Lauren was given a gift card for a coffee shop. Each morning, Lauren uses the card to buy one cup of coffee. The original amount of money on the gift card was $10 each cup of coffee costs $2. Make a table of values and then write an equation in terms of x, representing the amount money remaining on the card after buying x cups of coffee.
Answers
The amount of money left on the gift card, in term of the number of cups, a Lauren has bought is represented by the equation would be A = 10 - 2a.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that from the task content that the total amount of money Lauren has initially is $10.
Hence, each cup of coffee costs $2.
Since the amount of money Lauren has left each time,
That is related to the number of coffee cups bought by the equation;
A = 10 -2a.
where a ranges be between 0 and 5.
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Related Questions
What’s the answer to the questions below? Plsss help
Answers
According to the information we can infer that the parallel line would be AD or CF. Additionally, the perpendicular lines would be CB or FE.
How to identify parallel lines?To identify the parallel lines we must look at the figure and find the lines that have the same direction as the line BE and that would never intersect with the segment BE, according to the above, we can infer that the parallel lines would be:
ADCFOn the other hand, the lines perpendicular to CF would be CB or FE because they make 90° angles with segment CF. Additionally, the face that would be parallel to ABC is DEF.
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I need to verify the identities of two functions and find the inverse of a one-to-one function
Answers
we have that
\(f(x)=\frac{1}{x-2}\)Find out the inverse
Let
y=f(x)
\(y=\frac{1}{x-2}\)Exchange the variables (x for y and y for x)
\(x=\frac{1}{y-2}\)isolate the variable y
\(\begin{gathered} y-2=\frac{1}{x} \\ y=\frac{1}{x}+2 \\ f^{-1}(x)=\frac{1}{x}+2 \\ \end{gathered}\)Part 2
Verify the identity function
\((\text{fof}^{(-1)})=\frac{1}{(\frac{1}{x}+2)-2}\)simplify
\((\text{fof}^{(-1)})=\frac{1}{\frac{1}{x}}=x\)and
\((f^{(-1)}of)=\frac{1}{\frac{1}{x-2}}+2\)simplify
\(\begin{gathered} (f^{(-1)}of)=x-2+2 \\ (f^{(-1)}of)=x \end{gathered}\)therefore
\((f^{(-1)}of)=(fof^{(-1)})\)PLEASE HELP
The table of values represents an exponential function.
What is the y-coordinate of -3f(x-1) when x = 0
Enter your answer in the box.
SEE PHOTO
Answers
The y-coordinate of -3f(x-1) when x = 0 is -63
What is the y-coordinate of -3f(x-1) when x = 0From the question, we have the following parameters that can be used in our computation:
The table of values
So, we have
-3f(x - 1)
When x = 0, we have
y = -3f(0 - 1)
This gives
y = -3f(-1)
From the table, we have
y = -3 * 21
Evaluate
y = -63
Hence, the y-coordinate is -63
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A shirt has a list price of $24. It is on sale for $18. What is the rate of discount?
A. 6%
B. 25%
C. 18%
D. 33 (1/3)%
Answers
Answer:
25%
Step-by-step explanation:
24-25%=18
24 - 100%
6 - 25%
The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 managers reveals a sample mean of $45,420. The standard deviation of the population is known to be $2,050.
a). Compute a 95% confidence interval, as well as the margin of error.
b). Interpret the confidence interval you have computed.
Answers
Answer:
a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
Step-by-step explanation:
Question a:
We have to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a p-value of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
\(M = 1.96\frac{2050}{\sqrt{49}} = 574\)
The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.
The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.
The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
Question b:
The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
simplify 3 ( y − 1 + 2 y )
Answers
Answer:
9y - 3
Step-by-step explanation:
3(y - 1 + 2y)
3y - 3 +6y
9y - 3
10 point question and brainliest
two people need to answer for me to give brainliest
Landscape Elementary uses 14 reams of paper every 3 weeks. How many reams of paper do they use each week? Round the answer to the nearest hundredth and do not include a label.
Answers
Answer:
4.67 (nearest hundredth)
Step-by-step explanation:
In 3 weeks, Landscape Elementary uses 14 reams of paper.
In 1 week, Landscape Elementary uses 14/3 reams of paper. = 4.66666...
The digit at thousandth place is 6 and it is more than 5. Thus add 1 with hundredth digit.
4.66666... = 4.67 (nearest hundredth)
write and solve an inequality to find the possible values of x
Answers
The inequality that represents the value of x is (b) x > 80
Writing and solving the inequality for xfrom the question, we have the following parameters that can be used in our computation:
The figure
The general rule is that
The larger the side length, the larger the angle opposite it
using the above as a guide, we have the following:
1/8x > 10
So, we have
x > 80
Hence, the inequality is x > 80
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2. On a number line, P has coordinate -30 and Q has coordinate 27. Find PQ.
Answers
Find the measure of the supplement of a 10° angle.
Answers
Answer:
170°
Step-by-step explanation:
180 - 10 = 170
precalculus problem need help
Answers
1. <C= 90 degree
AC = 13.25 unit
<B= 60 degree
2. <C= 90 degree
AC = 13.
<B= 60 degree
1. Using Sine law
sin C/4 = sin 30/2 = sin B/ AC
so, sin C/4 = 1/4
sin C = 1
C= 90 degree
and, <B= 180 - 30- 90= 60 degree
So, sin 30/2 = sin 60/ AC
1/4 AC = √3/2
AC = 2√3
2. Using Sine law
sin 30/ 7.65 = sin B / 15.3
1/15.3 = sin B/15.3
sin B= 1
B = 90 degree
and, <C= 180 - 90 - 30 = 60
So, 1/15.3 = sin 60/ C
C = 13.25
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the diagram shows a regular pentagon a) work out the interior angle , b) work out the size of one angle
pls help
Answers
Measure of one exterior angle = 30 degree
Measure of one interior angle = 150 degree
In the given regular pentagon
Number of terms = 12
We know that,
Sum of all exterior angles = 360 degree
To find one exterior angle,
Divide the complete angle by number of terms
Therefore,
One exterior angle = 360/12 = 30 degree
Since,
Sum of all interior angles = 180 degree
And To find one interior angle,
subtract the interior angle by one exterior angle
Therefore,
One exterior angle = 180 - 30 = 150 degree
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Please help quick I need it
Answers
The area of the composite figure is 122.24 units².
How to find the area of a composite figure?The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.
Hence,
area of the composite figure = area of the rectangle + 2(area of semi circle)
Therefore,
area of the composite figure = 9 × 8 + 2(1 / 2 πr²)
area of the composite figure = 72 + πr²
where
r = 8 / 2 = 4 units
Therefore,
area of the composite figure = 72 + 3.14 × 4²
area of the composite figure = 72 + 3.14 × 16
area of the composite figure = 72 + 50.24
area of the composite figure = 122.24 units²
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24 in.10 in.12 in.6 in.26 in.Find total surface area
Answers
we know that
the total surface area of the triangular prism is equal to the area of its two triangular faces plus the area of its three rectangular faces
so
SA=2[(1/2)(26)(6)]+(26)(12)+(12)(24)+(12)(10)
SA=156+312+288+120
SA=876 in^2
the answer is
surface area is 876 square inchesHow many different three letter words can be formed from the alphabet HJKLM
Answers
Answer:
0
Step-by-step explanation:
Every word that I am typing for the explanation has at least one vowel contained in it. There is not a single vowel in those letters.
You are welcome!
Kayden Kohl
Eight Grade Student
PLEASE HELP THIS IS SERIOUS DUE IN 5 MINS
You have been saving $4.50 per week for the last several weeks.
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w o w
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True or False? The segments shown below could form a triangle.
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Answer:
True
Step-by-step explanation:
The rule is that every 2 sides' sum is greater than the other side.
So, let's test it.
9+4>11
9+11>4
11+4>9
it checks out!
Select the correct answer from each drop-down menu.
Answers
9514 1404 393
Answer:
3(x^3)y -6x(y^2) +93Step-by-step explanation:
The above-listed answer choices are the only ones that are self-consistent.
The quotient choices all have a leading coefficient of 3, and the result of dividing by <some number> is a leading coefficient of 1. Obviously, the <some number> must be 3 (first choice on the second menu).
Looking only at the constant term, we see that after division by 3, we have 3. So the original quotient constant term must be 3×3 = 9 (first choice on the first menu). Note that we have chosen the correct answer simply by looking at coefficients, not even bothering with actual division of variables.
Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
Answers
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
show that the volume of the unit cube is one
Answers
Check the picture below.
The function shown in the graph is vertically stretched by a factor of 8 to produce a new graph. Which function represents the new graph?
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Answer:
\(f(x)=8\sin(2\pi x)\)
Step-by-step explanation:
The explanation is attached below.
Answer: f(x)=8sin(2πx)
Step-by-step explanation
Hope this explanation helps. Please see the attachment.
Write this number in standard form 3 thousands, 16 tens,7 ones
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PLEASE HELP AS SOON AS POSSIBLE
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A) The Slope is: 2
B) The interpretation of the slope is that there are two races for each number of track meet.
C) The y-intercept from the graph is at: y = 4
D) Equation of the line is: y = 2x + 4
How to find the slope of the linear graph?The general form of equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
From the given graph, we can see that the slope is gotten from the formula:
A) Slope = (y₂ - y₁)/(x₂ - x₁)
Thus:
Slope = (10 - 4)/(3 - 0)
Slope = 6/3
Slope = 2
B) The interpretation of the slope is that there are two races for each number of track meet.
C) The y-intercept from the graph is at: y = 4
D) Equation of the line is:
y = 2x + 4
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solve this proportion: 5/a = 3/4
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Answer:
\(a = \frac{20}{3}\)
Step-by-step explanation:
factorise x³-4x²+x+6
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The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
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1 1/2 divided by 1/4
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Answer:
Step-by-step explanation:
22
Answer:
Step-by-step explanation:
1 1/2 divided by 1/4
well the answer is 6 :>
Write an equation for the function that includes the points ( 1, 4/5) and ( 2, 2/3).
Answers
Answer:
f(x) = -2/15x + 14/15
Step-by-step explanation:
Slope = (2/3 - 4/5)/(2 - 1)
= (10/15 - 12/15) = -2/15
Plug in a known point (into y=mx+b) to find y-intercept:
4/5 = -2/15(1) + b
12/15 = -2/15 + b
b = 14/15
Formulate:
f(x) = -2/15x + 14/15
Which function has the same range as f (x) = negative 2 StartRoot x minus 3 EndRoot + 8?
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g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8
The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.
Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).
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Use the order of operations to find the value of the following expression. (4-9)(-4-1)
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Step by step.
We know PEMDAS is the order of operations, so Parentheses is first.
(4-9) (-4-1)
(-5) (-5)
Now multiply (-5)(-5)
Answer is 25
Find the sum of the first 10 terms of the following series to the nearest Integra 3, 5, 25/3,...
Answers
Answer:
S(10)=3*(1-(5/3)^10)/(1-5/3)
Step-by-step explanation:
It is Geometric series with r:
r=5/3=(25/3)/5=5/3
a=3
Sum of G.S. in formula:
S(n)=a(1-r^n)/(1-r)
S(10)=3*(1-(5/3)^10)/(1-5/3)
=246.5725...