A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, there were 1140 downloads of the song, for a total download size of 4522 MB. How many downloads of the standard version were there?

Answer:

a. The 95% confidence interval for the difference in mean is C.I. = -3.6 < μ₂ - μ₁ < 4.96

B. We are 95% confident that the difference in mean FNE scores for bulimic and normal students is inside the confidence interval

c.  The assumptions made are;

The variance of the two distributions are equal

Step-by-step explanation:

The given parameters are;

The mean for the 11 students with an eating disorder, [tex]\overline x_1[/tex] = 13.82

The standard deviation for the 11 students with an eating disorder, s₁ = 4.92

The mean for the 14 students who do not have an eating disorder, [tex]\overline x_2[/tex] = 13.14

The standard deviation for the 14 students with an eating disorder, s₂ = 5.29

a. The 95% confidence interval for the difference in mean is given as follows;

[tex]\left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2}\sqrt{ \hat \sigma^2 \times\left( \dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right)}[/tex]

The pooled standard deviation, is therefore;

[tex]\hat{\sigma} =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]

Therefore;

[tex]\hat{\sigma} =\sqrt{\dfrac{\left ( 11-1 \right )\cdot4.92^{2} +\left ( 14-1 \right )\cdot 5.29^{2}}{11+14-2}} \approx 5.13241[/tex]

Where at degrees of freedom, df = n₁ + n₂ - 2 = 25 - 2 = 23 the critical-t = 2.07

\left (13.82- 13.14  \right )\pm 2.07 \times\sqrt{5.13241^2 *(\dfrac{1}/{11}+\dfrac{1}{14}\right)}

[tex]C.I. = \left (13.82- 13.14 \right )\pm 2.07 \times\sqrt{5.13241^2 \times\left(\dfrac{1}{11}+\dfrac{1}{14}\right)}[/tex]

Therefore, we get;

[tex]C.I. = 0.68\pm 4.28[/tex]

C.I. = -3.6 < μ₂ - μ₁ < 4.96

b. Therefore, given that the confidence interval extends from positive to negative, therefore, there is a possibility that there is no difference between the mean FNE scores for bulimic and normal students

B. We are 95% confident that the difference in mean FNE scores for bulimic and normal students is inside the confidence interval

c.  The assumptions made are;

The variance of the two distributions are equal

Answer:

2x-4=3x+9

    +4     +4

2x=3x+13

-3x -3x

-x=13

x= -13

Step-by-step explanation:

Answer:

The first one.

Step-by-step explanation:

Answer:

x=8/15

Step-by-step explanation:

2x-1/4+3x-2/3=25/12

2x+3x=25/12+1/4+1/3

5x=25/12+3/12+4/12

5x=32/12

5x=8/3

x=8/3÷5

x=8/15

Answer: 3 over 5

Step-by-step explanation:

Answer:

hewo nice to meet ya

Step-by-step explanation:

hi hello

Answer:

Hola!

*Spanish*

Gracias por los puntos!

Answer:

Your CORRECT answer will be B

Step-by-step explanation:

It is definantely not A, because it 102, not 120, so it b, c, or d.

102.081 sounds exact, but what about C? You cannot leave out the 0, so that's out too! 102.801? Say it out loud, doesn't make sense! So you have only one answer left, C.

Mark me brainliest!

Answer:

x=7°      y=4°

Step-by-step explanation:

7x+131=180

7x=180-131=49

x=49/7=7°

11x+y+99=180

77+y+99=180

y=180-99-77

y=4°

Answer:

It is x = 7 1/3

Step-by-step explanation:

2 feet is being used in the scale factor and 2 x 3 2/3 is 7 1/3.

Please mark as brainliest

Answer:

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

we have:

[tex]scale \: factor = \frac{smaller \: length}{larger \: length} [/tex]

let the length be x.

we have

[tex]2 = \frac{x}{3 \frac{2}{3} } [/tex]

[tex]x = 2 \times \frac{11}{3} [/tex]

[tex]x = 7 \frac{1}{3} [/tex]

so.

C .[tex]x = 7 \frac{1}{3} [/tex] is your answer

Answer:

24 different options

Step-by-step explanation:

3 cake type options

2 frosting options

4 radius sizes

3 * 2 * 4 = 24 different options

Answer:Answer: 26 ft.

Step-by-step explanation:

Answer:

Last option, $58.50

Step-by-step explanation:

Let's look at the graph, and let's do a simple analysis of the information that it shows.

We can see that in 2009, the price was between $30 and $40.

We can see that as the years pass by, the price increases, such that in the year 2013 the selling price spikes and ranges between a bit less than $50 to a little more than $50.

Then we can only expect that a few years later (in 2016) the price to be larger than $50.

The only option that has a price larger than $50 is the last one, $58.50, then that one is the only option that can be the correct one.

We also could do an exact calculation of this if we had the raw data, but as you can see in the graph, we can not know the exact price of each graphed point (we can only estimate it) so we will not get a nice interpolation by only using the given graph.

Answer:

Step-by-step explanation:

the concepts are confusing of what a function is.   f(x)  seems mysterious , huh

it's just a way to give a label to some set of terms.  Just think of it as a name of a person, but in a generic sense, like   hey "guy"   or hey "gal"  you can address many people that way.  f(x) is doing that same thing addressing by a name,  a set of math terms.  

a)  

in a)  we are addressing the g(x) function and we are also sending that function the number -2 as an input. so find the g(x) function and put in (-2) everywhere that there is an "x" , so

g(x)=[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11

g(-2) = [tex](-2)^{3}[/tex]-3[tex](-2)^{2}[/tex]+2(-2)+11

g(-2) = -8 -3(4) - 4 +11

g(-2) = -8 -12 -4 + 11

g(-2) = -24 + 11

g(-2) = -13

b)  

h(-1)  find the h(x) function and input a negative 1 where ever there is an x

h(x) =

h(-1) = [tex](-1)^{2}[/tex] - 3

h(-1) = 1 - 3

h(-1) = -2

c)

for c)  just combine like terms of the two given functions

g(x) - h(x)  =  [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - ([tex]x^{2}[/tex] - 3)

g(x) - h(x)  = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - [tex]x^{2}[/tex] + 3

g(x) - h(x)  = [tex]x^{3}[/tex]-4[tex]x^{2}[/tex]+2x + 14

d)

-2f(x) - h(x) = -2(3x + 2) - ([tex]x^{2}[/tex] - 3)

-2f(x) - h(x) = -6x - 4 - [tex]x^{2}[/tex] + 3

-2f(x) - h(x) = -6x - 1 - [tex]x^{2}[/tex]

-2f(x) - h(x) = - [tex]x^{2}[/tex] - 6x - 1

e)

f(h(x))  this gets a bit more confusing b/c it's  a composition of functions,  that's just a fancy way of saying the functions are nested. one inside the other.

f(x) = 3x + 2

h(x) = [tex]x^{2}[/tex] - 3

plug h(x) in to f(x) where ever there is an x in f(x)   , luckily there is only one x in f(x)  :)

f(h(x)) = 3([tex]x^{2}[/tex] - 3) + 2

f(h(x)) = 3[tex]x^{2}[/tex] - 9 + 2

f(h(x)) = 3[tex]x^{2}[/tex] - 7

f(h(x)) = 3[tex]x^{2}[/tex] + 0x + (-7)  

f)

f(x) = 3x + 2

g(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11

f(g(x)) = 3([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11) + 2

f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 33 + 2

f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 35

Hope that helps :)

Answer:

In order to maximize profit, each widget should sell for $26.70.

Step-by-step explanation:

The total amount of profit y given by the selling price of each widget x is given by:

[tex]y=-15x^2+801x-5900[/tex]

And we want to determine the price of each widget such that is yields the maximum profit.

Since the equation is a quadratic, the maximum profit will occur at the vertex of our parabola.

The vertex of a quadratic is given by:

[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]

So, let's find the vertex. In our equation, a = -15, b = 801, and c = -5900.

Therefore, the price that maximizes profit is:

[tex]\displaystyle x=-\frac{801}{2(-15)}=\$26.70[/tex]

Therefore, in order to maximize profit, each widget should sell for $26.70.

Notes:

Then substituting this back into the equation, the maximum profit is:

[tex]y_{\text{max}}=-15(26.7)^2+801(26.7)-5900=\$ 4793.35[/tex]

Answer:

area = 5.3 m²

Step-by-step explanation:

r = d/2 = 2.6/2

r = 1.3

area = πr² = (3.14)(1.3²) = 5.31 m²

The area of a circle is pi r^2

if the diameter is 2.6m

r=d/2

=1.3

area= 22/7*2.6^2

=21.245m^2

Round to the nearest 10th

=20m^2

Answer:20m^2

Answer:

We have to flip the coin 78 times.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

We suspect that the coin is fair.

This means that [tex]\pi = 0.5[/tex]

96.5% confidence level

So [tex]\alpha = 0.035[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.035}{2} = 0.9825[/tex], so [tex]Z = 2.108[/tex].

How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head?

n times, and n is found when M = 0.12. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.12 = 2.108\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.12\sqrt{n} = 2.108*0.5[/tex]

[tex]\sqrt{n} = \frac{2.108*0.5}{0.12}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.108*0.5}{0.12})^2[/tex]

[tex]n = 77.1[/tex]

Rounding up

We have to flip the coin 78 times.

Answer:

(5.4582 ; 6.8618)

Step-by-step explanation:

Given the data:

6 10 2 6 3 3 3 6 6 6 6 5 8 9 10 10 7 9 3 6 5 10 9 9 10 3 8 6 6 3 3 6 6 5 4 10 9 3 5 7 10 6 3 8 6 8 3 3 5 5

Sample mean, xbar = Σx / n

n = sample size = 50

ΣX = 308

xbar = 308 / 50 = 6.16

Using a Calculator :

The sample standard deviation, s = 2.469

Confidence interval = xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Tcritical at 95% ; df = 50 - 1 = 49

Tcritical = 2.010

Hence,

Margin of Error= 2.010 * (2.469/sqrt(50)) = 0.7018

Lower boundary : (6.16 - 0.7018) = 5.4582

Upper boundary : (6.16 + 0.7018) = 6.8618

(5.4582 ; 6.8618)

Answer:

[tex](7 \times 2 + 8) - ( {x}^{2} - 2) \\ (14 + 8) - ( {x}^{2} - 2) \\ 14 + 8 - {x}^{2} + 2 \\ 22 + {x}^{2} + 2 \\ 24 + {x}^{2} [/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

She has 36 shells

9+(9*3)

9+27

=36

Please mark as brainliest. :)

Answer:

the diameter is 18 inches

The area of the garden be  after he doubles the length and width is 160 square feet.

Given that,

Based on the above information, the calculation is as follows:

We know that

Area = (length) (width)

Now if the area is doubled

So,

= (2) (length)  (2) (width)

= 4(length) (width)

= 4 (40)

= 160

Therefore, we can conclude that option b is correct.

Learn more: brainly.com/question/24169758

i hope this helps- im not sure if its correct or not

Answer:

b is the answer

Step-by-step explanation:

a triangle equals up to 180 degrees and 75+43+62 equals 180

Answer:

C ) .   B= A/C

Step-by-step explanation:

A=bxc

A/C=B

Answer:

y = 6

Step-by-step explanation:

-2y = 4x – 4

y = -2x + 2

7x = -4(-2x+2) + 10

7x = 8x-8+10

7x = 8x+2

7x -2 = 8x

-2 = x

plug this into the first equation and the value of y is 6

The value of y using substitution method on the given simultaneous equations is; y = -2

We are given the equations;

-2y = 4x - 4 - - -(eq 1)

7x = - 4y + 10 - - - (eq 2)

From eq 1, divide through by -2 to isolate y;

y = -2x + 2

Substitute -2x + 2 for y in eq 2 to get;

7x = -4( -2x + 2) +10

Expand the bracket to get;

7x = 8x - 8 + 10

7x = 8x + 2

8x - 7x = 2

x = 2

Put 2 for x in y = -2x + 2 to get;

y = - 2(2) + 2

y = -4 + 2

y = -2

Read more about substitution method at; https://brainly.com/question/16863577

Answer:

23.75+0.35x=Y

Step-by-step explanation:

It starts at $23.75. $0.35 is per mile so that means it will have an x. Add the two up and it is y.

Answer:

24 square units is the answer

Answer:

the area is 32.5

Step-by-step explanation:

Answer: 0.05$ per ounce

Step-by-step explanation:

Answer:0.05 per oz.

Step-by-step explanation: divide 4.50 by the oz