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1 year ago

The number of compact discs N purchased each year, in millions, can be

Mathematics

1 answer:

Aleonysh [2.5K]1 year ago

8 0

Answer:

126.5 years

Step-by-step explanation:

N(t) = 384(1.13)^t

2,000,000,000 = 384(1.13)^t

(1.13)^t = 2,000,000,000/384

log [(1.13)^t) = log (2,000,000,000/384)

t × log 1.13 = log (2,000,000,000/384)

t = [log (2,000,000,000/384)]/(log 1.13)

t = 126.5

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the coordinates of a line segment are (1,6) and (11, -4). what is the length of the line segment? round your answer to the neare

ddd [48]

The length of the line segment AB where $A(x_A;\ y_A)$ and $B(x_B;\ y_B)$

$|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

We have: $A(1;\ 6);\ B(11;-4)$

subtitute

$|AB|=\sqrt{(1-11)^2+(6-(-4))^2}=\sqrt{(-10)^2+10^2}=\sqrt{100+100}\\\\=\sqrt{100\cdot2}=\sqrt{100}\cdot\sqrt2=10\sqrt2\approx14.1$

Answer: b. 14.1

3 0

2 years ago

Find the value of x.

Vladimir79 [104]

Answer:

x= 2√37

Step-by-step explanation:

First thing you want to do is find the length of the missing side where the the right angle is at. You can find that with the pythagorean theorem of the other triangle, since you are already given 2 sides.

Pythagorean Theorem

${a}^{2} + {b}^{2} = {c}^{2}$

a=2

b=?

c=2√2

Plug in and solve for b.

2^2+b^2=(2√2)^2

4+b^2=8

b^2=4

b=2

Now use the pythagorean theorem again to find your x side.

a=2

b=12

c=?

2^2+12^2=c^2

4+144=c^2

148=c^2

c=√148

c=2√37

4 0

2 years ago

A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

8 months ago

Pls help with this problem if u do thx <3

Vitek1552 [10]

<h3>2 Answers: Choice B and Choice D</h3>

======================================

Work Shown:

c = price of coat before discount

0.33c = discount = amount you save

c - 0.33c = original price minus discount = final price

c - 0.33c = 1c - 0.33c = (1-0.33)c = 0.67c = final price

In short, c - 0.33c = 0.67c

They are two ways of expressing the same thing.

You can think of it like saying 100% - 33% = 67%

If you save 33%, then you still have to pay the remaining 67% of the original cost.

-------------

Example:

Let's say the coat is $100 before the discount

c = 100

0.33*c = 0.33*100 = 33 dollars is how much you save

c - 0.33c = 100 - 33 = 67 dollars is the final price

0.67c = 0.67*100 = 67 matches with the previous figure above

8 0

2 years ago

Find all solutions to the equation:

crimeas [40]

Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5

That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n

The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.

Note: The variable n can be any integer.

7 0

2 years ago