Andrew decided so joys a tenner clench. Below is a chart that displays how many games of lenis he has played and the meatal cost of playing those panes. In this scenario, C ( y ) represents the total cost for playing games.
Answers
The linear function that represents the situation is of:
C(y) = 13y + 145.
The intercept is of:
C(0) = 145, meaning that the flat fee to pay the game is of $145.
What is the linear function?The slope-intercept representation of a linear function is given by the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the rate of change of the function.b is the y-intercept of the function, representing the initial value of the function.Two points of the function, from the table, are given as follows:
(8, 249) and (13,314).
The slope is given by the change in y of the two points divided by the change in x, hence:
m = (314 - 249)/(13 - 8) = 13.
Hence:
C(y) = 13y + b
When y = 8, C(y) = 249, hence the intercept b of the function is obtained as follows:
249 = 13(8) + b
b = 249 - 13 x 8
b = 145.
Meaning that the flat fee to pay the game is of $145.
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Related Questions
Connor borrows $8,000 at a rate of 19% interest per year. What is the amount due at the end of 7 years if the interest is compounded continuously?
$14,576.95
$30,248.35
$43,791.58
$29,215.37
Answers
Answer:
Step-by-step explanation:
30,248.35
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
Answers
Using the given function, the income for day 31 is
$10,737,418.24the total Income for working 31 days is
$21 474 836.47 How to find the income on day 31Using the given function an = a1 (r)^n-1
where
a1 = first day = 1
r = common ratio = 2
The income on day 31, n = 31
= 1 * 2^(31 - 1)
= 2^30
= 1,073,741,824 cents
= $10,737,418.24
Total Income for working 31 days n = 31
Using Sn= a1 (1-r^n) / 1 - r
Sn = (1 * (1 - 2^31)) / (1 - 2)
Sn = (1 - 2^31)) / - 1
Sn = (1 - 2147483648) /-1
Sn = 2147483647
Sn = 2,147,483,647 cents
Sn = $21 474 836.47
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10 = 2(x - 2)
How would I solve for X?
Answers
Answer:
x = 7Step-by-step explanation:
10 = 2(x - 2)
How would I solve for X?
10 = 2(x - 2)
10 = 2x - 4
14 = 2x
x = 7
--------------------
check
10 = 2(7 - 2)
10 = 2 x 5
10 = 10
the answer is good
Answer:
x=7
Step-by-step explanation:
Given:
A linear equation is given as:
[tex]10=2(x-2)[/tex]
To Find:
The objective is to solve the equation and find the value of x.
Explanation:
[tex]10=2(x-2)\\[/tex]
⇒ [tex]\frac{10}{2}=x-2[/tex]
⇒[tex]5=x-2[/tex]
⇒ [tex]x=7[/tex]
Final Answer :
The value of x is 7.
Given the function R(x) = x-7/x+2 find the values of a that make the function less than or equal to zero. Write the solution in interval notation
Answers
The solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function R(x) = x - 7 / x + 2
The given condition x - 7 / x + 2 ≤ 0
Solve the inequality as shown below
Here, the critical points are x = 7 and x = -2
Check the denominator for the critical point, x = -2 will not be suitable for the function as it becomes undefined,
Thus
−2<x≤7 or x (-2, 7]
Therefore, the solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
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Clara and toby are telemarketers. yesterday, Clara reached 6 people in 12 calls, while Toby reached 7 people in 13 phone calls. If they continue at those rates, who will reach more peoples in 40 phone calls? How many more?
Answers
Step-by-step explanation:
Firstly we determine how many people clara will reach in 40 phone calls.
6 people=12 calls
X people=40 calls.
make X the subject of the formula.
X=(6×40)÷12=20
So clara will reach 20 people in 40 phone calls.
Now lets determine how many people Toby will reach in 40 phone calls.
7 people=13 calls
Y people=40 calls.
Therefore making Y the subject of the formula we have,
Y=(7×40)÷13=21 people.
So toby will reach more people in 40 calls
A farmer purchased 480 meters of fencing, and will build a rectangular pen with it. To enclose the largest possible area, what should the
pen's length and width be? Model the pen's area with a function, and then find its maximum value.
To enclose the largest possible area, the pen's length should be__and width should be__.
Answers
The largest possible area will be 14400 meters², the pen's length should be 120 meters, and the width should be 120 meters.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
Let's assume that the length of the pen would be x.
We have been given the perimeter as 480 meters.
Let w be the width of the rectangle and l be the length of the rectangle
The perimeter of a rectangle = 2(l+w)
So, 480= 2(x + w)
240 = x + w
w = 240 - x
Length = x and width = (240 – x)
Area = x(240 - x) = 240x - x²
To get the maximum area, we equate the first derivative of the area to zero.
A = 240x - x²dA/dx = 240 - 2x = 0
2x = 240
x = 120
So, width = 240 – x = 240 – 120 = 120.
Maximum area = length × width
Maximum area = 120 × 120 = 14400 meters²
Thus, the pen should be 120 meters long and 120 meters wide, with a maximum possible area of 14400 meters².
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Liam is setting up folding chairs for a meeting. If he arranges the chairs in 7 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 5 rows of that same length, he has 17 left over. How many chairs does Liam have?
Answers
Answer: 47
Step-by-step explanation: Let's call the number of chairs Liam has x. We can set up the following equations to represent the problem:
7r = x - 5
5r = x - 17
Where r is the length of each row.
To solve for x, we can set the two equations equal to each other:
7r = x - 5
5r = x - 17
Then we can solve for x by combining like terms and solving for the value of x:
7r - 5r = x - 5 - x + 17
2r = 12
r = 6
We can substitute the value of r back into either of the original equations to solve for x:
7r = x - 5
7 * 6 = x - 5
x = 47
Therefore, Liam has 47 chairs.
Which statement is true about the algebraic expression 450 −15t?
A student has 450 marbles. Each of their t friends gives them 15 marbles. The expression represents the total marbles the student has.
A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
A student has 450 marbles. They give t marbles to one of their friend and 15 marbles to another. The expression represents the total marbles the student is left with.
A student has 450 marbles. One of their friends gives them t marbles and another friend gives them 15 marbles. The expression represents the total marbles the student has.
PLEASE HELP I'M SOOO CONFUSED
Answers
The statement that is true about the algebraic expression 450 −15t is B. A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
What is the definition of an algebraic expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
In this case, when a student has 450 marbles. They give t marbles to each of their 15 friends.
The expression represents the total marbles the student is left with will be:
= 450 - (15 × t)
= 450 - 15t
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The functions f(x) and g(x) are shown in the graph. What is g(x)?
Answers
g(x)=(x-2)^2
The sum of 10 and b, multiplied by 8
Answers
What are the distances from the point (x, y) to the focus of the parabola and the directrix?
Select two answers.
distance to the focus: √(x+3)²+(y-3)²
distance to the directrix: |y+4|
distance to the focus: √(x+3)²+(y-2)²
distance to the focus: √(x-2)²+(y+3)²
distance to the directrix: |y-4|
distance to the directrix: |x-4|
Answers
The distances from the point (x,y) are given as follows:
Distance to the focus: √(x+3)²+(y-2)².Distance to the directrix: |y - 4|.How to obtain the distance between two points?Suppose that we have two points with coordinates given by [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates of the focus of the parabola are given as follows:
(-3,2).
Hence the distance of the point (x,y) to the focus of the parabola is given as follows:
√(x+3)²+(y-2)².
The equation that defines the directrix is given as follows:
y = 4.
The y-coordinate of the point is of:
y.
Hence the distance is of:
|y - 4|.
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4.40x2.50
i really need this please
Answers
Answer:
11
Step-by-step explanation:
If it is correct, could you please give me brainliest? I would really appreciate it! Thank you!
Find the Maclaurin series of the following functions.
(b) g(x) = sin(3x^2)
Answers
The Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
The function is given in the question as
g(x) = sin(3x²)
Taylor (Maclaurin) series of sin(3x²) up to n = 3
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) =sin(3x²)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(sin(3x²))′ = 6xcos(3x²)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(6xcos(3x²))′=−36x2sin(3x2)+6cos(3x²)
Evaluate the 2nd derivative at the given point: (f(0))′′=6
3rd derivative: f(3)(x)=(f(2)(x))′=(6xcos(3x²))′=−36x2sin(3x²)+6cos(3x²)
Evaluate the 3rd derivative at the given point: (f(0))′′′=0
Now, use the calculated values to get a polynomial:
[tex]g(x)=0+\frac{0}{1!}x+\frac{6}{2!}x^2+\frac{0}{3!}x^3+\frac{0}{4!}x^4+\frac{0}{5!}x^5[/tex]
Thus, the Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
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Which set of rational numbers is arranged from least to greatest? (4 points) a −3.5, negative 1 over 4 , 2, 1 over 3 b −3.5, negative 1 over 4 , 1 over 3 , 2 c 2, 1 over 3 , negative 1 over 4 , −3.5 d negative 1 over 4 , 1 over 3 , 2, −3.5
Answers
The set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option (b).
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
The given sets of rational numbers are:
(a) -3.5, -1/4, 2, 1/3
(b) -3.5, -1/4, 1/3, 2
(c) 2, 1/3, -1/4, -3.5
(d) -1/4, 1/3, 2, -3.5
Note that 1/4 = 0.25 and 1/3= 0.33
Therefore, the set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option(b).
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SOLVE FOR P
-2p = -3p + 8
P=
Answers
Answer:
P= 8
Step-by-step explanation:
-1 (-2p = -3p + 8)
2p = 3p - 8
-p = -8
p = 8
to check this...
-2(8) = -3(8) + 8
-16 = -24 + 8
-16 = -16
+3p
1p=8
1/8=8
Write 50.001 in word form
Answers
A number is between 41 and 46. It has prime factors of 2 and 11. What is the number?
Answers
The answer you are looking for would be 44.
Step-by-step explanation:Here,
The number lies between 41 and 46 are 42, 43, 44, and 45
From the straightforward observation and according to the condition that must be divisible by 2 and 11 there is only one number that is divisible by both 2 and 11 is 44.
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I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
A positive integer is 6 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(5,9), then find the two integers.
Answers
The two integers are equal to 1 and 7 respectively.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let x represent the smaller number. Then the given relationships say ...
1/x + 2/(x+6) = 9/7
Multiplying by 7x(x+6), we have ...
7(x+6) +14x = 9x(x+6)
9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides
9x² +33x = 42 . . . . . . . . ...subtract 21x
3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3
(3x +14)(x -1) = 0 . . . . . . . . factor
Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.
Therefore, the two integers are equal to 1 and 7 respectively.
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How do I solve this?
Answers
11) (Level 2):
I believe if you just multiply the shaded area (10x6), then maybe subtract the non-shaded area (20cm and 10 cm). After doing this process, I believe you will get: 200-60 = 140! (But then again I could be wrong, I’ll admit it I’m not a pro but at least I gave effort!)
Fraction: 14/10
Decimal: 1.4
Percent: 140%
12) (Level 3):
I have absolutely no idea about this question and I don’t want to guess! Sorry!
please help please I need i real bad
Answers
Answer:
C
Step-by-step explanation:
Answer:
I think the Answer choice = C
Step-by-step explanation:
helppppp plsssssss
what is the average rate of change of the function on the interval from x = 3 to x = 5? f(x)=10(2)x Enter your answer in the box.
Answers
The average rate of change of the function on the interval from x = 3 to x = 5 is 40.
What is meant by average rate of change?In mathematics, the average rate of change is a measure of how much a dependent variable (such as y) changes in proportion to a change in the independent variable (such as x). It is calculated by dividing the change in the dependent variable by the change in the independent variable during a certain time period. If the value of y rises by 5 units when the value of x rises by 2 units, the average rate of change is 5/2 Equals 2.5 per unit change in x. Calculus students frequently use this idea to compute the slope of a line on a graph or to calculate the rate at which a function changes. It is a crucial idea in several domains.
How to solve?
f(x) = 10(2)x,the interval is from x = 3 to x = 5
At x = 3, 10(2)3 = 80
at x = 5, 10(2)5 = 160
total change over the interval from x = 3 to x = 5 is 160 - 80 = 80.
the length of the interval is 5 - 3 = 2,
average rate of change is 80 / 2 = 40.
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Hector saved $726 in 6 months. he saved the same amount each month. How much did hector save each month? I don’t have the answer and I don’t get it !
Answers
Answer:
He saved $121
Step-by-step explanation:
All you have to do is divide $726/6 which gives you $121.
Hope this helps!
Question 6 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. More than 1 solution
B. x = 4, y = 3
C. No solution
D. x = 3, y = 4
y-2x = -2
y-x = 1
Answers
Answer:
D x = 3 y = 4
(3.4)
Step-by-step explanation:
See below
Supposed you invest 1000 at 9% interest, compound monthly . Find the amount you have after 18 months
Answers
The amount you have after 18 months is $ 1143.96 .
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
[tex]A=P {(1 +\frac{r}{n})^{nt} }[/tex]
Given:
P = 1000 , r in decimal = 0.09 ,
n = 12 , t = 1.5 ( 18 months = one and a half years).
Substituting the values into the formula:
A = 1000 ( 1 + 0.09/ 12 ) ^[12 ( 1.5 )]
≈ 1000 ( 1.143960 )
= 1143.960
Rounding to the nearest cent, we get $ 1143.96 .
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40! points Which expression is equivalent to 2x + 7y + 4x - 3y * 1 point
6x + 10y
6x - 10y
6x + 4y
6x - 4y
Answers
2x+4x=6x
7y-3y= 4y
So the answer has to be D
7y - 3y = 4y
find the inverse of
f(x) = 4x + 2 over 3
Answers
Answer: f^-1(x)=(3x-2)/4
Step-by-step explanation:
1. Change the x and y
y=(4x+2)/3 → x=(4y+2)/3
2. Swap sides (optional)
x=(4y+2)/3 → (4y+2)/3=x
3. Multiply the equation by 3 on both sides
(4y+2)/3=x → (3)*(4y+2)/3=x*(3)
4. Subtract 2 from both sides
(3)*(4y+2)/3=x*(3) → 4y=3x-2
5. Divide 4 from both sides
4y=3x-2 → y=(3x-2)/4
6 Substitute f^-1(x) for y
y=(3x-2)/4 → f^-1(3x-2)/4
|6y-7|=-1 solve please
Answers
Answer:
no solution
Step-by-step explanation:
You want the solution to the absolute value equation |6y -7| = -1.
AnalysisThe expression on the left side of the equal sign is the output of the absolute value function. That output can never be negative: all negative input values are transformed to positive output values by the absolute value function.
The expression on the right side is negative. There is no value of the variable that will make the absolute value function give a negative output. There can be no solution.
Given f(x)=ln x, evaluate
a) f (e⁴)
b) f (e ㏑ 5)
c) f (e³ ㏑ 5)
Answers
The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.
What is the natural logarithm?
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Given,
f(x) = ln x,
a) f(e⁴)
f(e⁴) = In(e⁴)
= 4In(e)
= 4 * 1
f(e⁴) = 4
b) f(e ㏑ 5)
= f(e⁻⁵)
= [tex]f(e^{\frac{1}{5} })[/tex]
= In(1) - In(e⁵)
= 0 - 5In(e)
= 5*1
f(e ㏑ 5) = 5
c) f(e³ ㏑ 5)
[tex]= f(e^{\frac{3}{5} })[/tex]
= In(3) - In(e⁵)
= ln(3) - ln(5)
f(e³ ㏑ 5) = -0.5108
Hence, The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.
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NO LINKS!! You have 4 contestants in the second heat of the big race:
The equations for the contestants are:
1. Mr. Pace: y= 3/4x + 4
2. Mr. Glintz: y= 2/3x + 7
3. Ms. Liskey: y= 3x
4. Mr. Brininger: y= 1/2x + 10
Answers
Answer:
Part (c):
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerPart (d):
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sPart (e):
y = 3x + 2Step-by-step explanation:
Given equations:
[tex]\textsf{1.\;\;Mr.\;Pace}: \quad y = \dfrac{3}{4}x + 4[/tex]
[tex]\textsf{2.\;\;Mr.\;Glintz}: \quad y = \dfrac{2}{3}x + 7[/tex]
[tex]\textsf{3.\;\;Ms.\;Liskey}: \quad y = 3x[/tex]
[tex]\textsf{4.\;\;Mr.\;Brininger}: \quad y = \dfrac{1}{2} + 10[/tex]
Plot the lines on the given coordinate plane.
(See attachment).
Draw a line at y = 25 to represent the distance at the finish line.
Find the points of intersection of the linear equation of each contestant and the finish line equation y =25. The point with the smallest x-value is the contestant who is first place.
Mr Pace
[tex]\begin{aligned}\implies 25&= \dfrac{3}{4}x + 4\\\dfrac{3}{4}x&=21\\x&=28\; \sf seconds\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 25&= \dfrac{2}{3}x + 7\\\dfrac{2}{3}x&=18\\x&=27\; \sf seconds\end{aligned}[/tex]
Mr Liskey
[tex]\begin{aligned}\implies 25&= 3x\\x&=8.33\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 25&= \dfrac{1}{2}x + 10\\\dfrac{1}{2}x&=15\\x&=30\; \sf seconds\end{aligned}[/tex]
Therefore, the order in which the contestants reached the finish line is:
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerFrom inspection of the attached graph, Ms Liskey (red line) passes all three contestants. To find the time at which she passes the other contestants, substitute her equation into the contestant's equation and solve for x.
Mr Pace
[tex]\begin{aligned}\implies 3x&= \dfrac{3}{4}x + 4\\\dfrac{9}{4}x&=4\\x&=1.78\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 3x&= \dfrac{2}{3}x + 7\\\dfrac{7}{3}x&=7\\x&=3\; \sf seconds\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 3x&= \dfrac{1}{2}x + 10\\\dfrac{5}{2}x&=10\\x&=4\; \sf seconds\end{aligned}[/tex]
Therefore:
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sIf you want to win the race, either:
increase the slope of Ms Liskey's equation: y = 4xor add a value to Ms Liskey's equation: y = 3x + 2Solve the following quadratic
function by factoring:
f(x)=x²-10x+9
Enter the number that belongs in the green box.
x = 9; x = [?]
Answers
Answer:
1
Step-by-step explanation:
x²-10x+9 = 0
(x-9)(x-1) = 0
x-9 = 0 => x=9
x-1 = 0 => x=1