Answer:
[tex]8 \le f(4) - f(2) \le 10[/tex]
Step-by-step explanation:
Given
[tex]4 \le f'(x) \le 5[/tex]
Required
Determine the minimum and maximum value of f(4) - f(2)
This question will be answered using the following mean value theorem.
[tex]f'(x) = \frac{f(b) - f(a)}{b - a}[/tex]
In this case: [tex]b = 4[/tex] and [tex]a = 2[/tex]
So, we have:
[tex]f'(x) = \frac{f(4) - f(2)}{4 - 2}[/tex]
[tex]f'(x) = \frac{f(4) - f(2)}{2}[/tex]
Make f(4) - f(2), the subject:
[tex]f(4) -f(2) = 2 * f'(x)[/tex]
From the given range: [tex]4 \le f'(x) \le 5[/tex]
We have that; f'(x) is at minimum at 4
So, the minimum of f(4) - f(2) is:
[tex]f(4) -f(2) = 2 * 4[/tex]
[tex]f(4) -f(2) = 8[/tex]
We have that; f'(x) is at maximum at 5
So, the maximum of f(4) - f(2) is:
[tex]f(4) - f(2) = 2 * 5[/tex]
[tex]f(4) - f(2) = 10[/tex]
Hence, the minimum and maximum values can be expressed as:
[tex]8 \le f(4) - f(2) \le 10[/tex]
A box is filled with 4 red crayons, 8 blue crayons, and 2 yellow crayons.
A crayon is chosen at random from the box. Find the probability that it is a red or a yellow crayon.
Write your answer as a fraction in simplest form.
O
Х
?
Answer:
6/14 simplified to 3/7
Step-by-step explanation:
Solved it
Average Weekly Earnings The average weeklyearnings in dollars for various industries are listedbelow. Find the percentile rank of each value.
804 736 659 489 777 623 597 524 228
For the same data, what value corresponds to the 40th percentile
Answer:
a. 228- 6th, 489- 17th, 524- 28th, 597- 39th, 623- 50th, 659- 61th, 736- 72th, 777- 83th, 804- 94th
b. 597
Step-by-step explanation:
arrange the data:
228, 489, 524, 597, 623, 659, 736, 777, 804
a. percentile = ((number of items below position + 0.5)/ number of items ) 100
for 228 = (0+0.5/ 9) 100 = 6th
for 489 = (1+0.5/ 9) 100 = 17th
for 524 = (2+0.5/ 9) 100 = 28th
for 597 = (3+0.5/ 9) 100 = 39th
for 623 = (4+0.5/ 9) 100 = 50th
for 659 = (5+0.5/ 9) 100 = 61th
for 736 = (6+0.5/ 9) 100 = 72th
for 777 = (7+0.5/ 9) 100 = 83th
for 804 = (8+0.5/ 9) 100 = 94th
b. The corresponding value for the 40th = number of item( percentile)/ 100
= 9( 40) / 100 = 3.6 approximately 4th which is 597
Simplify:
3(8) ° •(3)-2
A -216
B 24/9
C -27
D 1/3
(help please) :(
Answer:
C I think
Step-by-step explanation:
Please, can someone help me on math? Struggling a bit.
The average combined SAT score for students at Brookstone High was 1000 in 2003, 1100 in 2004, 1210 in 2005, and 1331 in 2006. Predict the SAT score for Brookstone seniors in 2007. Explain your answer.
Derek has 6 feet of ribbon that he needs to cut into 2/3 feet pieces. How
many pieces of ribbon can Derek cut?
Answer:
The correct answer is 9 pieces of ribbon.
Step-by-step explanation:
9 is correct because if you do 6 divided by 2/3 you equal 9, therefore 9 is the correct answer
HAVE A GOOD DAY!
I need help please. This is due in 40 minutes:(
Given the diagram below, solve for x and y.
Answer:
x=14, y=37
Step-by-step explanation:
We know that (4y-10)° and 3x° are supplementary angles, meaning the total sum of the angles add up to 180°. (4y-10)° is also corresponding to the blank angle below (9x+12)°, making it a vertical angle. Since (4y-10)°=(9x+12)° because they are vertical angles, then that means we can solve for x:
Original Equation: (4y-10)°+3x°=180
New Equation: (9x+12)°+3x°=180
9x+12+3x=180
12x+12=180
12x=168
x=14
So x is 14
Because x=14, then y is:
4y-10+3(14)=180
4y-10+42=180
4y+32=180
4y=148
y=37
So y is 37
THE CORRECT ANSWER IS 12 FAVORS!!
Answer:
yes the answer in 12 fpavers
Step-by-step explanation:
wa
Which of the following represents the measures of all angles coterminal with a -220° angle?
O 360 + 140n, for any whole number n
O 360 + 140n, for any integer n
O 140 + 360n, for any whole number n
O 140 + 360n, for any integer n
The measurement of all angles co-terminal with a -220° angle is represented by 140+ 360 n, for any integer number n.
What are Co-terminal angles?These are the angles which shares the same initial line or terminal side. They are obtained by adding or subtracting 360° from the given angles.
Given, angle is -220° then its one positive co-terminal angle= -220°+360 = 140°
So, 140° is a positive co-terminal angle of -220°.
Therefore, co-terminal angle must be the type of 140°+360° n,
Learn more about Co-terminal angles.
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Which equation can be used to solve for x in the following diagram?
(6z- 15)°
Choose 1 answer.
z= (6z-15)
O z-(6z-15) = 90
O z+(6z- 15) = 90
4 of 7
Answer:
I'm answering this for points
find a number such that five more than one half the number is three times the number
Answer:
0.5
Step-by-step explanation:
can someone help me with this geometry problem?
=========================================================
Explanation:
The exterior angle is 137, so the interior angle adjacent to that is 180-137 = 43. This is interior angle U of triangle UVW.
Let's find the missing angle W
U+V+W = 180
43+68+W = 180
111+W = 180
W = 180-111
W = 69
We have three three interior angles of triangle UVW
U = 43V = 68W = 69The longest side is opposite the largest angle, so the longest side is UV
The shortest side is opposite the smallest angle, so the shortest side is VW
The order of the sides from smallest to largest is
VW < UW < UV
Refer to the diagram below.
The monthly expenditures on food by single adults in one city are monthly distributed with a mean of $410 and a standard deviation of $70
Answer:
is the whole question asked?
Express the function G in the form f ∘ g ∘ h
G(x) = 3/(7+√x)^2
What is the predicted value of fuel efficiency (in miles per gallon) for a car with a 2.5 cubic liters engine? Round your answer to two decimals, if needed.
Answer:
25.92
Step-by-step explanation:
Fuel efficiency is the measure or effort that is required to convert the chemical energy in the fuel to the kinetic energy which the cars needs to move. It is meant by how good or effectively the fuel is utilized by the vehicle. It is the ability of the engine to extract more energy from the fuel.
In the context, the size of the engine is 2.5 cubic liters. Then the predicted value of the fuel efficiency will be 25.92 miles per gallon.
ASAP PLS HELP DUE TODAY. WILL GIVE BRAINLIEST IF A GOOD ANSWER EXPLENATION AND CORRECT ANSWER
Rewrite 7 − 8 using the additive inverse and display the new expression on a number line.
Select one:
a.
7 + (−8)
An image of a horizontal number line is shown with labels from negative 2 to positive 8. An arrow begins at 0 and ends at 7. Another arrow begins at 7 and ends at negative 1.
b.
7 + 8
An image of a horizontal number line is shown with labels from 0 to 15. An arrow begins at 0 and ends at 7. Another arrow begins at 7 and ends at 15.
c.
7 − (−8)
An image of a horizontal number line is shown with labels from 0 to 15. An arrow begins at 0 and ends at 7. Another arrow begins at 7 and ends at 15.
d.
8 − 7
An image of a horizontal number line is shown with labels from negative 2 to positive 8. An arrow begins at 0 and ends at 8. Another arrow begins at 8 and ends at 1.
Answer:
[tex]7 + (-8)[/tex]
Step-by-step explanation:
Given
[tex]7 - 8[/tex]
(a): Write as additive inverse.
An additive inverse is of the form a + (-b)
In this case:
[tex]a = 7[/tex]
[tex]b = -8[/tex]
So, the expression can be represented as:
[tex]7 + (-8)[/tex]
(b): Number line representation
When the expression in (a) is solved.
The result is:
[tex]7 - 8 = 7 + (-8) = -1[/tex]
This means that the number line must accommodate 7 and -1.
Having said that, options (b) and (c) are out because their range is 0 to 15 and this excludes -1.
Option (d) is a wrong representation of [tex]7 - 8[/tex]
Hence, (a) is correct
PLEASE HELP THIS IS DUE AT 10 PM
Brandi wants to participate in an after-school program. She has to choose between one art class, three dance classes, bwo gymnastics classes, or three sports casses. She cannot decide, so she writes the name of each class on a slip of paper and draws one slip out of a bag. What is the probability that she does not draw a dance class?
Answer:
Step-by-step explanation:
Its 1/3 just put that it will be right I promise
You are buying bottles of glue for Mrs. Perro's class. A bottle of glue is $0.74. Which equation can be use to find the number bottles she purchased for $12.58?
#11 PLEASE HELP!!! URGENT!! NEED ASAP!!!
Answer:
See bolded answers
Step-by-step explanation:
Since 1=100%, then 1.15=115%, meaning x increased by 15% is correct
Since 1=100%, then 0.15=15%, meaning 15% of x is correct
Since 1=100%, then 0.85=85%, meaning x decreased by 15% is correct
Help please! This has to do with the Pythagorean theorem.
Answer:
x = 11.49
Step-by-step explanation:
Apply the pythagorean theorem to find x
Thus:
a² + b² = c²
Where,
a = x = ???
b = 8
c = 14 (hypotenuse)
Plug in the values
x² + 8² = 14²
x² + 64 = 196
x² = 196 - 64 (subtraction property of equality)
x² = 132
x = √132
x = 11.49 (approximated to nearest hundredth)
1. Find the slope of the line that passes thru the points (7,11) (13,17).
Answer:
go on cymath it helps alot with solving slopes
Step-by-step explanation:
the ratio of two numbers is 4:5 after adding 20 to the smaller number and subtracting 20 from the greater number the ratio becomes 14:13 find the number please help!
Answer:
The numbers are 120 and 150.
Step-by-step explanation:
Please see the attached pictures for the full solution.
A 2-liter bottle of spring water costs $2.02. A 3-liter bottle of the same water costs $2.79.
Which is the better deal? ..
find the value of x^2 +xy if x =4 and y = 3
The sum of two integers is 9 their difference is 5 what are the 2 integers
What the solution to -3=-3+5x+3x
Find the measure of angle A.
3)
74
16x + 1
19x
A
A) 82°
C) 57°
B) 69°
D) 49°
Answer:
I think its 69* but I be wrong so good luck
Step-by-step explanation:
the figure consists of a quarter circle and a parallelogram. what is the area of the composite figure? use 3.14 for . Round to the nearest whole number.
70in.²
84in.²
154in.²
224in.²
Answer:
224
Step-by-step explanation:
the area of a circle is [tex]\pi[/tex][tex]r^{2}[/tex], so for the circle plug in your numbers:
(3.14)([tex]14^{2}[/tex]) = 615.44
divide this by 4 because t=in the picture you only have a fourth of a circle:
615.44 / 4 = 153.86
the formula for area of a trapezoid is [tex]\frac{a + b}{2}[/tex] × h
so plug in your values: [tex]\frac{14+14}{2}[/tex] × 5
you get 70
add 70 and 153.22
70 + 153.22 = 223.22
this can round to 224
9) Eva can knit of a scarf in an hour. Her sister takes 3/4 of the time she takes. How long will her sister take to knit 8 similar scarves?
Answer:
it would take 360 minutes or 6 hours
Step-by-step explanation:
Answer:
6 hours
Step-by-step explanation:
3/4 of an hour is 45 mins, 45 minutes times 8= 360
Convert to hours and you get 6 hours.
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