The correct null hypothesis for this question is H0 : μ = 48° and H1 : μ ≠ 48°
What is null hypothesis ?
In statistical hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between a specified population parameter (such as μ) and a hypothesized value (such as 48° F in this case).
The alternative hypothesis (H1), on the other hand, is a statement that there is a significant difference between the population parameter and the hypothesized value. For this particular scenario, the null hypothesis is H0 : μ = 48° F, which means that the refrigerators are maintaining the true mean temperature of 48° F as they are supposed to. The alternative hypothesis is H1 : μ ≠ 48° F, which means that the refrigerators are not maintaining the true mean temperature of 48° F, as claimed by the owner of the brewery.
To test these hypotheses, a sample of refrigerator systems can be taken and their mean temperature can be calculated. If the sample mean is significantly different from 48° F, then the null hypothesis can be rejected in favor of the alternative hypothesis, indicating that the refrigerators are not maintaining the desired temperature.
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shawn deposits $100 every year into a savings account that pays interest at a rate of 3.5% per year, compounded annually. How much money will there be in his account at the end of 2 years
A-214.25
B-210.62
C-207
D-270
There will be $210.62 in Shawn's savings account at the end of 2 years, hence, option B is correct.
Using the compound interest formula,
A = P(1 + r)ⁿ where amount of money is A in the account after n years, principal (initial deposit) is P, interest rate per year (as a decimal) is r, and number of years is n. In this case, P = $100, r = 0.035, and n = 2. Plugging these values into the formula, we get,
A = $100(1 + 0.035)²
A = $100(1.072225)
A = $107.22
Therefore, Shawn will have $107.22 in his account at the end of 2 years, which is closest to option B-210.62 (if we assume the deposit is made at the end of each year).
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Four students designed and built air propelled rockets that were launched in the air. Their data are recorded in the table
Note that the rocket with the greatest acceleration is Rocket 3.
What is the justification of the above response?To find the rocket with the greatest acceleration, the formula to be used is;
Acceleration = net force/mass
Calculating the acceleration of each rocket sing the given data, we get:
Accel eration of rocket 1 = 12.0N/ 0.528 kg = 22.7m/s²
Acceleration of rocket 2 = 8.0N/ 0.426 kg = 18.8m/s²
Acceler ation of rocket 3 = 12.0N/ 0.515 kg = 23.3m/s²
Acceleration of rocket 4 = 8.0N/ 0.477 kg = 16.8m/s²
Given the above, we can confidently state that Rocket 3 is the rocket with the highest acceleration.
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You need to cordon off a rectangular crime scene with tape around
the edge to allow investigators to work. The rectangle measures 34
feet by 20 feet.
b. You also need to have the canine unit sniff the scene for drugs. The drug-sniffing dog needs about 6 seconds for each square foot of area. The Canine Unit that was sent to the scene needs to leave in an hour. Will the canine unit be able to complete the task in time?
MAGIC PENNY LAB
Wandering on the street one day, you notice a shiny penny on the
sidewalk. When you pick it up you learn that this isn't an ordinary penny, but
a magical one. The power of this penny is that it doubles in value each day for
a month. In other words, when you wake up the next day, you miraculously
have two pennies; on day three, four pennies; on day four eight pennies, and
so forth.
Based on this information, would you prefer to receive $1,000,000 or a
magical penny that doubles in value for 31 days? Justify your answer using
mathematics reasoning.
If we start with one penny and double the amount each day for 30 days, we will have a total of $10,737,418.23 at the end of the month.
To find the total amount of money after 30 days using a geometric series, we can start by noting that the amount of money earned each day is double the amount earned the previous day. If we let P be the initial penny on the first day, then the amount earned on the second day is 2P, the amount earned on the third day is 2(2P) = 2²P, the amount earned on the fourth day is 2(2²P) = 2³P, and so on. We can write the total amount of money earned over 30 days as:
P + 2P + 2²P + 2³P + ... + 2²⁹P
This is a geometric series with first term P and common ratio 2. We can use the formula for the sum of a geometric series to find the total amount of money earned:
total = P(1 - 2³⁰)/(1 - 2) = P(1 - 2³⁰)/(-1)
Simplifying this expression, we get:
total = P(2³⁰ - 1)
Substituting P = $0.01 (one penny), we get:
total = $0.01(2³⁰ - 1) = $10,737,418.23
Therefore, if we start with one penny and double the amount each day for 30 days, we will have a total of $10,737,418.23 at the end of the month.
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complete question;
If we have one penny the first day, we double that penny the next day, we then double the previous day's pennies, and so on for a 30-day month what geometric series should you use to find the total amount of money after 30 days, and what is that total?
Use linear approximation, i.e. the tangent line, to approximate
and find the equation of the tangent line……
Using the tangent line to f(x) at x=1, the linear approximation of 1/1.001 is approximately equal to 0.999.
What is linear approximation?Linear approximation is a method used in calculus to approximate the value of a function near a given point by using the tangent line to the function at that point. The tangent line is a straight line that "touches" the function at the given point and has the same slope as the function at that point. By using the equation of the tangent line, we can approximate the value of the function for values of x that are very close to the given point. Linear approximation is useful for estimating values of complicated functions that are difficult or impossible to calculate directly.
In the given question,
To find the equation of the tangent line to f(x) at a point near 1.001, we first need to find the derivative of f(x):
f(x) = 1/x
f'(x) = -1/x²
Now, let's choose a "nice" point near 1.001, such as x = 1. We can find the equation of the tangent line to f(x) at x = 1 using the point-slope form:
y - f(1) = f'(1)(x - 1)
Substituting in the values for f(1) and f'(1):
y - 1 = (-1/1²)(x - 1)
y - 1 = -x + 1
y = -x + 2
This is the equation of the tangent line to f(x) at x = 1.
To approximate 1/1.001 using this tangent line, we plug in x = 1.001 and solve for y:
y = -x + 2
y = -(1.001) + 2
y = 0.999
Therefore, using the linear approximation, 1/1.001 is approximately equal to 0.999.
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11 points used on this question
Answer:
Six of the plants grew to a full height of 16 to 17 inches.
Step-by-step explanation:
Zuza has a cube with each face painted a different color and wants to number the faces from 1 to 6, so that each pair of nonadjacent faces sums to 7. In how many different ways can such a numbering be done?
Answer:
Let's assume that the colors on the cube are numbered as follows:
Red
Blue
Green
Yellow
Purple
Orange
Without loss of generality, we can assume that the face numbered 1 is painted red. We can then use the following table to determine the colors of the other faces:
Face Number Color Opposite Face Number Opposite Color
1 Red 6 Orange
2 Blue 5 Purple
3 Green 4 Yellow
4 Yellow 3 Green
5 Purple 2 Blue
6 Orange 1 Red
We can start by choosing the color for face number 2, which must be one of the colors opposite to red (i.e., purple, green, or yellow). Let's say we choose purple. Then, the color for face number 5 must be one of the colors opposite to blue (i.e., green or yellow). Let's say we choose green. Then, the color for face number 3 must be one of the colors opposite to yellow (i.e., purple or orange). Let's say we choose orange. Now, the remaining three colors must be the ones that have not been used yet, which are blue, green, and yellow. We can then assign them to faces 4, 6, and 1, respectively.
Therefore, the numbering of the faces is as follows:
Face Number Color
1 Yellow
2 Purple
3 Orange
4 Green
5 Green
6 Blue
Note that we could have started by choosing green for face number 2 instead of purple, which would have led to a different numbering. However, we would have ended up with the same set of six colors.
In general, there are 3 choices for the color of face number 2, 2 choices for the color of face number 5, and 2 choices for the color of face number 3. After those choices are made, there is only one way to assign the remaining three colors to the remaining three faces. Therefore, there are:
3 x 2 x 2 x 1 = 12
different ways to number the faces of the cube as described in the problem.
Step-by-step explanation:
please leave thanks
Can someone help me with this I’ve been stuck
Answer:
The answer is (x+2) + (y-2)=2²
(-2,2)
Step-by-step explanation:
x= -2,y=2
(x-h) + (y-k)=R²
C(h,k)
where C is Centre
x+2=0,y-2=2²
(x+2)² + (y-2)²= 2²
Evaluate
Find (f + g) (4) given f(x) = x - 1 and g(x) = x + 2.
Answer:
If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s .
Step-by-step explanation:
Find the area of the circle. Use 3.14 for π. Round to the nearest whole number.
A
50 ft2
B
25 ft2
C
804 ft2
D
201 ft2
The area of the circle rounded to the nearest whole number is A 50 ft²
We see that the diameter of the circle in diagram is 8 feet. The area of the circle is calculated by the formula -
Area = πr², where r is the radius of the circle. Now, we know that radius is half the diameter. Thus, radius = 8/2
Divide the value
Radius of circle = 4 feet
The area of circle = 3.14 × 4²
Take square and multiply the value on Right Hand Side of the equation
Area of circle = 50.24 square feet
Rounding the number to the nearest whole number, we get 50 square feet
Hence, the area of the circle is A 50 ft².
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The question is attached in figure.
A scientist studies a population of squirrels in a certain region for several years. There are initially 24 squirrels and the squirrel population doubles every year.
Which function best represents the number of squirrels in the region at the end of x years? Justify your answer.
There are 12 inches in 1 foot. Whics proportion can you use to find the number of inches in 8 feet
Answer:
D
Step-by-step explanation:
Hope this helps
You are offered a job that pays $34,000 during the first year, with an annual increase of 5% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.05 times what it was in the previous year. What can you expect to earn in your fourth year on the job?
In your fourth year on the job, you can expect to earn $______
(Round to the nearest dollar)
In your fourth year on the job, you can expect to earn $41,327.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Compound Interest =P(1+r/n)^rt
We are given that;
In this case, P = 34,000, r = 0.05, and n = 4.
Plugging these values into the formula, we get:
A = 34,000(1 + 0.05)^4
A = 34,000(1.05)^4
A = 34,000(1.2155)
A = 41,327
Therefore, by the simple interest the answer will be $41,327.
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tom buys a condominium for $42,600. he makes a down payment of 15%. what is the amount of the down payment?
Answer:
The down payment of $42,600 at 15% would be $6,390.
Lucy has an unpaid balance of $700 on her credit card. The credit card company requires a minimum payment of 3% and charges an annual interest rate of 27%. Calculate Lucy's minimum payment, the amount of interest paid that month, and her unpaid balance. Round each to the nearest cent.
Lucy's new unpaid balance is $694.28 to the nearest cent.
Lucy's minimum payment can be calculated by multiplying her unpaid balance by the minimum payment percentage:
Minimum payment = 3% of $700 = 0.03 x $700 = $21
So, Lucy's minimum payment for the month is evaluated at $21.
As per the given information,
Monthly interest rate = 27% / 12 = 0.0225 / month
The interest charged for the month is then calculated by multiplying the monthly interest rate by the unpaid balance:
Interest charged for the month = 0.0225 x $700 = $15.75
So, Lucy will be charged $15.75 in interest for the month.
Finally, we can calculate Lucy's new unpaid balance after making the minimum payment and paying the interest charged for the month. This is given by:
Unpaid balance = (unpaid balance - minimum payment) x (1 + monthly interest rate)
Unpaid balance = ($700 - $21) x (1 + 0.0225) = $694.2775
Therefore, Lucy's new unpaid balance is $694.28.
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A random sample of 5000 adults in a country includes 752 who do not use the Internet. Construct a 95% confidence interval estimate of the percentage of adults in the country who do not use the Internet. Based on the result, does it appear that the percentage of adults in the country who do not use the Internet is different from 49%, which was the percentage in the year 2000? 4 S Construct a 95% confidence interval estimate of the percentage of adults in the country who do not use the Internet.
95 percent certainty that the actual percentage of adults who do not use the Internet in the country is between 12.99 and 17.09 percent.
What is a probability distribution used for?Probability distributions are widely used to define confidence intervals and to calculate critical regions (eg p-value) for hypothesis testing. It is used in many fields aspiring to informatics.
We can use the following formula to construct a 95% confidence interval estimate for the percentage of adults in countries who do not use the Internet:
CI = p ± z*(√.(p×(1-p)/n))
where:
p = Proportion of non-Internet adults in the sample
n = sample size
z = z-scores corresponding to the confidence level (95% in this case)
Combining the values, we get:
p = 752/5000 = 0.1504
n = 5000
z = 1.96 (95% confidence level)
CI = 0.1504 ± 1.96* (√(0.1504*(1-0.1504)/5000))
CI = 0.1299 - 0.1709
Thus, we can say with 95 percent certainty that the actual percentage of adults who do not use the Internet in the country is between 12.99 and 17.09 percent.
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()
A civil engineer tendered for two independent contracts, and . The probabilities that he will win the contract is 1 and not win
2
contract is 3 . What is the probability that he will win: 10
(i) both contracts;
(ii) exactly one of the contracts;
(iii) neither of the contracts?
Note that the probabilities that the engineer will win:
Both contracts is 1/6exactly one of the contracts is 1/2Neither of the contracts is 1/3.Let's denote the even of winning a contract as W and the event of not winning a contract as NW.
Thus, where we have:
P(W1) =1/2
P (NW1) = 1 - P(W1) = 1-1/2 1/2
P(W2) = 1/3
P(NW2) = 1-P(W2) = 1-1/3 = 2/3
1) To win both contracts, engineer need to have won contracts 1 and 2. Thus,
P(W1 and W2) = P(W1) *P(W2) = (1/2) * (1/3) = 1/6
2) To win only one contract, the engineer can either win contract 1 or contract 2 or vice versa.
Because they are independence,
P((W1 AND NW2) or (NW1 and W2)) = P(W1 AND NW2) + P(NW1 and W2)
= P(W1) * P(NW2) + P(NW1 * P(W2)
= (1/2) * (2/3) + (1/2) * (1/3)
= 1/2
3) With regard to the contractor winning neighter 1 or 2:
P(NW1 and NW2) = P(NW1) * P(NW2) = (1/2) * (2/3) = 1/3
Hence, it is correct to state that:
that the probabilities that the engineer will win:
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i need help with #12 please help me
De la Cruz Automotive has net working capital of $22,600, current assets of $56,500, equity of $62,700, and long-term debt of $31,900. What is the amount of the net fixed assets?
using the rule of 78 find the amount of unearned interest with finance charge 747 total payments 24 with remaining number of payments, when paid in full 8
If the loan is paid off in full after 8 remaining payments, the borrower is entitled to a refund of $218.87 of the finance charge.
The rule of 78:The Rule of 78 is a method used by lenders to calculate how much of the finance charge on a loan should be refunded to the borrower if the loan is paid off early.
Formula to calculate the portion of the finance charge that has been earned by the lender so far. The formula is:
[ n / (n(n+1)/2) ] × I
Where n is the total number of payments in the loan and I is the finance charge.
Here we have
The finance charge = 747
Total payments = 24
First, Add up the number of payments made so far and the remaining number of payments to get the total number of payments in the loan:
=> 24 + 8 = 32.
Using the formula (n / (n(n+1)/2)) x I
[ 32 / (32(32+1)/2) ] x 747 = 0.707 x 747 = 528.13
This implies the lender has earned $528.13 of the finance charge so far.
Subtract the amount earned by the lender so far from the total finance charge to find the amount of unearned interest:
=> 747 - 528.13 = 218.87
Therefore,
If the loan is paid off in full after 8 remaining payments, the borrower is entitled to a refund of $218.87 of the finance charge.
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A rectangle has a width of 4 units and a length of m units. What is the area (A = L x W) of the rectangle if m is:
2.2 units? A = ?answer square units.
Answer:
Answer: The area of rectangle is 4*m square unit.
Step-by-step explanation:
A cylinder has the net shown.
net of a cylinder with diameter of each circle labeled 2.8 inches and a rectangle with a height labeled 3 inches
What is the surface area of the cylinder in terms of π?
32.48π in2
23.52π in2
12.32π in2
5.88π in2
The surface area of the cylinder in terms of π is 32.48π in2.
What is surface area?Surface area is a measurement of the total area of a given surface of a three-dimensional object. It is a two-dimensional measurement and is expressed in units such as square feet or square meters. Surface area is an important concept in mathematics, physics, engineering, and other sciences. It is used to measure the size of objects, calculate the volume of a space, and to calculate the area of an object’s surface. Surface area can also be used to calculate pressure, force, and energy, as well as other properties of an object.
This is calculated by using the formula for the surface area of a cylinder, which is 2πr2 + 2πrh. In this case, the radius of the cylinder (r) is equal to the diameter (2.8 inches) divided by two; therefore, the radius is 1.4 inches. The height (h) of the cylinder is 3 inches. Substituting these values into the formula, the surface area of the cylinder is 2π (1.4)2 + 2π (1.4) (3) = 32.48π in2.
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A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is heads?
Write your answer as a fraction in simplest form.
I will give you 20 points of you answer this
Answer:
Median: 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6 : 4
Mean: 3.42 (3.42857142857)
Mean would change
FIRST OPTION
on an assignment there are two multiple-choice questions is four answer choices each do you have no idea what the correct answer is to either one so you guess what is the probability that you get both of them right but guessing explain your answer
The probability that you get both of them right but guessing is 1/16 or 6.25%.
The likelihood of getting both multiple-choice questions right when speculating can be calculated by increasing the likelihood of getting each address right together. Since there are four reply choices for each address.
The likelihood of speculating the proper reply for one address is 1/4. In this manner, the likelihood of getting both questions right is (1/4) x (1/4) = 1/16 or 6.25%.
This implies that in case you were to guess randomly on both questions, there's as it were a 6.25% chance that you just would get both of them right.
This illustrates that speculating isn't a solid strategy for replying to multiple-choice questions and it is superior to utilize information and thinking to create educated choices.
Hence, the likelihood of speculating both questions accurately is (1/4) x (1/4) = 1/16. In other words, there's a 1 in 16 chance of getting both questions right fair by speculating.
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The organizers of African Maths rewarded three of her most outstanding students 40% of the revenue generated from sponsors. If the first and second runners up got 35% and 25% respectively, how much was generated from sponsors if the best student got N400,000? 2 points
The total revenue generated from sponsors that was rewarded by the organizers of African Mathematics to three of her most outstanding students is 2500000 (in monetary units) by formulating linear equation.
The organizers of African Mathematics rewarded three of her most outstanding students 40% of the revenue generated from sponsors.
Let us say the total revenue generated from sponsors be x (monetary units).
Thus, total of (2/5)x (in monetary units) was rewarded by forming equation.
It is given that the first and second runners up got 35% and 25% of the revenue generated respectively and also the best student got 400,000 (monetary units).
Formulating a linear equation for the given problem we get,
40 % of x = 400000 + (35 % of (2/5)x) + ( 25% of (2/5)x) (in monetary units)
⇒(40/100) x = 400000 + (35/100)(2/5)x + (25/100)(2/5)x (in monetary units)
⇒ (40/100)x - [ (14/100)x + (10/100)x] = 400000 (in monetary units)
⇒ [tex]\frac{40x - 14x - 10x}{100} = 400000[/tex] (in monetary units)
⇒ (16/100)x = 400000 (in monetary units)
⇒ x = 2500000 (in monetary units)
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In our example 2 by 2 contingency table of Survival at 5 years (yes or no) by Age at Diagnosis ( =age 50), the data cell counts are presented as follows: under survival “yes” and age <50 cell count= 37, under survival “yes” and age >=50 cell count= 55, under survival “no” age <50 cell count=14, under survival “no” age >=50 cell count=75. What is the overall calculated Chi-sq value?
In our example 2 by 2 contingency table of Survival at 5 years (yes or no) by Age at Diagnosis the overall calculated Chi-sq value is 6.10 as per the given frequencies.
We can use the formula for Chi-sq:
Chi-sq = Σ [tex](O - E)^2 / E[/tex]
Where O = observed frequency and E = expected frequency.
Row totals: 92, 89, 181
Column totals: 51, 130, 181
Grand total: 181
Expected frequency for cell (1,1) = (9251) / 181 = 25.91
Expected frequency for cell (1,2) = (92130) / 181 = 66.09
Expected frequency for cell (2,1) = (8951) / 181 = 25.09
Expected frequency for cell (2,2) = (89130) / 181 = 63.91
Using the formula and plugging in the observed and expected frequencies, we get:
Chi-sq = [tex][(37-25.91)^2 / 25.91] + [(55-66.09)^2 / 66.09] + [(14-25.09)^2 / 25.09] + [(75-63.91)^2 / 63.91][/tex]
Chi-sq = 6.10
Therefore, the overall calculated Chi-sq value is 6.10.
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A 3-cup bottle of shampoo costs $18.96. What is the price per fluid ounce?
The price per fluid ounce of tthe shampoo is $0.79 per fluid ounce
What is the price per fluid ounce?From the question, we have the following parameters that can be used in our computation:
A 3-cup bottle of shampoo costs $18.96.
This means that
Cost = $18.96.
Size = 3-cup
So, we have
Unit rate = $18.96/3
Convert to fluid ounce
Unit rate = $18.96/24
Evaluate
Unit rate = $0.79
Hence the unit rate is $0.79 per fluid ounce
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Sandy works to deliver rock and gravel to various construction sites around the state
of Ohio.
W
Which of the following statements are true?
Delivering the rock and gravel is a service.
Delivering the rock and gravel is a good.
Rock and gravel is a service.
Rock and gravel is a good.
Answer:
1 and 4
Step-by-step explanation:
Delivery is a service, most services are not tangible and are from one person to another (person transporting from a to b) and a 'good' is a product/item where most of them are tangible (phone, CD's, etc).
The analysis phase of decision making includes
The following actions are often part of the decision-making process' analysis phase:
Describe the issue: Set explicit goals and objectives for the decision-making process and identify the specific issue that has to be solved.Information gathering: To assist in the decision-making process, gather pertinent facts and information from dependable sources.Evaluate the data: Go over the information to spot trends, correlations, and patterns that may shed light on the issue.Find alternatives: Come up with a number of possible fixes or courses of action that might take care of the issue.Alternatives should be evaluated by weighing their benefits and drawbacks in light of factors including viability, cost, impact, and efficacy.Decide on a strategy: Based on your investigation and evaluation of the choices, choose the best one.Learn more about decision-making here:
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