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2 years ago

The quotient of -8 and the sum of a and b

Mathematics

1 answer:

Mamont248 [21]2 years ago

3 0

Hi! I'm happy to help!

To solve this, you need to know what all of the terms mean. Quotient means division, and sum means addition. Knowing this we can set up our expression.

Because there is an operation inside of an operation (addition inside of division) we use parenthesis.

-8÷(a+b)

I hope this was helpful, keep learning! :D

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A newspaper vendor sells three papers to 135 customers, the papers are the daily times, the observer and the new Nigeria. 70 cus

IRINA_888 [86]

Answer:

3 customers brought all the three papers.

Step-by-step explanation:

Let, D, O and N represents the three newspapers.

D = The daily times

O = The observer

N = The new Nigeria.

According to the given information,

$n(D\cup O\cup N)=135, n(D)=70,n(O)=60,n(N)=50$

$n(D\cap O)=17, n(O\cap N)=15, n(D\cap N)=16$

We know that,

$n(A\cup B\cup C) = n(A) + n(B) + n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A) + n(A\cap B\cap C)$

Using this formula, we get

$n(D\cup O\cup N) = n(D)+n(O) + n(N)-n(D\cap O)-n(O\cap N)-n(N\cap D) + n(D\cap O\cap N)$

$135 =70+60+50-17-15-16 +n(D\cap O\cap N)$

$135 =132+n(D\cap O\cap N)$

$135 -132=n(D\cap O\cap N)$

$3=n(D\cap O\cap N)$

Therefore, 3 customers brought all the three papers.

5 0

2 years ago

A parallelogram has a length of 6 centimeters and a width of 4.5 centimeters. This parallelogram is dilated by a scale factor of

Arada [10]

Scale factor is given by:
(length of larger figure)/(length of smaller figure)=(width of larger figure)/(width of the smaller figure)=3.4
The length of the larger figure will be given by:
length=(scale factor)*(length of smaller figure)
=3.4*6=20.4 cm
width of the larger figure will be given by:
width=(scale factor)*(width of smaller figure)
=3.4*4.5
=15.3 cm
Therefore the dimension of the new parallelogram will be 20.4 cm by 15.3 cm

3 0

2 years ago

Use Euler's formula to derive the identity. (Note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b =

storchak [24]

Answer with Step-by-step explanation:

We have to prove that

$sin 2\theta=2sin\theta cos\theta$ by using Euler's formula

Euler's formula : $e^{i\theta}=cos\theta+isin\theta$

$e^{i(2\theta)}=(e^{i\theta})^2$

By using Euler's identity, we get

$cos2\theta+isin2\theta=(cos\theta+isin\theta)^2$

$cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)$

$(a+b)^2=a^2+b^2+2ab, i^2=-1$

$cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)$

$cos2\theta=cos^2\theta-sin^2\theta$

Comparing imaginary part on both sides

Then, we get

$sin2\theta=2sin\theta cos\theta$

Hence, proved.

8 0

2 years ago

Write 0.00658 in standard form

Svetllana [295]

Answer:

0.00658 = 6.58 * 10^-3

Step-by-step explanation:

The standard form is a way of writing numbers easily in powers of 10.

To write a number in standard form, we have to move the decimal point to the front of the first non zero number.

Depending on the position of the decimal point to the first non zero number, movement can be towards the right or towards the left. When we move towards the right, our power of 10 will be negative, when we move in the left direction, our power of 10 will be positive

In this question, we shall be moving towards the right. Thus, our power of 10 is negative. We shall be moving towards the right 3 three times

Thus our power would be 10^-3

Thus our standard form will be 6.58 * 10^-3

Kindly note that another pointer is, if the value of our number to be written in standard form is less than zero, then the standard form will come in negative powers of 10. If the value of the number is greater or equal to 1 at least, then then the standard form will be in positive powers of 10

5 0

2 years ago

A whole number from 1 to 15 inclusive is picked at random.

Helen [10]

Answer:

a) 3/7

b) 3/5

Explanation:

The figure attached shows the Venn diagram for the given sets.

a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?

From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.

There are a total of 7 multiples of 24, from 1 to 15.

Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:

b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?

The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.

The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.

Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:

8 0

2 years ago