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2 years ago

How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

1 answer:

7 0

$\left\lfloor\dfrac{1000}4\right\rfloor=250$

$\left\lfloor\dfrac{1000}6\right\rfloor=166$

$\left\lfloor\dfrac{1000}{\mathrm{lcm}(4,6)}\right\rfloor=\left\lfloor\dfrac{1000}{12}\right\rfloor=83$

$250+166-83=333$

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HELPP PLEASEEE

MrRa [10]

Answer: The answer to your question is 6 $\sqrt{3}$

Step-by-step explanation:

To solve this problem we will use proportions. We will compare the largest right triangle and the medium size triangle.

Medium triangle Large triangle

hypotenuse y 9 + 3

adjacent size 9 y

- Write the proportions

y/9 = (9 + 3)/y

-Solve for y

y² = 9(12)

y² = 108

y = $\sqrt{180}$

-Find the prime factors of 108

108 2

54 2

27 3

9 3

3 3

then, 108 = 2² 3³

-Expressthe root as fractional exponents

2²/² 3²/² 3¹/²

-Simplification

2(3)(3)¹/²

-Result

6 $\sqrt{3}$

8 0

2 years ago

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astra-53 [7]

Answer:

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Step-by-step explanation:

5 0

2 years ago

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frosja888 [35]

Answer

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Step-by-step explanation:

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2 years ago

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and vot

Zina [86]

<u>Answer: </u>

The number of ways to form the committee is formed = 637065

<u>Solution: </u>

The number of combinations of n things such that m things taken together are given by:-

$C_{(\boldsymbol{n}, \boldsymbol{m})}=\frac{n !}{m !(\boldsymbol{n}-\boldsymbol{m}) !}$

Given Data:

A committee consisting of 4 faculty members and 5 students is to be formed. There are 12 faculty members and 13 students eligible to serve on the committee.

Then, the number of ways to form the committee is formed given by :-

$\begin{array}{l}{12 C_{4} \times 13 C_{5}} \\\\ {=\frac{12 !}{4 !(12-4) !} \times \frac{13 !}{5 !(13-5) !}} \\\\ {=\frac{12 !}{4 ! 8 !} \times \frac{13 !}{5 ! 8 !}} \\\\ {\frac{12 \times 11 \times 10 \times 9 \times 8 !}{27 \times 8 !} \times \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8}{120 \times 8 !}} \\\\ {=637065}\end{array}$