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2 years ago

Which graph represents the piecewise-defined function?

Mathematics

2 answers:

Mrac [35]2 years ago

8 0

Answer:

LAST GRAPH is right

Step-by-step explanation

kifflom [539]2 years ago

5 0

Answer: The first option is correct.

Explanation:

The given piecewise function is,

$y=\begin{cases}-\frac{4}{5}x-3 & \text{ if } x$

From the piecewise function we can say that if x<0, then

$f(x)=-\frac{4}{5}x-3$

If $x\geq2$ , then

$f(x)=3x-10$

Since the f(x) is defined for x<0 and $x\geq2$ , therefore the function f(x) is not defined for $0\leq x$ .

In the graph 2, 3 and 4 for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.

Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for $0\leq x$ , hence the first option is correct.

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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviat

Harlamova29_29 [7]

Answer:

The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.

Step-by-step explanation:

We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.

Let us find the sample score that corresponds to z-score of bottom 4%.

From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.

Upon substituting these values in z-score formula we will get our sample scores (x) as:

$z=\frac{x-\mu}{\sigma}$

$-1.75=\frac{x-5.71}{0.08}$

$-1.75*0.08=x-5.71$

$-0.14=x-5.71$

$-0.14+5.71=x-5.71+5.71$

$5.57=x$

Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.

Now let us find sample score corresponding to z-score of 1.75 as upper limit.

$1.75=\frac{x-5.71}{0.08}$

$1.75*0.08=x-5.71$

$0.14=x-5.71$

$0.14+5.71=x-5.71+5.71$

$5.85=x$

Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected.

7 0

2 years ago

Let ????C be the positively oriented square with vertices (0,0)(0,0), (2,0)(2,0), (2,2)(2,2), (0,2)(0,2). Use Green's Theorem to

bonufazy [111]

Answer:

-48

Step-by-step explanation:

Lets call L(x,y) = 10y²x, M(x,y) = 4x²y. Green's Theorem stays that the line integral over C can be calculed by computing the double integral over the inner square of Mx - Ly. In other words

$\int\limits_C {L(x,y)} \, dx + M(x,y) \, dy = \int\limits_0^2\int\limits_0^2 (M_x - L_y ) \, dx \, dy$

Where Mx and Ly are the partial derivates of M and L with respect to the x variable and the y variable respectively. In other words, Mx is obtained from M by derivating over the variable x treating y as constant, and Ly is obtaining derivating L over y by treateing x as constant. Hence,

M(x,y) = 4x²y
Mx(x,y) = 8xy
L(x,y) = 10y²x
Ly(x,y) = 20xy
Mx - Ly = -12xy

Therefore, the line integral can be computed as follows

$\int\limits_C {10y^2x} \, dx + {4x^2y} \,dy = \int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy$

Using the linearity of the integral and Barrow's Theorem we have

$\int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy = -12 \int\limits_0^2\int\limits_0^2 xy \, dx \, dy = -12 \int\limits_0^2\frac{x^2y}{2} |_{x = 0}^{x=2} \, dy = -12 \int\limits_0^22y \, dy \\= -24 ( \frac{y^2}{2} |_0^2) = -24*2 = -48$

As a result, the value of the double integral is -48-

3 0

3 years ago

Sandra has 46 fewer coins than Martha. Sandra has 57 coins . how many coins does Martha have?

hoa [83]

M = 57+46
(Since she has 46 less then martha, you know to find how many martha has you have to add 46!)

M=103

So martha has 103 coins!

6 0

3 years ago

Please Answer Quick 65 Points ! !

NeTakaya

The correct answers are:

The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.

The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.

Further explanation:

Given equations are:

2x-y = -5

x+3y = 22

We have to check whether the given statements are true or not. In order to find that we have to put the points in the equations

Putting the point in 2x-y = -5

$2x - y = -5\\2(7) -19 = -5\\14-19 = -5\\-5 = -5$

Putting the point in x+3y=22

$7 + 3 (19) = 22\\7 + 57 = 22\\64 \neq 22$

The point satisfies the first equation but doesn't satisfy the second. So,

1. The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.

This statement is true as the point satisfies the first equation

2. The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.

This Statement is false.

3. The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.

This statement is true.

4. The ordered pair (7, 19) is a solution to the system because it makes both equations true.

This statement is false as the ordered pair doesn't satisfy both equations.

Keywords: Solution of system of equations, linear equations

Learn more about solution of linear equations at:

#LearnwithBrainly

5 0

3 years ago

B2-4b+4=0 using quadratic forumla

Ivan

Trying to factor by splitting the middle term

Factoring b2-4b+4
The first term is, b2 its coefficient is 1 .
The middle term is, -4b its coefficient is -4 .
The last term, "the constant", is +4 

Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4

Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4 .

-4 + -1 = -5 -2 + -2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2
 b2 - 2b - 2b - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
 b • (b-2)
 Add up the last 2 terms, pulling out common factors :
 2 • (b-2)
Step-5 : Add up the four terms of step 4 :
 (b-2) • (b-2)
 Which is the desired factorization

8 0

3 years ago

Read 2 more answers