Answer:
Basically it has to be divisible by 8, 9, and 10 because any number that is divisible by 2, 3, 4, 5, 6 must also be divisible by 8, 9 and 10. We know that the number has to end in 0, the sum of its digits must be divisible by 9 and the last three digits must be divisible by 8. Therefore, the smallest number is 10080 and the largest is 999360.
4.)6 2(6) + 4
9 2(9)+ 4
15 2(15) + 4
The probability is 1/5 to get a red ball in 1st draw and a white ball in 2nd draw.
<u>Step-by-step explanation:</u>
- There are 1 red ball and 4 white balls in a box.
- The total number of balls in the box = 1 red + 4 white = 5 balls.
The two balls are drawn without replacement.
<u>Drawing the first ball :</u>
The first draw should be a red ball.
The probability to get a red ball = No.of red balls / Total balls in the box.
We know that, No. of red balls is 1 and total balls in the box is 5.
P(red ball) = 1/5
<u>Drawing the second ball :</u>
The second draw should be a white ball.
The probability to get white ball = No.of white balls / Total balls in the box.
We know that,
No. of white balls is 4.
The total balls in the box after the first draw will be 4 balls.
P(white ball) = 4/4
The probability of getting a red ball on the first drawn and a white ball on the second draw = P(red ball) × P(white ball)
⇒ (1/5) × (4/4)
⇒ 4/20
⇒ 1/5
Therefore, the probability is 1/5 to get a red ball in 1st draw and a white ball in 2nd draw.
The following equation represents the function g in function notation,
g(x) = 3x - 14 [Option (A)]
Definition of a Function
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.
Given equation is,
y -3x = -14
⇒ y = -14 + 3x
or y = 3x - 14
Here, y stands for or represents the function g(x) which is a function of independent variable x.
Thus, the correct function notation is as follows,
g(x) = 3x - 14
Learn more about a function here:
brainly.com/question/12431044
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The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.
Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.
Let the polynomial function be c(x) = x
² -7x + 10
To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:
x
² -7x + 10 = 0
Factorizing the middle term, we get:
x
² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) =0
(x - 2)(x - 5)=0
x - 2 = 0 ⇒ x=2
x - 5 = 0 ⇒ x=5
Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.
