the rule for g that represents a vertical stretch by a factor of 6, followed by a translation 5 units down of the graph of f(x) = log₀(x) is g(x) = 6log₀(x) - 5.
The given function is f(x) = log₀(x)
To stretch the graph of f(x) vertically by a factor of 6, we multiply f(x) by 6, which gives:
g(x) = 6log₀(x)
To translate the graph of g(x) down 5 units, we subtract 5 from g(x), which gives:
g(x) = 6log₀(x) - 5
the concept of factors can also be applied to functions. Given a function f(x), a factor of f(x) is another function g(x) such that f(x) can be written as the product of g(x) and another function h(x).a factor is a number or algebraic expression that divides another number or algebraic expression evenly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers can divide 12 without leaving a remainder.
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If f(x) = 3x + 2, find f(2).
a. 2
b. 5
c. 8
d. 9
e. 12
Answer:
C
Step-by-step explanation:
Since the number in the parenthesis is treated as "x", for f(2), replace "x" with 2. So the equation will be f(2) = 3(2) + 2. Then multiply. f(2) = 6 + 2. Lastly add them up. f(2) = 8. The answer is 8.
what is the approximate probability that the actual proportion requiring aid will exceed that value? (round your answer to four decimal places.)
The approximate probability that the actual proportion requiring aid will exceed 0.08 is 0.5 (or 50%) rounded to four decimal places.
Given: The number of members in town = 400
The number of members requiring aid = 32
The proportion of members requiring aid = (number of members requiring aid) / (total number of members) = 32 / 400 = 0.08
To find the approximate probability that the actual proportion requiring aid will exceed this value, we need to assume a distribution for the proportion of members requiring aid. Assuming a normal distribution, we can use the Central Limit Theorem to approximate the sampling distribution of the sample proportion.
The standard error of the sample proportion is given by:
SE = √[p(1-p)/n]
where p is the population proportion and n is the sample size.
Substituting the values, we get:
SE = sqrt [(0.08 × 0.92) / 32] = 0.043
To find the probability that the actual proportion requiring aid will exceed 0.08, we can standardize the distribution using the z-score formula:
z = (x - p) / SE
where x is the value of the proportion we are interested in, p is the population proportion, and SE is the standard error of the sample proportion.
Substituting the values, we get:
z = (0.08 - 0.08) / 0.043 = 0
The probability that the actual proportion requiring aid will exceed 0.08 is equal to the probability of observing a z-score greater than 0, which is 0.5 (or 50%).
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The question is -
The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town? .08 What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)
answer question please but DO NOT ROUND IT . 1 / 3*5 + 2
[tex]=\frac{1}{15} +2\\[/tex]
⇒We can only add the numbers if they have the same denominator, to do so we can first convert 2 into a fraction
[tex]=\frac{1}{15} +\frac{2(15)}{1(15)} \\=\frac{1}{15} +\frac{30}{15} \\=\frac{31}{15} \\[/tex]
In a sale, the normal price of a boat is reduced by 15%
The sale price of the boat is £272 000
Work out the normal price of the boat.
Answer:
£320 000
Step-by-step explanation:
Let x = original price of the boat.
When you reduce a price by 15%, what percent remains in the sale price?
100% - 15% = 85%
After reducing the price of the boat by 15%, the sale price is 85% of the original price.
85% of x = £272 000
0.85x = 272 000
Divide both sides by 0.85
x = 320 000
Answer: £320 000
how many batteries n should be in the package in order for the probability to exceed 1%? give the smallest number n which works.
a) The probability that a battery does not reach the milestone in its first 8 hours of usage is 0.014 or 1.4%. b) The probability of this goal being met is 0.002 or 0.2%. c) The smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.
(a) To calculate the probability that a battery does not reach the milestone in its first 8 hours of usage, we need to calculate the area under the normal curve to the right of 8 hours. We can use the standard normal distribution to do this by first standardizing the value of 8 hours using the formula:
z = (x - mu) / sigma
where x is the value of 8 hours, mu is the mean of the distribution (7.36 hours), and sigma is the standard deviation (0.29 hours). Substituting these values, we get:
z = (8 - 7.36) / 0.29 = 2.21
Using a standard normal table or a calculator, we can find that the area to the right of z = 2.21 is approximately 0.014.
(b) We want to find the probability that at least 10 batteries out of a pack of 12 last until 7.5 hours of usage. This is a binomial distribution with n = 12 and p = the probability that a single battery lasts until 7.5 hours.
To find p, we can use the standard normal distribution again by standardizing the value of 7.5 hours:
z = (7.5 - 7.36) / 0.29 = 0.48
Using a standard normal table or a calculator, we can find that the area to the right of z = 0.48 is approximately 0.316. Therefore, the probability that a single battery lasts until 7.5 hours is 0.316.
Now we can use the binomial distribution formula to calculate the probability that at least 10 batteries out of 12 last until 7.5 hours:
P(X >= 10) = 1 - P(X < 10)
where X is the number of batteries that last until 7.5 hours, and P(X < 10) is the cumulative probability of 9 or fewer batteries lasting until 7.5 hours. Using a binomial calculator or a standard normal table, we can find that:
P(X < 10) = 0.998
Therefore, P(X >= 10) = 1 - 0.998 = 0.002 or 0.2%.
(c) We want to find the smallest value of n such that the probability of at least 10 batteries out of n lasting until 7.5 hours is greater than 1%. This is equivalent to finding the smallest n such that:
P(X >= 10) > 0.01
Using a binomial calculator or a standard normal table, we can find that:
P(X < 10) = 0.989 when n = 10
P(X < 10) = 0.970 when n = 11
P(X < 10) = 0.942 when n = 12
Therefore, the smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.
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Your question is incomplete, but probably the complete question is :
Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution.
(a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage.
(b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until 7.5 hours of usage. If n 12, what is the probability of this goal being met?
(c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.
Ava sells pottery at a market. Each piece of pottery costs $4.50 to make. Ava marks up the pottery by 250%. She then decides to have a sale of 30% off the retail price. What is the discounted price of each piece of pottery?
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
Explain about the discounted price?The interest rate that is adjusted to the projected cash flows of either an investment to determine its present value is referred to as the discount rate. The expected rate of return on investment that businesses or investors anticipate. The viability of an investment can be determined by computing the net present value via discounting.
Cost price = $4.50
Percentage increase = 250%.
Marked price = 4.50 + 2.5*4.50
Marked price = $15.75
Discount = 30%
Discounted price = 15.75 - 0.30*15.75
Discounted price = $11.025
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
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write the integral as the sum of the integral of an odd function and the integral of an even function.
We can write the integral of f(x) as the sum of the integral of the even component, e(x), and the integral of the odd component, o(x). This gives us the following equation: ∫f(x)dx = ∫e(x)dx + ∫o(x)dx
Integrals can be written as the sum of the integral of an odd function and the integral of an even function. This is because any function can be broken down into its even and odd components. Even functions are those that remain unchanged when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the same as the result for its negative. Odd functions are those that change sign when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the negative of the result for its negative.
The integral of an even function is the same regardless of whether it is written as the sum of the integral of an odd function and the integral of an even function, or if it is written just as an integral of the even function. The integral of an odd function is the negative of the integral of the even function when written as the sum of the two integrals.
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The bonus question asks for the application of the integral test to determine the convergence of the series given by 2n*e^(-a).
The integral test is a method used to determine the convergence or divergence of a series by comparing it to the integral of a related function. In this case, we are given the series 2n*e^(-a), and we can use the integral test because the terms of the series involve the variable 'n', and the function e^(-a) can be integrated.
To apply the integral test, we consider the integral of the function corresponding to the series. In this case, we integrate the function f(x) = 2x*e^(-a) from 1 to infinity. If this integral converges, then the series is also convergent. Conversely, if the integral diverges, then the series is divergent.
By evaluating the integral of f(x) and analyzing its convergence or divergence, we can determine whether the given series 2n*e^(-a) converges or diverges. Showing all the steps in evaluating the integral and discussing the convergence properties of the resulting integral will be necessary to receive full credit for this question.
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Oliver ask 20 children's how they travel to school you are other reasonOliver ask 20 children's how they travel to school here are the reason walkOliver ask 20 children's how they travel to school here are the reason what three bicycle 2 calculate the percentage of the children who travel to school by bicycle
From the given information provided, the percentage of children who travel by bicycle is 15%.
According to the given information, out of 20 children, 3 of them travel to school by bicycle. To calculate the percentage of children who travel to school by bicycle, we need to divide the number of children who travel by bicycle by the total number of children and multiply by 100.
Percentage of children who travel to school by bicycle = (Number of children who travel by bicycle / Total number of children) x 100%
= (3/20) x 100%
= 15%
Therefore, the percentage of children who travel to school by bicycle is 15%.
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housing costs: a government report on housing costs says that single-family home prices nationwide are skewed to the right, with a mean of $235,700. a. we collect price data from a random sample of 50 homes in orange county, california. why is it okay to use these data for inference even though the population is skewed?
It is fine to use these data because the price sample is random so bias will not interfere with the results.
Why is it okay to use this data?Based on the information, we can infer that it is correct to use the data from this sample because it is random, that is, it does not have a defined order. Therefore, it is not necessary to take bias into account because it will not have any influence on the results.
In accordance with the above, it would be incorrect to take the data from a non-random sample because information would be prioritizing and this would cause the results to be blinded.
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a dummy variable is used as an independent variable in a regression model when: group of answer choices the variable involved is interval. the variable involved is nominal. a curvilinear relationship is suspected. two independent variables interact.
A dummy variable is used as an independent variable in a regression model when the variable involved is nominal.
What is a dummy variable?A dummy variable, also known as an indicator variable, is a binary variable (having only two possible values). It is used to distinguish between groups or categories. It is used to investigate the effect of the predictor on the response in regression analysis.
In a regression model, a dummy variable is used as an independent variable when the variable involved is nominal. In regression analysis, the independent variable is the variable that is being tested to determine if it has a relationship with the dependent variable (the outcome variable).
The independent variable is also referred to as the predictor variable, while the dependent variable is referred to as the response variable.
Thus, the answer is: the variable involved is nominal
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simplify the following expression 4 + 4 + 4x
Answer:
Step-by-step explanation:
8+4x
right cone has a base with diameter 16 units.
me volume of the cone is 320 cubic units.
What is the length of a segment drawn from the apex to the edge of the circular base?
Answer:
The length of the segment is 8 units.
We can use the formula for the volume of a cone to calculate the height of the cone:
V = (1/3)πr^2h
320 = (1/3)π(8^2)h
h = 320/(1/3)(π)(64)
h = 8 units
Franklin is an ecologist monitoring the catfish population in Athena Lake each year. When he first started monitoring the population one year ago, he estimated that there were 800 catfish in the lake. Today, Franklin estimates the population has decreased to 760 and it will continue decreasing each year.
The exponential model for the population of catfish in Athena Lake is:
P(t) = 800 × e^{-0.0513t}
What is exponential ?
an exponential function is a function of the form:
f(x) = a^{x}
where a is a positive constant called the base, and x is the exponent. The base represents the factor being repeatedly multiplied, while the exponent represents the number of times the base is being multiplied by itself.
To model the decreasing population of catfish in Athena Lake, we can use an exponential function of the form:
P(t) = P0 × e^{-rt}
where:
P(t) is the population at time t
P0 is the initial population
r is the annual growth rate (in this case, a negative value representing a decreasing population)
e is the mathematical constant e (approximately 2.71828...)
t is the time elapsed (measured in years)
In this case, we know that the initial population P0 is 800, and that the current population P(1) is 760 (since Franklin started monitoring one year ago and estimates the population has decreased to 760). So we can use these values to solve for the annual growth rate r:
760 = 800 × e^{-r}
Dividing both sides by 800, we get:
0.95 = e^{-r}
Taking the natural logarithm (ln) of both sides, we get:
ln(0.95) = -r
Solving for r, we get:
r ≈ 0.0513
So the exponential model for the population of catfish in Athena Lake is:
P(t) = 800 × e^{-0.0513t}
where t is the time elapsed (measured in years).
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I will mark BRAINLYIST
Answer:
119% of 550
Step-by-step explanation:
add the percentages
each page number of a 488-page book is printed one time in the book. the first page is page 1 and the last page is page 488. when printing all of the page numbers, how many more 4's are printed than 8's?
the number of more 4's printed than 8's is 188 - 59 = 129.
We can approach this problem by counting the number of times the digit 4 appears and the number of times the digit 8 appears in the page numbers from 1 to 488.
First, let's count the number of times the digit 4 appears. We can break down the counting into three cases:
The digit 4 appears in the units place (page numbers 4, 14, 24, ..., 484): there are 49 such page numbers (from 4 to 484, incrementing by 10).
The digit 4 appears in the tens place (page numbers 40 to 49, 140 to 149, ..., 440 to 449): there are 50 such page numbers.
The digit 4 appears in the hundreds place (page numbers 400 to 488): there are 89 such page numbers.
Thus, the total number of times the digit 4 appears is 49 + 50 + 89 = 188.
Next, let's count the number of times the digit 8 appears. We can break down the counting into two cases:
The digit 8 appears in the tens place (page numbers 80 to 89, 180 to 189, ..., 480 to 489): there are 50 such page numbers.
The digit 8 appears in the hundreds place (page numbers 800 to 880): there are 9 such page numbers.
Thus, the total number of times the digit 8 appears is 50 + 9 = 59.
Therefore, the number of more 4's printed than 8's is 188 - 59 = 129.
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the anterior cruciate ligament (acl) is one of the ligaments that help stabilize the knee. surgery is often recommended if the acl is completely torn, and recovery time from the surgery can be lengthy. a medical center developed a new surgical procedure designed to reduce the average recovery time from the surgery. to test the effectiveness of the new procedure, a study was conducted in which 210 patients needing surgery to repair a torn acl were randomly assigned to receive either the standard procedure or the new procedure. (a) based on the design of the study, would a statistical
The outcomes of the statistical analysis can give medical professionals and patients important knowledge regarding the possible advantages of the new procedure.
what is probability ?The study of random events or phenomena is the focus of the mathematical field of probability. It is a way to gauge how likely something is to happen. It is represented by a number between 0 and 1, where 0 denotes the event's impossibility and 1 denotes its certainty. There are numerous ways to calculate probabilities, including utilizing theoretical or mathematical models, empirical data, and experimental data.
given
A statistical analysis would be useful to evaluate the effectiveness of the novel technique to the standard procedure based on the study's design.
The recovery periods of the two patient groups might be compared using statistical techniques like hypothesis testing and confidence intervals to assess the efficacy of the new therapy.
Researchers can establish whether the new approach is statistically significantly superior than the usual procedure in terms of minimizing recovery time by comparing the recovery times of the two groups.
The outcomes of the statistical analysis can give medical professionals and patients important knowledge regarding the possible advantages of the new procedure.
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I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:no
Step-by-step explanation:
using the Pythagorean theorem:
a^2+b^2=c^2
42^2+26^2=50^2
1764+676=2500
2440=2500
2440<2500
So the answer is no
Helen flips a coin and rolls a dice calculate the probability of getting 4 and tails
Answer:
1/12 or 0.0833
Step-by-step explanation:
P(Coin) = 1/2
P(Dice) = 1/6
1/2 × 1/6 = 1/12
The angle of depression from a lightbouse that is 32 meters in height to the base of a ship at the water’s edge measures 26°. To the nearest meter, hkw far js the ship to the base of the lighthouse?
The ship is about 65.6 meters away from the base of the lighthouse.
What is tangent function ?
Tangent is one of the three primary trigonometric functions, along with sine and cosine. In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.
The tangent function is denoted by "tan" and is defined mathematically as:
tan(theta) = opposite / adjacent
where theta is the angle, opposite is the length of the side opposite the angle, and adjacent is the length of the side adjacent to the angle.
According to the question:
We can use trigonometry to solve this problem. Let's draw a right triangle with the lighthouse at the top, the ship at the bottom, and the line connecting them as the hypotenuse. The angle of depression of 26° is the angle between the hypotenuse and the horizontal line passing through the lighthouse. We know the height of the lighthouse is 32 meters.
Let x be the distance between the ship and the base of the lighthouse, which is the adjacent side of the angle of depression. Then we can use the tangent function:
tan(26°) = opposite / adjacent
We know the opposite side is the height of the lighthouse, which is 32 meters. Solving for x:
x = opposite / tan(26°)
x = 32 / tan(26°)
x ≈ 65.6 meters
Therefore, the ship is about 65.6 meters away from the base of the lighthouse.
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I need to know if there both parallel
Answer:
No
Step-by-step explanation:
No. So if the number next to the "x" we're the same, it would have been. But they are different (one is -3 and one is 1/3)
an oil storage tank can be described as the volume generated by revolving the area bounded by about the x-axis. find the volume of the tank (in cubic meters). round to four decimal places.
The volume of the tank can be found using the given information as:[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]
How to find the volume of the tank?Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:
[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]
where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.
Therefore, the volume of the tank can be found using the given information as:
[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]
We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.
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find the next two terms 9.56,9.57,9.58,9,59
The next two terms in this arithmetic progression is 7.60 and 7.61.
What is arithmetic progression?An arithmetic prοgressiοn (AP) is a sequence where the differences between every twο cοnsecutive terms are the same. Fοr example, the sequence 2, 6, 10, 14, … is an arithmetic prοgressiοn (AP) because it fοllοws a pattern where each number is οbtained by adding 4 tο the previοus term. A real-life example οf an AP is the sequence fοrmed by the annual incοme οf an emplοyee whοse incοme increases by a fixed amοunt οf $5000 every year.
We know the Arithmetic progression formula:
[tex]\rm a_{n}=a_{1}+(n-1)d[/tex]
[tex]\rm a_n[/tex] = the nᵗʰ term in the sequence
[tex]\rm a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here 4 terms are given
5th and 6th terms are to be found,
Thus,
a₁ = 9.56
d = (9.56 -9.57) = 0.01
n = 5
Then
5th term is :
aₙ = a₁ + (n - 1)d
aₙ = 9.56 + (5 - 1)0.01
aₙ = 9.56 + (4)0.01
aₙ = 9.56 + 0.04
aₙ = 7.60
6th term is :
aₙ = a₁ + (n - 1)d
aₙ = 9.56 + (6 - 1)0.01
aₙ = 9.56 + (6)0.01
aₙ = 9.56 + 0.05
aₙ = 7.61
Thus, The next two terms in this arithmetic progression is 7.60 and 7.61.
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6. complete the interpretation for the p-value: if delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of or any statistic (larger, smaller) is .
If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.
This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.
The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.
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The complete question is:
Complete the interpretation for the p-value:
If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .
a counseling service records the number of calls to their hotline for the last year. what is the forecast for august if the forecast for june was 164 and the service uses exponential smoothing with an alpha of 0.7?
Forecast for August with an alpha of 0.7 and forecast of June 164 are to be calculated using exponential smoothing.
Exponential smoothing is a forecasting method that uses a weighted average of past time-series values to forecast future values. In a time-series, data values are obtained over time, such as over months or years, and then plotted in sequence.
The weights decrease exponentially as the observations get older. The EWMA formula used in exponential smoothing is as follows:
St=α × Yt-1+(1-α) × St-1
where,St is the smoothed statistic for the current period tYt is the original observation for the current period tSt-1 is the smoothed statistic for the previous period t-1α is the smoothing parameter 0≤α≤1, and usually close to 0.1.The smoothed statistic is also called the exponentially weighted moving average (EWMA).Calculating the forecast for August with alpha=0.7 and forecast of June 164 as follows:
St=α × Yt-1+(1-α) × St-1St =0.7 × 164+(1-0.7) × 164St=164
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what is 7x=14 show your work
Answer:
x=2
Step-by-step explanation:
7x=14
divide by 7 on each side to get x by itself
x=14/7
x=2
Some of the dimensions of a house are shown below.
Calculate the length u.
Give your answer in metres to 2 d.p.
56°
1.65 m
u
43°
Not drawn accurately
Using trigonometric relations we can see that u = 4.28m
How to find the length of u?First we can find the length of the shared side using the trigonometric relation:
tan(56°) = x/1.65m
1.65m*tan(56°) = x
2.45m = x
Then the length of the bottom side of the right triangle in the right side is iven by:
tan(43°) = 2.45m/y
Solving for y:
y = 2.45m/tan(43°)
y = 2.63m
Then the length of u is:
u = 1.65m + 2.63m = 4.28m
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After how many weeks do you think it would be unreasonable to continue counting
individual mosquitoes? And finally, at the end of the 13-week mosquito season, how
many mosquitoes would you expect to be in the trap? Use complete sentences to
explain both of your answers below.
(Table if needed)
Week | Mosquitos
0 | 8
1 | 12
2 | 18
3 | 27
We can expect approximately 90 mosquitoes in the trap at the end of the 13-week mosquito season.
How to determine how many mosquitoes would you expect to be in the trapBased on the given data, we can observe that the number of mosquitoes is increasing over time, and the increase is not constant. So, it would be unreasonable to continue counting individual mosquitoes after a certain point.
To estimate the number of mosquitoes at the end of the 13-week mosquito season, we can assume that the rate of increase remains constant over time. Using this assumption, we can find the average increase in mosquitoes per week, which is the difference between the number of mosquitoes in the last week and the number in the first week, divided by the number of weeks:
Average increase = (27 - 8) / 3 = 6.33
Then, we can use this average increase to estimate the number of mosquitoes in the 13th week:
Number of mosquitoes in the 13th week = 27 + 6.33 × 10 = 90.3
Since we cannot have a fraction of a mosquito, we can round this estimate to the nearest whole number.
Therefore, we can expect approximately 90 mosquitoes in the trap at the end of the 13-week mosquito season.
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Find the percentile rank for Susan who is 5th in a class of 58 students
From the given information provided, Susan's percentile rank in class is approximately 6.9%.
To find the percentile rank for Susan who is 5th in a class of 58 students, we need to use the following formula:
Percentile rank = (Number of students below Susan / Total number of students) x 100
Since Susan is the 5th student in the class, there are 4 students with higher ranks than her. Therefore, the number of students below Susan is 4.
Using the formula, we can calculate the percentile rank as:
Percentile rank = (4 / 58) x 100
Percentile rank = 6.9 (rounded to one decimal place)
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Suppose you are going to roll a 10-sided die 50 times and record p, the proportion of times that the roll is 3 orlower. Which of the following describes the sampling distribution of p?A. Mean = 15; Standard deviation = 0.0648; non-Normal.B. Mean = 15; Standard deviation = 3.24; approximately NormalC. Mean = 0.3; Standard deviation = 3.24; approximately NormalD. Mean = 0.3; Standard deviation = 0.0648; non-NormalE. Mean = 0.3; Standard deviation = 0.0648; approximately Normal
approximately Normal.
In the given problem, suppose you are going to roll a 10-sided die 50 times and record p, the proportion of times that the roll is 3 or lower. The question is asking us to determine the sampling distribution of p.The mean of p is given by: [tex]μp = 50 × 0.3 = 15[/tex]And
the standard deviation of p is given by: σp = sqrt[tex](50 × 0.3 × 0.7) = 3.24[/tex]
Therefore, the correct option is: Mean = 0.3; Standard deviation = 3.24;
for such more questions on approximately Normal
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A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
Blue
Green
Yellow
Purple
14
6
12
4
16
Based on these results, express the probability that the next spin will land on purple
as a fraction in simplest form.
Answer:
4/13
Step-by-step explanation:
total = 14 + 6 + 12 + 4 + 16 = 52
purple = 16
p(purple) = 16/52 = 4/13