# A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.

The probability that the next mattress sold is either king or queen-size is P=0.8.

Step-by-step explanation:

We have 3 types of matress: queen size (Q), king size (K) and twin size (T).

We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.

We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:

We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:

Finally, we know that the sum of probablities has to be 1, or 100%.

We can solve this by sustitution:

Now we know the probabilities of each of the matress types.

The probability that the next matress sold is either king or queen-size is:

The probability that the next mattress sold is either king or queen-size is 1.

### Explanation:

To calculate the probability of the next mattress sold being either king or queen-size, we need to consider the information given. Let's assign variables to represent the number of king, queen, and twin-size mattresses sold. Let K represent the number of king-size mattresses, Q represent the number of queen-size mattresses, and T represent the number of twin-size mattresses.

From the first piece of information, we know that Q = (K + T)/4 since the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined.

From the second piece of information, we know that K = 3T since three times as many king-size mattresses are sold as twin-size mattresses.

We can substitute the second equation into the first equation to eliminate K and solve for Q in terms of T. We get Q = (3T + T)/4 = 4T/4 = T.

Therefore, the probability of the next mattress sold being either king or queen-size is the combined probability of selling a king or queen-size mattress. This is the probability of selling a king-size mattress plus the probability of selling a queen-size mattress. Considering T as the total number of mattresses sold, the probability is P(K or Q) = (3T/4T) + (T/4T) = 4T/4T = 1.

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## Related Questions

HELP ASAP WILL MARK BRAINLY

Step-by-step explanation:

let x = 0.616161 (etc.)

make a second equation because you multiply by 100:

100x = 61.616161 (etc.)

subtract from each other

100x = 61.616161

x =  0.616161

you get

99x = 61

solve for x

Find an equation for the line parallel to 3x-5y=2 with​ y-intercept (0,1/5). Write the answer in ​ slope-intercept form.

y= 3x/5 - 2/5 .i think

HELP ASAP ILL GIVE YOU ALL!!! What is the coefficient of (6x^2-4x-5)-

32x-5

Step-by-step explanation:

6x^2-4x-5

36x-4x-5

32x-5

32x-5 would be the answer I’m pretty sure

Divide the fractions:

5/8 divided by 1/24 =

The answer to this question is 15.

Step-by-step explanation:

We know that dividing a fraction by another fraction is the same as multiplying a fraction by the other fractions reciprocal, where the numerator and denominator are switched.

5/8 ÷ 1/24 =

5/8 x 24/1 =

120/8

120 ÷ 8 = 15.

Hence, the answer to this question is 15.

Hope this helps! :D

15

Step-by-step explanation:

5/8 ÷ 1/24

5/8 ÷ 24/1

5/8 × 24/1 = 120/8

120/8 ⇒ 15/1 ⇒ 15

M1Q11.) What percent of women in their 40s taking a screening mammography receive a false positive?

Answer 4. Because there is a 1/10th(0.1) of 0.9851 to receive a false positive.

0.9851×0.1×100=9.851%

is approximately equal to 10%

33 + 2(5+8) - (6-2)2 =

51

Step-by-step explanation:

33+2(5+8)-(6-2)2

openthebracketsFIRST

2(5+8)=26

33+26-(6-2)2

33+18

=51