The value o f c based on The Mean Value Theorem is 1
The Mean Value Theorem stated that if f(x) is a continuous on [a,b] and differentiable on (a,b) then there is a c such that:
f'(c) = [tex]\frac{f(b)-f(a)}{b-a}[/tex] ... (i)
Based on the question, we got equations:
f(x) = 1 + x + x² ... (ii)
By using derivative, we get:
f'(x) = 1 + 2x ... (iii)
From the question, we get:
f(a) = f(0)
f(b) = f(2)
Then we need to find the value of both f(0) and f(2):
f(0) = 1 + (0) + (0)²
f(0) = 1 ... (iv)
f(2) = 1 + (2) + (2)²
f(2) = 7 ... (v)
We also need to find the equation for f'(c) based on equation (iii):
f'(x) = 1 + 2x
f'(c) = 1 + 2c ... (vi)
We will input equations (iv) and (v) into equation (i) to find another equation of f'(c):
f'(c) = [tex]\frac{f(2)-f(0)}{2-0}[/tex]
f'(c) = [tex]\frac{7-1}{2-0}[/tex]
f'(c) = [tex]\frac{6}{2}[/tex]
f'(c) = 3 ... (vii)
Then we will subtitute the equation (vi) with equation (vii) to find the value of c:
f'(c) = 1 + 2c
3 = 1 + 2c
2c = 2
c = 1... (viii)
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HELP I WILL GIVE 30 POINTS PLUS BRAINLESIT!!
Evaluate. 34+(12+14)2⋅2 Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
Step-by-step explanation:
138
Suppose you have selected a random sample of n 4 measurements from a normal distribution. Compare the standard normal z values with the corresponding t values if you were forming the following confidence intervals. (a) 80% confidence interval (b) 98% confidence interval (C) 90% confidence interval
The solutions are;
The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.
The critical value with a level of significance ‘of 0.01’ and degrees of freedom ‘of 3’ is 3.747.
The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.
Given;
Let's say you randomly choose n = 4 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.
(a) 80% confidence interval:
The z-value is obtained as shown below:
The level of significance is;
Locate the probability in the z table. Then, the corresponding row value is 1.2 and the column value is 08.
The critical value with a level of significance is 1.28.
α = 1 - 0.80 = 0.20
α/2 = 0.10
The t-value is obtained as shown below;
From the information, the sample size is 4.
df = n - 1 = 4 - 1
= 3
The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.
(b) 98% confidence interval:
The z-value is obtained as shown below:
The level of significance is;
Locate the probability in the z table. Then, the corresponding row value is 2.3 and the column value is 03.
The critical value with a level of significance is 2.33.
α = 1 - 0.98 = 0.02
α/2 = 0.01
The t-value is obtained as shown below;
From the information, the sample size is 4.
df = n - 1 = 4 - 1
= 3
The critical value with level of significance ‘0.01’ and degrees of freedom ‘3’ is 3.747
(C) 90% confidence interval:
The z-value is obtained as shown below:
The level of significance is;
Locate the probability in the z table. Then, the corresponding row value is 1.6 and the column value is 04.
The critical value with a level of significance is 1.64.
α = 1 - 0.90 = 0.10
α/2 = 0.05
The t-value is obtained as shown below;
From the information, the sample size is 4.
df = n - 1 = 4 - 1
= 3
The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.
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A fair coin is flipped 12 times. Find the probability that more than 3 of the flips turn up tails.
The probability of more than 3 of the flips turn up tails is 0.0528 i.e 5.28%.
The binomial distribution in contains n independent Bernoulli trials. A Bernoulli trial is a trial that happens to succeed (probability p) or fail (probability 1- p = q )
Suppose we have a variable X for a Bernoulli distribution with parameters n and p, which is written as The probability of x successes in n trials is P(X = x)
= ⁿCₓ pˣ(q)ⁿ ⁻ ˣ
Toss a fair coin 12 times.
Next is the probability that 3 or more flips will be a number.
The probability of success is (P) = 1/2 = 0.5
total number of tosses (n) = 12
we have x = 3
P(X = 3) = ¹²C₃(0.5)³x (1 - 0.5)¹²⁻³
= 220 (0.5)³ (1 - 0.5)⁹
P(X = 3) = 0.0528
P(X = 3) = 5.28%
Hence, the probability that more than 3 of flips turn up tails is 0.0528.
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Which function is graphed?
A. y = {x² +4, x≤ 2
-x+4, x<2
B. y = {x² +4, x>2
-x+4, x>2
C. y = {x²+4,x>2
-x+4, x≤2
D. y = {x² +4,x<2
-x+4, x >2
Option D, the function is graphed. And the condition is y = {x² +4,x<2
-x+4, x >2
What is a function?In a mathematical function from a set X to a set Y, exactly one element of Y is assigned to each element of X. The function's codomain and domain are respectively referred to as the sets X and Y as a whole.
Functions were initially thought of as the relationship between varying quantities and other variables. The impact of time on a planet's position serves as an example of this. The concept was historically developed with the development of infinitesimal calculus at the end of the 17th century, and up until the 19th century, the functions taken into consideration were differentiable.
Let us check option A first
y={x² +4, x≤ 2
-x+4, x<2
For, x² +4, x≤ 2
x 2 1 0 -1 -2
y 3 5 4 5 8
Here, the condition is satisfied
Now, we have to check the condition
-x+4, x<2
The condition is not satisfied.
Similarly, we have to check all the options.
And finally by checking all the conditions,
Option D is correct and the conditions are
y = {x² +4,x<2
-x+4, x >2
Therefore, the option D function is graphed.
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6w - 13w - 18 = -81 Solve for w.
Simplify your answer as much as possible.
The table how the height and weight of a few tudent in a cla. Height (inche) Weight (pound) height weight
58 122
59 128
60 126
62 133
63 145
64 136
66 144
68 150
70 152
Complete the following entence baed on your obervation. The data eem to have a correlation coefficient cloe to _____. Thi indicate that the weight of a tudent ______ a the height of the tudent increae
Correlation coefficient = 0.945 ( approx) and weight of a student increases as the height of the student increases.
What is correlation coefficient?
A statistical indicator of the strength of a linear link between two variables is the correlation coefficient. Its values may be between -1 and 1.
Main Body:
Here, value of x are =58, 59, 60, 62, 63, 64, 66, 68, 70
Value of y are, = 122, 128, 126, 133, 145, 136, 144, 150, 151.
∑x = 570, ∑y= 1236, ∑ = 36234, ∑ = 170694
∑xy=78617
Thus the correlation coefficient r =
formula is in the image,
Where n is the number of the term.
here n = 9
thus, correlation coefficient
r= [tex]\frac{9*78617- 570*1236}\sqrt{{9*36234- (570^{2} )}\sqrt{9*170794- (1235)^{2} }[/tex]
Thus, r= 0.94452987512
Which is closed to 0.95 and less than 1.
Therefore, weight of a student increases as the height of the student increases.
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26. Which is the correct coefficient of 147,000 when it is written in scientific notation?
A 147
B 1.47
C 14.7
D 0.147
The correct coefficient is 147
In scientific notation, a number is represented by an exponent, or the power of 10, multiplied by the coefficient, which appears before the times sign. For instance, 4.3 is the coefficient and 6 is the exponent in the equation 4.3 x 10^6, which is equivalent to 4,300,000 (four million three hundred thousand).
From the question, we have
147,000 = 147 *10^3
The correct coefficient is 147
Multiplication:
Mathematicians multiply two or more numbers to determine the sum of the parts. It is a fundamental mathematical procedure that is commonly used in real-world situations. Multiplication is used when groups of like sizes need to be combined. Multiplication is a mathematical operation that illustrates the fundamental idea of adding the same number again. The product of two or more numbers is what occurs from multiplying them, while the components are the quantities that are multiplied. Multiplying the numbers makes it simpler to repeatedly add the same quantity.
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The original price of a scarf was $16. During a store-closing sale, a shopper saved $12 on the scarf. What percentage discount did she receive? explanation
She received a discount of 75 percent from the sale of the scarf.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the original price of the scarf is $16, the money saved during the sale is $12.
Therefore:
The Amount the scarf was bought (Discounted price) = Original Price - Money saved
Discounted price =$16 - $12 = $4
Now the discount is given as;
Discount = (Amount saved / Original price) × 100%
Discount = ($12/ $16) × 100% = 75%
Therefore the discount of 75% was received.
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Write 1/7 root in index form
Answer:
30
Step-by-step explanation:
in index form the nth if a root number is X and that is X to the power so the seventh root of 30 is 30 to the power of 1/7
The Principal of Trinity High School wants to purchase custom tote bags for each of her teachers as a thank you gift. Each bag will be printed with the school mascot on the side. Depending on the cost, she may want to order some extra tote bags to hand out as prizes to students throughout the school year. The screen printing company says that if she orders 75 tote bags, the cost will be $635. If she orders 125 tote bags, the cost will be $1035. Assuming the cost of ordering a tote bags is a linear equation, determine the cost of ordering 110 tote bags.
From the given condition of number of tote bags ordered and there costs represents linear equation then cost of ordering 110 tote bags is equal to $915.
As given in the question,
Let us consider y be the cost of ordering a bag.
And x represents the number of bags to be ordered as per the cost.
It is given that Cost of ordering bags and number of tote bags represents the linear equation,
Standard form of Equation is :
y = mx + c
For order of x = 75 tote bags cost is y = $635.
635 = 75m + c __(1)
For order of x = 125 tote bags cost is y = $1035.
1035 = 125m + c ____(2)
Subtract (1) from (2) we get,
1035 = 125m + c
635 = 75m + c
400 = 50m
⇒m = 8
Substitute value of m in (1) we get,
635 = 75(8) + c
⇒c = 35
Equation is:
y = 8x + 35
When number of ordering bags x = 110 then,
y = 8(110) + 35
⇒ y = $915
Therefore, from the given condition of number of tote bags ordered and there costs represents linear equation then cost of ordering 110 tote bags is equal to $915.
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find the slope of the line (2,4) (2,-3)
Answer: The slope is undefined because the line is vertical
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-3 - 4) / (2 - 2) = -7/0 =undefined
This is a vertical line.
3. The graph represents the cost per person at
a pottery painting
studio. Find the
rate of change.
TOTAL COST ($)
5. Find the slope of
45
988 38994
40
30
15
2-3
# OF PEOPLE
A.
12
thr
D.
Answer:
the answer is 45/100=9/50 according to my solution
Simplify -4 3/4 - 8 4/5
Answer:
this equal to -13.55 hopefully this helps
Question Progress
The height of Dyffan is 75 centimetres.
The height of Logan is 80 centimetres.
Write the height of Dyffan as a fraction of the height of Logan.
Give your answer in its simplest form.
Answer:
15/16
Step-by-step explanation:
75/80
15/16
What is the formula of tan 45 degree Theta?
The value of tan(45°+Θ) after using trigonometric ratio is
1+tanΘ/ 1-tanΘ.
What is trigonometric ratios?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.
Here the given,
=> tan(45°+Θ)
Now using formula ,
=> tan(a+b) = [tex]\frac{tan a+tan b}{1-tan a*tanb}[/tex]
=> tan(45°+Θ)= (tan 45°+tanΘ)/(1-tan45°*tanΘ)
We know that tan 45°=1 then ,
=> tan (45°+Θ)= 1+tanΘ/ 1-tanΘ
Hence the formula for tan (45°+Θ) is 1+tanΘ/ 1-tanΘ.
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A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 12 granola bars and each large box has 18 granola bars. The camp bought a total of 15 boxes that have 240 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
A system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased include the following:
s + l = 15
12s + 18l = 240.
How to write the two equations for this system?In order to write a system of linear equations could be used to model and determine the number of small boxes purchased and the number of large boxes purchased, we would assign variables to the number of small boxes that were purchased, the number of large boxes that were purchased, and the total number of boxes respectively as follows:
Let the variable s represent the number of small boxes that were purchased.Let the variable l represent the number of large boxes that were purchased.Let the variable t represent the number of large boxes that were purchased.Translating the word problem into an algebraic equation, we have the following;
Since each small box has 12 granola bars and each large box has 18 granola bars, we have:
12s + 18l = 240.
For a total of 15 boxes altogether, we have:
s + l = 15
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Use properties to determine whether the expressions are equivalent. 8(9x − 2) and 72x − 2
Answer: No they are not equivalent.
Step-by-step explanation: 8(9x-2) = 72x-2
= 8(9x-2) = 72x - 16
= 72x -16 is not equivalent to 72x -2.
A fish 12 m below the surface of the ocean swims down 3 m. Then it swims
up 9m. What is the fish's new position? Show your work.
A bus travelling from Camiling to Tarlac City collects a travelling fee of 10 pesos per x²+5 Km. Determine the travelling cost in peso of a passenger going to a distance that is 3/2 times more distant than the average.
The cost for a passenger going to a distance that is 3/2 times more distant than the average is; 15 pesos
How to solve algebraic word problems?We are given that;
Average distance covered per passenger = x² + 5 Km.
Cost per average distance = 10 pesos
Cost per km = 10/(x² + 5) pesos per km
We are told that a passenger now goes a distance that is 3/2 times more distant than the average. Thus, this distance is;
(3/2)(x² + 5) Km
The cost for this given distance will be;
10/(x² + 5) * (3/2)(x² + 5)
= 10 * (3/2)
= 15 pesos
Thus, we conclude that the travelling cost in pesos is 15 pesos
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Use an example to explain how you can model percents greater than 100%
The sum of two numbers is 15. One less than three times the smaller is equal to the larger. Find the numbers.
Answer:
The numbers are:
4 and 11
Step-by-step explanation:
a + b = 15 Eq. 1
3a - 1 = b Eq. 2
Replacing Eq. 2 in Eq, 1
a + (3a - 1) = 15
a + 3a = 15 + 1
4a = 16
a = 16/4
a = 4
From Eq. 1:
a + b = 15
4 + b = 15
b = 15 - 4
b = 11
Check:
From Eq. 2:
3a - 1 = b
3*4 - 1 = 11
12 - 1 = 11
HELP ASAP PLEASE!!!!
Answer:
y=1,-4,-9,-14
Step-by-step explanation:
just replace x with the given value and find what it equals to
y=-5(0)+1
y=1
y=-5(1)+1
y=-5+1
y=-4
y=-5(2)+1
y=-10+1
y=-9
y=-5(3)+1
y=-15+1
y=-14
Hopes this helps please mark brainliest
Answer:
Please mark as brainiest
Step-by-step explanation:
when x = 0:
y= -5(0)+1
y=0+1
y=1
when x = 1:
y= -5(1)+1
y= -5+1
y= -4
when x = 2:
y= -5(2)+1
y= -10+1
y= -9
when x = 3:
y= -5(3)+1
y= -15+1
y= -14
edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a iob as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments. edith wants to earn ar reasr$185 a week working a combination of both jobs. which inequality can be used to represent the situation?
Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.
Given:
Edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a job as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments.
Edith wants to earn at least $185 a week working a combination of both jobs.
Let s and l be the hours of school and library.
s + l <= 2
20s + 15l >= 185.
Therefore Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.
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A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in
miles, , and her running speed, in miles per hour, when she runs:
The equation that describes the proportional relationship between the distance she runs in miles, and her running speed, in miles per hour, when she runs, is:
d = 0.5v.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with intercept zero, in which the output variable is given by the multiplication of the input variable and the constant of proportionality, given as follows:
y = kx
The distance as a function of the velocity and of the time in hours, is given as follows:
d = vt.
30 minutes is half an hour, hence the constant of the proportional relationship is given as follows:
v = 0.5.
Then the equation is:
d = 0.5v.
In which:
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Write a linear equation that passes through (5,2) and (6,4). *Please*
The line of equation that passes through (5,2) and (6,4) is 4x+y=22.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given points are (5,2) and (6,4)
The equation that passes from two points (x₁,y₁) and (x₂,y₂) is,
y-y₁=m.(x-x₁)
Where m=(y₂-y₁)/(x₂-x₁)
Then linear equation,
y-y₁=(y₂-y₁)/(x₂-x₁)×(x-x₁)
Substitute the values here,
y-2=(6-2)/(4-5) ×(x-5)
y-2=4/(-1)(x-5)
y-2=20-4x
4x+y=22
So the required linear Equation is 4x+y=22.
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Where is A after relfecting over the x axis the translate 3 units right
The coordinates of A is (0,2)
How can a image be reflected?
Behind a mirror's glass, people can see a reflection of themselves. The shiny surface creates that image when light rays strike it and reflect or bounce back, creating a "mirror image." Contrary to popular belief, the reflection is not mirrored from left to right as many people believe.
The coordinates of the point A is (-3,-2)
The rule of reflection over x-axis is
(x,y)→(x,-y)
So the point A after reflecting over the x-axis becomes
A(-3,-2)→ A(-3,2)
To move the point P(x,y), a units right and b units up we use
P(x+a,y+b)
As per the question as it moves 3 units right
∴ A(-3.2)
⇒A(-3+3,2)
The point A now is A(0,2)
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goes to the library to read books. When she goes to the library she always reads 3 books. She also goes to the bookstore to read books twice a week. Every time she goes to the bookstore she reads 1 book on Monday and 2 books on Thursday. Reading books is her favorite thing to do. Wendy never has a chance to read books on Saturday or Sunday. What are the possible days she goes to the library? How many books does Wendy read in 2 weeks?
The possible days Wendy goes to the library are Monday and Thursday.
The number of books that Wendy reads is 12 books.
How to calculate the value?From the information, when she goes to the library she always reads 3 books and she also goes to the bookstore to read books twice a week.
In this case, the total books read in two weeks will be:
= (2 × 3) × Number of weeks
= (2 × 3) × 2
= 6 × 2
= 12
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 35 pounds and each large box of paper weighs 60 pounds. There were 7 more small boxes shipped than large boxes and the total weight of all boxes was 815 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
35x + 65y = 815 and x + 7 = y are the system of equations that can be used to find the number of boxes.
What is an algebra?
One of the many different mathematical disciplines is algebra. Algebra is, broadly stated, the study of mathematical symbols and the guidelines for applying those symbols to formulas.
Given,
The weight of each small box = 35 pounds
The weight of each large box = 65pounds
The total weight of the boxes = 815pounds
There were7 times as many small boxes shipped as large boxes
Let 'x' be the number of small boxes and 'y' be the number of large boxes
The weight of 'x' small boxes = 35x pounds
The weight of 'y' large boxes = 65y pounds
The total weight of the two types of boxes together = 35x+65y
Since the total weight of the boxes is 815 pounds, we have
35x+65y = 815---------------------(1)
Since 7 more small boxes = large boxes, hence we have,
x + 7 = y ------------------------(2)
Solving both the equations we get,
x = 3.95 or 4
and, y = 10.95 or 11
The number of large boxes shipped = 11
The number of small boxes shipped = 4
∴ The number of small boxes shipped = 4 and the number of large boxes shipped = 11.
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the auditors have sampled 50 accounts from a population of 1,000 accounts receivable. the sample items have a mean book value of $200 and a mean audited value of $203. the book value in the population is $198,000. what is the estimated total audited value of the population using the difference method?
The estimated total audited value of the population using the difference method is $201,000.
The difference method works as follows :
A difference method is a mathematical expression of the form
f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient.
Given that,
A population of 1,000 accounts .
The sample items have a mean book of $200 and
A mean audited value of $203
Therefore, the difference of $203 - $200 = $3
Now, Apply the difference to the population of accounts and we get,
(1000 account × $3) = $3000
As Given in the question,
The book value in the population is $198,000 and we add the difference previously calculated of $3,000
So, we have = $198,000 + $3,000
= $201,000
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
x > 5 represents a line with an open circle at 5 and going indefinitely toward infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given inequality is - 3(2x - 5) < 5(2 - x).
- 6x + 15 < 10 - 5x.
- x < - 5.
x > 5 (think of moving x to make it positive).
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