11. There is a $10 monthly membership fee to download music. There is
a $0.50 fee for each song downloaded.
a. Write a linear equation that models the cost of downloading x songs
per month.
b. Graph the equation.
c. What is the cost of downloading 15 songs?

Answer:

1. EF ≈ 22.00

2. m∠E ≈ 36.20°

3. m∠F ≈ 53.81°

Step-by-step explanation:

1. Use the trigonometric function sine.

sin(60°) = EF / 25.4

EF = 25.4 sin(60°)

EF ≈ 22.00

2. Use the inverse of the trigonometric function sine (denoted arcsin).

sin(m∠E) = 15/25.4

m∠E = arcsin(15/25.4)

m∠E ≈ 36.20°

3. Use the inverse of the trigonometric function cosine (denoted arccos).

cos(m∠F) = 15/25.4

m∠F = arccos(15/25.4)

m∠F ≈ 53.81°

Jessica has three dice with 10 sides, 13 sides and 5 sides respectively and she rolls all dice once and if Z is number of ones occur then

The expectation value i.e, E(Z) is 0.376 and variance V[Z] = 0.321..

Indicator method :

This is a powerful way to find expected counts. This follows from the observation that the number of "good" outcomes in a trial can be counted by first coding each "good" outcome as one, coding each other outcome as zero, and then adding 1 and 0.

let X₁ be the outcome of a 10 sided die

X₂ be the outcome of 13 sided die

X₃ be the outcome of 5 sided die

let l₁ ,I₂ ,I₃ be three indicator functions such that

I₁ =1 if X₁ = 1

=0 otherwise

I₂ = 1 if X₂ = 1

=0 otherwise

I₃ = 1 if X₃ = 1

=0 otherwise

so Z denotes the number of ones showing when the three dice are rolled once.

so Z=I₁ +I₂ +I₃

so E[Z]=E[I₁]+E[I₂]+E[I₃]

so E[I₁]=1×P[X₁=1] = 1/10

E[I₂]=1×P[X₂=1] = 1/13

E[I₃]=1×P[X₃=1] = 1/5

so, E[Z]=1/10+1/13+1/5=49/130 = 0.3769

the variance = V[Z] = V[I₁]+V[I₂]+V[I₃] since the outcomes of the 3 different die are independent to each other hence no covariance term.

V[I₁]= 1²P[X₁=1]- E²[I₁]=1/10 -(1/10)²= 0.09

V[I₂]= 1²P[X₂=1]- E²[I₂]=1/13-(1/13)²= 12/169 = 0.071

V[I₃]= 1²P[X₃=1]- E²[I₃]=1/5 -(1/5)²= 4/25 = 0.16

so V[Z]= 0.09 + 0.071 + 0.16 = 0.321

Hence, the expectation value i.e, E(Z) is 0.3769..

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Using law of sine and triangle rule, the value of n will be; 443 inches

The law of sines establishes the relationship between the sides and angles of an oblique triangle(non-right triangle). Law of sines and law of cosines in trigonometry are important rules used for "solving a triangle".

We can apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The formula is given as;

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P then;

∠N +  ∠O  +  ∠P = 180

57 + 55 +  ∠P = 180  :

since Sum of angles in a triangle is equal 180 degrees

∠P= 180 - 112

∠P = 68

Using law of sine;

p / sin P = n / sin N

490 / sin68 = n / sin57

n = [(490 x sin 57) / sin 68]

n = 443 inches

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Answer:

-1/2

Step-by-step explanation:

Slope= [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex].

(5-2)/(-8+2)

Simplify:

3/-6

-1/2

Answer:48?

Step-by-step explanation:

I as of now am not completely sure of this is the correct answer.

The number of movies on which Avery's songs were played is 2 times

From the question, we have the following parameters that can be used in our computation:

Songs played in commercial = $40

Songs played in movie = $140

Total earnings = $480

Number of times played on commercial = 7

The above parameters when represented as an equation is

Total earnings = Songs played in commercial * Number of times played on commercial + Songs played in movie * Number of times played in a movie

Substitute the known values in the above equation, so, we have the following representation

40 * 7 + 140 * Number of times played in a movie = 480

Evaluate the products

280 + 140 * Number of times played in a movie = 480

So, we have

Number of times played in a movie = 200/140

Evaluate

Number of times played in a movie = 2

Hence, the number of times is 2 times

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The angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

what is the rate of change in calculus?

The rate of change defines the relationship between two changing variables. Consider a moving object that moves twice as much in the vertical direction (y) as it does in the horizontal direction (x). This can be expressed mathematically as y = 2x.

Let 'θ' represent the angle between the minute and hour hand.

Let θ1 be the angle between the minute hand and 12.

                     [tex]\frac{d\theta_2}{dt}=\frac{1}{60*12}\times2\pi\\\\\frac{d\theta_2}{dt}=\frac{\pi}{360}[/tex](Between hour hand and 12)

                     [tex]\theta=\pm(\theta_1-\theta_2)\\\\\frac{d\theta}{dt}=\pm(\frac{d\theta_1}{dt}-\frac{d\theta_2}{dt})\\\\\frac{d\theta}{dt}=\pm(\frac{\pi}{30}-\frac{\pi}{360})\\\\\frac{d\theta}{dt}=\pm5.5$ degree$[/tex]

Hence the angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

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The probability that a randomly chosen death is a white person who died of diabetes is 0.024 determined using the law of total probability.

The law of total probability is a fundamental rule that connects marginal probabilities to conditional probabilities and expresses the total probability of an outcome via several distinct events. The rule states that if the probability of an event is unknown, it can be calculated using the known probabilities of several distinct events. It is given by P(A ∩ B) = P(A|B)P(B)

In order to determine the probability of an event (D) with not enough information to calculate it directly, a related event, say W can be taken and use that to calculate the probability for D.

Let the events that a person from a certain race die be denoted as:

P(W) = 0.86; P(B) = 0.12; P(A) = 0.02

Let the events that a person from a certain race dies of diabetes be denoted as:

P(D/W) = 0.0.028; P(D/B) = 0.044; P(D/A) = 0.035

Probability that a randomly chosen death is a white person who died of diabetes

P(W) x P (D/W) = 0.86 x 0.028 = 0.02408 ≈ 0.024

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The equation of the line is [tex]y = -\frac{3}{4}x[/tex].

What is the equation of a line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

We have,

the line passes through the point (4,-3),

the points perpendicular to the line 4x - 3y = 3

The equation of a line in slope-intercept form is y = mx + c ( m is the slope and c is the y-intercept).

rearrange 4x - 3y = 3 into this form

subtract 4x from both sides

- 3y = - 4x + 3 ( divide all terms by - 3 )

[tex]y = \frac{4}{3}x - 1[/tex] ← in slope-intercept form

with slope m = 4/3,

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} = \frac{1}{-m} = \frac{1}{-\frac{4}{3} } = \frac{3}{-4}[/tex]

[tex]y = -\frac{3}{4}x + c[/tex] ← is the partial equation

To find c substitute (4, -3) into the partial equation,

-3 = -3 + c

c = -3 + 3

c = 0,

[tex]y = -\frac{3}{4}x[/tex]

Hence, the equation of the line is [tex]y = -\frac{3}{4}x[/tex] .

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Since, the average age of 33 fifth-graders is 11. the average age of 55 of their parents is 33. The average age of all of these parents and fifth graders is 24.75.

Average age of the population calculated as the arithmetic mean. Another parameter determining the average age of the population is the median age. High-level terms.

Given In the question:

Average age of 33 fifth graders is 11 years.

Average age of parents is 33 Years.

Therefore,

The sum of the ages of the fifth graders is 33 × 11,

and, the sum of the ages of the parents is 55 × 33.

Therefore, the total sum of all their ages must be 2178,

and given 33 + 55 = 88 people in total, their average age is

                                  = 2178/88

                                  = 99/4

                                  = 24.75    

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The mathematical domain of the function is 0<or = 5<or = -0.3

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

the type of behavior that is appropriate for a given person, object, or institution; the reason why something exists; a role. any formal event or gathering that is public or social. a variable connected to or reliant upon another variable: A price depends on both supply and demand.

According to the above statements:-

The mathematical domain of the functions are:-

0<or = 5<or = -0.3

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Answer:

WE need to factorise (2x+4y)(2x−4y)

Given identity is (x+a)(x+b)=x

2

+(a+b)x+ab

Here x=2x,a=b=4y

Thus we have (2x+4y)(2x−4y)=(2x) 2

+(4y−4y)+(4y)(−4y)=4x2

−16y 2

The correct option  b. trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.

Trial and error is attempting a way, seeing if it succeeds, and trying a different method if the first one doesn't.

Thus, trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.

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Answer:

D

Step-by-step explanation:

8 3/5 is a number greater than 8 but minor than 9

Answer:-9.9   -7 7.9 9.7

Step-by-step explanation:

A+B+C=180

55+80+x=180

135+x=180

x=180-135

x=45

Answer:b

Step-by-step explanation:

The probability of a person guessing the right combination be

1/720.

Given, a small combination lock on a suitcase has ​wheels, each labeled with the 10 digits from 0 to 9.

we have to find the probability of a person guessing the right combination if there is no repeating of any digit.

as, we need three digit number to unlock the suitcase.

total combinations of the lock be,

10×9×8

= 720

only one combination can open the suitcase,

So, the probability of a person guessing the right combination be

1/720.

Hence, the probability of a person guessing the right combination be

1/720.

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Check the picture below.

The graph which represents the equation f ( x ) = [ x + 1 ] is Option 4.

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = [ x + 1 ]

The function f ( x ) can be written as

y = [ x + 1 ] , where the equation f ( x ) = y

Substituting the value for x , we get

a)

when x = 0

The value of equation is

y = [ x + 1 ]

y = [ 0 + 1 ]

y = 1

So , the coordinates are ( 0 , 1 )

b)

when x = 1

The value of equation is

y = [ x + 1 ]

y = [ 1 + 1 ]

y = 2

So , the coordinates are ( 1 , 2 )

c)

when x = 2

The value of equation is

y = [ x + 1 ]

y = [ 2 + 1 ]

y = 3

So , the coordinates are ( 2 , 3 )

d)

when x = -1

The value of equation is

y = [ x + 1 ]

y = [ -1 + 1 ]

y = 0

So , the coordinates are ( -1 , 0 )

Hence ,

On plotting the points in the graph , we get the equation as y = x + 1

And the solution is Option D.

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The efficiency of slotted aloha by letting n approach infinity is 1/e and the maximum value of probability is 1/n.

Given that:

No. of nodes = (n)

The efficiency of slotted aloha by letting n approach infinity is E (p)= np(1-p)^(n-1).

By derivation,

E' (p) =  n(1-p)^(n-1) - np(n-1)(1-p)^(n-2)

E' (p) =  n(1-p)^(n-2) x [(1- p) - p(n-1)]

E' (p) =  n(1-p)^(n-2) x [1-np]

Let E'(p) =0

i.e. Either,  n(1-p)^(n-2) = 0

=> p = 1 (minima)

Or [1-np] = 0

=> p = 1/n (maxima)

So, for the value of p* = 1/n, we can maximize this expression.

When  p = 1/n, the efficiency of slotted aloha is

E(p*) = n.1/n (1-1/n)^(n-1)

E(p*) = (1-1/n)^(n-1)

E(p*) = (1-1/n)^n/(1-1/n)

Since, [tex]\lim_{n \to \infty} (1-1/n) = 1\\[/tex]

[tex]\lim_{n \to \infty} (1-1/n)^n = 1/e[/tex]

So, when n approaches infinite,

Efficiency =>  [tex]\lim_{n \to \infty} E(p*) = 1/e[/tex]

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The correct answer is The standard deviation for Portfolio P is less than 25

This response is accurate because a portfolio made up of two stocks with a correlation of less than one will always have a standard deviation that is lower than the standard deviation of the stocks added in accordance with their weight in the portfolio. For example, in this scenario, both stocks have a weight of 50% and a standard deviation of 25%, so their sum will be.

The portfolio standard deviation will be smaller than 25% since (0.5*25%) + (0.5*25%) = 25%.

Therefore, the standard deviation for Portfolio P is less than 25

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If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant

The coordinates of the point p = (x, y)

In the graph, there are four quadrants.

In first quadrant the x axis value and y  axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative

Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.

Therefore, the location of will be on third quadrant

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Answer:

A

Step-by-step explanation:

The others involve more multiplication and addition/subtraction rather than division.

Answer:

24

Step-by-step explanation:

Answer:

- 63

Step-by-step explanation:

Let's translate the sentences into expressions:

1. "product of negative 12 1/2 and 4.8" means:

      (-12 1/2)*(4.8)

    I'll simplify this by stating (-12.5)*(4.8)

2.   "three less than" means subtract 3, or

      -3

Now combine the two expressions:

   (-12.5)*(4.8) - 3

   (-60) - 3

= - 63

Answer:

Step-by-step explanation:

$28.75

The critical value of z separates the rejection region from the nonrejection region while observed value of z is the value calculated for a sample statistic such as x.

A critical value of z is used when the sampling distribution is normal, or close to normal. The critical value of z refers to the point that cuts off area under graph for the standard normal distribution separating the rejection and nonrejection region of the data. The Critical value of z can indicate what probability any particular variable will have. These values are typically obtained from a table such as the standard normal distribution table. The observed value of z is a value determined for a sample statistic x. It is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.

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Answer:If Amy is not tardy, then she will not get a detention

Step-by-step explanation:

Answer: 212.50

Step-by-step explanation: she has 60% or  127.5