PLEASE HELP!!!!!!
Matt, Steve and John sold magazines for a school fundraiser. John sold two less than Matt. Steve sold twice as many as John. Write a simplified expression representing the total amount of magazines sold
Answers
Answer:
4x - 6
Step-by-step explanation:
Matt: x
Steve: 2(x - 2)
John: x - 2
Total magazines sold:
x + 2(x - 2) + (x - 2)
x + 2x - 4 + x - 2
4x - 6
Related Questions
what is the distance between points (5,2) and (1,-3) on a coordinate plane?A 3B 4.1C 8.5D 6.4
Answers
We are asked to find the distance between the following two points
\((5,2)\: and\: (1,-3)\)Recall that the distance formula is given by
\(d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}\)\(\begin{gathered} \mleft(x_1,y_1\mright)=\mleft(5,2\mright) \\ (x_2,y_2_{})=(1,-3) \end{gathered}\)Let us substitute the given points into the above distance formula
\(\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1_{}-5_{}})^2+({-3_{}-2})^2} \\ d=\sqrt[]{({-4})^2+({-5})^2} \\ d=\sqrt[]{16^{}+25^{}} \\ d=\sqrt[]{41} \\ d=6.4 \end{gathered}\)Therefore, the distance between the given two points is 6.4
Option D is the correct answer.
The cost for new carpet is $8.55 per square yard, plus an installation fee. If 700 square yards of carpet cost $6164, write and solve a linear equation to find the cost of 1000 square yards.
Answers
Answer:
1. 6164 × 10 = 61640
2. 61640 ÷ 7 = 8845.71
Answer = $8845.71
Which of the following best describes why the Hours of Service Regulations were put into place?
To minimize the number of vehicles on the road at night
To reduce the number of accidents caused by fatigue
To protect the rights of shippers
Answers
Answer:
To reduce the number of accidents caused by fatigue
Step-by-step explanation:
I don't know if its right
Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
Answers
1. A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
In this case, the spinner's outcome of landing on region three is independent of landing on region six. Each spin is unrelated to the previous spin, and the outcome of one region does not affect the outcome of the other region. Therefore, the events are independent. The probability of landing on both region three and region six is the product of their individual probabilities: 1/8 * 1/8 = 1/64.
2. A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?
In this scenario, the events are overlapping. A jersey can be both purple and have a number greater than 5 at the same time. Therefore, the probability of it being purple or having a number greater than 5 is the sum of their individual probabilities, minus the probability of the overlapping event (purple jerseys with a number greater than 5). There are 4 purple jerseys out of 10 total jerseys, and there is 1 jersey with a number greater than 5 out of 10. However, there is one jersey that satisfies both conditions (purple and number greater than 5), so we need to subtract it from the sum. So the probability is (4/10 + 1/10) - (1/10) = 4/10 = 2/5.
3. A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?
In this scenario, the events are mutually exclusive. A chocolate cannot be both a milk chocolate and have no peanuts inside at the same time. Therefore, the probability of it being a milk chocolate or having no peanuts inside is the sum of their individual probabilities. There are 6 milk chocolates out of 10 total chocolates, and there are 7 chocolates without peanuts out of 10. So the probability is 6/10 + 7/10 = 13/10, which is greater than 1. However, probabilities cannot exceed 1, so we need to take the maximum value of 1. Therefore, the probability is 1.
4. You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?
In this case, the events are independent. The outcome of the coin flip does not affect the outcome of the die roll. The probability of the coin landing heads up is 1/2, and the probability of the die showing an even number is 1/2. To find the probability of both events occurring, we multiply their individual probabilities: 1/2 * 1/2 = 1/4.
I hope this clarifies the nature of each event. Let me know if you have any further questions!
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
A seat in Section A of the stadium is chosen at random. The fan sitting in that seat receives two free tickets to next week's game. Find the probability that a person in each color seat would receive the free tickets. 1. P(yellow) = 2. P(red) = 3. P(blue) = 4. P(blue or yellow) = 5. P(red or blue) = Red Blue Blue Blue Seats in Section A Red Red Blue Blue Red Red Blue Blue Red Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Answers
The probabilities are:
1. P(yellow) = 2/5
2. P(red) = 3/10
3. P(blue) = 3/10
4. P(blue or yellow) = 7/10
5. P(red or blue) = 3/5
To find the probability that a person in each color seat would receive the free tickets, we need to calculate the probabilities of each event.
1. P(yellow): There are 8 yellow seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a yellow seat at random is P(yellow) = 8/20 = 2/5.
2. P(red): There are 6 red seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a red seat at random is P(red) = 6/20 = 3/10.
3. P(blue): There are 6 blue seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a blue seat at random is P(blue) = 6/20 = 3/10.
4. P(blue or yellow): To calculate the probability of selecting a blue or yellow seat, we add the individual probabilities of selecting a blue seat and a yellow seat: P(blue or yellow) = P(blue) + P(yellow) = 3/10 + 2/5 = 7/10.
5. P(red or blue): To calculate the probability of selecting a red or blue seat, we add the individual probabilities of selecting a red seat and a blue seat: P(red or blue) = P(red) + P(blue) = 3/10 + 3/10 = 6/10 = 3/5.
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Find the value of p.
-25 = -4p + 19
Answers
4p= 19+25
2. Add 19 and 25
4p= 44
3. Divide by 4
p= 11
Answer:
9.75
Step-by-step explanation:
-25 = -4p + 19
-25 - 19 = -4p
-39 ÷ -4 = p
9.75 = p
What is the sun of the interior angles of the polygon shown below
Answers
the sum of the interior angles of the polygon shown below is nine.
Step-by-step explanation:
you look inside the polygon and add the angles all together
andy wants to make a screen saver for his new computer. the screen is 32 inches long by 18 inches wide. what is the area of the screen?
Answers
Answer:
The answer is 576 inches
A translation is shown on the grid below in which triangle A is the pre-image and triangle B is the image.
On a coordinate plane, triangle A is shifted 6 units to the right to form triangle B.
Which rule describes the x-coordinates in the translation?
x + 0
x + 6
x – 6
x + 4
Answers
Answer:
(b) x + 6
Step-by-step explanation:
You want the rule for the x-coordinate when the transformation is a right shift of 6 units.
Right shiftA point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.
The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:
x ⇒ x+6 . . . . . . the x-coordinate transformation rule
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Which answer shows shows the equation below written in different forms 9-3=6
Answers
The equatiοn 9 -3 = 6 can be written in different fοrms, but the correct one is 9 = 3 + 6.
Are expressiοns cοnsidered equatiοns?Every cοmbinatiοn οf a number, a variables, and οperatiοn symbοls is cοnsidered an expressiοn. An equatiοn is created by cοmbining twο expressiοns and jοining them with the equal sign.
Cοnditiοns οn the parameters are fοund in simple equatiοns. It is clear frοm an equatiοn that the answer οn the left and right are equivalent. The expressiοn tο the left οf the symbοl "=" is the LHS, while the expressiοn tο the right is the RHS. With the fοrm y = "sοme expressiοn invοlving x," a sοlutiοn invοlving x and y can be expressed, such as y = f. ( x). This final statement, which may be interpreted as "y equals f οf x," denοtes that y is a cοefficient οf x.
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Complete question:
Which answer shows the equation 9-3=6 below written in different forms?
6 + 3 = 9, 9 = 3 + 6, 9 - 6 = 3, 3 = 9 - 650 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
It would take 21 weeks for the population to surpass 16,000.
The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.
For the population to surpass 16,000, we can set up the following equation:
15,000 + 2500 sin(πt/52) = 16,000
Subtracting 15,000 from both sides, we get:
2500 sin(πt/52) = 1000
Dividing both sides by 2500, we get:
sin(πt/52) = 0.4
We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:
πt/52 = sin⁻¹(0.4)
Multiplying both sides by 52/π, we get:
t = (52/π) sin⁻¹(0.4)
Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.
t = (52/π) (0.4115)
t = 21.02
Therefore, it would take 21 weeks for the population to surpass 16,000.
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A customer left a
delivery guy a $3.50
tip.The tip was 20% of
the bill. How much
was the bill?
Answers
Answer:
$3.57
Step-by-step explanation:
3.50 x 0.20 = .07
3.50 + .07 = 3.57
The bill was $3.57
Answer:
4.20
Step-by-step explanation:
Tip calculator helps
Tell whether each outcome is impossible, unlikely, as
likely as not, likely, or certain. Then write the probability
in simplest form.
1.choosing a red crayon from a box of 24 different colored
Answers
Probability related question:
1. Choosing a red crayon from a box of 24 different colored crayons, including red crayons is likely
2. Rolling an odd number on a number cube (dice) containing numbers 1 through 6 is as likely and not .
3. Randomly picking a white card from a bag containing all red cards is unlikely .
4. Choosing a blue marble in a bag of marbles with 10 blue marbles, 2 white, and 1 red is certain .
1. Choosing a red crayon from a box of 24 different colored crayons, including red crayons is likely.
Explanation: Since the box contains red crayons and the total number of crayons is not specified, it is likely that at least one red crayon is present.
2. Rolling an odd number on a number cube (dice) containing numbers 1 through 6 is as likely as not.
Explanation: A standard six-sided dice contains three odd numbers (1, 3, and 5) and three even numbers (2, 4, and 6). Therefore, the probability of rolling an odd number is the same as rolling an even number, making it as likely as not.
3. Randomly picking a white card from a bag containing all red cards is unlikely.
Explanation: If the bag contains only red cards, there is no possibility of picking a white card. Therefore, it is unlikely.
4. Choosing a blue marble in a bag of marbles with 10 blue marbles, 2 white, and 1 red is certain.
Explanation: Since there are 10 blue marbles and the total number of marbles is not specified, it is certain that at least one marble will be blue.
Based on the explanations above, the option that remains is "impossible" for outcome 4.
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What is the meaning of "the notion of finiteness"?
Answers
The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.
In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.
In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.
This concept is essential to the development of computer programs that are efficient, reliable, and secure.
In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.
In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.
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What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
Answers
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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1) If the 10 kg sugar is Rs. 880 . Find the cost of 15 sugar
2) 50 students in a hostel have provisions for 21 days . How long would it last for 75 students?
Answers
1) If the 10 kg sugar is Rs. 880 . Find the cost of 15 kg sugar.....
Solution,
let the required cost be Rs x
Here , the quantities of sugar and their cost are direct proportion
So, 10 : 15 = 8: x
\( \: \frac{10}{15} = \frac{880}{x} \\ x = \frac{880 \times 15}{10} \\ x = Rs1320\)
Hence , the cost of sugar is Rs.1320
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2) 50 students in a hostel have provisions for 21 days . How long would it last for 75 students?
Solution,
Let the required number of a day = x
Here , the number of student and the number of days are in inverse proportion.
•°• 50 : 75. = x : 21
\( \frac{50}{75} = \frac{x}{21} \\ x = \frac{50 \times 21}{75} \\ x = 14 \: days \\ \)
Hence, the provisions last for 14 days for75 students
~nightmare 5474~
1) The cost of 15 kg sugar is; Rs. 1320
2) The number of days that it would take the provisions to last for 75 students is; 14 days
Proportion1) Cost of 10 kg = Rs. 880
Thus, by proportion the cost of 15 kg sugar will be;
(15 × 880)/10
>> 13200/10
>> Rs. 1320
2) We are told that;
50 students = provisions for 21 days
Thus for 75 students the number of days the provisions would last them is gotten by proportion;
(50 × 21)/75
>> 1050/75
>> 14 days
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PLEASE HELP SHAWTYYY
Answers
Answer:
Vertical
x=49
Step-by-step explanation:
6 less than 3 times a number
Answers
Answer:
3n - 6
Step-by-step explanation:
A line with a slope of 14/3 passes through the point (0,8). What is the equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
The equation of slope-intercept form of the line is y = 14/3x + 8.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.Given,
m = 14/3
the point = ( 0,8 )
A line with a slope of 14/3 passes through the point (0,8).
y - y₁ = m ( x- x₁)
y - 8 = 14/3 ( x - 0 )
3(y - 8 ) = 14x
3y - 24 = 14x
3y = 14x + 24
y = 14/3x + 8
Finally, the equation of the line is
y = 14/3x + 8
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The maximum boxes of raisins a worker at a factory can pack in an hour is 120. The working hours for a worker is 8 hours and the production quota is 7500 boxes. Find the minimum number of workers the factory needs to hire such that the production exceeds the quota
Answers
120x8=960
960x8=7680
So the company would need to hire 8 people for 8 hours to exceed the quota of 7500
Using the rules of inference show that s is a conclusion
1. p → q
2. q → r
3. (q → r) → s
4. p
how to solve?
Answers
"s" can be concluded from the premises
How to show that s is the conclusionTo use the rules of inference to show that "s" is a conclusion, we can use modus ponens,
This is a rule that allows us to infer a conclusion from a premise and its conditional statement.
Using modus ponens, we can infer "q" from "p → q" and "p".Next, using modus ponens, we can infer "r" from "q → r" and "q".Finally, using modus ponens, we can infer "s" from "(q → r) → s" and "q → r".Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".
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Drag each label to the correct location on the table.
A local café serves tea, coffee, cookies, scones, and muffins. They recently gathered data about their customers who purchase both a drink and a
snack. The given frequency table shows the results of the survey.
If approximately 24% of the customers surveyed have a scone with their tea and approximately 36% of the customers surveyed buy a muffin,
complete the column and row headings for the given table.
Cookie
Scone
Tea
Coffee
Muffin
Total
40
100
110
250
120
80
50
250
160
Total
180
160
500
Answers
Answer:
I got it right
Step-by-step explanation:
Answer:tea coffee cookies scones and muffins
Step-by-step explanation:
Factor the following expression using the GCF: 16b + 40ab
Answers
See photo below
A hardware store rents vacuum cleaners that customers may use for part or all of a day, up to 12 hours, before returning. The store charges a flat fee plus an hourly rate. Write a linear function f for the total rental cost of a vacuum cleaner.
A. f(x) = 6x + 14
B. f(x) = 3x + 14
C. f(x) = 3x + 22
D. f(x) = 6x + 24
Flat fee the store charges =
A reasonable domain for the function is: =
Cost to rent a vacuum for 7 hours =
Answers
The flat fee that the store charges is $14 and the cost for 7 hours is $56
A linear equation is on the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
let f for the total rental cost of a vacuum cleaner for x hours
Using the points (1, 20) and (3, 32) from the table:
\(f-f_1=\frac{f_2-f_1}{x_2-x_1} (x-x_1)\\\\f-20=\frac{32-20}{3-1} (x-1)\\\\f(x)=6x+14\)
The flat fee that the store charges is $14
The reasonable domain is 1 ≤ x ≤ 12
The cost for 7 hours is:
f(7) = 6(7) + 14 = 46
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Leonel has $25.00 to spend. He decided to buy a hat for $18.75 and spend the rest on wristbands. If each wristband costs $4.75, how many wristbands can Leonel buy
Answers
Answer:
1
Step-by-step explanation:
25 - 18.75 = 6.25
6.25 - 4.75 = 1.50
he won't have any more money left
Answer:
1
Step-by-step explanation: So first you
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Answers
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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Please help so lost, it is not making any sense
Answers
????????
Step-by-step explanation:
1,1,1
Express the given quantity in terms of the indicated variable.
The area (in ft) of a rectangle that is eight times as long as it is wide;
w = width of the rectangle (in ft)
ft2
X
Need Help?
Read it
Watch It
Master it
Answers
Answer:
X = 8W²Step-by-step explanation:
Area of a rectangle is expressed as Length * Width
X = L*W where X is the area of the rectangle in fe²
If the triangle is eight times as long as it is wide, then L = 8W
Substitute L = 8W into the formula for calculating the area of a triangle, we will have;
X = L*W
X = (8W)*W
X = 8W²
The expression X in terms of W is therefore X = 8W²
A sample of 150 college students reports sleeping an average of 6.4 hours on weeknights, with a standard error of 0.17 hours.
Question: Find a 95% confidence interval for the true average number of hours of sleep college students get on weeknights. Show your work here.
Interpret your 95% confidence interval in context of the situation.
Answers
a) A 95% confidence interval for the true average number of hours of sleep college students get on weeknights, using the lower and upper limits from a t-distribution table, is [6.07, 6.73] hours.
b) Based on the given sample, we can be 95% confident that the true average number of hours of sleep college students get on weeknights is between 6.07 and 6.73 hours.
What are the lower and upper limits of a 95% confidence interval?The lower and upper limits of a 95% confidence interval obtained from the t-distribution table can be computed as follows:
Lower limit = Sample Mean - T-value for CL x Estimated Standard Error of the mean
Upper limit = Sample Mean + T-value for CL x Estimated Standard Error of the mean
The sample size = 150
The sample mean = 6.4 hours
The standard error = 0.17 hours
The t-value for a 95% confidence level and 149 degrees of freedom, using a t-distribution calculator or a table = 1.976.
Lower limit = 6.4 - (1.976) (0.17)
= 6.07 hours
Upper limit = 6.4 + (1.976) (0.17)
= 6.73 hours
Thus, on average, college students sleep on weeknights between 6.07 and 6.73 hours.
Learn more about lower and upper limits of a 95% confidence interval at brainly.com/question/13982551.
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There are some blondes and redheads in a room. If 5 blondes went out and 5 redheads came in, there would be just as many blondes as redheads. However, if instead 5 redheads went out and 5 blondes came in, there would be twice as many blondes as redheads. How many redheads originally were in the room?
Answers
Answer:
7
Step-by-step explanation:
The original number of redheads and blondes in the room are 25 and 35 only.
Let's use algebra to solve this puzzle.
Let's assume the number of blondes originally in the room is B and the number of redheads originally in the room is R.
According to the first statement:
If 5 blondes went out, the number of blondes left in the room would be B - 5.
If 5 redheads came in, the number of redheads in the room would be R + 5.
Since there would be just as many blondes as redheads, we can set up the equation:
B - 5 = R + 5
Now, let's look at the second statement:
If 5 redheads went out, the number of redheads left in the room would be R - 5.
If 5 blondes came in, the number of blondes in the room would be B + 5.
Since there would be twice as many blondes as redheads, we can set up the equation:
2 × (R - 5) = B + 5
Now we have a system of two equations:
B - 5 = R + 5
2 × (R - 5) = B + 5
Let's solve this system of equations:
From equation (1), we can express B in terms of R:
B = R + 10
Now substitute this value of B into equation (2):
2 × (R - 5) = R + 10 + 5
2R - 10 = R + 15
2R - R = 15 + 10
R = 25
So, there were originally 25 redheads in the room. Now, to find the number of blondes originally in the room, use equation (1):
B = R + 10
B = 25 + 10
B = 35
Therefore, there were originally 25 redheads and 35 blondes in the room.
learn more about redheads here
brainly.com/question/28214512
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