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3 years ago

Calculate the standard deviation. Variance = 107.76. Mean = 34.2

Mathematics

1 answer:

Llana [10]3 years ago

8 0

Answer:

The standard deviation is 10.38

Step-by-step explanation:

Given;

Variance, v = 107.76

mean, x = 34.2

The standard deviation is given by;

standard deviation = √variance

standard deviation = √107.76

standard deviation = 10.381

standard deviation = 10.38 (two decimal places)

Therefore, the standard deviation is 10.38

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2x+5y=60 <br> 2x-5y=-20<br><br><br> Please show work!

sergejj [24]

(2x+5y=60)
- (2x-5y=-20)
-------------------
10y=80
y=8

2x+5(8)=60
2x+40=60
2x=20
x=10

8 0

4 years ago

For each of the following vector fields

olga nikolaevna [1]

(A)

$\dfrac{\partial f}{\partial x}=-16x+2y$

$\implies f(x,y)=-8x^2+2xy+g(y)$

$\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=10y$

$\implies g(y)=5y^2+C$

$\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}$

(B)

$\dfrac{\partial f}{\partial x}=-8y$

$\implies f(x,y)=-8xy+g(y)$

$\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x$

$\implies \dfrac{\mathrm dg}{\mathrm dy}=x$

But we assume $g(y)$ is a function of $y$ alone, so there is not potential function here.

(C)

$\dfrac{\partial f}{\partial x}=-8\sin y$

$\implies f(x,y)=-8x\sin y+g(x,y)$

$\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=4y$

$\implies g(y)=2y^2+C$

$\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}$

For (A) and (C), we have $f(0,0)=0$ , which makes $C=0$ for both.

4 0

3 years ago

Use the lim f(x)-f(a)/x-a to find the derivative.

Tresset [83]

Hello,

f(x)-f(a)= -3x²-5x+1-(-3a²-5a+1)=-3(x²-a²)-5(x-a)=-3(x-a)(x+a)-5(x-a)
=-(x-a)(3(x+a)+5)
=-(x-a)(3x+3a+5)

lim (f(x)-f(a))/(x-a)=- lim (3x+3a+5)=3a+3a+5=-6a-5
if a=1==>-6*1-5=-11

Otherwise
f'(x)=-6x-5
f'(1)=-6-5=-11

at point(1,-7)

4 0

3 years ago

In a game, if you roll a 5 on a 6-sided number cube, you lose a turn. What is the probability that you roll a 5? Explain your re

WITCHER [35]

The probability of you rolling a 5 would be 1/6 since the cube has 6 sides and only one of the sides has a 5.

The probability that you either roll a 5 or do not roll a 5 would be 6/6 because 1/6, the probability you WILL roll a 5, and 5/6, the probability you WON'T roll a 5 added together is 6/6.

The probability that you don't roll a 5 is 5/6 because there are 5 sides of the dice that are not 5.
Hope that helped!

3 0

3 years ago

3. The annual per capita consumption of fresh bananas in the United States can be approximated by a normal distribution, with a

svlad2 [7]

Answer:

The largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb

Step-by-step explanation:

Given

μ = Mean = 10.4 lb

σ = Standard deviation = 3 lb

Using a confidence level of 90%,

We'll need to first determine the z value that correspond with bottom 5% of consumption of banana

α = 5%

α = 0.05

So,

zα = z(0.05)

z(0.05) = -1.645 ----- From z table

Let x represent the largest annual per capita consumption of bananas

The relationship between x and z is

x = μ + zσ

By substitution;

x = 10.4 + (-1.645) * 3

x = 10.4 - 4.935

x = 5.465

Hence, the largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb

6 0

4 years ago