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10 months ago

How many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11?

Mathematics

1 answer:

sashaice [31]10 months ago

3 0

Answer:

130

Step-by-step explanation:

The number of integers meeting the criteria can be found by counting them using a counting formula.

<h3>Divisible by 7</h3>

Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...

7n ≤ 1000

n ≤ 142.857

There are 142 integers less than 1000 that are divisible by 7.

<h3>Divisible by 7 and 11</h3>

Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.

77n ≤ 1000

n ≤ 12.987

There are 12 integers less than 1000 that are divisible by both 11 and 7.

<h3>Divisible by 7, not 11</h3>

The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.

142 -12 = 130 integers divisible by 7, but not 11.

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Samantha is studying the population growth of an endangered birth. The growth can be modeled by the equation B(t) 100 + 3/5t^5 ,

solong [7]

The value of the population of the growth of an endangered birth after 5 years is 1975

<h3>How to determine the population after 5 years?</h3>

The population function is given as:

B(t) = 100 + 3/5t^5

At 5 years, the value of t is 5

So, we have

t = 5

Next, we substitute 5 for t in the equation B(t) = 100 + 3/5t^5

This gives

B(5) = 100 + 3/5 * 5^5

Evaluate the exponent

B(5) = 100 + 3/5 * 3125

Evaluate the product

B(5) = 100 + 1875

Evaluate the sum

B(5) = 1975

Hence, the value of the population of the growth of an endangered birth after 5 years is 1975

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8 months ago

Stephanie opened a savings account with $200.00. Each additional month, the account will increase by 10%. The function f(x)=200

spin [16.1K]

<span>B.
approximately $325</span>

6 0

2 years ago

Can you guys help me please!!

ella [17]

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1.C

2.C

3.D

4.D

5.D

6.A

7.C

8.B

9.A

10.C

11.A

12.B

13.D

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2 years ago

20. Rewrite the following expression as a fraction times the variable.<br> -8a/9

Schach [20]

Answer:

-8a times 1/9

Step-by-step explanation:

This can be thought of as -8a/1 times 1/9. (1/9 is the reciprocal of 9, so were just pulling the fraction apart)

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2 years ago

Which statement about the function f(x)=|x+3| is true?

Stels [109]

The given function f(x) = |x + 3| has both an absolute maximum and an absolute minimum.

What do you mean by absolute maximum and minimum ?

A function has largest possible value at an absolute maximum point, whereas its lowest possible value can be found at an absolute minimum point.

It is given that function is f(x) = |x + 3|.

We know that to check if function is absolute minimum or absolute maximum by putting the value of modulus either equal to zero or equal to or less than zero and simplify.

So , if we put |x + 3| = 0 , then :

± x + 3 = 0

±x = -3

So , we can have two values of x which are either -3 or 3.

The value 3 will be absolute maximum and -3 will be absolute minimum.

Therefore , the given function f(x) = |x + 3| has both an absolute maximum and an absolute minimum.

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2 months ago