How many bits does it take to store a 3-minute song using an audio encoding method that samples at the rate of 40,000 samples/second, has a bit depth of 16, and does not use compression

Answer:

The answer is C.

Step-by-step explanation:

Recall SohCahToa, where

[tex]\displaystyle \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex].

In the triangle, the opposite (to angle θ) is [tex]6[/tex], while the adjacent is [tex]2\sqrt{5}[/tex].

By substitution:

[tex]\displaystyle \tan(\theta)=\frac{6}{2\sqrt5}[/tex]

Simplify:

[tex]\displaystyle \frac{6}{2\sqrt{5} } \cdot\frac{\sqrt{5} }{\sqrt{5}} =\frac{6\sqrt{5}}{2(5)} =\frac{6\sqrt{5}}{10}=\frac{3\sqrt{5} }{5}[/tex]

The answer is C.

Answer:

Step-by-step explanation:

by synthetic division

3) 1   -1   -11    15

|       3     6   -15   (add)

____________

   1     2    -5 |0

x²+2x-5=0

[tex]x=\frac{-2 \pm\sqrt{2^{2} -4*1*-5} }{2*1} \\or~x=\frac{-2 \pm\sqrt{4+20} }{2} \\or~x=\frac{-2 \pm2\sqrt{6} }{2} \\or ~x=-1 \pm \sqrt{6}[/tex]

Answer:

14.69% probability that this happens

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

1000 people were given assurance of a room.

This means that [tex]n = 1000[/tex]

Let us assume that each customer cancels their reservation with a probability of 0.1.

So 0.9 probability that they still keep their booking, which means that [tex]p = 0.9[/tex]

Probability more than 900 still keeps their booking:

[tex]n = 1000, p = 0.9[/tex]

So

[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095[/tex]

901/1000 = 0.91

So this is 1 subtracted by the pvalue of Z when X = 0.91.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{0.91 - 0.9}{0.0095}[/tex]

[tex]Z = 1.05[/tex]

[tex]Z = 1.05[/tex] has a pvalue of 0.8531

1 - 0.8531 = 0.1469

14.69% probability that this happens

Answer:

1. it has different colors

Answer:

60

Step-by-step explanation:

Let's name "a number" "q."

The expression we can set up is 6+9q

Plug 6 in for q.

6+9(6)

6+54

60

Answer:

a) Real range of employees hired by each organization surveyed = 56

b) The cumulative percent of "new" employees with the lowest tenure =        30%

Step-by-step explanation:

a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.

Real range of employees hired by each organization surveyed = (89 - 34) + 1

Real range of employees hired by each organization surveyed = 56

b) It is clearly stated in the question that  the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.

Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%

Answer:

n = 296

Sample size n = 296

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

x+/-M.E

M.E = z√(p(1-p)/n)

Making n the subject of formula;

n = (p(1-p)/(M.E/z)^2) .....1

Given that;

Proportion p = 0.26

Number of samples n = ?

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values into equation 1;

n = (0.26(1-0.26))/((0.05/1.96)^2)

n = 295.649536

n = 296

Sample size n = 296

Answer:

a. Probability density function for the battery life

[tex]f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]

b. P(x<11) = 0.7143

Step-by-step explanation:

The question is incomplete

In October, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a. Give a mathematical expression for the probability density function of battery life.

b. What is the probability that the battery life for an iPad Mini will be 11 hours or less (to 4 decimals).

a. We model the battery life as random variable with an uniform distribution with parameters a (min. value)=8.5 hours and b (max. value)=12 hours.

The probability that the battery life takes any value between 8.5 and 12 is constant. Also, the probability that takes any value outside the interval (8.5, 12) is 0.

We can express that as:

[tex]f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]

The last is the probability density function for the battery life.

b. We can calculate P(x<11) using the cumulative density function or integrating the density function between x=0 (or x=a=8.5) and x=11.

[tex]P(x<11)=\int\limits^{11}_{8.5} \dfrac{1}{3.5} \, dx=\dfrac{1}{3.5}(x_2-x_1)=\dfrac{1}{3.5}(11-8.5)=\dfrac{2.5}{3.5}= 0.7143[/tex]

Answer:

plane

Step-by-step explanation:

Answer:

D. Plane

Step-by-step explanation:

A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.

Answer:

3481π or 10935.884

Step-by-step explanation:

Area = πr^2

Area = 3481π or 10935.884

Answer:

3√265

Step-by-step explanation:

The distance between the given points is √265. If all the side are the same length on an equilateral triangle, then the perimeter is 3 times as long.

Answer:

No

Step-by-step explanation:

It is not divisible by 6, for if you divide by 6, you will get a non natural number,

It is obviously divisible by 2.

So, No.

Answer:

no

Step-by-step explanation:

only by 2

614/2 = 307

614/6 = 102.33

Answer:

A production level of 30 thousand units (x = 30)

Step-by-step explanation:

To find the production level (value of x) that will yield the maximum revenue, we can take the derivative of the function R in relation to x and find when it is equal to 0:

dR/dx = -3x2 + 66x + 720 = 0

x2 - 22x - 240 = 0

Solving the quadratic equation using Bhaskara's formula, we have:

Delta = (-22)^2 + 4*240 = 1444

sqrt(Delta) = 38

x1 = (22 + 38)/2 = 30

x2 = (22 - 38)/2 = -8

The negative value is not valid for our problem, so we have that the value that gives the maximum revenue is x = 30

Answer:

21/55

Step-by-step explanation:

Simply multiply the top 2 together:

3 x 7 = 21

And the bottom 2 together:

5 x 11 = 55

21/55 is your answer!

Answer:

(a) The point estimate of the population mean HDL cholesterol level is 49.95.

(b) The point estimate of the value that separates the largest 50% of HDL levels from the smallest 50% is 47.5.

(c) The point estimate of the population standard deviation is 16.85.

Step-by-step explanation:

We are given a sample of 20 observations on HDL cholesterol level (mg/dl) obtained from the survey below;

35, 49, 51, 54, 65, 51, 52,  47, 87, 37, 46, 33, 39, 44,  39, 64, 94, 34, 30, 48.

(a) The point estimate of the population mean HDL cholesterol level is given by the sample mean of the above data, i.e;

        Sample Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

            =  [tex]\frac{35+ 49+ 51+ 54 +65 +51+ 52+ 47+ 87+ 37+ 46+ 33+ 39+ 44+ 39+ 64+ 94+ 34+ 30+ 48}{20}[/tex]  

            =  [tex]\frac{999}{20}[/tex]  =  49.95

So, the point estimate of the population mean HDL cholesterol level is 49.95.

(b) The point estimate of the value that separates the largest 50% of HDL levels from the smallest 50% is given by the Median of the above data.

Firstly, arranging the given data in ascending order we get;

30, 33, 34, 35, 37, 39, 39, 44, 46, 47, 48, 49, 51, 51, 52, 54, 64, 65, 87,  94.

Now, for calculating median we have to first observe that the number of observations (n) in our data is even or odd, i.e;

                      Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                      Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations is even, i.e. n = 20.

So,   Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]  

                      =  [tex]\frac{(\frac{20}{2})^{th} \text{ obs.}+(\frac{20}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{(10)^{th} \text{ obs.}+(11)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{47+48 }{2}[/tex]

        Median  =  47.5

Hence, the point estimate of the value that separates the largest 50% of HDL levels from the smallest 50% is 47.5.

(c) The point estimate of the population standard deviation is given by the following formula;

      Standard deviation, s  =  [tex]\sqrt{\frac{\sum(X-\bar X)^{2} }{n-1} }[/tex]

       =  [tex]\sqrt{\frac{ (30-49.95)^{2}+(33-49.95)^{2}+(34-49.95)^{2}+........+(94-49.95)^{2}}{{20-1}} }} }[/tex]

       =  16.85

Answer:

the vertex of the parabola is at the point; (5, -1)

which agrees with answer "B" in the list of options

Step-by-step explanation:

Notice that this is the equation of a parabola with branches that open horizontally (not vertically), since the variable the goes squared is the y-variable instead of "x".

By analyzing it we can then write it by isolating the term in "x" on one side of the equation, and use at the same time the fact that it is being written in "vertex" form:

[tex]-8\,(x-5)=(y+1)^2\\(x-5)=-\frac{1}{8} (y+1)^2[/tex]

Therefore, the "y-value" of the vertex must be that which renders zero in the expression squared, that is y = -1. On the other hand, the x-value of the vertex is that which renders zero for the variable "x":  x=5.

Then, the vertex of the parabola is at the point; (5, -1)

Accounting theories give an idea of ​​how to do it, how to follow it and the corresponding methodology, therefore the owner of a company must recognize these accounting theories to comply within the company.

We have the following accounting theories:

Comparable: It must be presented in a way, which may be compared thoroughly. Such as sales increased by way of 10% from the closing yr.

Relevant: Accounting information ought to be relevant; such as contemporary yr’s records with relevant facts have to be presented in economic report.

Consistent: Methods applied in accounting ought to be consistent; assume immediately line technique of charging depreciation is accompanied since last 5 years. If such technique is converting heavily, like instantly-line for this year and double declining technique inside the coming yr, then the system isn't regular and it doesn’t indicate smooth accounting.

Reliable: There should be reliability; such as coins bills are supported by way of respective vouchers of coins disbursements.

Answer:

2x/3 + 2= 16

=21

Step-by-step explanation:

Standard form:

2

3

x − 14 = 0  

Factorization:

2

3 (x − 21) = 0  

Solutions:

x = 42

2

= 21

Answer:

Postulate: A plane contains at least three points not all on one line.

Step-by-step explanation:

Given:

G and H are different points in a plane R.

Then a third Point exists in R not on GH.

Suppose there are three points G, H and K. These are non linear points which means they do not lie on the same line. Having three points on the plane means that the plane cannot be drawn with just two points.

These points would make a triangle which is plane R. This is because if the plane could be drawn with two points then that would form a line. But here we know that plane should have at least three points.

Answer:

y = 10 + 2x

or

y = 2x + 10

Step-by-step explanation:

She works a fixed 10 hours each week, so we start with

y = 10

Now she adds 2-hour increments. She can have 0, 1, 2, or another number of increments. x represents the number of increments. Since each increment is 2 hours, 2x represents the number of hours added by the increments. Now we add 2x to the fixed number of hours.

y = 10 + 2x

or

y = 2x + 10

Answer:

y = 2x + 10

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

x + 7 = 6x - 3

Subtract x from each side

x+7-x = 6x-x

7 = 5x-3

Add 3 to each side

7+3 = 5x-3+3

10 =5x

divide by 5

10/5 = 5x/5

2 =x

Answer:

x= 2

hope it helps!

Step-by-step explanation:

x + 7 = 6x - 3

Bring all the variables to one side

So get 6x to the other side

x+7-6x = -3

-5x +7 = -3

Take 7 to the other side

-5x= -3 -7

-5x = -3 + -7

-5x = -10

x = -10/-5

minus n minus becomes plus

x= 10/5

= 2

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

my chile

Answer:

The expression for the height of the plant is: f(x) = 8*(1.16)^x;

The value of f(x+1)/f(x) is 1.16.

Step-by-step explanation:

Since Diego's beanstalk grows at an exponential rate of 16% per day, then the expression that represents the height of the plant, "f", in function of days, "x", can be found as shown below:

Initially the height of the plant was:

[tex]f(0) = 8[/tex]

After the first day however it was:

f(1) = 8*(1 + \frac{16}{100}) = 8*(1.16)

While after the second day:

f(2) = f(1)*(1.16) = 8*(1.16)*(1.16) = 8*(1.16)²

And so on, therefore the expression is:

f(x) = 8*(1.16)^x

The value of f(x + 1)/f(x) is:

[8*(1.16)^(x + 1)]/[8*(1.16)^x]

[8*(1.16)*(1.16)^(x)]/[8*(1.16)^x] = 1.16

Answer:

y = [tex]-9 \frac{1}{2}[/tex]

Step-by-step explanation:

9x-4y = 20

Given that x = -2

Putting in the above equation

9(-2) -4y = 20

-18 - 4y = 20

-4y = 20+18

-4y = 38

Dividing both sides by -4

y = [tex]-\frac{38}{4}[/tex]

y = [tex]-\frac{19}{2}[/tex]

y = [tex]-9 \frac{1}{2}[/tex]

Answer:

19/-2

Step-by-step explanation:

the answer is referred in the picture with the working out. hope it was helpful

Answer:

[tex](\dfrac{94}{100})^{10} \ or\ \approx 0.54[/tex]

Step-by-step explanation:

Given :

Probability that a house in an urban area will be burglarized,

[tex]p =6\%=\dfrac{6}{100}[/tex]

To find:

Probability that none of the houses randomly selected from 10 houses will be burglarized = ?

[tex]P(r=0) =?[/tex]

Solution:

This question is related to binomial distribution where:

[tex]p =\dfrac{6}{100}[/tex]

[tex]\Rightarrow[/tex] Probability that a house in an urban area will not be burglarized,

[tex]q =1-6\%=94\%=\dfrac{94}{100}[/tex]

Formula is:

[tex]P(r=x)=_nC_xp^xq^{n-x}[/tex]

Where n is the total number of elements in sample space and

x is the number selected from the sample space.

Here, x = 10 and

x = 0

[tex]\therefore P(r=0)=_nC_0p^0q^{10-0}\\\Rightarrow 1 \times (\dfrac{6}{100})^0\times (\dfrac{94}{100})^{10}\\\Rightarrow 1\times (\dfrac{94}{100})^{10}\\\Rightarrow (\dfrac{94}{100})^{10}\\\\\Rightarrow (0.94)^{10}\\\Rightarrow \approx 0.54[/tex]

Answer:

No value of k will make AB=BA

Step-by-step explanation:

[tex]A=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right), $ $B=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right) \\\\\\AB=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)=\left(\begin{array}{ccc}3*2+2*-3&3*6+2*k\\-1*2+2*-3&-1*6+2k\end{array}\right)=\left(\begin{array}{ccc}0&18+2k\\-8&-6+2k\end{array}\right)[/tex]

[tex]BA=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)=\left(\begin{array}{ccc}0&16\\-6&-6+2k\end{array}\right)[/tex]

We can see that [tex]AB \neq BA[/tex]. Therefore, there is no value of k that will make it equal. In general, matrix multiplication is not commutative.

Answer:

D

Step-by-step explanation:

The perimeter is 54.6.

a   +  3a      + b = 54.6.   since a = 8.7,

8.7 + 3(8.7) + b = 54.6

8.7 + 26.1 + b = 54.6

34.8 + b = 54.6

b = 54.6 - 34.8

b = 19.8

They pretty much have the exact same examples in the instruction videos with different numbers; it helps to watch the videos again.

Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.

Yes, it's miles true.

Consider the machine as Ax = 0. in which A is 4x5 matrix.

From given dim Nul A=1. Since, the rank theorem states that

The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation

rank A+ dim NulA = n

dim NulA =n- rank A

Rank A = 5 - dim Nul A

Rank A = 4

Thus, the measurement of dim Col A = rank A = five

And since Col A is a subspace of R^4, Col A = R^4.

So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.