7
Which statement best describes the relationship
between storage space and number of music files?
As the number of files remains constant, the storage
space used decreases.
As the number of files remains constant, the storage
space used increases.
As the number of files increases, the storage space
used decreases.
Wh
As the number of files increases, the storage space
used increases.

Answer:

9

Step-by-step explanation:

p^2 -4p +4

Let p = -1

(-1)^1 -4(-1) +4

1 +4+4

9

Answer:

b. 1.15

Step-by-step explanation:

The z statistics is given by:

[tex]Z = \frac{X - p}{s}[/tex]

In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.

This means that [tex]X = \frac{13}{53} = 0.2453[/tex]

She find that the proportion of satisfied teachers nationally is 18.4%.

This means that [tex]p = 0.184[/tex]

Standard error:

p = 0.184, n = 53.

So

[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]

Z-statistic:

[tex]Z = \frac{X - p}{s}[/tex]

[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]

[tex]Z = 1.15[/tex]

The correct answer is:

b. 1.15

Answer:

2{3[9+4(7-5)-4]}

2{3[9+4(2)-4]}

2{3[13(2)-4]}

2{3[26-4]}

2{3[22]}

2{66}

132

Step-by-step explanation:

Answer:

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.

b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.

About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.6619.

[tex]p=X/n=370/559=0.6619[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02[/tex]

The critical z-value for a 90% confidence interval is z=1.6449.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948[/tex]

The 90% confidence interval for the population proportion is (0.6290, 0.6948).

Your answer would be 76.2% to the nearest tenth.

We can find this by first dividing 16 by 21 to get 0.7619. which is the proportion as a decimal. To convert this into a percentage, we need to multiply it by 100 to get 76.19% = 76.2% to the nearest tenth.

I hope this helps! Let me know if you have any questions :)

Answer:

The critical value of  [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex] are given by [tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Step-by-step explanation:

The function to be evaluated is [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex], the first derivative of the function must be taken in order to determine the set of critical numbers. Each derivative are found by using the differentiation rule for a sum of functions and rule of chain and subsequently simplified by trigonometric and algebraic means:

First derivative

[tex]f'(\theta) = - 6 \cdot \sin \theta +6\cdot \cos 2\theta[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (\cos^{2}\theta-\sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot [(1-\sin^{2}\theta-\sin^{2}\theta)][/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (1-2\cdot \sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2 - 4\cdot \sin^{2}\theta[/tex]

[tex]f'(\theta) = -4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2[/tex]

The procedure to determine the critical number of the given function are described briefly:

1) First derivative is equalised to zero.

2) The resultant equation is solved.

Then,

[tex]-4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2 = 0[/tex]

Whose roots are:

[tex]\sin \theta_{1} \approx 0.281[/tex] and [tex]\sin \theta_{2} \approx -1.781[/tex]

The sine function is a continuous function with a range between 1 and -1, so, only the first root offers a realistic solution. In addition, such function is positive at first and second quadrants and has a periodicity of [tex]2\pi[/tex] radians, the family of critical values are determined by the unse of inverse trigonometric functions:

[tex]\theta \approx \sin^{-1} 0.281[/tex]

There are two subsets of solutions:

[tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Answer:

[tex]P(\bar X>3.4) = 0.385[/tex]

Step-by-step explanation:

Relevant Data provided according to the question is as follows

[tex]\mu[/tex] = 3.2

[tex]\sigma[/tex] = 0.8

n = 4

According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-

[tex]z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }[/tex]

[tex]P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)[/tex]

[tex]= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }[/tex]

Now, we will solve the formula to reach the probability that is

[tex]= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }[/tex]

[tex]= 1 - P (Z \leq \frac{0.2}{0.4})[/tex]

[tex]= 1 - P (Z \leq 0.5})[/tex]

[tex]= 1 - \phi (0.5)[/tex]

= 1 - 0.6915

= 0.385

Therefore the correct answer is

[tex]P(\bar X>3.4) = 0.385[/tex]

So, for computing the probability we simply applied the above formula.

Answer:

its  21

Step-by-step explanation:

its not 21 i really dont know

Answer:

This question is very simple,

Ok first you will need to find the x and y intercepts by letting y=0 and x=0

First let x=0

so, 0-y=1

y=-1

let y=0

x-0=1

x=1

now we know

x-intercept=(1,0)

y-intercept=(0-1)

Hence, find the graph that has the two corresponding points and that would be the graph you are looking for.

Step-by-step explanation:

We assume that question b is asking for the distribution of [tex] \\ \overline{x}[/tex], that is, the distribution for the average amount of pollutants.

Answer:

a. The distribution of X is a normal distribution [tex] \\ X \sim N(8.6, 1.3)[/tex].

b. The distribution for the average amount of pollutants is [tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].

c. [tex] \\ P(z>-0.08) = 0.5319[/tex].

d. [tex] \\ P(z>-0.47) = 0.6808[/tex].

e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution.

f. [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.

Step-by-step explanation:

First, we have all this information from the question:

a. What is the distribution of X?

The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with [tex] \\ \mu = 8.6[/tex] ppm and [tex] \\ \sigma =1.3[/tex] ppm or [tex] \\ X \sim N(8.6, 1.3)[/tex].

b. What is the distribution of [tex] \\ \overline{x}[/tex]?

The distribution for [tex] \\ \overline{x}[/tex] is [tex] \\ N(\mu, \frac{\sigma}{\sqrt{n}})[/tex], i.e., the distribution for the sampling distribution of the means follows a normal distribution:

[tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].

c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?

Notice that the question is asking for the random variable X (and not [tex] \\ \overline{x}[/tex]). Then, we can use a standardized value or z-score so that we can consult the standard normal table.

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

x = 8.5 ppm and the question is about [tex] \\ P(x>8.5)[/tex]=?  

Using [1]

[tex] \\ z = \frac{8.5 - 8.6}{1.3}[/tex]

[tex] \\ z = \frac{-0.1}{1.3}[/tex]

[tex] \\ z = -0.07692 \approx -0.08[/tex] (standard normal table has entries for two decimals places for z).

For [tex] \\ z = -0.08[/tex], is [tex] \\ P(z<-0.08) = 0.46812 \approx 0.4681[/tex].

But, we are asked for [tex] \\ P(z>-0.08) \approx P(x>8.5)[/tex].

[tex] \\ P(z<-0.08) + P(z>-0.08) = 1[/tex]

[tex] \\ P(z>-0.08) = 1 - P(z<-0.08)[/tex]

[tex] \\ P(z>-0.08) = 0.5319[/tex]

Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is [tex] \\ P(z>-0.08) = 0.5319[/tex].

d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.

Or [tex] \\ P(\overline{x} > 8.5)[/tex]ppm?

This random variable follows a standardized random variable normally distributed, i.e. [tex] \\ Z \sim N(0, 1)[/tex]:

[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]

[tex] \\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ z = \frac{-0.1}{0.21088}[/tex]

[tex] \\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47[/tex]

[tex] \\ P(z<-0.47) = 0.31918 \approx 0.3192[/tex]

Again, we are asked for [tex] \\ P(z>-0.47)[/tex], then

[tex] \\ P(z>-0.47) = 1 - P(z<-0.47)[/tex]

[tex] \\ P(z>-0.47) = 1 - 0.3192[/tex]

[tex] \\ P(z>-0.47) = 0.6808[/tex]

Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is [tex] \\ P(z>-0.47) = 0.6808[/tex].

e. For part d), is the assumption that the distribution is normal necessary?

For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.  

f. Find the IQR for the average of 38 cities.

We must find the first quartile (25th percentile), and the third quartile (75th percentile). For [tex]\\ P(z<0.25)[/tex], [tex] \\ z \approx -0.68[/tex], then, using [2]:

[tex] \\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ (-0.68 *0.21088) + 8.6 = \overline{X}[/tex]

[tex] \\ \overline{x} =8.4566[/tex]

[tex] \\ Q1 = 8.4566[/tex] ppm.

For Q3

[tex] \\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ (0.68 *0.21088) + 8.6 = \overline{X}[/tex]

[tex] \\ \overline{x} =8.7434[/tex]

[tex] \\ Q3 = 8.7434[/tex] ppm.

[tex] \\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868[/tex] ppm

Therefore, the IQR for the average of 38 cities is [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.

Answer:

Ok, we have that f(x) is defined for all real values of x, except for x = x0.

[tex]\lim_{x \to \ x0} f(x)[/tex]

Does it exist? why?

Remember that when we are taking the limit we are not evaluating the function in x0, instead, we are evaluating the function in values really close to x0 (values defined as x0⁺ and x0⁻, where the sign defines if we approach from above or bellow).

And because f(x) is defined in the values of x near x0, we can conclude that  the limit does exist if:

[tex]\lim_{x \to \x0+} f(x) = \lim_{x \to \x0-} f(x)[/tex]

if that does not happen, like in f(x) = 1/x where x0 = 0

where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.

Answers:

a) 0.0625

b) 0.9375

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

Work Shown:

The probability of landing on heads is 1/2 = 0.5 since both sides are equally likely to land on. Getting 4 heads in a row is (1/2)^4 = (0.5)^4 = 0.0625

The event of getting at least one tail is the complement of getting all four heads. This is because you either get all four heads or you get at least one tail. One or the other must happen. We subtract the result we got from 1 to get 1-0.0625 = 0.9375

You can think of it like this

P(getting all four heads) + P(getting at least one tail) = 1

The phrasing "at least one tail" means "one tail or more".

Answer:

6 mg

Step-by-step explanation:

12 mg

0.018 g * 1000 mg/g = 18 mg

18 mg - 12 mg = 6 mg

Answer:

a) 32

b) none?

c) C & F

D) 9/5, 32?

Step-by-step explanation:

Step-by-step explanation:

input x , output y

if x= x1 then y=y1 and y1 is the only value then it is a function

if we get multiple values of y then it is not a function

Answer:

  82.5%

Step-by-step explanation:

It helps to start with the correct formula:

  f(x) = ((6)(1.0) +x(0.3))/(6 +x) . . . . parentheses are required

Then f(2) is ...

  f(2) = (6 +.3(2))/(6+2) = 6.6/8

  f(2) = 82.5%

The point that is a solution to the inequality shown in the graph is:

A. (0,5).

The points that are on the region shaded in blue are solutions to the inequality.

(3,2) and (-3,-6) are on the dashed line, hence they are not solutions. Point (5,0) is to the right of the line, hence it is not a solution, and point (0,5) is a solution, meaning that option A is correct.

More can be learned about inequalities at https://brainly.com/question/25235995

#SPJ1

Answer:

a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]  

b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]

[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]  

[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]  

And replacing we got:

[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.375)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

Part a

[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]  

Part b

[tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]

[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]  

[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]  

And replacing we got:

[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]

Answer:

The solution:

X = 16 and Y = -6

Step-by-step explanation:

The equations to be solved are:

x+y = 10 ------- equation 1

x+2y = 4 ----------- equation 2

we can multiply equation 1 by -1 to make the value of x and y negative.

This will give us

-x- y = - 10 ------- equation 3

x+2y = 4 ----------- equation 2

We will now add equations 3 and 2 together so that x will cancel itself out.

this will give us

y = -10 +4 = -6

hence, we have the value of y as -6.

To get the value of x, we can put this value of y into any of the equations above.  (I will use equation 1)

x - 6 = 10

from this, we have that x = 4

Therefore, we have our answer as

X = 16 and Y = -6

Answer:

When you multiply a difference of squares, two terms cancel each other out and result in a binomial instead of a trinomial. To understand this, you can use an example.

When you multiply (x-3) and (x+3), you can use FOIL to expand them. By doing this, you get x^2-3x+3x-9. As you can see, -3x and 3x cancel each other out, so this results in a binomial instead of a trinomial.

Answer:

when you multiply them the two terms cancel each other out which will result in a binominal

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.

The scale factor = ratio of any two corresponding sides of both similar figures.

Thus,

Scale factor of the similar figures given = 40/10 = 4.

This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.

Scale factor = 4

Answer:

The answer to the best prediction is 115.04

Step-by-step explanation:

We have to:

x = 102

They also tell us that:

y = 5.9 + 1.07 * x

If we replace we have:

y = 5.9 + 1.07 * (102)

y = 115.04

Therefore, the best predicted value of ModifyingAbove and with caret given that the older child has an IQ of 102 is 115.04

Answer:

$2.06

Step-by-step explanation:

$2.99 x 6 = $17.94

$20.00 - $17.94 = $2.06

Hope this helps

Answer: $0.26

Step-by-step explanation:

Cost of 6 pens

= 2.99 x 6

= 17.94

Add sales tax at 10%,

= 17.94 x 1.1

= 19.74

Change due to me

= 20 - 19.74

= 0.26

Answer:

1/90 = 1.11%

Step-by-step explanation:

We have that the number of ways of total selections and assignments possible is a permutation.

We know that permutations are defined like this:

nPr = n! / (n-r)!

In our case n = 10 and r = 2, replacing:

10P2 = 10! / (10 - 2)! = 10! / 8!

10P2 = 90

In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,

Probability would come being the following:

P = 1/90 = 1.11%

Answer:

when a straight line cuts two or more parallel lines then the angles forming on the side of transversal line exteriorly opposite to eachother is called exterior alternative angle.

for eg if AB //CD and EF is a transversal line meeting the parallel lines at G abd H then the exterior alternative angle are angle EGB = angle CHF and angle AGE=angle DHF are two pairs of exterior alternative angle .

hope its helpful to uh !!!!!!

Answer:

216 cm³

Step-by-step explanation:

The volume of a cube is denoted by V = s³, where s is the side length.

Here, the side length is 6 centimetres, so plug this into the formula to find V:

V = s³

V = 6³ = 6 * 6 * 6 = 216

The answer is thus 216 cm³.

~ an aesthetics lover

Answer:

216

Step-by-step explanation:

6³ = 216

Answer: B. Sameer did not use the correct equation

Step-by-step explanation:

12 IS three-fourths OF x

IS: equals

OF: multiplication

[tex]12=\dfrac{3}{4}x[/tex]

48 = 3x

16 = x

Answer:

it's b in Edg

Step-by-step explanation: