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MariettaO [177]
2 years ago
6

Each week you drive 150 miles. Your car gets 25 miles to the gallon and gas prices are $3 per gallon. How much gas money will yo

u spend on gas each week?
Mathematics
1 answer:
trapecia [35]2 years ago
4 0

x = 6 gal

The money spent for 6 gallons is 3*6 = $18.

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A company that produces fine crystal knows from experience that 13% of its goblets have cosmetic flaws and must be classified as
Kisachek [45]

Answer:

(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c) The probability that at most five must be selected to find four that are not seconds is 0.9453.

Step-by-step explanation:

Let <em>X</em> = number of seconds in the batch.

The probability of the random variable <em>X</em> is, <em>p</em> = 0.31.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.

The probability mass function of <em>X</em> is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...

(a)

Compute the probability that only one goblet is a second among six randomly selected goblets as follows:

P(X=1)={6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=6\times 0.13\times 0.4984\\=0.3888

Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b)

Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:

P (X ≥ 2) = 1 - P (X < 2)

              =1-{6\choose 0}0.13^{0}(1-0.13)^{6-0}-{6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=1-0.4336+0.3888\\=0.1776

Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c)

If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.

P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)

                            ={4\choose 0}0.13^{0}(1-0.13)^{4-0}+{5\choose 1}0.13^{1}(1-0.13)^{5-1}\\=0.5729+0.3724\\=0.9453

Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.

8 0
3 years ago
A manager at a local company asked his employees how many times they had given blood in the last year. The results of the survey
Lubov Fominskaja [6]

Answer:

Var(X) = E(X^2) -[E(X)]^2 = 4.97 -(1.61)^2 =2.3779

And the deviation would be:

Sd(X) =\sqrt{2.3779}= 1.542 \approx 1.54

Step-by-step explanation:

For this case we have the following distribution given:

X        0         1       2       3       4         5        6

P(X)  0.3   0.25   0.2   0.12   0.07   0.04   0.02

For this case we need to find first the expected value given by:

E(X) = \sum_{i=1}^n X_i P(X_I)

And replacing we got:

E(X)= 0*0.3 +1*0.25 +2*0.2 +3*0.12 +4*0.07+ 5*0.04 +6*0.02=1.61

Now we can find the second moment given by:

E(X^2) =\sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2)= 0^2*0.3 +1^2*0.25 +2^2*0.2 +3^2*0.12 +4^2*0.07+ 5^2*0.04 +6^2*0.02=4.97

And the variance would be given by:

Var(X) = E(X^2) -[E(X)]^2 = 4.97 -(1.61)^2 =2.3779

And the deviation would be:

Sd(X) =\sqrt{2.3779}= 1.542 \approx 1.54

 

8 0
3 years ago
The Punnett square shown presents a cross between two piranha. Both parents have large teeth.
Jlenok [28]
The parents both have large teeth, which is dominant. Two dominants make another dominant, so the baby will have large teeth.
5 0
3 years ago
Read 2 more answers
A hockey puck strikes a wall at an angle of 30 degrees. the puck then travels away from the wall at the same angle.
patriot [66]

Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.

<h3>What are supplementary angles?</h3>

Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,

30° + ∠y + 30° = 180°

60° + ∠y = 180°

∠y = 180° - 60° = 120°

Hence, the measure of the ∠y is 120°.

Learn more about Supplementary Angles:

brainly.com/question/2882938

#SPJ1

5 0
2 years ago
Please help, Easy maths.
svetoff [14.1K]

Answer:

x-5y

Step-by-step explanation:

6x-8y-5x+3y

Add or subtract like terms.

1x-5y

8 0
2 years ago
Read 2 more answers
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