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Troyanec [42]
3 years ago
7

How many of the first 1000 positive integers are multiples of both 4 and 5 but not 6 ?

Mathematics
1 answer:
castortr0y [4]3 years ago
5 0
Let's begin by breaking  each number down into its prime factors:    4 = 2 x 2    5 = 5    6 = 2 x 3 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4, 5, and 6 by multiplying all common and unique prime factors of each number:    common prime factors: 2    unique prime factors:  2,5,3    LCM = 2 x 2 x 5 x 3 = 60 Next, let's determine how many times 60 goes into 10,000 (excluding remainder):    10,000/60 = 166 and 2/3    Multiples of ALL 3 numbers (4,5,6) = 166  Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4 and 5 by multiplying all common and unique prime factors of each number:    common prime factors:  none
    unique prime factors:  2 x 2 x 5
    LCM = 2 x 2 x 5 = 20 Next, let's determine how many times 20 goes into 10,000:
    10,000/20 = 500
    Multiples of BOTH numbers (4 and 5) = 500 Finally, let's subtract the multiples of ALL three numbers (4,5,6) from the multiples of BOTH numbers (4 and 5) to get our answer:   Multiples of ONLY numbers 4 and 5 (excluding 6):       500 - 166 = <span>334</span>
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3 years ago
A restaurant makes pizzas with 6-inch diameters ad 12-inch diameters. Which of the following statement is true?
a_sh-v [17]

Answer:

The correct option is c: the area of the 6-inch pizza is 1/4 the area of the 12-inch pizza.

Step-by-step explanation:

The area (A) of each pizza is given by:

A = \pi r^{2}

Where:

r: is the radius

For the 12-inch pizza we have:

A_{12} = \pi (\frac{12 inch}{2})^{2} = 113.1 inch

And for the 6-inch pizza we have:

A_{6} = \pi (\frac{6 inch}{2})^{2} = 28.3 inch

The ratio between A₆ and A₁₂ is:

\frac{A_{6}}{A_{12}} = \frac{28.3 inch}{113.1 inch} = 0.25 = \frac{1}{4}

Hence:

A_{6} = \frac{A_{12}}{4}

Therefore, the correct option is c: the area of the 6-inch pizza is 1/4 the area of the 12-inch pizza.

I hope it helps you!            

4 0
3 years ago
Can you please help Imao the first answer gets the brainiest
Eduardwww [97]
Answer: 4 for the first one and 4.25

Explanation:


If you like this don’t forget to thank me and brilliant
7 0
2 years ago
A student answers a multiple-choice examination question that offers four possible answers. Suppose the probability that the stu
Nitella [24]

Answer: 0.9730

Step-by-step explanation:

Let A be the event of the answer being correct and B be the event of the knew the answer.

Given: P(A)=0.9

P(A^c)=0.1

P(B|A^{C})=0.25

If it is given that the answer is correct , then the probability that he guess the answer P(B|A)= 1

By Bayes theorem , we have

P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(C|A^c)P(A^c)}

=\dfrac{(1)(0.9)}{(1))(0.9)+(0.25)(0.1)}\\\\=0.972972972973\approx0.9730

Hence, the student correctly answers a question, the probability that the student really knew the correct answer is 0.9730.

7 0
3 years ago
You spin a spinner numbered 1 through 10. Find the probability of landing on an even<br> number.
DENIUS [597]

Answer:

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Step-by-step explanation:

6 0
3 years ago
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