The equation which represents Lisa's earnings, e, relative to the number of hours, h, that she works assume a proportional relationship is e = 7.5h
How to write equations?Amount Lisa makes for babysitting = $30
Number of hours Lisa babysit = 4 hours
Total earnings = e
Number of hours = h
If the relationship is proportional, then
k = constant of proportionality
e = k × h
30 = k × 4
30 = 4k
divide both sides by 4
k = 30/4
k = 7.5
So therefore,
e = k × h
e = 7.5 × h
e = 7.5h
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fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0,a), where should the station be located so as to minimize the expected distance from the fire?
The fire station should be located at the midpoint (a/2) of the road to minimize the expected distance from the fire.
The total distance cost will be infinite if we start at one point on a given line at an infinite distance. However, as we move this point toward the given points, the total distance cost begins to decrease. After a while, it then increases once more, reaching infinite at the other infinite end of the line. Therefore, the distance cost curve resembles a U-curve, and its bottom value must be determined.
The fire station should be located at the midpoint (a/2) of the road (0,a) to minimize the expected distance from the fire.
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Copy the problem and write a statement/reason proof
Answer:
..........................
Which of the inequalities are equivalent?
3x+6≤8+ 2x
5x-527x-9
12-3x <=18
-2-3x≥-3-x
The inequalities that are equivalent are 3x+6≤8+ 2x and 12-3x ≤18
What are inequalities?
Inequalities are simply defined as relations that makes a non-equal comparison between two mathematical expressions, equations or numbers.
It is mostly used to compare two numbers or expressions based on the magnitude on the number line.
Inequality signs in mathematic include;
< represents less than> represents greater than≤ represents less than or equal to≥ represents greater than or equal toGiven the inequalities;
3x + 6 ≤ 8 + 2x
collect like terms
3x - 2x≤ 8 - 6
subtract like terms
x ≤ 2
12-3x ≤18
collect like terms
3x≤ 18 - 12
3x ≤ 6
Divide both sides by 3
x ≤ 2
Hence, the inequalities are 3x+6≤8+ 2x and 12-3x ≤18
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Amelia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.60 plus $0.50 per mile. The total fare was $13.60, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
Answer:
18 miles
Step-by-step explanation:
m = # of miles
$4.60 + ($0.50/mi)m = $13.60
($0.50/mi)m = $13.60 - $4.60 = $9.00
m = ($9.00) / ($0.50/mi) = 18 miles
Peter expected to earn $425 in a week. In fact he earned $500. What was the percent of error?
The percent of error is 17.65% .
The percent of error is a way to measure the difference between the expected value and the actual value. In this case, Peter expected to earn $425 in a week but he actually earned $500.
So, the difference between the expected value and the actual value is $75. The percent of error is calculated by taking the difference between the actual value and the expected value, dividing that by the expected value, and multiplying the result by 100%.
In this case, (500-425)/425*100% = 17.65%, which means that Peter's actual earnings were 17.65% higher than what he expected to earn.
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how to find a vector perpendicular to another vector
A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.
You can utilize methods based on the dot-product and cross-product of vectors to create a vector that is perpendicular to another supplied vector. The total of the products of the relevant components is the dot-product of the vectors A = (a1, a2, a3) and B = (b1, b2, b3):
AB = a1 b2 + a2 b2 + a3 b3. The dot product of two vectors that are perpendicular is equal to zero.
The formula for calculating the cross-product of two vectors is AB = (a2 b3 - a3 b2, a3 b1 - a1 b3, a1 b2 - a2*b1).
A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=880(1. 958)^xy=880(1. 958)x
The change represents growth and percentage rate of increase is 95.8%.
The exponential function y = 880(1.958)^x is a function that models growth.
The base of the exponential function, 1.958, is greater than 1. This means that the function is increasing with respect to x, which is the independent variable.
For every unit increase in x, the function increases by a factor of 1.958. This is evident from the fact that 1.958 is raised to the power of x.
The percentage rate of increase is calculated by taking the difference between the base of the exponential function and 1, and then multiplying that difference by 100%.
In this case, the base of the exponential function is 1.958, so the percentage rate of increase is
(1.958- 1)*100 = 95.8%.
This means that for every unit increase in x, the value of y increases by 95.8% of its previous value.
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a) what is the probability that the company will make less than $2m? b) what is the probability that the company will make less than $1m or at least $2m?
The probability that the company will make less than $2m is 0.8 and b) the probability that the company will make less than $1m or at least $2m is 0.7
Here we are given respective probabilities of the revenue a company could make in a year.
a) Here we need to find the probability that it makes a revenue less than $ 2 million
This means that we need t find the probability that it makes revenue
less than $1M + greater than $1 M but less than $2M
= P(A₁) + P(A₂)
= 0.5 + 0.3
= 0.8
b)
The probability that the company will make less than $1M or at least $2M is
P(A₁ U A₃)
= P(A₁) + P(A₃) - P(A₁ ∩ A₃)
Since A₁ and A₃ are clearly mutually exclusive events, P(A₁ ∩ A₃) will be 0.
Hence we get
P(A₁ U A₃) = 0.5 + 0.2
= 0.7
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Complete Question
Assume the following in regard to a company’s annual revenue:
A₁ : Revenue < $1M; P(A₁) = 0.5
A₂ : Revenue > $1M but < $2M; P(A₂) = 0.3
A₃ : Revenue > $2M; P(A₃) = 0.2
a)What is the probability that the company will make less than $2M?
b)What is the probability that the company will make less than $1M or at least $2M
I need help solving
Answer: 189 degrees
Step-by-step explanation:
Since 17x + 2 = 16x + 9, we can solve for x:
17x + 2 = 16x + 9
Subtract 16x from both sides:
x + 2 = 9
Subtract 2 from both sides:
x = 11
The angle indicated in bold is 17x + 2, so we just substitute 11 into x and get 17 * 11 + 2, = 187 + 2 = 189 degrees :>
Answer? Please help.
Answer:
answer is no
Step-by-step explanation:
Benita buys 2 shirts for the same price, s. The sales tax rate is 6. 5%.
Write an expression to represent the total cost of the shirts in two different ways.
Enter the correct answers in the boxes
The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.
Now, According to the question:
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Benita buys 2 shirts for the same price, s.
The sales tax rate is 6. 5%.
Write an expression to represent the total cost of the shirts.
1 way, paid the cost of 2 shirts jointly
The total cost of the two shirts becomes,
Total cost = 2[ s + 0.065s]
Total cost = 2.13s
2nd way, paid the cost of two shirts individually,
total cost = s + 0.065s + s + 0.065s
= 2.13s
Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.
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His former car was able to travel 20. 28 miles per gallon. Is Xavier getting better gas
mileage in his new car? Explain.
Xavier is not getting better mileage with his new car.
it is given that
distance traveled by Xavier's new car in 20.28 gallons = 472miles
the mileage can be calculated using the formula = (distance traveled)/( gallons of fuel used).
So, the mileage of the new car = 472/20 = 23.06 miles per gallon, and the mileage of Xavier's former car = 20.28 miles per gallon.
From the above data, we can see that the mileage of the former car is greater than the new car.
Therefore, Xavier is not getting better mileage with his new car.
The given question is incomplete, the complete question is
Xavier's new car uses 25 gallons for 472 miles, His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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Can anyone help me with this problem
Answer:
-7
Step-by-step explanation:
angles in a triangle add up to 180⁰
90⁰+30⁰+(x+67)=180⁰
187+x=180⁰
x=180⁰-187⁰
x=-7
If point R has coordinates (x,y) and point S has coordinates (x + 1, y + 1), what is the distance between R and S?
The distance between the two points R and S is √2.
The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places.
The distance between the two points R and S can be calculated using the Pythagorean theorem. Given the coordinates (x, y) for point R and (x + 1, y + 1) for point S, the distance d between R and S is given by:
d = √((x + 1 - x)^2 + (y + 1 - y)^2) = √(1^2 + 1^2) = √2.
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i need an answer for this please
Answer:
-1
Step-by-step explanation:
top: -20/(-4) = 5
bottom: -49+44 = -5
5/(-5) =-1
Please help you will get 25 points!
Explore Part 2
Here is a number pyramid puzzle.
Each number is the product of the two numbers directly below it.
Complete the pyramid.
Answer:
Check image :D
Step-by-step explanation:
The image is the answer. I hope this helps you out :D
The average tuition for a full-time under-
graduate student in a public college in 2002 was $4,790. In
2012 it was $8,240. Using the linear function model, estimate
the cost of tuition in 2018.
The estimated cost of tuition in 2018 using this linear function model is $726,430
What is the linear function?
A linear function is a mathematical function that describes a straight line. The general form of a linear function is:
y = f(x) = mx + b
To estimate the cost of tuition in 2018 using a linear function model, we can use the two given data points to find the slope and y-intercept of the line.
First, we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) is the data point for 2002 and (x2, y2) is the data point for 2012.
Substituting the values, we get:
m = (8,240 - 4,790) / (2012 - 2002) = 3,450 / 10 = 345
Next, we can use one of the data points and the slope to find the y-intercept of the line. Let's use the data point for 2002:
y = mx + b
4,790 = 345 * 2002 + b
b = 4,790 - 345 * 2002 = -1,015,290
So, the equation of the line is y = 345x - 1,015,290
To estimate the cost of tuition in 2018, we can substitute x = 2018 into the equation:
y = 345(2018) - 1,015,290 = 726,430
Hence, the estimated cost of tuition in 2018 using this linear function model is $726,430
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find the length of the diagnol with work shown please
The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]
How can calculate a diagonal's length?If you know the width and height of a rectangle, you can find its diagonal. The diagonal is equal to the sum of the square roots of the width and height.If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w. Given a diagonal (d) and a width (w), its length is given by h = (d2w2). The diagonal is the line that passes across the centre of a square or rectangle and connects one corner to the other. Any square with two diagonals has sides that are both the same length.The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]7[tex]n^{2}[/tex] + 7[tex]n^{2}[/tex] = [tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]To learn more about diagnol refer to:
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8 of the tables at Joy's Italian Restaurant are full and the other 13 tables are empty. What is the ratio of the number of empty tables to the total number of tables?
The ratio of the number of empty tables to the total number of tables is 13:21
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, 8 of the tables at Joy's Italian Restaurant are full, and the other 13 tables are empty, we are asked to find the ratio of the number of empty tables to the total number of tables,
Number of empty table = 13
Total number of tables = 13 + 8 = 21
Ratio of the number of empty tables to the total number of tables = 13 / 21
Hence, the ratio of the number of empty tables to the total number of tables is 13:21
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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
The axis of symmetry of the graphed function is:
x = -2
How to find the axis of symmetry?Here we want to find the axis of symmetry of the graphed function, which is a quadratic one.
The axis of symmetry is a line of the form:
x = a
Where a is a real number
Such that it divides the graph of the function in two equal parts.
Notice that the parabola is perfectly divided by the line x = -2, so that is the axis of symmetry of the graphed function.
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is y=2.2x proportional
Answer:
yes
Step-by-step explanation:
A proportional relation has an equation of the form
y = kx,
where k is a real number.
y = 2.2x is an equation of the form y = kx with k = 2.2, so y = 2.2x is proportional.
Answer: yes
A sphere has a radius of 2 mm. What is the difference between the volume of the sphere and an approximation using a left sum with 16 intervals? Round to the nearest hundredth
The difference between the volume of the sphere and an approximation using a left sum with 16 intervals is 17.51 mm.
The term called volume in math is known as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we know that the sphere has a radius of 2 mm.
Then the volume of the sphere is calculated by using the formula,
=> V = 4/3πr³
Here we know that the value of r = 2.
Then the volume is calculated as,
=> V = 4/3 x π x 2³
When we simplify this one then we get,
=> V = 10.67π = 33.51
Here we need to find the difference between the volume of the sphere and an approximation using a left sum with 16 intervals is
=> 33.51 - 16
=> 17.51
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A line has a slope of 7 and passes through the point (-1, -8). Write its equation in slope-
intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
Step-by-step explanation:
we know the slope and we have a point , so
y = 7x + b
sub in the point ...
-8 = 7(-1) + b
-8 + 7 = b
b = -1
y = 7x - 1
The side view of a bookend is shown. The perimeter of the bookend is 58
centimeters.
A four-sided closed figure is shown. The lengths of the sides are five times m minus fourteen, two times m minus seven, three halves times m plus two, and three times m plus eight.
Part A. Write an equation in simplest form that represents the perimeter of the bookend in centimeters.
Part B. What is the value of m
?
Enter the correct answers in the boxes.
The equation in the simplest form that represents the perimeter of the bookend in centimeters is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Part A :
Perimeter of a closed figure is the sum of the lengths of it's boundary.
Given the lengths of the sides of the bookend as,
5m - 14, 2m - 7, 3/2 m + 2 and 3m + 8.
Perimeter is given as 58 centimeters.
(5m - 14) + (2m - 7) + (3/2 m + 2) + (3m + 8) = 58
(5m + 2m + 3/2 m + 3m) + (-14 - 7 + 2 + 8) = 58
23/2 m - 11 = 58
11 [tex]\frac{1}{2}[/tex] m - 11 = 58
Part B :
We have,
11 [tex]\frac{1}{2}[/tex] m - 11 = 58
11 [tex]\frac{1}{2}[/tex] m = 58 + 11
11 [tex]\frac{1}{2}[/tex] m = 69
23/2 m = 69
m = 6
Hence the required equation is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.
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Please help me i have a horrible grade in this class
If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
It is given that triangle ABC is similar to triangle DEF.
It can be seen in the image that ΔDEF is a dilated version of ΔABC.
In ΔABC the measurement of side AB = 23 units
In ΔABC the measurement of side BC = 11 units
In ΔDEF the measurement of side EF = 52 units
In ΔDEF the measurement of side DE = x units
Apply the formula for indirect measurement to find the measurement of side DE.
AB/DE = BC/EF
Substitute the values in the equation -
23/x = 11/52
23 × 52 = 11x
x = (23 × 52)/11
x = 1196/11
x = 108.72
Therefore, the measurement of DE is 108.72 units.
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HURRY 60 POINTS Question Consider the two-way table. Group 1 Group 2 Category A 36 20 Category B 12 35 Complete the table below to show the relative frequencies of the data in the first column. Enter numbers in the boxes as decimals to the hundredth place. Group 1 Category A Category B
Answer:
Category A 0.75
Category B 0.25
Hope it helps !!
Determine whether the underlined value is a parameter or a statistic_ The average score for a class of 28 students taking a calculus midterm exam was 72% Is the value a parameter or a statistic? A. The value is a statistic because the class of 28 students is a sample. b. The value is a parameter because the class of 28 students is a sample c. The value is a parameter because the class of 28 students is a population. d. The value is a statistic because the class of 28 students is a population.
The value is a parameter because the class of 28 students is a population.
A statistic is a measure calculated from a sample of the population, whereas a parameter is a measure that is calculated from the entire population. It is generally a numeric value that is used to characterise a population trait. A probability distribution is defined or described by a fixed value that is typically unknown.
The population's mean, variance, and standard deviation are just a few parameters. By employing statistical techniques like maximum likelihood estimation, these parameters are often calculated from a sample of data. In the given question, since from a class of 28, the average score was 72% of the population which is the total, this value is a parameter.
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an engine with a 12- gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour. the tank was full when the engine began running, and there are now 9.3 gallons left in the tank. create and solve an equation to find the number of hours x the engine has been running.
If the engine with 12 gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour , then the equation to find number hours the engine has been running is "12 - 0.6x = 9.3" .
the total capacity of the tank is = 12 gallon ;
the constant use rate of engine is = 0.6 gallons per hour ;
the amount of fuel left in the tank is = 9.3 gallons ;
let the number of hours the engine is running is = x hours ;
the above situation can be represented as ⇒ 12 - 0.6x = 9.3 ;
⇒ 12 - 0.6x = 9.3 ;
⇒ 12 - 9.3 = 0.6x ;
⇒ 0.6x = 2.7 ;
⇒ x = 2.7/0.6 ;
⇒ x = 4.5 hours
Therefore , the engine has been running for 4.5 hours .
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Please help me with this geometry question
A rectangle has a height of x+4x+4 and a width of x^2+3x+2
The area of rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.
Explain the term area of the rectangle?Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth. In other words, a rectangle's area is equal to the sum of its width and length.So, from the definition of the area of the rectangle.
Area = length x width
Given:
length/height = x+4x+4 = 5x + 4width = x^2+3x+2Thus,
Area = (5x + 4)(x^2+3x+2)
Simplifying,
Area = 5x(x^2+3x+2) + 4(x^2+3x+2)
Area = 5x³ + 19x² + 22x + 18
Thus, the area of the rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.
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The complete question is-
A rectangle has a height of x+4x+4 and a width of x^2+3x+2. Express the area of the entire rectangle.