What is the probability that a normal random variable with mean 6 and standard deviation
3 will fall between 5.7 and 7.5

Answer:

D.

Step-by-step explanation:

Mean : 7 + 5 + 6 + 4 + 7 + 8 + 12 = 12 + 10 + 7 + 20 = 30 + 19 = 49. 49/7= 7

Mode : 7.

Median 4 , 4, 6, 7, 7, 8, 12.    7 is the middle number

Answer:

Here is the answer . hope this helps.

Answer:

Step-by-step explanation:

In such cases use the vertical line test. If the graph is intersected at more than one point, it is not  a function.

Both the given graphs represent a function as both pass the vertical line test.

Answer:

Yes

Step-by-step explanation:

Whenever you are given a problem that's asking to see if a graph is a function or not, always use the vetical line test to determine that. In short, you draw a line accross each y axis point and if the line only goes accross one point throughout the graph then it's a function. Following the test we will see that both graphs are indeed functions.

Best of Luck!

Answer:

let side be t

t + x + y +x + y = 4x + 3y

t + 2x + 2y = 4x + 3y

t = 2x +y

so missing side length is 2x + y

Answer:

1/3

Step-by-step explanation:

Answer:

5.65%

Step-by-step explanation:

Find the percent of respondents that said they had experienced depression by dividing 113 by 2000:

113/2000

= 0.0565

Multiply this by 100:

0.0565(100)

= 5.65

So, 5.65% of the respondents said they had experienced depression in the past 12 months.

Answer:

Formula = base x height

10 x 4 = 40

Area = 40cm

Step-by-step explanation:

Answer:

0.300 + 0.030 + 0.004

or

0.100 x 3  +  0.01 x 3  +  0.001 x 4

Answer:

the slope is -2/1

You can find it by using the equation [tex]\frac{y_{1}- y_{2} }{x_{1}- x_{2} }[/tex]

so 3-1/1-2= 2/-1, which is also written as -2/1

Answer:

0.04

Step-by-step explanation:

first we change 1/5 into a decimal which is 0.2

the we just multiply it by itself which is

0.04

Answer:

x< -4/1 or x > 6/5

If our answers are different, just say so :)

she share it to thirty seven people

Answer:

18 inches²

Step-by-step explanation:

The formula for the area of a rectangle is: [tex]A=lw[/tex]

Substitute the given values for the variables.

[tex]A=(9)(2)=18[/tex]

Therefore, the area of the rectangle is 18 inches².

Answer: Area = 18 inches²

Concept:

Here, we need to know how to find the area of a rectangle.

Area (rectangle) = l × w

l = length

w = width

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

Given information

l = 2 inches

w = 9 inches

Given equation

Area = l × w

Substitute values into the equation

Area = 2 × 9

Area = 18 inches²

Hope this helps!! :)

Please let me know if you have any questions

Answer:

47

Step-by-step explanation:

x is one of the three angles of a triangle. The other two are given as 95 and 38.

Together all three have to make 180 degrees.

x + 95 + 38 = 180

x + 133 = 180

x = 180 - 133

x = 47

Answer:

47

Step-by-step explanation:

as we know that sum of a triangle is always=180°

so x+38°+95°=180

so x+133=180

and x=180-133

so x= 47

Answer:

C. $1.73

Step-by-step explanation:

$5.03

$3.30

---------

$1.73

Answer:

Large Box weighs

13.25 kg and Small box weighs 6.25 kg

Step-by-step explanation:

Let the large box be L and small box be S

According to question,

6L + 2S = 92 kg .... (i)

and 3L + 5S = 71 kg ....(ii)

Subtracting we get,

3L - 3S = 21 kg

or L - S = 7 kg

or L = 7 + S kg ... (iii)

Now, putting the value of L in eqn (i) we get

6 (7+S) + 2S = 92 kg

or 42 + 6S + 2S = 92

or 8S = 50

or S = 50/8

or S = 6.25 Kg

Then, 6L + (2×6.25) = 92 kg

or, 6L = 92 - 12.5

or, L = 79.5/6

or, L = 13.25 kg

Answer:

troop number and activity preference or b

Step-by-step explanation:

Answer:

Baton Rouge is 19 meters higher that New Orleans.

Answer:

m=79

t=54

Step-by-step explanation:

yes these are the answers

Answer:

angle  t =  54 degrees

angle m=79(alternate angles)

Step-by-step explanation:

angle p=126 degrees

angle z=79 degrees

angle p + angle t=180(allied angles)

      126 + t           =180

                t           =180-126

                        t =  54 degrees

u=79(vertically opposite angles)

therefore;

    angle m=79(alternate angles)

Answer:

Step-by-step explanation:

-3≤x≤3

Answer:

D.

Step-by-step explanation:

$230 + $360 = $590

$590 - $253* = $337

$337

*( total sum of all the bills )

9514 1404 393

Answer:

  x ≈ −2.10487278573

Step-by-step explanation:

I find a graphing calculator to be a very useful tool for the purpose. It shows the only real root is irrational and gives an approximation as x=-2.105.

The calculator also provides the means to perform Newton's method iteration easily to refine the value of the root to full calculator precision.

__

The Newton's method iterator for finding the next iteration of the root (x') is ...

  x' = x - f(x)/f'(x)

Starting with the approximation shown on the graph, it only takes two iterations to get the root to the full precision of the calculator.

Answer:

-3

Step-by-step explanation:

There are not just "the two ways" to represent this expression. There are two ways, surely, but they are not the only ways as implied.

You could expose 4 and get something like [tex]4(\frac{3}{4}-n)[/tex] or expose 3 and get something like [tex]3(1-\frac{4}{3}n)[/tex].

But you could also say something like [tex]3-(1+3)n=3-n-3n=-3(n-1)-n[/tex]... in fact there are a lot of ways to write any expression.

Hope this helps :)

Answer:

[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]

[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]

Step-by-step explanation:

we want to figure out the domain of the following function:

[tex] \displaystyle g(a) = \sqrt{1 + {a}^{2} } [/tex]

remember that, the domain of an even root function are all values of x for which the redicand is positive or 0 that is being said the domain of the function g(a) belong to [tex]\mathbb{R}[/tex] . another way to think about it, the domain of square root function f(x) belong to x≥0. In this case we have square variable in the redical so when we input a negative number, it yields a positive number with that said the domain of the function g(a) belong to all the real numbers.Thus,

[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]

we'd like to find the domain of the following function:

[tex] \displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]

in order to do so we need to simplify it further,so simplify addition in order to do so the first step is to figure out the LCM of the denominator i.e x(x+1) ⇒ x²+x, secondly divide the denominator of every fraction by the LCM and multiply the result by the numerator of very fraction ,then finally add them therefore,

[tex] \displaystyle f(x)=\frac{2x + 2+4x}{ {x}^{2} + x } \\ \displaystyle \boxed{\frac{6x + 2}{ {x}^{2} + x }} [/tex]

we know that the domain of a rational function are all the values of x for which the denominator is different than 0.

the denominator of the function would be 0 when x=0 and -1 thus,

[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]

and we're done!

Answer:

x = - 6, y = - 29

Step-by-step explanation:

Elimination:

2*(-5x + y = 1) = -10x + 2y = 2

9x - 2y = 4 = + (9x - 2y = 4) =

-x = 6

x = -6

9(-6)-2y=4

-54-2y=4

-2y=58

y=-29

Answer:

Step-by-step explanation:

2y = 3 -2x

Rearrange the equation to slope-intercept form

y = -x + 3/2

Slope of line is 3/2.

By the chain rule, if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then

[tex]\dfrac{\mathrm dz}{\mathrm dt} = \dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt} + \dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

We have [tex]f(x,y)=(x+y)e^y[/tex], for which

• [tex]\dfrac{\partial f}{\partial x} = e^y[/tex]

• [tex]\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y[/tex]

and [tex]x(t)=5t[/tex] and [tex]y(t)=1-t^2[/tex], so that

• [tex]\dfrac{\mathrm dx}{\mathrm dt} = 5[/tex]

• [tex]\dfrac{\mathrm dy}{\mathrm dt} = -2t[/tex]

Putting everything together, we get

[tex]\dfrac{\mathrm dz}{\mathrm dt} = 5e^y - 2t(x+y+1)e^y \\\\ \dfrac{\mathrm dz}{\mathrm dt} = 5e^{1-t^2} - 2t(5t-t^2+2)e^{1-t^2} = \boxed{\left(2t^3-10t^2-4t+5\right)e^{1-t^2}}[/tex]

The solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].

The chain rule explains how to calculate a composite function's derivative.

If you may write [tex]f(g(x))[/tex] , a function is composite. It's a function within a function, or a function of a function, in other words.

By the chain rule, we can write if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then,

[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]

As it is given to us, [tex]f(x,y)=(x+y)e^y[/tex], therefore, we can write,

And x(t)=5t, while y(t)=1-t², So,

Now, Substitute all the values together, in the equation,

[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]

Substituting the values we will get,

[tex]\dfrac{dz}{dt} &=(5 \times e^y)+[-2t(x+y+1)e^y]\\\\[/tex]

     [tex]=5e^{1-t^2}-2t(5t-t^2+2)e^{1-t^2}\\\\=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex]

Hence, the solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].

Learn more about Chain Rule:

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