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Allushta
14 days ago
15

Suppose we pick three people at random. For each of the 2.32 The following questions, ignore the special case where someone migh

t be born on February 29th, and assume that births are evenly distributed throughout the year.(a) What is the probability that the first two people share a birthday?(b) What is the probability that at least two people share a birthday?
Mathematics
1 answer:
Inessa [3.9K]14 days ago
7 0

Answer:

(a) 1 in 365 or 0.2740%

(b) 0.8227%

Step-by-step explanation:

(a) For the first person's birthday, the probability that the second person has the same birthday is 1 out of 365, so the chance that the first two share a birthday is:

P = \frac{1}{365}=0.2740\%

(b) There are four scenarios possible where at least two individuals share a birthday: first and second, first and third, second and third, all three sharing the same birthday. Hence, the probability that at least two share their birthdays is:

P =3* \frac{1}{365}+ (\frac{1}{365})^2\\ P=0.8227\%

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Moesha and Keyon are mailing invitations for their wedding. They have $50 to spend and each invitation costs $1.25 to mail. The
zzz [4051]

Answer:

The solution to the equation is 40

This indicates the max number of wedding invitations they can afford to send within their budget.

Step-by-step explanation:

To find the zero of the function, we set the dependent variable (here, m) to zero.

So we have;

0 = 50-1.25w

1.25w = 50

w = 50/1.25

w = 40

What implication does this have in this context?

Essentially, it means that the couple can send out invitations to a total of 40 people based on their budget.

7 0
3 days ago
The table shows the estimated number of lines of code written by computer programmers per hour when x people are working. A 2-co
tester [3976]

Answer:

Crearemos una tabla con estos valores según diferentes valores de x.

x                  A                 B                C               D

2              66.66          49.3            52.5           50

4             94.57            71.44           106.3         104  

6             134.14           103.57         160.1          158

8             190.27        150.14          213.9         212

10           269.91           217.64         267.7         266

12           382.85          315.5           321.5          320.

Por lo tanto, la función que mejor representa los datos es:

Opción C.

y=26.9x-1.3

Explicación paso a paso:

4 0
9 days ago
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –
Zina [3951]

Answer:

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

Step-by-step explanation:

Given the inequality is -3(2x - 5) < 5(2 - x)

First, simplify both sides:

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember that (-)(-) results in (+)

Thus, -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember that (+)(-) results in (-)

Then, 5(2 - x) = 10 - 5x

Now we have: - 6x + 15 < 10 - 5x

Subtract 15 from both sides

So: - 6x < -5 - 5x

Add 5x to both sides

Thus, - x < - 5

Note that since the coefficient of x is negative, we reverse the inequality sign when dividing both sides by it

∵ The coefficient of x is -1

Therefore, dividing both sides by -1 gives us x > 5

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

7 0
1 day ago
Read 2 more answers
5 Show different ways to make 492,623.
zzz [4051]

Step-by-step explanation:

Begin with expressing 492,623 in standard form.

4 hundred thousands + 9 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones.

We can rephrase this in varied forms by shifting a digit to the next lower place value. For instance, shifting the 4 one place right results in 49 ten thousands:

49 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones.

Next, we can move 49 ten thousands one place right to express it as 492 thousands, and shift 6 hundreds right to yield 62 tens.

492 thousands + 62 tens + 3 ones.

Alternatively, we can phrase it as:

4926 hundreds + 23 ones.

6 0
3 days ago
Two roots of the polynomial function f(x) = x3 − 7x − 6 are −2 and 3. Use the fundamental theorem of algebra and the complex con
lawyer [4047]

Answer:

-1

Step-by-step explanation:

The roots of the polynomial are -2 and 3. According to the zero product property:

x+2=0\\\\x-3=0 \\\\(x+2)(x-3)(x+a)=x^3-7x-6

Given that the last term in the cubic equation is -6, it indicates that a must equal 1 as the product of -2 and 3 already results in -6. This can be verified by expanding the three factors:

(x+2)(x-3)(x+1)=x^3+x^2-3x^2-3x+2x^2+2x-6x-6=x^3-7x-6

Thus, following the zero product property, the final value is -1.

Hope this clarifies!

7 0
14 days ago
Read 2 more answers
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