Find the domain and range of a function defined by a graph
Question
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Answer:

1

Hope that helps.

Answer:

1

Step-by-step explanation:

16/16=1

Hope this helps, if you have any questions, feel free to ask

Have a good day! :)

Answer:

If the correlation coefficient is 1, then the slope must be 1 as well.

Step-by-step explanation:

Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.

If the correlation coefficient is 1, then the slope must be 1 as well.

The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.

So, the false statement is:

If the correlation coefficient is 1, then the slope must be 1 as well.

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Answer:

41

Step-by-step explanation:

If Skylar has 4 times as many books as Karen, that means that you have to do a division problem to figure out how books Karen has. Because Skylar has 4 times as many books, and she has 164 books, the division problem is 164÷4=41 books.

The number of books Karen has will be 41.

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Let,

Skylar has x number of books

Karen has y number of books = 164

Given condition;

y=4x

164=4x

x=41 books

Hence Karen has 41 books.

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Answer:

[tex]a_{3} = 8[/tex]

Step-by-step explanation:

=> [tex]a_{n} = ar^{n-1[/tex]

Where n = 3, a = 8 and r = -1

=> [tex]a_{3} = (8)(-1)^{3-1}[/tex]

=> [tex]a_{3} = (8)(1)[/tex]

=> [tex]a_{3} = 8[/tex]

Answer:

the answer will be D

Step-by-step explanation:

Answer:

$11.25

Step-by-step explanation:

price = $30/lb

16 oz = 1 lb

1 portion = 6 oz = 6/16 lb = 3/8 lb

$30/lb * 3/8 lb = $11.25

Answer:

The estimated mean number of rockets hits in the region is 533.

Step-by-step explanation:

We are given the following information,

Number of rocket hits     |    Observed number of regions

0                                       |                       228

1                                        |                       214

2                                       |                        94

3                                       |                        32

4                                       |                         7

5                                       |                        0

6                                       |                        0

7                                       |                         1

We are asked to estimate the mean number of rocket hits in the region.

The mean or expected value is given by

[tex]\mu = \sum (x \cdot P(x)) \\\\\mu = (0 \cdot 228) + (1 \cdot 214) + (2 \cdot 94) + (3 \cdot 32) + (4 \cdot 7) + (5 \cdot 0) + (6 \cdot 0) + (7 \cdot 1) \\\\\mu = 0 + 214 +188+ 96 +28 +0+ 0 + 7 \\\\\mu = 533[/tex]

Therefore, the mean number of rockets hits in the region is 533.

Answer:

w and y are knights

Step-by-step explanation:

Of the six natives, W and Y are the knights.

In mathematics, reasoning entails making logical deductions from data or presumptions. Making sense of something can be defined as gaining comprehension of a situation, setting, or idea by relating it to what is already known or has already happened.

Given that you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight.

From the given data it is concluded that W and Y are the knights because their statement is W says: At most three of us are knights and Y says: Exactly two of us are knights.

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Answer:

Step-by-step explanation: Answer is 2√17 units

Distance =√ (−2−0) ^2−(5−(−3)) ^2

=√ (−2) ^2−(5+3) ^2

=√4+64

=√68

=2√17 units

Answer:

[tex]A(t)=500C_{in}(t)+[40-500C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]

Step-by-step explanation:

Volume of water in the Tank =500 gallons

Let A(t) be the amount of salt in the tank at time t.

Initially, the tank contains 40 lbs of salt, therefore:

A(0)=40 lbs

Rate of change of the amount of Salt in the Tank

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(C_{in}(t))( 5\frac{gal}{min})\\=5C_{in}(t)\frac{lbs}{min}[/tex]

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]=(\frac{A(t)}{500})( 5\frac{gal}{min})=\frac{A}{100}[/tex]

Therefore:

[tex]\dfrac{dA}{dt}=5C_{in}(t)-\dfrac{A}{100}[/tex]

We then solve the resulting differential equation by separation of variables.

[tex]\dfrac{dA}{dt}+\dfrac{A}{100}=5C_{in}(t)\\$The integrating factor: e^{\int \frac{1}{100}}dt =e^{\frac{t}{100}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{100}}+\dfrac{A}{100}e^{\frac{t}{100}}=5C_{in}(t)e^{\frac{t}{100}}\\(Ae^{\frac{t}{100}})'=5C_{in}(t)e^{\frac{t}{100}}[/tex]

Taking the integral of both sides

[tex]\int(Ae^{\frac{t}{100}})'=\int [5C_{in}(t)e^{\frac{t}{100}}]dt\\Ae^{\frac{t}{100}}=5*100C_{in}(t)e^{\frac{t}{100}}+C, $(C a constant of integration)\\Ae^{\frac{t}{100}}=500C_{in}(t)e^{\frac{t}{100}}+C\\$Divide all through by e^{\frac{t}{100}}\\A(t)=500C_{in}(t)+Ce^{-\frac{t}{100}}[/tex]

Recall that when t=0, A(t)=40 lbs (our initial condition)

[tex]A(t)=500C_{in}(t)+Ce^{-\frac{t}{100}}\\40=500C_{in}(t)+Ce^{-\frac{0}{100}}\\C=40-500C_{in}(t)\\$Therefore, the amount of salt in the tank at any time t is:\\\\A(t)=500C_{in}(t)+[40-500C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]

Answer: The lines are skew.

Step-by-step explanation: Two lines can only be parallel OR skew Or intersect each other. To determine that:

1) If the lines are parallel, divide the coefficient that precedes the variable of each equation and compare:

[tex]\frac{7}{8} \neq \frac{6}{8} \neq \frac{1}{4}[/tex]

Since they are not equal, L1 and L2 are not parallel.

2) If the lines intersect, when you equal the equations the variable is a valid statement:

25 + 7t = - 12 + 8t (1)

17 + 6t = - 17 + 8t (2)

t = - 11 + 4t (3)

Using (3) to solve the system:

t - 4t = - 11

3t = 11

t = [tex]\frac{11}{3}[/tex]

Substituing t in (1):

25 + 7(11/3) = -12 + 8(11/3)

25 + 77/3 = - 12 + 88/3

[tex]\frac{152}{3} = \frac{52}{3}[/tex]

Which is not true, so, the lines does NOT intersect.

As they are none of the other options, it can be concluded that the lines L1 and L2 are skew.

Answer: left 4 units

Step-by-step explanation: use the formula -b/2a to find the new x value. Or use a graphing calculator and compare the position of g(x) to f(x)

Answer:

Answer: left 4 units

Step-by-step explanation:

Answer:

The quotient in polynomial form= 2x + 6

Step-by-step explanation:

In order to calculate the quotient in polynomial form of the following synthetic division we would have to make the following:

According to the given data we have the following:

-1|2 8 6

Therefore, quotient in polynomial form would be calculated as follows:

                                  -1 | 2  8  6

                                          -2 -6

                                       2   6  0

Therefore, quotient in polynomial form= 2x + 6

The quotient in polynomial form= 2x + 6

Answer:

8.51 seconds

Step-by-step explanation:

Time to reach maximum height

=( Usin90)/2g

= 32/2*9.81

= 32/19.62

= 1.63 s

Max height = U²Sin²tita/g

= 32²/9.81

= 1024/9.81

= 104.38ft

Total height=104.38 + 128= 232.38

Time to fall back to the ground using the formula

h = ut+(1/2)gt²

U= 0

H= 232.38

g = 9.81

(232.38 *2 )/9.81= t²

47.376= t²

t = 6.88 s

Total time taken to hit ground

= 6.88 + 1.63

= 8.51 seconds

Steps to solve:

9(d - 93) = -36d

~Distribute

9d - 837 = -36d

~Subtract 9d to both sides

-837 = -45d

~Divide -45 to both sides

18.6 = d

Best of Luck!

Answer:

There are 50 large boxes.

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

  Let x = number of large boxes

       y = number of small boxes

 "There are 115 boxes in all"    means    x + y = 115      [eq1]

Now, the pounds for each kind of box is:

    (pounds per box)*(number of boxes)

So,

  pounds for large boxes     +    pounds for small boxes      =    4125 pounds

                 "the truck is carrying a total of 4125 pounds in boxes"

        (50)*(x)                   +              (25)*(y)                  = 4125    [eq2]

It is important to find two equations so we can solve for two variables.

Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2.  Let's solve for x:

   x = 115 - y          [from eq1]

    50(115-y) + 25y = 4125             [from eq2]

     5750 - 50y  + 25y = 4125           [distribute]

     5750 - 25y = 4125

      -25y = -1625

         y = 65             [divide both sides by (-25)]

 There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

  x = 115 - y

  x = 115 - 65

  x = 50

Answer:

The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.

Step-by-step explanation:

In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.

We take a sample of size n=64.

Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):

[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{54-49}{10.2/\sqrt{64}}=\dfrac{5}{1.275}=3.922\\\\\\P(M>54)=P(z>3.922)=0.00004[/tex]

The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.

Answer:

a. The volume of Pyramid A is double that of Pyramid B.

b. The new volume of B is equal to the volume of A.

Step-by-step explanation:

The base of pyramid A is a rectangle with length 10 meters and width 20 meters.

The base of pyramid B is a square of side length 10 meter.

Both pyramids have the same height, h.

The volume of a pyramid is given as:

V = lwh / 3

where l = length

w = width

h = height

The volume of Pyramid A is:

V = (10 * 20 * h) / 3 = 66.7h cubic metres

The volume of Pyramid B is:

V = (10 * 10 * h) / 3 = 33.3h cubic metres

By comparing their values, the volume of Pyramid A is double that of Pyramid B.

If the height of B increases to 2h, its new volume is:

V = (10 * 10 * 2h) / 3 = 66.7h cubic metres

The new volume of B is equal to the volume of A.

Answer:

720 ways

The number of ways in which the promotion can be made is 720 ways

Step-by-step explanation:

Given that;

The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president.

This is a permutation problem because the order of selection is relevant. They will be promoted to various positions.

N = nPr = n!/(n-r)!

n = 10, r = 3

Substituting the values;

N = 10P3

N = 10!/(10-3)! = 10!/7!

N = 720 ways

The number of ways in which the promotion can be made is 720 ways

We are given that the passenger's jet is flying at a speed of 185 miles per hour, with a direction of 36 degrees, and the wind speed being 47 mph with a direction of 120 degrees. From this, you could create a diagram is shown in the attachment.

[ 185 cos 36, 185 sin 36 ]

+ [ 47 cos 120, 47 sin 120 ]

_______________________

[ 185 cos 36 + 47 cos 120, 185 sin 36 + 47 sin 120 ]

√( 4263  + 33988 )^2

= ( About ) √38251 = 195.57 mph

Solution = 195.6 mph, 069°

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

Using FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

Answer:

[tex]\boxed{x^2-2x+1}[/tex]

Step-by-step explanation:

[tex](x-1)(x-1)[/tex]

Apply FOIL Method.

[tex]x(x-1)-1(x-1)[/tex]

[tex]x^2-x-x+1[/tex]

Combine like terms.

[tex]x^2-2x+1[/tex]

Answer:

multiply 0.85x40

Step-by-step explanation:

Answer:

D. No solution

Step-by-step explanation:

Instead of solving everything I just plugged the numbers on equations and saw that for some of them the numbers satisfied one or two equation but not all.  Also for some I saw that a number set makes the equation have no solution. For eg, I plugged option B into equation 3 and got 1305=756 which is never true so it is no solution.

Hope you understand :)

Answer:

1/4

Step-by-step explanation:

The probability of landing on an odd number is 2/4.

The probability of landing on a number greater than 5 is 2/4.

2/4 × 2/4

4/16 = 1/4

Answer:

Domain is  

{

x

∈

R

;

x

≠

−

5

}

Range is  

{

y

∈

R

;

y

≠

0

}

Step-by-step explanation:

Explanation:

Domain: Denominator should not be  

0

∴

x

+

5

≠

0

or

x

≠

−

5

Domain is any real value except  

x

=

−

5

or  

{

x

∈

R

;

x

≠

−

5

}

Range is any real value except  

y

=

0

or  

{

y

∈

R

;

y

≠

0

}

graph{1/(x+5) [-10, 10, -5, 5]}

Answer:

The better deal would be simple interest rate of 3.2%

Step-by-step explanation:

In order to calculate which bank would be the better deal If Parker decides to deposit $7,000 for 25 years, we would have to make the following calculation:

A. simple interest rate of 3.2%.

Therefore, FV= P*r*t

=$7,000*3.2%*25

=$5,600.

B. compound interest rate of 3%

Therefore, FV=PV(1+r)∧n

FV=$7,000(1+0.03)∧25

FV=$14,656

The better deal would be simple interest rate of 3.2%

Answer:

-978

Step-by-step explanation:

1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935

2.) Subtract 13,935 on both sides, to move that value to the left side, to further  isolate the variable m.

-735-13935=15m + 13935 - 13935

3.)-Simplify/Combine Like Terms

-14,670=15m

4.) Divide both sides by 15 to isolate and solve for m

-14,670/15=15m/15

5.) Simplify

-978=m    

6.) Rearrange so m is on left side and value is on right side

m=-978

Answer:

Olá!

`~~~~~~~~~~~~~~~~~~

3 (número inteiro positivo)

2 (antessor)

4 (sucessor)

Para provar isso, simplesmente multiplicamos entre 4 e 2:

4 x 2 = 8

Espero que isso tenha ajudado! Também seria bom se você me desse Brainliest!

Answer:

8 records were sold on Wednesday, and 24 records were sold on Thursday

Step-by-step explanation:

Let's call the number of records sold on Wednesday w, and the number sold on Thursday t.

t+w=32

t=3w

Substituting:

(3w)+w=32

4w=32

w=8

t=3w=3(8)=24

Hope this helps!

Answer:

Step-by-step explanation:

Using the formula

p +/- (z* √[p(1-p) /n]

Where p is sample proportion = 120/400= 0.3 z*= 1.96 (z score for 95% confidence) and n is 400.

0.3 + (1.96 √[0.3(1-0.3) / 400])

0.3 + (1.96 √[(0.3*0.7)/400

0.3 + (1.96√ (0.21/400))

0.3 + (1.96 √0.000525)

0.3 + (1.96* 0.023)

0.3 + (0.045)

= 0.345 ~ 35%

For the lower interview

0.3 - (0.045)

= 0.255 ~ 26%

Thus, a 95% confidence interval for this study is between 26% and 35%