Simplify (1/2)4<br> 1/16<br> 1/8 <br>1/4 <br>which one is correct

Suppose 88% of all batteries from a supplier have acceptable voltages. A certain type of flashlight requires two D batteries, an

ira [324]

Answer:

0.3036 = 30.36% probability that at least 9 of the flashlights function properly.

Step-by-step explanation:

For each flashlight, there are only two possible outcomes. Either it works, or it does not. Flashlights are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Flashlight works correctly if both its batteries have acceptable voltages:

Each battery has an 88% = 0.88 probability of working correctly(having acceptable voltage), so the probability of the flashlight working correctly is given by:

$p = (0.88)^2 = 0.7744$

10 flashlights.

This means that $n = 10$

What is the probability that at least 9 of the flashlights function properly?

This is

$P(X \geq 9) = P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{10,9}(0.7744)^{9}.(0.2256)^{1} = 0.2260$

$P(X = 10) = C_{10,10}(0.7744)^{10}.(0.2256)^{0} = 0.0776$

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.2260 + 0.0776 = 0.3036$

0.3036 = 30.36% probability that at least 9 of the flashlights function properly.

6 0

3 years ago

A manufacturing company packages peanuts for piedmont airlines. the individual packages weigh 1.4 grams with a standard deviatio

Kamila [148]

You should subtract 1.03 - 0.6 to get your answer(i really hope so cause i dont like giving wrong answers) 0.43(i was just gonna say "0.43" but no less than 20 characters):)

6 0

3 years ago

If the line is dilated by a factor of 1/3 , what is the equation of the resulting line?

rusak2 [61]

Answer:

The equation of a line on the plane is of the form $f(x)=mx+b$ , with m and b real numbers.

If the line is vertically dilated by a factor of $\frac{1}{3}$ , then the equation of the resulting line g(x) is $g(x)=\frac{1}{3}f(x)=\frac{mx+b}{3}=\frac{m}{3}x+\frac{b}{3}$ .
If the line is horizontally dilated by a factor of $\frac{1}{3}$ , then the equation of the resulting line g(x) is $g(x)=f(\frac{1}{3}x)=m(\frac{1}{3}x)+b=\frac{m}{3}x+b$ .

5 0

3 years ago

Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a · b) · c (a · b) · c has ---Select---

rodikova [14]

Answer:

(a) (a · b) · c has Meaningless because it is the dot product of two scalars.

(b) (a · b)c has Meaningful because it is a scalar multiple of a scalar and a vector .

(c) |a|(b · c) has Meaningful because it is the product of two scalars .

(d) a · (b + c) has Meaningful because it is the dot product of two vectors .

(e) a · b + c has Meaningless because it is the sum of a scalar and a vector.

(f) |a| · (b + c) has Meaningless because it is the dot product of a scalar and a vector .

4 0

3 years ago

A triangle has a perimeter of

lapo4ka [179]

Answer:

The smallest side is 7inches

Step-by-step explanation:

Let the shorter side be y.

The medium side is 4 more than the short side i.e

Meduim side = 4 + y

The longest side is 5 times the length of the shortest side i.e

Logest side = 5y.

Perimeter of the triangle = 53 inches

But the perimeter of a triangle is the Sum of all sides i.e

P = small + medium + large

53 = y + (4+y) + 5y

53 = y + 4 + y + 5y

Collect like terms

53 — 4 = 7y

49 = 7y

Divide both side by 7

y = 49/7

y = 7inches

Therefore the smallest side is 7inches

8 0

3 years ago

Simplify (1/2)4 1/16 1/8 1/4 which one is correct