Answer:
yes? what do you want to solve for
Step-by-step explanation:
that equation is correct
Select the correct answer from each drop-down menu.
An athletics shop makes ping pong paddles. A rubber trim is glued along the entire edge of the paddle. Approximately how long is the
trim?
The blade is a circle and has a circumference of approximately __ (6, 19, or 9) inches. The handle is a rectangle and has a perimeter of approximately ___ (8, 12, or 6) inches. Accounting for where the blade and the handle meet, the perimeter of the paddle is approximately___ (31, 17, or 27) inches.
The blade is a circle and has a circumference of approximately 6 inches. The handle is a rectangle and has a perimeter of approximately 12 inches. Accounting for where the blade and the handle meet, the perimeter of the paddle is approximately 31 inches. The length of the trim is the perimeter round the paddle = 31
How to calculate the length of the trim?To calculate the length of the trim is to find out the perimeter of the paddle and the handle.
The perimeter of the handle which is a rectangular shape= 2(length+width) = 2(4+2)= 12
The perimeter of the blade which is circular in shape= 2πr
where radius = 3
perimeter= 2×3.14×3= 18.84
The length of the trim = 12+18.84= 30.84
= 31 in (approximately)
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Answer: Circumference is 19 , Perimeter is 12, Perimeter is 27
Step-by-step explanation:
The circumference of a circle is pied. The diameter of the blade is about 6 inches. Therefore, the circumference of the circle is pie(6)=19 inches.
The perimeter of a rectangle is the sum of its four sides. Since the length of the entire paddle is 10 inches and the blade has a diameter of about 6 inches, the length of the handle is 4 inches. The width is 2 inches. Find the perimeter.
2l+2w=2(4)+2(2) = 12 in
The perimeter of the composite figure is the sum of the perimeters of the two parts, minus twice the distance where the figures meet.
The sum of the perimeter of the circle and rectangle is 19+12=31 inches.
The shared length is approximately 2 inches. So, 31-2(2)=27 inches.
The difference between the measures of two complementary angles is 88°. determine the measures of the two angles ?
The measures of the two complementary angles are 44° and 132°.
Given that the difference between the measures of two complementary angles of any given triangle is 88°, it means that one angle is 88° smaller than the other. To find the measures of the two angles, divide the sum of the difference by 2. That is given as, (88°/2) = 44°. One angle is given as 44°, and the other angle is equal to the sum of the two angles in a triangle, which is 180°, minus the first angle, which is 44°, which is equal to 136°.
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Translate the given phrase into an algebraic expression and simplify if possible: the difference of -10 and the product of p
and q.
Algebraic expression for statement : the difference of -10 and the product of p is
\(-10-pq\)
Given :
the difference of -10 and the product of p and q.
We need to translate the given statement into expression
Product means multiplication
Product of p and q is pq
Difference means the subtraction
Difference of -10 and pq can be written as
\(-10-pq\)
Algebraic expression for statement : the difference of -10 and the product of p is
\(-10-pq\)
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If you sleep 6 hrs out of 24 hrs how much percent do you sleep?
Answer:
25%
Step-by-step explanation:
I hope this helps you!!
Answer:
You sleep 25% of the day.
Step-by-step explanation:
First you change the equation into a fraction:
6 hrs out of 24 hrs = 6/24
Then you can simplify this fraction:
6/24 = 1/4
Lastly, convert the fraction to a percent:
1/4 = 25%
Brainliest would be greatly appreciated!!!!
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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Peter’s teacher says he may have his report card percentage based on either the mean or the median and he can drop one test score if he chooses.
84%, 71%, 64%, 90%, 75%, 44%, 98%
Which measure of center should Peter choose so he can have the highest percentage possible?
Peter should choose the mean after dropping one test score.
Peter should choose the mean without dropping one test score.
Peter should choose the median after dropping one test score.
Peter should choose the median without dropping one test score.
Answer:
A.
Step-by-step explanation:
Peter should choose to base his report card percentage on the median if he wants to have the highest percentage possible. To calculate the median, Peter would first order the scores from lowest to highest: 44%, 64%, 71%, 75%, 84%, 90%, 98%. Then, he would select the middle score as the median, which is 75%. If Peter drops his lowest score (44%), his percentage based on the median would be 80% ((64%+71%+75%+84%+90%+98%)/6). If he were to choose the mean, his percentage would also be 80%. However, since the median is not affected by extreme values like the 44% score, it is a more reliable measure of central tendency in this case.
I did this on homework b4 and got It right so this Is 100 percent right.
Answer:
Peter should choose the median after dropping one test score so he can have the highest percentage possible.
If we calculate the mean of all seven test scores, we get:
(84+71+64+90+75+44+98)/7 = 73.14%
If we calculate the median of all seven test scores, we get:
Arrange the scores in ascending order:
44, 64, 71, 75, 84, 90, 98
The median is 75.
If we drop the lowest score (44) and calculate the mean of the remaining six test scores, we get:
(84+71+64+90+75+98)/6 = 80.5%
If we drop the lowest score (44) and calculate the median of the remaining six test scores, we get:
Arrange the scores in ascending order:
64, 71, 75, 84, 90, 98
The median is 79.5%.
Therefore, Peter should choose the median after dropping one test score to have the highest possible percentage.
trip decided to go on a vacation to the beach after driving 60% of the way he decided to stop for lunch if you stopped for lunch after driving 240 miles how many total miles will he have to drive
Consider that 240 miles is the 60% of the way. If x is the total distance of the way, it is necessary that:
(60/100)x = 240
solve the previous equation for x:
x = 240(100/60)
x = 400
Hence, the total distance of theway is 400 miles
A cat eats 2/3 of a tin of cat food every day. How many tins of cat food will she eat in 1 week?
First, how many days are in a week?
7 days are in a weekSo 7x 2/3First, Convert any mixed numbers to fractions.
Then your initial equation becomes:
2/3×7/1
Applying the fractions formula for multiplication,
=2×7 x 3×1
=14/3
Simplifying 14/3, the answer is
4 and 2/3
Therefor, your answer is 4 2/3
Write this in a Algebraic expression. (Use x as your variable) The sum of x squared and y
Answer:
x^2+y
Step-by-step explanation:
simply because you have x squared and a variable y that needs to be added.
How do I solve 4x^2+6x=0 by factoring
Answer: \(x=0, -\frac{3}{2}\)
Step-by-step explanation:
\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)
Fill in the blank with the correct answer choice. A ___________ has exactly one pair of parallel lines. a. square c. trapezoid b. parallelogram d. rectangle Please select the best answer from the choices provided A B C D
Answer: C
Step-by-step explanation:
The rest of the quadrilaterals provided have 2 pairs of parallel lines.
The choice is:
CExplanation:
The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.
Here's what a trapezoid looks like :
\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)
Hence, this makes C the correct choice.what is the bed what is it
Answer:
A bed is a type of object a person uses to sleep on. It usually contains blankets and pillows
Step-by-step explanation:
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Which quadratic equation below could be used to represent the following situation?
The Cameron's have a triangular baseball pennant hanging from a flagpole in their yard. The pennant has an area of 50 ft
. The height of the triangle is 20 less than 6 times the length of its base. What equation will describe the area of the pennant?
Check the picture below.
\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=x\\ h=6x-20\\ A=50 \end{cases}\implies 50=\cfrac{1}{2}(x)(6x-20) \\\\\\ 50=\cfrac{6x^2-20x}{2}\implies \boxed{50=3x^2-10x}\)
The following meat offers are on special at the Shop -fillet at R150 per 5oog, Rump at R240 per kg ,Sosaties at R50 per 2oog, T-Bone R150 per 250g * Which of these types of meat is the cheapest to at but show your calculation .
How much the following will cost -
4kg of fillet -
2kg of Rump
3kg of Sosaties
1kg T-Bone
Answer:
How much the following will cost -
4kg of fillet - 1200
2kg of Rump: 480
3kg of Sosaties: 750
1kg T-Bone: 600
So,
Cheapest is 2kg of Rump fr R480
Step-by-step explanation:
How much the following will cost -
4kg of fillet - 150/500 gm as 1000 gram = 1 kg, so 300 for 1 kg now to calculate 4 kg (300×4=1200) so 1200 for 4 kg
2kg of Rump: 240/kg (2×240=480) so 480 for 2 kg
3kg of Sosaties: 50/200 gm so 1000 gm = 1 kg so 50×5=250 so 1 kg = 250 so 250×3=750
1kg T-Bone: 150/250 gm so 1000 gm = 1 kg so 250×4=1000 so 150×4=600 so 1 kg = 600
Please help I do not understand thanks
For function f(x) = 3x-2
and g(x)=x², workout
fg(x)
For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.
What is function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.
A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).
Four orders of functions live functions with return values and arguments.
This function accepts arguments and gives back a result.
functions that take arguments but have no return values.
functions with return values and no arguments.
functions that have no arguments or return values.
we are given two function f( x) and g( x);
f( x) = 3x- 2 and
g( x) = x2
So, for fg( x), we've to put value of g( x) into f( x);
Hence, the equation will be;
fg( x) = 3x2- 2.
thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.
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Use the model below to calculate 9÷1/3.
A green rectangle is divided into 9 equal parts arranged into 3 rows of 3 cells each.
A.
9/3
B.
3/9
C.
13 1/2
D.
27
Using thie model ,The answer is D. 27.
To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.
Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.
We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:
9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27
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What is the probability of obtaining twelve heads in a row when flipping a coin? Interpret this probability The probability of obtaining twelve heads in a row when flipping a coin is________
In this question you're given that a coin is flipped 12 times. Now I'll make some assumption here. The first assumption is that the coin is fair. That means the probability of getting ahead in a trial in the toss is the same as probability of getting a deal in the toss and that would be half And second. The all the 12 flips or tosses are independent of each other. And thirdly that the probability of getting ahead, it's the same in each toss and you can see that in each talks there's only two outcomes ahead or not ahead which is a so this is considered a success and this is a failure. It just happened to be the probability of the success and the probability of failure is the same at heart. So this actually follows a binomial distribution model. But in the event that you have not learned by normal distribution we can just go by simple probability multiplication rule. So in probability and it's times or is plus. But the assumption of independent trials and the coin is fair is still the same whether you're using binomial distribution or just simple probability multiplication rule, no Probability of obtaining 12 heads in a row when flipping a coin would be the first pulse, you get a hit. And the second course you also get ahead. And the third toss you get ahead. So on so forth. Up to the last toss, which is the 12th toss, you also get a hit. So it's hit for every toss. So what this means is that probability of first courses ahead is half so that's half now. N and in probability means multiple execution. So just times and second hand is second thoughts is also ahead. So there's a half and so N. S. A. Terms enter is ahead, so that's another half, so so on, so forth. All the way to the last end here. Mr toms And the 12 is also a hit. So this times, how so what we have here is half to the power of 12 since half is multiplying itself 12 times. And so the answer is 1/4 oh 96 Or 0.0002, 44 six, decimal places. Now, if you are using binomial distribution to solve this problem, you will be after this part here. You will be letting X be the number of heads. Oh 12 courses. Right, So X follows the binomial distribution Number of trials is 12, 12 horses. And probability of success in this case is probability of getting ahead in a in a toss is half, so probability of X equals two. R. Where r is the number of heads in 12 courses will be 12, choose our half to the power of our and one minus half is also half To the power of 12 minus are so probability of obtaining 12 heads in a role. So we will be looking at probability of X equals 2, 12. So just suck 12 into the arm. So is this and you will get the same answer of 0.000244
Use the quadratic formula to solve −16x2−12x+10=0x= Simplify your answers, using square roots as needed. If there is more than 1 solution, separate the answers with a comma.
Given:
\(-16x^2-12x+10=0\)Find:
Value of x with the help of quadratic formula.
Sol:
Quadratic formula:
\(\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}\)Use the formula :
\(\begin{gathered} -16x^2-12x+10=0 \\ \\ x=\frac{-(-12)\pm\sqrt{(-12)^2-4(-16)(10)}}{2(-16)} \\ \\ x=\frac{12\pm\sqrt{144+640}}{-32} \\ \\ x=\frac{12\pm\sqrt{784}}{-32} \\ \\ x=\frac{12\pm28}{-32} \\ \\ x=\frac{12+28}{-32};x=\frac{12-28}{-32} \\ \\ x=-1.25;x=0.5 \end{gathered}\)So the value of "x" is -1.25 and 0.5
1. Find the equation of the image of the circle x² + y2 + 16x-24y + 183 = 0 by rotated the line mirror 4x + 7y + 13 = 0. 2. The image of the circle (x - 3)² + (y-2)² = 1 in the line mirror ax + by = 19 is (x-1)³ + (y-16)2 = 1 then, find the values of (a, b). 3. Find the equation of a line passing through the origin and making an angle with the 4 line y-3x-5. 4. A parabola is drawn with its focus at (3,4) and vertex at the focus of the parabola y²-12x - 4y + 4 = 0. The n find equation of the parabola. 5. If the line ax + by + c = 0 touches the circle x² + y² - 2x = and is normal to the circle x² + y² + 2x - 4y + 1 = 0, then find the value of (a, b). 6. If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. -3 7.1² 14 231= [] then find the matrix A 8. Find the equation of the ellipse having its center at the point (2,-3), one and one vertex at (4, -3). 3 9. Find the value of x if-1 0 10. Solve the linear system using Cramer's rule a) 2 1 2 4 (6x - 4y = -12 8x - 3y = -2 X = 16 -21 3x + 2y = z = 5 b) x-y+3z = -15 (2x + y +7z = -28 one focus at (3,-3) 11. Find the value of k for which the following system of linear equations has infinite solutions: x + (k+1)y = 5 ((k+1)x + 9y = 8k - 1
Answer:
-72x - 53y + 287 = 0.
Step-by-step explanation:
To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.
The line mirror equation is given as 4x + 7y + 13 = 0.
The reflection of a point (x, y) in the line mirror can be found using the formula:
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
where A, B, and C are the coefficients of the line mirror equation.
For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.
Now, let's find the equations of the image of the circle.
The original circle equation is x² + y² + 16x - 24y + 183 = 0.
Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)
= (x - 8y - 8(4x + 7y + 13)) / 65
= (x - 8y - 32x - 56y - 104) / 65
= (-31x - 64y - 104) / 65
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)
= (y - 14x + 8(Ax + By + C)) / 65
= (y - 14x + 8(4x + 7y + 13)) / 65
= (57x + 35y + 104) / 65
Therefore, the equation of the image of the circle is:
(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0
Simplifying the equation, we get:
-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0
-72x - 53y + 287 = 0
So, the equation of the image of the circle is -72x - 53y + 287 = 0.
Findthe
y -intercept
oftheparabolay = x2 + 3x − 6.
Answer:
(0, -6) is the y-intercept.
Six different students went to a used book sale. They recorded the prices of the books that they bought and created the dot plots below. Each X represents 1 book. Which of the following dot plots report a purchase of 8 books? Select all that apply.
Answer:
Options 3, 4, and 5
Step-by-step explanation:
just count the x's.
If it equals 8, then its correct
My son and I are stuck on this one. Can anyone give some insight to this problem? Thank you.
Answer:
I made is clear for you, now you may match each one
Step-by-step explanation:
f(1)= 11, f(n)= 3*f(n-1)
11*3= 33, 33*3= 99, 99*3= 297, ...11, 33, 99, 297...⊕ middle
f(1)= -18, f(n)= f(n-1)+21
-18+21= 3, 3+21= 24, 24+21= 45, ...-18, 3, 24, 45, ...f(1)= -18, f(n)= f(n-1) + 22
-18+22= 4, 4+22= 26, 26+22= 48, ...-18, 4, 26, 48, ...f(1)= -18, f(n)= 2*f(n-1)
-18*2= -36, -36*2= -72, -72*2= -144, ...- 18, -36, -72, -144...⊕ bottom
f(1)= -18, f(n)= 6*f(n-1)
-18*6= -108, -108*6= -648, -648*6= -3888, ...- 18, - 108, - 648, -3888, ...⊕ top
f(1)= 11, f(n)= f(n-1) + 22
11+22= 33, 33+22= 55, 55+22= 77, ...11, 33, 55, 77, ...NeverReady batteries has engineered a newer, longer-lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.8 hours. Your statistics class questions this claim. You randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly,
Answer:
the probability is 0.0202
Step-by-step explanation:
The computation is shown below:
Given that
The Average life span = 17 hours
Standard deviation = 0.8 hours
Sample = 30 batteries
Sample mean = 16.7 hours
Now based on the above information
The probability is
\(P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202\)
Hence, the probability is 0.0202
1. How many degrees are in this angle, which is one-fourth of the circle?
Answer: 90 degrees
Step-by-step explanation: A circle is 360 degrees so since that is 1/4 you can divide
360/4 = 90 (: hope this helps
Answer:
90* x 4 = 360*
360* / 4 = 90*
Step-by-step explanation:
A circle has 360* all around.
In the angle that was drawn, it is 90*
The degrees for the space outside of 90* is x
x = ? 360* - 90* = 280* x = 280*
hope this helped
please help i d don't know i would really appreciate your help
Answer:
45
Step-by-step explanation:
hello there!
Remember all of the angles in a triangle will add up to equal 180 so to find the missing angle we subtract the given angles from 180
180 - 90 - 45 = 45 so the missing angle would equal 45
1
2
Active
A polynomial is factored using algebra tiles.
+x²+x+X
--X
k
Mark this and return
1
I
I'
T
1
1
I
10
Which polynomial was factored?
Ox²-2x-8
Ox²+2x-8
Ox²-2x-4
Ox²+2x-4
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(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.
Given are the polynomials,
1) x² - 2 x - 8
Factors = (x+2)(x-4)
2) x² + 2 x - 8
Factors = (x-2)(x+4)
3) x²-2x-4 = There will be no integral root.
4) x²+2x-4 = There will be no integral root.
Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.
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You spend 4/5 of an hour on your homework. You spend 1/2 of that time working on your science homework. How many minutes do you spend working on science homework?
Answer:
4/5 of an hour is 48 minutes so 48 minutes divided by 2 is 28 minutes
Step-by-step explanation:
Answer:
24 minutes.
Step-by-step explanation
4/5 = ?/60
4/5 = 48/60
half of 48 = 24
13 People fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is
5 feet deep on both sides of the street along a 2.7-mile section of a parade route.
The size of the crowd that is 5 feet deep on both sides of the street along a 2.7 -mile section of a parade route is 74,131 people.
How to calculate the crowd?The number of people that can fit comfortably in a 5 feet by 5 feet area = 13.
Therefore;
The ratio of the number of people per unit area = 13/(5 × 5) = 13/25
The area A occupied by the crowd = 5 feet × 2.7 mile × 2
2.7 miles = 14,256 feet
∴ A = 5 feet × 14,256 feet × 2 = 1,42,560ft²
We then have:
\(\frac{number\ of\ people}{1,42,560} = \frac{13}{25}\)
∴Number of people = 13/25 × 1,42,560 = 74,131.2 ≈ 74,131 people
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Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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