The area of the two lawns will be 105 square meters.
According to the question,
We have the following information:
The first lawn is 7 meters long and 4 meters wide. The second lawn has the same length and width which is 3 times as much as the first one.
So, the width of the second lawn = 4×3
Width of second lawn = 12 m
Now, the formula to find the area of the rectangle:
Length*width
Area of first lawn:
7×3
21 square meters
Area of second lawn:
7×12
84 square meters
Now, the area of two lawns = area of first lawn+ area of second lawn
Area = 21+84
Area = 105 square meters
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art contractors must locate an equipment staging area to serve three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5). traffic between the staging area and each of the sites is 30 trips a week, except for the site located at (5,5), which is only 10 trips a week. what is the best set of co-ordinates for the equipment staging area?
Using the concepts of co-ordinate geometry, we got that (1.14,3.17) is best set of co-ordinates for the equipment staging if art contractors must locate an equipment staging area to serve the three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5).
So, for x co-ordinates how we can find the output, for this we need to find that co-ordinate in which stagging area is maximum.
So that co-ordinate is given = [x-coordinate of point A + x-co-ordinate of point y)/2.0]-1.36
=>the best x-co-ordinate is =[(0+5)/2.0]-1.36
=>the best x-co-ordinate is =1.14,
Similarly, for the y-co-ordinate
the best y-co-ordinate is given by =[[y-co-ordinate of point A+ y-co-ordinate of point B]/2.0] +0.67
=>the best y-co-ordinate is given by =[(0+5)/2/0]+0.67=2.5+0.67
=>the best y-co-ordinate is given by=(
Therefore, the best x and y co-ordinate is (1.14,3.17)
Hence, when art contractors locate an equipment staging area to serve three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5). traffic between the staging area and each of the sites is 30 trips a week, except for the site located at (5,5), which is only 10 trips a week. the best set of co-ordinates for the equipment staging area is (1.14,3.17).
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Math 8
Writing Equations from a Graph
Date
Find the slope, y intercept and two points on each line. Then write the equation for each line.
Answer:
1. y=2x+4
2. y=x
3. y=-1/2x+1
4. y=-x+1
Step-by-step explanation:
the formula for these are y=mx+b. Your slope would be m and y intercept would be b. so y=2x+4 would mean that the slope is 2 and y intercept is 4. you can find the points by checking what points are on the blue line.
what does the adjusted r squared tell us about the relationship between sales, price, and advertising? the model explains about 90% of the variance in sales. the model explains about 60% of the variance in sales. the model explains about 80% of the variance in sales. the model explains about 70% of the variance in sales.
The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
Define the term adjusted r squared?R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.
R-squared describes how much the variance with one variable describes the variance of the other. So, if a model's R2 is 0.50, the model's inputs can explain roughly half of a observed variation.A score of 70 to 100 shows that a specific portfolio closely reflects the underlying stock index, whereas a score of 0 to 40 indicates a relatively poor correlation the with index.Higher R-squared scores also suggest that beta measurements are more reliable. The volatility of either a security or portfolio is measured by beta.Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
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Solve for x 5 x + 2 = 7 x − 4
Answer: x=3
Step-by-step explanation:
5x+2=7x-4
-5x +4 -5x +4
2x=6
divide both sides by 2
x=3
Write the prime factorization of 27.
Order the factors from least to greatest (for example, 2 × 2 × 3 × 5).
Answer:
3*3*3 or 3^3
Step-by-step explanation:
27/3=9/3=3
so 3*3*3 or 3^3
At a sale, suits were sold for $130 each. If the suits originally cost $200 each, what percentage of its original price was a suit sold for?
Answer:
70%
Explan your answer :
200-130=70 and 70% of 100 = 30% so
Answer: 65
Step-by-step explanation:
0.65
×
100
=
0.65×100=
65
%
65%
overbooking: a boeing 767-300 a boeing 767-300 aircraft has 213 seats. when someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an ibm research paper by lawrence, hong, and cherrier). how many reservations could be accepted for a boeing 767-300 for there to be at least a 0.95 probability that all reservation holders who show will be accommodated?
7.82 % is probability that all reservation holders who show will be accommodated.
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.If 236 are booked.
and there is only room of 213.
if 214 or 215 or 216 ............ etc
all the way to 236
there won't be enough seats.
P( X = 214 ) = ²³⁶C₂₁₄ * ( 0.9005 ) ²¹⁴ * ( 0.995 )²²
P( X = 214 ) = 0.08439109
= 8.44 %
P( X = 215 ) = ²³⁶C₂₁₅ * ( 0.9005 ) ²¹⁵ * ( 0.995 )²¹
= 0.0781522
= 7.82 %
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AWNSER PLSS !How can a negative number be written in scientific notation?
this is my last question please help asap!!
The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:
[tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]
The given function is [tex]g(x) = 5(2)^{x}[/tex],
Now calculating the average rate of change of function from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]
Now, calculate the average rate of change of function from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]
The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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8 Here are the descriptions of two numbers.
The smallest multiple of 5 greater than 1000
The largest multiple of 9 with three digits
Work out the difference between these two numbers.
a restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. the model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. what was the value of the correlation coefficient? responses 0.64 0.64 0.60 0.60 0.40 0.40 0.36 0.36 0.13
The value of the correlation coefficient is 0.60.
There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.
R² is the coefficient of determination, which measures how much variation can be explained by the regression line.
This means that, the R² value of the data is 36%
R² = 36% = 0.36
Correlation coefficients measure the strength of relationships between variables in the form of square roots.
That is ; R = √R²
R = √0.36
Hence, the correlation Coefficient, R is 0.60
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A famous piece of artwork was up for bid at a museum auction. The minimum bid was $25,000.
Determine which inequality represents the bid for the artwork.
b ≥ 25,000
b ≤ 25,000
b < 25,000
b > 25,000
The inequality that represents the bid for the artwork is A. b ≥ 25,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.
Let the minimum bid be b. This will be b ≥ 25,000.
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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Two friends visited a taffy shop. Gordon bought 8 pounds of strawberry taffy and 3 pounds of banana taffy for $66. Next, Levi bought 10 pounds of strawberry taffy and 3 pounds of banana taffy for $78. How much does the candy cost?
I NEED AN ANSWER ASAP LIKE BEFORE TOMORROW
The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given,
Let's say the cost per pound of strawberry taffy is "s" and the cost per pound of banana taffy is "b".
Then, the cost of 8 pounds of strawberry taffy and 3 pounds of banana taffy will be,
8s + 3b = 66
And,
The cost of 10 pounds of strawberry taffy and 3 pounds of banana taffy will be,
10s + 3b = 78
By solving both above equations,
2s = 12
s = $6
3b = 78 - 10(6)
b = $6
Hence, "The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6".
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assuming that earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 1046 kilometers due north of the other?
The difference between the distance between the two cities if of 14.842 latitudes.
The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.
Therefore, the earth has 181 latitudes.
Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.
Hence the distance covered by all 181 latitudes = 2 X radius of the Earth
= 2 X 6378 km
= 12756
Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be
12756/181
= 70.475 km
Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.
Therefore the difference in latitudes between the two cities is
1046/70.475
= 14.842 latitudes
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What is the minimum number of lawns Wallace must mow in order for him to earn at least $8?
Answer:1
Step-by-step explanation:
The answer is one because the graph starts at 12$ and Wallace only needs $8.
Dev’ car currently ha 18 gallon of ga in the tank. He ue about 0. 04 gallon for every mile he drive. Dev want to go on a car trip over the weekend and have at leat 2 gallon of ga left in hi tank to get to work on Monday. What i the olution of the inequality that determine how far Dev can travel over the weekend? (Example 2) Let x repreent the number of mile Dev travel
The solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Dave who is planning a car trip for weekend.
Assume that [x] represents the number of miles Dev can travel.
We can write the inequality as -
18 - 0.04x ≤ 2
0.04x ≤ 16
x ≤ 400 miles
Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
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P. USE REPRESENTATIONS Sheila plans to invest $2000 or less in two different accounts. The low
risk account pays 3% annual simple interest, and the high risk account pays 12% annual simple
interest. Sheila wants to make at least $150 in interest this year.
a. Define the variables, then write and graph a system of inequalities to show how Sheila can
split her investment between the accounts.
Inconclusion the amount she invested in each account is $1,000 invested at interest rate 12% .
What is interest rate?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.Let x represent the amount invested at 3%.
. 12x +.03(2000-x)= 150
.09x+ 60 = 150
Collect like terms
.09x = 90
Divide both side by .09x
x = 90/.09
x=$1000
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The altitude of a triangular sign is 18 inches less than 3 times its base. Define the functions that describe the altitude and base of the triangle, and then use these functions to build an area function of the triangle
Functions to build an area function of the triangle , A = b2 + 2b.
What Altitude of a Triangle?A perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude. A triangle can be drawn with three altitudes because it has three sides. There are various types of elevations in triangles. When computing the area of a triangle, the altitude, also known as its height, is indicated by the letter.The section of a perpendicular line traced from a triangle's vertex to the side directly across from it is the triangle's altitude. The base of the triangle that the altitude touches forms a straight angle. It is often referred to as a triangle's height and is represented by the letter "h." The distance between the vertex and its opposing side can be calculated to determine its size. It should be remembered that every triangle has three altitudes that can be drawn from each of the vertices. See the intersection of the triangle's three elevations by paying attention to the triangle in the illustration below. The "Orthocenter" is this location.According to our question-
Let b = the base
altitude = 2b + 4
A = b(2b+ 4)/2
A = b(b + 2)
A = b2 + 2b
Hence, Functions to build an area function of the triangle , A = b2 + 2b.
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The perimeter of an equilateral triangle is 10 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.)
Answer:
The side of the triangle is 14 in======================
Let the sides be t for triangle and s for square.
Difference of perimeters3t = 4s + 10Difference of sidest = s + 6Rearrange the second equations = t - 6Substitute this into first equation and solve for t3t = 4s + 103t = 4(t - 6) + 103t = 4t - 24 + 103t = 4t - 144t - 3t = 14t = 14Answer:
14 inches
Step-by-step explanation:
The side lengths of an equilateral triangle are the congruent.
The side lengths of a square are the congruent.
Let x be the length of one side of the equilateral triangle.
⇒ Perimeter of triangle = 3x
Let y be the length of one side of the square.
⇒ Perimeter square = 4y
Given:
The perimeter of the triangle is 10 inches more than the perimeter of the square.The side of the triangle is 6 inches longer than the side of the square.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}3x = 4y + 10\\x = y + 6\end{cases}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 3(y+6)=4y+10[/tex]
[tex]\implies 3y+18=4y+10[/tex]
[tex]\implies 18=y+10[/tex]
[tex]\implies y=8[/tex]
Therefore, the side length of the square is 8 inches.
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x=8+6[/tex]
[tex]\implies x=14[/tex]
Therefore, the side length of the triangle is 14 inches.
Write the point-slope form of the equation of the line through the given point with the given
slope.
3) through: (5, 1), slope
=
1
5
The point slope form of the equation is y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
What is equation of line ?
A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Here the given point ,
=> [tex](x_1,y_1)=(5,1)[/tex]
Slope m = [tex]\frac{1}{5}[/tex]
Here using equation formula
=> [tex]y-y_1 = m ( x- x_1)[/tex]
=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
Hence the point slope form of the equation is y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
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DUE TOMORROW PLS HELP!!
does anyone know how to solve the area and perimeter for this parallelogram pls help!!! In details !!!
Answer:
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example
You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).
Step-by-step explanation:
Find the x- and y-intercepts of the graph of -7x+10y=35. State each answer as an integer or an improper fraction in simplest form.
x-intercept
The x-intercept is where y=0.
[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]
y-intercept
The y-intercept is where x=0.
[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]
Solve the equation for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
3.5(x +2) = 17
Answer:2.86
Step-by-step explanation:
3.5(x +2) = 17
3.5x + 7 = 17
3.5x =17 - 7
3.5x =10
x = 10/3.5
x = 2.86
One out of every ten students in a school takes lunch to school. If there are two hundred students in the school, how many of them do not take lunch to school?
180 students do not take lunch to school.
From the question, we have
Number of students do not take lunch to school= 200-20
=180 students
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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(1 point) if you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
The largest area that can be enclose in straight wall is 2450 m².
What is meant by the largest area?Having to maximize or decrease a geometric figure's measurements, area, or volume is a special example of a geometry word problem.Let 'x' be the length of rectangle.
Let 'y' be the width rectangle.
Perimeter = 140 meters
2x + y = 140
y = 140 - 2x
Area = xy
Put the value of y in area.
Area = x(-2x + 140)
Area = -2x² + 140x
Differentiating the area with respect to x.
dA/dx = -4x + 140
Put dA/dx = 0 to get the critical point.
-4x + 140 = 0
x = 140/4
x = 35
Largest area at x = 35.
y = 140 - 2x
y = 140 - 2×35
y = 70
Area = xy
Area = 70×35
Area = 2450 m²
Thus, the largest area that can be enclose in straight wall is 2450 m².
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The Lopez family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
gallons per day
Answer: 4
Step-by-step explanation: in average, they drink 12/3 = 4 milk jugs per day.
The solutions of the equation x^2 - 6x + d = 0 are both integers. d is a prime number. Find d
The solutions of the equation x^2 - 6x + d = 0 are both integers and d is a prime number is 5.
How to determine the value of d?From the information, the solution of the equation x^2-6x+d=0 are integers
To find d, the numbers which can be added or subtracted to get -6 is needed which when multiplied will give a prime number
In this case - 5- 1 = -6
And when multiplied (-5×-1) will give +5 which is a prime number.
Therefore, x^2-6x+5=0
This illustrates that d is 5.
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A. 17 B. 117 C. 163 D. 173 In the figure above, n || p. Straight line m intersects both line n and line p. What is the value of r?
12. Choose the correct answer.
t
5/6
7/8
1/2
3/4
l'
m
Answer: angle 1 and 4
Step-by-step explanation:
evaluate the expression 8.2x- 6.1 when x=7
Answer:
51.3
Step-by-step explanation:
Since it's telling us that (x=7) then that means 8.2x is going to be multiplied
8.2(7) or 8.2 x 7.
Then you end up getting an answer of 57.4
But you are not finished yet and need to subtract 6.1
so 57.4 - 6.1 = 51.3
And your result will be (51.3)
I hope this helps you understand this problem!
