Answer:
Using the combination formula:
Number of combination of r object chosen from the total object i.e n is given by:
![\frac{n!}{r! \cdot (n-r)!}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7Br%21%20%5Ccdot%20%28n-r%29%21%7D)
As per the statement:
4 candy bars be chosen from a store that sells 30 candy bars
Number of candy bars chosen from a store that sells 30 candy bars(r)= 4
and
Total candy bars(n) = 30
then substitute in the given formula we have;
![\frac{30!}{4! \cdot (30-4)!}](https://tex.z-dn.net/?f=%5Cfrac%7B30%21%7D%7B4%21%20%5Ccdot%20%2830-4%29%21%7D)
⇒![\frac{30!}{4! \cdot (26)!}](https://tex.z-dn.net/?f=%5Cfrac%7B30%21%7D%7B4%21%20%5Ccdot%20%2826%29%21%7D)
⇒![\frac{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26!}{1 \cdot 2 \cdot 3 \cdot 4 \cdot (26)!}](https://tex.z-dn.net/?f=%5Cfrac%7B30%20%5Ccdot%2029%20%5Ccdot%2028%20%5Ccdot%2027%20%5Ccdot%2026%21%7D%7B1%20%5Ccdot%202%20%5Ccdot%203%20%5Ccdot%204%20%5Ccdot%20%2826%29%21%7D)
Simplify:
⇒![\frac{657720}{24} = 27,405](https://tex.z-dn.net/?f=%5Cfrac%7B657720%7D%7B24%7D%20%3D%2027%2C405)
therefore, 27,405 ways can 4 candy bars be chosen from a store that sells 30 candy bars
Answer:
8
Dont mind me if i am wrong!
Answer:
A)
Step-by-step explanation:
length = x +x + 2 = 2x + 2
Width = 2+ x
Area of rectangle = length *width
(x +2)(2x + 2) = 110
Use FOIL method
x*2x + x*2 + 2*2x + 2*2 = 110
2x² + <u>2x + 4x</u> + <u>4 - 110</u> = 0 {Combine like terms}
2x² +6x - 106 = 0
a = 2 ; b = 6 ; c = -106
b² - 4ac = 6² - 4*2*(-106)
= 36 + 848
= 884
![\sqrt{b^{2}-4ac}=\sqrt{884}= 29.73](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%3D%5Csqrt%7B884%7D%3D%2029.73)
![x =\dfrac{-b+\sqrt{b^{2}-4ac}}{2a} \ ; \ x==\dfrac{-b-\sqrt{b^{2}-4ac}}{2a}\\\\x = \dfrac{-6+29.73}{2*2} \ ; \ x =\dfrac{-6-29.73}{2*2} \ this \ is \ ignored \ as \ it \ is \ negative\\\\x=\dfrac{23.73}{4};](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-b%2B%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%20%5C%20%3B%20%5C%20x%3D%3D%5Cdfrac%7B-b-%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%20%3D%20%5Cdfrac%7B-6%2B29.73%7D%7B2%2A2%7D%20%5C%20%3B%20%5C%20x%20%3D%5Cdfrac%7B-6-29.73%7D%7B2%2A2%7D%20%5C%20this%20%5C%20is%20%5C%20%20ignored%20%5C%20as%20%5C%20it%20%5C%20is%20%5C%20%20negative%5C%5C%5C%5Cx%3D%5Cdfrac%7B23.73%7D%7B4%7D%3B)
x = 5.93 m
Answer:
the answer is in the link
Step-by-step explanation:
Answer:
There are 15 combinations.
Step-by-step explanation:
A restaurant is offering a dinner special that includes one starter and one entree.
Starter: bread-sticks, soup, salad
Entree: beef, fish, chicken, shrimp, pork
So, we have 3 starters and 5 entrees.
To know the possible dinner special combinations we will simply multiply the two.
![3\times5=15](https://tex.z-dn.net/?f=3%5Ctimes5%3D15)
Therefore, there are 15 combinations.