A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "Seven-eighths of my cats plus five." How many cats does the nemesis have?
The question presents a riddle that can be solved by setting up and solving an algebra equation. Based on the provided information, the solution to the problem is that the nemesis has 40 cats.
Explanation:The problem describes a riddle: "Seven-eighths of my cats plus five." This scenario is a typical mathematical representation of an algebra problem where you need to find the total number of cats.
Let us denote the total number of cats as 'C'. According to the riddle, 7/8 of the cats plus 5 equals the total cats. As per this, the equation can be written as 7/8*C + 5 = C. Solving this will lead us to find the number of cats.
Subtract 7/8*C from both sides of the equation: 5 = C - 7/8*C, which simplifies into: 5 = 1/8*C. To solve for 'C', we then multiply both sides of the equation by 8: 5*8 = C. Hence, the nemesis has 40 cats.
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Using simple linear regression, calculate the trend line for the historical data. say the x axis is april = 1, may = 2, and so on, while the y axis is demand. (round your intercept value to the nearest whole number and slope value to 2 decimal places.
Let f (x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f
The necessary and sufficient conditions for f ◦ g = g ◦ f are that a and c must be non-zero and have the same sign, while b and d can be any values.
Explanation:To determine the necessary and sufficient conditions for f ◦ g = g ◦ f, we need to find the values of a, b, c, and d that satisfy this equation.
a and c must be non-zero, as dividing by zero is undefined in functions.If a and c have different signs, f ◦ g and g ◦ f will have different slopes, which means they will not be equal. Therefore, a and c must have the same sign.If a and c have the same sign, b and d can be any values, as they won't affect the slopes of the functions.Therefore, the necessary and sufficient conditions for f ◦ g = g ◦ f are that a and c must be non-zero and have the same sign, while b and d can be any values.
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Felicia has 34 quarters,25 dimes and 36 pennies,how many coins does Felicia have?
In order to find the total number of coins, we need to add all the coins that she has:
34 coins + 25 coins + 36 coins = 95 coins
Felicia has a total of 95 coins.
The correct answer is C
Which function below has the largest slope? f(x) x f(x) −3 −10 −1 −7 1 −4 g(x) equals one half x plus 3 h(x) Lance gains 1 level each time he plays his favorite video game. He started at level 10.
Answer:
f(x)
Step-by-step explanation:
Alan bought 3 pencils and a notebook. The notebook cost $6, and he spent a total of $12. How much did each pencil cost? Use p to represent the cost of each pencil. A. ; each pencil cost $2.50. B. ; each pencil cost $1.50. C. ; each pencil cost $2. D. ; each pencil cost $2.
Cost of each pencil will be $2
What is Linear Equation ?A linear equation is an equation in which the highest power of the variable is always 1 .
Number of pencil bought = 3
Number of notebook bought = 1
Cost of each notebook = $6
Cost of each pencil = ? let say its = x
Total money spent = $12
according to question , linear equation will be :
3* (x) + 1 * (6) = 12
3x = 6
x = 2
cost of each pencil will be $2
answer is d) $2
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365 x 11? please answer!!!
The expression 365 multiplied by 11 is equal to 4,015.
We have,
Calculating 365 multiplied by 11 is the basic multiplication algorithm.
This algorithm involves multiplying each digit of the multiplier (11) by each digit of the multiplicand (365), starting from the rightmost digit and moving toward the left
365 multiplied by 11 equals 4,015.
To explain the calculation:
We can perform long multiplication to find the product of 365 and 11:
365
x 11
------
365 (multiply 365 by 1)
+3650 (multiply 365 by 10)
------
4015 (sum the two products)
Therefore,
365 multiplied by 11 is equal to 4,015.
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write an equation of the circle that is tangent to both axes with radius sqrt5 and center in quadrant 3
Gordon Rosel went to his bank to find out how long it will take for $2,500 to amount to $3,090 at 6% simple interest. Calculate the number of years. (Round time in years to the nearest tenth.)
Which number when multiplied by 3/4 gives a product between 3/4 and 1?
A: 0
B: 1/4
C: 3/4
D: 1 1/4
1 1/4 = 5/4
5/4 * 3/4 = 15/16
Answer is D 1 1/4
How to divide 546 divided 78
Kalesha is purchasing a laptop. The original price of the laptop is $900. The store is offering 10% off on all computers. Kalesha has a $100 gift card.
How should Kalesha determine the amount she will pay for her computer?The amount Kalesha will pay for her computer is:
$ 710
Step-by-step explanation:It is given that:
The original price of the laptop is $900.
The store is offering 10% off on all computers.
Kalesha has a $100 gift card.
Now in order to calculate the amount Kalesha will pay we first have to find the cost that will be reduced on a offer of 10% provided by the store and subtract this reduced price from the original price ; and finally we again subtract $ 100 from this resulting price.
When a offer of 10% is applied to the computer we have:
Price reduced on offer=10% of original price
i.e.
Price reduced on offer=10%×900
i.e.
Price reduced on offer=0.10×900
i.e.
Price reduced on offer=$ 90
Cost of Computer= Original price-Price reduced on offer
i.e.
Cost of computer= 900-90
i.e.
Cost of Computer=$ 810
Now, when Kalesha uses her gift card of $ 100 then,
Amount Kalesha will pay= $ (810-100)
i.e.
Amount Kalesha will pay= $ 710
which rate converts to a unit rate of 65 miles per hour
solve the system of equations by graphing 4x-5y=20
What is 5x923 in expanded
form
Nancy purchased bed sheets for 36.00. They were on sale for 25% off. What was the original price
845,001 rounded to the nearest ten thousand
Answer:
850,000
Step-by-step explanation:Meow
An arithmetic sequence has this recursive formula
Answer:
[tex]\text{The explicit formula is }a_n=7+(n-1)(-4)[/tex]
Option B is correct.
Step-by-step explanation:
Given the recursive formula of arithmetic sequence
[tex]a_1=7[/tex]
[tex]a_{n}=a_{n-1}-4[/tex]
we have to find the explicit formula for the above sequence.
[tex]a_{n}=a_{n-1}-4[/tex]
[tex]a_{n}-a_{n-1}=-4[/tex]
which is the common difference, d=-4
The explicit formula for A.P is
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_n=7+(n-1)(-4)[/tex]
Option B is correct.
Alex is saving money because she would like to purchase the new video gaming system that everyone has been talking about. After two weeks of saving, she had $47. After 24 weeks of saving, she had $430. Approximately how many dollars per week did Alex save on average between weeks 2 and 24?
What is the least number of line segments that make exactly 100 squares?
Answer with explanation:
First Possibility
→→100 Squares in a Row Requires 101 smaller line segments of equal length ,and 2 line segments of Larger Length having length equal to 100 times the length of one of the Smaller segments.
→→100 Squares in a Column Requires 101 smaller line segments of equal length ,and 2 line segments of Larger Length having length equal to 100 times the length of one of the Smaller segments.
So, total number of line segments =101 +2=103
Second Possibility
If you draw 11 line segments of equal length in a column and 11 line segments in a row, you can draw 100 square of equal size.
So, total number of line segments =11+11=22
help me with this I don't get it help4help?
He total cost (in dollars) of producing xx coffee machines is c(x)=2300+40x−0.9x2. c(x)=2300+40x−0.9x2. (a) find the exact cost of producing the 21st machine.
$2743.1 .
Cost of producing 21st machine = $2743.1 .
What is function?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input.When f and its derivatives are substituted into the equation, a solution is a function y=f(x) that satisfies the differential equation.The highest order of any derivative of the unknown function that appears in the equation is the order of a differential equation.Given function,
c(x)=2300+40x−0.9x².
To find the cost of producing the 21st machine,
We have to find c(21).
c(21) = 2300+40(21)−0.9(21)²
= 2300 + 840 - 0.9 x 441
= 2300 + 840 - 396.9
= $2743.1
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Final answer:
To find the exact cost of producing the 21st coffee machine, substitute x = 21 into the given cost function, resulting in a cost of $2743.1.
Explanation:
The question asks for the exact cost of producing the 21st coffee machine given the cost function c(x) = 2300 + 40x - 0.9x². To find this, we substitute x = 21 into the cost function.
First, let's plug in x = 21 into the cost function:
c(21) = 2300 + 40(21) - 0.9(21²)c(21) = 2300 + 840 - 0.9(441)c(21) = 3140 - 396.9c(21) = 2743.1Therefore, the exact cost of producing the 21st machine is $2743.1.
Find the cost of laminating decolam to a circular table of radius 1.4 m if the rate of decolam is rupees 50 per square metre
It takes Awan 8 1/3 minutes to run a mile, it takes Kate 1 1/5 time longer. How long does it take Kate to run one mile?
Answer:
10 minutes
Step-by-step explanation:
Given: It takes Awan [tex]8\frac{1}{3}[/tex] minutes to run a mile, it takes Kate [tex]1\frac{1}{5}[/tex] time longer.
To Find: How long does it take Kate to run one mile.
Solution:
Time taken by Awan to run a mile = [tex]8\frac{1}{3}[/tex] [tex]\text{minutes}[/tex]
= [tex]\frac{25}{3}[/tex] [tex]\text{minutes}[/tex]
Time taken by Kate to run a mile = [tex]1\frac{1}{5}\times\text{time taken by Awan}[/tex]
= [tex]\frac{6}{5}\times\text{time taken by Awan}[/tex]
Therefore,
on putting values
The time taken by Kate = [tex]\frac{6}{5}\times\frac{25}{3}[/tex] [tex]\text{minutes}[/tex]
= [tex]\frac{6\times25}{5\times3}[/tex]
= [tex]10[/tex] [tex]\text{minutes}[/tex]
Hence, the time taken by Kate to complete one mile is [tex]10[/tex] [tex]\text{minutes}[/tex]
the length of a banquet table is 3 feet longer than 5 times it's width. if the perimeter is 54 feet. What are the dimensions of the table?
This is a standard deviation contest. you must choose four numbers from the whole numbers 22 to 9595, with repeats allowed. choose four numbers that have the largest possible standard deviation. (give your answer in the form of comma separated list of numbers in ascending order.)
the sum of 5 times a number and 2 is equal to 4 times the number
5x +2 =4x
subtract 2 from each side
5x= 4x-2
subtract 4x from each side
x = -2
Find the area of a triangle with vertices at D(2,0), B(-1,0), and R(2,-7)
Find an equation of the sphere that passes through the origin and whose center is (â2,2,3). be sure that your formula is monic.
A construction firm is trying to decide which of two models of a crane to purchase. Model A costs $100,000 and requires $4,000 per year to maintain. Model B has an initial cost of $78,000 and a maintenance cost of $13,000 per year. For how many years must model A be used before it becomes more economical than B? (Round your answer to one decimal place.)