Cho hàm số f(x, y) = ln(x
2 + y
2
).
a) Tính f
′
x
, f′
y
;
b) Tính f
′
x
(2; 1), f′
y
(2; 1).

Answer:

The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 62, standard deviation of 8.

What is the approximate percentage of trees planted between 38 and 86?

38 = 62 - 3*8

86 = 62 + 3*8

So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Answer:

71 feet

Step-by-step explanation:

94×2=188

330-188=142

142÷2=71

The answer is 36 degrees

Step 1

Angle GEH=180-2x (angles on a a straight line are supplementary)

Step 2

4x= G^+GE^H(sum of exterior angle)

4x=x+(180-2x)

4x=180-x

4x+x=180

5x=180

x=36 degrees

Answer:

The mean is to the right of the median

Step-by-step explanation:

Given

Skewed right distribution

Required

Relationship between the mean and the median

The question would be better answered if there are options available. Since there are none, I will provide a general answer/explanation.

For a distribution that is right skewed, the mean is always on the right side of the median.

Answer:

Speed of the river = [tex]\frac{4}{3}[/tex] km per hour

Step-by-step explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km = [tex]\frac{\text{Distance}}{\text{Speed}}[/tex]

                                           = [tex]\frac{6}{4-v}[/tex] hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km = [tex]\frac{12}{4+v}[/tex] hours

Since, time taken by the boat in both the cases is same,

[tex]\frac{6}{4-v}= \frac{12}{4+v}[/tex]

6(4 + v) = 12(4 - v)

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v = [tex]\frac{24}{18}[/tex]

v = [tex]\frac{4}{3}[/tex] km per hour

Answer:

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

Answer:

The correct answer is the last one

Step-by-step explanation:

Step-by-step explanation:

[tex]\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}[/tex]

Rearranging the terms, we get

[tex]ydy = \dfrac{2xdx}{x^2 + 1}[/tex]

We then integrate the expression above to get

[tex]\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}[/tex]

[tex]\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k[/tex]

or

[tex]y = \sqrt{2\ln |x^2 + 1|} + k[/tex]

where I is the constant of integration.

Answer:

7.5 ft³/min

Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

dV/dt = d[2(10 - x)]/dt = -2dx/dt

Since dV/dt = 15 ft³/min,

dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min

Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

= -dx/dt

= -(-7.5 ft³/min)

= 7.5 ft³/min

And the height at this point when x = 8 inches = 8 in × 1 ft/12 in  = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

Answer:

B. [tex] y + 5 = 2(x + 2) [/tex]

Step-by-step explanation:

Point-slope equation is given as [tex] y - b = m(x - a) [/tex], where,

(a, b) = (-2, -5)

[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line (-2, -5) and (0, -1),

Slope (m) = (-1 -(-5))/(0 -(-2)) = 4/2

m = 2

✔️To write the equation in point-slope form, substitute a = -2, b = -5, and m = 2 into [tex] y - b = m(x - a) [/tex]

Thus:

[tex] y - (-5) = 2(x - (-2)) [/tex]

[tex] y + 5 = 2(x + 2) [/tex]

Answer:

[tex]P(x=4) = 0.200[/tex]

Step-by-step explanation:

Given

[tex]n=10[/tex] --- selected customers

[tex]x = 4[/tex] --- those that are expected to use the restroom

[tex]p =30\% = 0.30[/tex] --- proportion that uses the restroom

Required

[tex]P(x = 4)[/tex]

The question illustrates binomial probability and the formula is:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]

So, we have:

[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (1 - 0.30)^{10 - 4}[/tex]

[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (0.70)^6[/tex]

[tex]P(x=4) = 210* (0.30)^4 * (0.70)^6[/tex]

[tex]P(x=4) = 0.200[/tex]

Answer: 1, 4

Step-by-step explanation:

[tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]

Answer:

Hope this helps!

Answer:

98% confidence interval for the population mean =(1095.260,1288.740)

Step-by-step explanation:

We are given that

n=45

[tex]\mu=1192[/tex]

Standard deviation,[tex]\sigma=279[/tex]

We have to construct a 98% confidence interval for the population mean.

Critical value of z at 98% confidence, Z =2.326

Confidence interval is given by

[tex](\mu\pm Z\frac{\sigma}{\sqrt{n}})[/tex]

Using the formula

98% confidence interval is given by

[tex]=(1192\pm 2.326\times \frac{279}{\sqrt{45}})[/tex]

[tex]=(1192\pm 96.740)[/tex]

=[tex](1192-96.740,1192+96.740)[/tex]

=[tex](1095.260,1288.740)[/tex]

Hence, 98% confidence interval for the population mean (1095.260,1288.740)

Answer:

Answer is 3bu2(DeEZ)=1

Step-by-step explanation:

Answer:

14 inches

Step-by-step explanation:

Since F is inversely proportional to L,

[tex]f = \frac{k}{l} \\ when \: f = 40 \: l \: = 7 \\ \frac{k}{7} = 40 \\ k = 280 \\ when \: f = 20 \\ 20 = \frac{280}{l} \\ l = 14[/tex]

Answer:

(x, y) = (-34,-19)

Step-by-step explanation:

...................................................

Answer:

answer

x = -13/ 15, 0

Step-by-step explanation:

15x^2 + 13 x = 0

or, x(15x + 13) = 0

either, x = 0

or, 15x + 13 = 0

x = -13/15

Answer:

The answer should be C...............

imma sorry if I'm wrong

Answer:

36281629273781646181993836619946527189119292937467482919198$7473828191927364732818919283838292927383883829118661552621718919191019284746617171819001187373765252728

Step-by-step explanation:

173899918377+28910873638282

Answer:

[tex]F = 39.47[/tex]

Step-by-step explanation:

Given

[tex]n = 30[/tex] --- observations

[tex]p = 1[/tex] -- variables

[tex]SSR = 1,297[/tex]

[tex]SSE= 920[/tex]

Required

The F statistic

This is calculated using:

[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]

[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]

[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]

[tex]F = 1297 \div \frac{920}{28}[/tex]

Rewrite as:

[tex]F = 1297 * \frac{28}{920}[/tex]

[tex]F = \frac{1297 *28}{920}[/tex]

[tex]F = \frac{36316}{920}[/tex]

[tex]F = 39.47[/tex]

Answer:

Place value of 1 = 1 × 10 = 10

Step-by-step explanation:

In 382619,

Place of 1 = Tens

Place value of 1 = 1 × 10 = 10

Hi there!

[tex]\large\boxed{40x^{6}}[/tex]

Begin by simplifying (2x²)²

2² · (x²)² <-- Power rule for exponents, multiply them together:

4 · x⁴ = 4x⁴

Multiply by 10x². ADD exponents when multiplying.

10x² · 4x⁴ = 40 · x²⁺⁴

40x⁶

Answer:

0 is the answer assuming the whole thing is a fraction where the numerator is f(a+h)-f(a) and the denominator is h.

Step-by-step explanation:

If the expression for f is really a constant, then the difference quotient will lead to an answer of 0.

If the extra for f is linear (including constant expressions), the difference quotient will be the slope of the expression.

However, let's go about it long way for fun.

If f(x)=5, then f(a)=5.

If f(x)=5, then f(a+h)=5.

If f(a)=5 and f(a+h)=5, then f(a+h)-f(a)=0.

If f(a+h)-f(a)=0, then [f(a+h)-f(a)]/h=0/h=0.

Answer:

The total distance Allie traveled was 0.81 miles.

Step-by-step explanation:

Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:

12 + 60 = 72

72 x 60 = 4320

1000 feet = 0.189394 miles

4320 feet = 0.8181818 miles

Therefore, the total distance Allie traveled was 0.81 miles.

Answer:

A. 754 cm²

Step-by-step explanation:

Amount of cardboard needed = surface area of the cone

Curved surface area of the cone = πrl

Where,

π = 3.14

r = ½(20) = 10 cm

l = 24 cm

Plug in the values into the formula

Curved surface area = 3.14 × 10 × 24 = 753.6 ≈ 754 cm²

Answer:

-32

Step-by-step explanation:

f o h

f(x) = -3x -8

h(x) = [tex]\frac{x+8}{-3}[/tex]

foh = [tex]-3(\frac{x+8}{-3} )[/tex] -8  = x+8 -8 = x

foh(-32) = -32

Answer:

b=2

Step-by-step explanation:

Answer:

i put in 3 to make 23436 because 36 is divisible by 6