John recieved the greater discount and the original price of the bike is $120
John purchased the bike at a 20% discount off the original
price.
Let the price of the bike be x
The price at which John purchased the bike is x - 20% of x
= x - (20/100)x
=(80/100)x
Raul brought the bike at original price.
Raul's cost price is x
x is greater than (80/100)x
Raul purchased at a greater price than John, so the greater discount is recieved by John.
John got discount = (20/100) x
He saved = $24
(20/100)x = 24
20x =2400
x = 2400/20
x = 120
The original price is $120
Therefore, John recieved the greater discount and the original price of the bike is $120
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Sketch the graph of the line whose equation, in point-slope form, is y-3=9/5 (x+1). Also write the equation of this line in slope- intercept form .(y=mx+b )
Given the equation of the line in point-slope form:
[tex]y-3=\frac{9}{5}(x+1)[/tex]Based on this, one point of the line is (-1, 3). Now, the slope-intercept form of the equation is:
[tex]\begin{gathered} y-3=\frac{9x}{5}+\frac{9}{5} \\ y=\frac{9}{5}x+\frac{9}{5}+3 \\ \Rightarrow y=\frac{9}{5}x+\frac{24}{5} \end{gathered}[/tex]Then, another point of the line is (0, 24/5) = (0, 4.8). Finally, the graph of the equation is:
at this rate how many hours must Danielle babysit to earn $96
4 ---> 48
x ---> 96
[tex]\begin{gathered} 4\times96=x\times48 \\ 384=48x \\ \frac{384}{48}=\frac{48x}{48} \\ x=8 \end{gathered}[/tex]answer: 8 hours
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A rational number between the two given ones is -2/5, such that:
-1/3 > -2/5 > -1/2.
How to find a rational number between the two given ones?Rememeber that a rational number is any number that can be written as a quotient between two integer numbers.
Here we want to find a rational number between -1/3 and 1/-2, we can rewrite the second one as -1/2.
Now we want to find a number x such that:
-1/3 > x > --1/2
Remember that:
-1/3 ≈ -0.33...
-1/2 ≈ -0.5
So a number between these two is -0.4 which can be written as -2/5 (this is also rational).
That is the number we wanted to find.
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2) Create the first four terms based on the given recursive formulas below. Also determine if the
sequence you made is an arithmetic or geometric sequence:
G(1) = 18, G(n) = 2 · G(n − 1). H(1) = 3,H(n) = 5 · H(n − 1)
-
-
J(1) = 3, J(n) = J(n − 1) + 5 M(1) = 3, M(n) = 2 · (n − 1)
The first 4 terms of given recursive formulas will be as follows
G(n) = 18,36,72,144 (geometric sequence)H(n) = 3, 15, 75, 325 (geometric sequence)J(n) = 3, 8, 13, 18 (arithmetic sequence)M(n) = 3, 6, 12, 24 (geometric sequence)Recursive Expression:The recursive expression provides two pieces of information:
the first term in the sequence.
the pattern rule that takes each term from the previous term.
As we have G(1) = 18, G(n) = 2 · G(n − 1).
It's A geometric sequence with r as 2
∴ G(2) = 2 · G(2 − 1) = 2 · G(1) = 2(18) = 36.
∴ G(3) = 2 · G(3 − 1) = 2 · G(2) = 2(36) = 72.
∴ G(4) = 2 · G(4 − 1) = 2 · G(3) = 2(72) = 144.
As we have H(1) = 3, H(n) = 5 · H(n − 1).
It's A geometric sequence with r as 5
H(2) = 5 · H(2 − 1) = 5 . H(1) = 5(3) = 15.
H(3) = 5 · H(3 − 1) = 5 . H(2) = 5(15) = 75.
H(4) = 5 · H(4 − 1) = 5 . H(3) = 5(75) = 325.
As we have J(1) = 3, J(n) = J(n − 1) + 5
It's an arithmetic sequence with d as 5
J(2) = J(2 − 1) + 5 = J(1) + 5 = 3+5 = 8.
J(3) = J(3 − 1) + 5 = J(2) + 5 = 8+5 = 13.
J(4) = J(4 − 1) + 5 = J(3) + 5 = 13+5 = 18.
As we have M(1) = 3, M(n) = 2 · M(n − 1)
It's A geometric sequence with r as 2
M(2) = 2 · M(2 − 1) = 2 · M(1) = 2(3) = 6.
M(3) = 2 · M(3 - 1) = 2 · M(2) = 2(6) = 12.
M(4) = 2 · M(4 - 1) = 2 · M(3) = 2(12) = 24.
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Juanita works at a telemarketing company. She makes 12 sales calls per hour. Employees are encouraged to make more than 480 calls per week. Juanita has already made 180 calls this week. How many more hours, x, does Juanita need to work this week to reach the weekly goal of sales calls?
Using the mathematical operations of subtraction and division, Dan needs more than 25 hours to make more than 300 sales calls for this week to achieve the weekly goal.
What are the mathematical operations?Subtraction and division operations are two of the basic mathematical operations.
The subtraction operation involves operating on the minuend using the subtrahend to arrive at the difference.
In other words, the difference from a subtraction operation is the minuend minus the subtrahend.
The division operation is then applied to the difference above to arrive at the quotient.
The number of sales calls per hour = 12
The expected sales calls per week > 480
The number of sales calls already made by Juanita = 180
The more hours required to make more than 300, x, is 25 or more hours (480 - 180)/12
Thus, the number of more hours, using mathematical operations, that Juanita needs to reach the weekly sales calls goal is 25 or more hours.
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3) A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. What is the actual area of the park? Show how you know. (From Unit 1, Lesson 12)
Given:
Length of the park, l=4 inches
Width of the park, w=6 inches.
Here, 1 inch is equal to the 30 miles.
To find the actual area of the park:
Area of the park is, A=lw
That is,
[tex]\begin{gathered} A=4\times6 \\ =24\text{ inches} \end{gathered}[/tex]In miles,
[tex]\begin{gathered} A=24\times30 \\ =720\text{ miles} \end{gathered}[/tex]Hence, the area of the park in miles is 720 miles.
Which of the following are solutions to the equation below?
Check all that apply.
9x – 64 = 0
A. 8
B.
_ c.
C D.
3
F.
ო/დ
I
დო
3
J E. -8
დო
3
8
Answer:
C -8/3
F 8/3
Step-by-step explanation:
9x² - 64 = 0
==> 9x² = 64
==> x² = 64/9
x = ±√(64/9) = ±√64/√9 = ±8/3
It costs $5,600 to manufacture a Jet Ski. If the desired percent markup based on cost is 48%, how much should each Jet Ski sell for?
Each Jet Ski should sell for $8288.
What is selling price?
The amount a buyer pays for a good or service is known as the selling price. It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.
Let the selling price be x.
Therefore according to the question,
( x - 5600/ 5600) 100 = 48
=> x - 5600 = 48 . 56
=> x = 2688 + 5600
=> x = 8288
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Find BC.
Round to the nearest tenth.
C
12
A
87°
9
B
Answer:
C-10
A-90
B-10
Step-by-step explanation:
For rounding off to nearest tens, we compare the last digit.
A triangular priam has the following dimensions: width is 5 mm base is15 mm. What additional dimensions are needed to find the surface area ofthe prism?
If we need to determine the surface area of a prims we would have to add the areas of each of the faces of the prism, therefore, we would also require to know the length of the prism.
you are 37 years old and have accumulated $150,000 in your savings account. you intend to add a fixed amount each month for twenty years. for the first five (5) years you add $100 at the end of each month. then $ 200 at the end of the month for the remaining time. given that the account pays an interest rate of 6% per year compounded monthly, how much money will you have at age 58 in your savings account?
At age 58, the investor will have (Future Value) $571,816.64 in their savings account after accumulating $150,000 and then adding $100 monthly for five years and $200 monthly for fifteen years.
How is the future value at age 58 computed?The future value at age 58 can be computed in two tranches.
The first step is to compute the future value using the present value of the accumulated funds in addition to the periodic monthly investments.
The second step computes the future value using the present value of the funds after 5 years in addition to the periodic monthly savings.
Future Value at the end of the first 5 years:N (# of periods) = 60 months (5 x 12)
I/Y (Interest per year) = 6%
PV (Present Value) = $150,000
PMT (Periodic Payment) = $100
FV = $209,304.53
Sum of all periodic payments = $6,000 (60 x $100)
Total Interest = $53,304.53
Future Value at the end of the remaining years:N (# of periods) = 180 months (12 x 15 years)
I/Y (Interest per year) = 6%
PV (Present Value) = $209,304.53
PMT (Periodic Payment) = $200
Results:
Future Value (FV) = $571,816.64
Sum of all periodic payments = $36,000 ($200 x 180 months)
Total Interest = $326,512.11
Thus, you will have $571,816.64 as the future value in your savings account when you turn 58.
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D Question 6 6) sin A С 39 36 15 B 5 12 A) B) 12 13
B) 12/13
1) In this triangle, the sine of angle A is given by the opposite leg over the hypotenuse, so we can write it out. Since the hypotenuse is opposite to the right angle:
[tex]\begin{gathered} \sin (A)=\frac{36}{39} \\ \sin (A)\text{ = }\frac{12}{13} \end{gathered}[/tex]Note that we simplified that original ratio 36/39 dividing both numerator and denominator by 3
2) Hence, the answer is B) 12/13
consider a right triangle with acute angle of measure 0 and cos 0 = 4/5 use Pythagorean identity to write an equation that can be used to find Sim 0 is ( + ( 4/5 = 1
Question
Marco is writing a coordinate proof involving a right isosceles triangle. Marco places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis.
What coordinates should he assign to this third vertex of the isosceles triangle?
Responses
(2a, 2b)
begin ordered pair 2 a comma 2 b end ordered pair
(a, b)
begin ordered pair a comma b end ordered pair
(b, a)
begin ordered pair b comma a end ordered pair
(b, b)
69 billion and 580,000,000÷4,570,000=
create your own systems of equations that has a solution of (-2,4)
In this case we have the point (-2,4), since this represents the x and y coordinates of the solution of the system of equations, then:
x= -2
y= 4
Let's create the pair of equations:
1. ax+by=c
2. ex+fy=g
Randomly let's define the values of the coefficients a, b, e and f:
a= 1
b=2
e= -1
f= 4
With these values and the known coordinates of the solution, let's replace into the expressions of the system of equations and solve for c and g, like this:
the sum of negative three and a number, divided by seven, is negative two
Answer:
-3+x/7=-2 is equation, 7 is the answer
Step-by-step explanation:
-3+x/7=-2 add 3 to both sides.
x/7=1 multiply 7 to both sides
x=7 this is the answer
A jet flies at an average speed of 230
miles per hour. How long will it take to
fly from New York to Amsterdam, a
distance of 3,647 miles? (distance =
rate time)
.
Answer:
15
Step-by-step explanation:
Speed= 230 per hour
Distance=3,647
Formula
Time=Distance upon speed
divide 230 into 3,647=15 time
If f(x)= x² + 5x and g(x) = 3x + 2, finda. (f+g)(2) by evaluating f(2) and g(2).f(2)= g(2)=ƒ(2) + g(2) =b. (f+g)(x)=c. Evaluate your formula from part b at x = 2 to verify your answer to part a.(f+g)(2)=
Given:
f(x)= x² + 5x and g(x) = 3x + 2
Required:
To calculate
f(2)= g(2)=
(f+g)(x)=
(f+g)(2)=
Explanation:
a)-
[tex]\begin{gathered} f(2)=(x^2+5x)(2) \\ \\ =((2)^2+5(2)) \\ \\ =(4+10)=14 \\ \\ g(2)=(3x+2) \\ \\ =(3\times2+2) \\ \\ =(6+2)=(8) \end{gathered}[/tex][tex]\begin{gathered} f(2)+g(2) \\ \\ =(2^2+5\times2)+(3\times2+2) \\ \\ =(4+5\times2)+(3\times2+2) \\ \\ =(4+10)+(6+2) \\ \\ =(14)+(8) \\ \\ =22 \end{gathered}[/tex]b)-
[tex]\begin{gathered} f(x)+g(x) \\ \\ f(x)+g(x)=(x^2+5x)+(3x+2) \\ \\ determine\text{ the sign} \\ \\ x^2+5x+3x+2 \\ \\ \\ x^2+8x+2 \end{gathered}[/tex]c)-
[tex]\begin{gathered} (f+g)(x) \\ \\ (x^2+5x+3x+2)(2) \\ \\ (x^2+8x+2)(2) \\ \\ ((2)^2+8(2)+2) \\ \\ (4+16+2) \\ \\ (22) \end{gathered}[/tex]Required answer:
[tex]\begin{gathered} a)-22\text{ } \\ \\ b)-x^2+8x+2 \\ \\ c)-22 \end{gathered}[/tex]The probability distribution for arandom variable x is given in the table.Find the probability that x>5
The probability that x≥5
P (x≥5) = P(5)+P(10)+P(15)+ P(20)
P (x≥5)= 0.1+0.25+0.1+0.15
P (x≥5)= 0.6
This net represents an unfolded box. 4 in. 4x5=7 WXI- 2 sov 6 in. n 1 yo 10 in. sa 14 Sau What is the total surface area, in square inches, of this box?
The total surface area will be given by:
[tex]A=2A1+2A2+2A3[/tex]Where:
[tex]\begin{gathered} A1=40in^2 \\ A2=24in^2 \\ A3=6\cdot4=60in^2 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=2\left(40\right)+2\left(24\right)+2\left(60\right) \\ A=80+48+120 \\ A=248in^2 \end{gathered}[/tex]Answer:
248 in²
Find the distance between: (6,12) and (7,-4)
The formula for determining the distance betwwen two points is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt{(y2-y1)^2+(x2-x1)^2} \\ \text{From the information given,} \\ x1\text{ = 6, x2 = 7} \\ y1\text{ = 12, y2 = - 4} \\ \text{Distance = }\sqrt{(-4-12)^2+(7-6)^2} \\ \text{Distance = }\sqrt{-16^2+1^2}=\sqrt{257} \\ \text{Distance = 16.03} \end{gathered}[/tex]The distance is 16.03
Which is equivalent to multiplying a number by 10 to the power of 4
Answer: 10,000
Step-by-step explanation:
help me with this question please
Answer: 56
To solve this problem, we will use the formula for Combination which goes by
[tex]_{}C(n,r)=^nC_r=_nC_r=\frac{n!}{r!(n-r)!}[/tex]From the problem, we know that:
n = 8
r = 3
Since there are a total of 8 different movie soundtracks and we only need 3.
Substituting it on the formula,
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex][tex]C(8,3)=\frac{8!}{3!(8-3)!}[/tex][tex]C(8,3)=56[/tex]Therefore, there are 56 possible selections of movie soundtracks at the music store.
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write the word sentence as an equationa number w divided by 5 equals 6
a number : w
A number w divided by 5: w/5
equals (=) 6
[tex]\frac{w}{5}=6[/tex]III Comprehensive Mid term Review Part Question 2 of 60 (1 point) | Question Attempt: 1 of Unlimited 2 6 3 4 Convert 35°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. 5 C (F-32) 9 FC + 32 5 25 OF
Here, we want to make a unit conversion
Since we want to move from Fahrenheit to celsius, we are going to use the first formula
We simply are going to substitute the value of F = 35 into the equation
Thus, we have it that;
[tex]\begin{gathered} C\text{ = }\frac{5}{9}(35-32) \\ C\text{ = }\frac{5\times3}{9} \\ \\ C\text{ =}\frac{5}{3} \\ C\text{ = 1.7 deg celsius} \end{gathered}[/tex]Dilate the figure by the scale factor. Then enterthe new coordinates.A(1,3)B(4,2)K=3A’([?],[]).B'([10]C'([],[:]C(1,-3)Enter
The new coordinates after the dilation are as follows;
[tex]\begin{gathered} A^{\prime}\text{ (3,9)} \\ B^{\prime}\text{ (12,6)} \\ C^{\prime}\text{ (3,-9)} \end{gathered}[/tex]Here, we want to perform a dilation
Given a pre-image with coordinates (x,y) and a scale factor of k, the coordinates of the image will be;
[tex](x,y)\text{ = (kx,ky)}[/tex]Applying this to the given coordinates, we have;
[tex]\begin{gathered} A^{\prime}\text{ = }(3\times1,3\times3)\text{ = (3,9)} \\ B^{\prime}=\text{ (4}\times3,\text{ 2}\times3)\text{ = (12,6)} \\ C^{\prime}\text{ = (1}\times3,\text{ -3}\times3)\text{ = (3,-9)} \end{gathered}[/tex]the income for selling x units of a video game is R=257x. The cost to produce the game is C =193x +5248. In order to make a profit the income must be greater than the cost. find the vaule of X
The value of x when the income for selling x units of a video game is R=257x is x > 82.
What is the value of x?From the information given, it was stated that the income for selling x units of a video game is R=257x and that the cost to produce the game is C =193x +5248.
To make a profit the income must be greater than the cost. The value of x will be:
257x > 193x + 5248
Collect like terms
257x - 193x > 5248
64x > 5258
Divide
x > 5248/64
x > 82
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write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (5,65)
To write the equation of the line that passes through (10,80) (5,65)
we will use the formula;
[tex]y-y_1\text{ =}\frac{y_{2-}y_1}{x_2-x_1}(x-x_1)[/tex]x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65
substituting the above into the formula;
[tex]y\text{ - 80 = }\frac{65\text{ - 80}}{5\text{ - 10}}(\text{ x - 10)}[/tex]we will go ahead and simplify
[tex]y\text{ - 80 = }\frac{-15}{-5}(x-10)[/tex]y- 80 = 3(x - 10)
y- 80 = 3x - 30
y -3x -80 + 30 = 0
y - 3x - 50 = 0
The above is the equation of the line.
To write in a slope-intercept form simply means to write it in the form;
y = mx + b
where m is the slope and b is the intercept
Hence;
y = 3x + 50
The above is the equation of the line in a slope-intercept form