What is the solution to the linear equation?
2.8y + 6 + 0.2y = 5y – 14

I believe both answers are Shannon.

Answer:

Any polynomial of the form f(x)=rx²+(1-4r)x+(3r+6) passes through these points.

Step-by-step explanation:

Let f(x)=rx²+bx+c be a polynomial that passes through (1,7) and (3,9). This means that f(1)=7 and f(3)=9, that is,

f(1)=r(1)²+b(1)+c=r+b+c=7, and

f(3)=r(3)²+b(3)+c=9r+3b+c=9

We have the equations r+b+c=7 and 9r+3b+c=9. Substract the second equation minus 9 times the first to obtain -6b-8c=-54, then 6b+8c=54 or equivalently b=9-4c/3.

Substract the second equation minus 3 times the first to obtain 6r-2c=-12. Then 2c=6r+12, thus c=3r+6. We have written c in terms of r. Substitute in b=9-4c/3 to obtain b=9-4(r+2)=-4r+1. The polynomial acquires the form

f(x)=rx²+(1-4r)x+(3r+6).

The probability that it will take more than 6 minutes for all the customers in line to check out is 0.40.

We are given the probability distribution of x, the number of customers in line at a supermarket express checkout counter.

Moreover, we are given that each customer takes 3 minutes to check out.

It means that if there are 0 customers in line, i.e., x=0, then it will take 0 minutes for all the customers currently in line to check out.

If there is 1 customer in line, i.e., x=1, then it will take 3 minutes for all the customers currently in line to check out.

If there are 2 customers in line, i.e., x=2, then it will take 6 minutes for all the customers currently in line to check out.

If there are 3 customers in line, i.e., x=3, then it will take 9 minutes for all the customers currently in line to check out.

If there are 4 customers in line, i.e., x=4, then it will take 12 minutes for all the customers currently in line to check out.

If there are 5 customers in line, i.e., x=5, then it will take 15 minutes for all the customers currently in line to check out.

From above we note that if there are 3 or more customers in the line, then it will take more than 6 minutes (note that the case of check out time equal to 6 minutes is not included when we want 'more than 6 minutes') for all the customers currently in line to check out.

Thus, required probability is given by:

P(more than 6 minutes for all the customers currently in line to check out) = P(x ≥ 3)

= P(x=3) + P(x=4) + P(x=5)

= 0.20 + 0.15 + 0.05

= 0.40

Therefore, the probability that it will take more than 6 minutes for all the customers in line to check out is 0.40.

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Final answer:

Without specific information on the total number of customers or the distribution of customers in line, we cannot calculate a specific probability for it to take more than 6 minutes for all customers to check out, given that each customer takes 3 minutes.

Explanation:

The question is about the probability that it will take more than 6 minutes for all the customers in line to check out, given that each customer takes 3 minutes. The time it takes for all the customers to check out is determined by the number of customers in line. If there are two or more customers in line, it will definitely take more than 6 minutes for all of them to check out, because the checkout time is 3 minutes per customer.

So, the question of probability relates to the likelihood of there being two or more customers in line. Without information on the total number of customers, or the distribution of customers in line, we cannot calculate a specific probability.

Please note, this is a practical application of topics in probability and queue theory, involving concepts like mean arrival rate and service rate.

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Answer:

Picture 1:

Area of cemicircle 2 π = 6.28 sq.m (approximately)

Total area of figure = 24+6.28= 30.28 sq.m (approximately)

Picture 2:

area of rectangle = 256 sq.m

Area of triangle = 32 sq.m

Total area of figure = 288 sq.m

Picture 3:

Area of top rectangle = 2 sq ft

Area of bottom rectangle = 15 sq ft

Total area of figure = 17 sq ft

Picture 4:

Area of rectangle = 28 sq ft

Area of triangle = 6 sq ft

Area of shaded region = 22 sq ft

Answer:

Range : (-∞, 12] Or -∞ < x ≤ 12.

Step-by-step explanation:

Domain of function is represented by the x-values (input values) of the function given in the graph.

Similarly, Range of the function is define by the y-values (output values) on the graph of a function.

Since y-values on the graph are between 12 and negative infinity (Including 12),

Therefore, range of the function will be (-∞, 12] or -∞ < x ≤ 12

Answer:

-∞ < y ≤ 12

Step-by-step explanation:

For all Plato users

Answer:

m<1 = 60

m<2 = 30

m<3 = 80

Step-by-step explanation:

1. Solve for angle (1)

The sum of angles in any triangle is (180) degrees. As one can see, there is a (30) degree angle in this triangle, and a (90) degree angle. Bear in mind that the box around an angle indicates that it is a (90) degree angle. One can form an equation and solve for the unknown angle using this given information;

(30) + (m<1) + (90) = 180

Simplify,

120 + m<1 = 180

Inverse operations,

m<1 = 60

2. Solve for angle (2)

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this theorem here by stating the following,

m<2 = 30

Thus one gets their answer, the measure of angle (2) must be (30) degrees by the vertical angles theorem.

3. Solve for angle (3)

As states above, the sum of angles in a triangle is (180) degrees. Since one has found the measure of angle (2), one can form an equation and solve for the measure of angle (3) using the given information, combined with the information found.

(m<2) + (70) + (m<3) = 180

Susbtitute,

30 + 70 + (m<3) = 180

Simplify,

100 + m<3 = 180

Invers eoperations,

m<3 = 80