There are no values within the interval that satisfies the condition stated by Rolle's theorem.
What numbers does satisfy Rolle's theorem?In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:
f'(c) = [f(b) - f(a)] / (b - a), where a < c < b
Where:
f(a), f(b) - Values of the function evaluated at each interval limit.f'(c) - First derivative of the function evaluated at x = c.First, evaluate the function f(x) at x = - 4:
x = - 4
f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8
f(- 4) = - 64 - 64 + 64 + 8
f(- 4) = - 56
Second, evaluate the function f(x) at x = 4:
x = 4
f(4) = 4³ - 4 · 4² - 16 · 4 + 8
f(4) = 64 - 64 - 64 + 8
f(4) = - 56
Third, determine the first derivative of the function f(x) and evaluate it at x = c:
f(x) = x³ - 4 · x² - 16 · x + 8
f'(x) = 3 · x² - 8 · x - 16
x = c:
f'(c) = 3 · c² - 8 · c + 16
Fourth, find the roots of the quadratic function found in the previous step.
3 · c² - 8 · c + 16 = 0
In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.
Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.
Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.
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The owner of a small store buys coats for $40.00 each. Answer parts a and b. a. She sells the coats for $72.00 each. What percent of the purchase price is the sale price? The sale price is 180% of the purchase price. b. The owner increases the sale price by the same percent that you found in part a when she buys jackets for $25 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $260? Explain your answer. The owner must buy how many jackets?
The percent of the purchase price that the sales price is 80%.
The number of jackets that should sold so that total sales can be at least $260 is 6.
What is the percent of sales price and the number of jackets to be sold?The equation that can be used to determine the percent of the purchase price the sales price is:
Percent = (sale price / purchase price) - 1
($72 / $40) - 1 = 0.80 = 80%
The sales price of the $25 jackets if prices are increased by 80%
Sales price = (1 + percent) x purchase price
(1 + 0.8) x $25
1.8 x $25 = $45
The number of jackets to sell so that total jacket sales can be at least $260 is:
(sales price per jacket x number of jackets) ≥ $260
($45 x j) ≥ $260
$45j ≥ $260
j ≥ $260 / $45
j ≥ 5.8 ≈ 6
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What are the domain and range of f(x) = logx-5?
whats 66 - 100
please answer fast and correctly for brainliest
Answer: -34
Step-by-step explanation:
66 minus 100 is negative 34.
Complete the tasks to subtract the polynomials vertically. (1.3t3 0.4t2 â€"" 24t) â€"" (0.6t2 8 â€"" 18t) what is the additive inverse of the polynomial being subtracted? â€""0.6t2 (â€""8) (â€""18t) â€""0.6t2 (â€""8) 18t â€""0.6t2 8 â€"" 18t 0.6t2 (â€""8) 18t
The subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18) is given as follows:
1.3t³ - 0.2t² - 32t + 18.
How to subtract polynomials?Polynomials are subtracted subtracting the like terms, which are the terms that have the same symbolic variable and the same exponent.
For this problem, the subtraction is given by the expression presented as follows:
(1.3t³ + 0.4t² - 24t) - (0.6t² + 8t - 18).
The like terms of the expression are given as follows:
1.3t³ and 0t³ = 1.3t³.0.4t² - 0.6t² = (0.4 - 0.6)t² = -0.2t².-24t - 8t = (-24 - 8)t = -32t.0 - (-18) = 0 + 18 = 18.Hence the result of the subtraction of the polynomials is given as follows:
1.3t³ - 0.2t² - 32t + 18.
Missing InformationThe problem asks for the subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18).
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question 4: a school group went to a carnival on a field trip. the function c(x) represents the amount of money spent in dollars, where x is the number of students. does a possible solution of (29.5, $212.50) make sense for this function? explain your answer.
Step-by-step explanation:
only limited sense.
first of all, directly it does not make any sense. we can only send integer number of students on a field trip. not half-persons.
therefore, 29.5 students for a single field trip calculation does not make sense.
but : we could want to use the same function to calculate or analyze the costs of multiple field trips by using things like mean values of students participating. there fractions as student numbers make sense.
Please help me really fast
The equation of line parallel to the given line is found as y = -6x + 13.
What is meaning of the term parallel slopes?A line's slope is similar to the slopes of adjacent parallel lines, therefore m1 = m2. Additionally, the equations of a parallel line could be determined by applying the formulas; (y−y1)=m(x−x1) ( y − y 1 or by y = mx + c.The equation of the line is-
y = -6x + 1
The second line is parallel to the above line, thus the slopes of both the line are equal.
m1 = m2 = -6
The new line also passes from the point (1, 7)
(x1, y1) = (1,7)
Thus, the equation of the line will be calculated as-
y - y 1 = m2(x - x1)
y - 7 = -6(x - 1)
y - 7 = -6x + 6
y = -6x + 13
Thus, the equation of line parallel to the given line is found as y = -6x + 13.
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in the figure, h II o find the value of x and y
Answer:
y = 119
30 =x
Step-by-step explanation:
61 and y are same side interior angles and they add to 180
61+y = 180
y = 180-61
y = 119
y and 6x-61 are vertical angles and they are equal
y = 6x-61
119 = 6x-61
Add 61 to each side
119 + 61 = 6x
180 = 6x
Divide each side by 6
180/6 = x
30 =x
Answer:
y = 119°
x = 30°
Step-by-step explanation:
We know that if two lines are parallel, the co - interior angles are added up to 180°°.
Accordingly,
y + 61 = 180
y = 180 - 61
y = 119°
Also, we know that, vertically opposite angles are equal to each other.
y = 6x - 61
119 = 6x - 61
Now, we have to make x the subject.
For that, first, add 61 for both sides.
119 + 61 = 6x
180 = 6x
Now, divide both sides by 6.
30° = x
Screams Halloween Theme Park
reduced their admission rates by 10% this
year to try and increase their attendance. If
last year’s admission price was $35 per
person, what is this year’s admission price?
Answer:
$32.50
Step-by-step explanation:
10% of 35$ is $3.50 if ur decreasing $35 by 10% it will be $3.50-$35=$32.50
In a recipe, for every tablepoon of ugar there are four teapoon of alt. If a batch ue four tablepoon of ugar, how many teapoon of alt doe it ue?
tablepoon of ugar
teapoon of alt 1 4 4
There will be 16 teaspoons of salt is needed for the 4 tablespoons of sugar.
Given, In a recipe, for every tablespoons of sugar there are four teaspoons of salt.
If a batch use four tablespoons of sugar then we have to find the number of tablespoons of salt needed.
as, 1 sugar = 4 salt
4 sugar = 4×4 salt
4 sugar = 16 salt
So, the number of tablespoons of salt needed is 16 for the use of 4 tablespoons of sugar.
Hence, there will be 16 teaspoons of salt is needed for the 4 tablespoons of sugar.
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Convert 42°C into °F
Answer: 107.6
(42c x 9/5) +32
find the roots of each expression with rational exponents.
1.27⅓
2.225½
3.49³/²
(please show solution
you can write in on paper)
simplify each expression
For the given expressions the roots with rational exponents are as follow:
a. 27¹/³ = 3
b. 225 ¹/² = 15
c. 49 ³/² = 243
As given in the question,
For the given expressions the roots with rational exponents are as follow:
Solution of each expression is given by:
a. 27¹/³
Prime factors of 27 is equal to 3 × 3 × 3
27¹/³
= ( 3 × 3 × 3 )¹/³
= ( 3³ )¹/³
= 3
b. 225 ¹/²
Prime factors of 225 is equal to 3 × 3× 5× 5
225 ¹/²
= ( 3× 3× 5× 5)¹/²
= ( 15²)¹/²
= 15
c. 49 ³/²
Prime factors of 49 is equal to 7 × 7
49 ³/²
= ( 7 × 7) ³/²
= (7²) ³/²
= 7³
= 343
Therefore, for the given expressions the roots with rational exponents are as follow:
a. 27¹/³ = 3
b. 225 ¹/² = 15
c. 49 ³/² = 243
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Nick bought a new car.
Each year the car depreciates in
value by 12%.
Work out the number of years it takes for the car to half in value.
a professor wants to study the effectiveness of a new study tool for a course. there are 150150150 students registered for the course. the professor assigns each student a number from 111 to 150150150 and uses a random number generator to assign the first 757575 students selected to use the new study tool. the remaining 757575 subjects are assigned to use the previous study tool. what type of experiment design is this?
This is a "completely randomized" type of experiment design.
In terms of data analysis as well as accessibility, and simplicity a randomized design is perhaps most likely the shortest experimental study.
The investigator expects that sometimes extraneous influences would affect treatment conditions similarly in general, so that any substantial improvements across conditions may be allocated appropriately towards the individual entity.
Thus the above approach is right.
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its easy but im lazy please helppppp
y=1/58x
because in 3 hours its 174 miles.
let y=miles
x=time
so 174y=3x
divide by 3 on both sides
58y=x
isolate y by dividing by 58 on both sides
therefore you get the answer
Eli is following this recipe to bake bread rolls.
He uses 900 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
600 g flour
12 g salt
9 g yeast
45 ml oil
360 ml water
g salt
0
g yeast
0
ml oil
0
ml water
Answer:
1022
Step-by-step explanation:
360+600+12+45+9=1022
Suppose g(x) = f(x + 2) - 3. Which statement best compares the graph of g(x)
with the graph of f(x)?
• A. The graph of g(x) is shifted 2 units left and 3 units up.
• B. The graph of g(x) is shifted 2 units right and 3 units down. 3
• C. The graph of g(x) is shifted 2 units right and 3 units
up.
• D. The graph of g(x) is shifted 2 units left and 3 units down.
We deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x). The best choice is C.
Describe a graph.A diagram that shows how a variable varies in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or regions.
Right-shift a function
Inside the function's argument, subtract. For instance, is essentially moved b units to the right.
You go to the right while subtracting from the parameter of the function.
Accordingly, f(x) is moved two units to the right in g(x) = f(x - 2).
also to advance a function
Outside of the function, add. For instance, is essentially shifted up units.
G(x) = f(x - 2) + 3 hence says that f(x) is shifted up by 3 units.
Overall, then, using two transformations, we deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit upswing in the graph of g(x).
Therefore, choice C is right.
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the length of time for one individual to get to a construction site is a random variable having an exponential distribution with a mean of 4 minutes. what is the probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days?
The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.
Define probability.A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.
Given,
Mean = 4 minutes
= 1/4
= 0.25
The probability that someone will be attended to in less than three minutes on any given day is:
P( X ≤3)
= 1- e⁻⁰²⁵⁽³⁾
= 0.5267
The probability is:
P( X ≥ 4)
= P( X = 4) +P( X = 5 ) + ( X = 6)
= 0.2594 + 0.1159 + 0.216
= 0.3969
The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.
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Which inequality correctly orders the numbers -2/5, -11/3 and -2.5?
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal ≤
Greater than and equal ≥
The inequality that correctly orders the numbers is
-3.67 < -2.5 < -0.4
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
-2/5 = -0.4
-11/3 = -3.67
-2.5
Now,
We see that,
-0.4 is greater than -2.5 and -2.5 is greater than -3.67.
This can be represented as an inequality:
-3.67 < -2.5 < -0.4
Thus,
The inequality that correctly orders the numbers is
-3.67 < -2.5 < -0.4
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What is the amount of m
Answer:
N=138
Step-by-step explanation:
(4x+6) + N = 180
In order to complete this problem we need to solve for x. 4x+6=7x-21
Subtract on both sides
Subtract again
Divide
x=9
Plug it in now so 4 times 9 plus 6. 36, plus 6 = 42.
plug it in to the equation 42+N=180
-42 -42
138 = N
The dimensions of two rectangular prisms are shown below. How much more volume does the larger prism have than the smaller prism?
Answer:16/25 :D
Step-by-step explanation:does that help :3
For a given function f (x), the domain is -4 < x <7, the range is 2 < y < 9, and has the point (4,8) on the graph. If h (z) = f(x+4), then
the domain of h (z) would be
type your answer....
the range would be type your answer.....
and the corresponding point would be moved to (type your answer.....
type your answer.....
y< type your answer.....
Submit
The domain of h(z) would be (-8,3).
The range of h(z) would be (2,9).
Point (4,8) would be moved to (0,8)
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
For the function f(x):
Domain: (-4,7)
Range: (2,9)
The function f(x+4) is equal to 1 (f(x+4)).
This shows, inputs: -4, outputs: 1
Domain of f(x+4):
add -4 to the Domain values of f(x)
Domain:(-4-4,7-4)=(-8,3)
Range of f(x+4):
Multiply the range values of f(x) by 1
Range: (1*2,1*9)= (2,9)
Find, where the point (4,8) would be moved:
add -4 to 4, and multiply 8 by 1
(4-4,8*1)
=(0,8)
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what is 56/60 as a percentage
Answer:
93.33%
Step-by-step explanation:
56/60 as a percentage:
56/60 = 0.93333
0.93333 as a percent:
0.93333 * 100 = 93.33%
The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
We have to given that,
To change a number 56/60 into a percentage.
Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Hence, We can write as,
⇒ 56/60 × 100%
⇒ 5600/60
⇒ 93.33%
Therefore, The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
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suppose goop purchases 150 gallons of raw material. what is the probability that they will run out of raw material?
The probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.
We have following information,
the demand for the polymer is distributed normally .
Mean (μ) = 250 gallons and Standard deviations (σ) = 125 gallons
Selling price of poymer = $25 per gallons
cost price of raw material for polymer= $ 10 per gallons
Salvage value = $(-5)/ gallon
Now, Using the formula for normally distributed sample,
Z = ( X - μ ) /σ
where , X---> sample mean
μ ----> population mean
σ----> standard deviations
Z -----> Z-value
from question it is clear X = 150
putting all the values of variables in above formula we get, Z = ( 150-250)/125 = -100/125
= - 0.8
(-0.8) value of z = 0.21 = 21% , the value of z is measure from normal distribution table.
They will run out of raw material if demands exceds this quantity or
Probability ( out of stock ) = 1 - 0.21 = 0.79 = 79%
So, the probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.
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#Complete Question :
Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop's purchases raw material for $10 per gallon and Goop mrust spend $5 per gallon to dispose off all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) That is to say, the salvage value is $(-5)/gallon. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost. ?
1. Suppose Good purchases 150 gallons of raw material. What is the probability that they will run out of raw material? ?
1 Which of the following equations are
true? Select all that apply.
A 7+(-7) = 14
B -4+9=5
C 3-(-10) = -7
D -2-6=-8
Equations B and D are true.
How much water must be added to 14 liters of a 90%
acid solution to obtain a 40% acid solution?
17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Given that, there are 14 litres of a solution which is 90% acidic,
Let water added be x, then according to question,
0.90*14 = 0.40(x+14)
12.6 = 0.40x + 5.6
0.40x = 7
x = 17.5
Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
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if f(x) = 2x - 4 find f(k+1)
Answer: [tex]f(k+1)=2k-2[/tex]
Step-by-step explanation:
Substituting [tex]k+1[/tex] for [tex]x[/tex],
[tex]f(k+1)=2(k+1)-4\\\\f(k+1)=2k+2-4\\\\f(k+1)=2k-2[/tex]
Fleur is making 8 identical thank-you cards for her teachers. each card requires 2.5 sheets of yellow paper and some red paper. she uses a total of 30 sheets of paper. a. write an equation that can be used to determine the number of red sheets, r, required for each card. __
The required equation to determine the number of red sheets, r, required for each card is 8r + 20 = 30.
Let the required number of red paper be r. For one card, the 2.5 sheets of yellow paper are required. So, for 8 thank-you cards, the yellow papers required will be = 8×2.5
Number of yellow papers = 20
Total number of sheets required = Number of yellow sheets for 8 cards + Number of red sheets for 8 cards
Keep the values in formula to form the equation
30 = 20 + 8r
8r = 10
r = 10/8
r = 1.25
So, the equation for calculation of number of red papers for each card is 1.25.
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simplify the following
2²y + 3x² + 4y + 3x²y + 2y
Answer:
10y+3x^2+3x^2y
Step-by-step explanation:
^2 means square
2^2 is 4 and different variable cannot be added.
how long does it take lena to compress the accordion completely and then stretch it back out to a length of 50\text{ cm}50 cm50, start text, space, c, m, end text?
It takes Lena to compress the accordion completely and then stretch it back out to a length of 50cm.
It takes Lena 4.1 seconds to compress the accordion completely and then stretch it back out to a length of 50cm.
I am assuming the function without a T: [tex]A(t) = 25_{cos}(t)+65[/tex]
The function is graphed in the figure attached, and the blue line is [tex]y = 50cm[/tex].
From the graph we see that the accordion is completely stretched (has minimum length) at [tex]t = \pi[/tex] seconds, and stretches back to 50cm at [tex]t = 4.069s[/tex]; therefore, it takes Lena 4.069 seconds to stretch the accordion back again, which to the nearest tenth of a second is 4.1s.
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Answer: 1.3s
Step-by-step explanation:
If you're solving for [tex]A(t)=25cos( \pi t)+65\\[/tex]
What is the value of negative 7 divided by 5?
Answer:
-7/5 or -1.4
Step-by-step explanation: