The amount that Stephen owed after 2 weeks is $100.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Stephan borrowed $125 to buy an electric scooter and the function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
The amount after 2 weeks will be:
f(x) = 125 - 12.5x
= 125 - 12.5(2)
= 125 - 25
= $100
The amount is $100.
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Complete question
Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan. What is the amount owed after 2 weeks?
Use the given information to prove that angle 8 is congruent to angle 1. Use two-column proof.
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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Given the equation
2x² = 12x - 5
enter the values of a, b, and c, where a is a positive integer.
The values of a= 2, b= -12 and c= 5.
What is Quadratic Equation?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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he provider ordered lactated ringers (lr) to infuse at 75 ml/hr for the next 24 hours. how many liters of lr will infuse? (record answer to the tenth [one decimal place]. do not use a trailing zero.)
he provider ordered lactated ringers (lr) to infuse at 75 ml/hr for the next 24 hours. 18.0 liters of lr will infuse with rate of infusion.
First, we need to determine how many milliliters of LR will be infused over 24 hours. So, we need to multiply the rate of infusion (75 mL/hr) by the number of hours (24). This will give us the total number of milliliters that will be infused. In this case, it is 75 x 24 = 1800 mL. To determine the number of liters, we need to divide this by 1000 since there are 1000 mL in 1 L. Therefore, 1800 mL/1000 = 1.8 L. We can round this number up to the tenth (one decimal place), and the answer is 18.0 L.
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Damian works after school. each day he earns a set amount, plus an hourly wage. the function f(x) = 12x + 10 models the amount he earns each day for working x hours. how much does damian earn on friday if he works for 2.75 hours?
Answer:
$43
Step-by-step explanation:
[tex]f(2.75) = 12(2.75) + 10 [/tex]
[tex] f(2.75) = 33 + 10 = 43[/tex]
△ABC ha vertice A(1, 3), B(2, 5), and C(5, 3). What are the coordinate of B′ after the tranformation (x, y) ⟶ (–y, x), then tranlation 1 unit right and 4 unit up? help me out pl
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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What is ALWAYS true about the
coordinates of x-intercepts?
the x-value will be 0
the x-value will be equal to the y-value
the y-value will be 0
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
Varsity Press, a published of college textbooks, received a $70,000 promissory note at 12% ordinary interest for 60 days from one of its customers, Reader's Choice Bookstores. After 20 days, Varsity Press discounted the note at the Grove Isle Bank at a discount rate of 14.5%. The note was made on March 21.
a.) What was the maturity date of the note?
b.) What was the maturity value of the note?
c.) What was the discount date of the note?
d.) What proceeds did Varsity Press receive after discounting the note?
Answer:c
Step-by-step explanation: i did the test
I need help plssssssss
Answer:
a. 25%
b. 5%
Step-by-step explanation:
a. Take 60000 divided by 240000, then times 100% = 25%
So the solution for a is 25%
b. Take 12000 divided by 240000, then times 100% = 5%
So the answer for b is 5%
A cabin cruiser traveling with the current went 45 mi in 3 h. Traveling against the current, it took 5 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current.
The rate of cabin cruiser in calm water id 12 miles/h and the rate of the current is 3 miles/h.
let the speed of cabin cruiser in still water be x miles/h
let the speed of current be y miles/h
during travelling with the current, speed of cabin cruiser = (x+y) miles/h
during travelling against the current, speed of cabin cruiser =(x-y) miles/h
time taken during case 1 = [tex]\frac{45}{x+y}[/tex] =3 h --->given
=> x+y = 45/3
after solving x+y=15 ------ (i)
time taken during case 2(against current) = [tex]\frac{45}{x-y}[/tex] =5 --->given
=> x-y = 45/5
after solving x-y =9 -------- (ii)
adding equation (i) and (ii) we get
x+y+x-y = 15+9
=> 2*x=24
=> x= 12
so x= 12 miles/h
so y=15-x= 15- 12 = 3miles/h
so x = 12 miles/h ,y= 3miles/h
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help pls i don’t understand this cause my teacher can’t teach
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]
Funky Fro-Yo
The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in
the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes
you can fill your cup with yogurt and toppings for $0.40 per ounce.
1. Write an equation that gives the total cost in dollars, d, of attending the event if you
order z ounces of fro-yo.
2. If your cup weighs 14 ounces, how much would you pay in total for the evening?
1) An equation that gives the total cost in dollars, d, of attending the event if you order z ounces of fro-yo is d = $5 + $0.40z
2) 2. If your cup weighs 14 ounces, you would pay $10.6 in total for the evening.
Define equation.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts.
Given,
The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes you can fill your cup with yogurt and toppings for $0.40 per ounce.
1) Total cost = d
Total ounces = z
Equation
d = $5 + $0.40z
2) If cup weighs 14 ounces
d = $5 + 0.40(14)
d = $5 + $5.6
Total cost:
d = $10.6
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The table shows a school district's enrollment
for two successive years. Write a linear function
using the data (with x representing the year
number), and then use the model to predict the
enrollment in Year 4.
Year 1 - 8295
Year2 -8072
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]
Ue the given et to find |X∩Y|. U={a,b,c,d,…,x,y,z} X={t,e,a,,i,n,g} Y={,u,a,v,e}
Ue the given sets U={a,b,c,d,…,x,y,z} X={t,e,a,,i,n,g} Y={,u,a,v,e} therefore the elements in X n Y is a, e
we have to calculate |X∩Y|
U={a,b,c,d,…,x,y,z}
X={t,e,a,,i,n,g}
Y={,u,a,v,e}
X n Y= a, e
because in intersection set the elements coming in XnY is those which are common in X and Y
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designs for their
In popular online role playing game, players can create detailed
character's "costumes," or appearance. Abigail sets up a website where players can
buy and sell
these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
146 visitors purchased no costume.
230 visitors purchased exactly one costume.
A
31 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
exactly one costume as a decimal to the nearest hundredth.
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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Evaluate:
10 Σn=1 8(1/4) n -1= [?]
Mixed Number Form is 102184532768.
Evaluate:10 Σn=1 8(1/4) n -1= [?]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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Select the graph for the solution of the open sentence. Click until the correct graph appears.
2|x| < 4
Answer:
1st one
Step-by-step explanation:
So 2|x|<4 = |x|<2, and since absolute values are always positive, I believe it is the 1st one.(Sorry if its not right I'm not very good in this area.)
if the probability that a baby born in a certain hospital will speak in the next day is , what is the probability that at least babies out of a cluster of babies will speak tomorrow?
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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if $0.\overline{1331}$ is written as a fraction $\frac{a}{b}$ with $a$ and $b$ being positive integers with a greatest common divisor of 1, what is $a b$?
The value of a is 133 and b is 999.
A vinculum is a horizontal line that serves a variety of functions in mathematical notation. In decimal numbers, a bar across one or more consecutive digits indicates that the pattern of digits beneath the bar repeats indefinitely.
Given [tex]0.\overline{1331}[/tex]. This means that 1331 repeats many times in this expression. This expression is the same as 1330/9990.
1, 7, 19, and 133 are factors of 133, and 1, 3, 9, 27, 37, 111, 333, and 999 are the factors of 999. From this, the GCD is found to be 1.
Therefore, by simplifying, we get 1330/9990 = 133/999. The answer to a is 133 and b is 999.
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Mike has a box with 5 white marble, 3 green marble and 2 blue marble. he picks 2 marbles from the box. what is the probability that he will get two green marbles?
Answer:
1/15
Step-by-step explanation:
3/10 x 2/9
A rectangular closet is 4 feet long. It is 3 times as wide as it is long.
Label the diagram with the dimensions of the closet.
12
ft
4
ft
4
ft
4
ft
4
ft
Great job!
Find the perimeter of the closet.
12 ft
4 ft
4 ft
4 ft
4 ft
The perimeter of the closet is
feet.
The dimensions of the closet are 4 feet long and 12 feet wide and the perimeter is 32 feet
What is the perimeter of a rectangle?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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FILL IN THE BLANK. _________ are the characteristics of the individuals of the population being studied.
Answer:
Variables
Step-by-step explanation:
Variables are the characteristics of the individuals of the population being studied.
In which cases should we use mean, medium, mode, and range etc. respectively?
Answer:
Mean, median, mode, and range are all statistical measures that are used to summarize and analyze data. Mean is the arithmetic average of a set of numbers, calculated by adding all the numbers together and dividing by the total number of values. Median is the middle value in a set of numbers, which is the value that divides the data into two equal halves. Mode is the value that occurs most frequently in a set of numbers. Range is the difference between the largest and smallest values in a set of numbers.
Mean is commonly used to calculate the average value of a set of numbers. The Median is commonly used to find the middle value in a set of numbers, especially when the data is not evenly distributed. Mode is commonly used to find the most frequent value in a set of numbers. The range is commonly used to find the difference between the largest and smallest values in a set of numbers.
All of these measures are useful for different purposes, and which measure to use will depend on the data and the question being asked. In general, mean is used when the data is evenly distributed, median is used when the data is not evenly distributed, mode is used when the data is categorical rather than numerical, and range is used to measure the spread of the data.
Which of the following is an example of rational function?
1.f(x)=3x²+1 over x-1
2.x over 3 = 8 over 3
3.1 over 3x-1 +3<0
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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Find the slope of the line y=
10/19x+15.
Write your answer as an integer or as a simplified proper or improper fraction.
Answer:
10/19
Step-by-step explanation:
the slope of the line is the term that multiplies x
Answer: 10/19 is the slope
In triangle xyz, m∠y = 45.43° and m∠z = 38.7°. determine the measure of the exterior angle to ∠x. 44.57° 51.3° 75.75° 84.13°
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!
how much work is done raising an 8 lb mass to a height of 18 ft above the ground? (use decimal notation. give your answer as an exact number.)
Therefore, the work done in this problem comes out to be 144 ft pound.
Where is the work done?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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Prove that every point on the perpendicular bisestor of a segment is equidistant from the endpoint of segment​.
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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You are looking at buying a gym membership. Total Gym has a starting fee of $100 and costs $20 every month. Fitness Plus Elite costs $25 each month with an initial membership cost of $35. At what month will both memberships cost the same? Write and solve an equation to answer the problem. Explain what the answer means for the problem.
Answer:
The answer is 13 because that is the month that both memberships will cost the same amount of money.
Step-by-step explanation:
First translate the question into equations.
Total Gym:
100+20m
Where "m" equals the amount of months
Fitness Plus Elite
35+25m
Where "m" equals the amount of months
Set the equations equal to each other and solve for m, or the amount of months it takes to get the same price for each membership.
100+20m=35+25m Subtract 35 from both sides.
65+20m=25m Subtract 20m from both sides
65=5m Divide both sides by 5
13=m Both memberships will cost the same amount of money at 13 months. You can substitute this value into the original equations to check your work.
100+20(13)=$360
35+25(13)=$360
The answer is 13 because that is the month that both memberships will cost the same amount of money.
Am I correct? Since the measure of the triangle is always 18. So, I added 117+ 33 which gave me 150. Next, I subtracted 150 from 150 from one side. Then, I subtracted 180 from 150 which gave me 33.
The measure of the angle ∠ACD will be 150°. Then the correct option is D.
What is the triangle?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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what is the answer to 3^4 + 18 ÷ 3 +2
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