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Vika [28.1K]
3 years ago
9

A coin is tossed, and a standard number cube is rolled. What is the probability that the coin shows heads and the number cube sh

ows an even number? A. one-sixth B. 1 C. one-fourth D. one-half
Mathematics
1 answer:
Genrish500 [490]3 years ago
6 0
The correct answer to this question is this one: "C. One-Fourth."

The total possibility that the head and even no on dice appears is 3.

The total possible choices are 12 {head ->(1,2,3,4,5,6) & tail->(1,2,3,4,5,6)}. so the probability is 3/12= 1/4.


These are independent events so the total probability will be the product of the individual probabilities:

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Solve the system of equations using substitution or elimination. Show all work for credit.
Tomtit [17]
Using substitution:
first you have to express one variable in terms of the other, in this we can express y in terms of x:
y =  \frac{ -  \frac{1}{2} x + 2}{3}  \\ y =  - x + 9

Since both expressions are equal to y, you have to equal both expressions like this:
\frac{  - \frac{ 1}{2}x + 2 }{3}  =  - x + 9
Now you can solve the equation:
-  \frac{1}{2} x + 2 = 3( - x + 9) \\   - \frac{ 1}{2}x  + 2 =  - 3x + 27 \\  \\  -  \frac{1}{2} x + 3x = 27 - 2 \\   \frac{5}{2} x = 25 \\ x =  \frac{(25)(2)}{5}  \\ x = 10
Knowing x=10, you can use any of the expressions we found before to find y. In this case I'm going to use y= -x+9 because it's simpler but boy should give you the same result

y =  - (10) + 9 \\ y =  - 1
So, the answer is x=10 and y=-1
4 0
3 years ago
In a class there are 40 students 30 are boys and what is the percentage of girls ....​
Artyom0805 [142]

Answer:

25%

Step-by-step explanation:

Total= 40 students

boys +girls= 40

30 +girls= 40

number of girls

= 40 -30

= 10

Percentage of girls

=  \frac{10}{40}  \times 100\% \\ =  25\%

Alternatively,

percentage of girls

= 100% -(percentage of boys)

= 100\% - ( \frac{30}{40}  \times 100\%) \\  = 100\% - 75\% \\  = 25\%

6 0
3 years ago
An employee at a homemade wooden toy store earned $860 over the past week. The employee needs to pay 14% for Federal Income Tax
Sindrei [870]
Answer:
$713.8

Explanation:
14%of 860 = 120.4

3% of 860 = 25.8

so, subtract the sum of the above 2 values from 860.

860 - (120.4+25.8) = 860-146.2 = 713.8

Hope this helps

4 0
3 years ago
Read 2 more answers
Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC
Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

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ch4aika [34]
I think the answer is C.  The distance over which the force is applied. Hope this helps!
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