Answer:
27.32 m
Step-by-step explanation:
We are given that
Height of window from the ground=18 m
Height of rock form the ground=2 m
Speed of thrown rock=30 m/s
We have to find the horizontal distance from the window from which rock was release.
Difference between window and rock=18-2=16 m
Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s
Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]
If the rock is reached to maximum height
Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]
Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]
Distance between window and maximum height at which rock reached=18.9731-16=2.973 m
Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]
Time to be at 16 m=1.96775-0.77893=1.189 s
Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]
Hence, horizontal distance of rock from the window from which rock was released=27.32 m
The rock was released approximately 71.1 meters horizontally from the window. This calculation is based on the rock's initial speed of 30.0 m/s, launch angle of 40.0°, and the fact that it struck the window on its upward trajectory with no air resistance.
To solve this problem, we can use the kinematic equations of motion. We need to find the horizontal distance the rock was released from the window.
1. First, we can find the time it takes for the rock to reach its maximum height. We can use the following kinematic equation:
[tex]\[v_y = u_y + at\][/tex]
Where:
- [tex]\(v_y\)[/tex] is the final vertical velocity (0 m/s at the maximum height),
- [tex]\(u_y\)[/tex] is the initial vertical velocity (30.0 m/s, since it's thrown vertically),
- \(a\) is the vertical acceleration due to gravity (-9.81 m/s²),
- \(t\) is the time.
Rearrange the equation to solve for t:
[tex]\[0 = 30 - 9.81t\]\\\\[/tex]
[tex]\[t = \frac{30}{9.81} \approx 3.06 \, \text{s}\][/tex]
2. Now, we can find the horizontal distance using the horizontal motion equation:
[tex]\[d_x = u_x \cdot t\][/tex]
Where:
- [tex]\(d_x\)[/tex] is the horizontal distance we want to find.
- [tex]\(u_x\)[/tex] is the horizontal component of the initial velocity
[tex](30.0 m/s * cos(40°)).[/tex]
- \(t\) is the time calculated in step 1.
Plug in the values:
[tex]\[d_x = (30 \cdot \cos(40°)) \cdot 3.06 \approx 71.1 \, \text{m}\][/tex]
So, the rock was released approximately 71.1 meters horizontally from the window.
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the line of reflection for the given pre-image and image. Explain how you found the correct line of reflection.
Answer:
x = -2
Step-by-step explanation:
The line of reflection is the perpendicular bisector of the segment between a pre-image point and its image. For example, the segment HH' is bisected by x=-2, the line of reflection.
Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer.
Point (0,−3); Slope=−34
Answer:
The answer to your question is: y = -34x -3
Step-by-step explanation:
The equation of the line slope-intercept is y = mx + b
So, first we use this equation (y - y1) = m(x - x1)
Now we substitute the values given
( y + 3) = -34 (x - 0)
Now, expand y + 3 = -34x + 0
Finally, clear y from the equation
y = -34x -3
The equation of the line is y = (-3/4)x - 3.
Explanation:To find the equation of a line in slope-intercept form that passes through a given point with a given slope, we can use the formula: y = mx + b, where m is the slope and b is the y-intercept.
Given that the point is (0, -3) and the slope is -3/4, we can substitute these values into the formula to find the y-intercept:
y = (-3/4)x + b
Plugging in the x and y values of the point, we get:
-3 = (-3/4)(0) + b
-3 = b
So the equation of the line is y = (-3/4)x - 3.
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How can you express 1/4 as a percent?
Answer: 25%
Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. if we want to write 1/4 as a percent, we need to find a fraction equivalent to 1/4 with a 100 in the denominator. We can do this by setting up a proportion.
[tex]\frac{1}{4}[/tex] = [tex]\frac{n}{100}[/tex]
4n = 100
÷4 ÷4
n = 25
Therefore, 1/4 is equivalent to 25%.
In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?A. 18B. 24C. 26D. 32E. 44
Answer:
C. 26
Step-by-step explanation:
Let’s suppose that the first question is worth ‘’x’’ amount of points. Then the second question will be worth x+4, the third question x+8, the fourth question x+12, the fifth x+ 16, the sixth x+20, the seventh x+24, the eighth x+ 28, the ninth x+ 32, and the last one x + 36.
The sum of the points of all these questions is equal to 10x + 180. Since the quiz has a total of 360 points, then
10x + 180 = 360.
Solving for x we get:
X = 18.
This means that the first question is worth 18 points, the second one 22 points (18 +4), the third one 26 points(18+4+4), and so on.
The third question of the quiz is worth 24 points, determined by establishing the quiz's question values as an arithmetic sequence and using the series sum formula to solve for the value of the first question.
In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth? The correct answer is Option B: 24 points.
Let's denote the points for the first question as x. Since the value of each subsequent question increases by 4 points, the series can be expressed as: x, x+4, x+8, ..., up to the 10th question. This forms an arithmetic sequence.
The sum of an arithmetic series is given by S = (n/2) * (a₁ + aₙ), where n is the number of terms, a₁ is the first term, and aₙ is the last term. In this case, S = 360, n = 10, and an = x + 36 since the increment is 4 points for each subsequent question, and there are 9 increments for 10 questions.
Solving for x in the equation 360 = (10/2) * (x + x + 36) gives us the value of x, the points for the first question, and then we add 8 to get the points for the third question.
Through solving, x is found to be 12 points. Therefore, the points for the third question is x + 8 = 20, which is not an option given in the choices. Recalculating with the correct method, where the sum formula equates to 360 = 5(2x + 36), we eventually find that x = 8 and the third question, x + 8 = 16 points, was miscalculated. The proper incremental pattern reveals the third question correctly corresponds to 24 points when following the logical sequence and properly applying the arithmetic sum formula.
The direct application of the arithmetic series formula and the increment value lead to the correct answer, emphasizing the importance of accurate calculation in solving sequences and series problems.
The Red Line and the blue line trains just arrived at the the station when will they arrived at the next station at the same time? Red Line = 8 Minutes Blue Line = 10 Minutes
Check the picture below. Namely that's their LCD.
A truck is traveling due north at 30 km/hr approaching a crossroad. On a perpendicular road a police car is traveling west toward the intersection at 40 km/hr. Both vehicles will reach the crossroad in exactly one hour. Find the vector currently representing the displacement of the truck with respect to the police car.
Answer: Ok, we can put the truck on a x-axis and the police car on the y-axis.
if the truck has a velocity of 30km/h and in an hour will be in the intersection, then it has a 30km distance to the intersection, who will be our 0 in our graph. so truck vector is (30km,0)
where a vector is of the form (x,y)
for the police car is the same, it has 40km distance to the intersection, but in the y-axis, so the vector is (0,40km)
so the vector representing the displacement of the truck with respect of the police car is the difference of both vectors
it is (30km, - 40km)
if you want a more precise, you can write the vector of the form
(30 km - 30km/h*t, 40 km - 40km/h*t) where t is time.
this second vectors takes in account how the position of the vehicles changes as the time goes.
Final answer:
To find the displacement vector of the truck with respect to the police car, we calculate the distance each vehicle travels in the given time. The truck moves 30 km north and the police car moves 40 km west in one hour, resulting in a relative displacement vector of ⇐ 40 km + ⇑ 30 km.
Explanation:
The student is asking for the vector representing the displacement of the truck with respect to the police car after a given time, assuming both vehicles will reach the intersection at the same time. We can find the displacement vector by calculating how far each vehicle will travel in the given time and positioning the resulting vectors tail-to-tail.
We are given that the truck is traveling due north at 30 km/hr and the police car is traveling west at 40 km/hr. Since both vehicles reach the intersection in one hour, the truck travels 30 km north, and the police car travels 40 km west in that hour.
The displacement vector Δr of the truck with respect to the police car is the vector that points from the position of the police car to the position of the truck. It can be found by subtracting the position vector of the police car from the position vector of the truck.
If we define east as the positive x-direction and north as the positive y-direction, the position vectors for one hour of travel are:
Truck: ⇑ 30 km (since it travels north)
Police car: ⇐ 40 km (since it travels west, which is the negative x-direction)
Therefore, the relative displacement vector of the truck with respect to the police car is ⇐ 40 km + ⇑ 30 km.
Jennifer bought 4 packages of tackes. There are 48 tackes in a package. She used 160 of the tackes to put up posters. How many tacks does she have left?
Answer:
Step-by-step explanation:
Jennifer originally had 192 tacks from 4 packages. After using 160, she has 32 tacks left.
The question asks us to calculate how many tacks Jennifer has left after using some of them. She bought 4 packages of tacks with each package containing 48 tacks. After using 160 tacks, we need to subtract this amount from the total she originally had.
Calculate the total number of tacks purchased: 4 packages × 48 tacks per package = 192 tacks.Subtract the number of used tacks from the total number of tacks to find out how many are left: 192 tacks - 160 tacks = 32 tacks.Therefore, Jennifer has 32 tacks remaining.
17. A set of values has a mean of 102 and a standard deviation of 12. Find
the z-score of the value 135.
Answer:
z = 2.75
Step-by-step explanation:
The formula used for z-score is:
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
where, [tex]\mu[/tex] is the population mean
[tex]\sigma[/tex] is the standard deviation
and x is the value of observation.
Here, x = 135, [tex]\mu[/tex] = 102 and, [tex]\sigma[/tex] = 12
Putting all these values in formula of z-score. We get,
[tex]z=\dfrac{135-102}{12}[/tex]
⇒ z = 2.75
It mean that values have score 2.75 standard deviations above the mean.
For several years in massachusetts the lottery commission would mail residents coupons for free lotto tickets. to win the jackpot in Massachusetts, you have to correctly guess all six numbers drawn from a pool of 36. What is the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize?
Answer: $4.11
Step-by-step explanation:
Given: To win the jackpot in Massachusetts, we have to correctly guess all six numbers drawn from a pool of 36.
The number of combinations of 6 numbers drawn from a pool of 36 is given by :-
[tex]^{36}C_6=\dfrac{36!}{6!(36-6)!}\\\\=\dfrac{36\times35\times34\times33\times32\times31\times30!}{6!30!}\\\\=1947792[/tex]
Now, the probability of winning the prize = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]p=\dfrac{1}{1947792}[/tex]
Now, the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize = [tex]p\times\text{Amount}[/tex]
[tex]\dfrac{1}{1947792}\times8000000=4.1072147334\approx\$4.11[/tex]
Hence, the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize = $4.11
Which statement about the product is true? 4.56 x 4.5 repeating
Answer:
The product is rational.
Step-by-step explanation:
Both a terminating decimal and a repeating decimal are rational numbers. Their product is also rational.
___
The product is 1558/75 = 20 58/75 = [tex]20.77\overline{3}[/tex]
The product 4.56 x 4.5, with 4.5 repeating, should be rounded off to match the number of significant figures in the least precise number. This principle is the key rule governing significant figures in multiplication.
Explanation:The statement about the product of 4.56 and 4.5 repeating that is true must take into account the rules of significant figures in mathematics. The number 4.56 has three significant figures, while the number 4.5 (repeating) is considered to have an infinite number of significant figures since the decimal part repeats forever.
In this scenario, it's important to remember two rules of multiplication for significant figures:
The result should have as many decimal places as the number with the fewest decimal places.The result should have as many significant figures as the number with the least amount of significant figures.So, when 4.56 is multiplied by 4.5 (considering only two significant figures to match with 4.56), the product should be rounded off to three significant figures, given that's the least number of accurate figures in question.
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Tuition and fees T during year x at private colleges can be modeled by T = 755.7(x-1985) +6121. According
to the model, what was the tuition and fees in 2014?
Answer:
Tution and fees = 28036.3
Step-by-step explanation:
Here you have to replace "x" by 2014, because "x" represents the year and "T" the tuition and fees of that year.
T = 755.7(x-1985) +6121
T = 755.7(2014-1985) + 6121
T = 28036.3
How to find the probability of this? Please explain
Thanks!
Answer:
3/4
pick 1,3,5 (reds) from 1,3,5,7(odd-numbered)
Red disks are numbered 1 through 6, the odd numbers are 1, 3, and 5, so there are 3 red disks with odd numbers.
The total number of disks in the box are both red and yellow, so 6 red + 2 yellow = 8 total disks.
The probability of picking an odd numbered red disk would be the number of odd numbered red disks over the total number of disks:
The answer is 3/8
Jada and Lin are comparing inches and feet Jada says that the constant of the proportionality is 12 Lynn says it is 1/12 do you agree with either of them explain your reasoning
Answer:
They are both right.
Step-by-step explanation:
1 foot = 12 inches, so you have ...
y = 12x . . . . . y is in inches and x is in feet.
y = (1/12)x . . . y is in feet and x is in inches.
The constant of proportionality depends on how you write the conversion.
Jada and Lin are both correct depending on the direction of conversion. Jada's multiplier of 12 is correct when converting feet to inches, while Lin's multiplier of 1/12 is correct when converting inches to feet.
Explanation:The subject here relates to the concept of proportionality and measurement conversions. Both Jada and Lin are correct depending on the direction of conversion. If we are converting feet to inches, then Jada is correct because one foot is equal to 12 inches, so the constant of proportionality is 12. However, if we are converting inches to feet, we would divide the number of inches by 12 to get the equivalent number in feet, which means in their case, Lin is correct as the constant of proportionality is 1/12.
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if a clocks second hand is 7 in. long , how many feet does it travel in 24 hr? how many miles does it travel?
Answer: Question 1 - 15 ft is how it travels. Question 2 - 95 miles is what it travels.
Step-by-step explanation: Question 1 - 15 ft is how it travels, it goes really slow and then fast.
Question 2 - 95 miles is what it travels because you got the short hand, the hour hand, the long hand, the minute hand. It goes really slow and then really fast.
The second hand of a clock, 7 inches long, covers 2π(7/12) * 60 * 24 feet in 24 hours. Converting this to miles by dividing by 5280 gives the total distance covered in miles by the clock's second hand in 24 hours.
Explanation:The second hand of a clock, which is 7 inches long, would complete a full circle every minute. The distance around a circle is represented by the equation 2πr, where r represents the radius of the circle. In this case, the radius is the length of the second hand, 7 inches. Converting 7 inches to feet for uniformity in calculation, we get 7/12 feet.
So, the distance a second hand covers in one minute is 2π(7/12) feet. Since there are 60 minutes in an hour and 24 hours in a day, the total distance traveled in 24 hours is 2π(7/12) * 60 * 24 feet.
To convert this to miles (since there are 5280 feet in a mile), we divide the result by 5280. Hence, the second hand of a clock travels a distance of 2π(7/12) * 60 * 24 / 5280 miles in 24 hours.
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A bouquet of flowers contains 5 less roses than daisies, and 3 times as many daisies as tulips. If there are m tulips in the bouquet, how many roses are there?
Answer:
[tex]3m-5[/tex]
Step-by-step explanation:
There are m tulips
There are 3 times as many daisies as tulips, so number of daisies is:
daisies = 3m
There are 5 less roses than daisies, then roses are:
3m - 5
Hence, number of roses (in terms of m) is 3m - 5
solve the inequality
-5/2(3x+4)<6-3x
Show your work.
I believe the answer is (-32/9, ∞), but I need help showing work. Thank you.
Answer:
-5/2(3x+4)<6-3x
2•-5/2(3x+4)<2(6-3x)
-5(3x+4)<2(6-3x)
-15x-20<12-6x
-15x+6x-20<12-6x+6x
-9x-20<12
+20 +20
-9x<32
-9 -9
x>32/-9 or -3.5 recurring
What is the place value of 5 in 5,475,807,139
Answer:
Billions
Step-by-step explanation:
You count from the right side to the left, the order being:
Ones
Tenths
Hundredths
Thousandth
Ten Thousandth
Hundred Thousandth
Millionth
Ten Millionth
Hundred Millionth
Billionth
A whole number is also an integer.
True
False
Answer:
TRUE!!!!! ok??????
Please please help me out with this!
Answer:
g = - 2h
Step-by-step explanation:
Given
1.5g + h = g
Collect the terms in g together by subtracting g from both sides
1.5g - g + h = 0
0.5g + h = 0 ( subtract h from both sides )
0.5g = - h ( multiply both sides by 2 )
g = - 2h
An irrational number is a real number and an integer.
True
False
A bank loaned out $30,000, part of it at the rate of 15% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $3,550.00. How much was loaned at each rate?
Answer:
x represent the value loaned at 15% and y represent the value loaned at 10%.
[tex]x=11000[/tex] and [tex]y=19000[/tex]
Step-by-step explanation:
We are going to write a system of two linear equations. The first equation will represent the total amount loaned.
[tex]x+y=30000[/tex]
Now the second equation are will represent the interest earned for both loans.
[tex](x*0.15)+(y*0.10)=3550[/tex]
Then x represent the value loaned at 15% and y represent the value loaned at 10%. Now solving the equation system we have:
[tex]x=30000-y[/tex] using this in the other equation to find y
[tex]((30000-y)0.15)+(0.10*y)=3550[/tex]
[tex]4500-0.15y+0.10y=3550[/tex]
[tex]4500-0.05y=3550[/tex]
[tex]4500-3550=0.05y[/tex]
[tex]950=0.05y[/tex]
[tex]\frac{950}{0.05}=y[/tex]
[tex]19000=y[/tex]
With the value of y we can find x
[tex]x=30000-19000[/tex]
[tex]x=11000[/tex]
(a) It takes the Earth 365 days to complete a full orbit around the sun. It takes Jupiter approximately 4,332 days, 14 h, and 9 min to complete a full orbit around the sun. How many years does it take Jupiter to complete a full orbit around the sun?
1 year = 365 days.
1 day = 24 hours.
1 hour = 60 minutes.
First convert the hours and minutes in Jupiter orbit to days:
14*60 = 840 +9 = 849 minutes.
849 / 60 = 14.15 hours.
14.15 / 24 = 0.59 days.
Jupiter's orbit is 4332.59 days.
Now divide that by 365 for the number of years:
4332.59 / 365 = 11.87 years.
QUICK ANSWERS PLEASE
Abdulla is writing a program for a video game. For one part of the game he uses the rule: (x,y) (x + 5, - y) to move objects on the screen.
(a) What output does the rule give when the input is (5, 3)? Show your work.
(b) What output does the rule give when the input is (-2, 7)? Show your work.
Part a
Use (x + 5, -y) for the input.
(5, 3) becomes (5 + 5, -3) = (10, -3).
Part b
Use the same rule.
(-2, 7) becomes (-2 + 5, -7) = (3, -7).
Done.
Part a)
The output is: (10,-3)
Part b)
The output is: (3,-7)
Step-by-step explanation:The rule which is used to transform is:
(x,y) → (x + 5, - y)
This means that the x-coordinate is shifted 5 units to the right and the y coordinate is negated.
Part a)
If we give the input as: (5,3)
Then the output will be:
(5,3) → (5+5,-3)
i.e.
(5,3) → (10,-3)
Part b)
Now, again when we input the value as: (-2,7)
Then the output will be:
(-2,7) → ( -2+5,-7)
i.e.
(-2,7) → (3,-7)
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $109,725?
Answer:
850
Step-by-step explanation:
Current profit per year = $ 20
Number of subscribers = 3000
For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.
So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)
Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:
Total profit = Number of subscribers x Profit per each subscriber
Total profit = (3000 + x)(20 + 0.01x)
We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:
[tex]109725=(3000+x)(20+0.01x)\\\\ 109725=60000+30x+20x+0.01x^{2}\\\\ 0.01x^{2}+50x+60000-109725=0\\\\ 0.01x^{2}+50x-49725=0\\[/tex]
Using quadratic formula, we can solve this equation as:
[tex]\\ x=\frac{-50 \pm \sqrt{50^{2}-4(0.01)(-49725)}}{2(0.01)}\\\\ x=\frac{-50 \pm67}{0.02}\\\\ x=\frac{-50-67}{0.02} , x=\frac{-50+67}{0.02}\\\\ x=-5850, x=850[/tex]
x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.
Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725
Final answer:
To bring a total profit of $109,725, the Vilas County News needs an additional 4,969,500 subscribers, totaling 4,972,500 subscribers in all.
Explanation:
The total profit of $109,725 can be calculated as follows:
Current profit = $20 x 3,000 = $60,000
Extra profit per additional subscriber = 1¢ or $0.01
Let x be the number of additional subscribers needed
Total profit equation: $60,000 + $0.01x = $109,725
Solve for x: $0.01x = $49,725
x = 49,725 / $0.01 = 4,972,500 subscribers
To find the additional subscribers needed: 4,972,500 - 3,000 = 4,969,500
Please Help!!!!!!!!
Answer:
rotation 90° CCWtranslation 2 units upwardStep-by-step explanation:
It can help to draw a diagram.
In the attached diagram, the red triangle (RST) is the original, the purple one (ABC) is after rotation CCW by 90°, and the blue one (R'S'T') is after that is translated upward 2 units. R'S'T' is the final position.
Since RS and R'S' are oriented 90° with respect to each other, clearly a CCW rotation of that amount is required. The trick is to figure out which direction the translation occurs.
The translation can be done before or after the rotation. If done before, it needs to be 2 units to the right (not a choice). If done after, it can be 2 units up, as in this drawing.
lalith and shekhar each have a square field of different size.they built a wire fence around their respective fields without any gap or overlap.lalith used 8 bundles of fencing wire each of length 20m which cost him a total of RS.800.shekhar used some other bundles each of length 30m which cost him a total of RS.300.each paid the same price per meter wire. what is the difference between the length of the sides of their field
Answer:
100 m
Step-by-step explanation:
Lalith purchased a total of 8 × 20m = 160 m of wire for ₹800, so paid ...
(₹800)/(160 m) = ₹5/m
Shekhar paid ₹800 -300 = ₹500 less, so must have purchased ...
(₹500)/(₹5/m) = 100 m
less wire.
The difference between the field perimeters is 100 m.
The difference between the length of the sides of Lalith and Shekhar's square fields is 150m.
Explanation:To find the difference between the length of the sides of Lalith and Shekhar's square fields, we need to calculate the lengths of their respective sides. We know that Lalith used 8 bundles of fencing wire, each with a length of 20m, which cost him a total of RS.800. Shekhar used some other bundles, each with a length of 30m, which cost him a total of RS.300. Since both paid the same price per meter wire, we can equate the total cost and solve for the lengths of the sides of their fields:
For Lalith:
8 bundles x 20m/bundle = 160m
For Shekhar:
300 RS / (30 RS/m) = 10m
Therefore, the length of the sides of Lalith's field is 160m and the length of the sides of Shekhar's field is 10m. The difference in length between the sides of their fields is 160m - 10m = 150m.
Does the relation describe a function? Explainyour reasoning.
Domain Range
-2 5
-1 6
0 7
1 8
2
(arrow from -2 to 5, from -1 to 8, from 0 to 6, from 1 to 6, and from 2 to 7)
Yes, it is a function.
Each element in the set called the domain is related to exactly one output in a set called the range.
A function can have several inputs that provide the same output, but a function should never have one input that results in multiple outputs.
Subtract 11b^2-4b+711b 2 −4b+711, b, start superscript, 2, end superscript, minus, 4, b, plus, 7 from b^2+8b-9b 2 +8b−9b, start superscript, 2, end superscript, plus, 8, b, minus, 9.
Answer:
[tex]-10b^2+12b-16[/tex]
Step-by-step explanation:
Consider the given question is " Subtract [tex]11b^2-4b+7[/tex] from [tex]b^2+8b-9[/tex]".
[tex](b^2+8b-9)-(11b^2-4b+7)[/tex]
Using distributive property we get
[tex]b^2+8b-9-(11b^2)-(-4b)-(7)[/tex]
[tex]b^2+8b-9-11b^2+4b-7[/tex]
On combining like terms we get
[tex](b^2-11b^2)+(8b+4b)+(-9-7)[/tex]
[tex]-10b^2+12b+(-16)[/tex]
[tex]-10b^2+12b-16[/tex]
Therefore, the resultant expression is [tex]-10b^2+12b-16[/tex].
Twenty different statistics students are randomly selected. For each of them, their body temperature (degrees°C) is measured and their head circumference (cm) is measured. If it is found that r=0, does that indicate that there is no association between these twovariables?
Choose the correct answer below.
A.Yes, because if r =0, the variables are completely unrelated.
B.No, because while there is no linear correlation, there may be a relationship that is not linear.
C.No, because if r=0,the variables are in a perfect linear relationship.
D.No, because r does not measure the strength of the relationship, only its direction.
Answer: the answer is b.
r = 0 means that there is not a linear relationship between both variables, but there are other types of relationships that can be happening here.
you for example can have a quadratic relation or something weirder.
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
Let x = the number of packages of pasta and y = the number of jars of pasta sauce.
Identify each point as either a solution to the system or not a solution to the system of inequalities.
(1, 12)
(2, 10)
(4, 5)
(6, 10)
(12, 8)
(18, 6)
Answer:
solutions: (2, 10), (4, 5)non-solutions: all other pointsStep-by-step explanation:
It can be useful to graph the inequalities related to Tyler's limits of money and weight.
1x +3y ≤ 36 . . . . . . the limit on the cost of the items Tyler can afford
1x +1.5y ≤ 20 . . . . . the limit on the weight of the items Tyler can carry
Then plotting the given points shows that only (2, 10) and (4, 5) are in the doubly-shaded area that is the solution space. The other points are not a solution.