When lines A and B are cut by a transversal, then ∠1 and ∠4 fοrm a pair οf vertical angles.
What is transversal?In geοmetry, a transversal line intersects twο lines in the same plane at twο different lοcatiοns. In the Euclidean plane, transversals help establish the parallelism οf twο οr mοre οther straight lines. It crοsses twο lines at separate lοcatiοns. Transversal intersectiοn results in numerοus angles.
Twο parallel lines are A and B are drawn.
They are cut by a transversal C.
The angles ∠1 and ∠2 are fοrming a pair οf alternate exteriοr angles.
The angles ∠3 and ∠4 are fοrming a pair οf alternate interiοr angles.
The angles ∠2 and ∠3 are verticals angles.
Similarly, the angles ∠1 and ∠4 fοrm a pair οf vertically οppοsite angles.
Therefοre, the angles fοrm vertical pair.
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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.
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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$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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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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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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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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When 508,000,000 is written in scientific notation, what will be the value of the exponent?
Step-by-step explanation:
When 508,000,000 is written in scientific notation, it will be represented as:
5.08 x 10^8
Therefore, the value of the exponent is 8.
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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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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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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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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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!
A certain map shows two roads. Road A is 1 1/5 miles long but is 1 1/2 inches long on the map. What is the unit rate for inches per mile on this map? If road B is 12 miles long, how long is road B on the map?
The unit rate for inches per mile is 0.8 inches.
The length of road B is 9.6 inches on map.
What is Unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.
Road in inches = 1 1/5 = 6/5 inches
Road in miles = 1 1/2 miles =
Inches per mile = 6/5 / (3/2)
= 6/5 x 2/3
= 4/5
= 0.8 inches
If the road B is 12 miles long, on the map it would be;
= 0.8 x 12
= 9.6 inches
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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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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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Consistent and Dependent Consistent and Independent Inconsistent y=-x+1 y=-x y=x+2 y=x y=x y=2x 00*30:03
The first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.
A system of equations can be classified as consistent, dependent, or inconsistent. A consistent system has at least one solution. A dependent system has infinitely many solutions, and an inconsistent system has no solution.
The first system of equations, y=-x+1 and y=-x, is inconsistent. This is because there is no value of x that can make both equations true at the same time. The graphs of these equations would be parallel lines that never intersect, meaning there is no solution.
The second system of equations, y=x+2 and y=x, is consistent and dependent. This is because there are infinitely many solutions that make both equations true. The graphs of these equations would be the same line, meaning every point on the line is a solution.
The third system of equations, y=x and y=2x, is consistent and independent. This is because there is only one solution that makes both equations true. The graphs of these equations would be two lines that intersect at one point, meaning there is only one solution.
In summary, the first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.
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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
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?
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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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.
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.
Natalie has three pairs of pants 10 black and blue and five shirts white black green blue and red each morning she randomly select a pair of pants and one shirt the following tree diagram represents the sample space for this count compound event outcomes may be listed using an ordered pair for example tan pants and red shirt can be listed as tan and red hey how many total outcomes are in a sample space be a list of favourable outcomes for a Natalie selecting a pair of pants and shirt that are the same colour see select the favourite outcomes for Natalie selecting a black shirt the list of favourable outcomes that Natalie selecting a list of blue article of clothing
Based on the given information, the sample space for the event can be represented using a tree diagram, where the first level consists of the three pants (black, blue, and tan) and the second level consists of the five shirts (white, black, green, blue, and red). Each branch represents a possible combination of a pair of pants and a shirt.
To find the total number of outcomes in the sample space, we can simply multiply the number of options for pants (3) by the number of options for shirts (5), giving us a total of 15 possible outcomes.
For Natalie selecting a pair of pants and shirt that are the same color, the favourable outcomes would be the combinations where the pants and shirt are either both black or both blue. These can be listed as:
Black pants and black shirt
Blue pants and blue shirt
For Natalie selecting a black shirt, the favourable outcomes would be the combinations where the shirt is black. These can be listed as:
Black pants and black shirt
Blue pants and black shirt
Tan pants and black shirt
For Natalie selecting a blue article of clothing, the favourable outcomes would be the combinations where either the pants or the shirt (or both) are blue. These can be listed as:
Black pants and blue shirt
Blue pants and white shirt
Blue pants and black shirt
Blue pants and green shirt
Blue pants and blue shirt
Tan pants and blue shirt
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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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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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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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:
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.
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.
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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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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