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2 years ago

Dan rolls a fair dice and flips a fair coin. What is the probability of obtaining an even number and a head

Mathematics

1 answer:

quester [9]2 years ago

7 0

Answer: 1/4

Step-by-step explanation:

A die has 6 figures which are 1, 2, 3, 4, 5 and 6. There are 3 even numbers which are 2, 4 and 6. A coin has 2 outcomes which are head or tail.

The probability of getting an even number is 3/6 = 1/2.

The probability of getting a head is 1/2.

Therefore, the probability of obtaining an even number and a head will be:

= 1/2 × 1/2

= 1/4

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The altitude of a triangle is 2 m longer than its base. What are the dimensions of the altitude and the base if thearea of the t

HACTEHA [7]

Step-by-step explanation:

Let base of triangle be x m.

Therefore, altitude =( x + 2)m

$area \: of \: \triangle = \frac{1}{2} \times base \times altitude \\ \\ 40 = \frac{1}{2} \times x \times (x + 2) \\ \\ 80 = {x }^{2} +2x \\ \\ {x}^{2} + 2x - 80 = 0 \\ {x}^{2} + 10x - 8x - 80 \\ x(x + 10) - 8(x + 10) = 0\\ (x + 10)(x - 8) = 0 \\ x + 10 = 0 \: \: or \: \: x - 8 = 0 \\ x = - 10 \: \: or \: \: x = 8 \\ base \: can \: not \: be \: - ve \\ x \neq - 10 \\ x = 8 \\ x + 2 = 8 + 2 = 10 \\$

Therefore

Altitude = 10 m

Base = 8 m

8 0

3 years ago

What is the form of the two squares identity?

zvonat [6]

Answer:

Step-by-step explanation:

Consider all options:

A. False, because

$(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ab-cd)^2+(ac+bd)^2=a^2b^2-2abcd+c^2d^2+a^2c^2+2abcd+b^2d^2=\\ =a^2b^2+c^2d^2+a^2c^2+b^2d^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2\neq a^2b^2+c^2d^2+a^2c^2+b^2d^2$

B. False, because

$(a^2-b^2)(c^2+d^2)=a^2c^2+a^2d^2-b^2c^2-b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2-b^2c^2-b^2d^2\neq a^2c^2+b^2d^2+a^2d^2+b^2c^2$

C. False, because

$(a^2+b^2)(c^2-d^2)=a^2c^2-a^2d^2+b^2c^2-b^2d^2\\ \\(ac+bd)^2-(ad+bc)^2=a^2c^2+2abcd+b^2d^2-a^2d^2-2abcd-b^2c^2=\\=a^2c^2+b^2d^2-a^2d^2-b^2c^2\\ \\a^2c^2-a^2d^2+b^2c^2-b^2d^2\neq a^2c^2+b^2d^2-a^2d^2-b^2c^2$

D. True, because

$(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2= a^2c^2+b^2d^2+a^2d^2+b^2c^2$

6 0

3 years ago

Mr.Evans is paid $9.20 per hour for the first 40 hours he works in a week.He is paid 1.5 times that rate for each hour after tha

yKpoI14uk [10]

Answer:

I do not agree. If Mr. Evans worked 42.25 at a rate of $9.20 per hour for the first 40 hours and 1.5 times that rate after, he would have made a total of $399.05.

Step-by-step explanation:

In order to find the total amount that Mr. Evans would have earned last week, we need to first calculate how much he earned in his regular pay at 40 hours. For up to 40 hours, Mr. Evans makes $9.20 per hour, so his total wages earned after 40 hours is: 40 x 9.2 = $368.00. However, Mr. Evans also worked 2.25 hours of overtime at a rate of 1.5 times $9.20 or 9.2 x 1.5 = $13.80. At $13.80 for 2.25 hours, Mr. Evans would earn: 13.80 x 2.25 = $31.05. When you add his base pay of $368.00 plus his over time pay of $31.05, you get a total of $399.05.

8 0

3 years ago

22. Find the missing terms indicated by variables in the arithmetic sequence shown.

yuradex [85]

The complete sequence is<u> 24, 30, 36, 42, 48, 54, 60</u>

<h3>The nth term of an arithmetic progression</h3>

The nth term of an arithmetic progression is expressed according to the equation;

Tn = a + (n-1)d

where

a is the first term

n is the number of terms

d is the common difference

Determine the common difference

d = 42-b = b - 30

-b-b = -30-42

-2b = -72

b = 36

d = 36-30

d = 6

For the first term;

d = 30 - a

6 = 30 - a

a = 24

For the value of c

c = 42 + 6

c = 48

For the value of d

d = 48 + 6

d = 54

For the value of e

e = 54 + 6

e = 60

Hence the complete sequence is<u> 24, 30, 36, 42, 48, 54, 60</u>

Learn more on arithmetic sequence here: brainly.com/question/24989563

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6 0

1 year ago

Evaluate expression below if t=3 <br> 2t+7-t+1

Elena L [17]

Answer:

doo doo fart

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers