The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.
Find the probability:
The probability that Joshua beats Eric in ping pong AND pool?
The probability that Joshua beats Eric in ping pong OR pool?
Answer:
P(pp & pool) = 22%
There is 22% probability that Joshua beats Eric in ping pong AND pool.
P(pp OR pool) = 50%
There is 50% probability that Joshua beats Eric in ping pong OR pool.
Step-by-step explanation:
The probability Joshua beats Eric in ping pong is given by
P(pp) = 0.48
The probability Joshua beats Eric in pool is given by
P(pool) = 0.46
The probability that Joshua beats Eric in ping pong AND pool is given by
P(pp & pool) = P(pp)×P(pool)
P(pp & pool) = 0.48×0.46
P(pp & pool) = 0.22
P(pp & pool) = 22%
Therefore, there is 22% probability that Joshua beats Eric in ping pong AND pool.
The probability that Joshua beats Eric in ping pong OR pool is given by
P(pp OR pool) = P(pp)×0.52 + P(pool)×0.54
Where 0.52 is the probability that Eric beats Joshua in the ping pong match (1 - 0.48 = 0.52)
Where 0.54 is the probability that Eric beats Joshua in the pool match (1 - 0.46 = 0.54)
P(pp OR pool) = 0.48×0.52 + 0.46×0.54
P(pp OR pool) = 0.25 + 0.25
P(pp OR pool) = 0.50
P(pp OR pool) = 50%
Therefore, there is 50% probability that Joshua beats Eric in ping pong OR pool.
To calculate the probability of Joshua beating Eric in at least one game of ping pong or pool, taking into account the probabilities for each game.
Probability plays a key role in analyzing the chances of events happening. In this case, we have two independent events: winning ping pong and winning pool. The probability of Joshua winning at least one game can be calculated using the probabilities given for each game.
Calculate the probability of Joshua winning both games: 0.48 × 0.46 = 0.2208
Subtract this value from 1 to find the probability of Joshua winning at least one game: 1 - 0.2208 = 0.7792
Therefore, Joshua has a 77.92% chance of beating Eric in at least one of the games.
in simplest form 3n-13-5n+6n
Answer:
THE ANSWER IS 4n - 13
If rice costs $1.50 per kilogram, determine the cost of a pound of rice.
Given that $1.50 is the cost of one kilogram of rice and that one kilogram equals about 2.20462 pounds, the cost of one pound of rice will be about $0.68.
Explanation:To convert the costs from kilogram to pound, you need to know that one kilogram equals about 2.20462 pounds. Hence, if rice costs $1.50 per kilogram, we can calculate the cost per pound by dividing $1.50 by 2.20462.
This results in a cost of approximately $0.68 per pound of rice.
So, if you're looking to purchase a pound of rice under this cost scheme, it would set you back about $0.68.
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Roni recently bought a car for $18,000. Her research shows the car will depreciate by an average of $1,500 per year. If x represents the number of years Roni owns the car, which of the following equations represents the value of the car after x years?
A.
y = 18,000x - 1,500
B.
y = 1,500x - 18,000
C.
y = 18,000 + 1,500x
D.
y = 18,000 - 1,500x
Answer:
D is the answer
Step-by-step explanation:
If every year the value decreases by $1,500 that variable will change, but the price he bought the car at will not. That is why the x variable(standing for years) would go into the 1,500. And if each year the value decreases the answer would be D
Answer: D. y=18,000 - 1,500x
Step-by-step explanation: the answer is d.) because the cars value will go down as time pas, so 1,500 represent the money and x could represent one year and you subtract it from 18,000 which is the original value of the car.
A bucket contains exactly 3 marbles, one red, one blue and one green. A person arbitrarily pulls out each marble one at a time. Given the following: Event 1: The first marble removed is non-red Event 2: The last marble removed is non-red Which of the following statements is true? Group of answer choices The probability of either of these events happening is 33%. The probability of Event 1 occurring is the same as the probability of Event 2 occurring. Event 1 is independent of Event 2. The probability of both events happening is 50%.
Answer:
Check the explanation
Step-by-step explanation:
here are 6 possible sequences of removing 3 marbles. Let R be the red marble, B be the blue marble and G be the green marble. The possible sequences are: RBG, RGB, BGR, BRG, GRB and GBR.
Let A denotes Event 1 and B denotes Event 2.
The favorable cases for A are: BGR, BRG, GRB and GBR.
So, P(A) = 4/6 = 2/3.
The favorable cases for B are: RBG, RGB, BRG and GRB.
So, P(B) = 4/6 = 2/3.
The probability of both events happening is P(A \cap B).
Favorable cases for (A \cap B) are BRG and GRB.
Thus, P(A \cap B) = 2/6 = 1/3.
The probability of either of these events happening is P(A \cup B).
Favorable cases for (A \cup B) are RBG, RGB, BRG, BGR, GRB and GBR.
Thus, P(A \cup B) = 6/6 = 1.
Also, P(A \cap B) \neq P(A) P(B).
So, A and B are not independent.
Hence, Option (D) is the only true statement. (Ans).
Two figures are arranged as shown. Which of the following can be used to find the area of the figure shaded light gray.
Answer:
9² − x²
x(9-x)+9(9-x)
Step-by-step explanation:
The area of the shaded light gray square =
= the area of the whole square - the area of the shaded dark gray square
= 9² - x²
since x(9-x)+9(9-x) = 9x - x² + 9² - 9x = 9² - x²
then x(9-x)+9(9-x) is also a right answer.
Answer:
The answer is 9² - x² and x(9 - x) + 9(9 - x)
Step-by-step explanation:
Here, In a Figure, two square is given first which is small and shaded dark gray and second which is big and shaded light gray.
Now, For area of Small Square.
Length (l) = x
A = l²
A = (x)²
A = x²
Now, For area of Big Square.
Length (l) = 9
A = l²
A = (9)²
A = 81
Then, To find are of Shaded light gray square
Area of Big Square - Area of Small Square.
9² - x²
Thus, The answer is 9² - x² and
x(9 - x) + 9(9 - x)
-TheUnknownScientist
42.23
Which inequality has -12 in its solution set?
A
B
C
D
Answer:
a
Step-by-step explanation:
Step-by-step explanation:
Simple
x + 6 < - 8
x < - 8 - 6
x < - 14
x + 4 > - 8
x > - 8 - 4
x > - 12
Option B is the correct answer
The average student-loan debt is reported to be $25,235. A student believes that the student-loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean student-loan debt is $27,524 and the standard deviation is $6,000. Is there sufficient evidence to support the student's claim at a 5% significance level? Preliminary: Is it safe to assume that n ≤ 5 % of all college students in the local area? No Yes Is n ≥ 30 ? Yes No Test the claim: Determine the null and alternative hypotheses. Enter correct symbol and value. H 0 : μ = H a : μ Determine the test statistic. Round to two decimals. t = Find the p -value. Round to 4 decimals. p -value = Make a decision. Fail to reject the null hypothesis. Reject the null hypothesis. Write the conclusion. There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area. There is not sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 25235
For the alternative hypothesis,
µ > 25235
This is a right tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100,
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 27524
µ = population mean = 25235
s = samples standard deviation = 6000
t = (27524 - 25235)/(6000/√100) = 3.815
We would determine the p value using the t test calculator. It becomes
p = 0.000119
Since alpha, 0.05 > than the p value, 0.000119, then we would reject the null hypothesis. There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.
What is the factorization of 121b^4-49
The factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).
Explanation:The given expression is 121b^4 - 49. We can recognize that it is a difference of squares, which can be factored using the formula (a^2 - b^2) = (a + b)(a - b). In this case, a is 11b^2 and b is 7.
Therefore, the factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).
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Imagine that you and two friends are washing the dishes by hand after dinner. The order of operations required to wash a single dish are as follows: Rinse (15 seconds) Scrub with Soap (30 seconds) Rinse (15 seconds) Dry (15 seconds) One friend is assigned to Rinse, another is assigned to Scrub, and you are assigned to Dry. Initially, you do not pipeline your work. However, you suddenly notice that Game of Thrones is about to air on TV, so you decide to pipeline your work so that you can finish washing the dishes as quickly as possible. How many seconds will it take to wash 18 dishes using a pipelined approach
Answer:
it will take 1095 seconds to wash 18 dishes using a pipelined approach
Step-by-step explanation:
Let represent the identity of those three people with :
A
B
C
Now; let the function assigned to those the people be:
A = Rinse
B =Scrub with soap
C = Dry
For the first dish pipeline
A(RInse) = 15 seconds
B (Scrub with soap) = 30 seconds
A(RInse) = 15 seconds
C(Dry) = 15 seconds
The total time taken to complete one dish to wash = (15 +30+ 15+15)seconds = 75 seconds
However ; A cannot take the second dish for rinse until the first dish has not been rinse for the second time by A, A can only start rinse from the second dish when the first dish is at C for dry
SO; for the second dish:
B (Scrub with soap) = 30 seconds
A(RInse) = 15 seconds
C(Dry) = 15 seconds
B (Scrub with soap) = 30 seconds
A(RInse) = 15 seconds
C(Dry) = 15 seconds
Similiarly ; for the third dish
B (Scrub with soap) = 30 seconds
A(RInse) = 15 seconds
C(Dry) = 15 seconds
B (Scrub with soap) = 30 seconds
A(RInse) = 15 seconds
C(Dry) = 15 seconds
B (Scrub with soap) = 30 seconds
A(RInse) = 15 seconds
C(Dry) = 15 seconds
Therefore, the total time taken to was 18 dishes = time to wash the first dish + time remaining for 17 dishes
= 75 +(30+15+15)×17
= 1095 seconds
Hence, it will take 1095 seconds to wash 18 dishes using a pipelined approach
To wash 18 dishes using a pipelined approach, you can assign each friend a different task and work on multiple dishes simultaneously. The total time taken would be 75 seconds.
Explanation:In order to wash 18 dishes using a pipelined approach, you can assign each friend a different task and work on multiple dishes simultaneously. Here is the step-by-step process:
The first friend starts rinsing the first dish, which takes 15 seconds. While the first dish is being rinsed, the second friend starts scrubbing the second dish with soap, which takes 30 seconds. After 15 seconds, the first dish is rinsed and can be passed to you to dry while the second dish is still being scrubbed. The first friend can then move on to rinse the third dish, while the second friend continues scrubbing the second dish. The process continues in this manner, with each friend moving on to the next dish as soon as they finish their task on the current dish. Once the third friend finishes drying the first dish, they can start rinsing the fourth dish, and so on. The entire process repeats until all 18 dishes are washed.
The total time taken to wash the dishes using this pipelined approach can be calculated as follows:
Total time = (15 seconds) + (30 seconds) + (15 seconds) + (15 seconds)
Total time = 75 seconds
Since the pipelined approach allows you to work on multiple dishes simultaneously, the time taken to wash 18 dishes would be the same as washing a single dish, which is 75 seconds.
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What is the degree of vertex A?
Answer:
c. 6
Step-by-step explanation:
The degree of a vertex is the number of arc ends that intercept it. (The other end of the arc is irrelevant.)
Vertex A is connected to B (1), D (2), F (1), and itself (2). There are a total of 6 arc ends that meet vertex A. Its degree is 6.
A virus has infected 400 people in the town and is spreading to 25% more people each day. Write an exponential function to model this situation, then find the number of people that will be infected in 10 days. Is this growth or decay?
We have been given that a virus has infected 400 people in the town and is spreading to 25% more people each day. We are asked to write an exponential function to model this situation.
Since the number of infected people is increasing, so our model will be exponential growth model.
An exponential growth function is in form [tex]y=a(1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time.
Let us convert 25% into decimal form.
[tex]25\%=\frac{25}{100}=0.25[/tex]
The initial number of infected people is [tex]400[/tex], so our function would be [tex]y=400(1+0.25)^x[/tex].
[tex]y=400(1.25)^x[/tex]
To find the number of infected in 10 days, we will substitute [tex]x=10[/tex] in our given formula as:
[tex]y=400(1.25)^{10}[/tex]
[tex]y=400(9.3132257461547852)[/tex]
[tex]y=3725.290298\approx 3725[/tex]
Therefore, there will be approximately 3725 infected people in 10 days.
The number of people that will be infected in 10 days is approximately 3725. This represents exponential growth.
Step 1
To model the spread of the virus using an exponential function, we start with the initial number of infected people and the daily growth rate. The exponential growth formula is:
[tex]\[ P(t) = P_0 \times (1 + r)^t \][/tex]
Where:
- [tex]\( P(t) \)[/tex] is the number of people infected after t days
- [tex]\( P_0 \)[/tex] is the initial number of infected people
- [tex]\( r \)[/tex] is the growth rate
- t is the time in days
Given:
- Initial number of infected people, [tex]\( P_0 = 400 \)[/tex]
- Daily growth rate, r = 0.25 (since 25% more people are infected each day)
The exponential function becomes:
[tex]\[ P(t) = 400 \times (1 + 0.25)^t \][/tex]
[tex]\[ P(t) = 400 \times (1.25)^t \][/tex]
Step 2
To find the number of people infected in 10 days [tex](\( t = 10 \))[/tex]:
[tex]\[ P(10) = 400 \times (1.25)^{10} \][/tex]
Calculating this:
[tex]\[ P(10) = 400 \times (1.25)^{10} \][/tex]
Using a calculator:
[tex]\[ (1.25)^{10} \approx 9.3132 \][/tex]
[tex]\[ P(10) = 400 \times 9.3132 \approx 3725.28 \][/tex]
So, the number of people infected in 10 days is approximately 3725.
Write the equation in its equivalent exponential form: log5 25=2
What is the area of 1” by 3”
Answer:
2 sq. ft. ?
Step-by-step explanation:
hope we can be friends
can i please get brainliest
Matching angles are called
Answer:
Corresponding Angles.
Step-by-step explanation:
When two lines are crossed by another line (called the Transversal): The angles in matching corners are called Corresponding Angles.
A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 100 households from the city, which gave a mean water usage of 4500 gallons over a 1-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 600 gallons. Make a 90% confidence interval for the average monthly residential water usage for all households in this city
Answer:
The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.
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{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
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 = 1.645*\frac{600}{\sqrt{100}} = 98.7[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4500 - 98.7 = 4401.3 gallons
The upper end of the interval is the sample mean added to M. So it is 4500 + 98.7 = 4598.7 gallons
The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.
The volume of Box A
of Box A is the volume of Box B. What is the height of Box A
has a base area of 32 square centimeters?
32 cm?
10 cm
Box B
Box A
8 cm
16 cm
Answer:
4cm; 1.79 cm.
Step-by-step explanation:
Okay, this question is about the Calculation involving the volume of a box with a square base and a height.
So, the volume of the box = length × width × height ---------------------------(1).
Therefore, we are going to make use of Equation (1) to determine the solution to this question, so that we have;
For Box A; We are given our volume to be equal to 32cm^3, height = 2cm, length and width = x cm.
For Box B = 32 = 2x^2.
x^2 = 16..
x = 4.
Note that Length = width.
For box B=> 32 = 10x^2.
x = √3.2 cm. = 1.79 cm.
Final answer:
The height of Box A with a base area of 32 square centimeters is 1 cm.
Explanation:
To find the height of Box A, we need to use the formula for the volume of a rectangular box, which is V = length * width * height. Given that the base area of Box A is 32 cm2 and assuming that the volume of Box A is equal to the volume of Box B, we can express their volumes as proportional to each other based on their dimensions.
Box A has a volume of 32 cm³ with a base area of 32 square centimeters.
Volume of Box A = Base Area x Height = 32 cm² x Height = 32 cm³
Height of Box A is 1 cm.
Which equation is equivalent to
equivalent to ( 1/3)^x=27^x+2
Answer:
x=\frac{-3}{2}
Step-by-step explanation:
We have been given with the expression (1/3)^x=(27)^x+2
Now, to solve the equation firstly we have to make the base same on both sides
(1/3)^x=3^{-x}
27 can be written as 3^3
27^x=(3^3)^x=3^{3x}
Hence, given expression can be rewritten as
3^{-x}=3^{3(x+2)}
Now since, base is same we can equate the powers on both sides
-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6\Rightarrow x=\frac{-3}{2}
Therefore given expression (1/3)^x=(27)^x+2 is equivalent to x=\frac{-3}{2}
Equivalent means the simplified form of any given expression
The equation is equivalent to [tex]\(\boxed{3^x = 3^{-3x+2}}\)[/tex]
To solve the equation [tex]\((\frac{1}{3})^x = 27^{(x+2)}\)[/tex], we first need to express [tex]\(27\)[/tex] as a power of [tex]\(3\)[/tex], as [tex]\(27 = 3^3\)[/tex]. Then, we rewrite the equation as:
[tex]\[\left(\frac{1}{3}\right)^x = (3^3)^{(x+2)}\][/tex]
Now, we apply the properties of exponents, specifically the power of a power rule which states [tex]\((a^m)^n = a^{m \times n}\)[/tex], to simplify the expression:
[tex]\[\left(\frac{1}{3}\right)^x = 3^{3(x+2)}\][/tex]
Now, we have the same base on both sides of the equation. We can set the exponents equal to each other:
[tex]\[x = 3(x+2)\][/tex]
Now, let's solve for [tex]\(x\)[/tex]:
[tex]\[x = 3x + 6\][/tex]
[tex]\[x - 3x = 6\][/tex]
[tex]\[-2x = 6\][/tex]
[tex]\[x = \frac{6}{-2}\][/tex]
[tex]\[x = -3\][/tex]
Complete correct question:
Which equation is equivalent to [tex]( 1/3 )^x=27^{x+2}[/tex] ?
[tex]3^x=3^{-3x+2}[/tex]
[tex]3^x=3^{3x+6}[/tex]
[tex]3^{-x} =3^{3x+2}[/tex]
[tex]3^{-x} =3^{3x+6}[/tex]
B) the perimeter of the shape is 25.71cm
calculate the value of the radius x.
take pi to be 3.142
We have been given that the perimeter of a semicircle is 25.71 cm. We are asked to find the value of the radius.
We know that perimeter of a semicircle is [tex]\pi r+2r[/tex], where r is radius of perimeter.
Upon equating perimeter of semicircle formula with 25.71, we will get:
[tex]\pi r+2r=25.71[/tex]
[tex]3.142r+2r=25.71[/tex]
[tex]5.142r=25.71[/tex]
[tex]\frac{5.142r}{5.142}=\frac{25.71}{5.142}[/tex]
[tex]r=5[/tex]
Therefore, the radius of the semicircle is 5 cm.
Similarities between inferential and descriptive statistics
Final answer:
Descriptive and inferential statistics both analyze research data and are used together in scientific studies to summarize, describe, and make predictions about a population based on sample data.
Explanation:
Understanding the similarities between descriptive statistics and inferential statistics is fundamental in scientific investigations. Although these two types of statistics serve different purposes, they share some common ground. Both are used to analyze data collected from a research study and help in making decisions or drawing conclusions about that data.
Descriptive statistics summarize and describe the main features of a dataset. Common descriptive measures include the mean, median, mode (measures of central tendency), and the range, standard deviation, and variance (measures of dispersion). On the other hand, inferential statistics use a random sample of data from a population to make inferences about the overall population. It includes various hypothesis tests and confidence intervals to determine the probability of the occurrence of a particular event.
Both descriptive and inferential statistics rely on the same underlying data collection principles and are often used in tandem. Descriptive statistics generally precede inferential statistics in the data analysis process, providing a foundation for further analysis. Moreover, they both employ graphical and numerical methods to present and summarize data, ensuring the findings are communicated in a clear and easily understood manner.
Ultimately, understanding both types of statistics allows researchers to accurately describe, summarize, and make predictions or generalizations regarding their data, which are crucial steps in any scientific study.
Consider a drug testing company that provides a test for marijuana usage. Among 317 tested subjects, results from 25 subjects were wrong (either a false positive or a falsenegative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong. Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pless than<0.10.1 B. Upper H 0H0: pless than<0.10.1 Upper H 1H1: pequals=0.10.1 C. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pgreater than>0.10.1 D. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pnot equals≠0.10.1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. (Round to two decimal places as needed.) Identify theP-value for this hypothesis test. The P-value for this hypothesis test is nothing. (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. A. Fail to rejectFail to reject Upper H 0H0. There is notis not sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. B. RejectReject Upper H 0H0. There is notis not sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. C. RejectReject Upper H 0H0. There isis sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. D. Fail to rejectFail to reject Upper H 0H0. There isis sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong.
Answer:
We conclude that we fail to reject [tex]H_0[/tex] as there is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
Step-by-step explanation:
We are given that among 317 tested subjects, results from 25 subjects were wrong.
We have to test the claim that less than 10 percent of the test results are wrong.
Let p = proportion of subjects that were wrong.
So, Null Hypothesis, [tex]H_0[/tex] : p = 10% {means that 10 percent of the test results are wrong}
Alternate Hypothesis, [tex]H_A[/tex] : p < 10% {means that less than 10 percent of the test results are wrong}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p (1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of test results that were wrong = [tex]\frac{25}{317}[/tex] = 0.08
n = sample of tested subjects = 317
So, test statistics = [tex]\frac{0.08-0.10}{\sqrt{\frac{0.08 (1-0.08)}{317} } }[/tex]
= -1.31
The value of z test statistics is -1.31.
Now, the P-value of the test statistics is given by the following formula;
P-value = P(Z < -1.31) = 1 - P(Z [tex]\leq[/tex] 1.31)
= 1 - 0.9049 = 0.095
Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test. Since our test statistics is more than the critical value of z as -1.31 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that we fail to reject [tex]H_0[/tex] as there is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
The weights of soy patties sold by a diner are normally distributed. A random sample of 25 patties yields a mean weight of 4.2 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 4 ounces. What is the correct calculated value of the test statistic?
Answer:
[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]
The degrees of freedom are given by:
[tex] df =n-1=25-1=24[/tex]
And the p value would be given by:
[tex] p_v = P(t_{24}>2) =0.0285[/tex]
And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate
Step-by-step explanation:
Data provided
[tex]\bar X=4.2[/tex] represent the sample mean for the weigths
[tex]s=0.5[/tex] represent the sample standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =4[/tex] represent the value that we want to analyze
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We want to conduct a hypothesis in order to check if the true mean weigth is less than 4 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 4[/tex]
Alternative hypothesis:[tex]\mu > 4[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]
The degrees of freedom are given by:
[tex] df =n-1=25-1=24[/tex]
And the p value would be given by:
[tex] p_v = P(t_{24}>2) =0.0285[/tex]
And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate
Find the value of x
Answer:
x =89
Step-by-step explanation:
The sum of the angles of a quadrilateral are 360 degrees
88+154+x+29 = 360
Combine like terms
271 +x = 360
271+x-271 = 360-271
x =89
A Broadway theater has 700 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 50 comma main seats for $ 40 comma and balcony seats for $ 25. If all the seats are sold, the gross revenue to the theater is $ 26 comma 250. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 22 comma 750. How many are there of each kind of seat?There are orchestra seats?
main seats?
balcony seats?
Answer:
orchestra seats = 140 seats
main seats = 350 seats
balcony seats = 210 seats
Step-by-step explanation:
Let x = number of orchestra seats
Let y = number of main seats
Let z = number of balcony seats
Theater has 700 seats. Thus;
Total seat equation is;
x + y + z = 700 - - - - (1)
We are told Orchestra seats sell for $ 50, main seats for $ 40, and balcony seats for $ 25 and a gross revenue of $26,250
Thus ;
all seats revenue equation is;
50x + 40y + 25z = 26250 - - - (eq2)
Now, we are told that, when all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 22,750
Thus, we have;
½(50x) + 40y + 25z = 22,750
Which gives ;
25x + 40y + 25z = 22,750 ---(eq3)
Solving the 3 equations simultaneously, we have;
x = 140
y = 350
z = 210
What is the circumference of the following circle? if radius is 2
Known :
r = 2
Asked :
C = ...?
Answer :
C = 2πr
= 2 × 3.14 × 2
= 12.56
So, tge circumference of circle is 12.56
Hope it helpful and useful :)
Answer:
[tex]4\pi[/tex]
Step-by-step explanation:
The equation for the circumference of a circle is 2[tex]\pi[/tex]r. I remember it as Cherry Pies Are (r) Square. If you plug in 2 for r, it should get you the answer
how is adding 6+3 like adding 60+30
Answer:
because your just adding a zero at the end.
Step-by-step explanation:
Adding 6+3 is like adding 60+30 because both utilize the place value system and the commutative property of addition where units are added to units and tens to tens, respectively.
The question of adding 6+3 is similar to adding 60+30 due to the property of place value and the commutative property of addition. In both cases, you are adding units that are consistent within their respective places. In single-digit addition, such as 6+3, you are adding units to units. Similarly, in the addition of multi-digit numbers like 60+30, you are adding tens to tens. This is much like the property A+B=B+A, which holds true for ordinary numbers, meaning you'll get the same result regardless of the order in which you add them.
Emma correctly answered 21 of 25 questions. what percent of the question did Emma answer correctly?
A.21%
B.84%
C.16%
D.96%
E. None correct
Answer:
B
Step-by-step explanation:
21/25
Work Shown:
21/25 = 84/100 after multiplying top and bottom by 4
Since 84/100 = 84%, this means 21/25 = 84% as well
Alternatively, you can use a calculator or long division to find that 21/25 = 0.84 = 84%
One 50 pound of grass seed is enough to seed 10,000 square feet of ground. If your lawn is 400 feet by 285 feet how many packages of seed do you need to seed your entire lawn?
To seed the entire lawn, you will need 11.4 packages of grass seed.
Explanation:To determine the number of packages of grass seed needed, we need to find the area of the lawn. The area of a rectangle is given by the formula length * width. In this case, the length is 400 feet and the width is 285 feet. Multiplying these values together, we get an area of 114,000 square feet. Now, we can determine the number of packages needed by dividing the area of the lawn by the area covered by one package of seed. Since one package covers 10,000 square feet, we divide 114,000 by 10,000 to get 11.4 packages.
Learn more about grass seed packages here:https://brainly.com/question/32426485
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A total of 12 packages needed.
To determine how many packages of grass seed are needed to seed a lawn of 400 feet by 285 feet, follow these steps:
Calculate the lawn's total area by multiplying its length by its width: 400 feet * 285 feet = 114,000 square feet.
Since one 50-pound package of grass seed is enough for 10,000 square feet, divide the lawn's total area by 10,000 square feet to find the number of packages needed: 114,000 square feet / 10,000 square feet per package = 11.4 packages.
Because you can't purchase a fraction of a package, you'll need to round up to the nearest whole number, which means you require 12 packages of grass seed to cover the entire lawn.
It's also important to consider the seeding rate when determining the amount of seed required. However, in this case, the seeding rate is not needed since the question specifies one package covers a set amount of square footage.
Can anyone help me out
Answer:
62
Step-by-step explanation:
length of rectangle = 2* diameter = 24
width = diameter = 12
area = 24*12 - 2 * pi * 6^2 = 61.8
Your answer would be the second option, 62.
To answer this we need to find the area of the 2 circles, and then subtract this from the area of the rectangle to find the shaded area.
The equation for the area of a circle is πr², so for one circle this would be π × 6² = 36π. Since we're taking π = 3.14, this comes out as 113.04 as the area for once circle, which means the area for both circles would be 113.04 × 2 = 226.08.
To find the area of the rectangle, we need to notice that the height of the rectangle is the diameter of one circle, and the width is 2 multiplied by the diameter of the circle, because there are 2 diameters right next to each other. The diameter of one circle is 6 × 2 = 12, so this is the height, which means the width of the rectangle is 12 × 2 = 24. This means the area of the rectangle is 24 × 12 = 288.
Now the last step is to do 288 - 226.08 = 61.9 = 62.
I hope this helps!
Renee has a triangular garden with an area of 24 square feet. Which drawing shows Renee's garden?
3 ft.
6 ft.
6
ft.
Answer:
3 ft
Step-by-step explanation:
Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level. Person's Age Movie 18-23 yr 24-29 yr 30-35 yr Row Total Drama 10 14 10 34 Science Fiction 11 9 10 30 Comedy 7 9 13 29 Column Total 28 32 33 93 (a) What is the level of significance
Answer:
There is a relationship between the age of a young adult and the type of movie preferred.
Step-by-step explanation:
In this case we need to test whether there is a significance relationship between the age of a young adult and the type of movie preferred.
The hypothesis can be defined as:
H₀: Age of a young adult and movie preference are independent.
Hₐ: Age of a young adult and movie preference are not independent.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Consider the table below.
The formula to compute the expected frequencies is:
[tex]E_{i}=\frac{\text{Row Total}\times \text{Column Total}}{\text{Total}}[/tex]
The Chi-square test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}=2.6013[/tex]
The significance level of the test is, α = 0.05.
The degrees of freedom of the test is,
df = (r - 1)(c - 1)
= (3 - 1)(3 - 1)
= 2 × 2
= 4
Compute the p-value as follows:
p-value = 0.6266
*Use a Chi square table.
As the p-value is more than the significance level the null hypothesis was failed to be rejected.
Thus, concluding that there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred.