A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, there were 1420 downloads of the song, for a total download size of 5436 MB. How many downloads of the high-quality version were there?

to get the equation of any straight line, we simply need two points off of it, let's use those two in the table

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{Year}{x}&\stackrel{students}{y}\\ \cline{1-2} 1&8295\\ 2&8072\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{8295})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8072}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8072}-\stackrel{y1}{8295}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ -223 }{ 1 } \implies - 223[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8295}=\stackrel{m}{- 223}(x-\stackrel{x_1}{1}) \\\\\\ y-8295=-223x+223\implies {\Large \begin{array}{llll} y=-223x+8518 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{for year 4, x = 4}}{y=-223(4)+8518} \implies y=7626~students[/tex]

An example of a rational function is the first equation given, f(x)=3x²+1 over x-1.

A rational function is a type of function that can be expressed as the ratio of two polynomials. In this equation, the numerator is a polynomial of degree 2 (3x²+1), and the denominator is a polynomial of degree 1

(x-1).

The second equation given, x over 3 = 8 over 3, is not an example of a rational function. This equation is a rational expression, which is an expression that is the ratio of two polynomials, but it is not a function because it does not map a single input to a single output.

The third equation given, 1 over 3x-1 +3<0, is not an example of a rational function either. This equation is an inequality, not a function, and it does not have a ratio of two polynomials.

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On translating n 1 unit right and 4 unit up , we get the coordinates of B as  B'( 3, 9).

The given triangle ABC has the following vertices A(1, 3), B(2, 5), and C(5, 3).

We will apply the translation rule on the following triangle,

T⟨1, 4⟩

A(1, 3)

A( 1+ 1 , 3+ 4 ) = A( 2, 7)

B(2, 5)

B( 2+ 1 , 5+ 4 ) = B( 3, 9)

C(5, 3)

( 5+ 1 , 3+ 4 ) = C ( 6, 7)

Therefore , the coordinates of B'  is B'( 3, 9) as calculated after using the rule.

Translation rule is a rule in mathematics which moves a shape left , right , up or down. The newly formed shape is the same as before , just their direction gets changed.

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Answer:

[tex]84.13^{\circ}[/tex]

Step-by-step explanation:

By the exterior angle theorem, the answer is [tex]m\angle y+m\angle z=84.13^{\circ}[/tex].

Answer:

Step-by-step explanation:

USE THE EXTERIOR ANGLE THEROME!
FIRST

THE FOMULA

a+b=c

y+z=x

now we have to add y and z

45.43 + 38.7

which gives us 84.13!

Answer:

false

Step-by-step explanation:

The left side equals 0.01

The right side equals 0.4

The two sides are not equal. This is a false equation.

Answer:0.01=0.0001

Step-by-step explanation:

The formula for calculating the change in consumption is MPC x Change in Disposable Income.Thus, Tamba's change in consumption = 0.75 x $860 = $645

The marginal propensity to consume (MPC) is a measure of the proportion of an increase in disposable income that is spent on consumption. In Tamba's case, his MPC is 0.75, which means that for every $1 increase in his disposable income, he will spend 75 cents on consumption. The formula for calculating the change in consumption is MPC x Change in Disposable Income. Therefore, when Tamba's disposable income increased by $860, his consumption increased by 0.75 x $860 = $645.

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Answer:

b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)

first is Jamir total cost + the sales tax of 0.0875 of the total cost

a. this is wrong because both is the sales tax only, theres no total cost include

c. wrong because its just also sales tax only

d. wrong because the total cost must only multiplied by the sales tax

PART B

12(0.10) + 8(0.35)

= 1.2 + 2.8

= $4   as the total cost

4(1.035)

= $4.14 as after tax bill

The values of a= 2, b= -12 and c= 5.

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.

Quadratic equations are another name for it.

The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

Given:

Equation: 2x² = 12x - 5

Rewriting the equation

2x² - 12x + 5 =0

We know that the standard form of Quadratic Equation is

ax² + bx + c = 0

where a, b, and c are integers and a ≠ 0.

Now, Comparing the standard equation with Given equation we get

a= 2, b= -12, c= 5

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The measure of the angle ∠ACD will be 150°. Then the correct option is D.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The internal angles ∠A is 33° and ∠B is 117°.

Then the measure of the internal angle ∠C is given as,

∠A + ∠B + ∠C = 180°

33° + 117° + ∠C = 180°

∠C = 30°

The angle ∠C and angle ∠ACD are supplementary angles. Then we have

∠C + ∠ACD = 180°

30° + ∠ACD = 180°

∠ACD = 150°

The measure of the angle ∠ACD will be 150°. Then the correct option is D.

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The dimensions of the closet are 4 feet long and 12 feet wide and the perimeter is 32 feet

The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides.

P=2(l+w) where l=length and w = width

Given here rectangular closet is 4 feet long and It is 3 times as wide as it is long. Thus its width would be 12 feet

Now perimeter of the closet using the formula above we get

P = 2(4+12)

   = 32 feet

Hence the perimeter is equal to 32 feet.

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Answer:

A

Step-by-step explanation:

cos A = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

10/19

Step-by-step explanation:

the slope of the line is the term that multiplies x

Answer: 10/19 is the slope

If the cake can be represented as 1 = 10/10, that means we can find out how much cake is left by taking and then subtracting the amount Samuel ate. The expression [1 - 1/10] represents this situation.

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

Cake = 1 or 10/10

Samuel's bite = 1/10

The amount remaining is calculated as

Amount remaining = Cake - Samuel's bite

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

Amount remaining = 1 - 1/10

The above represents the required expression

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Answer:

89

Step-by-step explanation:

[tex] {3}^{4} + \frac{18}{3} + 2 \\ = 82[/tex]

o Answer:

It's 89 and I didnt mean to reaspond to this question so report it

Mixed Number Form is 102184532768.

10∑n=18(14)n−1

The sum of a finite geometric series can be found using the formula a(1−rn1−r)

where a is the first term and r

is the ratio between successive terms.

Find the ratio of successive terms by plugging into the formula r=an+1an

and simplifying.

r=14

Find the first term in the series by substituting in the lower bound and simplifying.

a=8

Substitute the values of the ratio, first term, and number of terms into the sum formula.

81−(14)101−14

Simplify.

34952532768

The result can be shown in multiple forms.

Exact Form:

34952532768

Decimal Form:

10.66665649…

Mixed Number Form:

102184532768

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Therefore, the work done in this problem comes out to be 144 ft pound.

The work a force does is calculated as the product of the object's displacement and the components of the applied force of the object in the displacement direction. Pushing a block with some force and accelerating the body results in work being completed.

Here,

Given : an 8 lb mass

a height = 18ft

So, we find the work done

Using formula

=> Work done = m*g*h

=>  Work done = weight * height

=>   Work done = 8*18

=> Work done=144 ft pound

Therefore, the work done in this problem comes out to be 144 ft pound.

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Answer:

B

Step-by-step explanation:

Answer: The answer is B

Step-by-step explanation:

if you divide 7 by 12 you will get a decimal and a non terminating 3

Answer: the answer should be C :)

Step-by-step explanation:

the slope (x) is -3/4 and the y-intercept is -2

By using the properties of angle, it can be proved that [tex]\angle 8 \cong \angle 1[/tex]

What is angle?

An angle is a figure formed by two straight lines that intersect each other. It is a measure of the amount of rotation between two lines or planes, typically measured in degrees or radians. Angles are used in mathematics to describe relationships between lines, shapes and objects, and they are also used in everyday life to measure and construct objects. Angles are an important part of geometry and trigonometry, and they are also used in physics, engineering, and other sciences.

[tex]\angle 8 \cong \angle 5[/tex]             Vertically Opposite angle

[tex]\angle 5 \cong \angle 1[/tex]              Corresponding angle

[tex]\angle 8 \cong \angle 1[/tex]               Transitivity property of congruency

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Answer:

  111 girls

Step-by-step explanation:

You have 924 people classified as 383 men, 356 women, and the remainder children. 2/5 of the children are boys, and you want to know the number of girls.

The number of children is ...

  924 -383 -356 = 185

The 3/5 of children that are not boys are girls, so ...

  girls = 3/5(185) = 111

There are 111 girls in the theater.

The probability that the next person will purchase exactly one costume is 0.57.

what is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

146 visitors purchased no costume.

230 visitors purchased exactly one costume.

31 visitors purchased more than one costume.

So, the total number of customers are,

146 + 230 + 31 = 407

The total visitors purchased exactly one costume are 230.

So,

P(Purchase exactly one costume) = 230 / 407 = 0.5651 ≈ 0.57

Hence, the probability that the next person will purchase exactly one costume is 0.57.

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Answer:

$43

Step-by-step explanation:

[tex]f(2.75) = 12(2.75) + 10 [/tex]

[tex] f(2.75) = 33 + 10 = 43[/tex]

Every point on the perpendicular bisector of a segment is equidistant from the endpoint is hence proved

The line segment AB and let MN is the perpendicular bisector of AB line segment.

we prove the required result by congruence of triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure

From the figure,

Let P be any point on the perpendicular bisector MN. Join A to P and B to P.

To show AP=BP

In ΔANP and ΔBNP

PN=PN {common side in both triangles }

∠PNA=PNB=90°{ MN is ⊥ bisector of AB}

AN=NB {N is mid point}

By SAS rule of congruent ΔANP≅BNP

By CPCT (corresponding Parts of congruent triangles)

AP=BP

But P is point on MN

Therefore, every point on the perpendicular bisector of line segment AB is equidistant from the segments endpoints.

Hence Proved.

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Answer:

Variables

Step-by-step explanation:

Variables are the characteristics of the individuals of the population being studied.

The sum of squares of two sides of a triangle is equal to another side of a triangle is called the Pythagorean theorem.

It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

c^2=a^2+b^2--------(1)

Where a,b, and c are sides of a triangle.

To measure the length of the missing side in a right triangle using the Pythagorean theorem:

c^2=a^2+b^2

By using this formula we can find the length of a missing side.

To understand more we have to solve an example:

let A, B, and C are points of a triangle AB, BC, and CA are the sides of the triangle.

Consider BC=3cm CA=4cm AB=?

Use equation(1) to find the length of AB

AB^2=BC^2+CA^2

AB^2=3^2+4^2

AB^2=9+16=25

AB=5cm

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Answer:

The y-value will be 0

Step-by-step explanation:

The x-value will be 0 when we find the y-intercept

the x-value will be equal to the y-value is only at origin (0,0)

The answer is  the y-value will be 0

The probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow is 47/128.

The probability that less than 2 babies will speak is

5C0 * (0.25)^0 * (0.75)^5 +  5C1 * (0.25)^1 * (0.75)^4

= (0.75)^5 +  5 * 0.25 * (0.75)^4

(0.75)^5+5*0.25*(0.75)^4 = 81/128

Therefore,

probability that 2 or more will speak is  

=  1- 81/128 = 47/128

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability display style q=1-pq=1-p).

This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.

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Answer:

Step-by-step explanation:

The greatest common divisor of two integers a and b is a divisor common to both integers that is greater than any other common divisor. The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.

To find the smallest possible value of a+b, we can start by trying to find the smallest possible values of a and b that satisfy the given conditions.

Since the greatest common divisor of a and b is 5, we know that both a and b must be divisible by 5. We can write a = 5x and b = 5y, where x and y are positive integers.

The least common multiple of a and b is 55, so we know that both a and b must be factors of 55. We can write 55 as the product of its prime factors: 55 = 5 * 11. Since a is divisible by 5, we know that a must be equal to 5 or 25. Similarly, since b is divisible by 5, we know that b must be equal to 5 or 25.

There are four possible pairs of values for a and b: (5,5), (5,25), (25,5), and (25,25). The smallest of these is (5,5), which gives us a+b = 5+5 = 10. Therefore, the smallest possible value of a+b is 10.

× is 7

(7×+5) is 54

(5×+19) is 59