The sale price S (in dollars) of an item is given by the formula S=L-rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).I’ve already solved problem (a) although I’m not sure if it’s correct but I need help with problem (b)The list price of the shirt is $30 and the sale price is $18. What is the discount rate?
Answers
Since the equation of the sale price S is
\(S=L-rL\)a)
To solve for r add rL to both sides
\(\begin{gathered} S+rL=L-rL+rL \\ S+rL=L \end{gathered}\)Subtract S from both sides
\(\begin{gathered} S-S+rL=L-S \\ rL=L-S \end{gathered}\)Divide both sides by L
\(\begin{gathered} \frac{rL}{L}=\frac{L-S}{L} \\ \\ r=\frac{L-S}{L} \end{gathered}\)b)
Since the list price of the shirt is $30, then
L = 30
Since the sale price is $18, then
S = 18
Substitute them in the equation of r to find it
\(\begin{gathered} r=\frac{30-18}{30} \\ \\ r=\frac{12}{30} \\ \\ r=\frac{2}{5} \\ \\ r=0.4 \end{gathered}\)The discount rate is 0.4
Related Questions
What is the values of this table?
Answers
Yes, the given values in the table represent the function.
Explain about the term function?A mathematical phrase that describes the connection between two variables is called a function.
The input serves as the independent variable, and the outcome serves as the dependent variable. The worth of the input determines the worth of the outcome. A function is a statement that has a single output for each potential input. Many curvilinear equations, including squared and cubed equations, as well as the majority of linear equations (aside from vertical lines) are functions.Check to see whether all potential inputs have only one output to determine if a relation is a function. In other words, the representation is a function if each value of x results in just one value of y.
From the given table:
x y
-4 6
-2 5
0 4
2 3
4 2
As for every input value of 'x', there is a only one output value.
We can say that the given value in the table represents the function.
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The correct question is-
Is the values in the table represent the function?
Question 2
What is the lateral surface area of the triangular prism with the given net?
Select one:
15
9
5
12
9
9
8
8
B
8
10
Answers
Answer:
the answer is B) 24.
Step-by-step explanation:
To find the lateral surface area of the triangular prism, we need to find the perimeter of the base and then multiply it by the height of the prism.
Looking at the net, we can see that the base is a triangle with sides of length 3 cm, 4 cm, and 5 cm. So the perimeter of the base is:
3 cm + 4 cm + 5 cm = 12 cm
The height of the prism is given as 2 cm. Therefore, the lateral surface area is:
12 cm x 2 cm = 24 cm²
So the answer is B) 24.
IF THIS HELPED, CAN YOU PLEASE GIVE 5⭐? thank you
Find the area between Z = –1.15 and Z = 1.10.
Group of answer choices
Approximately 0.21
Approximately 0.74
Approximately 0.86
Approximately 0.95
Approximately 0.99
Answers
The area between Z = –1.15 and Z = 1.10 is approximately 0.74.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Using a standard normal distribution table or a calculator, we can find the area to the left of Z = 1.10 and the area to the left of Z = -1.15.
We have to subtract the area to the left of Z = -1.15 from the area to the left of Z = 1.10 to get the area between Z = -1.15 and Z = 1.10.
Using a standard normal distribution table, we can find that the area to the left of Z = 1.10 is approximately 0.8643
The area to the left of Z = -1.15 is approximately 0.1251.
Subtracting the area to the left of Z = -1.15 from the area to the left of Z = 1.10, we get:
Area between Z = -1.15 and Z = 1.10 ≈ 0.8643 - 0.1251 = 0.7392
Therefore, the area between Z = –1.15 and Z = 1.10 is approximately 0.74.
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PLEASE SOMEONE HELP.
Functions are in the world all around us. You have used functions to model phenomena and to
make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you
can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or
even with the same function. A composition of functions is useful when a change in one function
will create a change in another function, which, in turn, affects a third function. For example,
suppose that humans build a housing development on land that was previously used as a corn
field. This change in land usage causes the number of birds in the area to decrease, which causes
the number of mosquitos to increase. You could model the increase in the number of mosquitoes
as a function of the number of birds in the area, which is a function of the number of humans that
live on that land.
You can also use the composition of functions to show that one function is the inverse of another
function. Recall that the graphs of inverse functions are reflections of each other over the line .
Think about these ideas as you read through the scenario below.
Last night it started raining as Hibah was closing up the store where she works. By 3 am, the roof
of the store developed a small hole and water began to leak onto the sales floor. The water
created a circular puddle on the floor. At any time, t,
in minutes, the radius of the puddle increases by 0.1
cm. The rain continued through the night, but stopped
by the time the morning shift arrived at the store at 7
am.
When the employees arrived at work, the leak and
water puddle were discovered. The employees
cleaned up the water puddle and placed a tall circular
bucket underneath the leak, which was still slowly
dripping. The capacity of the bucket can be expressed
as () = 83 + 42 − 6 + 5. By 10 am, the
amount of water in the bucket is () = 23 + 2 − 4 + 7.
Use the information given to explore some of the mathematical concepts you have practiced so
far by answering the questions below.
Answers
Answer:
Hibah's store developed a leak in the roof during a rainstorm, causing a circular puddle to form on the sales floor. The radius of the puddle increased by 0.1 cm per minute. The rain stopped by 7 am, when the morning shift arrived and discovered the puddle. The employees cleaned up the puddle and placed a bucket under the leak.
I hope that's what your looking for :)
mega mart sells a large 5kg cake for $2500 while a 2kg chocolate cake cost $1200 what is the cheapest price sam would payfor 10kg of cake for the party
Answers
The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.
To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.
At Mega Mart, a 5kg cake costs $2500.
Therefore, the price per kilogram for this cake is:
Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.
At the same time, a 2kg chocolate cake costs $1200.
So, the price per kilogram for this cake is:
Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.
Now, let's calculate the total price for 10kg of cake from each option:
Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.
Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.
Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.
Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.
Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.
In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.
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Find an equation of the tangent line to the curve at the given point. y = x3 − 3x + 2, (3, 20)
Answers
Answer:
\(y - 20 = 24(x - 3)\)
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, has the following format:
\(y - y_0 = m(x - x_0)\)
In which the point is \((x_0,y_0)\) and the slope is m.
(3, 20)
This means that \(x_0 = 3, y_0 = 20\). So
\(y - y_0 = m(x - x_0)\)
\(y - 20 = m(x - 3)\)
Slope:
The slope is the derivative of the function at the point:
The function is:
\(y = x^3 - 3x + 2\)
The derivative is:
\(y^{\prime}(x) = 3x^2 - 3\)
At the point, we have that \(x = 3\). So
\(m = y^{\prime}(3) = 3*3^2 - 3 = 27 - 3 = 24\)
So the equation to the tangent line to the curve a the point is:
\(y - 20 = 24(x - 3)\)
Consider the statement:
20% of 25 is 5
Value: 5
The number 5 is the
The number 25 is the
The number 20 is the
Answers
Answer:
5 is the correct answer
Step-by-step explanation:
20 divide by 100 because it is in percent and 20 miltiply by 100 and there is the sign of multiply (of) is also known as multiply soo 20\100 * 25 will be the answer 5
QUESTION IN PICTURE
Please explain your answer in steps, thank you.
Answers
We can complete the blanks with the following ratios:
(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags
Since we do not need a flag at the starting line, then 32 flags will be required in total.
How to obtain the number of flagsTo solve the problem, we would first convert 400 yds to feet and miles.
To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.
To convert to miles, we would have 0.227 miles.
Now, we divide the entire race distance by the number of miles divisions.
This gives us:
7.5 mi /0.227 mi
= 33 flags
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The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
Answers
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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220/(divide) by 31.25 step by step or write in paper and send
Answers
Answer:
7.04
Step-by-step explanation:
The computation is shown below:
Given that
220 would be divided by 31.25
i.e.
= 220 ÷ 31.25
= 7.04
After dividing the 220 from 31.25 it provides an answer i.e. 7.04
A line is parallel to y = 4x + 1 and
intersects the point (-2,-5). What is the
equation of this parallel line?
y = [?]x + [ ]
Answers
Answer:
-2,-5 is the value. The correct Answer
Which of the following is equivalent to 1/x/x+3
Answers
Answer:
I do not understand your question
please help me i need the answer
Answers
Answer:
A
Step-by-step explanation:
4.24 3 90° A 3 C сов А n this triangle, COBB Reset Next Edmentum. All rights reserved.
Answers
Answer
Cos A / Cos B = 1
Explanation
Cos = Adjacent / Hypotenus
Cos A = adjacent / hypotenus
Cos A = 3 / 4.24
Cos B = Adjacent / hypotenus
Cos B = 3 / 4.24
Cos A / Cos B = 3 / 4.24 * 4.24 / 3
Cos A / Cos B = 1
The graph of a linear function is shown on the coordinate grid. What is the slope of the graph of this function in decimal form?
Answers
The slope of the graph of this linear function is -1/2 in decimal form.
What is slope?
The formula to find the slope between 2 coordinates of a line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (6, 1) and (x2, y2) = (-6, -5)
slope = (-5 - 1) / (-6 - 6)
slope = -6/12
slope = -1/2
Therefore, the slope of the graph of this linear function is -1/2 in decimal form.
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The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. (c) The top 25% scores are above what value? Explicitly compute the value.
Answers
To find the value above which the top 25% of scores lie, we need to find the z-score corresponding to the 75th percentile and use it to compute the corresponding raw score.
The z-score corresponding to the 75th percentile can be found using a standard normal distribution table or calculator. The 75th percentile corresponds to a cumulative probability of 0.75, so we need to find the z-score such that the area under the standard normal curve to the left of that score is 0.75.
Using a standard normal distribution table, we can look up the z-score corresponding to a cumulative probability of 0.75, which is approximately 0.67.
Alternatively, we can use the inverse cumulative distribution function (also known as the percent point function) of the standard normal distribution to find the z-score. In Python, we can use the scipy.stats.norm.ppf function to do this:
from scipy.stats import norm
z_score = norm.ppf(0.75)
Either way, we find that the z-score corresponding to the 75th percentile is approximately 0.67.
To find the raw score corresponding to this z-score, we can use the formula:
z = (x - mu) / sigma
where x is the raw score, mu is the mean, and sigma is the standard deviation. Solving for x, we get:
``x = z * sigma + mu
Plugging in the values for `z`, `sigma`, and `mu`, we get:
x = 0.67 * 40 + 300
Simplifying the expression, we get:
x = 326.8
Therefore, the top 25% scores are above the value of 326.8.
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in an examination 45% students passed in science only 25% passed in english only and 5% students failed in both subjects if 200 students passed in english find the total number of students by using venn diagram
Answers
Step-by-step explanation:
\(\huge\mathfrak\pink{Answer}\)
Total number of students= y
(25/100) xy= 200
25 xy = 200 x 100
25y 20000
y = 20000/25
y 800
total number of students = 800
Step-by-step explanation:
\(\mathfrak\pink{Answer}\)
Total number of students= y
(25/100) xy= 200
25 xy = 200 x 100
25y 20000
y = 20000/25
y 800
total number of students = 800
how can you find the area and perimeter?
Answers
After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:
1. Rectangle:
• Area: A = length x width
• Perimeter: P = 2(length + width)
2. Square:
• Area: A = side x side (οr A = side²)
• Perimeter: P = 4 x side
3. Circle:
• Area: A = π x radius²
• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)
4. Triangle:
• Area: A = (base x height) / 2
• Perimeter: P = side1 + side2 + side3
5. Trapezοid:
• Area: A = ((base1 + base2) x height) / 2
• Perimeter: P = side1 + side2 + side3 + side4
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Zakhele needs to draw up a budget of his monthly expenses. He earns R6500 per month. His bills in one month are rent R1650, electricity R300, car payments R12500 and petrol R400, account repayment R12500 and groceries R1200 . Given his current expenses. How much money is available for saving
Answers
Answer: -R22,050
Step-by-step explanation:
To find how much money Zakhele has available for saving, we need to subtract his total expenses from his income. So, we have:
Total expenses = Rent + Electricity + Car payments + Petrol + Account repayment + Groceries
Total expenses = R1650 + R300 + R12500 + R400 + R12500 + R1200
Total expenses = R28,550
Income = R6500
Available money for saving = Income - Total expenses
Available money for saving = R6500 - R28,550
Available money for saving = -R22,050
Based on these numbers, it appears that Zakhele's expenses are greater than his income, and he does not have any money available for saving. In fact, he has a deficit of R22,050, meaning he would need to borrow money or dip into his savings to cover his expenses for the month. If there was an error in the numbers provided, please let me know so I can adjust my calculations accordingly.
A punter kicked a 41 yard punt. The pth of the football can be modeled by y=-0.035x2 + 1.4x + 1 where x is the distance in yards the football id kicked and y id the height in yards the football kicked
Answers
This means that the football’s height when it was kicked 41 yards away was -1.762 yards.
What is yard?A yard is a unit of length measurement in the imperial and US customary systems of measurement. It is equal to 3 feet or 36 inches.
The equation given is a parabolic equation which models the path of the football. It is a quadratic equation in the form of y = ax² + bx + c, where a, b, and c are coefficients that determine the shape of the path. The coefficient a represents the rate of change in the football’s height as it moves away from the punter. In this equation, a is -0.035, which indicates that the football’s height decreases as it moves away from the punter. The coefficient b indicates the rate of change in the football’s height as it moves back toward the punter, and in this equation, b is 1.4, which means that the football’s height increases as it moves back towards the punter. Finally, the coefficient c is 1, which indicates the height of the football when it is kicked.
In this case, the football was kicked 41 yards, so plugging x = 41 into the equation gives us y = -0.035(41²) + 1.4(41) + 1 = -1.762.
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Evaluate the expression.
-5 x -0.2 (-0.5 - negative one)
Write your answer as an integer or a decimal. Do not round.
V
Answers
Answer: 0.5
Step-by-step explanation:
-5*(-0.2(-0.5-(-1)))=
1*(-0.5+1)=
-0.5+1=0.5
0.5.
Step-by-step explanation:1. Write the expression.\(-5*-0.2 (-0.5 - (-1))=\)
2. Simplify the parenthesis.\(-5*-0.2 (-0.5+1)=\\\\-5*-0.2 (0.5)\)
3. Multiply.\(-5*-(0.1)=\\ \\0.5\)
Dimensions of a building are 728 feet by 800 feet. If 1 inch represents 8 feet, what are the dimensions of the building on the drawing?
Answers
Answer:
91in by 100in
Step-by-step explanation:
i need help with this please
Answers
Answer:
y = - 1 and x = 8
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the lune passes through.
The line passes through (8, - 1) with y- coordinate - 1, thus
y = - 1 ← equation of horizontal line.
--------------------------------------------------------------------
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (8, - 1) with x- coordinate 8 , thus
x = 8 ← equation of vertical line
the function has an average rate of change of
Answers
On solving the provided question, we can say that Therefore, the function has an average rate of change of -1.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The function has an average rate of change of -1.
R = 4-5/1-0
R = -1
Therefore, the function has an average rate of change of -1.
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Under Todd’s new cable television plan, his bill averages $63 per month. This is 140% of his average monthly bill last year when he had the basic cable package. What was his average monthly cable bill last year?
Answers
Answer:
45
Step-by-step explanation:
translation :
140% of x = $63
x = $63 ÷ 1.4
x = $45
FUN FACTS :
interesting: 100% means double that number or times 2
if a price is $20 & it increases 100% in price that means its $20 times 2 or $40
percent means per 100
cent means 100 in latin
that's why the decimal moves 2 spaces
for the 2 zeros in 100
chatgpt
Tenjing bought two television at rs 52000 he is sold one of them at 10% profit and another at 10% loss if the selling price of both the television are same find its total gain or loss percentage in the transaction
Answers
the transaction results in a net gain.Net gain percentage = Net gain / Total cost price × 100%=(2SP - 52000) / 52000 × 100%Now, we can use the above expressions to calculate the total gain or loss percentage in the transaction.
Let's assume that the cost price of the first television set is CP1 and that of the second is CP2. As per the given information, the total cost price of both television sets is 52000 rupees.
Therefore, CP1 + CP2 = 52000Assuming the selling price of both television sets is the same, let's assume it to be SP for convenience. Selling price is defined as the price at which a product is sold to the customer. Therefore, the selling price of both television sets will be SP.
Now, we have to calculate the net gain or loss percentage in the transaction.Gain or loss is calculated as the difference between the selling price and cost price.
Gain or loss on the first television set is 10% of CP1, and the gain or loss on the second television set is 10% of CP2. Therefore,Gain or loss on the first television = 10/100 × CP1 = 0.1CP1Loss or gain on the second television = 10/100 × CP2 = 0.1CP2The selling price of both television sets is the same.
Therefore,Selling price of the first television = SPSelling price of the second television = SPThe selling price of both television sets combined is:Selling price of both television sets = SP + SP = 2SPNow, let's calculate the net gain or loss percentage in the transaction.
Net gain or loss = Selling price - Cost price= (SP + SP) - (CP1 + CP2)= 2SP - 52000Now, we need to determine whether the transaction resulted in a gain or a loss. We know that the gain or loss on the first television is 0.1CP1, and the gain or loss on the second television is 0.1CP2.
Let's consider two
cases:Case 1: When CP1 < CP2 (the cost price of the first television is less than that of the second television)In this case, the gain on the first television is less than the loss on the second television, as 0.1CP1 < 0.1CP2. Therefore, the transaction results in a net loss.
Net loss percentage = Net loss / Total cost price × 100%=(2SP - 52000) / 52000 × 100%
Case 2: When CP1 > CP2 (the cost price of the first television is greater than that of the second television)In this case, the gain on the first television is greater than the loss on the second television, as 0.1CP1 > 0.1CP2.
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15% of the seats on an airplane are first class if there are 24 class seats how many seats are on the plane
Answers
Answer:
160
Step-by-step explanation:
there are 24 first class seats. 15% of the total number is 24. that would mean 5% of the total number is 8. 20 times 8 is 160.
Which of the following points satisfies the inequality x ≥ -3? (Select all that apply.)
(0, -2)
(5, -5)
(-3, 4)
(-4, 2)
Answers
Answer:
(0,-2)
(5,-5)
(-3,4)
Answer:(0,-2)(5,-5)(-3,4)
Step-by-step explanation:
What would the answer be?
Answers
The length of the arc CD is 14.13 centimeters.
How to find the length of CD?Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:
L = (a/360°)*2*pi*R
Where pi = 3.14
Here the angle is a = 45°
And R = 18cm, so we can replace that in the formula above to find the length.
L = (45°/360°)*2*3.14*18cm = 14.13cm
That is the length of the arc CD.
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Calculate the volume of a cube with sides measuring 2.5metres
Answers
Answer:
15.625 m³
Step-by-step explanation:
Volume of the cube
= side³
= (2.5 m)³
= 15.625 m³