HELP PLEASE 50 POINTS
A mechanic charges $125 plus $25 per hour of labor. The equation c=25n+125
describes the total she would charge for a service visit, where n represents the number of
hours of labor and c is the total cost. Graph the equation and using the graph, find how
much he charges when she works 3 hours.

The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is

[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]

where T is the set

[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]

(a) I've attached an image of the integration region.

[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]

(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.

Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:

[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]

[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]

Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.

Answer:

see explanation

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) , that is

f(x) - g(x)

= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1

= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms

= - 5x³ + 8x - 8

Substitute x = - 2 into this expression, thus

(f - g)(- 2)

= - 5(- 2)³ + 8(- 2) - 8

= - 5(- 8) - 16 - 8

= 40 - 16 - 8

= 16

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

Answer:

18

Step-by-step explanation:

Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:

10x + 33 = 0 or 11x + 60 = 0

10x = -33 or 11x = -60

x = -33/10 or x = -60/11

Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.

Answer:

the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.

Step-by-step explanation:

From the given information:

Sample size n = 200

The standard deviation for a sampling distribution for two brands are equally likely because the individual has no ability to discriminate between the two soft drinks.

∴

The population proportion [tex]p_o[/tex] = 1/2 = 0.5

NOW;

[tex]\sigma _p = \sqrt{\dfrac{p_o(1-p_o)}{n}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.5(1-0.5)}{200}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.5(0.5)}{200}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.25}{200}}[/tex]

[tex]\sigma _p = \sqrt{0.00125}[/tex]

[tex]\sigma _p = 0.035355[/tex]

However, in order to determine the symmetrical limits of the population percentage given that the z probability is 90%.

we use the Excel function as computed as follows in order to determine the z probability  = NORMSINV (0.9)

z value = 1.281552

Now the symmetrical limits of the population percentage can be determined as: ( 1.28, -1.28)

[tex]1.28 = \dfrac{X - 0.5}{0.035355}[/tex]

1.28 × 0.035355 = X - 0.5

0.0452544= X - 0.5

0.0452544 + 0.5 = X

0.5452544 = X

X [tex]\approx[/tex] 0.545

X = 54.5%

[tex]-1.28 = \dfrac{X - 0.5}{0.035355}[/tex]

- 1.28 × 0.035355 = X - 0.5

- 0.0452544= X - 0.5

- 0.0452544 + 0.5 = X

0.4547456 = X

X [tex]\approx[/tex] 0.455

X = 45.5%

Therefore , we can conclude that the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.

Answer:

The answer is 0.267949192

Step-by-step explanation:

I hope that is enough numbers.

Answer:

[tex]\boxed{x=15}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} =\frac{x}{20}[/tex]

[tex]\sf Cross \ multiply.[/tex]

[tex]4 \cdot x = 20 \cdot 3[/tex]

[tex]4x=60[/tex]

[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]

[tex]\frac{4x}{4} =\frac{60}{4}[/tex]

[tex]x=15[/tex]

Answer:

5

Step-by-step explanation:

There will be five equal part because Iyene takes 2 parts and nokob takes 3 parts

Thus, the total parts which have been shared is 2+3=5

Further more, every part is

[tex] \frac{280}{5} = 56[/tex]

Hence, there is 5 parts have been shared and every part is 56 dollars

Answer:

5 equal parts

Because one of the dudes will get 2 and the other one will get 3 parts

3+2 is 5

280/5=56 (1 part)

so iyene will get 56*2=112 and nokob will get 56*3=168

Answer:

$179.80

Step-by-step explanation:

799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.

Answer:

Step-by-step explanation:

Let us first generate the frequency table from the information given:

Hurricane number(X)       Frequency(f)                f(X)

6                                            9                                   54

8                                            13                                  104

12                                           16                                  192

14                                            12                                168

Total                                     ∑(f) = 50                          ∑f(x) =518

In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:

Let the last frequency be f

9 + 3 + 16 + f = 50

38 + f = 50

f = 50 - 38 = 12

Now, calculating mean:

[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]

Therefore mean number of hurricanes = 10.4 (to one decimal place)

Answer:

The probability is  [tex]P( X \le 4 ) = 0.0054[/tex]

Step-by-step explanation:

From the question we are told that

   The percentage that are on time is  p =  0.76

   The  sample size is n =  11

Generally the percentage that are not on time is

     [tex]q = 1- p[/tex]

     [tex]q = 1- 0.76[/tex]

     [tex]q = 0.24[/tex]

The  probability that no more than 4 of them were on time is mathematically represented as

        [tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]

=>     [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]

[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]

[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]

[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]

[tex]P( X \le 4 ) = 0.0054[/tex]

Answer:

3

Step-by-step explanation:

f(x)=3x-3

g(x)=-x^2+4,

f(2) = 3(2) -3 = 6-3 =3

g(-2) = -(-2)^2+4 = -4+4 = 0

f(2)-g(-2)= = 3-0 = 3

Answer:

20 %

Step-by-step explanation:

The experimental probability is 4/20 = 1/5 = .2 = 20 %

Answer:

Total distance travel by train =  70 km

Step-by-step explanation:

Given:

Speed of train = 70 km/h

Total time taken = 60 min = 60 / 60 = 1 hour

Find:

Total distance travel by train

Computation:

Distance = Speed × Time

Total distance travel by train = Speed of train × Total time taken

Total distance travel by train = 70 × 1

Total distance travel by train =  70 km

Answer:

A. –f(x)

Step-by-step explanation:

The transformation of a reflection about the x-axis is

f(x) -> -f(x).

So the answer is

A. –f(x)

Answer:

1) The dependent variable is : time to complete the maze

2) The analysis used should be : One -way within-subjects ANOVA ( B )

3) Null hypothesis is ; There will be no difference between any group means

4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

5) degree of freedom for the denominator = 11

6) critical F value = 3.49

Step-by-step explanation:

The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .

The analysis used should be : One -way within-subjects ANOVA ( B )

Null hypothesis is ; There will be no difference between any group means

Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11

The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F -  table the critical value would be 3.49

Answer:

The 2 Gallon Tank is Enough

Step-by-step explanation:

A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.

There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.

[tex]8 * 2 = 16[/tex]

So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.

Answer:

2 gallon tank

Step-by-step explanation:

16 pints is the same as 2 US gallons

Answer:

The function is  continuous at  x = 36

Step-by-step explanation:

From the question we are told that

      The  function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]  

       The  point at which continuity is tested is  x =  1

Now from the definition  of continuity ,

   At function is continuous at  k if  only  

       [tex]\lim_{x \to k}f(x) = f(k)[/tex]

So

      [tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]

                            [tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

                             [tex]= 7.2[/tex]

Now  

     [tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

     [tex]f(36) = 7.2[/tex]

So  the given function is continuous at  x =  36

because

          [tex]\lim_{x \to 36}f(x) = f(36)[/tex]

Answer:

The numbers:

-43    and     58

Step-by-step explanation:

a + b = 15

a = b - 101

then:

(b-101) + b = 15

2b = 15+101

2b = 116

b = 116/2

b = 58

a = b - 101

a = 58 - 101

a = -43

Check:

a + b = 15

-43 + 58 = 15

Answer:

Approximately 13.1521 units.

Step-by-step explanation:

To find the diagonal, we can use the Pythagorean Theorem.

Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:

[tex]a^2+b^2=c^2[/tex]

Substitute 9.3 for a and b, and let c equal d:

[tex](9.3)^2+(9.3)^2=d^2[/tex]

Instead of squaring, add the like-terms:

[tex]2(9.3)^2=d^2[/tex]

Take the square root of both sides:

[tex]d=\sqrt{2(9.3)^2}[/tex]

Expand:

[tex]d=\sqrt{2}\cdot\sqrt{(9.3)^2}[/tex]

The right cancels:

[tex]d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}[/tex]

Answer:

Step-by-step explanation:

The slope of a line is found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope and

(x1 , y1) and ( x2 , y2) are the points

Substituting the above values into the above formula we have

Slope of the line that passes through

(0,1) and (-8, -7) is

[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]

Hope this helps you

Answer:

The equation is y= -4x -8

Step-by-step explanation:

The -4 is the slope and the -8 is the y intercept

Answer:

Slope: -4

Line type: Straight and diagonal from left to right going down.

Rate of change: a decrease by 4 for every x vaule

y-intercept is: (0,-8)

x-intercept is: (-2,0)

Step-by-step explanation:

Slope calculations:

y2 - y1 over x2 - x1

0 - 4

-2 - ( -3) or -2 + 3

=

-4/1 =

-4

More slope info on my answer here: https://brainly.com/question/17148844

Hope this helps, and have a good day.

Answer:

800×200= 8 × 200 hundreds= 1600 Hundreds = 160000

Answer: x < 28

Step-by-step explanation:

Answer:

Hey there!

The area of a rectangle is the length times width.

Thus, we can write the equation, 600=30w.

Solving for the width, we get that the width is equal to 20 ft.

Let me know if this helps :)

Answer:

20 feet across.

Step-by-step explanation:

You will have to do a simple equation solve.

x is how many feet across the court is.

* could be our multiplying sign

600 = 30*x

Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.

That leaves 20 = x.

So it is 20 feet across.

Answer:

C(x)=1.2x+8,000.

Step-by-step explanation:

C(x)=cost per unit⋅x+fixed costs.

The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by

In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.

Suppose that you have to sell [x] number of bars to make profits. So, we can write -

{2x} - {1.20x} > {8000}

0.8x > 8000

8x > 80000

x > 10000

Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

Answer:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 1 to 3.

= -196.5

Step-by-step explanation:

Given

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to infinity

The expression that includes all terms up to order 3 is:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to 3.

= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)

= -125/2 + 100000/6 - 759375/5040

= -62.5 + 16.67 - 150.67

= - 196.5

Answer:

C. 42 square units

Step-by-step explanation:

This is a rectangle and to calculate the area of a rectangle we multiply length and width

The length of this rectangle is 7 units and the width is 6 units

6 × 7 = 42 square units

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

Answer:

[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]

Step-by-step explanation:

number of counties = 159

n number of people are mutually independent and equally likely home locations

considering the details given in the question

n ≤ 159

The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]

since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in

therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]