A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
p(x, y) y
0 1 2
x 0 0.10 0.03 0.01
1 0 08 0.20 0.06
2 0.05 0.14 0.33
(a) Given that X = 1, determine the conditional pmf of Y�i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1).
(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island?
(c) Use the result of part (b) to calculate the conditional probability P(Y ? 1 | X = 2).
(d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island?

Answer:

(x-5)^2 + (y+6)^2 = 4

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-5)^2 + (y- -6)^2 = 2^2

(x-5)^2 + (y+6)^2 = 4

Answer:

Choice A.

[tex]y = - {2}^{x} + 4[/tex]

Step-by-step explanation:

Use graphing calculator

Answer:

Choice A.

Step-by-step explanation:

Step-by-step explanation:

The value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The numerical expression is given below.

⇒ 1 + 32 – 10 ÷ 2

According to the PEMDAS rule, the computation wrapped in quotes or the parenthesis comes first in the sequence of operation.

This rule is used to solve the equation in a proper and correct manner.

PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.

⇒ 1 + 32 – (10 ÷ 2)

Simplify the numerical expression, then the expression will be

⇒ 1 + 32 – 5

⇒ 33 – 5

⇒ 28

Then the value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.

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Answer:

AC:y=x-1  CB:y=-x-5 AB:x=0

Step-by-step explanation:

Consider the triangle. The base AB is on the line x=0, the vertex C is (-2,-3)

The side AC is equal to BC. The angle ACB is 90 degrees. If the base is on the line x=o, it is on the axis Y.Explore the distance from the point C to the AB

c(-2,-3), the distance to the axis Y is equal to the modul of the coordinate x (-2), it is 2. The coordinates of point projected by the point C to the axis Y is N(0,-3). The modul of the height is 2, the height of the isosceles triangle to the base is the bisectrix, so the angle BCA is 90/2=45degrees, CBA is 180-90-45=45 degrees too

the heigt CN is equal to side NB, NB=2

Suppose B is (0,y) (x=0 because the base is on this line)

THe modul of the vector NB is equal to sqrt ((0-0)^2+(y+3)^2)= 2

modul (y+3)= 2

y=-1 or y=-5

(0,-1), (0,-5) - two points, one of them (suppose B) is (0,-5) when A is (0,-1) (A is remote from the point N on the same distance with B, because AB is the median too)

Find CB and AC

Use the equation for AC

(x-0)/(-2-0)= (y+1)/(-3+1)

x/-2= (y+1)/-2

x=y+1

y=x-1

For CB

(x-0)/ (-2-0)= (y+5)/ (-3-(-5))

x/-2= (y+5)/2

-x=y+5

y=-x-5

To test the effectiveness of the weight loss program, a PAIRED SAMPLE test distribution is used.

The weight loss data collated for the program for both the beginning and end of the program period was obtained with one subject or person having two separate readings, these shows that the samples are NOT INDEPENDENT.

When performing a test which involves DEPENDENT or MATCHED samples, whereby means of two measurements taken from the SAME subject are involved, a PAIRED SAMPLE TEST DISTRIBUTION IS ADOPTED.

Therefore, the effectiveness of the weight loss programme will be accurately evaluated using a PAIRED SAMPLE TEST.

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Answer:

C. 395.1

Step-by-step explanation:

Substitute the value for x:

[tex]V=0.95(8)^{2.9}\\V=395.1[/tex]

Answer:

D. -8x-4

E. 8x+6y-28

Step-by-step explanation:

D. 8(-x-1/2) = -8x-4

E. -8(-x-3/4y+7/2 = 8x+6y-28

The mean of the exam score is 65.56

The given exam data is as follows;

Possible Score range ----------- frequency (f) -------- score (x) -----------(fx)

40 - 50   -------------------------  21 ------------------- -----45 -------------- 945

50 - 60  --------------------------- 39------------------------55 ---------------2145

60 - 70 ----------------------------- 40---------------------- 65 ---------------- 2600

70 - 80 ------------------------------ 34 --------------------- 75 ----------------- 2550

80 - 90 ------------------------------ 28 --------------------- 85 ---------------- 2380

Note:[tex]score (x) = \frac{sum \ of \ the \ range }{2} , \ example \ \frac{40+49.99}{2} \approx 45[/tex]

The sum of the frequency (f) = 162

The sum of fx, ∑fx = 10620

The mean of the exam score:

[tex]\bar x = \frac{\Sigma fx }{\Sigma f} = \frac{10620}{162} = 65.56[/tex]

Therefore, the mean of the exam score is 65.56

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Answer:

-6

Step-by-step explanation:

(-12)+(-8)= -20

-20+14= -6

Answer:

x < -4

Step-by-step explanation:

-3x > 12

-----   ----

-3      -3

12 ÷ -3 = -4

Which means:

x < -4

(The sign changes because the equation is divided by a negative number)

Hope this helped.

Answer:

x <-4

Step-by-step explanation:

-3x > 12

Divide each side by -3. remembering to flip the inequality

-3x/-3 > 12/-3

x <-4

9514 1404 393

Answer:

  e = 225

Step-by-step explanation:

To eliminate the coefficient of e, multiply both sides of the equation by its reciprocal. The reciprocal of -1/75 is -75.

  (-75)(-3) = (-75)(-e/75)

  225 = e

Answer:

Yeah, x varies directly with (6 - y)

Step-by-step explanation:

[tex]x = 6 - y \\ x = k(6 - y) \\ x \: \alpha \: (6 - y)[/tex]

Answer:

With an ageing population, dietary approaches to promote health and independence later in life are needed. In part, this can be achieved by maintaining muscle mass and strength as people age. New evidence suggests that current dietary recommendations for protein intake may be insufficient to achieve this goal and that individuals might benefit by increasing their intake and frequency of consumption of high-quality protein. However, the environmental effects of increasing animal-protein production are a concern, and alternative, more sustainable protein sources should be considered. Protein is known to be more satiating than other macronutrients, and it is unclear whether diets high in plant proteins affect the appetite of older adults as they should be recommended for individuals at risk of malnutrition. The review considers the protein needs of an ageing population (>40 years old), sustainable protein sources, appetite-related implications of diets high in plant proteins, and related areas for future research.

Answer:

The shopping time (in minutes) of the nine shoppers are:

15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged  everything from least to greatest.)

We can see, that 3 shoppers shopped for 15-20 minutes.

And, 3 shoppers shopped for 21-26 minutes.

And finally, 3 shoppers shopped for 27-32 minutes.

So the answer for all 3 of the boxes is 3.

Let me know if this helps.

Answer:

See Below.

Step-by-step explanation:

We have the equation:

[tex]\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}[/tex]

And we want to show that:

[tex]\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}[/tex]

Instead of differentiating directly, we can first square both sides:

[tex]\displaystyle y^2 = 3e^{2x} -4x + 1[/tex]

We can find the first derivative through implicit differentiation:

[tex]\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4[/tex]

Hence:

[tex]\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}[/tex]

And we can find the second derivative by using the quotient rule:

[tex]\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}[/tex]

Simplify:

[tex]\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}[/tex]

Combine fractions:

[tex]\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}[/tex]

Simplify:

[tex]\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}[/tex]

Simplify:

[tex]6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}[/tex]

Q.E.D.

Answer:

C. 12, 8, 5

Step-by-step explanation:Side lengths of any triangle must conform to the triangle inequality theorem, which says that the sum of the lengths of any of the two sides of the triangle is greater than the length of the third side.

This means:

a + b > c

a + c > b

b + c > a

Let's check each of the options to see which set are possible lengths for a triangle:

A. 6, 5, 11

6 + 11 > 5 ===> 17 > 5

5 + 11 > 6 ===> 16 > 6

6 + 5 > 11 ===> 11 > 11 (INCORRECT. Does not confirm to tye theorem)

Therefore, this set cannot be possible side lengths for a triangle.

B. 8, 1, 2

8 + 1 > 2 ===> 9 > 2

1 + 2 > 8 ===> 3 > 8 (INCORRECT)

8 + 2 > 1 ===> 10 > 1

This set cannot be possible side lengths for a triangle.

C. 12, 8, 5

12 + 8 > 5 ===> 20 > 5

8 + 5 > 12 ===> 13 > 12

12 + 5 > 8 ===> 17 > 8

All are correct, therefore these are possible side lengths for a triangle.

Answer:

A=1/2(a+b)h

A=1/2(2cm+4cm)6cm

A=1/2×6cm×6cm

A=18cm²

Answer:

Hence the adjusted R-squared value for this model is 0.7205.

Step-by-step explanation:

Given n= sample size=20  

Total Sum of square (SST) =1000  

Model sum of square(SSR) =750  

Residual Sum of Square (SSE)=250  

The value of R ^2 for this model is,  

R^2 = \frac{SSR}{SST}  

R^2 = 750/1000 =0.75  

Adjusted [tex]R^2[/tex] :

[tex]Adjusted R^2 =1- \frac{(1-R^2)\times(n-1)}{(n-k-1)}[/tex]

Where k= number of regressors in the model.

[tex]Adjusted R^2 =1-(19\times 0.25/((20-2-1)) = 0.7205[/tex]

9514 1404 393

Answer:

  3070.06 square inches

Step-by-step explanation:

The area of the left triangle can be found using Heron's formula:

  s = semiperimeter = (53+71+58)/2 = 91

  area = √(s(s -53)(s -71)(s -58)) = √2282280 ≈ 1510.72

The area of the right triangle can be found using the trig formula ...

  area = 1/2ab·sin(C)

  area = 1/2(55)(71)sin(53°) ≈ 1559.34

Then the total area is ...

  1510.72 +1559.34 = 3070.06 . . . . . square inches

Answer:

pordondede donde eres?

Step-by-step explanation:

........................

Answer:

0.0625

Step-by-step explanation:

Given that :

Number of toppings = 4 (ground beef, black beans, refried beans, and sour cream)

The probability of choosing any particular topping at random from the four is :

Probability = required / total possible outcomes

Hence, P = 1 / 4 = 0.25

Hence, the probability of choosing : getting refried bean and sour cream :

P(refried bean) = 1/4

P(sour cream) = 1/4

P(refried bean and sour cream) = 1/4 * 1/4 = 1/16 =

0.0625

9514 1404 393

Answer:

  k = 3

Step-by-step explanation:

It is convenient to look at the line y=1 to see that f(0) = 1 and g(3) = 1. Then for x=3, g(3) = f(3 -k) = f(0) = 1

  k = 3

__

k is the amount by which the function has been shifted to the right. By comparing grid-intersection points on f(x) and g(x), we see that g(x) is 3 units to the right of f(x), so k = 3.

Answer: 3246/6= 541

if u wanna know if a # is divisible by 6 or not, see if the # is divisible by 2 or 3. if it works for both, then it is divisible by 6

Answer:

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

b) See step by step explanation

CI 90 %  =  (  0,296 ; 0,392)

c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)

d) the CI 95 % will be wider

Step-by-step explanation:

Sample Information:

Sample size n  =  250

number of people with milk intolerance  x = 86

p₁  =  86 / 250    p₁ = 0.344    and   q₁ =  1  - p₁   q₁ = 0,656

To calculate 90 % of Confidence Interval   α = 10%  α/2 = 5 %  

α/2 = 0,05     z(c) from z-table is:  z(c) =  1.6

Then:

CI 90 %  =  (  p₁  ±  z(c) * SE )

SE =  √ (p₁*q₁)/n   =  √ 0,225664/250

SE = 0,03

CI 90 %  =  (  0,344  ±  1,6* 0,03 )

CI 90 %  =  (  0,344 - 0,048 ;  0,344 + 0,048)

b) CI 90 %  =  (  0,296 ; 0,392)

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

c) We can support that with 90 % of confidence we will find the random variable between  this interval (  0,296 ; 0,392) .

d) CI 95 %      then significance level α = 5 %   α/2 = 2.5 %  

α/2  =  0,025      z(c) = 1.96   from z-table

SE = 0,03

And  as 1.96 > 1.6    the CI 95 % will be wider

CI 95% =  ( 0,344 ±  1.96*0,03 )

CI 95% =  (  0,344 ± 0,0588 )

CI 95% =  ( 0,2852 ; 0,4028 )

The answer would be D.

Answer: D

Step-by-step explanation:

Pretend that C is 12, pi is 3, and d is 4. 4=3/12, 4=3*12, 4=12-3, or 4=12/3? The only one that works is that last one, so the and is D: d=C/pi

Answer:

Right angled and isosceles

Answer:

12 free throw attempts

Step-by-step explanation:

First, find what percent of free throw attempts he misses:

6/10

= 0.6

So, he misses 60% of the time. Multiply 20 by 0.6 to find how many you would expect Lamar to miss out of 20 attempts:

20(0.6)

= 12

So, you would expect Lamar to miss 12 free throw attempts