Christina is making a blanket for her baby granddaughter. The blanket will have ribbon around all 4 edges. There will be:94 feet of ribbon on the top edge94 feet of ribbon on the bottom edge134 feet of ribbon on the left edge134 feet of ribbon on the right edgeHow much ribbon will Christina need to make the blanket?

Answer:

(a) X follows a Binomial distribution

(b) (i) P(X ≥ 2) = 0.28348

P(X = 1) = 0.39601

P(X ≤ 3) = 0.98800

Step-by-step explanation:

(a) In this situation, the variable X equal to the number of ducks that are infected follows a Binomial distribution because we have:

• n identical and independent events: The 7 ducks that are selected at random
• 2 possible results for every event: success and fail. We can call success if the duck is infected and fail if the duck is not infected.
• A probability p of success and 1-p of fail: There is a probability p equal to 15% that the ducks have the infection and a probability of (100%-15%) that they don't.

(b) So, the probability that X ducks are infected is calculated as:

Then, Probability P(X = 1) is equal to:

At the same way, probability P(X ≥ 2) is equal to:

P(X ≥ 2) = P(2) + P(3) + P(4) + P(5) + P(6) + P(7)

P(X ≥ 2) = 0.2097 + 0.0617 + 0.0109 + 0.0011 + 0.00006 + 0.00002

P(X ≥ 2) = 0.28348

And probability P(X ≤ 3) is equal to:

P(X ≤ 3) = P(0) + P(1) + P(2) + P(3)

P(X ≤ 3) = 0.3206 + 0.3960 + 0.2097 + 0.0617

P(X ≤ 3) = 0.988

Answers:

b)

i) 0.2834

ii) 0.3960

iii) 0.9880

Solution:

To solve this we need to use the binomial probability

P(X=k)=

a)

X= number of ducks infected

n=7

p=15%=0.15

P(X)= ; x=0,1,2,...,7

b)

First we need to calculate by the definition of binomial probability at k=0,1,2,3

P(X=0)= = 0.3206 ;

P(X=1)= = 0.3960 ;

P(X=2)= = 0.2097  ;

P(X=3)= = 0.0617  ;

(i) Find P(X≥2)

Using the complement rule, we have that : P(A´ )= 1-P(A)

P(X≥2)= 1- P(X<2)

= 1- ((P(X=0)+P(X=1))

= 1- 0.3206-0.3960

=0.2834

(ii) Find P(X=1)

We have to evaluate the definition of binomial probaility at k=1

Then we have that

P(X=1)= = 0.3960

(iii) Find P(X ≤ 3)

We have to use the addition tule for mutually exclusive events

Addition rule: P(A∪B)=P(A)+P(B)

P(≤3)= P(X=0)+ P(X=1) + P(X=2) + P(X=3)

=0.3206 + 0.3960+ 0.2097 + 0.0617

= 0.9880

Answer:

$40

Step-by-step explanation:

We are given two points (0, 40) and (4, 120).

Now to find the equation which represents A graph titled Camera Rentals plots the Number of Days on the x axis and the Amount in dollars on the y axis.

To Find equation we will use two point slope form.

Formula:

Substitute the values in the formula

The equation represents the situation :

where x is the number of days

y is the Amount in dollars

Now we are supposed to find the fixed amount charged.

So, we need to substitute x i.e. number of days=0

So,

Hence the fixed amount charged is $40.

Answer:

Each bottle of juice costs $1.34.

Step-by-step explanation:

From the information given, the equation would indicate that the total cost is equal to the price per bag of popcorn for the number of bags plus the price per pack of juice bottles for the number of packs.

Total cost=(1.68*1)+15x

Total cost=1.68+15x

Now, you can replace the total cost with $21.78 and solve for x:

21.78=1.68+15x

21.78-1.68=15x

20.1=15x

x=20.1/15

x=1.34

According to this, the answer is that each bottle of juice costs $1.34.

Final answer:

The cost of each bottle of juice is $1.02

Explanation:

Let's use "x" to represent the cost of each juice bottle in dollars. Sebastian bought a 15-pack of juice bottles, so the total cost of the juice bottles can be calculated as 15x dollars. He also bought a bag of popcorn for $1.68.

Therefore, the total cost before tax, which is $21.78, can be expressed as the sum of the cost of the juice bottles and the cost of the popcorn:

Total Cost = Cost of Juice Bottles + Cost of Popcorn

$21.78 = 15x + $1.68

Now, we can isolate "x" by subtracting $1.68 from both sides of the equation:

$21.78 - $1.68 = 15x

$20.10 = 15x

To find the cost of each juice bottle (x), we divide both sides by 15:

x = $20.10 / 15

x = $1.02

So, each bottle of juice costs $1.02.

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Answer:

17. +5-2-1=+2

18. -7-6-2=15

19. +11-9-4=-2

20.+4-8+6=+2

Final answer:

The best linear model to represent the town's population could be either P(t) = 1.12t + 0.20 or P(t) = 1.12t + 0.02, depending on the specific data in the scatter plot. Both these options follow the general form of a linear equation.

Explanation:

The question is related to a scatter plot, linear equation, and population study. We're looking to determine the best linear equation that models the town's population from 2000 to 2019 based on the given scatter plot. The general form of a linear equation is y = mx + b, where m represents the slope (rate of change), and b is the y-intercept (starting value). Typically, in this kind of scenario:

• 't' would be the years after 2000,
• 'm' would represent the rate of change of the population, and
• 'b' would be the starting population.

Without the actual scatter plot, it's impossible to choose the most accurate option. However, options A & D are most likely because they conform to the general form. Option A, P(t) = 1.12t + 0.20, and Option D, P(t) = 1.12t + 0.02, are both viable options depending on the specific data presented in the scatter plot.

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Answer:

P(t)=1.12t+0.20

Step-by-step explanation:

Hope it helps lov