Find the range of the following piecewise function.
f(x) =
(3x-2 if -1<(or equal to)x<0
2x+3 if 0<(or equal to)x<5

9514 1404 393

Answer:

  -1

Step-by-step explanation:

We notice that we want term a1 and have terms a17 and a33. These terms (every 16-th term) form an arithmetic sequence. The middle term (a17) is the average of the other two, so we have ...

  a17 = (a1 +a33)/2

  2a17 -a33 = a1 = 2(10) -21 = -1

  a1 = -1

_____

Additional comment

You could go to the trouble to find the general term of the sequence.

  an = a1 +d(n -1)

  a17 = a1 + d(17 -1) = 10

  a33 = a1 + d(33 -1) = 21

Subtracting the first equation from the second, we have ...

  16d1 = 11

  d1 = 11/16

Using the first equation, we find ...

  a1 +(11/16)(17 -1) = 10

  a1 = 10 -11 = -1 . . . . same as above.

Answer:

A. False

B. True

C. False

D. True

Step-by-step explanation:

Only three dimensional subspace for R3 is R3 itself. In a 3 d subspace there are 3 basis vectors which are all linearly independent vectors. Dimension of a vector is number of subspace in that vector. Finite set can generate infinite dimension vector space.

Answer:

Does the answer help you?

Answer:

The value of the test statistic is 59.75.

Step-by-step explanation:

The test statistic for the population standard deviation is:

[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

In which n is the sample size, [tex]\sigma_0[/tex] is the value tested and s is the sample standard deviation.

A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents.

This means that [tex]n = 45, s^2 = 1.1[/tex]

The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces.

0.9 is the value tested, so [tex]\sigma_0 = 0.9, \sigma_0^2 = 0.81[/tex]

What is the value of the test statistic

[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

[tex]\chi^2 = \frac{44}{0.81}1.1 = 59.75[/tex]

The value of the test statistic is 59.75.

Answer:

C is wrong!

Step-by-step explanation:

The explanation is in the picture!

9514 1404 393

Answer:

  54

Step-by-step explanation:

The fraction of the total that work outside the home is ...

  outside/(outside +inside) = 6/(6+4) = 6/10

Then the number of those surveyed who work outside the home is ...

  (6/10)(90) = 54 . . . work outside the home

Answer:

SA = 153.9m^2

Step-by-step explanation:

SA = 4[tex]\pi[/tex][tex]r^{2}[/tex]

r = 3.5

SA = 4[tex]\pi[/tex][tex](3.5)^{2}[/tex]

SA = 4[tex]\pi[/tex](12.25)

SA = 49[tex]\pi[/tex]

SA = 153.9m^2

Answer:

8x-21

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

(2x-7)(2x+7)

Step-by-step explanation:

7                       4

-----------   + ------------

4x^2 -49    2x+7

Factor  ( notice that it is the difference of squares)

7                       4

-----------   + ------------

(2x)^2 - 7^2    2x+7

7                       4

-----------       + ------------

(2x-7)(2x+7)    2x+7

Get a common denominator

7                       4(2x-7)

-----------       + ------------

(2x-7)(2x+7)    (2x-7)(2x+7)

Combine

7 +4(2x-7)

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

(2x-7)(2x+7)  

7 +8x-28

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

(2x-7)(2x+7)  

8x-21

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

(2x-7)(2x+7)  

Answer:

(8x - 21) / (2x + 7)(2x - 7)

Step-by-step explanation:

7 / (4x^2 - 49)+ 4 / (2x + 7)

= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)

LCM = (2x + 7)(2x - 7)   so we have

(7 + 4(2x - 7) / (2x + 7)(2x - 7)

=   (8x - 21) / (2x + 7)(2x - 7).

F + V = E + 2

⇨ 9 + 14 = E + 2

⇨ 23 = E + 2

⇨ 23 - 2 = E

⇨ 21 = E

Hence , the number of edges in polyhedron is 21.

The number of edges of a polyhedron with 9 faces and 14 vertices have will be 21.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

here, we have,

Using Euler's formula, the number of the edges does a polyhedron with 9 faces and 14 vertices have

We know the formula for the edges of the polyhedron will be

By Euler's Formula

F + V = E + 2

The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.

Then we have

Solution

F = 9

V = 14

E = ?

Substuting the values

⇨ 9 + 14 = E + 2

⇨ 23 = E + 2

⇨ 23 - 2 = E

⇨ 21 = E

Hence , the number of edges in polyhedron is 21.

More about the polygon link is given below.

brainly.com/question/17756657

#SPJ2

The set of numbers that Diane can choose is:

{54, 60, 66, 72, 78, 84, 90}

Finding common multiples of 2, 3, and 6:

A number is a multiple of 2 if the number is even.

A number is a multiple of 3 if the sum of its digits is multiples of 3.

A number is a multiple of 6 if it is a multiple of 2 and 3.

Then we only need to look at the first two criteria.

First, let's see all the even numbers in the range (49, 95)

These are:

{50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94}

All of these are multiples of 2.

Now we need to see which ones are multiples of 3.

To do it, we sum its digits and see if that sum is also a multiple of 3.

50: 5 + 0 = 5 this is not multiple of 3.

52: 5 + 2 = 7 this is not multiple of 3.

54: 5 + 4 = 9 this is multiple of 3, so 54 is a possible number.

And so on, we will find that the ones that are multiples of 3 are:

54: 5 + 4 = 9.

60: 6 + 0 = 6

66: 6 + 6 = 12

72: 7 + 2 = 9

78: 7 + 8 = 15

84: 8 + 4 = 12

90:9 + 0 = 9

Then the numbers that Diane could choose are:

{54, 60, 66, 72, 78, 84, 90}

If you want to learn more about multiples, you can read:

https://brainly.com/question/1553674

Answer:

Answer:

2+2

Step-by-step explanation:

2 + 4!

3-5

3_4

3-6

2-5

2+5

2_3

2-5

Answer:

(A) 12x³ - 12x

(B) -288

(C) y = -288x - 673

(D) x = 0, 1, -1

Step-by-step explanation:

See images. If it's not clear let me know.

Answer:

answer 11

Step-by-step explanation:

I think it the right answer

Answer:

gold price : $58.72/gram

$58,720 per kilo(1000) grams

Step-by-step explanation:

Answer:

use m a t h w a y

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

we want to prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.

well, to do so let the two unequal positive numbers be [tex]\text{$x_1$ and $x_2$}[/tex] where:

the AM,GM and HM of [tex]x_1[/tex] and[tex] x_2[/tex] is given by the following table:

[tex]\begin{array}{ |c |c|c | } \hline AM& GM& HM\\ \hline \dfrac{x_{1} + x_{2}}{2} & \sqrt{x_{1} x_{2}} & \dfrac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } \\ \hline\end{array}[/tex]

[tex] \displaystyle \rm AM \times HM = \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } [/tex]

simplify addition:

[tex] \displaystyle \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]

reduce fraction:

[tex] \displaystyle x_{1} + x_{2} \times \frac{1}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]

simplify complex fraction:

[tex] \displaystyle x_{1} + x_{2} \times \frac{x_{1} x_{2}}{x_{1} + x_{2}} [/tex]

reduce fraction:

[tex] \displaystyle x_{1} x_{2}[/tex]

rewrite:

[tex] \displaystyle (\sqrt{x_{1} x_{2}} {)}^{2} [/tex]

[tex] \displaystyle AM \times HM = (GM{)}^{2} [/tex]

hence, PROVEN

[tex] \displaystyle x_{1} > x_{2}[/tex]

square root both sides:

[tex] \displaystyle \sqrt{x_{1} }> \sqrt{ x_{2}}[/tex]

isolate right hand side expression to left hand side and change its sign:

[tex]\displaystyle\sqrt{x_{1} } - \sqrt{ x_{2}} > 0[/tex]

square both sides:

[tex]\displaystyle(\sqrt{x_{1} } - \sqrt{ x_{2}} {)}^{2} > 0[/tex]

expand using (a-b)²=a²-2ab+b²:

[tex]\displaystyle x_{1} -2\sqrt{x_{1} }\sqrt{ x_{2}} + x_{2} > 0[/tex]

move -2√x_1√x_2 to right hand side and change its sign:

[tex]\displaystyle x_{1} + x_{2} > 2 \sqrt{x_{1} } \sqrt{ x_{2}}[/tex]

divide both sides by 2:

[tex]\displaystyle \frac{x_{1} + x_{2}}{2} > \sqrt{x_{1} x_{2}}[/tex]

[tex]\displaystyle \boxed{ AM>GM}[/tex]

again,

[tex]\displaystyle \bigg( \frac{1}{\sqrt{x_{1} }} - \frac{1}{\sqrt{ x_{2}}} { \bigg)}^{2} > 0[/tex]

expand:

[tex]\displaystyle \frac{1}{x_{1}} - \frac{2}{\sqrt{x_{1} x_{2}} } + \frac{1}{x_{2} }> 0[/tex]

move the middle expression to right hand side and change its sign:

[tex]\displaystyle \frac{1}{x_{1}} + \frac{1}{x_{2} }> \frac{2}{\sqrt{x_{1} x_{2}} }[/tex]

[tex]\displaystyle \frac{\frac{1}{x_{1}} + \frac{1}{x_{2} }}{2}> \frac{1}{\sqrt{x_{1} x_{2}} }[/tex]

[tex]\displaystyle \rm \frac{1}{ HM} > \frac{1}{GM} [/tex]

cross multiplication:

[tex]\displaystyle \rm \boxed{ GM >HM}[/tex]

hence,

[tex]\displaystyle \rm A.M>G.M>H.M[/tex]

PROVEN

Answer:

The sample proportion of students who prefer vanilla ice cream is 0.56.

Step-by-step explanation:

Sample proportion of students who prefer vanilla ice cream:

Sample of 375 students.

Of those, 210 said they prefer vanilla ice cream.

The proportion is:

[tex]p = \frac{210}{375} = 0.56[/tex]

The sample proportion of students who prefer vanilla ice cream is 0.56.

Answer:

the answer is B ...Extreme Values

Answer:I just need points

Step-by-step explanation:

Hey

Answer:

24 years

Step-by-step explanation:

total ratio =8

older student=40 years

3/8*40 ÷ 5/8=24

Answer:

No. It is EF and GH

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The answer will be EF and GH, both are 7 units long.

Explanation:

Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by

[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]

Integrating this expression, we get

[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]

or

[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]

[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]

[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]

[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]

Answer:

where is your diagram?

Step-by-step explanation:

Answer:

χ²R = 8.643

χ²L = 42.796

0.20 < σ < 0.45

Step-by-step explanation:

Given :

Sample size, n = 23

The degree of freedom, df = n - 1 = 23 - 1 = 22

At α - level = 99%

For χ²R ; 1 - (1 - 0.99)/2= 0.995 ; df = 22 ; χ²R = 8.643

For χ²L ; (1 - 0.99)/2 = 0.005 ; df = 22 ; χ²L = 42.796

The confidence interval of σ ;

s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]

0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)

0.2008 < σ < 0.4467

0.20 < σ < 0.45

Answer:

A' (-2,3)

B' (-1,1)

C' (-4,0)

Step-by-step explanation:

Given coordinates:

A (3,0)

B (4,-2)

C (1,-3)

We want to find the location of the coordinates after a translation of <-5,3>

Explanation of translation

<-5,3>

Subtract 5 from the x value and add 3 to the y value

Applying translation

A (3,0) ---------> (3-5,0+3) ---------> (-2,3)

B (4,-2) ---------> (4-5,-2+3) ---------> (-1,1)

C (1,-3) ---------> (1-5,-3+3) ---------> (-4,0)

So the new coordinates would be

A' (-2,3)

B' (-1,1)

C' (-4,0)

Answer:

105 sq ft + 31 sq ft

Step-by-step explanation:

=  136 sq ft

Hope it helps✌✌