Step-by-step explanation:
conditions : x≠0 and x≠-a and b≠1
1/(x+a) = b/x ⇌ 1×x = b(x+a) ⇌ x = bx + ba ⇌ (1-b)x = ab ⇌ x = ab/(1-b)
Each question has four choices, then the probability to guess a correct answer is
![p= \frac{1}{4}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B1%7D%7B4%7D%20)
and the probability to select incorrect choice is
![q=1-p=1- \frac{1}{4} = \frac{3}{4}](https://tex.z-dn.net/?f=q%3D1-p%3D1-%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20)
.
You have a 5-question multiple-choice test, then n=5. The <span>probability that you will guess exactly three out of five questions correctly is </span>
<span /><span>
</span><span>
![C_n^kp^nq^{n-k}=C_5^3p^3q^{5-3}= \dfrac{5!}{3!\cdot 2!} \left( \dfrac{1}{4} \right)^3\left( \dfrac{3}{4} \right)^2=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2} \cdot \dfrac{9}{1024} =](https://tex.z-dn.net/?f=C_n%5Ekp%5Enq%5E%7Bn-k%7D%3DC_5%5E3p%5E3q%5E%7B5-3%7D%3D%20%5Cdfrac%7B5%21%7D%7B3%21%5Ccdot%202%21%7D%20%5Cleft%28%20%5Cdfrac%7B1%7D%7B4%7D%20%5Cright%29%5E3%5Cleft%28%20%5Cdfrac%7B3%7D%7B4%7D%20%5Cright%29%5E2%3D%5Cdfrac%7B1%5Ccdot%202%5Ccdot%203%5Ccdot%204%5Ccdot%205%7D%7B1%5Ccdot%202%5Ccdot%203%5Ccdot%201%5Ccdot%202%7D%20%5Ccdot%20%5Cdfrac%7B9%7D%7B1024%7D%20%3D)
</span>
![= \dfrac{90}{1024} = \dfrac{45}{512}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B90%7D%7B1024%7D%20%3D%20%5Cdfrac%7B45%7D%7B512%7D%20)
.
<span />
Answer:
D
Step-by-step explanation:
point-slope form is y-y1=m(x-x1) . since the slope is 2 and not -2, you can automatically eliminate choices A and C. since the y-value in the point, (1,-1), is -1, you will add it to y because you are subtracting a negative. (- - = +) therefore, the final equation, in point-slope form, is y+1=2(x-1), or answer choice D.
Answer:
40
Step-by-step explanation:
Two ways we can solve this problem:
1. Graphically
2. Mathematically
Because you already solved it graphically, I will show you how to do so mathematically. Of course, graphically is much much easier and more efficient in this problem.
Let's break the problem down.
First, we are given a graph which contains a slope.
To find slope, we use the technique -> rise/run
Picking 2 obvious points from the graph, we can see
1st point -> (10, 20)
2nd point -> (40, 80)
Now, let's find the slope
![\frac{80-20}{40-10} = \frac{60}{30} = 2](https://tex.z-dn.net/?f=%5Cfrac%7B80-20%7D%7B40-10%7D%20%20%3D%20%5Cfrac%7B60%7D%7B30%7D%20%20%3D%202)
Now, we have an equation y = 2x, where y = number of pies and x = cups of sugar
We want to find how many cups of sugar we need to bake 80 pies. Simply substitute 80 = number of pies = y
y = 2x -> 80 = 2x
Solving for x, divide both sides by 2
40 = x
We need 40 cups of sugar.
Answer:
(1) 820
(2) 1920
Step-by-step explanation:
(1) solving 20 x 41, using associative property.
20 * 41 = (2 x 10) x 41 = 2 x (10 x 41)
= 20 x 41 = 2 x 410
= 820 = 820
(2) distribute 32 as 30 + 2 and solve.
60 x 32
= 60 x (30 + 2) = 60(30) + 60(2)
= 1800 + 120
= 1920