Answer:
25/4Step-by-step explanation:
The mean value theorem for integrals for the function f(c) over a given interval [a, b] is expressed as g prime(c) = g(b) - g(a)/b-a. The idea is that there is a value c in between the interval [a, b] for the function given.
Given the function g(x) = 5√x within the interval [4,9]
g prime (c) = g(9) - g(4)/9-4
g(9) = 5√9
g(9) = 5*3 = 15
g(4) = 5√4
g(4) = 5*2 = 10
g prime c) = 15-10/9-4
g prime (c) = 5/5
g prime(c) = 1
So we are to find the number for which g prime (x) = g prime(c)
If g(x) = 5√x = [tex]5x^{1/2}[/tex]
g prime (x) = [tex]5/2 \ x^{-1/2}[/tex]
g prime (x) = 5/2√x
Since g prime (c) = 1 then;
5/2√x = 1
5 = 2√x
√x = 5/2
x = (5/2)²
x = 25/4
The value of c guaranteed by the mid value theorem is 25/4
The possible value of c for [tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex] is 6.25
The function is given as:
[tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex]
Calculate f(4) and f(9)
[tex]\mathbf{f(4) = 5\sqrt 4 = 10}[/tex]
[tex]\mathbf{f(9) = 5\sqrt 9 = 15}[/tex]
Substitute c for x in f(x)
[tex]\mathbf{f(c) = 5\sqrt c }[/tex]
Calculate f'(c)
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
So, we have:
[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{9 - 4}}[/tex]
[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{5}}[/tex]
This gives
[tex]\mathbf{f'(c) = \frac{15 -10 }{5}}[/tex]
[tex]\mathbf{f'(c) = \frac{5 }{5}}[/tex]
[tex]\mathbf{f'(c) = 1}[/tex]
Also, we have:
[tex]\mathbf{f'(x) = \frac 52x^{-1/2}}[/tex]
Substitute c for x
[tex]\mathbf{f'(c) = \frac 52c^{-1/2}}[/tex]
Substitute 1 for f'(c)
[tex]\mathbf{\frac 52c^{-1/2} = 1}[/tex]
Multiply through by 2/5
[tex]\mathbf{c^{-1/2} = \frac 25}[/tex]
This gives
[tex]\mathbf{c^{1/2} = \frac 52}[/tex]
Square both sides
[tex]\mathbf{c = \frac{25}4}[/tex]
[tex]\mathbf{c = 6.25}[/tex]
Hence, the possible value of c is 6.25
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According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017 . Data for the sale of randomly selected 40 homes sold in Greene County, Ohio, in showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in . Round your answer to four decimal places.
P-value =
Answer:
t= 1.89736659
Step-by-step explanation:
Solve.
5x – 10 <20
O (-00, 2]
O (-0,2)
O (-00, 6]
O (-0, 6)
You can use both the t statistic and the z statistic to test hypotheses about the mean of population. The test that uses the t statistic is typically referred to as a t test, while the test that uses z statistic is commonly called a z test.
Which of the following statements are true of the t statistic? Check all that apply.
a. If you know the population standard deviation, you should use the t statistic.
b. The t statistic could be considered as an estimated z statistic.
c. The t statistic provides a relatively poor estimate of z with small sample sizes.
d. The formula for the t statistic is t = (M - s) / SM.
Answer:
An apple a day keeps the doctor away
Step-by-step explanation:
Type in the answer
Its gonna be right
easy math please help!
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
Write in expanded form
3
(-a)
Answer:
-3a
Step-by-step explanation:
3(-a)
Expand brackets.
3 × -1a
-3a
A pile of 55 coins consisting of nickels and dimes is worth $3.90 . Find the number of each.
Answer:
23 dimes, 32 nickels
Step-by-step explanation:
Let n equal the number of nickels and d be the number of dimes. We can use the information given to create a system of equations, as follows:
The total number of coins (the number of nickels plus the number of dimes) is 55, giving us the equation n + d = 55.
The total amount is $3.90. Since each nickel is worth $0.05 and each dime is worth $0.10, we get the equation 0.05n + 0.10d = 3.90.
Multiplying the second equation by 20, we get n + 2d = 78. We can subtract the first equation to get d = 23. Substituting this into the first equation, we get that n = 32.
Therefore, there are 23 dimes and 32 nickels.
Answer: 100 penny 2 qtrs 50 noclke
Step-by-step explanation:
Determine the value of x using a trigonometric ratio.
A) 10.11 units
B) 4.98 units
C) 4.18 units
D) 8.49 units
We have a known hypotenuse, but unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.
sin(angle) = opposite/hypotenuse
sin(50) = x/6.5
6.5*sin(50) = x
x = 6.5*sin(50)
x = 4.97928888027336 make sure your calculator is in degree mode
x = 4.98
Answer is choice B
Answer:
b
Step-by-step explanation:
Penyelesaian
0.02 m: 3 cm: 4.6 cm = 2 cm : 3 cm: 4.6 cm
= 2 : 3 : 4.6
20 : 30 : 46
10 : 15
23
Latih Diri 4.1a
1. Wakilkan hubungan antara tiga kuantiti berikut dalam bentuk a : b:c.
(a) 2 minggu kepada 16 hari kepada 1 minggu
(b) 0.1 kg kepada 50 g kepada 0.25 kg
(c) 4 minit kepada 120 saat kepada 1.6 jam
(d 3 m kepada 480 cm kepada 6 400 mm
2. Tahir membayar RM5.60 untuk sepinggan nasi beriani, RM1.20 untuk segelas teh
dan 30 sen untuk sekeping kuih. Wakilkan hubungan harga bagi nasi beriani, teh dan
kuih dalam bentuk a:b:c.
76
BAB 4
Answer:
a:b:c
1a) 14:16:7
b) 2:1:5
c) 2:1:48
d) 15:24:32
2) 56:12:3
Step-by-step explanation:
Untuk membentuk nisbah tiga kuantiti, pertama-tama kita menukar masing-masing menjadi unit yang sama.
a) 2 minggu hingga 16 hari hingga 1 minggu
Menukar semuanya menjadi bilangan hari, kerana ia sangat setanding.
2 minggu = 14 hari
16 hari = 16 hari
1 minggu = 7 hari
2 minggu hingga 16 hari hingga 1 minggu = 14 hari hingga 16 hari hingga 7 hari
14: 16: 7
b) 0.1 kg hingga 50 g hingga 0.25 kg
Menukar semua menjadi gram
= 100 g hingga 50 g hingga 250 g
= 100: 50: 250
Bahagikan dengan 50
= 2 : 1 : 5
c) 4 minit hingga 120 saat hingga 1.6 jam
Menukar semua menjadi beberapa saat
= 240 saat hingga 120 saat hingga (1.6 × 60 × 60) saat
= 240 saat hingga 120 saat hingga 5,760 saat
= 2: 1: 48
d) 3 m hingga 480 cm hingga 6 400 mm
Menukar semua ini menjadi mm
= 3000 mm hingga 4800 mm hingga 6400 mm
Membahagi hingga 200 mm
= 15:24:32
2) RM5.60 hingga RM1.20 hingga 30 sen
Menukar semuanya kepada sen
= 560 sen hingga 120 sen hingga 30 sen
Membahagi hingga 10
= 56: 12: 3
Semoga ini Membantu !!!
English Translation
Solution
0.02 m: 3 cm: 4.6 cm = 2 cm: 3 cm: 4.6 cm = 2: 3: 4.6
20:30:46
10:15:23
Self Training 4.1a
1. Represent the relationship between the following three quantities in the form a: b: c.
(a) 2 weeks to 16 days to 1 week
(b) 0.1 kg to 50 g to 0.25 kg
(c) 4 minutes to 120 seconds to 1.6 hours
(d) 3 m to 480 cm to 6 400 mm
2. Tahir pays RM5.60 for a plate of beriani rice, RM1.20 for a glass of tea and 30 cents for a piece of cake.
Represent the price relationship for beriani rice, tea and cake in the form of a: b: c.
Solution
To form a ratio of three quantities, we first convert each of them to the same units.
a) 2 weeks to 16 days to 1 week
Converting all of it to number of days, as itnis very comparable.
2 weeks = 14 days
16 days = 16 days
1 week = 7 days
2 weeks to 16 days to 1 week
= 14 days to 16 days to 7 days
14 : 16 : 7
b) 0.1 kg to 50 g to 0.25 kg
Converting all into grams
= 100 g to 50 g to 250 g
= 100 : 50 : 250
Divide through by 50
= 2 : 1 : 5
(c) 4 minutes to 120 seconds to 1.6 hours
Converting all into seconds
= 240 seconds to 120 seconds to (1.6×60×60) seconds
= 240 seconds to 120 seconds to 5,760 seconds
= 2:1:48
(d) 3 m to 480 cm to 6 400 mm
Converting all of this to mm
= 3000 mm to 4800 mm to 6400 mm
Dividing through by 200 mm
= 15:24:32
2) RM5.60 to RM1.20 to 30 cents
Converting it all to cents
= 560 cents to 120 cents to 30 cents
Dividing through by 10
= 56:12:3
Hope this Helps!!!
Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Determine the probability that at least one contain regular soda.
Answer:
161/184 or 0.875
Step-by-step explanation:
Total number of cans = 24 cans
Total number of diet soda = 3 cans
Total number of regular soda = 21 cans
We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly
We have two ways for this happening
a) two of the cans are regular soda
b) one of the cans is regular , while one is diet
Hence,
Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)
Probability(that two of the cans are regular soda) = 21/24 × 20/23
= 35/46
Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23
= 21/184
Probability (that at least one contain regular soda) = 35/46 + 21/184
We find the Lowest common multiple of the denominators = 184
= 35/46 + 21/184
= (35 × 4) + (21 × 1)/184
= 140 + 21/184
= 161/184
= 0.875
Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875
Find the slope of the line passing through the given points. State whether the line is increasing, decreasing, horizontal, or vertical. (7,3) and (8,7)
Answer:
slope = 4
The line is increasing
Step-by-step explanation:
slope can be found through the equation [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. So, if we plug these points in, we get [tex]\frac{7-3}{8-7}[/tex], which simplifies to 4. So, the slope is 4.
Since the slope is positive, the line is increasing.
If F(x) = f(g(x)), where f(−4) = 8, f '(−4) = 3, f '(−3) = 5, g(−3) = −4, and g'(−3) = 6, find F '(−3). F '(−3)
Answer:
F'(-3) = 18
Step-by-step explanation:
Let g(x) = u and apply the chain rule
[tex]F(x)=f(g(x))=f(u)\\F'(x)=\frac{df(u)}{du}[/tex]
[tex]\frac{du}{dx}=g'(x)[/tex]
[tex]\frac{df(u)}{du}*\frac{du}{dx} = \frac{df(u)}{dx}\\F'(x)= \frac{df(u)}{du}*g'(x)\\F'(x)= f'(u)*g'(x)\\F'(x)= f'(g(x))*g'(x)[/tex]
We now have all of the necessary definite values to solve the expression for x= -3:
[tex]F'(-3)= f'(g(-3))*g'(-3)\\F'(-3)= f'(-4)*6\\F'(-3)= 3*6\\F'(-3)= 18[/tex]
Finally, we have that F'(-3)= 18.
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 3, 1) and point K is at (negative 8, 11). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –6 –5 5 7
Answer: (-5, 5)
Step-by-step explanation:
J = (-3, 1) K = (-8, 11) ratio 2 : 3 --> 2 + 3 = 5 segments
x-distance from J to K: -8 - (-3) = -5 units
y-distance from J to K: 11 - 1 = 10 units
Divide those distance into 5 segments:
x = -5/5 = -1 unit per segment
y = 10/5 = 2 units per segment
The partition is 2 segments from J:
x = -3 +2(-1) = -5
y = 1 + 2(2) = 5
The partition is located at (-5, 5)
Answer:
5
Step-by-step explanation:
stephano walks 2/5 mile in 1/4 hour. What is stephano's speed in miles?
The radius of a sphere is 11 cm.what is the surface area of the sphere? Round to the nearest tenth.
Answer:
The answer is
1520.5 cm²Step-by-step explanation:
Surface area of a sphere is given by
S = 4πr²
where r is the radius
From the question r = 11cm
So the surface area of the sphere is
4π(11)²
= 4(121)π
= 484π
= 1520.5308
Which is
1520.5 cm² to the nearest tenth
Hope this helps you
4 (5 points)
What is the range of y =|3x + 1)?
a) {y\y >0}
b) {y\y > 1}
8
c) {all real numbers)
d) {y|y23]
Answer:
[0, infinity)
Step-by-step explanation:
clarence, I believe you meant y = |3x + 1|. The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).
Which of the following statement is incorrect?
4
A.3/4<4/5
B.5/6>0.83
C.2/3>0.66
D.1/3>0.3
درا
Answer:
None,
they are all correct.
Step-by-step explanation:
A)
3/4 - 75%
4/5 - 80%
3/4 < 4/5
B)
5 ÷ 6 = .83333333333
5/6 > .83
C)
2 ÷ 3 = .666666666
2/3 > .66
D)
1 ÷ 3 = .33333333333
1/3 > .3
Thus,
all of the given statements are correct.
Hope this helps :)
Cerra Co. expects to receive 5 million euros tomorrow as a result of selling goods to the Netherlands. Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days. Assume that these percentage changes are normally distributed. Use the value-at-risk (VaR) method based on a 95 percent confidence level. What is the maximum one-day percentage loss if the expected percentage change of the euro tomorrow is 0.5 percent
Answer:
The maximum one-day percentage loss = -1.15%
Step-by-step explanation:
Let assume that with the normal distribution, 95% of observations are smaller than 1.65 standard deviations above the mean.
Given that:
Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days.
if the expected percentage change of the euro tomorrow is 0.5 percent
and that Z value at 95% C.I level = 1.65
∵ The maximum one-day percentage loss = (expected percentage change - Z-Value) × standard deviation
The maximum one-day percentage loss = (0.5 - 1.65) × 1
The maximum one-day percentage loss = -1.15 × 1
The maximum one-day percentage loss = -1.15%
How can I factor these complex conjuages? a^2 + b^2 and a^2 - b
Answer:
1) [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2+i^2b[/tex]
Step-by-step explanation:
1) [tex]a^2+b^2[/tex]
=> [tex]a^2 - (-1)b^2[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2-i^2b^2[/tex]
=> [tex](a)^2-(ib)^2[/tex]
Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]
=> [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2-b[/tex]
=> [tex]a^2+(-1)b[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2+i^2b[/tex] (It cannot be simplified further)
Answer:
[tex]\boxed{(a+ib)(a-ib)}[/tex]
[tex]\boxed{a^2+i^2b}[/tex]
Step-by-step explanation:
[tex]a^2 + b^2[/tex]
Rewrite expression.
[tex]a^2- (-1)b^2[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2- i^2 b^2[/tex]
Factor out square.
[tex]a^2-(ib)^2[/tex]
Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]
[tex](a+ib)(a-ib)[/tex]
[tex]a^2-b[/tex]
Rewrite expression.
[tex]a^2+(-1)b[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2+i^2b[/tex]
What is the simplified form of 144x^36?
O 12x6
O 12x18
O 72x6
072x18
Answer:
B
Step-by-step explanation:
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Step-by-step explanation:
Unit rate = 24 ÷ 8 = 3 tires
Answer:
Step-by-step explanation:
24 tires/8hours
please help me out with these questions. Its trigonometry.
Find the value of the lettered angles
In case the pic's not clear;
[tex] \cos \alpha = \sin(50 + \alpha ) [/tex]
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
Step-by-step explanation:
i) sin (2θ) = cos 30°
[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
*********************************************************************************************
ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
1. Draw the multiplication table on the set P= {3,5,7,9) in modulo twelve.
(b) From your table, evaluate;
(0 (305) (509)
() (589)®(789)
3*5 ≡ 15 ≡ 3 (mod 12)
3*7 ≡ 21 ≡ 9 (mod 12)
3*9 ≡ 27 ≡ 3 (mod 12)
5*7 ≡ 35 ≡ 11 (mod 12)
5*9 ≡ 45 ≡ 9 (mod 12)
7*9 ≡ 63 ≡ 3 (mod 12)
Your table should look like the attached.
It's unclear what you're supposed to evaluate for part (b)...
helPpppppppppPPppppPPPPPPppppppPPPPPPPPPpppppppp
Charli believes that if he flips a coin 650 times, it will land heads up exactly 325 times. What would you tell charli about her prediction?
Answer:
What I would tell Charli is that his prediction is somewhat right because there is a 50/50 chance of landing the coin on each side because 325 is half of 650.
Step-by-step explanation:
Find the distance between a point (–7, –19) and a horizontal line at y = 3. Question 18 options: A) 13 B) 22 C) –16 D) 16
Answer: B) 22
Step-by-step explanation:
y coordinate of line = 3
y coordinate of point = -19
On a number line, distance between 3 & -19 = 22
Which expressions are equivalent to: 3(−2a - 4)+3a? A: -6a - 12 +3a B: 3a+12 C: none of the above smh
Answer:
AStep-by-step explanation:
3(−2a - 4)+3a
=-6a - 12 +3a
A: -6a - 12 +3a
[tex]hope \: this \: helps[/tex]
Answer:
the answer is A
Step-by-step explanation:
you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a
Of the following points, name all that lie on the same horizontal line? (1,-2) (-1,2) (-2,1) (2,-1)
Hey there!
If a line is horizontal, the entire line is at the same elevation. On a line, the elevation is the y-value. So, all of the points with the same y-value are on the same horizontal line.
We see that all of these points have different y-values so none of them would be on the same horizontal line.
I hope that this helps! Have a wonderful day!
What is the range of possible sizes for side x? x, 8.0, and 8.8
Answer:
0.8 < x < 16.8
Step-by-step explanation:
8.0 + 8.8 = 16.8
The range of possible sizes for the side x are 0.8 < x < 16.8.
What is Triangle?A triangle is a geometrical shape in two dimensional geometry which has three sides, three vertices and three angles.
The sum of all the three angles inside the triangle is supplementary.
This implies that if a, b and c are the three interior angles of a triangle, then, a + b + c = 180°.
If two sides of a triangle are given, then the third side of the triangle will always be in between the difference of the length of the other two sides and the sum of the length of the other two sides.
Here two lengths are given as 8.0 and 8.8.
Difference of the lengths = 8.8 - 8.0 = 0.8
Sum of the lengths = 8.8 + 8.0 = 16.8
So the x lies between 0.8 and 16.8.
Hence the range of the possible length of the given triangle is 0.8 < x < 16.8.
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Y= 2/3x – 18 What is the rate of change from -5 to 10? What is the average rate of change from 0 to 3?
Answer:
this is all i got for the second question.
Step-by-step explanation:
That is, the average rate of change of from 3 to 0 is 1. That is, over the interval [0,3], for every 1 unit change in x, there is a 1 unit change in the value of the function. Here is a graph of the function, the two points used, and the line connecting those two points.
hope this kinda helps
-lvr
A bowl of Halloween candy contains 7 chocolate candies and 3 lemon candies. Tanya will choose one piece of candy at random.
Write the equation of the line in point-slope form that passes through (1, -4) and has a slope of 1/4.
Answer:
y + 4 =(1/4)(x - 1)
Step-by-step explanation:
The point slope equation is y - k = m(x - h), where (h, k) is the given point and m is the given slope.
In this particular case we have y + 4 =(1/4)(x - 1)