What is the rate of change?

a. -2
b. -1/2
c. 1/2
d. 2

Answer:

a

[tex]P(G = 2 ,  Y= 1 , R = 2) = 0.13184 [/tex]

b

[tex]P(G = R ) =  0.13919  [/tex]

Step-by-step explanation:

From the question we are told that

   The probability of the traffic light being green is [tex]p_g = \frac{3}{8}[/tex]

   The probability of the traffic light being red is  [tex]p_r = \frac{1}{2}[/tex]

   The probability of the traffic light being yellow is  [tex]p_y = \frac{1}{8}[/tex]

   The number of days of observation is n = 5

Generally the probability distribution function for a multinomial distribution is mathematically represented as

          [tex]Pr( X_1 = x_1 \ and \ . . .  \ and  \  X_k =x_k) =  \left \{ {{ \frac{n!}{x_1 ! , . . . x_k !} p_1^{x_1} * \cdots *p_k^{x_k} \ \ \ \ \ \ \  when \  \sum x_i = n } \atop {0 }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \    otherwise  \ } \right[/tex]

Generally the probability that P[G=2, Y=1, R=2]

     [tex]P(G = 2 ,  Y= 1 , R = 2) = \frac{5!}{ 2! * 1! * 2!} *  [\frac{3}{8} ]^2 * [\frac{1}{8} ]^1 * [\frac{1}{2} ] ^2[/tex]

=> [tex]P(G = 2 ,  Y= 1 , R = 2) = 0.13184 [/tex]

Generally the probability that P[G=R] is mathematically represented as

          [tex]P(G = R ) =  P( G =  2 ,  Y = 1 ,  R = 2) + P( G =  0 ,  Y = 5 ,  R = 0)+ P( G =  1 ,  Y = 3 ,  R = 1)[/tex]

Here

    [tex] P( G =  0 ,  Y = 5 ,  R = 0) =  \frac{5!}{ 0! * 5! * 0!} *  [\frac{3}{8} ]^0 * [\frac{1}{8} ]^5 * [\frac{1}{2} ] ^0[/tex]

    [tex] P( G =  0 ,  Y = 5 ,  R = 0) =  0.0000305176 [/tex]

Also  

     [tex] P( G =  1 ,  Y = 3 ,  R = 1)=  \frac{5!}{ 1! * 3! * 1!} *  [\frac{3}{8} ]^1 * [\frac{1}{8} ]^3 * [\frac{1}{2} ] ^1[/tex]

    [tex] P( G =  1 ,  Y = 3 ,  R = 1)=  0.0073242 [/tex]  

[tex]P(G = R ) =  0.13184 +  0.0000305176+ 0.0073242 [/tex]

[tex]P(G = R ) =  0.13919  [/tex]

Answer:

Option (d)

Step-by-step explanation:

If the current salary of Sione is represented by the function m(t - 1),

Next year his salary m(t) gets hike of 3%.

So, the next year salary of Sione will be represented by,

m(t) = m(t - 1) + 3% of m(t - 1)

      = m(t - 1) + 0.03 × m(t - 1)

      = m(t - 1)(1 + 0.03)

      = 1.03m(t - 1)

Since, at the end of year 1 his salary was $55000,

Recursive function will be,

m(t) = 1.03m(t - 1) = 55000

Therefore, Option (d) will be the answer.

Answer:

5. 4

6. 1

7. 2

8. -1

Step-by-step explanation:

Coefficient is usually the whole number in the beginning. I believe 5-7 are correct. I'm a little iffy about 8. Good luck!

Answer:

Step-by-step explanation:

Number of red roses = 108

Number of white roses = 144

Number of yellow roses = 48

Number of purple roses = 72

If the number of roses in each bunch are identical,

Number of bunches of roses = HCF of number of roses

Factors of 144 = 3×3×2×2×2×2×1

Factors of 108 = 3×3×3×2×2×1

Factors of 72 = 3×3×2×2×2×1

Factors of 48 = 3×2×2×2×2×1

Common factors of 144, 108, 72, 48 = 3 × 2 × 2 × 1 = 12

Therefore, number of bunches of roses with equal number of roses = 12

Number of red roses in each bunch = [tex]\frac{108}{12}=9[/tex]

Number of white roses in each bunch = [tex]\frac{144}{12}=16[/tex]

Number of yellow roses in each bunch = [tex]\frac{48}{12}=4[/tex]

Number of purple roses in each bunch = [tex]\frac{72}{12}=6[/tex]

Answer:

5

Step-by-step explanation:

9×5/9=45/9

=5

just multiply the stuff in parantheses and then add and then divide.

Answer:

5

Step-by-step explanation:

3^2*(2+3); 9*5=45

(2+1)*3; (3)*3=9

So 45/9 =5

Answer:

0

Step-by-step explanation:

look at the first numbers

Answer:

1,0,1,1,0,1,1,1,0,1,1,1,1,0

hope it helped :)

Step-by-step explanation:

Answer:

-2/3

Step-by-step explanation:

-2/3

Answer:

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

Step-by-step explanation:

4/9 is the answer

hope this helps

Step-by-step explanation:

Simplifying mixed numbers

Following are the steps to simplify mixed fractions: Find the highest common factor (HCF) of numerator and denominator of the fraction part. Divide both the numerator and the denominator by HCF. The whole number part will remain the same.

Answer:

8^1/3= 2

:-))))

Answer

the next two terms are

0.000032

0.0000064

Answer:

a=60

Step-by-step explanation:

since there are 6 total "a" values (2 angles worth just a, 2 angles worth 2 a)

you divide the total angle number by 6: 360/6=60

a=60

hope this helps!! <3

Step-by-step explanation:

10x+4y.............

Answer:

B. 7x + 6y

Step-by-step explanation:

  3x + 7y -5x +9x -y

= (3x - 5x +9x) + (7y - y)

= 7x + 6y

Answer:

337.60

Step-by-step explanation:

I divided what he earned by what he worked and multiplied that number by 40

Answer:

14.$403.46 or  $403.50(rounded)

15.11.55 or 11.60(rounded)

Step-by-step explanation:

Commission is when you get a percent added to the amount of money you have already so with that being said-397.50+1.5%

She uses 24% so with that being said to find the amount left you have to subtract the percent from the original amount-15.2-24%

Answer:

9

Step-by-step explanation:

No of customers that enter the restaurant is equal to 4 times the number of people that buy a hotdog from the hotdog cart plus 11.

The number of customers that enter their restaurant is equal to 1 times the number of  people that buy a hotdog from the hotdog cart plus 38.

The equation that shows the given condition,

4x + 11 = 1x + 38

x is the no of people

Taking the like terms,

4x-1x=38-11

3x=27

x = 9

So, there are 9 people buying a hotdog  from the hotdog cart.

hope it helps!

Answer:

107.9 ft

Step-by-step explanation:

Imagine Kite is a point A. The person ,who keeps the string is point B.

The height of flying is AC=85 ft.  So we have right triangle ABC :angle C=90 degrees, angle B is 52 degrees. Length of AB (triangle ABC hypotenuse) is the length of the string.

AB=AC/sinB=85/sin52=107.8665...=approx 107.9 ft

The length of the string is 86.1 ft.

As per the given data:

Height of the kite flying from the ground = 78 ft

The angle of elevation of the kite from the ground = 65°

From the diagram, we can clearly observe the right-angled triangle with perpendicular as 78 ft if formed.

The length of the string is the hypotenuse.

By using the trigonometric ratio sinθ.

sinθ = Perpendicular / Hypotenuse

sin65° = 78 / Hypotenuse

0.906 = 78 / Hypotenuse

Hypotenuse = 78 / 0.906

Hypotenuse = 86.1 ft

Hence, the length of the string is 86.1 ft.

To learn more about Trigonometry, click:

brainly.com/question/29002217

#SPJ2

Answer:

2/15

Step-by-step explanation:

BRANIEST PLS

Answer: 2/15 is the answer hope this help

Step-by-step explanation:

Answer:

(1)  n = 9

(2) n = 15

(3) r = -8

Plz mark brainliest:)

Answer:

Step-by-step explanation:

1.4=n/9+3

4-3=n/9

1=n/9 cross multiply

2. -7=-8+n/15

-7+8=n/15

1=n/15 Cross multiply

n=15

3.-11=r/2-7

-11+7=r/2

-4=r/2cross multiply

-8=r

r=-8

Answer:

I think the answer is 3

Answer:

Step-by-step explanation:

Tax = 8% of 23

      = [tex]\frac{8}{100}*23[/tex]

      = [tex]\frac{184}{100}[/tex]

      = $ 1.84

Answer

The answer is $1.84

Step-by-step explanation

The formula for calculating the sales tax on a good or service is: selling price x sales tax rate, and when calculating the total cost of a purchase, the formula is: total sale amount = selling price + sales tax.

Answer:

a = [tex]\frac{h-r}{b}[/tex]

Step-by-step explanation:

Given

h = ab + r ( subtract r from both sides )

h - r = ab ( isolate a by dividing both sides by b )

[tex]\frac{h-r}{b}[/tex] = a

Answer: 21

Step-by-step explanation: I got it right

Answer:

x = 7

Step-by-step explanation:

Answer:

1.50(d)=p

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

I solved it and got it right

Answer: 1.5 pounds per crate