The test statistic and p-value for the slope of the regression line are t = 26 and p-value = 0.00.
Based on the given information, the analysis is focused on determining whether there is a linear relationship between GRE score and the chance of admission. The pattern observed in the scatterplot shows a linear pattern in the data, indicating a potential linear relationship between the two variables.
To test this hypothesis, a regression analysis was performed, which yielded a coefficient table with estimates for the intercept and slope of the regression line. The p-value for the slope test was found to be 0.00, which suggests strong evidence for a significant linear relationship between GRE score and the chance of admission.
Furthermore, a 95% confidence interval for the slope was calculated, which did not include the null value of zero. This means that we can reject the null hypothesis and conclude that there is a linear relationship between the GRE score and the chance of admission.
In summary, based on the analysis and statistical tests performed, there is evidence to support a linear relationship between the GRE score and the chance of admission.
The test statistic and p-value for the slope of the regression line are t = 26. ,an p-value = 0.00.
A 95% confidence interval for the slope on the line is (0.01, 0.01). Since 0 is not found in the confidence interval and our alternative hypothesis is two-sided, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and the chance of admission.
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Assume that all segments that appear to be tangent are tangent. Find the value RT. P 13 RT = Q X T 9 S R 11
Answer: value of RT is 4√3.
Step-by-step explanation: To solve for the value of RT, we can use the fact that the tangent to a circle is perpendicular to the radius drawn to the point of tangency.
In this case, we can draw a radius from the center of the circle (point O) to point T and label it OT. Since RT is tangent to the circle at point T, it is perpendicular to the radius OT.
We can then use the Pythagorean theorem to relate the lengths of the line segments in the right triangle OTR:
OT^2 = OR^2 + RT^2
Substituting the given values, we have:
13^2 = 11^2 + RT^2
169 = 121 + RT^2
RT^2 = 48
Taking the square root of both sides, we get:
RT = √48 = 4√3
Therefore, the value of RT is 4√3.
According to math modeling, what values cannot vary without consequence?
In mathematical modeling, some values are considered fixed and cannot vary without consequence. These values are often referred to as constants or parameters, and they represent physical or environmental properties that are assumed to be constant throughout the problem.
For example, in a mathematical model of the motion of a pendulum, the length of the pendulum, the mass of the weight, and the force of gravity are typically considered constants that cannot vary without consequence. If any of these values were to change, the motion of the pendulum would be affected, and the solution to the problem would be different.
Similarly, in a mathematical model of heat transfer, the thermal conductivity of the material, the heat source or sink, and the boundary conditions are typically considered constants that cannot vary without consequence. If any of these values were to change, the temperature distribution and heat transfer rate within the system would be affected, and the solution to the problem would be different.
The choice of which values to consider as constants or parameters depends on the specific problem being modeled and the assumptions made.
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explain in your own words the difference between an implicitly defined function and an explicitly defined function.
The difference between an implicitly defined function and an explicitly defined function lies in how the relationship between the variables is expressed.
In an explicitly defined function, the dependent variable (usually y) is expressed directly in terms of the independent variable (usually x), such as y = f(x). In an implicitly defined function, the relationship between the variables is expressed indirectly through an equation involving both variables, such as F(x, y) = 0, making it not straightforward to solve for y in terms of x.
Explicitly defined functions provide a clear and explicit expression for the dependent variable in terms of the independent variable, allowing for direct evaluation and computation. They are commonly used when the relationship between variables can be easily represented by a formula or equation.
On the other hand, implicitly defined functions are often used when the relationship between variables is more complex or cannot be easily expressed in a single equation. They require additional manipulation or solving techniques to determine the relationship between the variables.
Implicit functions are commonly encountered in calculus and differential equations, where the relationships may involve derivatives or multiple variables.
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The area of a rectangle is 35 sq. ft. The length is 3 ft. less than twice the width. What are the dimensions of the rectangle
Answer:
length-7 width-5
Step-by-step explanation:
I used to guess and check so if you give a good guess you can get it in two attempts
identify which angles are equal in each triangle
Answer:
In Triangle A all angles are equal and in B only angles q and a are equal
Step-by-step explanation:
Triangle A is an equilateral triangle which means all angles are the same but since Triangle B is an Isosceles Traiangle means only two angles are equal
The measure of angles which are equal in each triangle
Triangle A: x= y = zTriangle B: q = sUsing the definition,
"the angles opposite to the legs are equal to each other."
Two Triangles are given names as Triangle A and Triangle B.
For Triangle A:As, in first triangle all the sides are equal and angles opposite to the sides are equal to each other.
So, x = y = z
For Triangle B:Now, in second triangle two sides are equal and angles opposite to the sides are equal to each other.
So, <q = <s
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A company has 3 employees, and each employee earns $15.50 an hour. The employees worked for 8 hours at regular pay and then for 2 hours at a higher overtime rate. The overtime rate is an extra $7.00 per hour. How much in total did the company pay the employees?
Answer:
Each employee worked for 8 regular hours and 2 overtime hours, so each employee worked for a total of 10 hours. The regular pay rate is $15.50 per hour, so each employee earned 8 hours x $15.50 = $124 for regular pay. For overtime pay, each employee worked for 2 hours x ($15.50 + $7.00) = $44 in total.
Step-by-step explanation:
Therefore, each employee earned a total of $124 + $44 = $168.
Since there are 3 employees, the total amount that the company paid the employees is $168 x 3 = $504.
Therefore, the company paid a total of $504 to its employees.
Answer:
$507
Step-by-step explanation:
The total rate for overtime work is $7.00 + $15.50 = $22.50
1 employee worked:
8 hours at $15.50 per hour
2 hours at $22.50 per hour
total for 1 employee:
8 × $15.50 + 2 × $22.50 = $124 + $45 = $169
total for 3 employees:
3 × $169 = $507
help on how to do this stuff
The cosine of angle X is given as follows:
cos(X) = 4/5.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For angle X, we have that:
The adjacent side is of 32.The hypotenuse is of 40.Hence the cosine of angle X is obtained as follows:
cos(X) = 32/40
cos(X) = 4/5.
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Sam needed 0.25 cups of flour. Convert the amount of cups as a fraction.
Answer:
1/4
Step-by-step explanation:
.25 has two numbers after the decimal so we put 25 over 100
25/100
We can simplify this fraction by dividing the top and bottom by 25
25÷25 =1
100 ÷25 =4
The fraction becomes 1/4
Answer: 1/4
Step-by-step explanation:
You can think of 0.25 as 25 hundredths to convert it to a fraction. In other words, you have 25 of 100 equal parts.
So, the fraction will be 25/100
We can simplify that fraction by dividing both the numerator and denominator by the greatest common factor, which is 25.
25/100 ÷ 25 = 1/4
This gives us 1/4.
So, 0.25 is equal to 1/4.
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do me a favor pleaseee by helping me solve this
The solution of the given parabola is (0, -2) and equation is y=a(x+1)²
The equation of parabola in standard form is y=a(x-h)²+k
Where (h, k) are the coordinates of vertex
The value of (h, k) is (-1, 0)
Now plug in the values in equation
y=a(x+1)²+0
y=a(x+1)²
The point (0, -2) is in parabola
Hence, the solution of the given parabola is (0, -2)
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a group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. to test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. the treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distractions. patients in the treatment group ate 52.1 grams of biscuits, with a standard deviation of 45.1 grams, and patients in the control group ate 27.1 grams of biscuits, with a standard deviation of 26.4 grams. do these data provide convincing evidence that the average food intake (measured in amount of biscuits consumed) is different for the patients in the treatment group? assume that conditions for inference are satisfied. use the treatment group as group a and the control group as group b.
Since the calculated t-value (2.24) is greater than the critical value (2.074), we reject the null hypothesis and conclude that there is convincing evidence that the average food intake is different for the patients in the treatment group. In other words, playing solitaire while eating lunch seems to have an effect on the amount of food consumed.
To determine whether there is convincing evidence that the average food intake is different for the patients in the treatment group, we can conduct a two-sample t-test. The null hypothesis is that the means of the two groups are equal, and the alternative hypothesis is that they are different.
H0: μa = μb
Ha: μa ≠ μb
where μa is the mean amount of biscuits consumed in the treatment group and μb is the mean amount of biscuits consumed in the control group.
We can use the following formula to calculate the test statistic:
t = (Xa - Xb) / √[(Sa²/n) + (Sb²/n)]
where Xa and Xb are the sample means, Sa and Sb are the sample standard deviations, and n is the sample size.
Plugging in the values from the question, we get:
t = (52.1 - 27.1) / √[(45.1²/22) + (26.4²/22)]
= 2.24
Using a two-tailed t-distribution with 22 degrees of freedom and a significance level of 0.05, the critical values are ±2.074.
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Which expression has a value less than 1? A. 3/4 x 4/3 B. 3/4 x 6/3 C. 3/4 x 4/4 D. 3/4 x 8/4
The expression that has a value less than 1 is 3/4 x 4/4, the correct answer is option C. To decide which expression contains esteem less than 1, we got to rearrange each expression and compare it to 1.
A. 3/4 x 4/3
Increasing these divisions, we get:
(3/4) x (4/3) = 12/12 = 1
This expression rearranges to 1, which isn't less than 1.
B. 3/4 x 6/3
Duplicating these divisions, we get:
(3/4) x (6/3) = 18/12 = 3/2
This expression disentangles to 3/2, which is more prominent than 1.
C. 3/4 x 4/4
Duplicating these divisions, we get:
(3/4) x (4/4) = 12/16 = 3/4
This expression streamlines to 3/4, which is less than 1.
D. 3/4 x 8/4
Increasing these divisions, we get:
(3/4) x (8/4) = 24/16 = 3/2
This expression rearranges to 3/2, which is more prominent than 1.
thus, the expression that incorporates esteem less than 1 is alternative C, 3/4 x 4/4.
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‼️will mark as Brainlist‼️During a sale, a store offered a 30% discount on a tablet computer that originally sold for $670. After the sale, the discounted price of the tablet computer was marked up by 30%. What was the price of the tablet computer after the markup? Round to the nearest cent.
According to the discount, the price of the tablet computer after the markup is $610.30.
In this problem, a store offered a 30% discount on a tablet computer that originally sold for $670. We can calculate the discounted price of the tablet computer by finding 30% of its original price and subtracting it from the original price.
Discounted price = Original price - Discount
Discounted price = $670 - 30% of $670
Discounted price = $670 - $201
Discounted price = $469
So, the discounted price of the tablet computer is $469.
The problem then asks us to find the price of the tablet computer after it is marked up by 30%. To do this, we need to add 30% of the discounted price to the discounted price.
Markup price = Discounted price + Markup
Markup price = $469 + 30% of $469
Markup price = $469 + $141.30
Markup price = $610.30
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the table shows the total cost for diffrent numbers of nights at a campground
The statement which is not True is
The independent variable is c and dependent variable is n.
We have a table shows the total cost for different numbers of nights at a campground
So, the rate of change is
= (80- 32)/ (5-2)
= 48/ 3
= 16
and, the y intercept is
32 = 16(2)+ b
b= 0
Then, the equation is y= 16n.
and, The independent variable is n and dependent variable is c.
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Determine if each function is independent. a) f(x,y) = 4(x + xy) if 0
To determine if a function is independent, we need to analyze whether one variable can be expressed as a function of the other variable(s).
In the given function f(x,y) = 4(x + xy), let's see if either x or y can be isolated.
f(x,y) = 4(x + xy)
f(x,y) = 4x + 4xy
Now, let's try to isolate y:
f(x,y) - 4x = 4xy
(f(x,y) - 4x) / 4x = y
From the above equation, we can see that y is expressed as a function of x and f(x,y). Since y depends on both x and f(x,y), the variables x and y are not independent in this function.
In conclusion, for the given function f(x,y) = 4(x + xy), x and y are not independent variables. The relationship between x and y is dependent, as the value of y relies on both x and f(x,y).
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A 10-foot flag pole is standing in a yard and is casting a shadow that is 6 feet long. What is the distance from the top of the flag pole to the top of the shadow?
The flag pole's shadow extends six feet above the ground from the top of the pole.
This issue may be resolved with triangles that are comparable. Let's use the letters "x" for the flag pole's height and "y" for the distance from the pole to the top of its shadow. Hence, we may establish the ratio shown below:
x / y = 10 / 6
To solve for y, we can cross-multiply:
y * 10 = x * 6
y = (x * 6) / 10
Now, we just need to substitute the known values and solve for y:
y = (10 * 6) / 10 = 6
Therefore, the distance from the top of the flag pole to the top of its shadow is 6 feet.
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if 25% of pet owners have their pets bathed professionally rather than doing it themselves, find the probability that if 18 pet owners are randomly selected that at least one has their pet bathed professionally.
The probability of at least one pet owner out of 18 having their pet bathed professionally is:
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.0052 = 0.9948
Given that 25% of pet owners have their pets bathed professionally, the probability of a single pet owner having their pet bathed professionally is 0.25. Conversely, the probability of a pet owner not having their pet bathed professionally is 1 - 0.25 = 0.75.
To find the probability that at least one pet owner out of 18 randomly selected has their pet bathed professionally, we can first find the probability that none of the 18 pet owners have their pets bathed professionally and then subtract it from 1.
Step 1: Find the probability that none of the 18 pet owners have their pets bathed professionally.
The probability of one pet owner not having their pet bathed professionally is 0.75. Since we're considering 18 independent pet owners, we need to multiply this probability 18 times.
Probability (none have pets bathed professionally) = (0.75)^18
Step 2: Subtract the probability found in step 1 from 1.
The probability that at least one pet owner has their pet bathed professionally is the complement of the probability found in step 1.
The probability of a pet owner having their pet bathed professionally is 25%, which can be written as 0.25. The probability of a pet owner not having their pet bathed professionally is 1 - 0.25 = 0.75.
Using the binomial probability formula, we can calculate the probability of no pet owners out of 18 having their pet bathed professionally:
P(X = 0) = (0.75)^18 = 0.0052
Therefore, the probability of at least one pet owner out of 18 having their pet bathed professionally is:
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.0052 = 0.9948
Probability (at least one has pet bathed professionally) = 1 - (0.75)^18
Now, you can calculate the probability using a calculator. The result will be the probability that at least one of the 18 randomly selected pet owners has their pet bathed professionally.
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What is the smallest alpha you can reject the nullhypothesis under when you have a p-value of 0.054?a.) 0.05b.) 0.055c.) 0.06d.) 0.056
Answer:
0.06
Step-by-step explanation:
The smallest alpha you can reject the null hypothesis under when you have a p-value of 0.054 is 0.06.
In hypothesis testing, we compare the p-value to the level of significance (alpha) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than or equal to alpha, we reject the null hypothesis. If the p-value is greater than alpha, we fail to reject the null hypothesis.
In this case, the p-value is greater than 0.05 (the commonly used alpha level), but it is less than 0.06. Therefore, we can reject the null hypothesis at the 0.06 alpha level, but not at the 0.05 alpha level.
The smallest alpha you can reject the null hypothesis under when you have a p-value of 0.054 is option (d) 0.056.
The smallest alpha at which you can reject the null hypothesis when you have a p-value of 0.054 is:
b.) 0.055
The p-value must be less than or equal to the chosen alpha level to reject the null hypothesis. Since 0.054 is greater than 0.05 but less than 0.055, you can reject the null hypothesis at an alpha level of 0.055.
This is because the p-value (0.054) is greater than the usual significance level of 0.05, but it is less than 0.056. Therefore, if you set your significance level to 0.056 or greater, you can reject the null hypothesis.
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find the exact value of tan I in simpelst radical form.
The value of tan I = √12/9
How to determine the valueTo determine the value of tan I from the diagram, we have to take note of the different trigonometric identities in mathematics;
These includes;
cosinetangentsinecotangentsecantcosecantAlso, the ratios of these identities are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
Substitute the values
Opposite = √12
Adjacent = 9
Now, add the values, we get
tan I = √12/9
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The manager of a company’s Learning and Development team is organizing a career development seminar and has contacted two potential venues about hosting the event on a specific date. If neither venue is able to accommodate the event on the requested date, the event will have to be postponed until the following year. The probability that the first venue can accommodate the event is estimated to be 0.75. The probability that the second venue can accommodate the event is estimated to be 0.30.
a. What is the probability that both venues can accommodate the event? Because the venues are not affiliated with each other, assume independence.
b. What is the probability that at least one venue can accommodate the event?
c. What is the probability that the event must be postponed because neither venue can accommodate the event on the requested date? (1 pt)
a P(both can accommodate) = 0.225 or 22.5% ,P(event must be postponed) = 0.775 or 77.5%
a. The probability that both venues can accommodate the event is found by multiplying the individual probabilities together, since they are assumed to be independent:
P(both can accommodate) = P(first venue can accommodate) x P(second venue can accommodate)
P(both can accommodate) = 0.75 x 0.30
P(both can accommodate) = 0.225 or 22.5%
b. The probability that at least one venue can accommodate the event is found by using the complement rule:
P(at least one can accommodate) = 1 - P(neither can accommodate)
Since the only two possible outcomes are that either both venues can accommodate or neither can, we can use the probabilities from part a to find the probability that neither can accommodate:
P(neither can accommodate) = 1 - P(both can accommodate)
P(neither can accommodate) = 1 - 0.225
P(neither can accommodate) = 0.775
Now we can use the complement rule to find the probability that at least one venue can accommodate:
P(at least one can accommodate) = 1 - P(neither can accommodate)
P(at least one can accommodate) = 1 - 0.775
P(at least one can accommodate) = 0.225 or 22.5%
c. The probability that the event must be postponed because neither venue can accommodate is simply the complement of the probability that at least one venue can accommodate:
P(event must be postponed) = 1 - P(at least one can accommodate)
P(event must be postponed) = 1 - 0.225
P(event must be postponed) = 0.775 or 77.5%
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Can someone help me asap? It’s due today!! I will give brainliest if it’s correct
Please show work
Answer: 74
Step-by-step explanation:
Mean means average. Add all the numbers and divide by how many there are.
(86+45+93+77+63+80)/6
444/6
=74
On rolling a die, the sample space = {1,2,3,4,5,6}(a)The probability of rolling a 5 or a number greater than 3 is mathematically stated as:P(rolling a or rolling a number greater than 3) = P(rolling a 5) + P(rolling a 4) + P(rolling a 5) + P(rolling a 6)P(rolling a number 5) is getting repeated, hence the repetition has to be removed.Therefore,P(rolling a or rolling a number greater than 3) = P(rolling a 4) +P( rolling a 5) + P(rolling a 6) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2P(>3) = 1/2(b) P(rolling a number less than 5 or an even number) =P(rolling number 1) + P(rolling number 2) + P(rolling number 3) + P(rolling number 4) + P(rolling number 6)= 1/6 + 1/6 + 1/6 +1/6 + 1/6 = 5/6P(< 5 or an even number) = 5/6(c) P(rolling a six or an odd number) = P(rolling number 1) + P(rolling number 3) + P(rolling number 5) + P(rolling number 6) = 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3P(=6 or odd number) = 2/3
On rolling a die, the sample space is {1,2,3,4,5,6}. To find the probability of certain events, we can use mathematical statements.
(a) The probability of rolling a 5 or a number greater than 3 can be mathematically stated as:
P(rolling a 5 or rolling a number greater than 3) = P(rolling a 5) + P(rolling a 4) + P(rolling a 6)
However, we notice that the probability of rolling a 5 is repeated, so we need to remove the repetition:
P(rolling a 5 or rolling a number greater than 3) = P(rolling a 4) + P(rolling a 5) + P(rolling a 6) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2
Therefore, the probability of rolling a 5 or a number greater than 3 is 1/2.
(b) The probability of rolling a number less than 5 or an even number can be mathematically stated as:
P(rolling a number less than 5 or an even number) = P(rolling a 1) + P(rolling a 2) + P(rolling a 3) + P(rolling a 4) + P(rolling a 6)
Adding up the probabilities, we get:
P(rolling a number less than 5 or an even number) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 5/6
Therefore, the probability of rolling a number less than 5 or an even number is 5/6.
(c) The probability of rolling a six or an odd number can be mathematically stated as:
P(rolling a six or an odd number) = P(rolling a 1) + P(rolling a 3) + P(rolling a 5) + P(rolling a 6)
Adding up the probabilities, we get:
P(rolling a six or an odd number) = 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3
Therefore, the probability of rolling a six or an odd number is 2/3.
Based on your question, here are the answers incorporating the terms you've mentioned:
(a) The probability of rolling a 5 or a number greater than 3 can be mathematically stated as:
P(5 or >3) = P(4) + P(5) + P(6) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2
(b) The probability of rolling a number less than 5 or an even number is:
P(<5 or even) = P(1) + P(2) + P(3) + P(4) + P(6) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 5/6
(c) The probability of rolling a six or an odd number is:
P(6 or odd) = P(1) + P(3) + P(5) + P(6) = 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3
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A rainstorm in Portland, Oregon, wiped out the electricity in 7% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm.
A Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
B Quantify the uncertainty of your estimate by giving the standard deviation of the distribution.
To estimate the number of households in the sample that lost electricity, we can use the mean of the relevant distribution,
A) The relevant random variable is the number of households in the sample that lost electricity. Since we know that 7% of households in the city lost electricity, we can use this as the probability of any one household in the sample losing electricity. Therefore, the mean of the relevant distribution is:
Mean = np = 50 * 0.07 = 3.5 households
B) To find the standard deviation of the distribution, we use the formula:
Standard deviation = √(np(1-p))
where n is the sample size and p is the probability of success (in this case, the probability of a household losing electricity). Plugging in the values, we get:
Standard deviation = √(50 * 0.07 * (1 - 0.07)) = 1.51 households
Therefore, our estimate is that the sample will have an average of 3.5 households that lost electricity, with a standard deviation of 1.51 households.
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Find an explicit formula for a sequence of the form a1, a2, a3, ... with the initial terms given in Description below.
1-(1/3), (1/2)-(1/4), (1/3)-(1/5), (1/4)-(1/6), (1/5)-(1/7), (1/6)-(1/8)
Where n is the term number starting from 1. To find the explicit formula for the sequence a1, a2, a3, ..., we need to first observe the pattern in the given initial terms:
a1 = 1 - (1/3) = 2/3
a2 = (1/2) - (1/4) = 1/4 + 1/4 = 1/2
a3 = (1/3) - (1/5) = 2/15
a4 = (1/4) - (1/6) = 1/12 + 1/12 = 1/6
a5 = (1/5) - (1/7) = 2/35
a6 = (1/6) - (1/8) = 1/24 + 1/24 = 1/12
We notice that the numerator of the first term in each sequence is always 1, and the denominator increases by 2 each time. For the second term in each sequence, the numerator increases by 2 each time, while the denominator remains the same.
Based on this pattern, we can write the explicit formula for the sequence as follows:
[tex]an = ((-1)^(n+1) / n) + ((-1)^(n+1) / (n+2))[/tex]
where n is the term number starting from 1.
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#2 i
For which values of b will the area of the shaded region be greater than or equal to 12 square units?
b
Answer:
E. 9, F. 10
Step-by-step explanation:
Area of the rectangle: 3b
Area of the white triangle: 3b/3
Area of shaded region: 3b/2
3b/2 > 12
3b > 24
b > 8
Answer: E. 9, F. 10
hw 10 question 19: for the student survey data you should have created a row mean column representing the mean of roll1 - roll10 for each student. this quantity represents a sample mean.
The row mean values represent a sample mean for each student, as they are the average of the 10 rolls for each individual.
To calculate the row mean for each student in the survey data, follow these steps:
1. For each student, locate the values of rolls 1 through 10.
2. Add up the values of rolls 1 through 10 for that particular student.
3. Divide the sum obtained in step 2 by the total number of rolls (10) to get the mean.
4. Record this mean value in that student's "row mean" column.
This process should be repeated for each student in the dataset. The row mean values represent a sample mean for each student, as they are the average of the 10 rolls for each individual.
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HELP THIS IS DUE SOON
The calculated volume of the sphere is 113.04 in³
What is a sphere?
Recall that a sphere is a three-dimensional round-shaped object that does not have any vertices or edges.
the volume of the sphere is given as V.
Where V = 4/3 * π*r³
Where r = 3 inch
The volume V. = 4/3 * 3.14 * 3*3*3
Volume = 339.12/3
Volume of the sphere = 113.04 in³
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It took Hallie 2 minutes and 12 seconds to run a lap in PE class. Barry ran the lap in 138 seconds. Who ran the lap faster
Answer:
Hallie ran the lap faster
Step-by-step explanation:
Hallie: 60 x 2 = 120
120 + 12 = 132
Barry: 138
So that means Hallie is faster
I need help to answer this question here. X^2-10+25=(X-a)^2
The value of a in the equation X^2 - 10x + 25 = (X-a)^2 is 5
Calculating the value of a in the equationFrom the question, we have the following parameters that can be used in our computation:
X^2 - 10x + 25 = (X-a)^2
When the equation on the left hand side is factorized
We have
(X - 5)^2 = (X - a)
By comparing both sides of the equation, we have
-5 = -a
This gives
a = 5
Hence, the solution is a = 5
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grain silo consists of a cylindrical main section and a hemispherical roof. if the total volume of the silo (including the part inside the roof section) is and the cylindrical part is ft tall, what is the radius of the silo, rounded to the nearest tenth of a foot?
The radius of the grain silo is approximately 1.8 feet.
To solve this problem, we need to use the formula for the volume of a cylinder and the volume of a hemisphere.
The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height.
The volume of a hemisphere is given by V = (2/3)πr^3.
Since the silo consists of a cylindrical main section and a hemispherical roof, we can find the total volume by adding the volume of the cylinder and the volume of the hemisphere.
So,
Total volume = V_cylinder + V_hemisphere
= πr^2h + (2/3)πr^3
= πr^2(3h/3) + (2/3)πr^3
= (3πr^2h + 2πr^3)/3
We know that the total volume of the silo is given, so we can set up an equation:
(3πr^2h + 2πr^3)/3 = given volume
Simplifying this equation, we get:
3πr^2h + 2πr^3 = 3 x given volume
Dividing both sides by π and factoring out r^2, we get:
3rh + 2r^2 = 3 x (given volume)/π
Now we can plug in the given values and solve for r.
Let's assume the given volume is 1000 cubic feet and the height of the cylindrical part is 20 feet.
Then,
3rh + 2r^2 = 3 x 1000/π
3r x 20 + 2r^2 = 955.03
60r + 2r^2 = 955.03
2r^2 + 60r - 955.03 = 0
Using the quadratic formula, we get:
r = (-60 ± sqrt(60^2 - 4 x 2 x (-955.03)))/4
r = (-60 ± 67.2)/4
r = 1.8 or r = -33
Since the radius cannot be negative, we choose the positive solution:
r = 1.8 feet (rounded to the nearest tenth of a foot).
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When a customer places an order at Ying Ying's bakery, there is an 8%, percent probability that the customer will report a food allergy. One day, 12 customers place orders at Ying Ying's bakery. Assuming that each of the 12 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
At Ying Ying's bakery, there's an 8% probability that a customer will report a food allergy.
When dealing with 12 customers, we can calculate the probability that at least one customer will report a food allergy by first finding the probability that none of them report a food allergy, and then subtracting that value from 1.
The probability that a single customer doesn't report a food allergy is 1 - 0.08 = 0.92. For all 12 customers not to report a food allergy, the probability is 0.92^12 = 0.3981 (rounded to four decimal places).
Now, subtract this probability from 1: 1 - 0.3981 = 0.6019.
Therefore, the probability that at least one customer will report a food allergy is 0.6019 or 60.19%.
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