1) When q = 13, the expression q - 10 is; 3
2) When x = 4.2, the expression 34.5x is; 144.9
3) The simple interest you would earn in 2.5 years is; $5.25
How to solve Algebra Word problems?1) We want to evaluate the following expression;
q - 10 when q = 13.
Thu, we will plug in 13 for q to get;
13 - 10 = 3
2) We want to evaluate the following expression;
34.5x when x = 4.2
Plug in 4.2 for x to get;
34.5 * 4.2 = 144.9
3) The formula for simple interest is;
I = PRT/100
Where;
P is principal
R is rate
T is time
We are given;
P = $70
R = 3% = 0.03
Time; T = 2.5 years
Thus;
I = 70 * 0.03 * 2.5
I = $5.25
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HELP PLEASEE
MATHHHHHHH
Answer:
24
Step-by-step explanation:
divide the sides added together by the middle
If TR = 11 ft, find the length of PS. Round to the nearest hundredth.PTR16°Sarc PS =ft
Given:
TR = 11 Ft
∠RTS = 16°
Let's determine the length of Arc PS,
Step 1: Let's first determine the angle of Arc PS.
∠RTS = 16°
∠PTQ = 16° ; Vertical angle pair of ∠RTS
Since ∠QTR = ∠PTS under the rule of vertical angles, we can now determine the measure of ∠PTS or Arc PS.
We get,
[tex]\angle RTS\text{ + }\angle PTQ\text{ + }\angle QTR\text{ + }\angle PTS=360[/tex][tex]16\text{ + }16\text{ + }\angle PTS\text{ + }\angle PTS=360[/tex][tex]32\text{ + }2\angle PTS=360^{}[/tex][tex]\angle PTS=\frac{360^{}\text{ - 32}}{2}[/tex][tex]\angle PTS=\frac{328}{2}[/tex][tex]\angle PTS=164^{\circ}[/tex]Step 2: Let's determine the perimeter of the circle.
[tex]\text{ Perimeter = }2\pi r[/tex][tex]\text{ = 2}\pi(11)[/tex][tex]\text{ Perimeter = 22}\pi[/tex]Step 3: Let's determine the length of Arc PS.
[tex]\text{ Arc Length = (}\frac{\theta}{360})(\text{Perimeter of the Circle)}[/tex][tex]\text{ = (}\frac{164}{360})(22)(3.14)[/tex][tex]\text{ Arc Length = }31.469777\ldots\text{ }\approx\text{ 31.47 ft.}[/tex]Therefore, the length of Arc PS is 31.47 ft.
Estimate the intercepts of the graph of the function.
The graph of y equals two-thirds x minus 1 is shown. The graph appears to pass through the points ordered pair 0 comma negative 1 and ordered pair three-halves comma 0.
The x-intercept is about
, and the y-intercept is about
.
The x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .
X intercept of a function is defined as the point where the graph crosses the x axis ,
and the y intercept of the function is defined as the point where the graph crosses the y axis .
In the question ,
it is given that
the function is y= (2/3)x-1
to find the x intercept we substitute y as 0 in the equation
On substituting y as 0 , in the equation , we get
0 = (2/3)x-1
1=(2/3)x
x=1*(3/2)
x=3/2
the x intercept is 3/2.
to find the y intercept we substitute x as 0 in the equation
On substituting x as 0 , in the equation , we get
y=(2/3)*0-1
y=0-1
y= -1
so, the y intercept is -1 .
Therefore , the x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .
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Find the standard form of the equation
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y = x² +6x -16[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.
So, the values of x, when y = 0 are the roots of the given quadratic function.
that is : x = -8 and x = 2
And it can be represented as :
[tex]\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0[/tex]
[ h1 and h2 represents roots of the quadratic function ]
[tex]\qquad \tt \rightarrow \: (x -2)(x + 8) = 0[/tex]
It can be further simplified as :
[tex]\qquad \tt \rightarrow \: {x}^{2} -2x +8x -16 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x {}^{2} +6x -16 = 0[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
The value of x such that f(x) and g(x) have equal values is 3
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of x?From the question, we have
f(x) = -2x + 4
g(x) = 2x - 8
The question implies that the functions have equal values
This means that
f(x) = g(x)
Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms
2x + 2x = 8 + 4
Evaluate the like terms
4x = 12
Divide both sides of the equation by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsSee attachment for the graph of the functions
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Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.
T= {x|x is an integer and -5
The set T can be rewritten by listing its elements as T = {-4}.
What are sets?A set is a grouping of unique components that are denoted by curly brackets and commas.The term "elements of a set" refer to the collection of items in a set. A collection of fruits or a collection of images are two examples. Sets are additionally shown as follows.Set A = {a, b, c, d}. These are the elements of set A: a, b, c, and d.
Given:
Set T is equal to {x | x is an integer and -5 < x < -3}.
By examining the interval in the set, the set can also be written as something else.
It should be noted that the interval consists of two inequalities combined so that x > -5 and x < -3.
As -4 > -5 and -4 < -3 via the number line so it is the only element listed in the required set notation.
Hence, the set can be rewritten as
T = {-4}
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The complete question is: "Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.
T = {x | x is an integer and -5 < x < -3}."
To rent a certain meeting room, a college charges a reservation fee of $13 and an additional fee of $4 per hour. The chemistry club wants to spend at most $33 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
pls help me with my question
Given the figure of an object consists of a cylinder and a rectangular prism.
We will find the volume of the cylinder using the following formula:
[tex]V=\pi r^2h[/tex]As shown, the diameter of the base = d = 3 ft
So, the radius = r = d/2 = 3/2 = 1.5 ft
And the height = h = 4 ft
Use π = 3
so, the volume of the cylinder will be as follows:
[tex]V=3*1.5^2*4=27\text{ }ft^3[/tex]Now, we will find the volume of the rectangular prism using the following formula:
[tex]V=l*w*h[/tex]As shown, the length = l = 7 ft
The width = w = 4 ft
The height = h = 4 ft
So, the volume of the rectangular prism will be as follows:
[tex]V=7*4*4=112\text{ }ft^3[/tex]So, the total volume of the object will be =
[tex]27+112=139\text{ }ft^3[/tex]So, the answer will be V = 139 ft³
HelloI’m having trouble on the *calculus* portion on my ACT PREP GUIDEI need help solving this
First, we find the value of r:
[tex]\begin{gathered} a_n=\frac{2^n}{5^{n+1}\cdot n} \\ a_{n+1}=\frac{2^{n+1}}{5^{n+1+1}\cdot(n+1)} \\ a_{n+1}=\frac{2^{n+1}}{5^{n+2}\cdot(n+1)} \end{gathered}[/tex]Then r is calculated as follows:
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{a_{n+1}}{a_n}| \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{5^{n+2}\cdot(n+1)}\text{ / }\frac{2^n}{5^{n+1}\cdot n} \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{5^{n+2}\cdot(n+1)}\times\frac{5^{n+1}\cdot n}{2^n}| \end{gathered}[/tex]Multiplying
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{2^{n+1}\cdot5^{n+1}\cdot n}{5^{n+2}\cdot(n+1)\cdot2^n} \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{2^n}\cdot\frac{5^{n+1}}{5^{n+2}}\cdot\frac{n}{n+1}| \\ r=\lim _{n\to\infty}|2^{n+1-n}\cdot5^{n+1-(n+2)}\cdot\frac{n}{n+1}| \end{gathered}[/tex]Simplify
[tex]r=\lim _{n\to\infty}|2^1\cdot5^{-1}\cdot\frac{n}{n+1}|[/tex]Apply exponential properties
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{2}{5}\cdot\frac{n}{n+1}| \\ r=\lim _{n\to\infty}|\frac{2n}{5\cdot(n+1)}| \\ r=\lim _{n\to\infty}|\frac{2n}{5n+5}| \end{gathered}[/tex]Applying the limit, the solution is
[tex]r=\frac{2}{5}=0.4[/tex]So, r = 0.4 and since r is less than 1, the series converges.
Answer: From the ratio test, r = 0.4. The series converges.
oris is playing a game. She rolls three six-sided number cubes to tell her how many squares to move. If two number cubes show 4 and 3, how many different possible numbers of squares may she move on her turn?
6 possible values of squares that she can move.
What is possibility or probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.
Hence she has 6 different possible numbers of squares she can move.
The possibilities are:
-8 squares (if she rolls a 1)
-9 squares (if she rolls a 2)
-10 squares (if she rolls a 3)
-11 squares (if she rolls a 4)
-12 squares (if she rolls a 5)
-13 squares (if she rolls a 6)
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On a horizontal number line, -43 is located to the left of -35.
Step-by-step explanation:
On a horizontal number line, -43 is located to the left of -35. TRUE because -43 is farther away (to the left) from 0 than -35.
In angle VWX, VX is extended through point X to point Y,
m/VWX = (x + 14)°, m/XVW = (x +9)°, and
m/WXY = (5x - 10)°. What is the value of x?
Answer:
11
Step-by-step explanation:
This will form triangle VWX. So we have values for ∠VWX and ∠XVW but we don't have value for ∠WXV.
Since ∠WXV and ∠WXY are supplementary angles
=> ∠WXV + ∠WXY = 180
=> ∠WXV = 180 - ∠WXY
So the angles of triangle VXY
∠VWX + ∠XVW + ∠WXV = 180
(x + 14) + (x + 9) + (180 - (5x - 10)) = 180
x + x - 5x + 14 + 9 + 180 + 10 = 180
-3x + 213 = 180
-3x = - 33
x= 11
solve similar triangles (advanced) khan academy. solve for x
Answer: 10/3
Step-by-step explanation:
[tex]\frac{2}{6}=\frac{x}{10}\\\\x=\frac{10}{3}[/tex]
Find the difference.
(-3x²-xy-3y²) - (6x²-4xy+y²)
Enter the correct answer.
The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is
(-9x²+3xy-4y²).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Numerical ExpressionNumbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
Algebraic ExpressionUnknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
= (-3x²-xy-3y²) - (6x²-4xy+y²)
= -3x²-xy-3y² - 6x²+4xy-y²
= (-9x²+3xy-4y²)
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In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?
a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer: ?
b) Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer: ?
1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.
2) After 8 years of straight-line depreciation, the car's value will be $19,080.
What is depreciation?Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.
Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.
Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.
Price of an automobile in 2003 = $30,600
Annual depreciation = $1,440
The car's value after t years = $19,080.
Equation Solution:Value after t years = 30,600 - 1,440t
If 19,080 = 30,600 - 1,440t
1,440t = 30,600 - 19,080
1,440t = 11,520
t = 8 (11,520/1,440)
t = 8
= 8 years
Check:
x = 30,600 - 1,440t
x = 30,600 - 1,440(8)
x = 30,600 - 11,520
x = 19,080
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In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43) and matching the number on the gold ball (1 through 31). If one ticket is purchased, what is the probability of winning the jackpot?
Suppose the monthly charges for cell phone plans are normally distributed with mean and standard deviation $.(a) Draw a normal curve with the parameters labeled.(b) Shade the region that represents the proportion of plans that charge than $.(c) Suppose the area under the normal curve to the of X$ is 0.1587. Provide an interpretation of this result.
SOLUTION
(a) From the information given in the question,
We will select a curve with 58 at its center which represents the mean and
[tex]\begin{gathered} 58-17=41 \\ 58+17=75 \end{gathered}[/tex]41 and 75 at the left and right sides. That is gotten by subtracting and adding the standard deviation of 17.
Hence the answer is Graph D
(b) The region that represents less than 41 is seen in graph B
Hence graph B is the answer
(c) Option A
The probability is 0.1587 that a randomly selected cell phone plan in this population is less than $41 per month
LET f(x)=4x+1 and g(x)=x²-5 (find (f+g) (x)
The function operation ( f + g )(x) of the functions f( x ) = 4x + 1 and g( x ) = x² - 5 is x² + 4x - 4.
What is the function operation ( f + g )(x) in the function?A function is simply a relationship that maps one input to one output.
Each x-values must have one y-value to qualify as a function.
Given the data in the question;
f( x ) = 4x + 1g( x ) = x² - 5( f + g )(x) = ?First, set up the function operation
( f + g )(x) = f(x) + g(x)
Replace the function designators f(x) and g(x) with the actual functions.
( f + g )(x) = f(x) + g(x)
( f + g )(x) = ( 4x + 1 ) + ( x² - 5 )
Collect and add like terms
( f + g )(x) = 4x + 1 + x² - 5
( f + g )(x) = 4x + x² - 5 + 1
( f + g )(x) = 4x + x² - 4
Reorder the function
( f + g )(x) = x² + 4x - 4
Therefore, the function operation ( f + g )(x) is x² + 4x - 4.
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Can someone help me with this please and thank youuu
The correct answer is:
[A]: " ∡2 is supplementary to ∡3 " .
___________________
The other answer choices given—which are correct statements—only prove that " a || b " {that is: "Line A" is parallel to "Line B".}
___________________
7.5.PS-13 Identify the solid from its net. Choose the correct answer below. o triangular prism o rectangular prism o square pyramid O triangular pyramid Click to select your answer and then click Check Answer.
The net image of a figure is a visual representation of the original figure.
From the given net image, the solid that has the net image can be said to be a traingular
Only #29,33,37,41,49 please show work THANK YOU
29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i
33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i
37) – 4 i = 4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 4 i = 0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] = 4[tex]e^{\frac{3\pi}{2}i}[/tex]
41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]
49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex] = [tex]\sqrt{26}e^{-0.197i}[/tex]
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It is estimated that 29% of the earths surface isn’t covered by water what percentage of the earths surface is water-covered
Answer: 71%
Explanation:
100% - total earth surface
29% - earth surface uncovered by water
100 - 29 = 71% of surface covered by water
Hello I need help please
olution
e have the following statement:
If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:
A) supplementary angles
In a certain instant lottery game, the chances of a win are stated as "4 in 25." Express the indicated degree of likelihood
as a probability value between 0 and 1 inclusive
The probability is
the probability of winning a lottery game out of all the games played is 0.16.
We are given that:
In a lottery game, the chances of win are = 4 in 25
So, this means that:
if a person plays 25 games of lottery, then he will probably win 4 games out of them.
So, we get that:
Total games = 25
Win games = 4
Probability = win games / total games
Substituting the values, we get that:
Probability = 4 / 25
P = 0.16
Therefore, we get that, the probability of winning a lottery game out of all the games played is 0.16.
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find an equation of the form f(x)=ax^2+bx+c. must solve algebraically and check using a calculator (state, the steps used to perform the check).
f(1)=4, f(2)=13, f(4)=46
By using algebra resolution methods for systems of linear equations, we find that the equation of the form f(x) = a · x² + b · x + c that passes through the three points is equal to f(x) = (5 / 2) · x² + (3 / 2) · x.
How to determine the quadratic equation that passes through three points
In this problem we must determine the coefficients of a quadratic equation that passes through the points (x₁, y₁) = (1, 4), (x₂, y₂) = (2, 13) and (x₃, y₃) = (4, 46). First, we need to create a system of linear equations by substituting on y and x thrice:
(x₁, y₁) = (1, 4)
a · 1² + b · 1 + c = 4
a + b + c = 4
(x₂, y₂) = (2, 13)
a · 2² + b · 2 + c = 13
4 · a + 2 · b + c = 13
(x₃, y₃) = (4, 46)
a · 4² + b · 4 + c = 46
16 · a + 4 · b + c = 46
Then, we find a system of three linear equations with three variables that offers an unique solution:
a + b + c = 4 (1)
4 · a + 2 · b + c = 13 (2)
16 · a + 4 · b + c = 46 (3)
There are different methods to find the solution to this system, we proceed to use algebraic substitution:
By (1):
c = 4 - a - b
(1) in (2) and (3):
4 · a + 2 · b + (4 - a - b) = 13
3 · a + b = 9 (2b)
16 · a + 4 · b + (4 - a - b) = 46
15 · a + 3 · b = 42 (3b)
By (2b):
b = 9 - 3 · a
(2b) in (3b):
15 · a + 3 · (9 - 3 · a) = 42
15 · a + 27 - 9 · a = 42
6 · a = 15
a = 15 / 6
a = 5 / 2
By (2b):
b = 9 - 3 · (5 / 2)
b = 9 - 15 / 2
b = 18 / 2 - 15 / 2
b = 3 / 2
By (1):
c = 4 - 5 / 2 - 3 / 2
c = 4 - 8 / 2
c = 4 - 4
c = 0
The coefficients of the quadratic equation are (a, b, c) = (5 / 2, 3 / 2, 0).
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Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To
make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts
that cost $3.00 per pound. He mixes 10 pounds at a time.
How many pounds of Virginia peanuts does Sergio use? How many pounds of Spanish peanuts does Sergio use?
How many pounds of Virginia peanuts does Sergio use?
Assume he is making 10 lb of the $3.40 mixture
Let x = no. of pounds of the Virginia ($3.50) peanuts
Then (10-x) = no. of pounds of the Spanish ($3) peanuts
The Equation:
3.5x + 3(10-x) = 3.4(10)
3.5x + 30 - 3x = 34
.5x = 34 - 30
x = 4/.5
x = 8 pounds of Virginia peanuts
:
(b)How many pounds Spanish peanuts does Sergio use?
Spanish peanuts must be 2 pounds since the total is 10 pounds
:
Check:
3.5(8) + 3(2) = 3.4(10)
28 + 6 = 34
To measure the height of a building, a person stands away from the base and measures the angle of elevation to the top of the building to be 48∘. Moving 170 feet closer, the angle of elevation to the top of the building is 73∘. How tall is the building?
The height of the building is 118. 89 feet
What are trigonometric identities?Trigonometric identities are simplify defined as arithmetic expressions or equations relating to many trigonometric functions, and is also known for holding true for all the values in the domain of the functions.
The different types of trigonometric identities includes;
sinecosinetangentcotangentsecantcosecantThe trigonometric ratios for major identities are;
sine = opposite/hypotenuse
tangent = opposite/adjacent
cosine = adjacent/hypotenuse
From the information given;
cos 43 = x/170
cross multiply
x = cos 43(170)
expand the bracket
x = 124.33 feet
To determine the height of the building is the opposite side
sin 73 = x/ 124.33
cross multiply
x = sin 73(124.33)
expand the bracket
x = 118. 89 feet
Hence, the value is 118. 89 feet
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Please help I’ll mark you as brainliest if correct!!!
Answer:
[tex]a=22\\b=6\\c=14\\d=8[/tex]
Step-by-step explanation:
So (Didn't even know what it was until now), is a square where all rows, columns, and diagonals sum up to the same number.
So, from the diagonal of 7, 15, and 23, but adding them up, we can tell that each row, column, and diagonal should sum up to 45.
If we know that, you can solve it either arithmetically or algebraically (I'm going to sovle them algebraically)
Here are the equations I used to solve for each:
[tex]7+16+a=45\\23+a=45\\a=22\\\\24+15+b=45\\39+b=45\\b=6\\\\15+16+c=45\\31+c=45\\c=14\\\\14+23+d=45\\37+d=45\\d=8[/tex]
Any further questions? Just leave a comment.
What amount of sales will produce a commission of $102.00 if the commission rate is 8.5%?
You would need sales of $[
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.5 MB.
Yesterday, there were 870 downloads of the song, for a total download size of 2946 MB. How many downloads of the high-quality version were there?
Number of high-quality version downloads:
X
The number of high-quality version downloads is 300.
Given:
Size of the standard version = 2.8 megabytes (MB).
Size of the high-quality version = 4.5 MB.
Total number of downloads = 870
Total download size = 2946 MB
Let the number of high-quality version downloads be x.
Then the number of standard version downloads will be 870 - x.
Now the sum of the number of downloads of each type multiplied by their sizes equals 2946 MB.
So the equation is,
4.5x + 2.8(870 - x) = 2946
4.5x + 2436 - 2.8x = 2946
1.7x = 2946 - 2436
1.7x = 510
x = 510/1.7
x = 300
Therefore, the number of high-quality version downloads is 300.
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