The requried total cost of filling her three bottles with olive oil is 2250 x $0.0084 = $18.90.
What is simplification?Simplification is the process of using rules of arithmetic and algebra to eliminate extraneous terms, factors, or operations from an expression, with the objective of obtaining a more manageable, manipulable, or solvable expression. One approach to simplification involves combining like terms, factoring, or utilizing the distributive property when simplifying an algebraic expression.
Here,
Each bottle holds 0.75 liters, which is equivalent to 750 milliliters. So, Jane fills a total of 3 x 750 = 2250 milliliters of olive oil.
The cost of the olive oil is $0.21 for every 25 milliliters, which means the cost per milliliter is $0.21/25 = $0.0084.
Therefore, the total cost of filling her three bottles with olive oil is 2250 x $0.0084 = $18.90.
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It costs Jane $18.90 to fill her three bottles with olive oil, each holding 0.75 liters.
Calculating the Cost of Olive Oil
Jane has three bottles that each hold 0.75 liters. To find out how much it costs her to fill these bottles with olive oil, we need to make a few calculations.
Step-by-Step Calculation:
→ Total volume Jane needs:
= 3 bottles x 0.75 liters
= 2.25 liters
→ Convert liters to milliliters:
= 2.25 liters x 1000
= 2250 milliliters
→ Cost of 25 milliliters of oil: $0.21
→ Number of 25 milliliter increments in 2250 milliliters:
= 2250 / 25
= 90 increments
→ Total cost:
= 90 x $0.21
= $18.90
Therefore, it costs Jane $18.90 to fill her three bottles with olive oil.
There was a trucking strike that caused a prime ingredient in your menu item to shoot up 17%. You were paying $12 per package. How much will you have to increase the price of the menu item if you wish to maintain your current dollar profit margin on the menu item? a) $2.04 b) $6.37 c) $7.15 d) $9.44
The amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
There was a trucking strike that caused a prime ingredient in your menu item to shoot up by 17%. You were paying $12 per package.
The increases in the price of the ingredient = 17% of 12
Increase = 0.17 × 12
Increase = 2.04
Therefore, the amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).
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The price of the menu item should be increased by $2.04.
Let's begin by calculating the new cost per package after the price increase. If the original cost per package was $12 and it increased by 17%, we calculate the increase as follows:
Increase = 12 * 0.17 = 2.04
The new cost per package will be:
New cost = 12 + 2.04 = 14.04
To maintain the same dollar profit margin on your menu item, you need to increase the price by the same amount as the cost increase, which is $2.04.
Male cardinal birds sing to attract females. An ornithologist wants to test the claim that the true mean duration of songs sung by male cardinals is more than 6 seconds. She takes a SRS of 35 male cardinals and finds a sample mean duration of 6.31 seconds and a sample standard deviation of 1.2 seconds. Which of the following is the appropriate test statistic to test this claim? a. 1.5063 Ob.0.0074 c. 5.465 d. 1.5283 e. 0.0437
Answer:
[tex]t=\frac{6.31-6}{\frac{1.2}{\sqrt{35}}}=1.5283[/tex]
d. 1.5283
Step-by-step explanation:
Data given and notation
[tex]\bar X=6.31[/tex] represent the sample mean
[tex]s=1.2[/tex] represent the sample standard deviation
[tex]n=35[/tex] sample size
[tex]\mu_o =6[/tex] represent the value that we want to test
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 6 seconds, the system of hypothesis are :
Null hypothesis:[tex]\mu \leq 6[/tex]
Alternative hypothesis:[tex]\mu > 6[/tex]
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{6.31-6}{\frac{1.2}{\sqrt{35}}}=1.5283[/tex]
d. 1.5283
1
Find the surface area of the triangular
3 cm
4 cm
10 cm
5 cm
Step-by-step explanation:
you are going to have to be more specific... please let us know which ones are the legs
Please help me, Please I will give you 15 points and brainliest
The King Cobra is a roller coaster. It sells more than 900 tickets each day. What inequality can you write to show the ticket sales, t? How would you graph the solutions of the inequality?
Answer: The inequality could be t > 900. Draw a number line so it includes 900. Draw an open circle on 900. Shade all the numbers greater than 900, or to the right.
Step-by-step explanation:
Inequality- Inequality is the something that is equal to the something or less than that of the sign give the conditions on which the graph is drawn on the basis of sales occured profits occured
It is the dotted line drawn if the curve is increasing or decreasing then the sign comes <,> It is the solid line occurs drawn if the sales occur according to the profit occurs constantly or equal to the at least value [tex]\leq \geq[/tex] sign indicatesExplanation to the above is the that mentioned below:
The graph of inequality makes the solid line. Due to the roller coaster king cobra the ticket sales more than 900 each day and its constantly increasing day by day It providing smooth curve on the daily basis due to the sell of tickets more with constant rate.Thus we conclude that from the above the graph of the equation is solid line.
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5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13 pls help
Answer:
infinite solutions
Step-by-step explanation:
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13
Ditribute
-15x -10 -x +3 = -16x - 20+13
Combine like term
-16x -7 = -16x -7
Add 16x to each side
-16x+16x -7 = -16x+16x-7
-7 =-7
This is always true so we have infinite solutions.
answers
All real numbers are solutions
step by step
5(−3x−2)−(x−3)=−4(4x+5)+13
Step 1: Simplify both sides of the equation.
5(−3x−2)−(x−3)=−4(4x+5)+13
5(−3x−2)+−1(x−3)=−4(4x+5)+13(Distribute the Negative Sign)
5(−3x−2)+−1x+(−1)(−3)=−4(4x+5)+13
5(−3x−2)+−x+3=−4(4x+5)+13
(5)(−3x)+(5)(−2)+−x+3=(−4)(4x)+(−4)(5)+13(Distribute)
−15x+−10+−x+3=−16x+−20+13
(−15x+−x)+(−10+3)=(−16x)+(−20+13)(Combine Like Terms)
−16x+−7=−16x+−7
−16x−7=−16x−7
Step 2: Add 16x to both sides.
−16x−7+16x=−16x−7+16x
−7=−7
Step 3: Add 7 to both sides.
−7+7=−7+7
0=0
If probability of catching a cold is 0.03, what is the probability of 3 people out of six catching a cold?
Answer:
[tex]P(X=x)=0.0004928[/tex]
Step-by-step explanation:
-This is a binomial probability problem.
-Given the probability of catching a cold is 0.03, n=6
#The probability of exactly 3 people catching a cold is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X=3)={6\choose3}0.03^3(1-0.03)^3\\\\=0.0004928[/tex]
Hence, the probability of exactly 3 in 6 people catching a cold is 0.0004928
A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging machine will lower the proportion of bags that are damaged. The company selected a random sample of 150 bags from the old machine and found that 15 percent of the bags were damaged, then selected a random sample of 200 bags from the new machine and found that 8 percent were damaged. Let pˆO represent the sample proportion of bags packaged on the old machine that are damaged, pˆN represent the sample proportion of bags packaged on the new machine that are damaged, pˆC represent the combined proportion of damaged bags from both machines, and nO and nN represent the respective sample sizes for the old machine and new machine. Have the conditions for statistical inference for testing a difference in population proportions been met?
A No, the condition for independence has not been met, because random samples were not selected.
B No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes.
C No, the condition that the distribution of pˆO−pˆN is approximately normal has not been met, because nN(pˆC) is not greater than or equal to 10.
D No, the condition that the distribution of pˆO−pˆN is approximately normal has not been met, because nO(1−pˆC) is not greater than or equal to 10.
E All conditions for making statistical inference have been met.
If the conditions for statistical inference for testing a difference in population proportions been met then we can say that -(E )All conditions for making statistical inference have been met.
Step-by-step explanation:
We can test the claim and the assumptions about the population proportion under the following conditions
The method of random sampling should be adopted by the company so as to ensure that the observation conducted is independent and not biased The outcome data of the sampled unit must give rise to two outputs -On that is said to be successful and the other that is said to be a failure
Thus we can say that by studying the question we can say that the above mentioned condition have been met.Hence
If the conditions for statistical inference for testing a difference in population proportions been met then we can say that -(E )All conditions for making statistical inference have been met.
The conditions for statistical inference for testing a difference in population proportions have not been met.
Explanation:In order to test for a difference in population proportions, certain conditions need to be met. Firstly, the condition for independence must be met, which means that random samples need to be selected. Secondly, the distribution of the difference in sample proportions needs to be approximately normal. This is determined by checking whether nO(pC) is greater than or equal to 10 and nO(1-pC) is greater than or equal to 10. In this case, the conditions for statistical inference have not been met because random samples were not selected (option A) and nN(pC) is not greater than or equal to 10 (option C).
Someone please help, this is my last resort
Answer:
34 5/8
Step-by-step explanation:
you just add all the numbers on the left and the two drawer numbers then boom!!
At the end of the current year, Accounts Receivable has a balance of $4,375,000; Allowance for Doubtful Accounts has a debit balance of $21,300; and sales for the year total $102,480,000. Using the aging method, the balance of Allowance for Doubtful Accounts is estimated as $205,000.
a. Determine the amount of the adjusting entry for uncollectible accounts.
Answer:
$226,300
Step-by-step explanation:
Given Allowance for Doubtful Accounts is estimated as $205,000 and Allowance for Doubtful Accounts has a debit balance of $21,300
#The amount of the adjusting entry for uncollectible accounts is calculated as below:
[tex]Adjustment \ Cost=Allowance\ Doubtful\ Accounts +Doubtful \ Accounts \ Debit \ Balance\\\\=205000+21300\\\\\$226,300[/tex]
Hence, the amount of the adjusting entry for uncollectible accounts is $226,300
In a survey of 468 registered voters, 152 of them wished to see Mayor Waffleskate lose her next election. The Waffleskate campaign claims that no more than 32% of registered voters wish to see her defeated. Does the 95% confidence interval for the proportion support this claim?
Answer:
The 95% confidence interval for the proportion is (0.2824, 0.3672). The upper limit of the interval is higher than 32% = 0.32, which means that the confidence interval does not support this claim.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 468, \pi = \frac{152}{468} = 0.3248[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3248 - 1.96\sqrt{\frac{0.3248*0.6752}{468}} = 0.2824[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3248 + 1.96\sqrt{\frac{0.3248*0.6752}{468}} = 0.3672[/tex]
The 95% confidence interval for the proportion is (0.2824, 0.3672). The upper limit of the interval is higher than 32% = 0.32, which means that the confidence interval does not support this claim.
In this problem, we apply mathematical concepts related to statistics to determine whether a campaign claim is supported by a survey. The calculation of a 95% confidence interval supports Mayor Waffleskate's claim that no more than 32% of voters want her defeated.
Explanation:The subject in question refers to confidence intervals and population proportions, both of which are topics in statistics. To answer it, we need to construct a 95% confidence interval for the proportion of voters who wish to see Mayor Waffleskate defeated in the election, based on a sample size of 468 voters, of which 152 express this sentiment.
The first step is to calculate the sample proportion (p), which is the number of 'successes' over the sample size, or in this case 152/468, which equals approximately 0.325.
Next, we apply the formula for the confidence interval for a population proportion, which i
Because the confidence interval (0.278, 0.372) includes the value of 0.32 stated by the Waffleskate campaign, it can be concluded that the claim that no more than 32% of registered voters wish to see her defeated is plausible or supported by this survey at the 95% confidence level.
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what is the measure of angle x?
20
70
80
110
Answer:
70
Step-by-step explanation: The sum of all interior angles in a triangle equal 180 degrees. Your problem already shows an angle of 90 degrees ( right angle) and an angle of 20 degrees.
180-90-20=70
Answer:
70°
Step-by-step explanation:
Every triangle's angles add to 180°
Therefore,
90+20=110
180-110=70°
Write the word sentence as an equation. Then solve the equation.
10 more than a number c is 3
Answer:
Equation: 10+c=3
Answer: c=-7
Step-by-step explanation:
1. 10+c=3
2. c=3-10
3. c=-7
Answer:
c=-7
Step-by-step explanation:
c+10=3
Subtract 10 from both sides
c=-7
What is 10.9 as a fraction
Answer:
109/10 or 10 9/10
Step-by-step explanation:
Dividing something by 10 puts it one place after the decimal point.
so 9/10 becomes 0.9.
Answer:
10 9/10
Step-by-step explanation:
One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if it satisfies the given conditions.
Answer:
The number of ways to award the prizes if it satisfies the given conditions is 94,109,400.
Step-by-step explanation:
There are 100 tickets that are distributed among 100 different people.
Four different prizes are awarded, including a grand prize.
The selection of the four wining tickets can be done using permutations.
Permutation is an arrangement of all the data set in a specific order.
The formula to compute the permutation of k objects from n different objects is:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
In this case we need to compute the number of selection of the 4 winning tickets accordingly from 100 tickets.
Compute the number of ways to select 4 winning tickets as follows:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
[tex]^{100}P_{4}=\frac{100!}{(100-4)!}[/tex]
[tex]=\frac{100!}{96!}[/tex]
[tex]=\frac{100\times99\times98\times97\times96!}{96!}[/tex]
[tex]=94109400[/tex]
Thus, the number of ways to award the prizes if it satisfies the given conditions is 94,109,400.
Help me plz i neEd answer
Answer:
C)[tex]64 feet^{2}[/tex]
Step-by-step explanation:
The formula for the area of a trapezium is :
[tex]\frac{a+b}{2} *height[/tex]
A is the top line
B is the bottom line
To work this out you would first add 6 to 10, which is 16. Then you would divide 16 by 2, which is 8. Then you would multiply 8 by 8, which is 64 [tex]feet^{2}[/tex]
1) Add 6 to 10.
[tex]6+10=16[/tex]
2) Divide 16 by 2.
[tex]16/2=8[/tex]
3) Multiply 8 by 8.
[tex]8*8=64 feet^{2}[/tex]
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows
From Hamilton Butler Clermont
Southern Gas 10 20 15
Northwest Gas 12 15 18
Develop a network representation of this problem.
The question involves creating a network representation for multiple-source, multiple-destination distribution, for which nodes represent suppliers and counties, arcs represent the paths with capacities and costs, depicting the logistics of natural gas distribution by Tri-County Utilities, Inc.
Explanation:
The student is asking for a network representation for a supply and distribution problem faced by Tri-County Utilities, Inc. This is related to operations research within the business field, specifically dealing with the optimization of supply chain logistics. The company must distribute natural gas, supplied by Southern Gas and Northwest Gas, to three different counties with varying demand and distribution costs. The aim is to represent this scenario using a network graph that visualizes the routes between the suppliers (Southern Gas and Northwest Gas) and the counties (Hamilton, Butler, and Clermont) along with the distribution costs for each route.
To create a network representation, start with two nodes representing the suppliers and add three additional nodes representing the counties. Then, six directed arcs are drawn from the suppliers to the counties. The capacities of the arcs emanating from Southern Gas should be labeled with 500 units, and those from Northwest Gas should be labeled with 400 units. Likewise, the demand at each county node should be assigned (Hamilton with 400 units, Butler with 200 units, and Clermont with 300 units). Lastly, the costs should be labeled on each of the arcs as provided: from Southern Gas to Hamilton, Butler, and Clermont, the costs are 10, 20, and 15 (in thousands of dollars) respectively, and from Northwest Gas, the costs are 12, 15, and 18 (in thousands of dollars).
Final answer:
The detailed answer explains how to create a network representation for the gas supply problem.
Explanation:
Network Representation:
To develop a network representation of this problem, we can create a graph with nodes representing the counties and the suppliers, and edges representing the distribution costs per unit between them. Here's a simple representation:
Nodes: Hamilton County, Butler County, Clermont County, Southern Gas, Northwest Gas
Edges with Costs:
Hamilton County to Southern Gas - $10
Butler County to Southern Gas - $20
Clermont County to Southern Gas - $15
Hamilton County to Northwest Gas - $12
Butler County to Northwest Gas - $15
Clermont County to Northwest Gas - $18
Simplify 16 – 1.42 + (–1.5) *
Answer:
13.08
Step-by-step explanation:
The simplified result of the given mathematical expression (16 – 1.42 + (–1.5)) is 13.08. This is achieved by following the order of operations for addition and subtraction.
Explanation:To answer this question, we need to simplify the given expression which includes subtraction and addition of numbers.
The expression is 16 – 1.42 + (–1.5). To simplify, we follow the order of operations, which for this question is just addition and subtraction from left to right.
First, subtract 1.42 from 16, which gives us 14.58.
Next, we need to add -1.5 to 14.58. When we add a negative number, it's the same as subtracting that number. Therefore, 14.58 - 1.5 = 13.08.
The simplified result of 16 – 1.42 + (–1.5) is 13.08.
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A rental car agency charges $30.00 per day
plus per mile $0.15. Another rental car
agency charges $36.00 per day plus $0.10
per mile. How many miles would have to be
driven in one day for both rental agencies
to cost the same amount to rent?
Step-by-step explanation:
A rental car agency charges $30.00 per day plus per mile $0.15.
Let x be the number of miles travelled by car
Their total cost = 30 + (0.15x) ... (1)
Another rental car agency charges $36.00 per day plus $0.10 per mile
Their total cost = 36 + (0.10x) ... (2)
Equating (1) and (2), we get
30 + (0.15x) = 36 + (0.10x)
36 - 30 = 0.15x - 0.10x
6 = 0.05x
x = 120 miles
They should travel 120 mils in one day for both rental agencies to cost the same amount to rent
Final answer:
To find the number of miles that would have to be driven in one day for both rental agencies to cost the same, set up an equation and solve for the number of miles , The two rental agencies would cost the same amount to rent if 120 miles were driven in one day.
Explanation:
Let's denote the number of miles driven in one day as x. The total cost for the first rental car agency would be $30.00 + $0.15x, and the total cost for the second agency would be $36.00 + $0.10x. In order for both rental agencies to cost the same amount, we can set up the equation:
$30.00 + $0.15x = $36.00 + $0.10x
Simplifying the equation, we get:
$0.05x = $6.00
Dividing both sides of the equation by $0.05, we find:
x = $120.00
Therefore, the two rental agencies would cost the same amount to rent if 120 miles were driven in one day.
Look at the diagram.
Which term describes IG?
Answer: Angle Bisector
Step-by-step explanation: You divided into two equal angles, you bisected. You turned F, I, G and I, G, H into two separate triangles.
Kim wants to buy a car. Help Kim compute the monthly payment on a loan, given the loan amount, the annual percentage rate of interest, and the number of monthly payments.The program should allow Kim to input the loan amount, interest rate, and how many payments she wants to make.It should then compute and display the monthly payment.You will need the following variables:Payment LoanAmt InterestRateMonthlyRate NumberMonthsYou will need the following formulas:MonthlyRate = InterestRate/1200Note: when the user enters InterestRate as a percentage, it must be divided by 100 to make it a decimal (i.e., 18% = 18/100 = 0.18).The InterestRate offered by car dealers is an annual rate so this must be divided by 12 to get the MonthlyRate.The formula given above combines the two steps (i.e., annual rate of 18% = 18/100 = 0.18 and the monthly rate is 0.18/12 = 0.015 or 18/(100*12) = 18/1200.Payment = LoanAmt * MonthlyRate * (1 +MonthlyRate)^NumberMonths (divided by) ((1 +MonthlyRate)^NumberMonths -1)Note: The formula must be entered carefully, exactly as shown.
Answer:
The complete Python program to calculate the monthly payment on a loan with step by step explanation is given below.
Python Code with Explanation:
# get the loan amount from the user
LoanAmt=eval(input("Please enter the loan amount: "))
# get the annual interest rate from the user in percentage form
InterestRate=eval(input("Please enter the annual interest rate in percentage: "))
# get the number of months from the user
NumberMonths=eval(input("Please enter the number of months: "))
# convert the annual interest rate into monthly interest rate and also into decimal form according to the equation given in the question
MonthlyRate = InterestRate/1200
# implement the given equation to find out the required monthly payment, the operator (**) is used to raise to the power
Payment = (LoanAmt*MonthlyRate (1+MonthlyRate)**NumberMonths)/((1+MonthlyRate)**NumberMonths -1)
# finally, print the monthly payment
print("The monthly payment is: ", Payment)
Output:
Please enter the loan amount: 1500
Please enter the annual interest rate in percentage: 15
Please enter the number of months: 12
The monthly payment is: 135.38746851773584
Bonus:
You can use this command to limit the digits after the decimal point
For example following code will limit to 2 digits after the decimal point.
print(format(Payment, '.2f'))
A survey of 25 young professionals fond that they spend an average of $28 when dining out, with a standard deviation of $10. (a) Find and interpret the 95% confidence interval for the average spending. (b) Based on your answer in part (a), can you conclude statistically that the population mean is less than $30? Explain
Answer:
a) The 95% of confidence intervals for the average spending
(23.872 , 32.128)
b) The calculated value t= 1< 1.711( single tailed test) at 0.05 level of significance with 24 degrees of freedom.
The null hypothesis is accepted
A survey of 25 young professionals statistically that the population mean is less than $30
Step-by-step explanation:
Step:-(i)
Given data a survey of 25 young professionals fond that they spend an average of $28 when dining out, with a standard deviation of $10
The sample size 'n' = 25
The mean of the sample x⁻ = $28
The standard deviation of the sample (S) = $10.
Level of significance ∝=0.05
The degrees of freedom γ =n-1 =25-1=24
tabulated value t₀.₀₅ = 2.064
Step 2:-
The 95% of confidence intervals for the average spending
([tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha }\frac{S}{\sqrt{n} } )[/tex]
[tex](28 - 2.064 \frac{10}{\sqrt{25} } ,28 + 2.064\frac{10}{\sqrt{25} } )[/tex]
( 28 - 4.128 , 28 + 4.128)
(23.872 , 32.128)
a) The 95% of confidence intervals for the average spending
(23.872 , 32.128)
b)
Null hypothesis: H₀:μ<30
Alternative Hypothesis: H₁: μ>30
level of significance ∝ = 0.05
The test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{28-30 }{\frac{10}{\sqrt{25} } }[/tex]
t = |-1|
The calculated value t= 1< 1.711( single tailed test) at 0.05 level of significance with 24 degrees of freedom.
The null hypothesis is accepted
Conclusion:-
The null hypothesis is accepted
A survey of 25 young professionals statistically that the population mean is less than $30
If (x) = 38 + 10xand g(x) = 4X- 2, find (f+ g(x).
Ο
Α. 17x- 2
Ο
Β. 3* + 6x + 2
Ο
C. 38 + 14χ- 2
Ο
D. 38 - 6x+2
Answer:
38 + 10x + 4x - 2
14x + 36
answer is c
6x
A racing car consumes a mean of 86 gallons of gas per race with a standard deviation of 7 gallons. If 41 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 3.1 gallons? Round your answer to four decimal places.
Answer:
0.0046 = 0.46% probability that the sample mean would differ from the population mean by more than 3.1 gallons
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 86, \sigma = 7, n = 41, s = \frac{7}{\sqrt{41}} = 1.0932[/tex]
If 41 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 3.1 gallons?
Less than 86 - 3.1 = 82.9 or more than 86 + 3.1 = 89.1. Since the normal distribution is symmetric, these probabilities are equal, which means that we can find one of them and multiply by 2.
Less than 82.9
pvalue of Z when X = 82.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{82.9 - 86}{1.0932}[/tex]
[tex]Z = -2.84[/tex]
[tex]Z = -2.84[/tex] has a pvalue of 0.0023
2*0.0023 = 0.0046
0.0046 = 0.46% probability that the sample mean would differ from the population mean by more than 3.1 gallons
Final answer:
The probability that the sample mean of 41 racing cars would differ from the population mean by more than 3.1 gallons is 0.0046 or 0.46%.
Explanation:
To calculate the probability that the sample mean of 41 racing cars would differ from the population mean by more than 3.1 gallons, you use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough. In this case, 41 is usually considered large enough. The formula to calculate the z-score for a given sample mean difference is z = (X - µ) / (σ/√n), where X is the sample mean, µ is the population mean, σ is the standard deviation, and n is the sample size.
First, we calculate the standard error of the mean (SEM): SEM = σ/√n = 7/√41 ≈ 1.0934. Next, we calculate the z-score for a difference of 3.1 gallons: z = 3.1 / 1.0934 ≈ 2.8354.
Now, we look up the z-score in standard normal distribution tables or use a calculator to find the probability corresponding to a z-score of 2.8354, which gives us the probability of a sample mean being 3.1 gallons or more away from the population mean on one side. However, since the question asks for the probability of the sample mean differing by more than 3.1 gallons on either side, we have to multiply this probability by 2 to get the final answer.
To obtain the final probability, we use statistical software or tables, which typically provide the probability for the region beyond a certain z-score. If P(z > 2.8354) is the probability of being beyond 2.8354 standard deviations from the mean on one side, the probability of being more than 3.1 gallons away from the mean on either side is 2 * P(z > 2.8354). Assuming P(z > 2.8354) = 0.0023 (from a standard normal distribution table), the final probability would be 2 * 0.0023 = 0.0046 or rounded to four decimal places, 0.0046.
Please Help!
Look at the pattern.
What is the ratio of the area of the unshaded parts to the area of
the shaded parts in Figure 4? Express your answer as a ratio in its
simplest form.
Answer:
16:27
Step-by-step explanation:
16 white squares and 27 shaded squares
The ratio of the area of the unshaded parts to the area of the shaded parts is 4/5.
What is ratio?The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
To find the ratio:
Required ratio = number of unshaded columns / total number of shaded columns
In the given figure 1,
Total no. of columns =3 x 3 = 9
Number of columns shaded = 9 -1 = 8
In the given figure 2,
Total no. of columns = 4 x 4 = 16
Number of columns shaded = 16 - 4 = 12
In the given figure 3,
Total no. of columns = 5 x 5 = 25
Number of columns shaded = 25 - 9 = 16
Similarly;
In the figure 4,
Total no. of columns = 6 x 6 = 36
Number of columns shaded = 36 - 16 = 20
Required ratio = number of unshaded columns / total number of shaded columns
Required ratio = 16 / 20
Required ratio = 4/5
Therefore, the ratio is 4/5.
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pablo and greg both received gift cards for the same amount to a popular clothing store.Pablo bought 2 pairs of jeans and has $36 remaining on his gift card. greg bought 5 pairs of the same jeans and has no money left on his gift card. what is the cost of 1 pair of jeans.
Answer:
12
Step-by-step explanation:
let y be the value of the gift card and x be the cost of a pair of jeans
The equation for Pablo
y-2x=36 Add 2x to both sides
y=36+2x
The equation for Greg
y-5x=0 Add 5x to both sides
y=5x
Now that we have isolated y in both equations, lets set them equal to each other
36+2x=5x Subtract 2x from both sides
36=3x Divide both sides by 3
12=x x=12, which means that 1 pair of jeans costs $12
Final answer:
The cost of one pair of jeans is $12.
Explanation:
To find the cost of one pair of jeans, we can set up an equation using the information given.
Let's say the cost of one pair of jeans is x. Pablo bought 2 pairs of jeans, so he spent 2x.
He has $36 remaining on his gift card, which means the total amount he spent is the original amount on the gift card minus the remaining balance, which is 2x = original amount - $36.
Greg bought 5 pairs of jeans, so he spent 5x.
He has no money left on his gift card, so the total amount he spent is 5x = original amount.
We can write these two equations:
2x = original amount - $36 ... Equation 1
5x = original amount ... Equation 2
To solve this system of equations, we can substitute Equation 2 into Equation 1:
2x = 5x - $36
3x = $36
x = $12
Therefore, the cost of one pair of jeans is $12.
The vertices of triangle ABC are as
follows:
A: (0, 6)
B: (0, -3)
C: (-3, 4)
What is the length of side AB?
Solution:
Answer:
The length of side AB is 9 units.
Step-by-step explanation:
In order to find this answer, you must use the distance formula.
[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
x2 = 0
x1 = 0
y2 = -3
y1 = 6
Since both x values are equal to zero, we do not need to plug these into our formula. It will just cancel out. Therefore, just plug in the y values.
[tex]\sqrt{(-3-6)^2}[/tex]
-3 - 6 = -9
(-9)^2 = 81
sqrt(81) = 9 units
Suppose you toss a coin 100
times and get 67
heads and 33
tails. Based on these results, what is the probability that the next flip results in a tail
?
The probability of getting a tail on the next coin flip remains at 50 percent, regardless of the previous series of outcomes because each coin flip is an independent event.
Explanation:The question is concerned with the probability of getting a tail after having tossed a coin 100 times and obtaining 67 heads and 33 tails. Despite the past results of these tosses, the coin still has a 50 percent chance of landing on heads or tails on any given flip. This concept is based on the idea that each coin flip is an independent event with its own probability, unaffected by previous outcomes.
To answer the student's question directly, the probability that the next flip results in a tail is still 50 percent because past results do not change the probability of future coin flips. This is supported by the law of large numbers, which states that as the number of trials increases, the relative frequency of results will get closer to the expected probability.
Help me plz or I will fail
Answer:
D - Can't be determined
Step-by-step explanation:
10 * 2 *4 * 16 = 1280
1280/2 = 640
Concert marketing: The college’s performing arts center wanted to investigate why ticket sales for the upcoming season significantly decreased from last year’s sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail. Which of the following is a reason that the marketing staff should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail? Check all that apply. Group of answer choices The sample needs to be random, but we don’t know if it is. The actual count of community residents who received the concert brochure by mail is too small. The actual count of students who community residents who didn’t receive the concert brochure by mail is too small. n(p‐hat) is not greater than 10. n(1 minus p‐hat) is not greater than 10.
Answer:
Correct options are A,B,D:
The sample needs to be random, but we don't know if it is. The actual count of community residents who received the concert brochure by mail is too small. n(1 minus p‐hat) is not greater than 10.Step-by-step explanation:
Concert marketing: The college’s performing arts center wanted to investigate why ticket sales for the upcoming season significantly decreased from last year’s sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail.
The college's performing arts center should not calculate a confidence interval for the proportion of community residents who received the concert brochure by mail because there is no information on the randomness of the sample, and both n(p-hat) and n(1 minus p-hat) are less than 10.
Explanation:The college's performing arts center should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail based on the collected survey data for a few reasons. First, the sample needs to be random to provide a representative subset of the population, and there is no information provided to confirm that the sample used was random. Secondly, n(p-hat) is not greater than 10, which refers to the number of successes (7 residents received the brochure) not meeting the minimum requirement for the normal approximation to be valid. Lastly, n(1 minus p-hat) is also not greater than 10, indicating that the number of 'failures' (103 residents did not receive the brochure) also does not meet the condition for the central limit theorem to apply. Both the latter points touch upon the requirements for constructing a confidence interval for a proportion which is that np-hat as well as n(1-p-hat) should both be greater than 10 to approximate the binomial distribution with the normal distribution.
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A textile mill wishes to establish a control procedure on flaws in towels it manufactures. Using an inspection unit of 50 units, past inspection data show that 100 previous inspection units had 850 total flaws. What type of control chart is appropriate? Design the control chart such that it has two-sided probability control limits of α=0.06, approximately. Give the center line and control limits.
Answer:
•A c-chart is the appropriate control chart
• c' = 8.5
• Control limits, CL = 8.5
Lower control limits, LCL = 0
Upper control limits, UCL = 17.25
Step-by-step explanation:
A c chart is a quality control chart used for the number of flaws per unit.
Given:
Past inspection data:
Number of units= 100
Total flaws = 850
We now have:
c' = 850/100
= 8.5
Where CL = c' = 8.5
For control limits, we have:
CL = c'
UCL = c' + 3√c'
LCL = c' - 3√c'
The CL stands for the normal control limit, while the UCL and LCL are the upper and lower control limits respectively
Calculating the various control limits we have:
CL = c'
CL = 8.5
UCL = 8.5 + 3√8.5
= 17.25
LCL = 8.5 - 3√8.5
= -0.25
A negative LCL tend to be 0. Therefore,
LCL = 0
The appropriate control chart for the textile mill is the p-chart. The center line is 8.5 flaws per unit, and the control limits can be calculated using the formula LCL = p - Z * sqrt((p(1-p)) / n) and UCL = p + Z * sqrt((p(1-p)) / n).
Explanation:The appropriate control chart for the textile mill to establish a control procedure on flaws in towels is the p-chart. This chart is used to monitor the proportion of defects in a process. The center line of the p-chart is calculated using the formula p = defects / units inspected. In this case, the center line is 850 / 100 = 8.5 flaws per unit. The control limits are calculated using the formula:
Upper Control Limit (UCL) = p + Z * sqrt((p(1-p)) / n)Lower Control Limit (LCL) = p - Z * sqrt((p(1-p)) / n)Where p is the proportion of defects, Z is the Z-score corresponding to the desired level of significance (such as 0.06), and n is the number of units inspected. The Z-score can be calculated using a Z-table or a statistical software. The control chart is used to determine if the process is in control or if there are any special causes of variation that need to be addressed.