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kow [346]
3 years ago
7

Adam has 10 blocks numbered 1 through 10. Which describes the probability of randomly choosing a block that has an even number?

Mathematics
1 answer:
Licemer1 [7]3 years ago
3 0

Answer:

\dfrac{1}{2}

Step-by-step explanation:

Given that:

10 number of blocks which have numbers from 1 through 10.

To find:

Probability of randomly choosing a block that has an even number.

Solution:

The given set of numbers is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

There are a total of 5 Even numbers are {2, 4, 6, 8, 10}.

And There are a total of 5 Odd number are {1, 3, 5, 7, 9}.

Formula for probability of an event <em>E</em> can be observed as:

P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}

Here, Event <em>E </em>is randomly choosing an even number.

Number of favorable cases = 5

Total number of cases = 10

Therefore, the required probability is:

P(E) = \dfrac{5}{10}\\\Rightarrow P(E) = \dfrac{1}{2}

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The diagram shows a 3 cm x 5 cm x 4 cm cuboid
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Answer:

a) The length of segment AC is approximately 5.83 centimeters.

b) The angle ACD is approximately 34.5º.

Step-by-step explanation:

a) Since AB \perp BC, the length of segment AC is determined by Pythagorean Theorem, that is:

AC = \sqrt{(5\,cm)^{2}+(3\,cm)^{2}}

AC \approx 5.831\,cm

The length of segment AC is approximately 5.831 centimeters.

b) Since AB \perp BC \perp AD, the length of segment AD is determined by this Pythagorean identity:

AD = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}+(4\,cm)^{2}}

AD \approx 7.071\,cm

The angle ACD is determined by the following trigonometric expression:

\cos C = \frac{AC}{CD}

\cos C = \frac{5.831\,cm}{7.071\,cm}

\cos C = 0.825

C = \cos^{-1} 0.825

C \approx 34.448^{\circ}

The angle ACD is approximately 34.448º.

4 0
2 years ago
A coin is tossed twice. What is the probability of the coin landing heads up both times
FromTheMoon [43]
1/2 is the probability the coin would land heads up both times.
8 0
3 years ago
How would we rewrite the equation of y = 1/3x -10 if we moved its graph down six units?
levacccp [35]

If you didn't change the slope of the line, but you moved it
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                  y = 1/3 x - 16 .

3 0
3 years ago
Question 1 (1 point)
Naily [24]

Answer:

P ( -1, -3)

Step-by-step explanation:

Given ratio is AP : PB = 3 : 2 = m : n  and points A(5,6) B(-5,-9)

We will calculate coordinates of the point P which divides line segment AB  in the following way:

xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1

xp = -1

yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3

yp = -3  

Point P( -1, -3)

8 0
3 years ago
Given that y = 18 + 3x²<br> i) express x in terms of y
fgiga [73]

Answer:

\sqrt{-6 + \frac{y}{3}} = x

Step-by-step explanation:

y = 18 + 3x²

- 18 - 18

__________

\frac{-18 + y}{3} = \frac{3x^2}{3} \\ \\ -6 + \frac{y}{3} = x^2 \\ \\ \sqrt{-6 + \frac{y}{3}} = x

I am joyous to assist you anytime.

6 0
3 years ago
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