Step-by-step explanation:
The lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.
Let L = length of rectangle area and W = width of rectangle area.
Let the length of the side that divides the area be parallel to the width of the area.
The total length of fencing F = 2L + 2W + W
F = 2L + 3W
Since the area is a rectangle, its area is A = LW
Since the area = 2400 square feet,
LW = 2400 ft²
So, L = 2400/W
Substituting L into F, we have
F = 2L + 3W
F = 2(2400/W) + 3W
F = 4800/W + 3W
To find the value at which F is minimum, we differentiate F with respect to W.
So, dF/dW = d(4800/W + 3W)/dW
dF/dW = -4800/W² + 3
Equating dF/dW to zero, we have
-4800/W² + 3 = 0
-4800/W² = - 3
W² = -4800/-3
W² = 1600
W = √1600
W = 40 ft
To determine if this is a value that gives minimum F, we differentiate F twice to get
d²F/dW² = d(-4800/W² + 3)/dW
d²F/dW² = 14400/W³ + 0
d²F/dW² = 14400/W³
substituting W = 40 into the equation, we have
d²F/dW² = 14400/(40)³
d²F/dW² = 14400/64000
d²F/dW² = 0.225
Since d²F/dW² = 0.225 > 0, W = 40 is a minimum point for F
Since L = 2400/W
So, L = 2400/40
L = 60 ft
So, the lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.
100 Points Please help ASAP
Question 1(Multiple Choice Worth 1 points)
(04.07 LC)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation and causation.
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Question 2(Multiple Choice Worth 1 points)
(04.07 MC)
Trey believes there is a correlation between the number of texts sent in class and GPA. He collected data and found that the line of best fit for the data can be modeled by the equation y = 3.9 − 0.3x.
Identify the slope and the type of association.
The slope is −3.9, which indicates a negative correlation.
The slope is 3.9, which indicates a positive correlation.
The slope is 0.3, which indicates a positive correlation.
The slope is −0.3, which indicates a negative correlation.
Question 3(Multiple Choice Worth 1 points)
(04.07 MC)
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
Question 4(Multiple Choice Worth 1 points)
(04.07 MC)
Based on the time recorded for 700 attendees at an amusement park, the average amount of time spent at the park was 7.25 hours with a margin of error of ±1.65 hours. If 3,000 people attended the park on a given day, what is the estimated range of total hours the attendees spent in the park?
8,375 to 16,800 total hours spent in the park
16,800 to 21,785 total hours spent in the park
16,800 to 26,700 total hours spent in the park
16,800 to 35,885 total hours spent in the park
Question 5(Multiple Choice Worth 1 points)
(04.07 MC)
Data regarding fuel efficiency of an airliner were collected. The graph shows the correlation between the distance traveled (in thousands of miles) and the altitude (in thousands of feet):
image of a scatter plot with Distance Traveled on the x axis and Altitude on the y axis with 2 comma 2, 3 comma 10, 5 comma 15, 10 comma 20, 15 comma 15, 18 comma 10, and 19 comma 2
Estimate the average rate of change from x = 15 to x = 19.
−3.25
4
−4
−0.31
Question 6(Multiple Choice Worth 1 points)
(04.07 MC)
An observational study determined that there is a strong correlation between sitting close to the television and poor eyesight. Can it be determined that sitting too close to the television causes poor eyesight? Explain.
Causation cannot be proven because everyone watches television.
Causation can be proven because it is well known that sitting close to the television causes poor eyesight.
Causation can be proven because an experiment was used to prove this hypothesis.
Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.
Question 7(Multiple Choice Worth 1 points)
(04.07 LC)
Aretha wanted to gather data about the cost of local bowling leagues in her area. She plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20.
Identify and interpret the y-intercept in this model.
The y-intercept is 20. This is the cost per month.
The y-intercept is 20. This is the cost of registration.
The y-intercept is 15. This is the cost of registration.
The y-intercept is 15. This is the cost per month.
Question 8(Multiple Choice Worth 1 points)
(04.07 MC)
Analyze the following statement:
Marcus notices that he runs faster in the mornings rather than the evenings.
Is the statement an example of correlation or causation?
Correlation, because time of day doesn't cause a person to run faster or slower
Causation, because Marcus has noticed this over several trials
No relationship, because time of day has nothing to do with how fast a person runs
There is not enough information to make a conclusion
Question 9(Multiple Choice Worth 1 points)
(04.07 MC)
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Question 10(Multiple Choice Worth 1 points)
(04.07 MC)
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
3
0.98
1.21
0.33
Answer:
1.Based on the data, this is an example of correlation and causation.
2.The slope is −0.3, which indicates a negative correlation.
3.$5972.65
4.16,800 to 26,700 total hours spent in the park.
5. -3.25
6.Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.
7.The y-intercept is 20. This is the cost of registration.
8.Correlation, because time of day doesn't cause a person to run faster or slower
9.$53,700
10.0.33
Please mark as brainliest :)))
Comment if u need explanation of any answer
The table below shows the number of hours the Carrera family has been driving and the number of miles they’ve driven. Which of the following equations best represents this relationship?
*
Captionless Image
y = 84x
y = 56x
y = 1.5x
Not here
The equation that best represents this relationship given in the table is y = 56x.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a table below that shows the number of hours the Carrera family has been driving and the number of miles they’ve driven.
We can find the slope of the line from the table as follows -
m = (168 - 84)/(3 - 1.5)
m = 56
Now, we can write -
y = 56x + c
84 = 56 x 1.5 + c
c = 0
So, the equation would be -
y = 56x
Therefore, the equation that best represents this relationship given in the table is y = 56x.
To solve more questions on straight lines, visit the link below-
brainly.com/question/29030795
#SPJ1
a machine makes 36 trophies every hour. The machine makes trophies for 8 and a half hours each day, on 5 days of the week. The trophies are pack into boxes. Each box holds 8 trophies.
How many boxes are needed for all the trophies made each week?
Answer: 1530
Step-by-step explanation: First, you would want to calculate how many are made in one day. 36 trophies are made per hour, for 8 1/2 hours. 36 x 8.5(8 and a half) is 306, so in one day, 306 are made. Then, all you have left is to multiply it by 5, for five days, and that would be 1530. Hope This Helps.
Find the length of the third side. If necessary, write in simplest radical form.
Express this equation:
Answer:
(14x +49)^2
Step-by-step explanation:
PLEASE GIVE BRAINLIEST THANK YOU!!!
Sophie and Addison work at a dry cleaners ironing shirts. Sophie can iron 20 shirts per hour, and Addison can iron 30 shirts per hour. Sophie and Addison worked a combined 11 hours and ironed 260 shirts. Determine the number of hours Sophie worked and the number of hours Addison worked.
The number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x and y be the number of hours for Sophie and Addison:
x + y = 11
20x + 30y = 260
After solving the above two linear equations by substitution:
x = 7 hours
y = 4 hours
Thus, the number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
Sharifa's white ball rolled 143 centimeters in 4 seconds and her green ball rolled 112 centimeters in 3 seconds. Which ball rolled at a greater rate of speed?
Question 3 options:
A: white ball
B: green ball
C: The white and green ball rolled at the same rate of speed.
D: red ball
If Sharifa's white ball rolled 143 centimeters in 4 seconds and her green ball rolled 112 centimeters in 3 seconds. The ball that rolled at a greater is: B: green ball.
How to find the speed?Using this formula to find the fastest and the slowest speed
Speed for white ball :
Speed for white ball = 143 centimeters /4 seconds
Speed for white ball = 34.75
Speed for green ball:
Speed for green ball = 112 centimeters /3 seconds
Speed for green ball= 37.33
37.33 is greater than 34.75 which means that green ball is the fastest.
Therefore the correct option is B.
Learn more about speed here:https://brainly.com/question/14935741
#SPJ1
compare adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
Define exponents.A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. mn indicates that m has been multiplied by itself n times if m is a positive number and n is its exponent.
Given,
Adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
The exponents and variables must match in order to add exponents. The exponents are left constant while the variable coefficients are added. The addition only includes terms with the same variables and powers. Exponents can be multiplied and divided according to this rule.
To learn more about exponents, visit:
https://brainly.com/question/5497425
#SPJ1
Half of A's money plus one, fifth of B's makes #100. Two
Thirds of A's money plus two-fifth of B's makes # 150.
How much money has each?
The money A has is #150 and the money B has is #125.
According to the question,
We have the following information:
Half of A's money plus one-fifth of B's makes #100. Two-thirds of A's money plus two-fifth of B's makes # 150.
So, we will convert these verbal phrases into expression.
Now, let's take the amount of A to be #x and the amount of B to be #y.
x/2 + y/5 = 100
Using the least common factor of 2 and 5:
5x+2y = 1000
5x = 1000-2y ...(1)
2x/3 + 2y/5 = 150
Adding the fractions using the least common multiple of 3 and 5:
(10x+6y)/15 = 150
Using the cross multiplication method:
10x+6y = 2250
Now, putting the value of 5x from equation 1:
2(1000-2y)+6y = 2250
2000-4y+6y = 2250
2y = 2250-2000
2y = 250
y = 250/2
y = #125
Now, putting this value of y in equation 1:
5x = 1000-2y
5x = 1000-2*125
5x = 1000-250
5x = 750
x = 750/5
x = #150
Hence, the money A has is #150 and the money B has is #125.
To know more about money here
https://brainly.com/question/11959984
#SPJ1
Solve: 9l5n - 8l - 3 < 15
Answer:
9l^5n-8l-3<15
Step-by-step explanation:
2 ( X + 9 ) - 15 = -3
Answer:
x = -2
Step-by-step explanation:
2(x + 9) - 15 = -3 Distributive property
2(x) + 2(9) -15 = -3
2x +18 - 15 = -3 Combine like terms
3x + 3 = -3 Subtract 3 from both sides
3x = -6 Divide both sides by 3
x = -2
Reduce 4hours 20minutes by 12%
Step-by-step explanation:
by 12 % seconds
based on the results of the simulation, is there convincing statistical evidence at the significance level of 0.05 that the event of audrey selling at least 7 of the 30 selected tickets is unlikely to have occurred by chance alone? responses yes, because the distribution of the trials in the simulation is skewed to the right. yes, because the distribution of the trials in the simulation is skewed to the right. yes, because the number in the histogram with the greatest frequency is 4, not 7. yes, because the number in the histogram with the greatest frequency is 4, not 7. yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. no, because the simulation suggests that it is likely that audrey could sell anywhere from 0 to 11 of the selected tickets. no, because the simulation suggests that it is likely that audrey could sell anywhere from 0 to 11 of the selected tickets. no, because the simulation suggests that audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time.
No, there isn't any statistical proof because, according to the simulation, Audrey would sell at least 7 out of the 30 chosen tickets roughly 13.8% of the time.
What exactly is statistical proof?
A type of explanation known as statistical evidence is one that is based on information that has been gathered and then assessed using a mathematical model.
Based on the information provided, the students created the following simulation:
Choose 88 red chips and the rest 600 blue chips.
30 chips are chosen at random, with no replacements.
When choosing the 30 chips, keep track of and record the amount of red chips.
Therefore, we may say that there is no statistical proof that the occurrence happened by chance alone at = 0.05.
Learn more about statistical evidence here:
brainly.com/question/12785170
#SPJ4
Graph the solution of the inequality 2x - (3-x) > x + 1 on the number line.
Ο Α.
-5 -4 -3 -2 -1 0 1
OB.T
0 с.
2
+
-5 -4 -3 -2 -1 0 1 2
F
OD. |▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
+ +
3
10Ø|||
-5 -4 -3 -2 -1 0 1 2 3
-5 -4 -3 -2 -1 0 1 2
+43
3
4 5
14
4 5
++
4 5
+
4 5
The solution of the inequality is x>2 and the graph is attached below.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. When two values are compared, an inequality shows whether one is higher, lower, or simply not equal to the other.
The given inequality is 2x - (3-x) > x + 1,
Now, solving the inequality by opening the bracket,
2x - (3-x) > x + 1
[tex]2x - 3 + x > x + 1[/tex]
3x - 3 > x + 1
Subtracting x from both sides and adding 3 on both sides,
2x > 4
x > 2
So, the graph is attached below and Option D is correct.
Therefore, after solving the given inequality, we get x > 2 and the graph is attached below.
To learn more about Inequalities visit here:
https://brainly.com/question/24372553
#SPJ1
The U.S. Bureau of the Census
predicted that the population of
Florida would be about 17.4 million in
2010 and then would increase by
about 0.22 million per year until 2015.
Which of the following linear models
predicts the population, y, of Florida
(in millions) in terms of x, the number
of years since 2010.
A. y = 17.4x + 0.22
B. y = -0.22x + 17.4
C. y = 0.22x + 17.4
D. y = -17.4x + 0.22
The linear model that predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010 is y = 17.4+0.22x.
According to the question,
We have the following information:
The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015.
Now, y is the population.
So, we will have the total population in 2010 and 0.22 times the number of years.
So, the expression will be:
y = 17.4+0.22x
Hence, the correct option is C.
To know more about linear model here
https://brainly.com/question/21632115
#SPJ9
Can you help me, please?
Answer: 19
Step-by-step explanation:
Find slope intercept form
Answer: y=x+4
Step-by-step explanation:
The formula for slope-intercept form is y=mx+b where
m is the slope and b is the y-intercept.
Formula for working out the slope: y2-y1/x2-x1
Put the values in the equation: 4-3/0-(-1). Answer is 1/1 which is 1.
y-intercept: put one of the x and y values from the graph into the equation y=mx+b. Here, I'm going to choose the point (0,4).
The equation is now 4=1(0) + b
Working out for equation:
4=0+b
4=b
The final equation is y=x+4.
You can also use the graph to help you find the y-intercept! First, look at the y-axis. Then the point that passes it is your y-intercept!(Remember it's the y value not the x)
Simplify your answer as much as possible please.
Answer:
3/5=w
Step-by-step explanation:
the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.
Answer:
16/5
Step-by-step explanation:
10x3/5=10x w-2/2
If an additional worker can produce an additional 20 units of output which can be sold for $4 per unit, what is the maximum wage that this perfectly competitive firm should pay to hire this worker?.
The maximum wage that this perfectly competitive firm should pay to hire this worker = $80
The options for this question
A) $80 minus the firm's profit markup
B) It depends on what the going wage rate is in the labor market.
C) $80
D) There is insufficient information to answer the question.
now, we need to find the maximum wage that this perfectly competitive firm should pay to hire this worker
given that
the additional worker can produce an additional 20 units of output and that can be sold for$4 per unit
maximum wage = additional units × sold per unit
= 20 × 4 = 80
the maximum wage = $80
To learn more about output:
https://brainly.com/question/20459166
#SPJ4
HELP ME PLS!!!!!!!!!
Answer:
It's a positive correlation.
Step-by-step explanation:
It's gradually going up, even if there's a few points that are a bit uncorrelated.
the population of the world in 2010 was 7 billion and the annual growth rate was estimated at 1.2 percent per year. assuming that the world population follows an exponential growth model, find the projected world population in 2044. round your answer to one decimal place.
With annual growth rate of 1.2% per year, the projected world population in 2044 is 10.5 billion
The formula for the exponential growth model is:
X(t) = Xo (1 + r)^t
Where:
X(t) = value of X at time t
Xo = initial value
t = time interval
r = growth rate
Parameters given:
Xo = 7 billion = 7 x 10⁹
t = 2044 - 2010 = 34
r = 1.2% = 0.012
Hence,
X(t) = 7 x 10⁹ (1 + 0.012)³⁴
X(t) = 10.5 x 10⁹ = 10.5 billion
Therefore,
The projected world population in 2044 = 10.5 billion
Learn more about growth rate here:
https://brainly.com/question/13223520
#SPJ4
use your knowledge of angle relationship to solve for X in the diagram below. By your solution by name in the geometric relationship.
Answer:
Solution
Here ,
5x +7 = 9x-63 (Corresponding angle)
or, 5x-9x =-63-7
or, -4x =-70
or, X=17.5
Hence the value of X is 17.5 degree.
Here is a scatterplot showing the relationship between the number of turnovers and the number of points scored for players in a recent NBA season. The correlation for these data is r = 0.92.
Interpret the correlation
Yes.There is a strong , positive association,so an increase in turnovers causes an increase in points for NBA players..
Given that,
This scatterplot illustrates the correlation between a player's turnover rate and their points scored during a recent NBA season. 3000 2500 2000 Points 1500 and r= 0.92
r = 0.92 A strong positive (upward sloping) linear relationship
While a correlation of 0.10 would be a modest positive correlation, a correlation of 0.97 is a significant negative correlation.
Hence, Yes. Because there is a significant positive correlation, more turnovers result in more points for NBA players.
Learn more about correlation here:
brainly.com/question/28898177
#SPJ4
Find the ending balance :
Principal: $600
Interest rate :5%
Time : 6 years
Answer:
3816
Step-by-step explanation:
A line that includes the point (5, –10) has a slope of 0. What is its equation in slope -intercept form?
Answer:
0
Step-by-step explanation:
Slope = (y-y1)/(x-x1)
0
Sal has already finished startfraction 5 over 9 endfraction of the 45 math problems he was assigned. If each math problem took him three-fifths of a minute to finish and this pace continues, which expression can be used to determine the amount of time it will take him to finish his remaining homework? 45 times startfraction 5 over 9 endfraction times three-fifths 45 times startfraction 5 over 9 endfraction divided by three-fifths 45 times startfraction 4 over 9 endfraction times three-fifths 45 times startfraction 4 over 9 endfraction divided by three-fifths.
The correct expression to determine the amount of time is 45 times startfraction 4 over 9 endfraction times three-fifths.
Sal has finished = 5/9 of 45 maths problems
So, the remaining number of maths problems = 1 - 5/9
The remaining number of maths problem = (9 - 5)/9
The remaining number of maths problem = 4/9 of 45
Amount of time to solve 1 problem = 3/5 of a minute
Amount of time to solve 4/9 problems = 45×4/9 × 3/5 of a minute.
Hence, 45 times startfraction 4 over 9 endfraction times three-fifths is the correct expression to find the time.
Learn more about fractions -
https://brainly.com/question/17220365
#SPJ4
WHAT DOES Y EQUAL PLS HELP ASAP
The standard form of quadratic function is f(x) = 1(x-2)2 - 6
A quadratic function is a two-degree function. A parabola is the graph of a quadratic function. A quadratic function has the general form f(x)=ax2+bx+c, where a, b, and c are real numbers and a0. A quadratic function has the standard form f(x)=a(xh)2+k. The vertex (h,k) has the coordinates h=-b2a,k=f(h)=f(b2a).
Given points (5,3) and (2,-6)
We know that the General form of a quadratic function is
f(x) = ax2+bx+c
Standard form = a(x-h)2 + k
Here point(x,y) = (5,3) and vertex (h,k) = (2,-6)
y = a(x-h)2 + k
3 = a(5-2)2 – 6
3 = a(3)2 – 6
3 + 6 =9a2
9= 9a2
a2 = 9/9
a2=1
a=1
Now substitute a value in standard form
f(x) = 1(x-2)2 – 6
Therefore the standard form of quadratic function is f(x) = 1(x-2)2 – 6
To learn more about standard form visit
https://brainly.com/question/17264364
#SPJ1
Solve this system of 3 variables with elimination. Once you eliminate 1 variable to get down to only 2, you can use Desmos but show all work/steps first.
3x − 4y + z = 2
−9x + 12y − 3z = − 6
4x − 2y − z = -16
The value of the x, y, and z for the given system of equations are; x = -2/3, y = -1/2, and z = 1.
First, let us understand the equation:
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given the system of equations;
3x − 4y + z = 2 ...........equation 1
−9x + 12y − 3z = − 6 ...........equation 2
4x − 2y − z = -16 ...........equation 3
Add equation 1 to equation 3, we will get;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 ...........equation 4
Multiply equation 3 by 3 and subtract from equation 2, we will get;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42 ...........equation 5
Multiply equation 4 by 3 and add it to equation 4, we will get;
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Put z = 1 in equation 5, we will get;
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
x = -2/3
y = -1/2
Thus, the value of the x, y, and z for the given system of equations are; x = -2/3, y = -1/2, and z = 1.
To learn more about equations visit:
brainly.com/question/25180086
#SPJ1
-4(5x - 3) + 12
equation answer pls
Answer:
72
Step-by-step explanation:
five and five-sixths minus three and three-fourths plus two and one-half equals blank line.
Answer:
4 7/12
Step-by-step explanation: