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melamori03 [73]

3 years ago

6

You have a bag with two coins. One will come up heads 40% of the time, and the other will come up heads 60%. You pick a coin ran

domly, flip it and get a head. What is the probability it will be heads on the next flip?

1 answer:

Gnom [1K]3 years ago

5 0

Answer:

13/50

Step-by-step explanation:

First, we need to put all the possible scenarios.

Let's call coin A as the coin that flips head 40% of the time, and coin B the 60% of the time.

Now, 40% in fraction is 40/100 = 4/10 = 2/5 for coin A. This is the probability of the coin A to get head. (Pa)

60% of the time is 60/100 = 6/10 = 3/5. Probability to get head in coin B (Pb)

Now, we don't know which coin is picked, all we know is that the first flipping is head. so, as the coins are picked randomly, we have 1/2 probability to choose either coin A or coin B, so, let's suppose we picked coin A:

Pa = 1/2 * 2/5 = 2/10 * 2/5 = 4/50

If the coin picked is coin B:

Pb = 1/2 * 3/5 = 3/10 * 3/5 = 9/50

So, finally the probability that if we flip the coin a second time, to get a head, no matter which coin was picked, is just the sum of both probabilities so:

P = 4/50 + 9/50 = 13/50

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Trapezoids and kites

lisov135 [29]

QUESTION 3

The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 36\degree +70\degree+m$ .

$\Rightarrow 106\degree+m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

But the two remaining opposite angles of the kite are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

QUESTION 4

RH is the hypotenuse of the right triangle formed by the triangle with side lengths, RH,12, and 20.

Using the Pythagoras Theorem, we obtain;

$|RH|^2=12^2+20^2$

$|RH|^2=144+400$

$|RH|^2=544$

$|RH|=\sqrt{544}$

$|RH|=4\sqrt{34}$

QUESTION 5

The given figure is an isosceles trapezium.

The base angles of an isosceles trapezium are equal.

Therefore $m$

QUESTION 6

The measure of angle Y and Z are supplementary angles.

The two angles form a pair of co-interior angles of the trapezium.

This implies that;

$m$

$\Rightarrow m$

$\Rightarrow m$

QUESTION 7

The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 48\degree +110\degree+m$ .

$\Rightarrow 158\degree+m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

But the two remaining opposite angles are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

QUESTION 8

The diagonals of the kite meet at right angles.

The length of BC can also be found using Pythagoras Theorem;

$|BC|^2=4^2+7^2$

$\Rightarrow |BC|^2=16+49$

$\Rightarrow |BC|^2=65$

$\Rightarrow |BC|=\sqrt{65}$

QUESTION 9.

The sum of the interior angles of a trapezium is $360\degree$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

But the measure of angle M and K are congruent.

$\Rightarrow m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

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6 0

3 years ago

Translate the sentence into an equation. Six more than the quotient of a number 5 and 9 equals . Use the variable y for the unkn

sashaice [31]

the answer is 6+5y=9

7 0

3 years ago

A pair of $36 jeans were on sale at Jim's Jeans for 1/3 off. The same pair of jeans were $42 at David's Denims. The jeans were o

nikklg [1K]

Complete question :

A pair of $36 jeans were on sale at Jim's Jeans for 1/3 off. The same pair of jeans were $42 at David's Denims. The jeans were on sale for 2/3 off.

A.) which store had the better buy

B.) how much will you pay at the store that has the better buy

Answer:

A.)David's denim has the better buy

B.) $14

Step-by-step explanation:

Jim's Jean store :

Cost of Jean = $36

Discount = 1/3 off

Discounted cost = $36 - (1/3 * $36)

Discounted cost = $36 - $12 = $24

David's Denim:

Cost of Jean = $42

Discount = 2/3 off

Discounted cost = $42 - (2/3 * $42)

Discounted cost = $42 - $28 = $14

David's denim has the better buy with a discounted price lower than the discounted price at Jim's store.

Cost at store with the better buy is $14

8 0

3 years ago

7x < 10<br> please solve

Anvisha [2.4K]

Answer: The answer would be x < 10/7

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

7*x (10)>0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1 Pull out like factors :

7x - 10 = -1 • (7x + 10)

Equation at the end of step

1

:

STEP 2

:

2.1 Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

7x+10 < 0

2.2 Divide both sides by 7

x+(10/7) < 0

Solve Basic Inequality :

2.3 Subtract 10/7 from both sides

x < 10/7

Inequality Plot :

2.4 Inequality plot for

7.000 x - 10.000 > 0

One solution was found :

x < 10/7

4 0

3 years ago

A machine packs at a constant rate of 2/3 of a box every 1/2 minuet. What’s is the number of boxes per minute that’s the machine

lions [1.4K]

For this case what we can do is the following rule of three:
2/3 of a box ------> 1/2 minutes
x of a box ---------> 1 minute
Clearing x we have:
x = (1 / (1/2)) * (2/3)
Rewriting:
x = 2 * (2/3)
x = 4/3
Answer:
the number of boxes per minute that the machine packs is:
x = 4/3

4 0

4 years ago