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2 years ago

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You want to make five-letter codes that use the letters A, F, E, R, and M without repeating any letter. What is the probability

that a randomly chosen code starts with M and ends with E?

1 answer:

Feliz [49]2 years ago

4 0

Answer:

The probability that a randomly chosen code starts with M and ends with E is 0.05 ....

Step-by-step explanation:

According to the given statement we have to make five letter code from A, F, E, R, and M without repeating any letter. We have to find that what is probability that a randomly chosen code starts with M and ends with E.

Thus the probability of picking the first letter M = 1/5

After that we require the sequence (not E, not E, not E) which is equal to:

= 3/4 * 2/3* *1/2

= 1/4

Now multiply 1/5 and 1/4

1/5 * 1/4

= 1/20

= 0.05

Therefore the probability that a randomly chosen code starts with M and ends with E is 0.05 ....

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Two children are sharing 1/2 of a sandwich. how much will each child get

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Each child will get 1/4 of the sandwich.

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Chandresh is helping his father paint the fence in their back yard. The fence is represented by the shaded part of the diagram b

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B. The total area painted is 864; they must buy two cans of paint.

Step-by-step explanation:

Step 1:

A rectangle's area can be calculated by multiplying its length and its width. The wall is made up of 5 different types of rectangular walls. All walls are 8 feet tall but the length varies.

Step 2:

The area of the 20 feet long wall = $(length)(width)= (20)(8) =160,$

The area of the 10 feet long wall = $(length)(width)= (10)(8) =80,$

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The area of the 4 feet long wall = $(length)(width)= (4)(8) =32,$

The area of the 15 feet long wall = $(length)(width)= (15)(8) =120.$

The area of all the walls = 432 square feet.

Since there are two sides for every wall, total area = $432(2)=864$ square feet.

Step 3:

If one paint can covers 500 square feet,

the number of cans required to paint 864 square feet = $\frac{864}{500} = 1.728$ cans.

so 2 paint cans are needed to paint 864 square feet which is option B.

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2 years ago

We suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in y

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Answer:

D) a chi square test for independence.

Step-by-step explanation:

Given that we suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in years), so we choose a random sample of drivers who have similar automobile insurance coverage and collect data about their ages and insurance premiums.

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1 year ago

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

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Explanation #2

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So what you know is : 17 large dogs, $215 total, $5 for a small dog, $10 for a large dog!

In order to figure out how many small dogs are at the shelter you will need to make this information into an equation!

Since it is 10/ large dog this is 10x
Since it is 5/small dog this is 5y

So now you know that 10x+5y=215

Since you are given the # of large dogs, you can put in that number for x

10(17)+5y=215

170+5y=215 Step 1) Multiply 10 x 17
5y=215-170 Step 2) Move everything without a letter to one side
5y/5=45/5 Step 3) Divide by 5 (Both sides!) to get the y all alone
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