Answers
Answer:
i think the answers are m=4 and n=10
Related Questions
HURRY AND ANWSER BRO ILL GIVE BRAINLIST AND POINT
Question 4(Multiple Choice Worth 2 points)
(Line of Fit MC)
Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 4.05 + 0.4d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.
What is the w-intercept of the line of fit and its meaning in terms of the scenario?
4.05; for each additional day after the kitten is born, its weight is predicted to increase by 4.05 ounces
4.05; a kitten who is just born is predicted to weigh 4.05 ounces
0.4; for each additional day after the kitten is born, its weight is predicted to increase by 0.4 ounces
0.4; a kitten who is just born is predicted to weigh 0.4 ounces
Answers
A kitten who is just born is predicted to weigh 4.05 ounces and its weight is predicted to increase by 0.4 ounces. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Information was gathered on the weight, in ounces, of cats for the initial three months after birth. A line of fit was drawn through the dispersed plot and had the condition w = 4.05 + 0.4d, where w is the heaviness of the cat in ounces and d is the age of the little cat in days.
A kitten who is just born is predicted to weigh 4.05 ounces and its weight is predicted to increase by 0.4 ounces. Then the correct option is B.
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solve for x and 5x+2y=9
Answers
Answer:
Step-by-step explanation:
242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424 242424242424242424242424242424242424The distance from Earth to the sun is about 1.47 X 10^11 meters. The distance from Earth to the moon is 3.71 X 10^8 meters. The distance from Earth to the sun is about how many times larger than the distance from the Earth to the moon? Round your answer to the nearest whole number!
Answers
The distance from Earth to the Sun is 396 times larger than the distance from the Earth to the moon.
Scientific notation.
This is a mode of expressing large numbers of great power. Its helps in the simple expression of numbers so that some arithmetic operations can be performed as required.
In the given question, we have;
distance from Earth to the Sun = 1.47 X 10^11 meters
and
distance from Earth to moon = 3.71 X 10^8 meters
Thus,
to determine by how much is the distance between the Earth and Sun greater than that between the Earth and moon;
n = distance from Earth to the Sun/ distance from the Earth to the moon
= 1.47 X 10^11/ 3.71 X 10^8
= 3.962 x 10^2
n = 396
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3
6
4
8
7
5
Select all the correct answers.
Answers
The statement 4, 6 and 7 is enough to prove that 45° + m∠AOW = 90°.
What is congruence?A harmonious relationship, agreement, or correspondence are all concepts that are denoted by the mathematical term "congruence," which is used in a variety of contexts.
The two geometric figures are said to be congruent, or to be in the relation of congruence, if they can be superimposed on one another so that their entire surfaces match. If two triangles have the same two sides and included angle, they are said to be congruent.
The idea of a "rigid body," which can be moved from one place to another without changing the internal relationships between its parts, appears to be the foundation for congruence.
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You go to the mall to buy some new shoes. You have a coupon for $25 off the price of a pair of
shoes. When you arrive at the store, you find out that the shoes are on sale for 25% off. If
c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost
of shoes after the markdown, which of the following composition functions represents receiving
the sale price of the shoes and then applying the coupon?
Answers
Answer:
50%
Step-by-step explanation:
25%+25%
The composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.
Given that, c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost of shoes after the markdown.
Here, the composition function is
c(s(x))= 0.75x-25
Therefore, the composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.
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PLSSS HEPP MEEE THYYY
Answers
In November 2018, the frequency tree shows us that 35 students aged 15 years old had part-time work.
That number 35 drops to 23 a year later in 2019. There are two reasons for this:
The student lost their job. They got fired or quit their job.The 15 year old student had a birthday and turned 16.Case (2) mentioned above only works if the student's birthday is before April 2019.
Jada told Noah that she has $4.20 worth of quarters and nickels in her pocket and 20 coins all together. Figure out how many of each type of coin she has.
Answers
Answer: We can set up a system of equations to solve this problem. Let x be the number of quarters and y be the number of nickels. We know that:
x + y = 20 (the total number of coins)
0.25x + 0.05y = 4.20 (the total value of the coins in dollars)
We can use the first equation to solve for one variable in terms of the other, and then substitute that into the second equation to get a single equation with one variable.
For example:
x = 20 - y
0.25(20-y) + 0.05y = 4.20
5-0.25y + 0.05y = 4.20
5= 4.20
y = 20 - 5
y = 15
x = 20 - 15
x = 5
So Jada has 5 quarters and 15 nickels in her pocket.
Step-by-step explanation:
HELP I NEED HELP IVE BEEN STUCK IN THIE FOR 3 HOURS STRAIGHT
Answers
Answer:
OK the so the answer is this,
A - Irregular - It is an irregular polygon as the sides and angles are unequal.
B - Neither - As circle is not a polygon.
C - Irregular - Again, it is an irregular for the same reason.
D - Regular - Sides and angles are equal
E - Regular - Equilateral triangle
(Look at picture) thanks! <3
Answers
Answer:
The annual passenger revenue of the rail transport corporation was $930 million when:
R = 930
-20|t-15| + 1,010 = 930
-20|t-15| = 80
|t-15| = 4
So, we can see that t-15 = 4 and t-15 = -4 both lead to an annual revenue of $930 million dollars.
To find the values of t, we add 15 to both sides of the equation:
t-15 = 4 => t = 19
t-15 = -4 => t = 11
So, the years where the passenger revenue was $930 million are:
2011
2019
Janelle bought a beach chair on sale at 60% of. The original price was 46.95. Find the the amount of discount in dollars
Answers
The amount of discount in dollars is 28.17
To find the amount of the discount, we need to multiply the original price by the percentage that was discounted.
Discount = Original Price x (Discount Percentage/100)
Discount = 46.95 x (60/100) = 28.17
So, the amount of discount in dollars is 28.17
Every week, Estella has guitar lessons.
A guitar is shown. The caption says that Guitar Lessons are thirty-five dollars per lesson.
Question 1
Part A
Complete the expression to represent the change in Estella’s account balance due to guitar lessons after 2 years.
Answers
1. The completion of the mathematical expression to represent the change in Estella's account balance due to guitar lessons after 2 years is 52 - 35x, where x is the number of years.
2. After two years, the account balance will be $-18, without reflecting interest.
What is a mathematical expression?A mathematical expression is a combination of variables, constants, numbers, and mathematical operands (addition, subtraction, division, and multiplication).
A mathematical expression may not convey any meaning since it sounds like a phrase in the English language that does not make complete sense.
The unit rate (cost per lesson) for guitar lessons = $35
Estella's account balance = $52
Let the number of years = x
Lesson period, x = 2 years
Mathematical Expression: 52 - 35x
Solution: 52 = 35(2)
= $-18
Thus, after 2 years of guitar lessons, Estella will be indebted to the bank by $18 if she does not deposit an additional amount in her account.
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Question Completion:Expression: 52 - 35
(Look at picture) Ty for the help
Answers
Find the area of the rectangle below be sure to include the correct unit in your answer
Answers
Answer:
The area is 48 feet^2
Step-by-step explanation:
The area of a triangle can be calculated with the following formula:
area=1/2(base)(height)
Substitute in the numbers and find the answer.
a=(0.5)(6)(16)=48
HELP!
The Sum of three consecutive odd integers is 93 Find the integers
Answers
Therefore, the three consecutive odd integers that add up to 93 are 33, 35, and 37.
Find the integers?The sum of three consecutive odd integers is 93. This means that the integers must be odd numbers that come after each other in order.If we look at this problem another way, we can say that the integers must add up to 93.Since odd integers only come in odd numbers, we can divide 93 by 3 to get 31.This means that the three consecutive odd integers must add up to 31 each.Starting with the first integer, we can see that it must be an odd number that is divisible by 3. The first odd integer that is divisible by 3 is 33. Now that we have the first integer, we can use this number to find the other two.To do this, we must add 2 to 33 to get 35. This is the second integer. To get the third integer, we must add 2 to 35 to get 37.To learn more about the integers refer to:
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solve w/4+11/12=1/2-w/6
Answers
The simplified value of the equation is w = -1.
What is simplification?To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given equation w/4 + 11/12 = 1/2 - w/6
the equation is written as,
w/4 + w/6 = 1/2 - 11/12
solving by LCM
(3w + 2w)/12 = (6 - 11)/12
5w = -5
w = -5/5
w = -1
Therefore the value of w is -1.
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ANYONE GOOD AT MATH! PLEASE HELP!
Answers
Answer:
To find f(2), we substitute 2 for x in the equation of the parabola F(x) = x^2 - 2x - 3:
F(2) = 2^2 - 2(2) - 3 = 4 - 4 - 3 = -3
So f(2) = -3
To find g(-3), we substitute -3 for x in the equation of the line g(x) = x - 2:
g(-3) = -3 - 2 = -5
So g(-3) = -5
The correct solution to this question is as follows:
f(2)= -3 & g(-3)=-5
Step-by-step explanation:
[tex]f(x)=x^{2} -2x-3[/tex]
[tex]f(2)=2^{2} -2(2)-3[/tex]
[tex]f(2)=4 -4-3[/tex]
[tex]f(2)=-3[/tex]
[tex]g(x)=x-2[/tex]
[tex]g(-3)=-3-2[/tex]
[tex]g(-3)=-5[/tex]
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Sonji paid $25 for two scarves, which were different prices. When she got home she could not find the receipt. She remembered that one scarf cost $3 more than the other. What was the price of the more expensive scarf?
$11
$12
$13
$14.
Answers
Answer: the answer is $13
Step-by-step explantion
To show work subtract 25 from all the answer so it would be:
$25 - $11 = $13 (13 is 3 more than 11) so $13 would be the answer because it said to find the scarf that cost $3 more than the other one so that means the the less expensive scarf is $11$25 - $12 = $13 (13 is 1 more than 12)$25 - $13 = $12 (12 is 1 less than 13)$25 - $14 = $11 (11 is 3 less than 14)teacup mass and 4 cups is $1280
Answers
The mass per cup for the objects will be 320g and 272g respectively.
What is mass?
Mass simply means the weight that an object contains.
The mass of a teapot and 4 cups is 1,280 grams. The mass per cup will be:
= Mass / Number of cups
= 1280 / 4
= 320g
The mass of the same teapot and 10 cups is 2,720 grams. The mass per cup will be: = 2720 / 10 = 272g
Hence, the mass per cup for the objects will be 320g and 272g respectively.
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Complete questions:
The mass of a teapot and 4 cups is 1,280 grams. The mass of the same teapot and 10 cups is 2,720 grams. Each cup has the same mass. What is the mass?
To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Answers
Answer: Shayla's method for determining whether a graph of a relation is a function is not completely accurate. While it is true that a function can only have one y-intercept, the converse is not necessarily true. A graph can have exactly one y-intercept and still not be a function.
For example, a vertical line has exactly one y-intercept, but it does not define a function because the same value of x can have multiple y-values.
It is also important to note that a graph can be a function even if it does not intersect the y-axis at all.
A more accurate way to determine whether a graph represents a function is to use the vertical line test. This test states that if a vertical line can be drawn through the graph such that it intersects the graph in more than one point, then the graph does not represent a function. If a vertical line can be drawn through the graph such that it intersects the graph in exactly one point, then the graph represents a function.
Step-by-step explanation:
Write the expression as a product of polynomials: p(c–d)+c–d
Answers
The simplified expression as a product of polynomials is given as follows:
(c - d)(p + 1).
How to simplify the expression?
The expression for this problem is defined as follows:
p(c - d) + c - d.
The expression can be defined as an addition in which the terms are given as follows:
p(c - d).(c - d).The common factor to both of the terms of the addition is given as follows:
(c - d).
The quotients of each term relative to the common factor are given as follows:
p(c - d)/(c - d) = p.(c - d)/(c - d) = 1.Hence the simplified expression is given as follows:
(c - d)(p + 1).
(the plus sign for p + 1 is because the expression is an addition and not a subtraction).
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If i scored 88 on one test and a 93 on the other what was the average score
Answers
Explanation:
The average is calculated by adding the numbers and dividing them by the amount of numbers we have. So 88+93 and we get 181
And then we divide it by 2 (181/2)
The average score is 90.5
Step-by-step explanation:
"average" or "mean value" are calculated by adding all data points up and dividing that sum by the number of data points.
e.g. if you eat 1 popsicle today, ate 2 popsicles yesterday and 3 the day before, you have 3 data points : 3, 2, 1.
in my example you had
(3 + 2 + 1)/3 = 6/3 = 2 popsicles every day on average.
the same principle here.
you have 2 days points. and your average score is
(88 + 93)/2 = 181/2 = 90.5
Select all the correct answers.
Which functions are the same as their inverse functions?
0
○
O
f(x) = x-1 x = -5
x+59
g(x) = x= 1, x ‡ 1
x−
Oh(x) =
x+3
x-2, x2
x+1
k(x) = ² ±¹, x ‡ 1
Answers
Answer:
Hi!
0 is basically inverse 0
any integer Inverse change the function
Hot dogs come in packages of 10. Buns come in packages of 8. What is the least number of packages of each you have to buy to have the same number of hot dogs and buns? Drag and drop an answer into each box to complete the statement. You need to buy packages of hot dogs and 1 4 5 packages of buns. 8 10 12
Answers
Therefore , the solution of purchased so that the consumer has an equal amount of each LCM if hot dogs are packaged with 10 dogs per pack .
How many hot dog buns are included in a package?"Sandwich rolls or hot dog buns are typically sold in packs of eight because the buns are baked in clusters of four in pans designed to hold eight rolls." Because hot dogs are sold by the pound and store-bought standard-sized hot dogs weigh 1.6 ounces,
Here,
purchased so that the consumer has an equal amount of
each if hot dogs are packaged with 10 dogs per pack and hot dog buns are packaged with 8 buns per pack LCM is 40.
hot dog buns are packaged with 8 buns per pack LCM is 40. 4 packages of hot dogs and 5 packages of buns are required.
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How to solve this equation -7^2-(-1)
Answers
-7^2 = 49
49-(-1) = 49+1
49+1= 50
Final answer is 50
George spent $109.65 for a radio, which was 43% of his savings. How much did he have in savings before
he purchased the radio?
Enter your answer in number form only. Do not attach a label.
Answers
The savings before he purchased the radio is
What is the percentage?A percentage is a figure or ratio that can be stated as a fraction of 100.
If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given cost of radio = $109.65
and $109.65 is 43% of his savings,
let saving be x
according to conditions,
43% of x = 109.65
43x/100 = 109.65
43x = 109.65 × 100
x = 10965/43
x = $255
Hence the saving of George is $255.
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Set up and solve a proportion for the following application problem. If 3 pounds of grass seed cover 403 square feet, how many pounds are needed for 6045 square feet? HELP
Answers
The number of pounds needed for 6045 square feet will be 45.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If 3 pounds of grass seed cover 403 square feet.
The ratio of the number of pounds of seed to the area that covers the seed.
Let 'x' be the pounds needed of seed. Then the equation is given as,
x / 6045 = 3 / 403
x = 6045 × 3 / 403
x = 15 · 3
x = 45
The number of pounds needed for 6045 square feet will be 45.
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NO LINKS!!
For problems 11 and 12, plot the points in the coordinate plane. Then find the perimeter and area of the polygon.
11. A(-2, 1), B(2, 5), C(5, 1) (round your answers to the nearest tenth.)
Perimeter:______________
Area: __________
12. A(-3, 5), B(1, 6), C(3, -2), D(-1, -3)
Perimeter:
Area:
Answers
Given vertices:
A(-2, 1), B(2, 5), C(5, 1)Plot the points (see attached).
AC is the base of the triangle:
AC = 5 - (-2) = 7 unitsAdd BD, the height. It will help to find the length of the other two sides and the area:
AD = 4 units and DC = 3 units (from the graph)BD = 5 - 1 = 4 unitsFind AB and BC using Pythagorean:
[tex]AB = \sqrt{4^2+4^2}=\sqrt{32} =5.7\ units[/tex][tex]BC=\sqrt{4^2+3^2}=\sqrt{25}=5\ units[/tex]Perimeter: 7 + 5.7 + 5 = 15.7 units
Area: 1/2*7*4 = 14 units²
Question 12Given vertices:
A(-3, 5), B(1, 6), C(3, -2), D(-1, -3)Plot the points (see attached).
As we see this is a rectangle.
Find two adjacent sides using distance equation:
[tex]AB = \sqrt{(1 - (-3))^2+(6-5)^2} =\sqrt{16+1}=\sqrt{17}=4.1\ units[/tex][tex]AD = \sqrt{(-1 - (-3))^2+(-3-5)^2} =\sqrt{4+64}=\sqrt{68}=2\sqrt{17} =8.2\ units[/tex]Perimeter: 2(4.1 + 8.2) = 2(12.3) = 24.6 units
Area: √17 * 2√17 = 2*17 = 34 units²
Answer:
11. Perimeter: 17.7 units
11. Area: 14 square units
12. Perimeter: 24.7 units
12. Area: 34 square units
Step-by-step explanation:
Question 11Given vertices of the polygon:
A = (-2, 1)B = (2, 5)C = (5, 1)Plot the given points in the coordinate plane (see attachment 1).
From inspection, we can see that the polygon is a triangle with the following dimensions:
Base = 7 unitsHeight = 4 units[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
The length of AC is 7 units.
To find the length of AB and BC, use the distance formula.
[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(2-(-2))^2+(5-1)^2}\\&=\sqrt{(4)^2+(4)^2}\\&=\sqrt{16+16}\\&=\sqrt{32}\\&=4\sqrt{2}\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(5-2)^2+(1-5)^2}\\&=\sqrt{(3)^2+(-4)^2}\\&=\sqrt{9+16}\\&=\sqrt{25}\\&=5\;\sf units\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Perimeter}&=AB+BC+AC\\&=4\sqrt{2}+5+7\\&=12+4\sqrt{2}\\&=17.6568542...\\&=17.7\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{2}\cdot 7\cdot 4\\\\&=\dfrac{7}{2} \cdot 4\\\\&=\dfrac{28}{2}\\\\&=14\;\sf square\;units\end{aligned}[/tex]
Question 12Given vertices of the polygon:
A = (-3, 5)B = (1, 6)C = (3, -2)D = (-1, -3)Plot the given points in the coordinate plane (see attachment 2).
From inspection, we can see that the polygon is a rectangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Since AB = DC and BC = AD, find the length of AB and BC using the distance formula.
[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-3))^2+(6-5)^2}\\&=\sqrt{(4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(3-1)^2+(-2-6)^2}\\&=\sqrt{(2)^2+(-8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\\&=2\sqrt{17}\;\sf units\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Perimeter}&=AB+BC+CD+AD\\&=2(AB+BC)\\&=2(\sqrt{17}+2\sqrt{17})\\&=2(3\sqrt{17})\\&=6\sqrt{17}\\&=24.7386337...\\&=24.7\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area}&=AB\cdot BC\\&=\sqrt{17} \cdot 2\sqrt{17}\\&=34\;\sf square\;units\end{aligned}[/tex]
The expression 3 1/2x + 18 represents the perimeter of the rectangle shown. Write an expression that represents the length of the strangle
Answers
Answer:
L = 1/2x
Step-by-step explanation:
The perimeter of a rectangle is the sum of all four sides. In this case, the perimeter is represented by the expression 3 1/2x + 18.
Since the perimeter of a rectangle is the sum of the lengths of all four sides, so, if we know the perimeter and one side's length, we can find the length of the other side.
We can use the expression 3 1/2x + 18 to find the length of the rectangle.
Let's assume that the length of the rectangle is represented by the variable L and the width is represented by the variable W.
So we know that the perimeter of the rectangle is represented by the expression 3 1/2x + 18 and the perimeter of a rectangle is 2(L + W)
So we can write the equation
2(L + W) = 3 1/2x + 18
Expanding the left side of the equation:
2L + 2W = 3 1/2x + 18
Now we know that one of the sides of the rectangle is 1/2x so
L = 1/2x
Therefore, the expression that represents the length of the rectangle is 1/2x
A study was developed to evaluate effectiveness of a weight loss diet plan. An ad was placed in two towns to locate study participants who were to follow the diet. In Town A, the clinicians asked each dieter to report how much weight they had lost over the previous 6 weeks while following the diet. In Town B, the clinicians weighed each dieter at the beginning of the study and again after 6 weeks on the diet program. The weight lost was calculated as the difference between the beginning weight and the weight after 6 weeks. At the end of the study, it was determined that Town B had lost significantly less weight than Town A. a) What is the population of interest in this situation? b) Identify source(s) of bias in this study.
Answers
Answer:
a) The population of interest in this situation is individuals who are following a weight loss diet plan.
b) There are several sources of bias in this study:
Self-report bias: Town A relies on self-reported weight loss, which may not be accurate as participants may not accurately report their weight loss or may exaggerate their progress.
Measurement bias: Town B uses a different method of measuring weight loss than Town A, which could introduce a bias in the results.
Selection bias: Participants in this study are self-selected, which means that individuals who are more motivated or more likely to succeed in the diet may be more likely to sign up for the study. This can lead to a bias in the results as the sample may not be representative of the population of interest.
Hawthorne effect: Participants in Town B may have changed their behaviors simply because they knew they were being weighed, which could lead to a bias in the results.
Placebo effect: Participants in Town A may have lost weight due to the mere act of participating in a study and receiving attention, which could lead to a bias in the results.
The average cost of making rx televisions per week is
C(x) = x² - 40x+500 dollars per television.
a How many televisions should be made per week to
minimise the average cost?
b
<
Find the minimum average cost.
How many televisions are made per week if the average
cost is $200 per television?
Answers
Answer:
Step-by-step explanation:
a. To minimize the average cost, we need to find the value of x that minimizes the cost function C(x) = x² - 40x + 500.
This is the same as finding the minimum value of the parabola represented by the function. The vertex of the parabola is the point at which the parabola reaches its minimum or maximum value. The vertex form of a parabola is given by C(x) = a(x - h)² + k, where (h, k) is the vertex.
By comparing the given function with the vertex form of a parabola, we can find the vertex:
C(x) = x² - 40x + 500
= a(x - h)² + k
= (x - h)² + k
The x-coordinate of the vertex h = 40/2 = 20
So the minimum average cost occurs when 20 televisions are made per week.
b. To find the minimum average cost, we need to substitute the value of x = 20 into the cost function:
C(x) = x² - 40x + 500
= 20² - 40*20 + 500
= 400 - 800 + 500
= 100
So the minimum average cost is $100 per television.
If the average cost is $200 per television, we can set C(x) = 200 and solve for x:
200 = x² - 40x + 500
0 = x² - 40x + 300
This is a quadratic equation that can be solved by factoring or by using the quadratic formula.
we can factor it as
0 = (x-50)(x-6)
x = 50 or x = 6
The number of televisions made per week if the average cost is $200 per television is 50 or 6. Since 50 is much higher than 20, the minimum average cost, it is not physically possible to make 50 televisions with the average cost of $200 per television. So the answer is 6 televisions per week.
