Answer:
x = 2
Step-by-step explanation:
(2x+3)/5 = 7/5
Multiply both sides by the LCM of the denominators (5)
2x+3 = 7
2x = 7-3
2x = 4
x = 4/2
x = 2
ANSWER
![2 \frac{1}{4}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B4%7D%20)
EXPLANATION
We want to find the constant that must be added to
![{x}^{2} - 3x](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%203x)
to form a perfect square.
Comparing the given expression to
![a{x}^{2} + bx + c](https://tex.z-dn.net/?f=%20a%7Bx%7D%5E%7B2%7D%20%20%2B%20bx%20%2B%20c)
we have
a=1 , b=-3 , and c=0.
We need to add
![{( \frac{b}{2a} })^{2}](https://tex.z-dn.net/?f=%20%7B%28%20%5Cfrac%7Bb%7D%7B2a%7D%20%7D%29%5E%7B2%7D%20)
We substitute the values to get,
![{( \frac{ - 3}{2(1)} })^{2} = \frac{9}{4}](https://tex.z-dn.net/?f=%7B%28%20%5Cfrac%7B%20-%203%7D%7B2%281%29%7D%20%7D%29%5E%7B2%7D%20%20%3D%20%20%5Cfrac%7B9%7D%7B4%7D%20)
We change this to mix numbers to get,
![2 \frac{1}{4}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B4%7D%20)
The last choice is correct.
Answer:
![P(M) = \frac{52}{390}= 0.133](https://tex.z-dn.net/?f=%20P%28M%29%20%3D%20%5Cfrac%7B52%7D%7B390%7D%3D%200.133)
![P(T) = \frac{64}{390}= 0.164](https://tex.z-dn.net/?f=%20P%28T%29%20%3D%20%5Cfrac%7B64%7D%7B390%7D%3D%200.164)
![P(W) = \frac{70}{390}= 0.179](https://tex.z-dn.net/?f=%20P%28W%29%20%3D%20%5Cfrac%7B70%7D%7B390%7D%3D%200.179)
![P(Th) = \frac{59}{390}= 0.151](https://tex.z-dn.net/?f=%20P%28Th%29%20%3D%20%5Cfrac%7B59%7D%7B390%7D%3D%200.151)
![P(F) = \frac{60}{390}= 0.154](https://tex.z-dn.net/?f=%20P%28F%29%20%3D%20%5Cfrac%7B60%7D%7B390%7D%3D%200.154)
![P(S) = \frac{43}{390}= 0.110](https://tex.z-dn.net/?f=%20P%28S%29%20%3D%20%5Cfrac%7B43%7D%7B390%7D%3D%200.110)
![P(Su) = \frac{42}{390}= 0.109](https://tex.z-dn.net/?f=%20P%28Su%29%20%3D%20%5Cfrac%7B42%7D%7B390%7D%3D%200.109)
As we can see the relative frequencies are not too different the average for all the relative frequencies is
and the maximum absolute difference |0.143-0.109|= 0.034 is not enough higher to conclude that we have significant difference from the average or expected value.
Step-by-step explanation:
For this case we have the frequency of the number of times that the outcome happens per each day of the week:
Day Frequency
Monday 52
Tuesday 64
Wednesday 70
Thursday 59
Friday 60
Saturday 43
Sunday 42
We can begin findind the total for the frequency and we got:
52+64+70+59+60+43+42=390
And now we can calculate the relative frequency for each case like this:
![P(M) = \frac{52}{390}= 0.133](https://tex.z-dn.net/?f=%20P%28M%29%20%3D%20%5Cfrac%7B52%7D%7B390%7D%3D%200.133)
![P(T) = \frac{64}{390}= 0.164](https://tex.z-dn.net/?f=%20P%28T%29%20%3D%20%5Cfrac%7B64%7D%7B390%7D%3D%200.164)
![P(W) = \frac{70}{390}= 0.179](https://tex.z-dn.net/?f=%20P%28W%29%20%3D%20%5Cfrac%7B70%7D%7B390%7D%3D%200.179)
![P(Th) = \frac{59}{390}= 0.151](https://tex.z-dn.net/?f=%20P%28Th%29%20%3D%20%5Cfrac%7B59%7D%7B390%7D%3D%200.151)
![P(F) = \frac{60}{390}= 0.154](https://tex.z-dn.net/?f=%20P%28F%29%20%3D%20%5Cfrac%7B60%7D%7B390%7D%3D%200.154)
![P(S) = \frac{43}{390}= 0.110](https://tex.z-dn.net/?f=%20P%28S%29%20%3D%20%5Cfrac%7B43%7D%7B390%7D%3D%200.110)
![P(Su) = \frac{42}{390}= 0.109](https://tex.z-dn.net/?f=%20P%28Su%29%20%3D%20%5Cfrac%7B42%7D%7B390%7D%3D%200.109)
As we can see the relative frequencies are not too different the average for all the relative frequencies is
and the maximum absolute difference |0.143-0.109|= 0.034 is not enough higher to conclude that we have significant difference from the average or expected value.
In order to test this more formally we can use a chi square test but the problem not ask for this.
Answer:
c.) 476
Step-by-step explanation:
-19; -14; -9; -4; 1;............aₙ
aₙ = 5n - 24
a₁₀₀ = 5(100) - 24
a₁₀₀ = 476