The true mean number of pushups that can be performed, as determined by the t-distribution, is within a 95% confidence interval of (9, 21).
Since we know the sample standard deviation for this issue, the t-distribution is applied.
Given,
The sample mean, x = 15 .
The sample standard deviation, s = 9 .
The sample size, n = 10 .
As a result, df = 9. Next, we determine the number of degrees of freedom, which is one less than the sample size.
The crucial value for a 95% confidence interval is then determined by looking at the t-table or using a calculator, yielding t = 2.2622.
The margin of error;
M = t × s/n
Then,
M = 2.2622 × 9/√10 = 6
The confidence interval is:
x ± M
Then
x - M = 15 - 6 = 9
x + M = 15 + 6 = 21
Therefore,
The confidence interval is (9, 21).
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New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.a) Create a probability model for this game.b) Find the expected value and standard deviation of your prospective winnings.c) You play this game five times. Find the expected value and standard deviation of your average winnings.d) 100 people play this game. What's the probability the person running the game makes a profit?
The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.
Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.
The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).
a) To create a probability model follow the steps. Let X is an occurrence of an event. The table is attached here.
b) The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).
[tex]\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}[/tex]
Also,
[tex]\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}[/tex]
And the standard deviation is calculated using the formula, σ=√Var[X].
[tex]\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}[/tex]
c) The expected value and standard deviation for playing the game 5 times are calculated as follows.
The expected value is,
[tex]\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}[/tex]
The standard deviation is,
[tex]\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}[/tex]
d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,
The population mean, μ(Y) = -$0.28
The standard deviation for a population of 100 is,
[tex]\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}[/tex]
The z-score for mean winning is,
[tex]\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}[/tex]
For a person to make a profit, the mean winning of the player should be less than the z-score. Then,
The P-value from the z-table, P(z<0.153)=0.5608
The answer is 0.561.
The complete question is -
You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?
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Does anyone know the answer or how to solve this please?
Answer: Choice (E) [tex]\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]
=========================================================
Explanation:
The goal is to find what xz is equal to (in terms of x, y, and z)
We are given [tex]\text{z}= \frac{\text{x}^2}{\text{zy}^2}[/tex]
The only thing we're missing on the left hand side is x.
Let's multiply both sides by x.
[tex]\text{z} = \frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \text{x}*\frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \frac{\text{x}*\text{x}^2}{\text{zy}^2}\\\\\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]
This points us to choice (E) as the final answer.
Point W is located at (6, 4) on the coordinate plane. Point W is reflected over the y-
axis to create point W'. Point W' is then reflected over the -axis to create point
W". What ordered pair describes the location of W"?
Answer:
W'(-6,4)
Step-by-step explanation:
W (6,4) When it is reflective over the y axis it is now not six to the right of the y axis, it is now 6 to the left.
W' ( -6,4)
W' (-6 4) is now reflected over the x axis. Instead of being 4 units above the x axis, it is now 4 unit below
W" (-6,-4)
which congruence theorem can be used to prove δabr ≅ δacr? a aas b sss c asa d sas
Congruence theorem used here are;-
1. HL theorem
2. SAS theorem
3. SSS theorem
Given,
Triangles ACR and ABR have a common side (hypotenuse of two right triiangles).
ABR and ACR form a right angle.
The AB and AC sides line up.
The BR and CR sides line up.
1. The HL theorem can be used since two triangles have congruent hypotenuses and pairs of legs.
2. Because two triangles contain two pairs of congruent legs and a pair of included right angles between these legs, you can utilize the SAS theorem.
3. Because two triangles have two pairs of congruent legs and congruent hypotenuses, you can utilize the SSS theorem.
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Question is incomplete. Completed question is given below;-
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.
Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.
HL
SAS
SSS
ASA
AAS
What is the equation of the line that passes through the point (−3,4) and has a slope of −2?
Answer:
y=−2x−2
Step-by-step explanation:
You are sent to the store to buy sliced meat for a party. You are told to get
roast beef and turkey, and you are given $30. Roast beef is $4.29/lb and
turkey is $3.99/lb. Write an equation in standard form to relate the pounds
of each kind of meat you could buy at the store with $30.
Write an expression for how much money is spent on roast beef?
Answer:
The Answer is 4.29x + 3.99y = 30
Suppose we observe an unending sequence of days on which the umbrella appears. show that, as the days go by, the probability of rain on the current day increases monotonically toward a fixed point. calculate this fixed point.
The probability computed is <0.8967,0.1033> which roughly shows that, as 90 days pass by, the probability that it will rain on a given day will be increasing monotonically towards a fixed point.
The chance that an event will occur ranges between 0 and 1. Where 0 shows that the event is impossible to occur and 1 shows that the event is bound to occur. If the chance of occurring an event is more than the chance of its not occurring then, it is more likely that the event will occur.
If we take the example of tossing a coin, we can say that the probability that a head will occur or a tail will occur will remain the same, i.e., 50%. The occurrence of heads or tails is equally likely.
These mathematical standards are used in varied fields of gambling, technology, finance, architecture, philosophy, science, etc.
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Simplify to a single power of 6:
Answer: its 4
Step-by-step explanation: trust me bro i had this question too
Directions: Find the interior angle sum for each regular polygon. Round your answer to the nearest tenth if necessary.
This polygon's angles measure
???
degrees.
Answer:
below
Step-by-step explanation:
The SUM of a n-gon 's interior angles formula is :
SUM = ( n-2) * 180 n = 7 for this figure ( 7 angles)
(7-2) * 180 = 900 degrees
EACH angle in this REGULAR polygon is then 900 / 7 = 128.57°
Find the coordinate Z
Answer:
199.728.0294..........….
Graph the following features:
what percent of the variability is accounted for by the relationship between the two variables and what does this statistic mean
95% of the associations we would anticipate to see by chance are weaker than the statistical relationship between the two variables.
Statistical connection:
A statistical relationship states that if one variable (X) changes, another will systematically rise (Y).
Given,
Statistical significance is the degree to which a statistical link exists between two variables.
Here, we must determine whether it is stronger than the proportion of associations we would anticipate to occur by chance.
While researching the posed question, we discovered that the statistical correlation is more than the 95% chance correlation rate.
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SSS,SAS, or none? congruent triangles
please help if u can, and explain! tysm (:
In 3rd step Henry made a mistake by taking the division operator rather than taking subtraction.
What is Number system?A number system is defined as a system of writing to express numbers.
The given problem is 5⁴5⁶/5²
We know that when bases are same then powers will be added
5⁴⁺⁶/5²
5¹⁰/5²
When denominator is taken up then the sign of denominator power value changes to negative.
5¹⁰⁻²
5⁸
Hence, in 3rd step Henry made a mistake by taking the division operator than subtraction.
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Secretary of State Roxana Tillerson is worried about malpractice at the 4 processing centers for Green Cards in the country. Green Card applications are given a grade g on a scale 0-100. They are assigned randomly to different centers and thus Tillerson expects all centers to have similar mean scores. She collects the data in the table. #applications g 8g 9360 67.50 14.85 9870 67.17 15.10 0 1 2 3 7020 67.28 14.79 5040 66.77 15.16 4 rows x 3 columns At this point she just wants to decide whether or not to initiate a deeper investigation into malpractice at all sites. Does she have sufficient evidence for this, at 9% significance? SSTr number (rtol=0.01, atol=0.0001) SSE number (rtol=0.01, atol=0.0001) Fx number (rtol=0.01, atol=0.0001) P-val number (rtol=0.01, atol=0.0001) (a) Yes, she has enough evidence (b) No, she cannot make a conclusion Select the key assumptions in the test you used. (a) All the sampled data come from a uniform distribution. (b) The populations are independent and therefore their covariances are one. (c) All the sampled data come from a normal distribution. (d) The populations are independent and therefore their covariances are zero. (e) All sample sizes are equal ? ? ?
The p-value is 0.0388 at 9% significance, so (a) Yes, she has enough evidence with assumptions used in the test is (c) all the sampled data come from a normal distribution and (d) the populations are independent and therefore their covariances are zero.
How to determine whether the evidence is sufficient or not?All data in attached table
First, we must calculate the grand mean. So,
Grand mean ([tex]\bar{\bar{g}}[/tex]) = [tex]\frac{\bar{g_{1}} + \bar{g_{2}} + \bar{g_{3}} + \bar{g_{4}}}{k}[/tex]
= (67.5 + 67.17 + 67.28 + 66.77) / 4
= 67.18
Next, we calculate SSTr
SSTr = [tex]\sum n_i(\bar{g_{i}} - \bar{\bar{g}})^2[/tex]
= 9360(67.5-67.18)^2 + 9870(67.17-67.18)^2 + 7020(67.28-67.18)^2 + 5040(66.77-67.18)^2
= 1,876.875
Then, we calculate SSE
SSE = [tex]\sum(n_i-1)Sg_i^2[/tex]
= (9360-1)(14.85^2) + (9870-1)(15.1^2) + (7020-1)(14.79^2) + (5040-1)(15.16^2)
= 7,007,556.804
Before we calculate F test, we first calculate the N value with this formula,
N = [tex]\sum n_i[/tex]
= 9360 + 9870 + 7020 + 5040
= 31,290
Then, for F test use this formula,
F = [tex]\frac{SSTr/(k-1)}{SSE/(N-k)}[/tex]
= [tex]\frac{1876.875/(4-1)}{7007556.804/(31290-4)}[/tex]
= 2.793
Next, for p-value we use p value calculator for f test with following data,
F-ratio value = 2.793
DF-numerator = k - 1 = 4 - 1 = 3
DF-denominator = N - k = 31290 - 4 = 31286
and we get the p-value is 0.0388
Since, 0.0388 < 9% of significance, so she has enough evidence to initiate a deeper investigation.
Thus, assumptions used in the test is all the sampled data is normal distribution and the population are independent with covariances are zero and the result is yes, she has sufficient evidence.
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Functions h and k are inverse functions, and both are defined for all real numbers. Using this relationship, what is the value of each function composition?.
The value of each function composition is
koh(3) = 3 and hok(-4b) = -4b
Given, Functions h and k are inverse functions, and both are defined for all real numbers.
The functions h and k are inverse functions
A function is said to have an inverse function when it is one-one and onto both.
Also, the composition of function f and function g is defined as fog i.e. f is defined on the range of g and vice-versa.
Then, foh(x) = x for all the real numbers and also,
hof(x) = x for all the real numbers.
Therefore, the value of each function composition foh at x = 3 and hof at x = -4b is 3 and -4b respectively.
Hence, the value of each function composition foh at x = 3 and hof at x = -4b is
foh(3) = 3 and hof(-4b) = -4b.
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What is the solution to this equation?
3(4x + 3) = 2x-5(3-X) + 2
Answer: The answer to this question is x= -22/5
ASAP PLEASE! Complete the square.
[tex]m^2-8m[/tex]
Find the missing term that completes the square.
[tex]m^2-8m+?[/tex]
(Simplify your answer. Type an integer or a fraction.)
Answer:
16
Step-by-step explanation:
Let us assume the square is (m-a)²
We have to find a
(m-a)² = m² -2am + a²
We are given
m² -8m
Comparing terms
2a = 8
a = 4
so the square is (m-4)²
which is m² - 8m + 16
At 1,000 units of output, the fixed cost of production is $12,500 per week. Total cost of producing 1,000 units per week is $28,500 per week. The variable cost of producing 1,000 units of output per week is equal to _____.
The variable cost of producing 1000 units per week is equal to $16000.
Variable costs are those that change with volume. Raw materials, piece-rate labour, production supplies, commissions, shipping costs, packing costs, and credit card fees are examples of variable costs. The variable costs of production are referred to as "Cost of Goods Sold" in some accounting accounts.
Given,
Fixed cost of production per week =$12500
Total cost of producing 1000 units per week =$28500
then,
variable cost of producing 1000 units per week = 28500-12500=$16000
Thus, the variable cost of producing 1000 units per week is equal to $16000.
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a number, y, is equal to twice the sum of a smaller number and 3. the larger number is also equal to 5 more than 3 times the smaller number. which equations represent the situation? 2 x minus y
The final two equations which represent the given situation are:
2x - y = -6 and 3x - y = -5.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a linear equation of two variables.
Suppose,
The larger number is 'y' and the smaller number is 'x'.
First relation,
'y' is equal to twice the sum of a smaller number (x) and 3. So we represent this as:
y = 2(x+3)
y = 2x + 6
2x - y = -6 ............(1)
Second relation,
The larger number (y) is equal to 5 more than 3 times the smaller number (x). So we represent this as:
y = 5 + 3x
3x - y = -5 .............(2)
Hence, the final two equations which represent the given situation are:
2x - y = -6 and 3x - y = -5.
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The equation c = 10.75p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store.
Which description is true based on the equation of the proportional relationship?
For $0.09, you can buy 1 pound of shrimp.
For $1, you can buy 10.75 pounds of shrimp.
For $10.75, you can buy 10.75 pounds of shrimp.
For $10.75, you can buy 1 pound of shrimp.
Answer: For $1, you can buy 10.75 pounds of shrimp.
Step-by-step explanation: Because p represents pounds and there are 10.75 lbs, and c represents cost. Therefore the answer is: For $1, you can buy 10.75 pounds of shrimp.
Whats the surface area of the triangular prism?
Answer:
426 cm^2
Step-by-step explanation:
Find:
11/3÷2/3
the question is five and
Answer:
[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]
Step-by-step explanation:
Division of fractions can be represented as multiplication by one of the fractions' reciprocal. (Skip, Flip, and Multiply)
So,
[tex]\dfrac{11}{3} \div \dfrac{2}{3} = \dfrac{11}{3} \times \dfrac{3}{2}[/tex]
And we can simplify this to:
[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]
What are the products 4/9 X 6 and 6 X 4/9
HELP NOW PLEASE
Answer: Both products are 2.6 repeating
the strong law of large numbers states that, with probability 1, the successive arithmetic averages of a sequence of iid random variables converge to their common mean . what do the successive geometric averages converge to? t
The successive geometric averages of a sequence of iid random variables converge to the common geometric mean.
the strong law of large numbers states that, with probability 1, the successive arithmetic averages of a sequence of iid random variables converge to their common mean . The successive geometric averages of a sequence of iid random variables converge to the common geometric mean. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of a collection of numbers, denotes the central tendency of that set of numbers. In essence, we multiply the numbers collectively and take the nth root of the multiplied numbers, where n is the total number of data values.
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Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = -4 when x = 2, find y when x = 3 .
ur answer should have ,-6
When X = 3 then Y = -6
Here is the explanation:
If Y1 = -4 when X1 = 2
and if X2 = 3 when Y2 = ?
The formula is
[tex]\frac{Y2}{X2} =\frac{Y1}{X1}\\\\Y2 = \frac{Y1}{X1} x X2\\\\Y2=\frac{-4}{2}x3\\\\Y2=-6[/tex]
Hence if X = 3 then Y = -6
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Study the sequences (0, 6, 12, 18, 24, . . .) and (1, 6, 36, 216, 1,296, . . .), and answer these questions:
Which of the two sequences is an arithmetic sequence?
What is the common difference of the arithmetic sequence?
Can you think of any other mathematical relationship that exhibits a common difference between numbers?
Answer:
Step-by-step explanation:
In the first sequence, subtracting the previous term from each term starting from the second one gives these values: (0, 6, 12, 18, 24, . . .) is an arithmetic sequence.
How to find the common difference in the arithmetic sequence?
Common difference = second term - first term
The difference between the terms is constant. This sequence is an arithmetic one, with the common difference being 6.
Common difference = 6.
Just by looking at the terms in the second sequence,
(1, 6, 36, 216, 1,296, . . .), the difference between the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.
Like arithmetic sequences, linear equations show a common difference between numbers.
Answer: In the first sequence, subtracting the previous term from each term starting from the second one gives these values:
6 – 0 = 6, 12 – 6 = 6, 18 – 12 = 6, and 24 – 18 = 6.
The difference of the terms is constant. This sequence is an arithmetic one, with the common difference being 6.
Just by looking at the terms in the second sequence, (1, 6, 36, 216, 1,296, . . .), it’s clear that the difference of the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.
Like arithmetic sequences, linear equations show a common difference between numbers.
Step-by-step explanation: Edmentum Answer
Independent random samples taken at two companies provided the following information regarding annual salaries of the employees. The population standard deviations are also given below. Company A Company B Sample Size 72 50 Sample Mean (in $1000) 48 43 Population Standard Deviation (in $1000) 12 10 a. We want to determine whether or not there is a significant difference between the average salaries of the employees at the two companies. Compute the test statistic. b. Compute the p-value; and at a=.05, test the hypotheses. c. Which company, if either, appears to have the higher salary? Provide a 95% confidence interval for the difference between the population mean salary of employees for the two companies.
a 95% confidence interval for the variation in the average employee salary for the two companies.
a. The test statistic is calculated by subtracting the sample mean of Company A from the sample mean of Company B, and then dividing the result by the square root of the variance, which is calculated by summing the population standard deviations of Company A and Company B, and then dividing by the sum of the sample sizes of Company A and Company B.
Test statistic = (48 - 43) / √(12^2 + 10^2) / (72 + 50) = 0.766
b. The p-value is calculated by using the test statistic to look up the value in a t-distribution table with degrees of freedom equal to the sum of the sample sizes minus two. The p-value is 0.239.
At a=.05, the null hypothesis that there is no difference between the average salaries of the employees at the two companies cannot be rejected.
c. Company A appears to have the higher salary. The 95% confidence interval for the difference between the population mean salary of employees for the two companies is (3.073, 5.927).
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mr. smith has a maximum of $50 to spend at a museum. a ticket to the museum costs $7. he can spend p dollars to buy other things at the museum. write the inequality that can be used to find the values for p and solve for p.
The inequality that can be used to find the values for p is p + 7 ≤ 50.
Given the information,
Mr. Smith can only spend up to $50 at a museum. The museum admission ticket is $7. He can use his P dollars to purchase other items from the museum.
The total budget is $50.
The cost per ticket is $7
⇒ Total spent ≤ Total Budget
⇒ p + 7 ≤ 50
⇒ p ≤ 43
Therefore, p + 7 ≤ 50 will be the inequality that aids in determining the range of values for p.
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please help thank you very much
Answer:
x = 1, y = 20
Step-by-step explanation:
The question is asking the length of two wires, so instead of area, we are looking at the perimeter.
For the triangle, the equation looks like this:
(2-x) + 15 + y
For the rectangle, the equation looks like this:
(5-x) + (y-6) × 2
Let's say that x = 2, and y = 12.
The triangles new equation would look like this:
(2-2) + 15 + 12 = 27
The rectangles new equation would look like this:
(5-2) + (12-6) × 2 = 18
The wires are the same length, so these numbers can't be correct.
Let's say that x = 1 and y = 20.
The triangles new equation would look like this:
(2-1) + 15 + 20 = 36
The rectangles new equation would look like this:
(5-1) + (20-6) × 2 = 36
These numbers are the same, so therefore the answer is
x = 1 and y = 20.