in a sample of 10 cards, 4 are red and 6 are blue. if 2 cards are selected at random from the sample, one at a time without repl
2 answers:
You might be interested in
Answer:
x = tan⁻¹(⅘)
Step-by-step explanation:
We can solve for x by using trigonometric ratios (sin, cos, and tan)
We need to apply the appropriate ratio that uses the two sides 8 and 10 from the perspective of x. See attached image for information about ratios. (Source: Math is Fun)
The tangent ratio is opposite divided by adjacent. It will relate x to the two sides. So we would write
tan(x) = ⁸⁄₁₀
Then we simplify and move the tan to the other side by multiplying both sides by the inverse of tan (since you cannot divide by tan)
tan(x) = ⅘
x = tan⁻¹(⅘)
Then we can use a calculator to evaluate x
If you want to find y, now that you have two angles of the triangle, you can find the sum of 90 + x and subtract that from 180 (since all angles of a triangle add up to 180) to find y.
<u><em>Answer:</em></u>
a. The first car wash charges more for the basic fee
b. 6 extras must be chosen for the total cost to be the same
<u><em>Explanation:</em></u>
The complete question is shown in the attached diagram
<u>The general form of the linear equation is:</u>
y = mx + c where m is the slope and c is the y-intercept
The y-intercept represents the initial value which, in the given problem, is the basic fee
<u>For the first car wash, we are given the equation:</u>
y₁ = x + 9
<u>Now, we will start by getting the equation for the second car wash:</u>
<u>1- getting the slope:</u>
The equation now is: y = 1.5x+c
<u>2- getting the y-intercept:</u>
To get the y-intercept, we will simply choose a point, substitute with it in the equation from 1 and solve for c. I will use point (2,9)
y = 1.5 x + c
9 = 1.5 (2) + c ............> c = 6
<u>The equation for the second car wash is:</u>
y₂ = 1.5x + 6
<u>Part 1:</u>
As mentioned above, the y-intercept represents the basic fee
<u>For the first car wash:</u>
y₁ = x + 9 ................> The basic fee is $9
<u>For the second car wash:</u>
y₂ = 1.5x + 6 ..............> The basic fee is $6
It is clear that the basic fee for the first car wash charges more for the basic fee
<u>Part 2:</u>
In both equations, x represents the number of extras. We want the total cost to be the same. So, we will simply equate y₁ and y₂ and solve for x
x + 9 = 1.5x + 6
1.5x - x = 9 - 6
0.5x = 3
x = 6
<u>Let's verify:</u>
<u>For x = 6:</u>
y₁ = x + 9 = 6 + 9 = $15
y₂ = 1.5x + 6 = 1.5(6) + 6 = $15
Total cost is the same. This means that 6 extras must be chosen for the total cost to be the same
Hope this helps :)
<h3><u>The function that represents the price P of the car after x years is:</u></h3>
<em><u>Solution:</u></em>
<em><u>The decreasing function is given as:</u></em>
Where,
y is future value
a is initial value
r is decreasing rate in decimal
t is time period
From given,
a = 25000
number of years = x
future value = P
Therefore,
Thus the function is found