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mash [69]
2 years ago
3

In a box of 50 markers, 30 markers are either red or black and 20 are missing their caps. If 12 markers are either red or black

and are missing their caps, find the probability that a randomly selected marker is red or black or is missing its cap.
a 0.38
b. 1
c 0.76
d. 0.24
Mathematics
1 answer:
Eddi Din [679]2 years ago
7 0

Answer:

c 0.76

Step-by-step explanation:

Red or Black  (A)= 30

Missing cap (B)= 20

Red or black and missing cap (A&B) = 12

Total number of markers = 50

The total number of markers that are red or black or is missing its cap is:

n= A+B-(A\cap B)=30+20-12=38

The probability of picking of those markers randomly is:

P=\frac{38}{50}=0.76

The probability that a randomly selected marker is red or black or is missing its cap is 0.76.

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Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to
nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)

Step-by-step explanation:

Part 1)

The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

\displaystyle L \approx f'(a)(x-a) + f(a)

We want to verify that the expression:

1-36x

Is the linear approximation for the function:

\displaystyle f(x) = \frac{1}{(1+9x)^4}

At <em>x</em> = 0.

So, find f'(x). We can use the chain rule:

\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)

Simplify. Hence:

\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}

Then the slope of the linear approximation at <em>x</em> = 0 will be:

\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36

And the value of the function at <em>x</em> = 0 is:

\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1

Thus, the linear approximation will be:

\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x

Hence verified.

Part B)

We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.

In other words:

\displaystyle \left| f(x) - L(x) \right | \leq 0.1

By definition:

\displaystyle -0.1\leq f(x) - L(x) \leq 0.1

Therefore:

\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)

4 0
2 years ago
Suppose you have a litter of mice which consists of 8 males and 4 females. If you randomly grab two of them, what is the probabi
tiny-mole [99]

Answer:

The probability that they are both male is 0.424 (3 d.p.)

Step-by-step explanation:

The first step is to find the probability of the first selection being male. This is calculated as number of male mice divided by total number of mice in the litter

Prob (1st male) = 8 ÷ 12 = 0.667

Next is to find the probability of the second selection also being male. Note that the question states that the first mice was selected without replacement. This means the first mouse taken results in a reduction in both the number of male mice and total number of mice in the litter.

Prob (2nd male) = (8 - 1) ÷ (12 - 1) = 7/11 = 0.636

Therefore,

Prob (1st male & 2nd male) = 0.667 × 0.636 = 0.424

5 0
2 years ago
Which statements describe an object in motion that has no external force acting on it? Check all that apply.
Step2247 [10]

Answer: it moves at a constant speed and stays in the same direction

Step-by-step explanation:

It does this because there is no friction or nothing pushing on it therefore there is nothing to slow it down or speed it up

5 0
2 years ago
Read 2 more answers
A hospital takes record of any birth that occurs there every day. On one day, the hospital reports that 35 of the 62 babies born
andre [41]

Answer:

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standar
Llana [10]

Answer:

a) The probability that a random movie is between 1.8 and 2.0 hours = 0.2586.

b) The probability that a random movie is longer than 2.3 hours is 0.0918.

c) The length of movie that is shorter than 94% of the movies is 1.4 hours

Step-by-step explanation:

In the above question, we would solve it using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation

a) A random movie is between 1.8 and 2.0 hours

z = (x-μ)/σ,

x1 = 1.8,

x2 = 2.0

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z1 = (1.8 - 1.9)/0.3

z1 = -1/0.3

z1 = -0.33333

Using the z score table

P(z1 = -0.33) = 0.3707

z2 = (2.0 - 1.9)/0.3

z1 = 1/0.3

z1 = 0.33333

p(z2 = 0.33) = 0.6293

= P(- 0.33 ≤ z ≤ 0.33)

= 0.6293 - 0.3707

= 0.2586

The probability that a random movie is between 1.8 and 2.0 hours = 0.2586

b) A movie is longer than 2.3 hours

z = (x-μ)/σ,

x1 = 2.3

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z = (2.3 - 1.9)/0.3

z = 4/0.3

z = 1.33333

P(z = 1.33) = 0.90824

P(x>2.3) = = 1 - 0.90824

= 0.091759

≈ 0.0918

The probability that a random movie is longer than 2.3 hours is 0.0918.

3) The length of movie that is shorter than 94% of the movies.

z = (x-μ)/σ

Probability (z ) = 94% = 0.94

Movie that is shorter than 0.94

= P(1 - 0.94) = P(0.06)

Finding the P (x< 0.06) = -1.555

≈ -1.56

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

-1.56 = (x - 1.9)/ 0.3

Cross multiply

-1.56 × 0.3 = x - 1.9

- 0.468 + 1.9 = x

= 1.432 hours

≈ 1.4 hours

Therefore, the length of movie that is shorter than 94% of the movies is 1.4 hours

5 0
2 years ago
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