Answer:
Step-by-step explanation:
Let the no of cars be x and no of buses be y.
x + y = 60 -> y = 60 - x
6x + 30y = 600
with the available equations let us calculate the values of x and y.
6x + 30 * (60-x) = 600
6x + 1800 - 30x = 600
24x = 1200
x cars = 50
y buses = 10
maximum profit = 50 * 2.5 + 10 * 7.5 = $200
a) The objective function to maximize profit is: 2.5C + 7.5B using constraints 6C + 30B ≤ 600 and C + B ≤ 60. b) The parking lot should accept 50 cars and 10 buses to maximize profit. The maximum profit will be $200.
We need to set up a linear programming model to maximize profit from parking cars and buses.
A. Model Formulation:
Let C represent the number of cars and B represent the number of buses.
Objective Function: Maximize Profit = 2.5C + 7.5B
Constraints:
Space constraint: 6C + 30B ≤ 600 (square meters)Vehicle limit: C + B ≤ 60 (vehicles)Non-negativity constraints: C ≥ 0, B ≥ 0B. Solution:
First, we convert the inequalities to equations and solve:
6C + 30B = 600 ⟶ C + 5B = 100 C + B = 60We solve these equations simultaneously:
1. C + 5B = 100 (Equation 1)
2. C + B = 60 (Equation 2)
Subtract Equation 2 from Equation 1:
(C + 5B) - (C + B) = 100 - 60
⟶ 4B = 40 ⟶ B = 10
From Equation 2, we get:
C + 10 = 60 ⟶ C = 50
Maximum Profit Calculation:
Substituting C = 50 and B = 10 into the objective function:
Profit = 2.5(50) + 7.5(10) = 125 + 75 = 200
Therefore, to maximize profit, the attendant should accept 50 cars and 10 buses.
Maximum profit is $200.
Complete question:
The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50. How many of each should be accepted to maximize Profit?
a. Set up for the solution of this Linear Programming (LP) problem.
b. Using part (a), how many of each should be accepted to maximize Profit? What is the maximum profit?
Sean and Katherine have been married for two years. They want to start a family soon. However, before having a child, they would like to secure their future and the future of their child. Which financial option will help them secure their family’s future?
A.
invest in in several real estate options
B.
invest in high-risk shares that promise big returns
C.
invest in a joint insurance and retirement plans
D.
become entrepreneurs or invest in a profit-making business
Answer:
C.
invest in a joint insurance and retirement plans
Step-by-step explanation:
this would be the obvious answers because there no risks that would compromise their future
Is the function linear or nonlinear?
_ y = 2x3 + 1
Answer:
it's linear because the line doesn't go through the origin
Step-by-step explanation:
i know that bc it says. +1
hope this helps!
what are the domain range of f(x)= 1/5 power of x
Answer:
Domain: all real numbers
Range: all real numbers
Step-by-step explanation:
I'm assuming you mean the function [tex]f(x)=x^{\frac{1}{5}}[/tex]. That's usually written
f(x) = x^(1/5) with the ^ meaning "to the power of..." and the fraction exponent in parentheses so as not to be confused with x^1/5 which could mean x to the first power, divided by 5.
Fractional exponents are used to indicate roots. In this case, x is being raised to the 1/5 power, so this is the fifth root of x, written [tex]\sqrt[5]{x}[/tex]. The 5 is called the root index.
For odd roots, like this one, the domain is all real numbers--x can be any number at all. So the domain is all real numbers.
The range is also all real numbers. Attached is a graph of this function. It might not look like it, but the graph rises to the right to any height. The larger x gets, the larger the 5th root gets. A similar thing happens on the left--the smaller x gets, the smaller the 5th root gets.
EDIT: see the comment. For the function [tex]f(x)=(1/5)^x[/tex], the domain is all real numbers. The range is positive real numbers. I'll attach a graph!
A sample of students is taken from the school's A honor roll. The school estimates that there are actually 360 students on the A honor roll. Using this sample, how many students on the A honor roll are 8th graders?
By multiplying the individual probabilities of being a music student and being on the honor roll and then multiplying by the total on the honor roll, we find the expected number of music students on the honor roll to be 16.
Explanation:To determine the expected number of music students who are also on the honor roll, we can use the concept of expected value in probability.
Assuming that being a music student and being on the honor roll are independent events, we can multiply the probability of a student being a music student by the probability of a student being on the honor roll.
The probability of randomly selecting a music student from the 300 students is the number of music students divided by the total number of students, P(Music) = 50/300.
The probability of a student being on the honor roll is P(Honor Roll) = 97/300. So, the expected number of music students on the honor roll would be the product of these two probabilities times the total number of students on the honor roll, which the school estimates to be 360.
The calculation: Expected number = [tex]P(Music) \(\times\) P(Honor Roll) \(\times\) Total Honor Roll = (50/300) \(\times\) (97/300) \(\times\)[/tex]
Which three-dimensional object is formed when the shape is rotated about the axis as shown?
pyramid
cylinder
cone
triangular prism
The three-dimensional object formed when the shape is rotated about the axis is a cone.
What is a cone?A cone is a solid which tapers from a circular base to a point. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.
here, we have,
we know that,
When a right triangle is rotated about an axis, a cone is formed.
Find the attached figure to visualize the rotation.
Rotation of the base AB of the right triangle results in the circular base of the cone while rotation of hypotenuse AC results in the lateral surface of the cone.
Hence, The three-dimensional object is formed when the shape is rotated about the axis is a cone.
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The point A has coordinates A(2, 4). What are the coordinates of A′ for the dilation D1.5(A)?
Answer:
[tex]A'(3,6)[/tex]
Step-by-step explanation:
The given coordinate is [tex]A(2,4)[/tex].
It's important to know that a dilation implies a bigger figure than the original. In this case, we have a factor of dilation of 1.5, which means each coordinate must be multiplied by it.
So, using the factor of dilation, we have
[tex]A(2,4) \implies A'(3,6)[/tex]
Because [tex]2 \times 1.5 = 3[/tex] and [tex]4 \times 1.5 = 6[/tex]
Therefore, the right answer is [tex]A'(3,6)[/tex]
The coordinates of [tex]\( A' \)[/tex] after dilating point [tex]\( A(2, 4) \)[/tex] by a factor of [tex]\( 1.5 \)[/tex] are [tex]\( {(3, 6)} \)[/tex].
To find the coordinates of [tex]\( A' \)[/tex] after dilating point [tex]\( A(2, 4) \)[/tex] by a scale factor of [tex]\( 1.5 \)[/tex], we use the formula for dilation:
If [tex]\( A'(x', y') \)[/tex] is the image of [tex]\( A(x, y) \)[/tex] under dilation with scale factor [tex]\( k \)[/tex], then:
[tex]\[ x' = k \times x \][/tex]
[tex]\[ y' = k \times y \][/tex]
Given:
[tex]\( A(2, 4) \)[/tex]
Scale factor [tex]\( k = 1.5 \)[/tex]
Now, calculate the coordinates of [tex]\( A' \)[/tex]:
[tex]\[ x' = 1.5 \times 2 = 3 \][/tex]
[tex]\[ y' = 1.5 \times 4 = 6 \][/tex]
please i need help it is due in 2 mins
Answer:
mean = 9.3
median = 10
mode =13
Step-by-step explanation:
First put the data in order from smallest to largest
1,1,7,9,9,10,11,13,13,13,15
The mean is the sum of all the numbers divide by how many numbers we have
(1+1+7+9+9+10+11+13+13+13+15)/11102/11=9.272727=9.3
median is the middle number
11/2 = 5.5
The sixth number is the median= 10
mode is most often 13 appears the most
Find the x and y intercepts: 7x - 2y = 28
Answer:
x-intercept(s): ( 4, 0)
y-intercept(s): ( 0, -14)
PLEASE HELP!!!! for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
sue has just one evening to study for her math test she believes the more she still needs to hire her test score will be
here are the statements
1) The range will be from 0 to 100 points
2) The dependent variable will be her test score
3) The independent variable be the number of hours to study
4) The domain will be from 0 to 25 hours
THE TABLE SHOWS THE AGES OF THE SWIMMERS ON DION'S SWIM TEAM.THE MEAN AGE OF THE SWIMMERS IS 10.WHAT DOES THE MEAN REPRESENT
Answer:
The mean is the balancing point of the swimmers' ages.
Step-by-step explanation:
I just took the I-Ready Quiz and got it correct. :D
The mean in mathematics refers to the average of a set of given numbers. Mean is commonly referred to as average.
Mean is the average number, which is calculated by the formula:
[tex]\rm mean = \dfrac{sum\; of\; all\; the\; given\; numbers}{\text{total observation}}[/tex]
For instance, the mean age of swimmers is 10, which means that the average age of all the swimmers is 10. The age of each swimmer can be near to 10, as 9, 10, 11, or 12.
Given the ages of swimmers are:
[tex]\text{mean} = \dfrac{10 + 10 + 11 + 9}{4}\\\text{mean} = \dfrac{40}{4}[/tex]
mean = 10
Thus, the mean of the given data is 10.
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A man bought a refrigerator, an air conditioner, a TV set and a gas cooker for $150.00, $400.00, $180.00 and $300.00 respectively. In addition he pays 15% VAT for each item. Calculate
Total VAT collected from him
Total amount he had to pay.
Answer:
1184.5
Step-by-step explanation:
150+400+180+300=1030
1030 × 15% = 154.5
(15% is also 0.15)
1030 + 154.5 = 1184.5
I hope this helps you :)
637.2 x 8.49 estimate
Answer: 5409.828
Step-by-step explanation: calculator
How far is point E(5,3) from the origin ?
Answer:
It is 5.84 units away from the origin.
Step-by-step explanation:
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2}} [/tex]
Therefore:
[tex]d = \sqrt{ {(5 - 0)}^{2} + {(3 - 0)}^{2} } \\ d = \sqrt{ {5}^{2} + {3}^{2} } = \sqrt{25 + 9} \\ d = \sqrt{34} = 5.83951...[/tex]
Final answer:
The distance from point E(5,3) to the origin is calculated using the Pythagorean theorem, resulting in \/34 units.
Explanation:
The question asks how far point E(5,3) is from the origin. To find the distance between a point and the origin in a Cartesian coordinate system, we use the Pythagorean theorem. Specifically, the distance ( extit{d}) can be calculated using the formula extit{d} = \/((x_2 - x_1)² + (y_2 - y_1)²), where ( extit{x_1}, extit{y_1}) represents the coordinates of the first point (in this case, the origin (0,0)) and ( extit{x_2}, extit{y_2}) represents the coordinates of the second point (in this case, point E(5,3)).
Plugging in the values, we get extit{d} = \/((5 - 0)² + (3 - 0)²) = \/(5² + 3²) = \/(25 + 9) = \/34. The exact distance between point E and the origin is \/34 units, which can also be approximated as a decimal if necessary.
Alison bought some shirts for her
clothing store for $15 each. She received
$50 off her entire purchase and spent a total of $440. How many shirts did Alison purchase for her store?
Answer: $29.10
Step-by-step explanation: 10.20 + 18.90 = $29.10
The base of a triangular prism has an area of 18 square inches. If the height of the prism is 4.5 inches, then what is the volume of the prism?
Answer:
81 inches squared
Step-by-step explanation:
You just multiply the area by the hight and get your answer
A cartoon last is one 1/2 of an hour. A movie is 6 times longer than the cartoon. How many minutes does it take to watch both the cartoon and the movie? (1hour = 60 minutes)
Final answer:
The cartoon lasts 30 minutes, and the movie is six times longer, adding up to 210 minutes to watch both.
Explanation:
The subject at hand is the duration it takes to watch a cartoon and a movie. The cartoon lasts half an hour (30 minutes), while the movie is six times longer than the cartoon. To find the duration of the movie, we multiply its relative length by the duration of the cartoon. So, 6 times 30 minutes is 180 minutes. To calculate the total time to watch both the cartoon and the movie, we add the two durations together. Therefore, 30 minutes for the cartoon plus 180 minutes for the movie equals 210 minutes in total.
On a graph, points are grouped closely together and increase.
Try to draw a line to approximate the points in the graph. Is the correlation between the variables positive or negative? Explain.
It is positive because the slope is negative.
It is positive because the slope is positive.
It is negative because the slope is negative.
It is negative because the slope is positive.
Answer: B
Step-by-step explanation:
Answer:B
Step-by-step explanation:
50 POINTS!
a) Write a polynomial for the perimeter of this shape. Simplify the polynomial. (The polynomial is in the photo)
b) Determine the perimeter of the shape when d = 5 m.
Answer:
a) 4d + 18
b) 38 inches
Step-by-step explanation:
a) The perimeter is simply the sum of all the exterior side lengths.
On the top, we've got d and d + 3.
On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.
The bottom is the same length as the top two lengths, so it's:
d + (d + 3) = 2d + 3
And, the right side is 6.
Adding these together, we have:
d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18
b) We just need to substitute 5 in for d:
4d + 18
4 * 5 + 18 = 20 + 18 = 38 inches
AnswerAnswer:
a) 4d + 18
b) 38 inches
Step-by-step explanation:
a) The perimeter is simply the sum of all the exterior side lengths.
On the top, we've got d and d + 3.
On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.
The bottom is the same length as the top two lengths, so it's:
d + (d + 3) = 2d + 3
And, the right side is 6.
Adding these together, we have:
d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18
b) We just need to substitute 5 in for d:
4d + 18
4 * 5 + 18 = 20 + 18 = 38 inches
Step-by-step explanation:
21.
In the standard equation for a line, what does the variable b stand for?
y = mx + b
X-coordinate
y-coordinate
y-intercept
slope
Answer:
b = y intercept
Step-by-step explanation:
y = mx +b
This is the slope intercept form of a line
The m is the slope and the b is the y intercept
A sports store I'd having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccers bags for $155. Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189. What is the cost of a soccer ball and the cost of a soccer ball ?
Answer:
- The price of a soccer ball is $14.5
- The price of a soccer bag is $5
Step-by-step explanation:
To solve this problem, we call:
s = the price of a single soccer ball
b = the price of a soccer bag
We have:
1) A soccer coach purchases 10 soccer balls and 2 soccers bags for $155: so we can write
[tex]10s+2b=155[/tex] (1)
2) Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189: so we can write
[tex]12s+3b=189[/tex] (2)
So we have a system of two equations in two unknown variables:
[tex]10s+2b=155\\12s+3b=189[/tex]
We solve it by multiplying eq.(1) by 3 and eq(2) by 2, and we get:
[tex]30s+6b=465\\24s+6b=378[/tex]
Now we substract eq(2) from eq(1) and we get:
[tex]6s=87[/tex]
So
[tex]s=\frac{87}{6}=14.5[/tex]
And by using eq(1) we also find the value of b:
[tex]10s+2b=155\\b=\frac{155-10s}{2}=\frac{155-10(14.5)}{2}=5[/tex]
So:
- The price of a soccer ball is $14.5
- The price of a soccer bag is $5
To solve this problem, we can set up a system of equations and use the elimination method to find the values of x and y. The cost of a soccer ball is $14.5 and the cost of a soccer bag is $5.
Explanation:To solve this problem, we can set up a system of equations. Let's use x to represent the cost of a soccer ball and y to represent the cost of a soccer bag.
From the first equation, we have 10x + 2y = 155. From the second equation, we have 12x + 3y = 189.
We can solve this system of equations using substitution or elimination method. I will use the elimination method.
Now we can substitute the value of x into one of the equations to find the value of y.
Therefore, the cost of a soccer ball is $14.5 and the cost of a soccer bag is $5.
factorise this expression as fully as you can 12x^3-9x^2
The factor of the expression 12x³ – 9x² will be 3x² and (4x – 3).
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ 12x³ – 9x²
Then the factor of the expression will be
⇒ 3x²(4x – 3)
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Which description accurately describes the tide represented by the image below?
Image of the sun and moon at a 90 degree angle to Earth. An oval is around Earth that points toward and away from the moon to show the tidal bulges.
High tide
Lunar tide
Neap tide
Spring tide
Answer:
neap tide
Step-by-step explanation:
Answer:neap tide is the correct one
Step-by-step explanation:
Find the quotient.
158
152
A) 1516
B) 1510
C) 156
D) 154
Answer:
D
Step-by-step explanation:
What function can be used to model the coronavirus growth A)linear b)quadratic c) exponential d) none of the above
9+___=10
1+____=10
200+500+2000-3000
Answer:
1
Step-by-step explanation:
To solve the equations, subtract the given number from the sum on the left side of the equation to find the missing number. For the arithmetic expression, perform the operations in order.
Explanation:In the first equation, you must find a number that, when added to 9, equals 10. To do this, subtract 9 from 10, which gives you 1. Therefore, the missing number is 1.
In the second equation, you need to find a number that, when added to 1, equals 10. Subtract 1 from 10 to get 9. So, the missing number is 9.
In the last equation, you simply need to perform the arithmetic operations in order: 200 + 500 = 700, 700 + 2000 = 2700, and finally 2700 - 3000 = -300. Therefore, the result of the expression 200 + 500 + 2000 - 3000 is -300.
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FULL POINTS AND BRAINLIEST
2. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Answer:
2) y = x + 2
3) slope: height increases by 1 unit per unit increase in x
Intercept: initial height (at birth) was 2 units
Step-by-step explanation:
Using (38,40) and (48,50)
Slope: (50-40)/(48-38)
= 10/10
= 1
y = mx + b
y = x + b
40 = 38 + b
b = 2
y = x + 2
Answer:
see below
Step-by-step explanation:
There are (60,61) and (20,23) are the points that I used to find the slope for the line of best fit
m= (y2-y1)/(x2-x1)
m = (23-61)/(20-60)
= -38/-40
= .95
We use the slope intercept form of the equation
y= mx+b
y = .95x+b
Substituting in the point (20,23)
23 = .95(20) +b
23 = 19+b
Subtracting 19 from each side
23-19 = 19+b-19
4 =b
The equation is
y =.95x+4
The slope is how much y changes for each change in x. You did not tell us what the units of x and y are.
The y intercept is what the y value is when x is zero. The y value is 4 when x is zero
help me answer this thanks
Answer:
C = 73
Step-by-step explanation:
Formula used: a²+b²=c²
A and B represent the numbers other than the hypotenuse, so C equals the hypotenuse. It doesn't matter which number you put as A or B. Here's the equation we're working with:
(55)² + (48)² = C²
That simplifies to:
3025 + 2305 =C²
5329 = C²
Now, C needs to be by itself in order for us to get the answer, so the next step is to do inverse operations. The inverse of sqauring a number (x²) is to square root it (√x). Here is the new equation we are working with:
√5329 = √C
That simplifies to:
73 = C
Hope this is correct!
In the equation (x+2)^2+(y-3)^2=4 the diameter of the circle is.....
Answer:
4
Step-by-step explanation:
(x+2)^2+(y-3)^2=4
From this equation, we can find the radius of this circle.
(x+2)^2+(y-3)^2= 2^2
radius = 2
diameter = 2*radius = 2*2 = 4
A company randomly surveyed employees to determine the most important reasons for being late to work. The results are shown on the Pareto graph. Approximately how many employees took part in the random survey? A) 50 B) 100 C) 130 Eliminate D) 150
Answer: this answer is 130
Step-by-step explanation:
Which shows one way to determine the factors of x + 11x2 – 3x – 33 by grouping?
O x2(x + 11) + 3(x – 11)
O x²(x – 11) – 3(x – 11)
O x2(x + 11) + 3(x + 11)
O x2(x + 11) – 3(x + 11)
Answer: x^2 (x + 11) - 3 (x + 11)
Answer:
Answer: x^2 (x + 11) - 3 (x + 11)
Step-by-step explanation:
Edge