256 \][/tex]
[tex]\[ b^2 = 256 - 36 \][/tex]
[tex]\[ b^2 = 220 \][/tex]
To find [tex]\( b \)[/tex], we take the square root of both sides:
[tex]\[ b = \sqrt{220} \][/tex]
Using a calculator, we find:
[tex]\[ b \approx 14.8 \][/tex]
So, the ladder can reach up to approximately 14.8 feet on the building to help save the cat.
A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to finish the season with a 90% winning percentage?
A.
12
B.
14
C.
15
D.
27
Answer:D.27
They already won 12 games (80% of 15%) and need or win 15 more.
Check: 15+12 =27 =90%
30 30
Answer:
C
Step-by-step explanation:
First, find out how many games they won:
x/15 = 80/100
Cross multiply
x × 100 = 15 × 80
100x = 1200
x = 12
They won 12 out of 15 games
Second, find out how many wins out of 30 games are needed to have a 90% winning percentage
x/30 = 90/100
Cross multiply
x × 100 = 30 × 90
100x = 2700
x = 27
27 game wins are needed to have a 90% winning percentage
Lastly, find the difference between 27 wins (total needed) and 12 wins (total number of wins they currently have)
27 - 12 = 15
They need to win 15 more games to have a 90% winning percentage
What is the volume of air in the beach ball that has a 12 inch diameter
To find the volume of air in a beach ball with a 12-inch diameter, one must calculate the volume of a sphere using the formula V = 4/3 π r^3, with the radius being half the diameter, resulting in approximately 904.78 cubic inches.
Explanation:The question you're asking pertains to the calculation of the volume of a sphere, as the beach ball is essentially a spherical object. When you have a diameter, the radius (which is half of the diameter) is necessary for the volume calculation. The formula for the volume of a sphere is given by V = 4/3 π r^3, where V is the volume, π (pi) is approximately 3.14159, and r is the radius of the sphere.
First, we convert the diameter into the radius by dividing by 2: 12 inches / 2 = 6 inches. Then, we use the formula to calculate the volume: V = 4/3 π • (6 inches)^3.
Therefore, the volume is: V = 4/3 π • 216 inches^3. After calculating this, we find that the volume of air inside the beach ball is approximately 904.78 cubic inches, assuming no other factors are affecting the volume, such as the thickness of the ball's material.
Sue has 18 sweets. Tony also has 18 sweets. Sue gives Tony x sweets. Sue then eats 5 of her sweets. Tony then eats half of his sweets. Write the expression for the number of sweets Sue and Tony now have.
Answer:
suee has 18-x-5
tony has 18+x-((18+x)/2)
Step-by-step explanation:
Can i get brainliest plz
Answer:
s(18 - x)-5 t(18x/2) is initial
they now have;
t( 9x) s(13-x)
Step-by-step explanation:
A state map has a circle-shaped compass.
The radius of the compass is 15 millimeters. What is the approximate area of the compass? (Use 3.14 for .)
A.
47.1 mm2
B.
94.2 mm2
C.
706.5 mm2
D.
1,413 mm2
Answer:
C
Step-by-step explanation:
Using the formula for the area of a circle (A = πr²), with a radius of 15 mm and π approximated as 3.14, the area of the compass is found to be 706.5 mm². Option C is the correct answer.
To find the area of the compass, which is circle-shaped, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Given the radius of the compass is 15 millimeters, we substitute 15 mm for r in the formula:
A = π(15 mm)²
A = 3.14(225 mm²)
A = 706.5 mm²
Therefore, the approximate area of the compass is 706.5 mm², which corresponds to option C.
Help? I can't seem to understand arithmegic sequence.
A sequence [tex]\{a_n\}[/tex] is arithmetic if the difference between consecutive terms is some fixed number, regardless of which pair of consecutive terms you pick out of the sequence.
For example, the following sequences are arithmetic:
1, 2, 3, 4, 5, 6, ... (difference = 1)
-25, -20, -15, -10, -5, ... (difference = 5)
2. Carla's sequence is not arithmetic, because the differences between consecutive terms are all different:
13 - 11 = 2
17 - 13 = 4
25 - 17 = 8
She can adjust the sequence by changing the last two numbers to 15 and 17, since this makes the difference fixed:
13 - 11 = 2
15 - 13 = 2
17 - 15 = 2
and so on.
3. The sequence
45, 48, 51, 54, ...
is arithmetic with difference 3 between terms. Recursively, we can write the [tex]n[/tex]th term, [tex]a_n[/tex], in terms of the previous, [tex](n-1)[/tex]th term, [tex]a_{n-1}[/tex]:
[tex]a_n=a_{n-1}+3[/tex]
By this definition, we can just as easily write the [tex](n-1)[/tex]th term in terms of the [tex](n-2)[/tex]th term:
[tex]a_{n-1}=a_{n-2}+3[/tex]
Then, substituting this into the previous equation, we have
[tex]a_n=(a_{n-2}+3)+3=a_{n-2}+2\cdot3[/tex]
We can continue this process to write [tex]a_n[/tex] in terms of [tex]a_1[/tex]:
[tex]a_{n-2}=a_{n-3}+3\implies a_n=a_{n-3}+3\cdot3[/tex]
[tex]a_{n-3}=a_{n-4}+3\implies a_n=a_{n-4}+4\cdot3[/tex]
and so on. (You might notice that the subscript of the term on the right side, and the number of 3s being added, together sum to [tex]n[/tex].) The pattern continues down to
[tex]a_n=a_1+(n-1)\cdot3[/tex]
The first term in this sequence is [tex]a_1=45[/tex], so we have
a. [tex]a_n=45+3(n-1)=42+3n[/tex]
where [tex]n=1,2,3,\ldots[/tex].
b. You can fill in the blanks by just adding 3 to the previous term:
45, 48, 51, 54, 57, 60, 63, 66, 69, ...
Then, using the formula found in (a), the 15th term of the sequence is
[tex]a_{15}=42+3\cdot15=87[/tex]
Alanna tried to solve an equation step by step.
4c=12
4c/=12.4
c=48
Find Alanna's mistake.
Answer:
step 1
Step-by-step explanation:
Alanna divided one side of the equation by 4 but multiplied the other side by 444. Alanna should have divided both sides of the equation by 4 to isolate c.
Alanna's mistake was dividing the equation by 12.4 instead of dividing both sides by 4.
Alanna made a mistake in the second step of solving the equation. The correct step should be as follows:
Step 1: 4c = 12
Step 2: Divide both sides by 4, not 4.4: (4c) / 4 = 12 / 4
Step 3: c = 3
So, the correct solution is c = 3, not c = 48 as Alanna calculated.
Alanna's mistake in solving the equation 4c = 12 occurred during the second step of the process. When attempting to isolate the variable "c," she divided both sides of the equation by 4, but her error lies in the value she used for this division. Instead of correctly dividing by 4, she mistakenly divided by 4.4.
The correct approach in this situation is to perform the same mathematical operation on both sides of the equation to maintain its balance. Dividing both sides by 4 allows us to isolate "c" and find its value. When we divide 12 by 4, we get 3, which is the correct solution to the equation.
In contrast, Alanna's incorrect division by 4.4 led her to the erroneous result of c = 48. This error likely arose from a simple calculation mistake. It's crucial to pay attention to each step of solving equations to avoid such errors, as they can significantly affect the final solution and lead to incorrect conclusions.
In summary, Alanna's mistake was dividing both sides of the equation by 4.4 instead of 4, resulting in the incorrect solution c = 48, when the correct solution is c = 3.
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I WILL MAKE U THE BRAINLIEST
Answer: 4/3
Step-by-step explanation:
The method of SOH CAH TOA helps tremendously in this equation.
TOA is the one necessary for this problem as it means tangent = opposite side/adjacent side.
Opposite side = 4
Adjacent side = 3
Opposite side/adjacent side = 4/3
A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g.
What is its density? (answer in g/mL)
Answer:
0.00037037037 m3 / kg
Step-by-step explanation:
2 divided by -12 what is the answer?
Answer:
-1/6
Step-by-step explanation:
When dividing 2 by -12 you would use 2 as the numerator and -12 as the denominator and then simplify it by dividing both by two to end up with -1/6
1. Over 6 days, Jim jogged 6.5 miles, 5 miles,
3 miles, 2 miles, 3.5 miles, and 4 miles.
What is the mean distance that Jim jogged
each day?
A 3.75 miles © 4.5 miles
B 4 miles
D 6.5 miles
Answer:
B. 4 miles
Step-by-step explanation:
Jim ran a total of ...
6.5 +5 +3 +2 +3.5 +4 = 24 . . . . miles
Then his average was ...
(24 miles)/(6 days) = 4 miles/day
Several students tested plant growth for given conditions. Which student’s data is most representative of average plant growth for the tested conditions? Alicia tested 6 plants. Brenden tested 24 plants. Caitlin tested 3 plants. Diego tested 12 plants. Alicia Brenden Caitlin Diego
Step-by-step explanation:
Step 1: Find the correct answer
The more plants tested, the better average that you will have. Therefore, since Brenden tested 24 plants, which is the most, his data is the most representative of average plant growth.
Answer: Option B, Brenden
Answer:
Brenden
Step-by-step explanation:
Larger the sample size, better representative it is of the population
shawn has a bag containing seven balls: one green, one orange, one blue, one yellow, one purple, one white, and one red. All balls are equally are equally likely to be chosen. Shawn will choose one ball without looking in the bag. What is the possibility that Shawn will choose the purple ball out of the bag?
hi
Seven Balls , one of each color. Then 1/7 possibility to choose purple
3. A lawn had a length of 10 feet and a width
of 8 feet. What is the perimeter of the
lawn?
1. 80 feet
2. 80 square feet
3. 36 square feet
4. 36 feet
Evalúe 3z + 6 when Z=4
A) 4
B) 6
C)8
D)18
Answer:
D 18
Step-by-step explanation:
3z + 6
Let z=4
3*4 +6
Multiply first
12+6
Then add
18
Known :
z = 4
Asked :
3z + 6 = ...?
Answer :
3z + 6
= 3(4) + 6
= 12 + 6
= 18
So, the value of 3z + 6 is 18 (D)
Hope it helpful and useful :)
Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 3 can be selected. Using simple random sampling, what is the probability that each sample of size 3 is selected?
Answer:
10% probability that each sample of size 3 is selected
Step-by-step explanation:
Each sample has the same probability of being selected.
There are 10 samples.
This means that the probability of each sample being selected is:
1/10 = 0.1
10% probability that each sample of size 3 is selected
The probability of each possible sample that can be drawn from a finite population of size N can be calculated using the hypergeometric distribution.
The formula for calculating the probability of getting k successes (in this case, a successful sample of size 3) in a sample of size n, drawn without replacement from a population of size N, is:
P(k) = (C(k, K) * C(n - k, N - K)) / C(n, N)
where C(k, K) is the number of ways to choose k items from a set of K items, and C(n - k, N - K) is the number of ways to choose n - k items from a set of N - K items.
For part (a), N = 4, n = 3, and K = 3. Therefore, there is only one possible successful sample of size 3, and the probability of getting that sample is:
P(3) = (C(3, 3) * C(0, 1)) / C(3, 4) = 1/4
For part (b), N = 6, n = 3, and K = 3. Therefore, there is only one possible successful sample of size 3, and the probability of getting that sample is:
P(3) = (C(3, 3) * C(0, 3)) / C(3, 6) = 1/20
For part (c), N = 12, n = 3, and K = 3. Therefore, there are C(3, 12) = 220 possible successful samples of size 3, and the probability of getting any one of them is:
P(3) = (C(3, 3) * C(0, 9)) / C(3, 12) = 1/220
For part (d), N = 18, n = 3, and K = 3. Therefore, there are C(3, 18) = 816 possible successful samples of size 3, and the probability of getting any one of them is:
P(3) = (C(3, 3) * C(0, 15)) / C(3, 18) = 1/816
Therefore, the probabilities of each possible sample of size 3 that can be drawn from the given populations are:
(a) 1/4
(b) 1/20
(c) 1/220
(d) 1/816
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Find the least common multiple of 12,4, and 9
Answer:
3
Step-by-step explanation:
12 divided by 4 is 3, 3 times 3 is 9 bam
Answer:
36
Step-by-step explanation:
12 = 2 * 2 * 3 = 2^2 * 3
4 = 2 * 2 = 2^2
9 = 3 * 3 = 3^2
For the least common multiple, use common and not common factors with the largest exponent.
Use 2^2 and 3^2
LCM = 2^2 * 3^2 = 4 * 9 = 36
Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x. Maris earns a
monthly salary of $4,000 plus a 4% commission on her sales, x. For what value of sales, x, will Jose's earnings be greater than Maris' earnings?
Choose the inequality that could be used to solve this problem.
3,500 + 0.06x > 4,000 + 0.04x
3,500 + 0.6x > 4,000 + 0.4x
3,500 + 6x > 4,000 + 4x
3,500 + 0.06x < 4,000 + 0.04x
Answer:
(A)3,500 + 0.06x > 4,000 + 0.04x
Step-by-step explanation:
Jose's Earnings
Monthly Salary = $3,500
6% commission on his sales, x =0.06x
Total = 3500+0.06x
Maris' Earnings
Monthly Salary = $4,000
4% commission on her sales, x =0.04x
Total = 4000+0.04x
If Jose's earnings be greater than Maris' earnings, then:
3500+0.06x > 4000+0.04x
Which relationship is likely ONLY a correlation and NOT one of causation?
Q:
A:
A) As the temperature increases, the number of air conditioners being used increases.
B) As the price of a gallon of gas increases, the number of gallons of gas sold decreases.
C) As the number of visitors to a park increases, the number of flowers in bloom at the park increases.
D) As the amount of time a student spends studying for a test decreases, the student’s score on the test decreases.
Answer:
C) As the number of visitors to a park increases, the number of flowers in bloom at the park increases
Step-by-step explanation:
Many people visit parks in the summer, which is when the flowers are supposed to bloom/blossom.
What is the value of cosine theta in the diagram below?
Charlene is wrapping the box below. How much wrapping paper will she need? *
Answer:
286 in³
Step-by-step explanation:
7×5 = 35
35×2 = 70in
9×5 = 45
45×2 = 90in
9×7 = 63
63×2 = 126in
70+90+126
=286in³
Smart phone sales since 1990
A.Linear B.Quadratic C.Exponential
Half life of a pesticide
A.Linear B.Quadratic C.Exponential
Throwing a baseball in the air
A.Linear B.Quadratic C.Exponential
Population of a colony of feral cats
A.Linear B.Quadratic C.Exponential
Grade on a test compared to hors of studying A.Linear B.Quadratic C.Exponential
Driving at a constant rate of speed
A.Linear B.Quadratic C.Exponential
Answer:
the last one is linear
the throwing a baseball in the air is quadratic
half life of a pesticide is exponential
thats all i know
Step-by-step explanation:
On the first day it was posted online, a music video got 600 views. The number of views that the video got each day increased by 20% per day. How many total views did the video get over the course of the first 23 days, to the nearest whole number?
Answer: there were 195,742 total views after 23 days
Step-by-step explanation:
Which equation is equivalent to
log5x3 - logr2 = 2?
10 og 5x*
102
5x
log
10
- 102
5x+x
log
10
102
Answer:
B
Step-by-step explanation:
The solution of the equation are,
⇒ 5x = 10²
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The expression is,
⇒ log 5x³ - log x² = 2
Now, We can simplify by the definition of logarithmic we get;
⇒ log (5x³ / x²) = 2
⇒ log (5x) = 2
⇒ 5x = 10²
Thus, The solution of the equation are,
⇒ 5x = 10²
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Use the graph of the function y = 4x to answer the following questions.
The domain of the function is
to
because an exponent can be any real number.
Answer: negative infinity to positive infinity.
Step-by-step explanation:
Answer:
The domain of the function is negative infinity
to positive infinity because an exponent can be any real number.
Next, The range of the function is zero
to positive infinity because 4x is always positive.
Step-by-step explanation:
Edge test
Ed fills his water bottle with 1.2 liters of water. After his bike ride ,he drinks 200 millimeters of the water . How much is left in Ed’s water bottle.
Answer:
1 Litre
Step-by-step explanation:
Convert to similar units. 1.2L = 1,200 ml
1200 - 200 = 1000 or 1L
1 litre of water is left in his water bottle
What is the sum of the interior angles of a polygon with 5 sides
Answer:
540°
Step-by-step explanation:
Your consulting firm is submitting a bid for a big contract. From previous data, you know your firm has a 51% of successfully landing the contract. The agency to which you submitted your bid has asked for more information about your bid. Past experience indicates that for 70% of successful bids and 44% of unsuccessful bids, the agency asks for more information. (In other words, if you successfully bid, then the probability the agency asks for information is 70%, etc.) If an agency asks for more information, what is the probability the bid is successful
Answer:
P(S/A) = 0.6235
Step-by-step explanation:
Let's call S that you successfully bid, S' that you unsuccessfully bid, A that the agency asked for more information and A' that the agency didn't asked for more information.
So, the probability P(S/A) that the bid is successful given that the agency asks for more information is calculated as:
P(S/A) = P(S∩A)/P(A)
Where P(A) = P(S∩A) + P(S'∩A)
Then, the probability P(S∩A) that you successfully bid and the agency asked for more information is:
P(S∩A) = 0.51 * 0.7 = 0.357
Because your firm has a 51% of successfully landing the contract and if you successfully bid, then the probability the agency asks for information is 70%.
At the same way, the the probability P(S'∩A) that you unsuccessfully bid and the agency asked for more information is:
P(S'∩A) = (1-0.51) * 0.44 = 0.2156
So, P(A) and P(S/A) are equal to:
P(A) = 0.357 + 0.2156 = 0.5726
P(S/A) = 0.357/0.5726 = 0.6235