We know that the bank charges $2.25 per month plus $0.10 per bill paid using the service. Let x be the number of bills paid using the service.
The total cost of the service is:
Cost = 2.25 + 0.10x
We also know that the charges are always between $3.50 and $5.00. So we can write this as an inequality:
3.50 <= Cost <= 5.00
To find the number of bills, we can substitute the expression for cost into the inequality:
3.50 <= 2.25 + 0.10x <= 5.00
We can solve this inequality by isolating x on one side:
0.10x >= 1.25
x >= 12.5
So the number of bills paid using the service is greater than or equal to 12.5.
She could pay exactly 12 bills, 13 bills, 14 bills and so on.
The solution is x >= 12.5
Let's call the number of bills paid per month as "x"
We know that the total cost is:
$2.25 (fixed monthly fee) + $0.10x (cost per bill paid)
We also know that the total cost is between $3.50 and $5.00
Therefore, $3.50 <= $2.25 + $0.10x <= $5.00
To solve for x, we can first isolate x by subtracting $2.25 from both sides of the inequality:
$1.25 <= $0.10x <= $2.50
Now we can divide both sides of the inequality by $0.10 to get:
12.5 <= x <= 25
It means that the number of bills paid per month using the service is between 12 and 25 bills, Debbie can pay at least 12 bills and at most 25 bills.
The equation y 4.3x can be used to determine the total cost, y, in dollars, of z pounds
of apples. What does the number 4.3 represent in the equation?
The price of one pound of apples is represented in the equation by the number 4.3 by the price in dollars of x pounds of apples, where x is pounds.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14.
given
y = 4.3x
the price in dollars of x pounds of apples, where x is pounds.
The price of one pound of apples is represented in the equation by the number 4.3.
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For a part-time job, Jeannie conducted a survey with two questionnaires, Type A
and Type B. She chose 500 homes and mailed questionnaires at a cost of $.19 for
Type A and $.23 for Type B. If the total cost of the mailing was $106.20, how
many of each type did she mail?
Out of the 500 homes, 226 Type A forms were sent while 274 Type B forms were sent.
How many of the forms were sent?To determine the number of forms sent, we can begin by identifying how much Jeannie spent on mailing each of the questionnaires. The sum of $0.19 and $0.23 is $0.42. Now, we will find out how much of these were the total cost as follows:
Type A:
$0.19 / $0.42 × $106.20
= $48.
Type B:
$0.23 / $0.42 × $106.20
= $58.2
Next, we will determine how much of these went into the 500 homes as follows:
Type A:
$48 / 106.2 × 500
= 225. 9 ≈ 226 homes
Type B:
$58.2 / $106.2 × 500
= 274 homes
So, while Type A was sent to 226 homes, Type B was sent to 274 homes.
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A textbook store sold a combined total of 280 history and math textbooks in a week. The number of history textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold
The number of maths books sold is 70 and the number of history books sold is 210.
Let no of maths book sold be x.
According to the question, the number of history books sold is three times the number of maths books sold.
Therefore the number of history books sold is 3x.
Given: Total books sold = 280
So, x + 3x = 280
Solving the equation, we get:
4x = 280
x = [tex]\frac{280}{4}[/tex]
x = 70 (Number of maths books sold)
3x = 3 × 70 = 210 (Number of history books sold)
Thus the number of maths books sold is 70 and the number of history books sold is 210.
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What is a pair of 3 called?
A "pair of 3" is not a commonly used term.
A set of 3 numbers can be called a triplet, or a set of 3 items can be called "a set of three".
Please let me know if you want me to clarify about something else.
There are 4 boxes on a shelf A, B, C and D.................
=======================================================
Explanation:
The weight of A is 2/3 that of B. This flips to saying "the weight of B is 3/2 that of A". Because 3/2 = 1.5, we can then have this equation
B = 1.5A
The statement "C is 75% the weight of D" leads to the equation
C = 0.75D
----------------------------
The sum of A and B is triple that of the sum of C and D, giving us this equation:
A+B = 3(C+D)
Plug in the previous two equations we found in the previous section. Afterward, solve for the variable "A".
A+B = 3(C+D)
A+1.5A = 3(0.75D+D)
2.5A = 3(1.75D)
A = 3(1.75D)/2.5
A = 2.1D
----------------------------
Let's revisit the first equation we set up, and then apply substitution like so:
B = 1.5A
B = 1.5*2.1D
B = 3.15D
----------------------------
There's a lot of equations to keep track of. The key equations are these:
A = 2.1D
B = 3.15D
C = 0.75D
The one common factor of all these equations is the variable "D". This will be useful when setting up the ratio A:B:C:D
We'll go from the ratio
A:B:C:D
to
2.1D:3.15D:0.75D:1D
afterward we can divide all four parts by the GCF variable D, to arrive at
2.1:3.15:0.75:1
----------------------------
This last section will focus on converting each part of that ratio into integers. This is done by multiplying all four parts by 100 (as shown in the 2nd step).
Then we divide all parts by the GCF 5 to get the final reduced ratio.
2.1:3.15:0.75:1
100*2.1:100*3.15:100*0.75:100*1
210:315:75:100
5*42:5*63:5*15:5*20
42:63:15:20
How do you solve piecewise defined functions step by step?
To solve a piecewise defined function, you should follow these steps:
1. Understand the definition of the function. A piecewise defined function is a function that is defined differently on different intervals of its domain.
2. Identify the different intervals on which the function is defined. These intervals are usually separated by vertical asymptotes, which are points where the function is undefined.
3. Determine the formula for the function on each interval. This is usually given in the problem statement, but if not, you will need to figure it out from the context.
4. Find the domain and range of each formula. The domain of a function is the set of all input values for which the function is defined, and the range is the set of all output values.
5. Determine any discontinuities in the function. These are points at which the function is defined differently on different intervals, and they will be vertical asymptotes.
6. Sketch the graph of the function by plotting points and connecting them with line segments.
7. If the function is a piecewise continuous function, Analyze it further by finding its limits, derivatives, integrals, or other properties of interest as you would with any other function.
8. Evaluate the function for a given input value, you need to determine which interval the input value belongs to and then use the appropriate formula for that interval to find the output value.
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When graphing polynomials we can determine the end behavior by the?
When graphing polynomials, we can determine the end behavior by the degree of the polynomial and the coefficient of the leading term.
The degree of a polynomial is the highest exponent of the variable found in the equation. The coefficient of the leading term is the number that is multiplied by the variable in the leading term. The end behavior of a polynomial can be determined by examining the sign of the coefficient and the degree of the polynomial.
For example, let's consider the polynomial equation y = x^3 - 2x^2 + 5x + 7. The degree of this polynomial is 3, and the coefficient of the leading term is 1. This means that the end behavior of this polynomial equation will be increasing, since the coefficient and degree are both positive. To confirm this, we can calculate the limit of the polynomial as x approaches positive and negative infinity. As x approaches positive infinity, the limit of y is positive infinity (∞), and as x approaches negative infinity, the limit of y is also positive infinity (∞). This confirms that the end behavior of this polynomial equation is increasing.
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5
Mary noticed a spider web on
her patio that formed a right
triangle. She determined the
diagonal length was 15 inches and
the height measured 12 inches.
She could not reach the top to
measure. How long is the top of
the spider web?
Answer: The diagonal and the height of the right triangle form the legs of the triangle, and the unknown length is the hypotenuse. To find the length of the hypotenuse, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
So, if the legs of the right triangle measure 12 inches and 15 inches, the hypotenuse c can be calculated as follows:
c² = a² + b²
c² = 12² + 15²
c² = 144 + 225
c² = 369
Therefore, the length of the hypotenuse c is the square root of 369.
c = √369
c = 19.1 inches
Therefore, the top of the spider web is 19.1 inches long.
Step-by-step explanation:
How do you solve y =- 3x?
the solution of equation y=x+2 and y=3x-2 are x= 2 and y=4
y = x+2 ------------ equation 1
y = 3x -2 ------------ equation 2
in the first equation y = x +2
in the second equation y = 3x -2
this mean equation 1 = equation 2
then we can equate the two together to get one of the variable
remember, we have to unknown variables which are x and y, so we need to isolate y to get x
x + 2 = 3x -2
let collect the like terms
x - 3x = -2 -2
let us factorize out x on the right hand side of the equation
x(1 - 3) = -4
x(-2) = -4
-2x = -4
divide both sides by -2
-2x/-2 = -4/-2
x = 2
to find y put x in any of the above equations
let us use equation one
y = 2 + 2
y = 4
complete question
How do you solve, y=x+2 y=3x-2
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Here is a question on angle measures in real-life.
Angle FED is equal to what amount?
Answer:235
Step-by-step explanation: its because.......
Joyce has a health insurance plan at work with a $20 copay for doctor’s visits and a $10 copay for generic prescription drugs. During the most recent calendar year, she made five doctor visits and filled eight prescriptions. How much did she spend in total on copayments?
She spends a total of $ 180 in copayments, $20 for medical visits and $10 for generic prescriptions.
what is unitary method ?The system process is a strategy for addressing issues that entails first figuring out the price of a single item, than multiplication that value to figure out the needed value. Simply put, the unit technique is employed to extract a single unit quantity from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and inverse are equivalent in terms of mathematics, algebra, linear algebra, mathematical, or math and science of matrices or operators.
given
$20 for copay for doctor’s visits
$10 copay for generic prescription
for 5 doctor visits = 20*5 = $100
for 8 prescriptions = 10 * 8 = $80
so total = 100+ 80 = $180
She spends a total of $ 180 in copayments, $20 for medical visits and $10 for generic prescriptions.
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56 unit needed, 6 unit per cae what i the number of cae and the number of additional unit?
As per the unitary method, the number of care is 9 and the number of additional method is 2.
The term unitary in set theory is defined as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Here we have given that the total number of units is 56.
And here we also know that the number of units in each care is 6.
Now, we have to find the total number of care, that can be obtained by dividing the total care by the units in each care,
then it can be written as,
=> 56/6
When we divide the term then we get the quotient as 9 and the remainder as 2.
Therefore, while looking into these we have identified that there are 9 cares and 2 additional units are in the group.
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Help please!!! I’ll give brainliest!!!! (3x² - 4xy + y²)(4x + 3y)
By solving the given expression we get this simplified expression 12x³ - 7x²y - 8xy² + 3y³.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
To simplify the expression (3x² - 4xy + y²)(4x + 3y), we can use the distributive property of multiplication to expand the expression as follows:
(3x² - 4xy + y²)(4x + 3y) = 3x²(4x) - 4xy(4x) + y²(4x) + 3x²(3y) - 4xy(3y) + y²(3y)
Simplifying each term, we get:
12x³ - 16x²y + 4xy² + 9x²y - 12xy² + 3y³
Combining like terms, we get:
12x³ - 7x²y - 8xy² + 3y³
Therefore, the simplified expression is 12x³ - 7x²y - 8xy² + 3y³.
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A plot of land is 24.6 acres in size. A field next to the plot of land contains 18.9 acres. A local developer buys both pieces of property to make a community center that will use 9/25 of the total property purchased. How many acres of land will the developer need to build the community center? (Please explain how you got the answer)
A. 8.86 acres
B. 6.80 acres
C. 15.66 acres
D. 7.83 acres
Acres of land needed by the developer to build a community center that will use up 9/25 of the property is 15.66 acres, option C.
How to calculate the acre?The size of land required to build a community center is calculated as follows:
First plot size = 24.6 acres
Field size = 18.9 acres
The local developer purchases both (24.6 + 18.9) acres to have a total of 43.5 acres.
The amount needed to build a community center is 9/25
Therefore 43.5 x 9/25 = 15.66 acres
9/25 of a 43.5 acres purchased by local developer will require only 15.66 acres.
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- Hair grows at a rate of 1/64 inch per day. Write this number using negative exponents.
Answer:
[tex]4^{-3}[/tex]
Step-by-step explanation:
[tex]4^{3}[/tex] = 64
Take the reciprocal of both sides.
1/64 = [tex]4^{-3[/tex]
A florit hop keep a contant ratio of roe to tulip at 5 : 3. If the hop ha 70 roe, how many tulip do they have?
As per the given ratio, the number of roses is 45 and the number of tulips is 27
The term ratio also known as proportion is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0
Here we have given that the ratio of roses to tulips is 5: 3.
Here we also know that the shop has 72 tulips on Friday morning.
And then let us consider that if the florist uses up half of each type of flower to fill an order, then the ratio of roses to tulips in the shop change is calculated as,
=> 5x + 3x = 72
=> 8x = 72
Then the value of x is calculated as,
=> x = 9
Therefore, the number of roses is
=> 5(9) = 45
And the number of tulips is written as,
=> 3(9) = 27
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Where do we find value table?
The proper method of finding a value table has been mentioned and explained below.
Value tables are a part of domain definition. The value table is maintained at the domain level and thus, is also called domain-level validation. Whenever you create a domain, you can enter the required values. Whenever you use this Domain, the system will make it so that you are forced to enter only these values. This is a sort of master check.
This means that if you want to enter values into this table you have to create a development request & transport the same. The system, then, proposes the value table as a check table. The check against the value table only takes place when a foreign key is defined
.
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What is the 3 4 5 Triangle rule in construction?
I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees. According to this rule, a triangle is a right triangle if the diagonal between its two points measures 5, even though one of its sides measures 3 and the other measures 4.
Aim for a measuring ratio of 3:4:5, to create an absolutely square corner. To put it another way, you need a length of three feet on the straight line, four feet on the perpendicular line, and five feet crosswise. You will get a corner that is exactly square if all three measurements are accurate.
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what is the probability of 45 heads in 100 tosses of a coin given the probability of heads is 50%? binomial distribution
The probability of 45 heads in 100 tosses of a coin given the probability of heads is 50% is 7.1%.
Coin Toss Probability CalculationThe binomial probability formula is used to calculate the probability of getting a certain number of heads (or success) in a certain number of coin tosses (or trials) when the probability of getting a head (or success) in each individual coin toss is known. The formula is:
P(x) = (n choose x) * (pˣ) * (1-p)^(n-x)
Where,
P(x) is the probability of getting x heads (or success) in n coin tosses (or trials)
n is the number of coin tosses
x is the number of heads (or success)
p is the probability of getting a head (or success) in a single coin toss
1-p is the probability of getting a tail (or failure) in a single coin toss
(n choose x) is the binomial coefficient, which is the number of ways to choose x heads (or success) from n coin tosses (or trials)
In this case, the probability of getting 45 heads in 100 tosses of a coin with a probability of heads of 50% can be calculated using the formula: (100 choose 45) * (0.5⁴⁵) * (0.5⁵⁵) which is approximately 0.071, or 7.1%.
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evaluate the expression
How do you solve for R?
sqrt( A / pi ) =r is the solution for r and r is called as radius in the formula A=πr^2
A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.
Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).
A model is, for example, the method for the area of a circle, πr2.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
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Given: x = 1+a/1-b
solve for a when x=12
By solving the given expression when x=12 we get a = 11-12b
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
Given,
expression ,
x = (1+a) / (1-b )
By putting x =12
we get,
12 = (1+a) / (1-b)
12 * (1-b) = 1+a
12- 12b =1+a
a = 12-12b-1
a = 11 - 12b
Hence , By solving the given expression we get a = 11-12b
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9+ a/6=8
show work
solve a
Answer:
a = -6
Step-by-step explanation:
9+a/6=8 1. -9 both sides
(6)a/6= -1(6) 2. multiply 6 on both sides
a = -6
I really need help with this worksheettt please
Answer:
2x² + x + 3
Step-by-step explanation:
2x² + x + 3
2x² + (5/2)x + 3
help me ughhhhh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! the whole question didnt fit so there are two screenshots
The solutions of x + 2 = 2ˣ + 1 are x = 0 and 1.
The answers are given in the attached image.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given:
Two functions,
f(x) = x + 2 and g(x) = 2ˣ + 1.
The graph of the functions on the same coordinate plane is given in the attached image.
The blue line represents the graph f(x) and the green represents g(x).
Then f(x) = g(x)
x + 2 = 2ˣ + 1.
The solution is the x-value of the point of intersection.
That means,
x = 0 and 1
Therefore, the solutions of the f(x) = g(x) are x = 0 and 1.
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Do you multiply in dilation?
Yes, dilation is a type of transformation that involves multiplying the coordinates of a figure by a scale factor.
This scale factor can be greater than 1, which is an enlargement, or less than 1, which is a reduction. To calculate the coordinates of a dilation, the following formula is used: (x, y) → (kx, ky), where (x, y) are the coordinates of the original point and (kx, ky) are the coordinates of the transformed point. The scale factor, k, is the same for both the x and y coordinates. For example, if the scale factor is 2 and the original coordinates are (2, 4), the new coordinates would be (4, 8). This means that the point (2, 4) has been enlarged to (4, 8).
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Will E. Wait works at Willy Wonka's Chocolate Factory. His annual salary is $58,500.
He is paid biweekly. What is Will's biweekly gross salary?
Your answer
Answer: 562.50
Step-by-step explanation:
A ring-shaped region is show below. it’s inner radius is 6 in, and it’s outer radius is 9 in. Find the area of the shaded region. Use 3.14 for pi. Do not round your answer.
The required area of the shaded region is 141.3 sq. in.
What is area of circle?A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m^2, cm^2, etc., is the unit of area. Area of a circle is equal to r2 or d2/4, where = 22/7 or 3.14.
According to question:inner radius = 6 in, outer radius= 9 in
are of small circle = πr^2
Area = π(6)^2 = 36π sq. in
Similarly
Area of big circle = πr^2
Area = π(9)^2 = 81π sq. in
So,
Area of shaded region = 81π - 36π
Area of shaded region = 45π
Area of shaded region = 141.3 sq. in
Thus, required area is 141.3 sq. in.
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The price of strawberries at Fine Foods is shown in the graph. At best Market, the price y for x pounds of strawberries is given by y=2.90x. Which store sells strawberries at a cheaper unit price?
The store that sells strawberries at a cheaper unit price is Fine Foods.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents the number of pounds of strawberries.y represents the price in dollars.k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 2/1 = 6/3 = 10/5 = 14/7
Constant of proportionality (k) = 2.
Therefore, an equation for the price of strawberries at Fine Foods is y = 2x and as such, it sells strawberries at a cheaper unit price.
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Which of the following is a factor of p x x 2 − 4x − 5?(x+5)(x - 1)(x+5)(x + 1)(x + 1)(x - 5)(x - 1)(x - 5)
(x+5)(x - 1) is a factor of p(x) = x² - 4x - 5
We can see that by applying polynomial long division or by applying synthetic division, both of these methods will give the same result.
x² - 4x - 5 = (x + 5)(x - 1)q(x) + r(x)
where q(x) and r(x) are the quotient and remainder of the polynomial division respectively. Since r(x) = 0, it means (x + 5)(x - 1) is a factor of p(x) = x² - 4x - 5.