To draw a heart, one would be choosing 1 card of 13 possible hearts, and 0 from the remaining 39 non-hearts. With respect to the entire deck, one would be choosing 1 card from 52 total cards. So the probability of drawing a heart is
When Michelle replaces the card, the deck returns the normal, so the probability of drawing any card from a given suit is the same,
. In other words, drawing a spade is independent of having drawn the heart first.
So the probability of drawing a heart, replacing it, then drawing a spade is
.
Answer: f(2)=5
Step-by-step explanation:
f(2)=2(2)+1=5
f(2)=5
Given
Rob is twice Joshua's age
Nick is 5 years older than Joshua.
sum of all their ages is 45.
Find the age of nick.
To proof
As given
Rob is twice Joshua's age
let Joshua's age = x
than Rob age = 2x
Nick is 5 years older than Joshua.
Nick age = 5 + x
sum of all their ages is 45
than the equation becomes
Joshua's age + Rob age + Nick age = 45
put the value
x + 2x + 5 + x = 45
4x = 40
x = 10
Joshua's age = 10 year
than Rob age = 20 year
Nick age = 5 + 10
= 15year
Hence proved
Answer:
Step-by-step explanation: it is negative 42 it is just the opposite cause the thumbs is down negative up positive
Answer:
Step-by-step explanation:
f(x) is quadratic function and g(x) is linear (since AP in the right column).
<u>Find the equation of the function f(x), use the points on the graph:</u>
- c = 5 as the y-intercept is (0, 5)
- a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
- a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4
<u>The function is:</u>
Find the equation of g(x)
<u>Find the slope of g(x):</u>
- m = (1 - 7)/(-1 + 4) = -2
<u>Use (-4, 7) to find its equation:</u>
- y - 7 = -2(x + 4)
- y = -2x + 7 - 8
- y = -2x - 1
<h3>See the required comparison below</h3>
<u>The y-intercepts:</u>
- f(x) ⇒ 5,
- g(x) ⇒ -1
- -5 < - 1
<u>Values at x = 3:</u>
- f(3) = -3² + 4(3) + 5 = 8
- g(3) = -2(3) - 1 = - 7
- 8 > 7
<u>Average rate of change in the interval [2,5]:</u>
- f(x) ⇒ (0 - 9)/(5 - 2) = -3
- g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
- -3 < -2
<u>Max of function in the interval [-5, 5];</u>
- f(x) ⇒ 9, vertex of the function
- g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
- 9 = 9
