The balance after 9 years is $1139.94 rounded to the nearest cent.
The formula to use in this case is A = P(1 + r)^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Given the information in the problem, we know that:
P = $800.00 (the principal or starting amount)
r = 0.04 (the interest rate as a decimal)
n = 1 (the interest is compounded annually)
t = 9 (the number of years)
Plugging these values into the formula, we get:
A = $800.00(1 + 0.04)^9
To solve for A, we need to calculate (1 + 0.04)^9
=1.04^9
=1.041.041.041.041.041.041.041.041.04
=1.424928
A = $800.00*1.424928
A = $1139.94
So the balance after 9 years is $1139.94 rounded to the nearest cent.
Therefore, The balance after 9 years is $1139.94 rounded to the nearest cent.
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A = $800.00(1 + 0.04)^9
To solve for A, we need to calculate (1 + 0.04)^9
=1.04^9
=1.041.041.041.041.041.041.041.041.04
=1.424928
A = $800.00*1.424928
A = $1139.94
A line passes through the points (0,5) and (1,9). What is its equation in the slope-intercept form
The equation of the line in slope intercept form is y = 4x + 5.
How to represent equation of a line?The equation of line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptA line passes through the points (0, 5) and (1,9). The slope of the line can be found as follows;
m = slope = 9 - 5 / 1 - 0
m = 4 / 1
m = 4
Hence, let' find the y-intercept of the equation using (0, 5).
y = 4x + b
5 = 4(0) + b
b = 5
Therefore, the equation of the line is y = 4x + 5.
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how to find the vertex
A salesperson earns commission on the sales that she makes each month.
• The salesperson earns a 4% commission on the first $4,000 she has in sales.
• The salesperson earns a 6% commission on the amount of her sales that are greater than $4,000.
Part A
This month the salesperson had $9,000 in sales. What amount of commission, in dollars did she earn?
A $485
B $500
$460
$480
Part B
The salesperson earned $670 in commission last month. How much money, in dollars, did she have in sales last month?
Enter your answer in the box.
A. The answer for part A is $460.
B. The answer for part B is 11,166.67 dollars
What are the Profit and Loss?
A. To find the commission earned on the first $4,000 in sales, we can multiply $4,000 by 4% which is (4,000 * 0.04) = 160 dollars
To find the commission earned on the remaining amount of sales above $4,000, we can subtract $4,000 from $9,000 to find the amount of sales above $4,000 which is (9,000 - 4,000) = 5,000
then we can multiply $5,000 by 6% which is (5,000 * 0.06) = 300 dollars
So the total commission earned is 160 + 300 = 460 dollars.
So the answer for part A is $460.
B. To find the amount of money in sales, we can use the commission formula: commission = (sales * rate)
The commission rate for sales above $4,000 is 6% and the commission earned is $670.
So, we can set up the equation as : 670 = (sales * 0.06)
We can solve this equation to find the value of sales by dividing both sides of the equation by 0.06
sales = 670 / 0.06
sales = 11,166.67
So the answer for part B is 11,166.67 dollars.
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A radar gun measured the speed of a baseball at 5 miles per hour. If the baseball was going 4.2 miles per hour, what was the percent error in this measurement?
The percent error is a measure of how accurate a measurement is. It is calculated by taking the difference between the measured value and the true value, dividing that difference by the true value, and then multiplying by 100 to get a percentage.
In this case, the true value of the baseball's speed is 4.2 miles per hour and the measured value is 5 miles per hour. To find the percent error:
(5 - 4.2) / 4.2 * 100 = 0.190476 * 100 = 19.0476%
So the percent error in this measurement is 19.0476%. This means that the measurement was off by 19.0476% from the true value.
Alternatively, we can round it to 19% for ease of interpretation
Therefore, the percent error in this measurement is 19%.
What is derivative of log 2x?.
The derivative of log 2x is 1/x. This is obtained by applying the formula of derivative of log x.
Let y is the given function = log 2x.
Differentiating with respect to x on both sides, we have,
d/dx(y) = d/dx(log 2x)
dy/dx = 1/2x × d/dx(2x)
dy/dx = 1/2x × 2
dy/dx = 1/x
Chain rule is applied in the above solution.
Its formula is given as, d/dx [f(g(x)] = d/dx [f(g(x)] × d/dx[g(x)]
where, f(x) and g(x) are a function of function.
In the above solution, f(x) is log x and g(x) is 2x.
Thus, the derivative of log 2x is 1/x.
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Algebraic expression : A number increased by three times the number
The algebraic expression for the a number that has been multiplied by three is: x + 3*x. In this statement, x stands for the number, while 3*x, or 3x, stands for the number times three.
What is the Algebraic expression?An algebraic expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions can be evaluated for specific values of the variables in order to find a numerical result.
What sort of algebraic expression would that be?A mathematical statement with variables, constants, coefficients, or algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 5x2+6xyc. Algebraic expression do not utilize equal signs, in contrast to algebraic equations.
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When the degree of a polynomial is 2 it is called *?.
A polynomial of degree 2 is called a quadratic equation. It is a type of equation that can be solved by using the quadratic formula, which looks like this:
where x is the unknown variable and y is the solution to the equation. The quadratic equation can be written in several different ways, but all of them involve solving for y using equations similar to the one above.
Polynomials of degree 2 are common in everyday life, and are used to solve problems such as solving for the slope or height of a line, determining the points at which two lines intersect, or finding the distance between two points.
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What is longitude and latitude explain with diagram?.
Longitude and latitude are geographic coordinates that indicate a location on the Earth's surface. They are used to locate a specific point on a map or globe.
Longitude is the measure of a location's east-west position on the Earth's surface. It is measured in degrees east or west of the Prime Meridian, which is an imaginary line that runs from the North Pole to the South Pole through the Royal Observatory in Greenwich, England. Longitude values range from -180 degrees (West) to 180 degrees (East).
Latitude, on the other hand, is the measure of a location's north-south position on the Earth's surface. It is measured in degrees north or south of the Equator, which is an imaginary line that runs around the Earth's middle, dividing it into the Northern and Southern Hemispheres. Latitude values range from -90 degrees (South) to 90 degrees (North).
The diagram below illustrates how longitude and latitude work together to pinpoint a location on the Earth's surface. The intersection of the red line (longitude) and the blue line (latitude) represents the specific location.
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Show that (3x+4) is a factor of f(x)=6x^2+5x-4, and find the other factor.
Answer:
2x -1
Step-by-step explanation:
You want to show that (3x+4) is a factor of f(x) = 6x^2+5x-4, and you want the other factor.
FactorsWhen the product, f(x), is divided by one of its factors, the remainder will be zero and the quotient will be the other factor.
The attached long division shows the remainder (bottom line) is zero, and the quotient (top line) is (2x -1), the other factor.
The other factor is (2x -1).
What is the value of S unit?.
The value of S, i.e., prependicular length in right angled triangle is twelve units.
We have, a right angled triangle ABC as see in above figure. From the above figure, we get the following information,
The base length of right angled ∆ ABC, BC = 9 units
The perpendicular length/height of
∆ ABC , AC = S units
The hypotenuse length of ∆ ABC, AB
= 25 units
We have to calculate the value of S i.e., the prependicular length. Using the Pythagoras threoem to solve the value of S,
(hypotenuse)²= (base)² + (prependicular)²
=> AB² = BC² + AC²
=> 15² = 9² + S²
=> 225 = 81 + S²
=> 225 - 81 = S²
=> S² = 144
=> S = ±√144
=> S = ± 12
but S, is represent the length and it's value is always positive. Therefore, the required value of S is 12 units.
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For the above figure, What is the value of S units?.
The triangle with coordinates (2,-3),(2,1),(-4,2) is reflected
across the y-axis and then translated by vector
(3,-2).
Part A
Find the new coordinates
Part B
What is the composition of functions for the
given sequence of transformations?
(x, y) → (
Answer:
PART A : points to graph (7,0)(1,-1)(2,-5)
PART B: (x, y) => (-x+3, y-2)
Explanation step by step :
Reflected across y axis means y-coordinate of every point remains same and x-cordinate become opposite
(x, y) become (-x, y)
Here,
(-4, 2) become (4, 2)
(2, 1) become (-2, 1)
(1,-3) become (-1,-3)
Similarly a point P(x, y) translated by vector <3, -2> means the point P become P'(x+3, y-2)
(4, 2) become (7,0)
(-2, 1) become (1, -1)
(-1,-3) become (2,-5)
So the composition of function for the given sequance of transfermation is (x, y) = (-x+3, y-2)
Note : graph not accurate, just for explanation.
What is the gradient of y =- 3x 6?.
The gradient is −3 and the y-intercept is 6.
The gradient of a function is defined to be a vector field. Generally, the gradient of a function can be found by applying the vector operator to the scalar function. (∇f (x, y)).
This kind of vector field is known as the gradient vector field. Now, let us learn the gradient of a function in the two dimensions and three dimensions.
The gradient should take a scalar function (i.e., f(x, y) and produces the vector function (∇ f).
The vector ∇f(x, y) should lie in the plane.
The gradient of a function can be found by applying the vector operator to the scalar function. I.e., ∇f (x, y).
y+3x=6
Rearrange the equation to the slope-intercept form,
y=mx +b,
where ,
m is the slope and b is the y-intercept.
Subtract 3x from both sides.
y=−3x+6
The gradient is −3 and the y-intercept is 6.
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AWARDING THE MOST POINTS FOR BEST ANSWER! HELP ME ANSWER THIS FAST!!!!!!!!!!!!
The Johnson family buys furniture and appliances for a new house for $10,000. 00 with a credit card that has a 15% APR.
The Johnsons make a $325. 00 monthly payment. How many months will it take to pay off the balance? Enter your answer as a whole number, such as: 20
Total thirty-nine months will be take by Johnson family to pay off the balance, $10,000.00.
The monthly payment is the amount paid per month to pay off the principle in the time period of the loan. If your rate is r%, divide r/100 by 12 to calculate your monthly interest rate. Formula for monthly payment is, M = Pr(1+r)ⁿ/{(1+r)ⁿ - 1 }
where, P --> principle
r--> rate of interest in months
n --> number of periods (in months )
In this problem, Johnson family bought the furniture and appliances for a new house that is principle, P = $10,000
Rate of interest, R = 15%
In terms of months, R = 0.15/12
= 0.0125 per month
Monthly payment, M = $325.00
Plugging all known values in above formula we get, $325.00 = {$10,000 × 0.0125(1 + 0.0125)ⁿ}/{(1+ 0.0124)ⁿ - 1 }
=> 325 = 125(1.0125)ⁿ/{(1.0125)ⁿ - 1}
=> 325 {(1.0125)ⁿ - 1} = 125(1.0125)ⁿ
=> 325(1.0125)ⁿ - 325 = 125(1.0125)ⁿ
=> 325(1.0125)ⁿ - 125(1.0125)ⁿ = 325
=> 200 (1.0125)ⁿ = 325
=> (1.0125)ⁿ = 325/200 = 13/8 = 1.6250
Taking natural logarithm both sides
=> ln(1.0125)ⁿ = ln (1.6250)
=> n ln(1.0125) = ln (1.6250) = 0.4855
=> n×0.0124 = 0.4855
=> n = 0.4855/0.0124 = 39.153 ~ 39
Hence, required months are 39.
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HELP
18 kg of apples cost $106.20. How much would 31 kg cost?
(second post cause why not)
Answer:
$182.90
Step-by-step explanation:
Find the cost per kg. To do so, divide the total cost, with the amount of kg that is bought:
(Total Cost/Total weight) = (cost/unit):
[tex]\frac{106.20}{18} = 5.9\\\\[/tex]
$5.9 per kg of apple.
~
Next, solve for the amount that 31 kg of apples would cost. Multiply the unit cost with the amount of kg of apples purchased:
(Total weight of apples x Cost per kg for apples) = Total cost:
[tex]31 * $5.9 = Total Cost\\Total Cost = 182.9[/tex]
$182.90 is your answer.
~
) A plan of a play boat is drawn to a scale of 1: 20. If the actual area of the base of the boat is 0.64m², calculate the area on the map in square centimeters.
The area on the map in square centimetres is 64 cm².
The scale of the plan is 1:20, meaning that for every 1 unit of measurement on the plan, the corresponding measurement on the actual boat is 20 units.
If the actual area of the base of the boat is 0.64 m², then the area on the map will be:
(0.64 m²) * (1/20)² = 0.0064 m²
To convert this to square centimetres, we multiply by 10,000 (since 1 m² = 10,000 cm²):
0.0064 m² * 10,000 = 64 cm²
Therefore, the area on the map in square centimetres is 64 cm².
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Answer:
16 cm²
Step-by-step explanation:
The scale of the map indicates the ratio of the linear dimensions of the map to the actual ones. Then the area of the map will correlate with the actual one, as with a scale square:
S map = S actual * (1:20)²
S map = 0.64 m² * 1/400
S map = 0.0016 m²
But we know that 1 meter contains 100 cm, so 1 m² = 10,000 cm². Then:
0.0016 m² * 10000 = 16 cm²
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How many isoceles triangles are there if each of its sides have an integral length and it's perimeter is 144
Answer:
[tex] \sf \: 34 \: isosceles \: triangle \: - - - - - - - - - - - - - - - - - - - - - - - - [/tex]
Step-by-step explanation:
[tex]b = 144 - 2a < 2a [/tex]
So, that
[tex]a > 36[/tex]
and 2a < 144 so that
[tex]a < 72[/tex]
since a = b implies a = 48
{37,38,39.......71}/{48}
There are 71-37 = 34 isosceles triangle
simplify: -3 | -2 | + 4 | - 5 |
Step-by-step explanation:
the absolute value always generates the positive value of the argument, no matter what the sign of the argument is.
+ stays +
- turns to +
so, we actually have
-3×2 + 4×5 = -6 + 20 = 14
In the diagram below, QR is parallel to NO. If the length of NO is the same as the length of QP, NP=21, and QR=10, find the length of QP. Figures are not necessarily drawn to scale. State your answer in the simplest radical form, if necessary.
Using properties of Similar triangles, The measure of QP is 14.49.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
Similar triangles differ in size but have the same shape. Corresponding angles are identical in similar triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.
Given two triangles,
ΔPQR and ΔPNO are Similar,
So, their sides are present in the ratio -
NO / QR = NP / PQ
We are given, QR = 10
NP = 21
On putting the values in the NO / QR = NP / PQ equation,
⇒ NO / 10 = 21 / QP
As NO = QP (given)
We can write as -
QP / 10 = 21 / QP
⇒ QP² = 10 × 21
⇒ QP² = 210
⇒ QP = 14.49
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R m O Q Figure 1 1. Figure 1 shows the right angled triangle PQR, whose vertices are located at P(-6, -2) and Q(6,6). It is further given that PQR = 90°. (a) Find an equation for the straight line 1, which passes through Q and R. [3]
Right angled triangle PQR, whose vertices are located at P(-6, -2) and Q(6,6). It is further given that PQR = 90° . y = 0.666666666667 x + 2 is the equation of the straight line .
What is called straight line?y = 0.6666666667x + 2 Points ( -6 , -2 ) , ( 6 , 6 ) ( 6 , 6 ) Formula (y = mx + b) y = 0.666666666667 x + 2 Slope in metres : 0.66666666667 , 2. Y-intercept 0. 6666666666 x Plus any number of parallel lines 1.5 x + any number for parallel lines.
Any line without curves is said to be straight. Consequently, a straight line is one that is uncurved and stretches beyond infinity on both sides. a diagram of a graph in which each edge is a section of a straight line. Additional terms to consider are grid drawing, orthogonal drawing, planar straight-line graph, and Bresenham's algorithm. A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, also known as the y-intercept, and m is the gradient.
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The movie marathon starts at 1:15 p.m. and ends at 8:05 p.m. How long is the movie marathon?
What is a limit class 12?.
Limits are the rate of change of a function and also used in many other concepts such as continuity, differentiability and many other concepts in calculus.
In calculus, limits are used to study the behavior of a function as the input, or independent variable, approaches a specific value. The limit of a function at a particular point, say x = a, is defined as the value that the function approaches as the independent variable x gets arbitrarily close to a, but not necessarily equal to it.
The notation for a limit is usually represented as:
lim x->a f(x) = L
Which means as x approaches a, f(x) approaches L.
Properties of limits include:
1) The limit of a constant is equal to the constant.
2) The limit of a sum, difference, or product of functions is equal to the sum, difference, or product of their limits, respectively.
3) The limit of a function at a point is unique, if it exists.
Limits are an essential concept in calculus as they are used to define the derivative, which is the rate of change of a function and also used in many other concepts such as continuity, differentiability and many other concepts in calculus.
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
The percentage of the people that surveyed shop at a local grocery store is 57%.
How to find the percentage?The total number of respondents = 76The number of people who buy at the local grocery store = 43
The percentage [tex]=\frac{43}{76} \\\\[/tex]
= 0.5657 * 100%
= 57 %
A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. The symbol "%" is frequently written after the number to indicate percentages. Adding "percent" or "pct" after the number can also be used to indicate them. The formula for calculating the percentage difference between two values is to divide the absolute value of the difference between two numbers by their average.To learn more about ratio, refer:
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Find the domain and range.
Answer:
Domain: x ≥ 4
Range: y ≥ 6
Step-by-step explanation:
Rotate 180 about the origin
The vertices of the rotation of 180⁰ are P'(2, 2), Q'(-1, 2), R'(-2, 4) and S'(3, 4)
What is the rotation about an angle?The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle
When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.
Before Rotation After Rotation
(x, y) (-x, -y)
Let P(-2, -2), Q(1, -2), R(2, -4) and S(-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.
Here, the given is rotated 180° about the origin. So, the rule that we have to apply here is
(x, y) ----> (-x, -y)
Based on the rule, we have to find the vertices of the rotated figure.
Also, (x, y) ----> (-x, -y)
P(-2, -2) ----> P'(2, 2)
Q(1, -2) ----> Q'(-1, 2)
R(2, -4) ----> R'(-2, 4)
S(-3, -4) ----> S'(3, 4)
There, the vertices of the rotated figure are
P'(2, 2), Q'(-1, 2), R'(-2, 4) and S'(3, 4)
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Complete question:
Let P(-2, -2), Q(1, -2), R(2, -4) and S(-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.
Sadie drove 13 miles inhours. On average, how fast did she drive, in
miles per hour? Enter your answer as a whole number, proper fraction, or
mixed number in simplest form.
Answer type: Mixed number
Submit Answer
miles per hour
attempt 1 out of 2
If one is the sole factor that connects a fraction's numerator and denominator, then that fraction is said to be in its simplest form.The mixed fraction is 33*3/4
Enter your response in the simplest form ?As an illustration, the fraction 89 has only one common component between the digits 8 and 9, which is 1.Since fractions always work or can be calculated when they are in their simplest form, we simplify them.When two numbers are represented together, they are called mixed numbers.
Based on the given conditions, formulate:45 / 1/1/3
Convert the expression into a fraction: 45/1/1+1/1
Expand the fraction to get the least common demominator: 45/ 3/1*3+1/3
Calculate the product or quotient:45/3/3 +1/3
Write the numerators over common denominator:45/3+1/3
Calculate the sum or difference:45/4/3
Divide a fraction by multiplying its reciprocal:45* 3/4
Write as a single fraction:45* 3/4
Calculate the product or quotient:135/4
Convert to mixed fraction: 33*3/4
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What two numbers multiply to -24 and add 36
Two numbers are: - 36.65 and 0.655. This can be solved by using the concept of equation.
What is an equation?An equation is an algebraic expression that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 7x + 14 = 35 consists of the two equations 7x + 14 and 35, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
By deleting parenthesis and grouping like words, each side of the equation may be made simpler. The changeable item on one side of the equation can be separated using addition or subtraction. To determine the variables, apply divisions or multiplication.
Given that,
two numbers multiply to -24 and add 36.
Let, two numbers are: x and y
Now, xy = -24 ............. (1)
or, y = - 24/x
x + y = 36 .............. (2)
Next, put y = - 24/x in equation no. (2) we get -
x + (-24/x) = 36
or, x² - 24 = 36x
or, x² - 36x - 24 = 0
or, x = -36.65
so, y = (-24/x) = (-24/ - 36.65)
y = 0.655
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A car is traveling at a speed of 2 feet per second. What is the car's speed in miles per hour? How many miles will the car travel in 3 hours? In your computations, use the fact that mile is equal to feet. Do not round your answers.
Answer:
Step-by-step explanation:
The car is moving at 1.36 miles per hour. It will travel 4.09 miles in 3 hours. If you drive like this, I would suggest speeding up.
For what values of b will f x )= log x be a decreasing function?.
The range of
The logarithmic function f(x) = log_b x is a decreasing function if and only if b > 1.
To see why, consider that for any positive real number x, log_b x increases as x increases. This can be seen by using the definition of logarithms: log_b x is the power to which b must be raised to produce x. As x increases, the power to which b must be raised to produce x must also increase, so log_b x must increase as well.
Therefore, if b > 1, then log_b x is a strictly decreasing function, because as x increases, the power to which b must be raised to produce x increases at an increasing rate, so log_b x decreases at an increasing rate. On the other hand, if 0 < b < 1, then log_b x is a strictly increasing function, because as x increases, the power to which b must be raised to produce x increases at a decreasing rate, so log_b x increases at a decreasing rate.
It is important to note that for b = 1, the logarithmic function is undefined, as log_1 x is not defined for any positive real number x.
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I WILL GIVE YOU 100 POINTS. PLEASE HELP ME
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
A 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 37.6 HCF.
B 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 58.2 HCF.
C 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 38.2 and 78.7 HCF.
D 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 58.9 and 78.7 HCF.
A buffet offers a container of pulled pork. One customer eats 1/2 pound of pulled pork. A second customer eats 3/4 pound of pulled pork. If the container of pulled pork now has 1 4/8 pounds, how much pulled pork was in the container originally?
