Answer:
1. z = 0.184
2. P-value = 0.427
3. The null hypothesis is that the proportion of treated subjects that experienced headaches is not significantly higher than 9%.
The null hypothesis is failed to be rejected.
4. At a significance level of 0.01, there is not enough evidence to support the claim that more than 9% of treated subjects experienced headaches.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that more than 9% of treated subjects experienced headaches.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.09\\\\H_a:\pi>0.09[/tex]
The significance level is 0.01.
The sample has a size n=275.
The sample proportion is p=0.095.
[tex]p=X/n=26/275=0.095[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.09*0.91}{275}}\\\\\\ \sigma_p=\sqrt{0.000298}=0.017[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.095-0.09-0.5/275}{0.017}=\dfrac{0.003}{0.017}=0.184[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.184)=0.427[/tex]
As the P-value (0.427) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that more than 9% of treated subjects experienced headaches.
What is the equation of a line that goes through the point (0, 2) and has a slope of 1?
Answer: y=x+2
Step-by-step explanation:
The slope-intercept equation is y=mx+b. The m is slope, and the b is the y-intercept. Since we are given the slope, we can fill it into m. We also know that the y-intercept is on the y-axis, meaning the x-coordinate is 0. The point we were given is (0,2). This means the y-intercept is 2. Our equation is y=x+2.
Answer:
y=x+2
Step-by-step explanation:
Slope intercept form is:
y=mx+b
where m is the slope and b is the y-intercept.
We know that this line has a slope of 1. Therefore, we can substitute 1 in for m.
y=1x+b
1x is equal to just x, so change 1x to x.
y=x+b
Now we must find the y-intercept, or b.
Y-intercepts are where the line crosses the y axis. The x-coordinate is always a 0.
Therefore, (0,y) is the coordinates of a y-intercept, and the "y" is the y-intercept.
We are given the point:
(0,2)
Since the x-coordinate is a 0, the y-intercept is 2. Substitute 2 in for b.
y=x+b
y=x+2
The equation of the line is y=x+2
A baseball card collector buys and opens 360 packs of 1989 Fleer baseball cards. He is told that there is a 2.3% chance of anyone pack containing the coveted Billy Ripken error card. Find the mean and standard deviation of the random variable "number of Billy Ripken error cards ound", where n-360
Answer:
Mean: 8.28
Standard deviation: 2.84
Step-by-step explanation:
This random variable "number of Billy Ripken error cards found" can be described by the binomial distribution, with sample size n=360 (number of packs) and probability of success p=0.023 (probabillity of a pack containing the coveted Billy Ripken error card).
Then, the mean and standard deviation are calculate as for the binomial distribution:
[tex]\mu=np=360\cdot 0.023=8.28\\\\\sigma=\sqrt{np(1-p)}=\sqrt{360\cdot 0.023\cdot 0.977}=\sqrt{8.08956}\approx2.84[/tex]
which linear is represented by the graph?
Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6 period time frame:
Period : 1, 2, 3, 4, 5, 6
Demand: 200, 245, 190, 270, 280, 300
Use a 2 period moving average to forecast the demand for period 7.
Answer:
Forecast demand for period 7 is 290.
Step-by-step explanation:
The given number of period = 6
Since it is given that in period 1, the demand is 200 and at period 6 the demand is 300. However, to find the forecast demand for period 7, just add the demand of period 1 and period 6, then divide by 2.
Here, the following is the calculation.
Forecast demand for period 7 = (280 + 300) / 2
= 290
Which of the following shows the intersection of the sets? {7, 8, 9, 10} {9, 10, 11, 12}
Answer:
{9, 10}
Step-by-step explanation:
The intersection of sets are the numbers that appear in both sets. In this case the only numbers that appear in both sets are 9 and 10.
Answer:
{ 9,10}
Step-by-step explanation:
The intersection of the sets is what the two sets have in common
{7, 8, 9, 10} ∩{9, 10, 11, 12}
{ 9,10}
A survey was conducted to determine the amount of time, on average, during a given week SCAD students spend outside of class on class work (projects, homework, and studying). The data shows: 5, 7, 11, 14, 18, 22 (in hours). Calculate the standard deviation by using the appropriate formula. Round your answer to three decimal places.
Answer:
Standard Deviation = 5.928
Step-by-step explanation:
a) Data:
Days Hours spent (Mean - Hour)²
1 5 61.356
2 7 34.024
3 11 3.360
4 14 1.362
5 18 26.698
6 22 84.034
6 days 77 hours, 210.834
mean
77/6 = 12.833 and 210.83/6 = 35.139
Therefore, the square root of 35.139 = 5.928
b) The standard deviation of 5.928 shows how the hours students spend outside of class on class work varies from the mean of the total hours they spend outside of class on class work.
The second of two numbers is 7 times the first. Their sum is 72. Find the numbers.
Answer:
first number: 9 second number: 63
Step-by-step explanation
lets make a ratio!
since one number is 7 times less than the other, the ratio would be: 1:7.
now to find the answer, you'd have to do 1+7 divided by 72. so basically
x=72/8
then solving that should be simple!
x=9
so 7x would be 63.
The probability that a grader will make a marking error on any particular question of a multiple-choice exam is 0.10. If there are ten questions and questions are marked independently, what is the probability that no errors are made
Answer:
0.9^10
Step-by-step explanation:
The probability to make an error in 1 question =0.1 => The probability that this one particular question will be answered correctly is P=1-0.1=0.9
There are 10 questions that are independent from each other .
The probability to be answered correctly is 0.9 each. So the probability to answer correctly to all of them is
P(10quest=correct) =0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9=0.9^10
Express the confidence interval 0.555 less than 0.777 in the form Modifying above p with caret plus or minus Upper E.
Complete Question
Express the confidence interval 0.555 less than p less than 0.777 in the form Modifying above p with caret plus or minus Upper E.
Answer:
The modified representation is [tex]\r p \pm E = 0.666 \pm 0.111[/tex]
Step-by-step explanation:
From the question we are told that
The confidence interval interval is [tex]0.555 < p < 0.777[/tex]
Now looking at the values that make up the up confidence interval we see that this is a symmetric confidence interval(This because the interval covers 95% of the area under the normal curve which mean that the probability of a value falling outside the interval is 0.05 which is divided into two , the first half on the left -tail and the second half on the right tail as shown on the figure in the first uploaded image(reference - Yale University ) ) which means
Now since the confidence interval is symmetric , we can obtain the sample proportion as follows
[tex]\r p = \frac{0.555 + 0.777}{2}[/tex]
[tex]\r p =0.666[/tex]
Generally the margin of error is mathematically represented as
[tex]E = \frac{1}{2} * K[/tex]
Where K is the length of the confidence interval which iis mathematically represented as
[tex]K = 0.777 -0.555[/tex]
[tex]K = 0.222[/tex]
Hence
[tex]ME = \frac{1}{2} * 0.222[/tex]
[tex]ME = 0.111[/tex]
So the confidence interval can now be represented as
[tex]\r p \pm E = 0.666 \pm 0.111[/tex]
Norah has $50,000 to invest. She is considering two investment options. Option A pays 1.5% simple interest. Option B pays 1.4% interest compounded annually. Drag dollar amounts to the table to show the value of each investment option after 5 years, 10 years, and 20 years rounded to the nearest dollar. the answer choices are: 58,027 53,500 53,750 57,458 66,028 65,000
Answer:
Option A
5 years: $53,750
10 years: $57,500
20 years: $65,000
Option B
5 years: $53,599
10 years: $57,458
20 years: $66,028
Answer:
the corrects answers
Option A
5 years: $53,750
10 years: $57,500
20 years: $65,000
Option B
5 years: $53,599
10 years: $57,458
20 years: $66,028
In a survey of 1309 people, 825 people said they voted in a recent presidential election. Voting records show that 60% of eligible voters actually did vote. Given that 60% of eligible voters actually did vote,
(a) find the probability that among 1309 randomly selected voters, at least 825 actually did vote.
(b) What do the results from part (a) suggest?
Answer:
a) P(X>825)
b) This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.
Step-by-step explanation:
We know a priori that 60% of the eligible voters did vote.
From this proportion and a sample size n=1309, we can construct a normal distribution probabilty, that is the approximation of the binomial distribution for large samples.
Its mean and standard deviation are:
[tex]\mu=n\cdot p=1309\cdot 0.6=785.4\\\\\sigma =\sqrt{np(1-p)}=\sqrt{1309\cdot 0.6\cdot 0.4}=\sqrt{314.16}=17.7[/tex]
Now, we have to calculate the probabilty that, in the sample of 1309 voters, at least 825 actually did vote. This is P(X>825).
This can be calculated using the z-score for X=825 for the sampling distribution we calculated prerviously:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{825-785.4}{17.7}=\dfrac{39.6}{17.7}=2.24\\\\\\P(X>825)=P(z>2.24)=0.0126[/tex]
This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.
Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively. Assume the time of wheel throwing and time of firing are independent random variables.
A) What is the probability that a piece of pottery will befinished within 95 minutes?
B) What is the probability that it will take longer than 110minutes?
Answer:
a) 8.23% probability that a piece of pottery will be finished within 95 minutes
b) 0.28% probability that it will take longer than 110 minutes.
Step-by-step explanation:
Normal distribution:
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.
Two variables:
Means [tex]\mu_{a}, \mu_{b}[/tex]
Standard deviations [tex]\sigma_{a}, \sigma_{b}[/tex]
Sum:
[tex]\mu = \mu_{a} + \mu_{b}[/tex]
[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}[/tex]
In this question:
[tex]\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3[/tex]
So
[tex]\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100[/tex]
[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61[/tex]
A) What is the probability that a piece of pottery will befinished within 95 minutes?
This is the pvalue of Z when X = 95.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{95 - 100}{3.61}[/tex]
[tex]Z = -1.39[/tex]
[tex]Z = -1.39[/tex] has a pvalue of 0.0823
8.23% probability that a piece of pottery will befinished within 95 minutes.
B) What is the probability that it will take longer than 110 minutes?
This is 1 subtracted by the pvalue of Z when X = 110.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 100}{3.61}[/tex]
[tex]Z = 2.77[/tex]
[tex]Z = 2.77[/tex] has a pvalue of 0.9972
1 - 0.9972 = 0.0028
0.28% probability that it will take longer than 110 minutes.
Write and solve the equation and then check your answer. A number increased by twenty-six is forty-two. Which statements are correct? Check all that apply. This is an addition problem. This is a subtraction problem The correct equation is s + 26 = 42. The correct equation is s – 26 = 42. To solve the equation, add 26 to both sides. To solve the equation, subtract 26 from both sides.
Answer:
equation= s+26=42
to solve,subtract 26 from both sides
Step-by-step explanation:
lets say the number is S
to increase is to add
S+26=42
solution
S+26(-26)=42-26
S=16
Answer:
A: This is an addition problem.C: The correct equation is s + 26 = 42. F: To solve the equation, subtract 26 from both sides.Explanation: Correct on Edg 2020.
A grocery store estimates that customers arrive at the rate of 15 per hour. The cashier can serve customers at a rate 20 per hour. Calculate the average number of customers in a line. Group of answer choices
Answer:
The average number of customers in a line = 2.25
Step-by-step explanation:
We are given;
Mean arrival rate;a = 15 customers per hour
Mean service rate;s = 20 customers per hour
Now, we want to find the average number of customers in the line. It is given by the formula;
N_q = a(W_q) = a²/(s(s - a)
Plugging in relevant values, we have;
N_q = 15²/(20(20 - 15))
N_q = 225/100
N_q = 2.25
I need to find for both f(-1) and f(1) it’s
Answer:
f(-1) = -8
f(1) = -12
Simplify the expression:
9a – 7a + 4 – 4 + 8
Answer:
2a + 8
Step-by-step explanation:
9a - 7a + 4 - 4 + 8
=> 2a + 12 - 4
=> 2a + 8
www.g "A political discussion group consists of 6 Democrats and 10 Republicans. Three members are selected to attend a conference. Find the probability that the group will consist of all Republicans."
Answer:
[tex]Probability = \frac{3\\}{14}[/tex]
Step-by-step explanation:
Given
Republicans = 10
Democrats = 6
Total = Republicans + Democrats = 10 + 6 = 16
Selection = 3
Required
Probability that all selected members are Republicans
This implies that all selected members are republicans and none are republicans
This is calculated by (Number of ways of selecting 3 republicans * Number of ways of selecting 0 Democrats) / (Total number of possible selections)
First; the number of ways the 3 republicans from 10 can be selected needs to be calculated;
[tex]^{10}C_3 = \frac{10!}{(10-3)!3!}[/tex]
[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]
[tex]^{10}C_3 = \frac{10*9*8*7!}{3!7!}[/tex]
Divide numerator and denominator by 7!
[tex]^{10}C_3 = \frac{10*9*8}{3*2*1}[/tex]
[tex]^{10}C_3 = \frac{720}{6}[/tex]
[tex]^{10}C_3 = 120[/tex]
Next, the number of ways that 0 republicans can be selected from 6 will be calculated
[tex]^6C_0 = \frac{6!}{(6-0)!0!}[/tex]
[tex]^6C_0 = \frac{6!}{6!0!}[/tex]
[tex]^6C_0 = 1[/tex]
Next, the total number of possible selection will be calculated; In other words number of ways of selecting 3 politicians fro a group of 16
[tex]^{16}C_3 = \frac{16!}{(16-3)!3!}[/tex]
[tex]^{16}C_3 = \frac{16!}{13!3!}[/tex]
[tex]^{16}C_3 = \frac{16*15*14*13!}{13!3!}[/tex]
[tex]^{16}C_3 = \frac{16*15*14}{3!}[/tex]
[tex]^{16}C_3 = \frac{16*15*14}{3*2*1}[/tex]
[tex]^{16}C_3 = \frac{3360}{6}[/tex]
[tex]^{16}C_3 = 560[/tex]
Lastly, the probability is calculated as follows;
[tex]Probability = \frac{^{10}C_3\ *\ ^6C_0}{^{16}C_3}[/tex]
[tex]Probability = \frac{120\ *\ 1}{560}[/tex]
[tex]Probability = \frac{120\\}{560}[/tex]
Simplify fraction to lowest term
[tex]Probability = \frac{3\\}{14}[/tex]
Compare using >, <, or
9 hours
450 minutes
Answer:
9 hours > 450 minutes
Step-by-step explanation:
An hour is a period of 60 minutes. 9 times 60 (9 hours) is 540 minutes.
540 > 450 minutes.
9 hours is more than 450 minutes.
9 hours > 450 minutes
Answer:
9 hours > 450 minutes
Step-by-step explanation:
We want to compare 9 hours with 450 minutes.
Let's first convert them to the same units of time: minutes.
There are 60 minutes in an hour, so there are 60 * 9 = 540 minutes in 9 hours.
Clearly, 540 is greater than 450, so we would use > to show that:
9 hours > 450 minutes
~ an aesthetics lover
I NEED HELP PLEASE, THANKS! :)
Answer:
7/2
Step-by-step explanation:
notice that if you substitute x by five you get 0/0 wich a non-defined form
The trick is to simplify by x-5
(x²-3x-10)/(2x-10)You get using the Euclidien division : x²-3x-10 = (x-5) (x-2)so : (x-2)(x-5)/2*(x-5) = (x-2)/2 substitute x by 5 to get 7/2 [tex]\lim_{x\to \5} \frac{x^{2} -3x-10}{2x-10}[/tex] = 7/2Hey there! :)
Answer:
[tex]\lim_{x \to 5} = 7/2[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\frac{x^{2}-3x-10 }{2x-10}[/tex]
Factor the numerator and denominator:
[tex]\frac{(x - 5)(x+2) }{2(x-5)}[/tex]
'x - 5' is on both the numerator and denominator, so it gets cancelled out and becomes a "hole".
This means that at x = 5, there is a hole. There is a limit at x ⇒ 5. Find the hole by plugging 5 into the simplified equation:
[tex]\frac{((5)+2) }{2}[/tex] = 7/2
Therefore:
[tex]\lim_{x \to 5} = 7/2[/tex]
The table shows three unique functions. (TABLE IN PIC) Which statements can be used to compare the characteristics of the functions? Select two options. f(x) has an all negative domain. g(x) has the greatest maximum value. All three functions share the same range. h(x) has a range of all negative numbers. All three functions share the same domain.
Answer:
Correct answers are:
g(x) has the maximum greatest value.
h(x) has a a range of all negative numbers.
Step-by-step explanation:
Let us learn about the domain and range of a function first.
Domain of a function is the input that we give to the function for which there is a valid output.
For example, let us consider a function:
[tex]y=F(x) = x^2[/tex]
So, the value of 'x' that we provide to the function is known as the domain of function.
Range of a function is the output value when any input is given to the function.
For example,
[tex]y=F(x) = x^2[/tex]
Let us put x = 4, which will be in the domain of function.
the output will be y = 16 which will be in the range of the function.
Now, let us consider the given functions f(x), g(x) and h(x).
Domain of f(x) i.e. the value of x for which the output is defined is:
{-2, -1, 1, 2}
Range of f(x) = [tex]\{4, 4\frac{1}2, 5\frac{1}2, 6\}[/tex]
Max value of f(x) = 6
Domain of g(x) i.e. the value of x for which the output is defined is:
{-2, -1, 1, 2}
Range of g(x) = [tex]\{6, 6\frac{1}2, 7\frac{1}2, 8\}[/tex]
Max value of g(x) = 8
Domain of h(x) i.e. the value of x for which the output is defined is:
{-2, -1, 1}
Range of h(x) = [tex]\{-3, -2\frac{1}2, -1\frac{1}2\}[/tex]
Max value of h(x) = [tex]-1\frac{1}2[/tex]
For x = 2, the value of h(x) is not given i.e. it is not defined at x = 2, so it is not in the domain. So, domain of all the three functions is not same.
So, the correct options are:
g(x) has the maximum greatest value.
h(x) has a a range of all negative numbers.
Answer:
B,D
Step-by-step explanation:
Edge 2020 100%
Use the Pythagorean theorem to calculate the diagonal of a TV is it's length is 36 inches and its width is 15 inches. Round your final answer to one decimal place.
Answer:
39 inches
Step-by-step explanation:
sqrt(15^2 + 36^2) = 39
(a) 18 ÷ 2 = 9 because___×___=___
Answer: 2 x 9 = 18
Step-by-step explanation:
Multiplication is division’s inverse operation.
What is the solution to the inequality below?
x < 5
A. x< 25 or x>-25
B. x < 25 or x>0
O C. x< 25 and x > 0
O D. x < 25 and x>-25
Answer:
C. x < 25 and x ≥ 0
Step-by-step explanation:
Fastest and easiest way to do this is to graph the inequality and find out the lines.
3/(2x-1)+4=6x/(2x-1)
X=?
Every new computer costs $702.37 from a local store. The nearby school has a policy that every 3 children must have at least 1 computer. If each class has 24 children, how much money should the school spend on computers if there is 17 classes?
Division is one of the four fundamental arithmetic operations. The amount of money the school needs to spend on computers is $95,522.32.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The number of students in a class is 24, while the number of classes is 17. Therefore, the number of students in the classes should be,
[tex]\text{Total number of students} = 24 \times 17 = 408[/tex]
Now, since, there should be a computer for every 3 students, therefore, the number of computers that will be needed are,
[tex]\text{Number of computer} = \dfrac{\text{Number of students}}{3} = \dfrac{408}{3} = 136[/tex]
The cost of a single computer is $702.37, therefore, the cost of 136 computers will be,
[tex]\rm Total\ cost= (\text{Cost of a single computer}) \times 136\\\\ Total\ cost= (\$702.37) \times 136\\\\ Total\ cost= \$95,522.32[/tex]
Hence, the amount of money the school needs to spend on computers is $95,522.32.
Learn more about Division:
https://brainly.com/question/369266
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Simplify. n 6 • n 5 ÷ n 4 • n 3 ÷ n 2 • n
━━━━━━━☆☆━━━━━━━
▹ Answer
n⁸
▹ Step-by-Step Explanation
n⁶ * n⁵ ÷ n⁴ * n³ ÷ n² * n
n⁶ * n⁵ * n⁻⁴ * n³ ÷ n²
n⁶ ⁺ ⁵ ⁻ ⁴ ⁺ ³ ⁻ ²
n⁸
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
2^9
Step-by-step explanation:
The other answer says n^8 I believe? Tried this and the answer ended up being n^9.
how do you graph y=–7/3x+2. PLEASE HELP ME
Graph the line using the slope and y-intercept, or two points.
Slope: -7/3
y-intercept: 2
Please mark me as brainliest if possible. Stay safe and God bless you!!
<3
- Eli
Suppose Melissa borrows $3500 at an interest rate of 14% compounded each year,
Assume that no payments are made on the loan.
Do not do any rounding.
(a) Find the amount owed at the end of 1 year
(b) Find the amount owed at the end of 2 years.
PLEASE HELPPP!!!
A regular hexagon is inscribed in a circle. The circle is inscribed in a square. If the side length of the square is 25 cm, what is the length of each side of the hexagon?
Answer:
12.5
Step-by-step explanation:
to find the length of one side of the hexagon, draw diagonal lines, which will be six diagonals, this will divide the hexagon into, 6 equilateral triangles. The diagonals are equal in length to the side of the square (25 cm.) and the sides of the equilateral triangles are just half of this (12.5 cm.)
25/2=12.5
What is the solution to the following equation?
X/3 - 14 = -2
Answer:
x = 36
Step-by-step explanation:
x/3 - 14 = -2
x - 42 = -6
x = -6 + 42
x = 36
Hope this helps! :)
Answer:
x= 36
Step-by-step explanation:
X/3 - 14 = -2
Add 14 to each side
X/3 - 14+14 = -2+14
x/3 = 12
Multiply each side by 3
x/3 * 3 = 12*3
x = 36