Chứng minh các hàm số sau là liên tục tại mọi điểm x R 
a. f x x ( ) 6 3  
b. f x( ) = mx +b
c. Hãy nêu ý nghĩa của hàm liên tục trong kinh tế? Trình bày một vài ví dụ minh
họa?

Answer:

e < 24 is the inequality which shows the possible earnings per share.

Explanation:

x, will stand for the variable for earnings and less than, means it will not be higher nor the same as 24. Thus, being leaves us with one sign. The open part facing 24 means that 24 is the bigger number, therefore the smaller side represents that x has to be smaller than 24.

Answer: x<24

Step-by-step explanation:

x, will stand for the variable for earnings and less than means it will not be higher nor the same as 24. Thus being leaves us with one sign. The open part facing 24 means that 24 is the bigger number therefore the smaller side represents that x has to be smaller than 24.

Answer:

4

Step-by-step explanation:

Slope = y2-y1/x2-x1

We need to find two points on the graph, let's take these two points:

(x1, y1) (X2,y2)

(0,-6) and (2,2)

(2-(-6)/ (2-0) = 8/2 = 4

Answered by Gauthmath

Answer:

a) P(79 <= P <= 81) = 0.9968

b) P( X >  81 ) = 0.0002

Step-by-step explanation:

mean value = 75 GPa

standard deviation = 1.7 GPa

a) Determine P(79 <= P <= 81)

given that : n = 25

attached below is the detailed solution

P(79 <= P <= 81) = 0.9968

b) Determine how likely the sample mean diameter will exceed 81

given that n = 36

mean diameter = 81

P( X >  81 ) = 0.0002

Answer:

c) The less than symbol should be replaced with the less than or equal to symbol.

Step-by-step explanation:

3(-4 - n/-2) < 5

The equation written above could be interpreted as :

The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5

This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.

The equation should be used with a ≤ sign and expressed thus :

3(-4 - n/-2) ≤ 5

This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5

Answer:

C

Step-by-step explanation:

Answer:

19.95

Step-by-step explanation:

Take the amount of his salary and multiply by 5 1/4 %

380 * .0525

19.95

Answer:

77.5

Step-by-step explanation:

Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B

Answer:

21%

Step-by-step explanation:

Percentage reduction is (999.99-789.99)/(999.99)=21%

Answer:

8√2

Step-by-step explanation:

4√(10) -2

= 4√8

=4√4×2

=4×2√2

=8√2

Answer:

C

Step-by-step explanation:

To figure out which pairs lie on -2x+4y = 16, we can plug the x and y values into the equation to see if they work. We need all pairs of x and y values in a table to work for the answer to be correct

A)

x=-4, y=2

-2x+4y = -2 * (-4) + 4 * (2) = 8 + 8 = 16. This works. Note that two negatives multiplied together make a positive, and 4*2 = 8

x=0, y=8

-2x + 4y = -2 * (0) + 4 * (8) = 0 + 32 = 32. This does not work, as 32 is not 16. Note that anything multiplied by 0 is 0

B)

x=8, y=0

-2x+4y = -2 * (8) + 4 * (0) = -16. This is not equal to 16. Note that a negative multiplied by a positive is still a negative

x=2, y=3

-2x + 4y = -2 * (2) + 4 * (3) = -4 + 12 = 8. This is not equal to 16.

C)

x=0, y=4

-2x + 4y = -2 * (0) + 4 * (4) = 0 + 16 = 16. This works

x=4, y=6

-2x + 4y = (-2)* (4) + 4 * (6) = -8 + 24 = 16. This works. As both pairs of values in the table works, this is the correct answer. Nevertheless, we can check D to make sure.

D)

x=-2, y=5

-2x+4y = -2 * (-2) + 4 * (5) = 4 + 20 = 24. This is not 16

x=-8, y=0

-2x+4y = -2 * (-8) + 4 *  (0) = 16. This works, but the other pair does not work, so D is incorrect

Answer:

C

Step-by-step explanation:

Edge 2022

Answer:

Step-by-step explanation:

brilliant has 9 letters

brilliant has 1 B (1/9)

brilliant has 1 R (1/9)

brilliant has 2 I's (2/9)

brilliant has 2 L's (2/9)

brilliant has 1 A (1/9)

brilliant has 1 N (1/9)

brilliant has 1 T (1/9)

The plane you want is parallel to another plane, x - y + z = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.

The plane must also pass through the point (0, 4, 4) since it contains r(t). Then the equation of the plane is

⟨x, y - 4, z - 4⟩ • ⟨1, -1, 1⟩ = 0

x - (y - 4) + (z - 4) = 0

x - y + z = 0

Answer: Option B is correct

Step-by-step explanation: edge 2021

Answer:

b

Step-by-step explanation:

Answer:

Does the answer help you?

9514 1404 393

Answer:

  r = 2.5

Step-by-step explanation:

The constant of proportionality can be found by solving the equation for r:

  r = y/x

Then any corresponding values of x and y can be used to find r:

  r = 25/10 = 2.5

The constant of proportionality is 2.5.

Answer:

let us do one night

Step-by-step explanation:

Agg-77182882

(#(+2+

Answer:

252 options

Step-by-step explanation:

Please let me know if you want an explanation for why this is the answer (comment on this answer). A lot of people don't actually read the explanations, so I wouldn't want to waste my time. However, if you would like it I would be more than happy to type one out for you. Thanks!

Answer:

volume of shaded region = 112.94 [tex]cm^{3}[/tex]

Step-by-step explanation:

Volume of a cylinder = [tex]\pi r^{2}h[/tex]

volume = 22/7 * [tex]2.5^{2}[/tex] * 14.6

volume = 286.67 [tex]cm^{3}[/tex] approx

volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

volume = [tex]\frac{4}{3} *\frac{22}{7}*2.4^{3}[/tex]

volume= 57.91 [tex]cm^{3}[/tex] approx

No, of sphere = 3

Volume of 3 sphere = 3 * 57.91

                                 =173.73 [tex]cm^{3}[/tex]

Now , volume of shaded region = volume of cylinder - total volume of sphere

volume of shaded region = 286.67 - 173.73

                                          =112.94 [tex]cm^{3}[/tex]

Answer:

15km

Step-by-step explanation:

hope it is well understood?

Answer:

5 times.

Step-by-step explanation:

First, look at the values of each line at the 1-hour mark.

For line A (the bicyclist), the distance is about 25 km.

For line B (the pedestrian), the distance is about 5 km.

To determine how many times greater the bicyclist distance is than the pedestrian, divide the values:

[tex]\frac{25\text{km}}{5\text{km}}=5[/tex]

Therefore, the distance covered by the bicyclist for 1 hour is 5 times greater than the distance covered by the pedestrian for the same amount of time.

Answer:

mean: 84

median: 85

mode: 85

explainations for d and e below.

Step-by-step explanation:

mean:

(85+80+96+72+78+85+92)/7 = 544/7 = 84

median:

sort them in order from least to greatest first

72, 78, 80, 85, 85, 92, 96

find the middle number in that order, that's your median. in this case, it's 85.

mode:

number that appears the most in the order; the frequency. in this case as well, it's also 85.

answer for d:

the reason why the mean is lower than the median is because of the fact we were figuring out the average and had to divide, unlike the median where it's just the middle of the order we have.

answer for e:

(85+80+96+72+78+85+92+100)/8 = 644/8 = 80.5%

p.s: please subscribe to #gauthmath# sub reddit if you can for more help.

Answer:

15km

Step-by-step explanation:

hope it is well understood

Answer:

Step-by-step explanation:

Maximum value is when cos x = 1

So it is -2 + 4(1) = 2.

Minimum value, when  cos x = -1:

= -2  + 4(-1) = -6.

Answer:

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

Step-by-step explanation:

So let's first look at cos(x) on interval (0,21].

How many rotations is that? Does it at least contain 1 full rotation? If it contains one full rotation that means all the values from -1 to 1 (inclusive) are tagged? If it doesn't contain a full rotation, we might have to dig a little deeper.

So we know x=0 isn't included and that's when cosine is first 1,but this doesn't mean 1 won't be hit later.

Let's figure out the number of rotations:

21/(2pi)=3.3 approximately

This means we make at least 3 rotations.

So this means we definitely will have all the values from -1 to 1 tagged (inclusive).

Now let's look at whole function.

f(x) = -2 + 4 cos x

-2+(-4) to -2+4 will be the range of the function

So the minimum is -6 and the maximum is 2.

So the min occurs when cos(x)=-1 and the max occurs when cos(x)=1.

We have a little over three rotations and remember we can't include x=0.

cos(x)=1

when x=2pi (one full rotation)

when x=4pi (two full rotations)

when x=6pi (three full rotations)

We will stop here because cosine won't be 1 again until a fourth full rotation

cos(x)=-1

when x=pi (half rotation)

When x=3pi (one + half rotation)

When x=5pi (two+half rotation)

We can't include x=7pi (three+half rotation)

because this one is actually not in the interval because 3.5 is more than 3.3 .

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

Answer:

[0.6969, 0.7695]

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

They randomly survey 401 drivers and find that 294 claim to always buckle up.

This means that [tex]n = 401, \pi = \frac{294}{401} = 0.7332.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 - 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.6969[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 + 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.7695[/tex]

The 90% confidence interval for the population proportion that claim to always buckle up is [0.6969, 0.7695]

Answer:

0.81859

Step-by-step explanation:

Given that the length of recovery days for patients with knee surgery is normally distributed with :

Mean, μ = 123 days

Standard deviation, σ = 1 day

The proportion of patients that will recover with 121 and 124 days :

We obtain the Probability of Z score :

Z = (x - μ) / σ

P(Z < (x - μ) / σ) < Z < P(Z < (x - μ) / σ)

P(Z < (121 - 123) / 1) < Z < P(Z < (124 - 123) / 1)

P(Z < - 2) < Z < P(Z < 1)

Using the normal distribution table :

P(Z < 1) - P(Z < - 2)

0.84134 - 0.02275

= 0.81859

Answer:

1.33

Step-by-step explanation:

62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.

Answer:

x = 2.56, y = -2.63

Step-by-step explanation:

I first multiplied the second equation by two, getting

4x-6y = 26

I then subtracted the equations

 4x+2y = 5

- 4x-6y = 26

--------------------

      8y = -21

y = -2.63

with y solved, I plugged it into the second equation to get x:

2x-3(-2.63) = 13

2x+ 7.89 = 13

2x = 5.11

x = 2.56

I hope this helped! ;D

Answer:

All Equal to 0

Step-by-step explanation:

0 = 0

3 - 3 = 0

0/4 = 0

12 - 3*4 = 0

Answer:

216 m²

Step-by-step explanation:

Surface area of a cube = 6a², when a = length of one side

so,

6a²

= 6×6²

= 6×36

= 216 m²

Answered by GAUTHMATH

Answer:

216 m²

Step-by-step explanation: