Suppose f(x) is continuous on [3,6] and −3≤f′(x)≤5 for all x in (3,6). Use the Mean Value Theorem to estimate f(6)−f(3).
Answer: -9 ≤ f(6) - f(3) ≤ 15
Step-by-step explanation:
In order to use the Mean Value Theorem, it must be continuous and differentiable. Both of these conditions are satisfied so we can continue.
Find f(6) - f(3) using the following formula:
[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]
Consider: a = 3, b = 6
[tex]\text{Then}\ f'(c)=\dfrac{f(6)-f(3)}{6-3}\\\\\\\rightarrow \quad 3f'(c)=f(6) - f(3)[/tex]
Given: -3 ≤ f'(x) ≤ 5
-9 ≤ 3f'(c) ≤ 15 Multiplied each side by 3
→ -9 ≤ f(6) - f(3) ≤ 15 Substituted 3f'(c) with f(6) - f(3)
Given the coordinates (0,0) and (4, 1), the distance is:
Answer:
[tex]\sqrt{17}[/tex] or ≈4.12
Step-by-step explanation:
Use the distance formula
d= √(x₂ - x₁) ² + (y₂-y₁) ²
d= √(4-0)² + (1-0)²
d= √16 + 1
d= √17
Need help ASAP please!!
Answer:
AOB = 73
BOC = 107
Step-by-step explanation:
So make an equation.
9x + 27 = 180
9x = 153
x = 17
AOB = 73
BOC = 107
Classify the triangle by its sides, and then by its angles.
6 in.
8 in.
10 in.
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
acute
obtuse
right
triangle.
Answer: scalene and right
Step-by-step explanation:
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer: A
Step-by-step explanation:
To multiply matrices, multiply each term in Row 1 of the first matrix with each term in Column 1 of the second matrix and then find their sum. Repeat for Row1×Column2, Row2×Column1, and Row2×Column2.
[tex]\left[\begin{array}{ccc}1&4&-1\\3&2&2\end{array}\right] \times \left[\begin{array}{cc}2&-1\\0&3\\5&2\end{array}\right] \\\\\\=\left[\begin{array}{ccc}1(2)+4(0)-1(5)&1(-1)+4(3)-1(2)\\3(2)+2(0)+2(5)&3(-1)+2(3)+2(2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-3&9\\16&7\end{array}\right][/tex]
Meru Peak is 765 m higher than Mt. Kilimanjaro. If the sum of their heights is 12,555 m, find the height of Mt. Kilimanjaro.
Answer:
Step-by-step explanation:
Let P=Mount Peak
Let K=Mount Killimanjaro
The equation should then be
12555=P+K ...1
P=K+765 ... 2
sub equation 2 into 1
12555=P+P+765
12555=2P+765
12555-765=2P+765-765 (subtracting 765 from both sides)
11790=2P
P=5895, now that we know P
we just make a new equation that was similiar to 1
12555=5895+K
K=6660
the height of Mount K is 6660 Metres
1. If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest?
Ans: years
2. The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other
number is ….
Answer:
1) 48 years.
2) Question incorrect.
11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.
Step-by-step explanation:
Let the ages of Kissi, Esinam and Lariba be x, y and z respectively.
Ratio of the ages of Kissi and Esinam is 3:5
x:y = 3:5
(x/y) = (3/5)
5x = 3y
x = (3y/5) (eqn 1)
Ratio of the ages of Esinam and Lariba is 3:5
y:z = 3:5
(y/z) = (3/5)
5y = 3z
z = (5y/3) (eqn 2)
The sum of their 3 ages is 147
x + y + z = 147 (eqn 3)
Substituting the values of x and z from eqn 1 and 2 into eqn 3, we have
(3y/5) + y + (5y/3) = 147
(49y/15) = 147
y = (147×15/49) = 45.
x = (3y/5) = (3×45/5) = 27
z = (5y/3) = (5×45/3) = 75
The ages of Kissi, Esinam and Lariba are then 27, 45 and 75 respectively.
The difference in the ages of the oldest amf the youngest is thus, 75 - 27 = 48 years.
2) This question seems to be faulty and incorrect as 11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.
Hope this Helps!!!
In a group of 50 patrons, 14 patrons like lattes and espressos, 11 patrons like
espressos and cappuccinos, 7 patrons like lattes and cappuccinos, and 3
patrons like all 3 coffee drinks. Altogether, 22 patrons like lattes, 30 patrons
like espressos, and 23 patrons like cappuccinos. How many patrons don't like
any of these coffee drinks?
Answer:the answer would be 4. Hope this helps.
Step-by-step explanation:
Using the formula of union of three events, the number of patrons who didn't like any of given coffee drinks = 4.
What is union of three events?Union of three events : P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C).
n (latte ∩ espressos) = 14
n (espressos ∩ cappuccinos) = 11
n (lattes ∩ cappuccinos) = 7
n (latte ∩ espressos ∩ cappuccinos) = 3
n (lattes) = 22
n (espressos) = 30
n (cappuccinos) = 23
n(latte ∪ espressos ∪ cappuccinos) =
= n (lattes) + n (espressos) + n (cappuccinos) - n (latte ∩ espressos) - n (espressos ∩ cappuccinos) - n (lattes ∩ cappuccinos) + n (latte ∩ espressos ∩ cappuccinos)
= 22 + 30 + 23 - 14 - 11 - 7 + 3
= 46
n (universe) = 50
Number of patrons who didn't like any of these drinks =
= n (universe) - n (latte ∪ espressos ∪ cappuccinos) = 50 - 46 = 4
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Which equation does not represent a linear function of x?
a. y = -3 over 4 x
b. y = x over 2
c. y = - 3 + 2x
d. y = 3x2 - 2
fand f are functions.
If f(4) = 2 then f'(2) = ?
Answer:
4
Step-by-step explanation:
[tex] \because \: f(4) = 2 \\ \therefore \: {f}^{ - 1} (f(4)) = {f}^{ - 1} (2) \\ \therefore \: 4 = {f}^{ - 1} (2) \\ \huge \red{ \boxed{{f}^{ - 1} (2) = 4}}[/tex]
Answer:
4 four
Step-by-step explanation:
hope it helps you
Any help would be great
Answer:
2/3
Step-by-step explanation:
[tex]\dfrac{12}{18}= \\\\\\\dfrac{6\times 2}{6\times 3}= \\\\\\\dfrac{2}{3}[/tex]
Hope this helps!
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\frac{12}{18}=\frac{x}{3}[/tex]
[tex]18x=12 \times 3[/tex]
[tex]18x=36[/tex]
[tex]\frac{18x}{18y} =\frac{36}{18}[/tex]
[tex]x=2[/tex]
[tex]=\frac{2}{3}[/tex]
The probability that a randomly chosen sales prospect will make a purchase is 20%. What is the probability (to three decimal places) that the salesperson will make four or more sales if six sales calls are made on a given day
Answer:
1.7%
Step-by-step explanation:
We have to calculate the probability that the salesperson will make four or more sales if six sales calls are made on a given day, that is:
P (x => 4)
Therefore, we must calculate when x = 4, when x = 5, and when x = 6 and add. p = 0.2, n = 6
P (x = r) = nCr * p ^ r * (1 - p) ^ (n-r)
Also, nCr = n! / (r! * (n-r) !, now replacing:
P (x = 4) = 6! / (4! * (6-4)! * 0.20 ^ 4 * 0.80 ^ (6-4)
P (x = 4) = 15 * 0.001024 = 0.01536
P (x = 5) = 6! / (5! * (6-5)! * 0.20 ^ 5 * 0.80 ^ (6-5)
P (x = 5) = 6 * 0.000256 = 0.001536
P (x = 6) = 6! / (6! * (6-6)! * 0.20 ^ 6 * 0.80 ^ (6-6)
P (x = 6) = 1 * 0.000064 = 0.000064
now,
P (x => 4) = P (x = 4) + P (x = 5) + P (x = 6)
P (x => 4) = 0.01536) + 0.001536 + 0.000064
P (x => 4) = 0.01696 = 0.017
It means that the probability is 1.7%
One side of a rectangle is 14 meters. The perimeter of the rectangle is 44 meters. What is the area of this rectangle?
how to differentiate functions
Answer: see boxed answers below
Step-by-step explanation:
(i) multiply the exponent to the coefficient then subtract 1 from the exponent.
[tex]y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}[/tex]
(ii) Use the division formula: [tex]y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}[/tex]
[tex]a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}[/tex]
Identify which of the following is NOT equivalent to 2 3/4
Answer:
Step-by-step explanation:
mabey its c
The equation which is equivalent to [tex]2^{\frac{2}{3} }[/tex] will be equal to [tex]\sqrt[4]{2^3}[/tex]. Hence, option C is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
[tex]2^{\frac{2}{3} }[/tex] = 1.68
Now, let's check the options,
A.
[tex](2^{\frac{1}{4} } )^{\frac{1}{2} }[/tex] = 1.09 ≠ 1.68, hence this is incorrect.
B.
[tex]2\frac{1}{4}*2\frac{1}{2}[/tex] = 9/4 × 5/2 = 5.625 ≠ 1.68, hence, this is incorrect.
C.
[tex]\sqrt[4]{2^3}[/tex] = 1.68 = 1.68, hence, this is correct.
D.
√8 = 2.82 ≠ 1.68, hence, this is incorrect.
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g(x)4x^2-16x+7 completing the square
By completing the square the function will be, g(x)=4(x-2)²-9
What is standard form of the equation?The standard form of the quadratic equation will be ax²+bx+c=0.
Equate the given equation with standard form of equation and determine the values of a, b, and c.
a=4
b=-16
c=7
For completing the square, add and subtract [tex]\frac{b^2}{4a}=\frac{(-16)^2}{4\times4}=16[/tex] in the given equation.
g(x)=4x²-16x+16-16+7
g(x)=(4x²-16x+16)-9
g(x)=4(x²-4x+4)-9
The term x²-4x+4 is equivalent to (x-2)².
g(x)=4(x-2)²-9
So, the given function is same as g(x)=4(x-2)²-9.
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I need help!!!! I don’t understand and it’s very confusing
Answer:
C
Step-by-step explanation:
I explained in my last answer but someone deleted it
algebra parabola question see picture above
Answer:
see below
Step-by-step explanation:
(-1, -9) is a vertex or minimum.
(-4, 0) is an x-intercept / zero of the function / solution
(2, 0) is also an x-intercept / zero of the function / solution
The parabola has a minimum.
to shift the graph of an equation some number of units to the_ you subtract that number from each X in the equation
Answer:
A. right
Step-by-step explanation:
Replacing x with (x-h) in a function shifts the graph to the right h units.
__
See the attachment for an example.
According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes with a standard deviation of 8.1 minutes. What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean
Answer:
By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean
By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean
95% of commuters in Boston has a commute time within 2 standard deviations of the mean
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.
Hence, 95% of commuters in Boston has a commute time within 2 standard deviations of the mean
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Find the value of x in the figure below
88°
Step-by-step explanation:
sum of angle=720
95+120+120+172+125+x=720
632+x=720
×=720-632
x=88
Answer:
[tex] \boxed{x \degree = 88 \degree} [/tex]
Step-by-step explanation:
Sum of the interior angles of a hexagon is 720°
[tex] = > x \degree + 172 \degree + 120 \degree + 95 \degree + 120 \degree + 125 \degree = 720 \degree \\ \\ = > x \degree + 172 \degree + 240 \degree + 220 \degree = 720 \degree \\ \\ = > x \degree + 172 \degree + 460 \degree = 720 \degree \\ \\ = > x \degree + 632 \degree = 720 \degree \\ \\ = > x \degree = 720 \degree - 632 \degree \\ \\ = > x \degree = 88 \degree[/tex]
2(x+3)+5 simplified expression
Answer:
2x+11
Step-by-step explanation:
2(x+3)+5
Distribute
2x+ 6 +5
Combine like terms
2x+11
Answer:
2x + 11
Step-by-step explanation:
First distribute 2 to the x + 3
2x + 6 + 5
Combine the constants
6+5=11
2x + 11
The simplified expression is 2x + 11
In a preschool, there are 5 students per teacher. There are 10 teachers in the school. How many students are in the school?
2
5
15
50
Answer: 50 student in the school
Step-by-step explanation: 5x10=50 so that’s the answer.
The system of equations above has solution (x,y).
What is the value of x ?
Answer: [tex]\frac{21}{4}[/tex]
Step-by-step explanation:
Multiply each side by 2 to get rid of the fraction on the right side. That basically gets rid of the 1/2 and the 2.
Youre now stuck with 2x + y = 21. They gave us y which is 2x. 2x + 2x = 4x
You now have 4x = 21
Divide each side by 4 to get x = 21/4
Need help finding the answer
Answer:
D
Step-by-step explanation:
When there is an negative sign inside in a radical, then we remove that and put out of the radical classifying as "i". Then, reduce 63 into smallest form and we can write it as 9 and 7. 9 is a perfect square of 3 so we put it outside and the answer is D.
A can of beans has surface area 320cm squared . Its height is 14 cm. What is the radius of the circular top?
Steps:
All cans take on the shape of a cylinder, unless you have seen interesting shape of cans like a starfish.
The formula for surface area of a cylinder is
SA = 2πr2 + 2πrh
where:
r = radius
h = height
Since we know the surface area and height, we can plug them in. Note that we can factor out the 2π. You will see why we factor out 2π rather than 2πr.
2π(r2 + (20)r) = 396
2π(r2 + 20r) = 396
Divide both sides of the equation by 2π to isolate the r terms.
r2 + 20r = 63.025
Subtract 63.025 on both sides of the equation.
r2 + 20r - 63.025 = 0
Use the quadratic formula to solve for r:
r = (-b ± √(b2 - 4ac)) / 2a
where:
a = 1
b = 20
c = -63.025
Plug in these values into the formula. You should get two solutions because of the plus/minus sign. Accept the positive value of r.
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Hope this helps.
Which letter has at least one line of symmetry?
W
Z
S
F
Answer:
Both F and Z have symmetry.
Write the equation 2x - 3y = 6 in slope-intercept form.
Answer:
[tex] y = \frac{ 2}{ 3} x - 2[/tex]
Step-by-step explanation:
[tex]2x - 3y = 6 \\ - 3y = - 2x + 6 \\ \\ y = \frac{ - 2}{ - 3} x + \frac{6}{ - 3} \\ \\ \huge \purple{ \boxed{ y = \frac{ 2}{ 3} x - 2}} \\ this \: is \: in \: the \: slope - intercept \: form.[/tex]
Answer:
y = 2/ 3 x − 2
Step-by-step explanation:
slope intercept is y=mx+b
The square of a number is 12 less than 7 times the number.what is the number?
Answer:
n = 3 or n = 4
Step-by-step explanation:
Let the unknown number be n.
Then:
n² = 7n - 12
In standard quadratic form, we have:
n² - 7n + 12 = 0
In factored form, we have:
(n - 3)(n - 4) = 0, and so
n = 3 and n = 4
Please answer this correctly
Answer:
A=450
Step-by-step explanation:
A=a+b
2h=12+33
2·20=450
Answer:
Area=450
Step-by-step explanation:
[tex]a+b/2h[/tex]
