A) The monthly percentage rate of Felix is; 1%
B) The monthly percentage rate of Oscar is; 1.25%
C) The amount that Oscar will pay more than Felix is; $2
What is the monthly Percentage Rate?A monthly interest rate is simply how much percentage interest you would be charged in one month while annual percentage interest rate is defined as the percentage interest rate you will be charged annually.
A) We are told that Felix was given a card with APR of 12%.
Thus;
Monthly percentage rate = 12%/12 = 1%
B) We are told that Oscar was given a card with an APR of 15%. Thus;
Monthly percentage rate = 15%/12 = 1.25%
C) We are told that each of them had an average daily balance of $800 for a specific month.
Thus;
Amount paid by Felix = 800 * 1%
Amount paid by Felix = $8
Amount paid by Oscar = 800 * 1.25%
Amount paid by Oscar = $10
Difference in Payments = $10 - $8 = $2
Thus, Oscar pays $0.96 more than Felix.
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Indigo has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $296.71.
She buys 3 bicycle reflectors for $12.34 each and a pair of bike gloves for $33.66.
She plans to spend some or all of the money she has left to buy new biking outfits for $68.49 each.
Which inequality can be used to determine
o
o, the maximum number of outfits Indigo can purchase while staying within her budget?
68.49
o
+
367.39
≤
700
68.49o+367.39≤700
68.49
+
367.39
o
≥
700
68.49+367.39o≥700
68.49
o
+
367.39
≥
700
68.49o+367.39≥700
68.49
+
367.39
o
≤
700
68.49+367.39o≤70
The inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
The given parameters are:
Budget = $700
New bicycle = $296.71
Three bicycle reflectors = $12.34 each
Pair of a bike gloves = $33.66.
New biking outfits = $68.49 each.
Let the number of new biking outfits be x
So, we have the inequality;
New bicycle + 3 times price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget
This gives;
296.71 + 3( 12.34) + 33.66+ 68.49x ≤ 700
296.71 + 68.49x ≤ 700
Solve the inequality
367.39 + 68.49x ≤ 700
Hence, the inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700
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Solve on the interval (0,2%): (sin x + 1)2 sin x-3 sinx-2) = 0 O A. x = 7T,X = 2 x=51 O 3 7T O В. x= N ***= 7+ x = 117 6 6 T T o C. X=2.7 x= 3 O D. x=2x-x-5 2 * = 4
Given:
(sinx + 1)(2sin²x - 3sinx - 2) = 0
sinx + 1 = 0
sinx = -1
Take the arcsin of both-side
x = sin⁻' (-1)
x = -90= -90 + 360 = 270 = 3π / 2
x =3π / 2
Similarly,
2sin²x - 3sinx - 2 = 0
let y = sinx
2y² - 3y - 2 = 0
Factorising the above;
2y² - 4y + y - 2 = 0
2y(y-2) + 1(y-2) = 0
(2y+1)(y-2) = 0
Put sin x back in for y so we can see what it's really supposed to be.
(2sinx + 1 )(sinx -2) = 0
Either one of the terms 2sin x + 1 or sin x - 2 can be 0 for this equation to be true. Let's solve each of them separately.
2sinx + 1 = 0
2sinx = -1
sinx = -1/2
Take the arcsin of both-side.
x= sin⁻' (-1/2)
x = - 30 = -30+360 = 330 ,
x = 7π /6 or 11π/6
Therefore, the correct option is B. x= 3π / 2 , 7π /6 , 11π/6
The total cost of three shirts and two sweatshirts is $203.75. If the sales tax rate on clothing is 6%, how much money will be owed to the cashier?
The money owed by the cashier after selling three shirts and two sweatshirts for $203.75 and 6% clothing tax is $215.975.
The percentage tax is the tax amount charged for the item. The tax amount is given by dividing the per cent by 100 and multiplying it by the total amount of the item.
The total cost of three shirts and two sweatshirts is $203.75 and the tax is 6%.
The tax amount will be,
Tax amount = [tex]\frac{6}{100}\times203.75[/tex]
[tex]=12.225[/tex]
So, the total money owed by the cashier will be,
Total money owed by cashier [tex]=203.75+12.225[/tex]
= $215.975
Therefore, the money owed by the cashier after selling three shirts and two sweatshirts is $215.975.
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Could you quickly glance over my paper and see if it looks generally right? You dont need to go in depth i just need someone to say if i did something extremely wrong.
We need to check if y=8 and x = -1 are perpendicular or parallel.
The line y=8, is a straight line for which the y-values within it are equal to 8, therefore it is parallel to the x-axis.
The line x=-1, is a straight line for which all the values have the same value of x, which is -1, therefore it is parallel to the y-axis.
The lines are, therefore, perpendicular.
If 40% of 95 is 38, what is 4% of 95?
If 40% of 95 is 38, what is 4% of 95?
Answer: 3.8
True or False?
Point (-0.6,1) is a solution of the inequality 2y+5x+7>3.
Answer:
True
Step-by-step explanation:
to determine if the point is a solution, substitute x = - 0.6 and y = 1 into the left side of the inequality and compare resul with right side.
2y + 5x + 7
= 2(1) + 5(- 0.6) + 7
= 2 - 3 + 7
= - 1 + 7
= 6 > 3 ← True
then (- 0.6, 1 ) is a solution of the inequality
GRADED HW ASSIGNMENT I need help I’m stuck on this question and it’s regarding volume and scientific notation
ANSWER:
1.8176 * 10^-20 m^3
STEP-BY-STEP EXPLANATION:
Given:
Wide = 0.000000284 m
Long = 0.000000025 m
High = 0.00000256 m
Because it is rectangular in shape, the volume is the product of the three measurements, just like this:
[tex]\begin{gathered} V=0.000000284*0.000000025*0.00000256 \\ \\ V=1.8176*10^{-20}\text{ m}^3 \end{gathered}[/tex]The volume is 1.8176 * 10^-20 cubic meters
The triangles in the figure below are similar.
image b125a080d0e9444e9eebf9b6644403df
Which proportion is correct?
A.
x20=96
x
20
=
9
6
B.
x20=915
x
20
=
9
15
C.
2015=x6
20
15
=
x
6
D.
x20−x=156
x
20
−
x
=
15
6
The perimeter of the triangle is 12 in.
What is perimeter of similar triangle?
The perimeter of similar triangle is equal to the ratio of the similar sides of the triangle. The ratio of two similar perimeters of two similar shapes is equal to the ratio of the lengths of their corresponding sides.
Here, perimeter of triangle PQR = sum of all the side
=12+20+16
=48
The ratio of the corresponding side = 12/3
=4/1
Hence, the perimeter of triangle xyz = ?
perimeter of triangle PQR /perimeter of triangle xyz =4/1
48/x =4/1
x = 48/4
=12
Hence, the perimeter of triangle xyz = 12
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where Ais the initial amount present and A is the amount presenteStrontium-90 is a radioactive material that decays according to the function A(t) = Age-0.02441at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90.ce(a) What is the decay rate of strontium-90?(b) How much strontium-90 is left after 30 years?(c) When will only 200 grams of strontium-90 be left?(d) What is the half-life of strontium-90?-stilCOREcio (a) The decay rate of strontium-90 is %.(Type an integer or a decimal. Include the negative sign for the decay rate.)LiolewMat
The given information is:
- The function of decay is:
[tex]A(t)=A_0e^{-0.0244}[/tex]Where A0 is the initial amount of strontium-90, A is the amount present at time t (in years).
- The initial amount is 800 grams.
a. What is the decay rate of strontium-90?
The given formula is written in the form:
[tex]A(t)=A_0e^{rt}[/tex]Where r is the decay rate in decimal form, so:
[tex]r=-0.0244*100\%=-2.44\%[/tex]The decay rate is -2.44%.
b. How much strontium-90 is left after 30 years?
Replace t=30 and solve:
[tex]\begin{gathered} A(30)=800g*e^{-0.0244*30} \\ A(30)=800g*e^{-0.732} \\ A(30)=800g*0.481 \\ A(30)=384.8g \end{gathered}[/tex]There is 384.8 grams after 30 years.
c. When will only 200 g of strontium-90 be left?
A(t)=200g, then replace it and solve for t:
[tex]\begin{gathered} 200g=800g*e^{-0.0244t} \\ \frac{200g}{800g}=e^{-0.0244t} \\ \ln(\frac{200g}{800g})=\ln e^{-0.0244t} \\ -1.386=-0.0244t \\ t=\frac{-1.386}{-0.0244} \\ t=56.8 \end{gathered}[/tex]There will be 200 g left after 56.8 years.
d. What is the half-life of strontium-90?
The half-life is when A(t)=A0/2, then if we replace this into the decay formula we obtain:
[tex]\begin{gathered} \frac{A_0}{2}=A_0*e^{-0.0244t} \\ Simplify\text{ A0 on both sides} \\ \frac{1}{2}=e^{-0.0244t} \\ \ln(0.5)=\ln e^{-0.0244t} \\ -0.693=-0.0244t \\ t=\frac{-0.693}{-0.0244} \\ t=28.4 \end{gathered}[/tex]The half-life of strontium-90 is 28.4 years.
I need help on #13 please !!! Also with the (circle the vertex on the graph and draw the axis of symmetry) !
Given the quadratic equation
[tex]2x^2-16x+24=0[/tex]we want to solve for the vertex and its axis of symmetry.
To easily identify these properties of quadratic equation, we must put the equation first into its vertex form. The first step to write it in its vertex form is to move the constant on the right-hand side of the equation
[tex]\begin{gathered} 2x^2-16x=-24 \\ x^2-8x=-12 \end{gathered}[/tex]After that, we add the square of b/2 on the equation above. The value of b on the quadratic equation is -16. We have
[tex]x^2-8x+(\frac{-8}{2})^2=-12+(\frac{-8}{2})^2[/tex]Simplify the equation above
[tex]\begin{gathered} x^2-8x+16=-12+16 \\ x^2-8x+16=4 \end{gathered}[/tex]We write the expression on the left-hand side as perfect square, which is (x-4)^2.
[tex](x-4)^2=4[/tex]Transfer 4 to left-hand side to write the vertex form of the quadratic equation
[tex](x-4)^2-4=0_{}[/tex]The vertex form has the general equation
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex of the parabola.
Based on the vertex form of the quadratic formula, the vertex exists at (4,-4). Also, the axis of symmetry is equal to h, which is in this case, equal to 4.
The representation of a vertex and axis of symmetry in a quadratic plot will be
Answer: Vertex = (4,-4)
Axis of symmetry = 4
Simplify (4+2i)(1+5i)
The simplyfied expression is: -6 + 22i
To multiply two complex numbers, we need to apply distributive propiertie with each term of each parentheses. In this case:
[tex]\mleft(4+2i\mright)\mleft(1+5i\mright)=4\cdot1+4\cdot5i+2i\cdot1+2i\cdot5i[/tex]Now we can solve:
[tex]4+20i+2i+(2\cdot5)i^2[/tex]i^2 is (-1). Then:
[tex]\begin{gathered} 4+22i+10(-1) \\ 4-10+22i \\ -6+22i \end{gathered}[/tex]-6+22i is the simplified expression
what is the total area of the figure below in square inches
Solution:
Given the composite figure below;
The figure is made up of a triangle and a trapezoid of the following side measures,
[tex]\begin{gathered} For\text{ the triangle:} \\ b_1=6\text{ in} \\ h_1=8\text{ in} \\ For\text{ the trapezoid:} \\ a=10\text{ in} \\ b_2=16\text{ in} \\ h_2=9\text{ in} \end{gathered}[/tex]To find the total area, A, of the figure, the formula is
[tex]\begin{gathered} A=Area\text{ of a triangle}+Area\text{ of a Trapezoid} \\ A=\frac{1}{2}b_1h_1+\frac{1}{2}(a+b_2)h_2 \\ Where \\ b_1\text{ is the base length of the triangle} \\ h_1\text{ is the height of the triangle} \\ b_2\text{ is the side length of the trapezoid} \\ h_2\text{ is the height of the trapezoid} \end{gathered}[/tex]Substituting the values of the variables into the formula above
[tex]\begin{gathered} A=\frac{1}{2}(6)(8)+\frac{1}{2}(10+16)(9) \\ A=24+117=141\text{ in}^2 \\ A=141\text{ in}^2 \end{gathered}[/tex]Hence, the total area, A, of the figure is 141 square inches.
The finance charge on Lauren’s credit card bill last month was
$13.50. Her APR is 18%. What was her average daily balance?
Answer:
$900
Step-by-step explanation:
You want to know Lauren's average daily balance if she was charged a $13.50 finance charge on a card with an APR of 18%.
Finance chargeThe finance charge is the product of the monthly interest rate and the average daily balance. The monthly rate is 1/12 of the annual rate. This tells us ...
finance charge = ADB × 18%/12
$13.50 = ADB × 0.015
ADB = $13.50/0.015 = $900
Lauren's average daily balance was $900.
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a bus drives for 3hrs and 30 mins at an average speed of 56mph.
how far does the bus drive
Answer: 196 miles
Step-by-step explanation: speed = 56 = distance / time
time = 3.5 hours
distance = speed x time = 56 x 3.5 = 196 miles
Answer:
196 miles
Step-by-step explanation:
If it drove for 56 miles per hour and rod for 3 1/2 hours the if we multiply 56 by 3 we have 168 miles and 1/2 of 56 is 28.
So the bus drove 196 miles
Pls help fast (10 points)
Need answer fast
Answer:
1.75
Step-by-step explanation:
1/4 (5 - -2)
1/4(5 + 2)
1/4(7)
7/4
1 3/4
Find (g∘k)(1)for g(x)=11x2−4x+6and k(x)=4x−11. (g∘k)(1)=
The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:
[tex]k(1)=4(1)-11=4-11=-7[/tex]Now, find g(k(1)), it means, g(-7):
[tex]g(-7)=11(-7)^2-4(-7)+6=573[/tex](g°k)(1)=573.
For what value of x must ABCD be a parallelogram? 14-7=12x+1
Answer:
Step-by-step explanation:
14-7=7
7-1=6
6=12x
x=0.5
Based on the pattern in the table, what is the value of a?
-64
Powers of 2
2-²
2-3
244
2-5
2-6
Value
1
2
4
1
80
1
16
1
32
a
Answer:
equation and fraction addition and subtraction
The cost of renting a lawnmower at the Rent-a-Center is given by the formula c = 4 +4h, where c is the total cost in dollars and h is the number of hours the mower isrented. What is the cost of renting the mower for 3 hours?2:
The cost of renting the mower for 3 hours is $16.
Formula:
[tex]c=4+4h[/tex]Where:
c= total cost in dollars
h= number of hours the mower is rented.
So, we simply have to substitute h=3 ( mower rented for 3 hours) and solve:
[tex]c=4+4(3)[/tex][tex]c=4+12[/tex][tex]c=16[/tex]Michelle has a math assignment with 60 problems you saw one picture of the problems of school then Michelle solve 1/4 of the problems at home how many problems does Michelle have left to solve
Step 01:
Data
total math problems = 60
problems solved = 1/4
problems
Step 02:
If the number of bacteria in a colony doubles every 236 minutes and there is currently a population of 9,085 bacteria, what will the population be 708 minutes from now?
We could state an exponential model.
Number of bateria will be given by:
[tex]N=N_0e^{kt}[/tex]where k=growth constant and t=time in minutes.
We're given that N0 is the initial population, which is:
[tex]N_0=9,085[/tex]We also know that, when t=236 min, N=2(9,085) = 18,170:
[tex]18,170=9,085e^{k(236)}^{}[/tex]We're going to solve this equation to find the value of k:
[tex]\begin{gathered} \frac{18,170}{9,085}=e^{236k} \\ 2=e^{236k} \\ \ln 2=\ln e^{236k} \\ \ln 2=236k \\ k=\frac{\ln 2}{236} \end{gathered}[/tex]Then, our expression is:
[tex]N=9,085e^{\frac{\ln 2}{236}t}[/tex]To find the population of bacteria after 708 minutes, we replace t by 708:
[tex]N=9085e^{\frac{\ln2}{236}(708)}=72680[/tex]Therefore, the population of bacteria 708 minutes from now, is 72680.
Which equation represents the same line as the points in the table?
Input (x) Output (y)
−6 0
0 −2
3 −3
y= −1/3x−2y is equal to negative 1 third x minus 2
y=−2x−1/3y is equal to negative 2 x minus 1 third
y=−1/3x−6y is equal to negative 1 third x minus 6
y=−6x−2
The equation that represents the same line as the points in the table is y = - 1 / 3 x - 2
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptUsing the table let's find the slope of the line as follows:
(-6, 0)(0, -2)
slope = m = -2 - 0 / 0 + 6
slope = - 2 / 6
slope = - 1 / 3
Therefore, let's find the y-intercept of the line using (0, -2).
y = - 1 / 3x + b
-2 = - 1 / 3 (0) + b
b = -2
Therefore, the equation of the table is y = - 1 / 3 x - 2
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What is 2/3 ÷8? also it needs to be a proper fraction or a improper fraction
[tex]\cfrac{2}{3}\div 8\implies \cfrac{2}{3}\div \cfrac{8}{1}\implies \cfrac{2}{3}\times \cfrac{1}{8}\implies \cfrac{2}{8}\times \cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{3}\implies \cfrac{1}{12}[/tex]
geometry i need help with this assignment this is only the front so make sure to watch for the back
The values of the area of the shaded region are;
1. Area = 36, perimeter = 28
2. Area = 16, perimeter = 16
3. Area = 22, perimeter = 30
4. Area = 29, perimeter = 28
6. Area = 53.9
What is the area of a figure?The area of a figure is the area bounded by the line that serves as the boundary of the figure.
The areas and perimeters of the figures are found as follows;
1. The figure consists of two rectangles
The dimension of the small rectangle at the top are;
Length = 4, Width = 3
Area = 3 × 4 = 12
Dimensions of the larger rectangle are;
Width = 4, Length = 6
Area = 4 × 6 = 12
The area of the composite figure is therefore; A = 3 × 4 + 6 × 4 = 36
The sum of the length of the sides, which is the perimeter, P = 8 + 3 + 4 + 3 + 4 + 6 = 28
2. The figure consists of a right triangle at the top rectangle;
The leg lengths of the right triangle are; 3 and 4
The area of the right triangle = 0.5 × 3 × 4 = 6
The dimension of the rectangle are; Length = 5, width = 2
Area of the rectangle = 5 × 2 = 10
Area of the composite figure is therefore, A = 0.5 × 4 × 3 + 2 × 5 = 16
The perimeter of the composite figure, P = 4 + 3 + 2 + 5 + 2 = 16
3. The figure is a composite figure that is found by subtracting the area of a rectangle from the area of a right triangle as follows;
The dimensions of the triangle are;
Leg lengths; (8 + 4) = 12 and (3 + 2) = 5
Area of the right triangle = 0.5 × (8 + 4) × (3 + 2) = 30
Dimensions of the rectangle left blank are;
Length = 4, width = 2
Area of the rectangle = 4 × 2 = 8
Therefore;
Area of the composite figure = 0.5 × (8 + 4) × (3 + 2) - 4 × 2 = 22
Length of the hypotenuse side = √((8 + 4)² + (3 + 2)²) = 13
The perimeter of the composite figure = 3 + 13 + 8 + 2 + 4 = 30
4. The figure is a composite figure that consist a large rectangle and small rectangle.
Dimensions of the large rectangle are;
Length = 2 + 2 + 3 = 7
Width = 5
Area of the large rectangle = 7 × 5 = 35
Dimensions of small rectangle are;
Length = 3, width = 2
Area of the small rectangle = 3 × 2 = 6
Area of the composite figure = 35 - 6 = 29
The perimeter = 2 × (2 × 2 + 3) + 2 × 5 + 2 × 2 = 28
6. Area of the circle = π × 14²/4
Area of the square = 10 × 10 = 100
The area of the shaded region = π × 14²/4 - 100 ≈ 53.9
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Fancy food catering prepares 3696 fluid ounces of fruit punch foe a wedding reception. they plan to divide the punch equally among 4 different punch bowls. each serving of punch 6 ounces. how many servings of fruit punch are available at the reception?
Fruit punch is served during the reception in 154-ounce cups using division.
Describe a division.Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groupings. When dividing numbers, we divide a bigger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
For instance, 4 2 Equals 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.
The division is represented mathematically by a symbol consisting of a tiny horizontal line with dots above and below the line. The division of two integers is represented by one of two fundamental division symbols.
Total fruit punch foe prepared = 3696 ounces
Number of punch balls = 4
Each serving has = 6 ounces of punch
So, 4 servings will have
4 × 6 = 24
The number of servings of fruit punch available at reception is given by
3696÷24
= 154
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Hello pls help!!
The half-life of carbon-14 is 5,730 years. Suppose a fossil is found with 20 percent as much of its carbon-14 as compared to a living sample. How old is the fossil?
A. 13,307 years
B. 3,235 years
C. 1,331 years
D. 32, 346 years
Please help it's very urgent!!
Answer:
13,307 years
Step-by-step explanation:
The expression for the decay of a radiactive material is:
A = B*(1/2)^(t/HL),
where A is the amount remaining, B is the initial amount, t is time (in years), and HL is the half life (in years).
We learn that A is 20% of B, so let's rewrite for that:
0.20B = B*(1/2)^(t/HL)
and we can divide both sides by B to leave us:
0.20 = (1/2)^(t/HL)
The HL is 5730 years:
0.20 = (1/2)^(t/5730)
We need to solve this expression for t, the time (in years) that is required before we have 20% of the carbon remaining.
The answer I get, by graphing, is 13,305 years, The closest to this is A) 13,307 years. An algebraic solution might result in a slightly different number.
find the total surface area of a solid cube given that its volume is 343 m square.
find the volume of a solid cube given that its total surface area is 216.
Step-by-step explanation:
what is the basic unit of length ? m or meter ?
a cube is like a 3-dimensional square : all side lengths are equal.
the volume of a cube =
side³
side³ = 343 m³
side = cubic root(343) = 7 m
a cube has 6 sides (look at dice). the surface of a cube is therefore 6 times the area of a side² square.
so, for side = 7 the surface area of the cube is
6 × 7² = 6 × 49 = 294 m²
and in the other direction, when we have the surface area (216 m²) :
216 m² = 6 × side²
36 = side²
side = sqrt(36) = 6 m
the volume of that cube is then
6³ = 216 m³
A student has a container with a volume of 2.5 Liters. He estimates the volume to be 2.6 liters By what percent is the student's estimate off?
The student's estimate is off by 4%.
The total points possible for each task are added. A student's semester average is the total points earned divided by the total points available. A method of testing hypotheses about the mean of a small sample drawn from a normally distributed population when the standard deviation of the population is unknown.
Calculation:-
A container with a volume of 2.5 Liters.
Estimates volume = 2.6 L
The student's estimates off by percent = 2.6 - 2.5 = 0.1
percentage = 0.1/2.5 =100
= 4%.
Student's t-test is used when comparing two independent groups but ANOVA extends the t-test to more than two groups. Both methods are parametric and assume the normality of the data and equal variance between comparison groups.
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Marc sold 500 tickets for the school play. Student tickets cost $2 and adult tickets cost $5. Marc's sales totaled $1,789.a.) Write a system of equations that can be used to determine how many of each type of ticket Marc sold.b.) Solve the system to determine how many adult tickets and how many student tickets Marc sold.
Given that:
- Marc sold 500 tickets for the school play.
- Student tickets cost $2.
- Adult tickets cost $5.
- The total amount of money from the sale was $1,789.
a.) Let be "x" the number of student tickets Marc sold for the school play, and "y" the number of adult tickets Marc sold for the school play.
You can represent the total number of tickets he sold with this equation:
[tex]x+y=500[/tex]You can represent the total amount of money from the sale with this equation:
[tex]2x+5y=1789[/tex]Now you can set up this System of Equations that can be used to determine how many of each type of ticket Marc sold:
[tex]\begin{cases}x+y={500} \\ 2x+5y={1789}\end{cases}[/tex]b.) You can solve the System of Equations using the Elimination Method:
1. Multiply the first equation by -2:
[tex]\begin{cases}(-2)(x+y)=(-2)({500)} \\ 2x+5y={1789}\end{cases}[/tex][tex]\begin{cases}-2x-2y={-1000} \\ 2x+5y={1789}\end{cases}[/tex]2. Add the equations:
[tex]\begin{gathered} \begin{cases}-2x-2y={-1000} \\ 2x+5y={1789}\end{cases} \\ ---------- \\ 0+3y=789 \\ 3y=789 \end{gathered}[/tex]3. Solve for "y":
[tex]\begin{gathered} y=\frac{789}{3} \\ \\ y=263 \end{gathered}[/tex]4. Substitute the value of "y" into the first original equation and solve for "x":
[tex]\begin{gathered} x+263=500 \\ x=500-263 \\ x=237 \end{gathered}[/tex]Hence, the answers are:
a.)
[tex]\begin{cases}x+y={500} \\ 2x+5y={1789}\end{cases}[/tex]b.)
[tex]x=237\text{ \lparen Number of student tickets Marc sold\rparen}[/tex][tex]y=263\text{ \lparen Number of adult tickets Marc sold\rparen}[/tex]The orange figure below is a scale drawing of theblack figure. What is the scale factor, rounded tothe nearest whole number?
Scale factor is given by the formula below:
[tex]\text{Scale factor =}\frac{new\text{ length}}{\text{old length}}[/tex]Using the right-hand side
new length = 1
old length= 3
substitute the values into the formular
[tex]\text{scale factors= }\frac{1}{3}=0.33333\approx0[/tex]