To find the value of k for which the matrix A has one eigenvalue of multiplicity 2, we can use the characteristic equation of the matrix. The characteristic equation is det(A-λI)=0. For a given matrix, this equation will yield a polynomial equation of degree equal to the dimension of the matrix.
In this case, the equation is (λ+4)(λ-2) = 0. Solving this equation gives us two distinct eigenvalues of λ= -4 and λ=2. This means that for any value of k, the matrix A will have two distinct eigenvalues, and thus cannot have one eigenvalue of multiplicity 2. Therefore, the matrix A cannot have one eigenvalue of multiplicity 2 no matter what value of k is used.
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The federal excise tax on cigarettes is $3.80 per carton. In Wisconsin the state excise tax on cigarettes is $17.70 per carton. If a carton of cigarettes contains 10 packs, what is the total excise tax per pack in Wisconsin?
The total excise tax per pack is $2.15.
What is the total excise tax?The total excise tax is the sum of the federal excise tax and the state excise tax.
Excise tax is the tax that is levied at the moment of manufacture of a good or service. Excise tax is usually levied on alcoholic or tobacco products.
Total excise tax = federal excise tax + state excise tax
$3,80 + $17.70 = $21.50
The total excise tax per pack can be known by dividing the total excise tax by the total number of packs.
Total excise tax per pack = $21.50 / 10 = $2.15
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21. A path 1 m wide is built along the border and inside a square garden of side 30 m. Find:
(i) the area of the path
(ii) the cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m2
(i) The area of the path is 120x - 4x² square meters.
(ii) The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² is (900 - 120x + 4x²) × 40
To find the area of the path and the remaining portion of the garden, we need to first find the dimensions of the inner square after the path has been constructed.
Let the width of the path be "x" meters. Then the dimensions of the inner square garden will be (30-2x) meters on each side.
(i) The area of the path can be found by subtracting the area of the inner square from the area of the outer square.
Area of outer square = 30 × 30 = 900 sq.m.
Area of inner square = (30-2x) × (30-2x) = 900 - 120x + 4x² sq.m.
Area of path = Area of outer square - Area of inner square
= 120x - 4x² sq.m.
(ii) The remaining portion of the garden is the area of the inner square.
Area of remaining portion = (30-2x) × (30-2x) sq.m.
= 900 - 120x + 4x² sq.m.
The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² can be found by multiplying the area of the remaining portion by the rate.
Cost of planting grass = Area of remaining portion × Rate
= (900 - 120x + 4x²) × 40
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16. Patrick created a design for a T-shirt with a space theme for his science project.
He drew the image and its dilation on a coordinate plane. What is the scale
factor of the dilation?
The scale factor of a dilation is the ratio between the lengths of corresponding sides of the original and dilated figures. If the length of the top side of the original figure is 5 units and the length of the top side of the dilated figure is 10 units, then the scale factor is 2.
What is scale factor?The scale factor is a number that is used to compare two measurements of the same object or design. It is the ratio between the two measurements, and is used to determine the size difference between the two. Scale factors can be used to scale objects up or down in size.
In other words, the scale factor is the multiplier used to stretch or compress the original figure. In Patrick's case, the scale factor can be determined by comparing the lengths of the corresponding sides of the original and dilated figures. For example, if the length of the top side of the original figure is 5 units and the length of the top side of the dilated figure is 10 units, then the scale factor is 2.
Since the dilation is on a coordinate plane, Patrick can also find the scale factor by comparing the coordinates of the original figure and the dilated figure. For example, if the coordinates of one of the vertices of the original figure are (2, 4) and the coordinates of one of the corresponding vertices of the dilated figure are (4, 8), then the scale factor is 2.
The scale factor of the dilation in Patrick's science project is an important concept and can be found by comparing the lengths of the corresponding sides of the original and dilated figures or by comparing the coordinates of the original and dilated figures.
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Which interval contains a local maximum for this function?
Analyze the table of values for the continuous function, f(x), to complete the statements.
Which interval contains a local minimum for this function?
The interval that contains a local minimum for this function is (0,2).
Explain the term local minimum?A local maximum is present on the graph of the function y = f(x) at the location where the graph shifts from increasing towards decreasing.
The tangent possesses zero slope at this location.At the point when the graph shifts from declining to increasing, a local minimum is present.Local maxima are points in an interval where the values of the function at those points are never greater than the values of a function nearby.By first differentiating f(x), which is continuous and twice differentiable, with regard to x, and then equating it to 0, we can determine its greatest value.Thus, over the span, a local minimum happens (0,2)
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The table for the function is given:
e y-coordinate of the y-intercept of the polynomial fu f(x)=-2x^(5)-3x^(2)+2x-3x^(4)-6x^(3) Submit Answer
The y-intercept of a polynomial function is the point at which the graph of the function intersects the y-axis.
This occurs when the x-coordinate is 0. So, to find the y-intercept of the given polynomial function, we need to substitute 0 for x and simplify:
f(x)=-2x^(5)-3x^(2)+2x-3x^(4)-6x^(3)
f(0)=-2(0)^(5)-3(0)^(2)+2(0)-3(0)^(4)-6(0)^(3)
f(0)=0-0+0-0-0
f(0)=0
Therefore, the y-intercept of the given polynomial function is (0,0).
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6. This table shows the population of a town from years 2000 to 2008.
Year Population
x y
2000 236,732
2001 238,645
2002 239,839
2003241,046
2004 242,078
2005 245,259
2006 249,432
2007 254,538
2008 259,851
What is the average rate of change between the years 2002 and 2007?
A 2,398.25
B. 2,939.8
C. 3,335.33
D. 3,373.4
The average rate of change between the years 2002 and 2007 was 2,.939.8 (option B).
How to calculate the average rate of change?In demographics, the average rate of change refers to how much the population of a city, country, etc. changes over a year period usually by increasing or decreasing. Due to this, the rate of change can be calculated by using the following formula change in the population/ number of years.
239,839 (population in 2002) - 254,538 (population in 2007)
2007 - 2002 = 5 years (number of years)
14699 / 5 years = 2,.939.8 (option B)
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DESCRIPTIVE ANALYTICS
A producer of computer aided design software for the aerospace
industry receives numerous calls for technical support. Tracking
software is used to monitor response and resolution
In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.
Descriptive analytics is a method used to collect, analyze and summarize data. In the case of the aerospace industry, descriptive analytics can be used to track the response and resolution of technical support calls. This helps to provide insights into the quality of service and make decisions about future changes to optimize the process.
In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.
By analyzing this data, the producer can gain insights into the most common types of technical support issues, the average response and resolution times, and any trends or patterns in the data. This information can then be used to improve the technical support process, identify areas for improvement, and develop strategies to prevent future technical support issues.
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According To The Texas Parks And Wildlife Department, There Are About 40 White-Tailed Deer Per Square Mile In Each Of 35 Texas Counties. A Rectangular Area On A Ranch In One Of These Counties Measures \( 2.25 \) Miles By \( 6.7 \) Miles. How Many White-Tailed Deer Are Expected To Live In This Rectangular Area?
603 white-tailed deer are expected to live in the rectangular area. To find the total number of white-tailed deer in the rectangular area, we need to find the area of the rectangle first. The area of a rectangle is given by the formula:
Area = length × width
In this case, the length is 2.25 miles and the width is 6.7 miles. So, the area of the rectangle is:
Area = 2.25 × 6.7
Area = 15.075 square miles
According to the given information, there are about 40 white-tailed deer per square mile in each of 35 Texas counties. We need to find how many white-tailed deer are expected to live in a rectangular area that measures 2.25 miles by 6.7 miles.
Now, we can find the total number of white-tailed deer in the rectangular area by multiplying the area by the number of deer per square mile:
Total number of deer = 15.075 × 40
Total number of deer = 603
Therefore, there are expected to be 603 white-tailed deer in the rectangular area.
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Find the missing side of each triangle round your answer to the nearest 10th if necessary.
Answer: x = 9
Step-by-step explanation:
We must use Pythagorean's Theorem, a² + b² = c².
Let a = x
a² + 12² = 15²
a² + 144 = 225
a² = 81
a = 9
x = 9
Hope this helps!
$26 and all cell phone cases cost $14. Derrick is buying these products as gifts for his friends plans to spend at least $150
To find out how many of each product Derrick can buy, we can use algebra. Let's call the number of headphones x and the number of cell phone cases y. We can set up an equation to represent the situation:
26x + 14y = 150
Now we can solve for one of the variables in terms of the other. Let's solve for y:
14y = 150 - 26x
y = (150 - 26x)/14
Now we can plug in different values for x and see what values of y will result in a total cost of at least $150. For example, if x = 1, then y = (150 - 26)/14 = 8.86. This means that Derrick could buy 1 pair of headphones and 8 cell phone cases for a total cost of $150.
Similarly, if x = 2, then y = (150 - 52)/14 = 7. This means that Derrick could buy 2 pairs of headphones and 7 cell phone cases for a total cost of $150.
We can continue plugging in different values for x until we find a combination of products that will cost at least $150. Alternatively, we could use a graphing calculator or an online graphing tool to graph the equation and find the intersection points with the line y = 150. These intersection points will represent the combinations of products that will cost at least $150.
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Help, I can’t solve this question
A. Is 88
B. Is 24
C. Is none
D. Is 17 because
8 12 17 22 29
X. X. X. X
What inequality whose solution set is represented by this graph???
The inequality that represents the set of solutions above the straight line is: x-3y<5
What is a linear inequality?
A linear inequality is an inequality in which one side is a linear expression in one or more variables, and the other side is a constant, or another linear expression. The solution set of a linear inequality is a region in the coordinate plane that satisfies the inequality.
Calculate the inequality to represent the set of solution by shaded region:
A linear inequality can be represented by a shaded region on the coordinate plane. The boundary of the region is a straight line, and the shaded region represents all the points in the plane that satisfy the inequality. In this case, the line that intersects the x-axis at (5,0) and the y-axis at (0, -5/3) represents the boundary of the region.
To find the inequality that represents the set of solutions above the line, we first need to find the equation of the line. We can use the point-slope form of the equation of a line, which relates the slope of the line and a point on the line to the equation of the line.
We know that the line passes through the points (5,0) and (0, -5/3), so we can calculate the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two points through which the line passes.
m = (-5/3 - 0) / (0 - 5) = 1/3
Now we can use the point-slope form of the equation of the line to write the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is one of the two points through which the line passes.
Using the point (5,0) as (x1, y1), we get:
y - 0 = (1/3)(x - 5)
y = (1/3)x - 5/3
3y = x - 5
To represent the set of solutions above the line, we need to use the greater than symbol. So the inequality that represents the set of solutions above the straight line is:
x-3y<5
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Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal.
The inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:
[tex]$$s \geq \frac{525}{p}$$[/tex]
What is profit ?In business and finance, profit refers to the monetary gain earned by a business or individual after subtracting the expenses from the total revenue. In other words, profit is the difference between the amount of money earned from selling goods or services and the total cost of producing or delivering those goods or services. Profit is often used as a key performance indicator (KPI) to measure the financial success of a business or individual.
According to given information ?Let's assume that the cost of making one t-shirt is c and Lee sells each t-shirt for p.
To make at least $400 profit, Lee's revenue from sales p must be greater than or equal to the sum of the startup costs $125 and the desired profit $400:
[tex]$$p\times s \geq 125+400$$[/tex]
We can simplify this inequality to:
[tex]$$p\times s \geq 525$$[/tex]
Therefore, the inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:
[tex]$$s \geq \frac{525}{p}$$[/tex]
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15. On a 45 questions exam, a student gets 40%. How many questions did this student get correct? 16. A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C. What percent of the weight of this tablet is vitamin C? 17. Five years ago, a secretary made $11,200 annually. The secretary now makes $17,920 annually. By what percent has this secretary's salary been increased? 18. A typist was able to increase his speed by 120% to 42 words per minute. What was her original typing speed? 19. A salesperson makes a commission of 12% on the total amount of each sale. If, in one month, she makes a total of $8,520 in sales, how much has she made in commission? 20. A salesperson receives a salary of $850 per month plus a commission of 82% of her sales. If, in a particular month, she sells $22,800 worth of merchandise, what will be her monthly earnings?
15. The student got 18 questions correct.
16. The weight of vitamin C in that tablet is 14%.
17. The secretary's salary has been increased by 60%.
18. The typist's original typing speed was 21 words per minute.
19. The salesperson made $1,022.40 in commission.
20. The salesperson's monthly earnings will be $19,546.
How to calculate the percentage?15. On a 45 questions exam, a student gets 40%.
The number of correct questions that the student got is
= 40% × 45 questions
= 18 questions
16. A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C.
The percent of the weight of this tablet is vitamin C is
= 35mg/250mg × 100%
= 14%
17. Five years ago, a secretary made $11,200 annually. The secretary now makes $17,920 annually.
The percentage the secretary's salary has been increased by
= ($17,920/$11,200 × 100%) - 100%
= 160% - 100%
= 60%
18. A typist was able to increase his speed by 120% to 42 words per minute.
Her original typing speed was
= 42/120% × 100%
= 42/1.2
= 21 words per minute
19. A salesperson makes a commission of 12% on the total amount of each sale. In one month, she makes a total of $8,520 in sales.
In that month, she made a commission of
= $8,520 × 12%
= $1,022.40
20. A salesperson receives a salary of $850 per month plus a commission of 82% of her sales. In a particular month, she sells $22,800 worth of merchandise.
Her monthly earnings will be
= $850 salary + 82% × $22,800
= $19,546
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Ranjit made pies for a fundraiser. He cut all the pies into eighths. After the first day of the fundraiser Ranjit sold 10 slices and had 2- of the pies left. Write and solve an equation to determine how many pies Ranjit made for the fundraiser.
If Ranjit made pies for a fundraiser. The number of pies Ranjit made for the fundraiser is: 26.
How to find the number of pies Ranjit?Let p = total number of pies that Ranjit made
Let s = Total number of slices of pie that he made.
Since each pie is cut into 8 slices, we have:
s = 8p
After the first day of the fundraiser, Ranjit sold 10 slices, which means he had s - 10 slices left. Since he had 2 whole pies left, we know that he had 16 slices left. Therefore:
s - 10 = 16
Substituting s = 8p, we get:
8p - 10 = 16
Adding 10 to both sides, we get:
8p = 26
Dividing both sides by 8, we get:
p = 3.25
This means that Ranjit made 3.25 pies for the fundraiser.
The total number of slices would have been:
s = 8p = 8(3.25) = 26
On the first day, he sold 10 slices, which means he had 16 slices left. This matches our initial calculation and confirms that our solution is correct.
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Twenty-seven times the weight in kilogram of a baby elephant increased by 400 pounds is less than the weight in kilogram of an adult elephant
The weight of the baby elephant is less than 212.59 kilograms which can be calculated using inequality.
To solve this problem, we need to use the inequality and the given information to find the weight of the baby elephant and the adult elephant. We can write the inequality as follows:
27w + 400 < a
Where w is the weight of the baby elephant in kilograms, and a is the weight of the adult elephant in kilograms. We can rearrange this inequality to get:
w < (a - 400)/27
Now, we can plug in the given information to find the weight of the baby elephant and the adult elephant. For example, if the weight of the adult elephant is 6000 kilograms, we can plug this into the inequality and get:
w < (6000 - 400)/27
w < 212.59
Similarly, we can plug in different values for the weight of the adult elephant to find the weight of the baby elephant.
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Help! Please, thank you
Answer:
Step-by-step explanation:
OK so im not that smart im only in 8th grade but i think the answers either A or B. hope i kind of helped you and good luck and have a nice day.
Plot the points A(-1,-2), B(1, 6), C(3, 1) on the coordinate axes below. State the coordinates of point D such that A, B, C, and D would form a parallelogram. (Plotting point D is optional.)
Point D's coordinates are (-3, 3).
We may use the fact that the opposite sides of a parallelogram are parallel and the same length to get the coordinates of point D such that ABCD forms a parallelogram.
First, we may determine the segment AB's length and slope:
Length AB = sqrt((1 - (-1))² + (6 - (-2))²) = sqrt(64) = 8
Slope AB = (6 - (-2)) / (1 - (-1)) = 8/2 = 4
As AB and CD are parallel, CD's slope must likewise be 4.
Next, we may determine segment AB's midpoint, which will coincide with segment CD's midpoint:
Midpoint AB is equal to ((-1+1)/2, ((-2+6)/2)). (0,2)
Point D will therefore have the same coordinates as the point that is symmetric to point C around the centre of AB. The following is where to find this point:
Midpoint AB - C = (20-3, 22-1) = D = 2 * (-3, 3)
Hence, point D's coordinates are (-3, 3).
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find the volume pls help asap
Answer: I think the answer is B. 241.13
Step-by-step explanation:
Formula for the volume of a cube is length of an edge cubed.
[tex]6^3=216[/tex]
Formula for the volume of a cone is [tex]\pi r^2\frac{h}{3}[/tex]
Half of 4 is 2, so the equation will be [tex]\pi 2^2\frac{6}{3}=25.13[/tex]
Add them together to get the answer
[tex]216+25.13=241.13[/tex]
I might be wrong, because I haven't done this in a long time, but I tried to do as much as possible, so forgive me if this is wrong.
If you travel 200 miles in four hours, then your average speed for the trip is average speed =200/(no response) =( (No Response) mi/h
If you travel 200 miles in four hours, then your average speed for the trip is 50 miles per hour. This is calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).
Start with the formula for average speed: average speed = total distance / total timePlug in the given values for total distance and total time: average speed = 200 miles / 4 hoursSimplify the equation by dividing 200 by 4: average speed = 50 mi/hThe final answer is 50 miles per hour.So, if you travel 200 miles in four hours, your average speed is 50 mi/h.
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Jeremy has GHC 502. 0. He gave Owiredu 3/10 of his money. How much did he give Owiredu?
The amount ( 3 /10 ) of total money given by Jeremy to Owiredu is equal to GHC 150.6.
Total amount of money with Jeremy in GHC is equal to 502.0
Amount of fraction of the money Jeremy gave to Owiredu is equal to
3 / 10.
Amount of money Jeremy gave to Owiredu is equal to
= ( 3 / 10 ) of GHC 502.0
= ( 3 / 10 ) × GHC 502.0
Multiply 3 to the 502.0 in the given expression we get,
= GHC ( 1506 / 10 )
Divide 1506 by 10 in the given expression we get,
= GHC 150 .6
Therefore, amount of money Jeremy gave to Owiredu is equal to GHC 150.6.
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HELP PLEASE I WILL GIVE POINTS PLEASE HELP PLS PLS
Answer:
Air
Step-by-step explanation:
it's asking you to look at the chart and find which substance is densest by comparing it to how fast sound can move through it (the speed of sound in the substance). In my opinion copper is not the densest material because sound moves through it the fastest; which means the particles in copper are not as densely held together. Air however, shows that sound can only travel 330 meters per second which is incredibly slow compared to the other listed materials, so by that logic it must be the densest.
The variable a is jointly proportional to b and c. If a=79 when b=6and c=3, what is the value of a when b=3 and c=7? Round your answer to two decimal places if necessary.
The value of a is 92.17 when b=3 and c=7.
What is jointly proportional ?Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.
The variable a is jointly proportional to b and c, which means that a = k*b*c, where k is the constant of proportionality.
We can use the given values of a, b, and c to find the value of k:
79 = k*6*3
79 = 18k
k = 79/18
Now that we know the value of k, we can use it to find the value of a when b=3 and c=7:
a = k*b*c
a = (79/18)*3*7
a = 92.17
Therefore, the value of a when b=3 and c=7 is 92.17.
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Clay has a bag that contains 4 white marbles and 10 black marbles. Clay chooses a marble from the bag without looking, records the color, replaces it, then
chooses another marble. What is the theoretical probability that Clay chooses a white marble both times?
• 2.04%
O 8.16%
0 28.57%
O 51.02%
!!
Explanation:
There are 4 white marbles out of 4+10 = 14 total
4/14 = 2/7 is the probability of randomly picking a white marble.
(2/7)*(2/7) = 4/49 is the probability of picking two whites in a row, when the first marble is replaced.
Use a calculator to find that 4/49 = 0.0816 approximately.
That converts to 8.16% after moving the decimal point two spots to the right. This is equivalent to multiplying by 100.
19 Zul's password to unlock his mobile phone screen consists of 4 digits. Each digit can be chosen from 0, 1, 2, ..., 9. What is the probability to unlock the screen in one attempt if he knows (a) the first three digits are 970? (b) there are three 1s? (c) the last two digits are 00?
Answer:
(a) Since Zul's password consists of 4 digits and the first three digits are 970, there is only one possible digit for the fourth digit. Thus, the probability to unlock the screen in one attempt is 1/10.
(b) If there are three 1s in the password, there is only one possible arrangement for the other digit. There are four places where the other digit can be placed, so there are four possible passwords. Thus, the probability to unlock the screen in one attempt is 4/10^4, which simplifies to 1/2500.
(c) If the last two digits are 00, there is only one possible arrangement for the first two digits. There are ten possible digits for the third digit and one possible digit for the fourth digit. Thus, the probability to unlock the screen in one attempt is 1/(101010*1), which simplifies to 1/1000.
A punter kicked a 41 yard punt. The pth of the football can be modeled by y=-0. 035x2 + 1. 4x + 1 where x is the distance in yards the football id kicked and y id the height in yards the football kicked
As per the given distance, the maximum height reached by the football is 15.4 yards.
To find the maximum height reached by the football, we need to find the vertex of the parabolic path. The vertex of a parabola represents the highest point on the path. In this equation, the vertex can be found by using the formula:
x = -b / 2a
where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.
By comparing the given equation with the standard form of the quadratic equation (y = ax² + bx + c), we can find that a = -0.035 and b = 1.4.
Substituting these values in the formula, we get:
x = -1.4 / 2(-0.035)
x = 20
This means that the maximum height is reached when the football has traveled a distance of 20 yards. To find the maximum height, we need to substitute this value of x back into the original equation:
y = -0.035(20)² + 1.4(20) + 1
y = 15.4
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Complete Question:
A punter kicked a 41-yard punt. The path of the football can be modeled by y=-0.035x² + 1.4x + 1 where x is the distance in yards the football is kicked and y is the height in yards the football kicked.
what is the maximum height reached by the football?
Eyeglassomatic manufactures eyeglasses for different retailers. The number of days it takes to fix defects in a pair of eyeglasses and the probability that it will take that number of days are in the table.
a) State the random variable.
Select an answer
rv X = the number of eyeglasses made
rv X = the probability that it will take that number of days to fix
rv
b) If you were to make the corresponding histogram for this frequency table, what shape would the histogram be?
✓ Select an answer
Right-skewed
Uniform
Left-skewed
Bell-shaped
c) Find the mean number of days to fix defects.
Put the numeric answer rounded to 3 decimal places in the first box and the correct units in the second box.
The mean number of days to fix defects is 3.2 days.
The random variable in this case is the number of days it takes to fix defects in a pair of eyeglasses. Therefore, the correct answer is:
rv X = the number of days to fix defects
The corresponding histogram for this frequency table would be right-skewed. This is because there is a higher probability of it taking fewer days to fix the defects, with the probability decreasing as the number of days increases.
To find the mean number of days to fix defects, we need to multiply each number of days by its corresponding probability and then sum the results. The formula for this is:
mean = ∑(x * P(x))
Where x is the number of days and P(x) is the probability of it taking that number of days.
Using the data from the table, we can calculate the mean as follows:
mean = (1 * 0.1) + (2 * 0.2) + (3 * 0.3) + (4 * 0.25) + (5 * 0.1) + (6 * 0.05)
mean = 0.1 + 0.4 + 0.9 + 1 + 0.5 + 0.3
mean = 3.2
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What is the difference in area between a circle with a
radius of 10cm and regular pentagon inscribed in it, to the nearest
whole?
The difference in area between a circle with a radius of 10cm and regular pentagon inscribed in it is 142cm².
The difference in area between a circle with a radius of 10cm and a regular pentagon inscribed in it can be found by first finding the area of the circle and then the area of the pentagon, and then subtracting the two values.
To find the area of the circle, we use the formula
A = πr²,
where r is the radius of the circle. In this case, r = 10cm, so the area of the circle is:
A = π(10cm)²
A = 100π cm²
To find the area of the regular pentagon, we can use the formula
A = (1/4)n*a² * cot(π/n),
where n is the number of sides of the polygon and a is the length of one side. Since the pentagon is inscribed in the circle, we can use the radius of the circle to find the length of one side of the pentagon.
The length of one side of the pentagon is:
a = 2r * sin(π/n)
a = 2(10cm) * sin(π/5)
a = 11.756cm
Now we can plug this value into the formula for the area of the pentagon:
A = (1/4)(5)(11.756cm)² * cot(π/5)
A = 172.047cm²
Finally, we can subtract the area of the pentagon from the area of the circle to find the difference in area:
Difference in area = 100π cm² - 172.047cm²
Difference in area = 314.159cm² - 172.047cm²
Difference in area = 142.112cm²
To the nearest whole, the difference in area between the circle and the pentagon is 142cm².
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Are all equilateral triangles similar? Use transformation to explain.
Solve each equation on the interval [0,2????). Make sure to use proper solution set notation. a. tan 3x = √3/3 b. 2tetha/3 = -1 c. sin(2x - ????/4 ) = √2/2 d. 2 cos^2 x + 3 cos x + 1 = 0
The solution sets are written in proper solution set notation, using the set builder notation {x | condition}. The "n ∈ Z" indicates that n is an integer.
Solving each equation on the interval [0, 2π):
a. tan 3x = √3/3
3x = tan^-1(√3/3)
3x = π/6
x = π/18
Solution set: {π/18 + 2nπ/3 | n ∈ Z}
b. 2θ/3 = -1
2θ = -3
θ = -3/2
Solution set: {-3π/2 + 2nπ | n ∈ Z}
c. sin(2x - π/4) = √2/2
2x - π/4 = π/4
2x = π/2
x = π/4
Solution set: {π/4 + nπ | n ∈ Z}
d. 2 cos^2 x + 3 cos x + 1 = 0
(2 cos x + 1)(cos x + 1) = 0
2 cos x + 1 = 0 or cos x + 1 = 0
cos x = -1/2 or cos x = -1
x = 2π/3 or x = π
Solution set: {2π/3 + 2nπ, π + 2nπ | n ∈ Z}
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