Answer:Best corral has a width and length of 50 feet, enclosing an area of 2500 square feet. Let's calculate the width (W) of the rectangle as a function of it's length (L). So we have W = (200 - 2*L)/2 W = 100 - L Now the area of the rectangle is A = WL Substitute the equation for W. A = (100 - L)L A = 100L -L^2 Let's make an initial guess of 40 ft and add an error component of e. So we'll use the length of (40+e) and see what we get. A = 100L -L^2 A = 100(40+e) - (40+e)^2 A = 4000 + 100e - (1600 + 80e + e^2) A = 4000 + 100e - 1600 - 80e - e^2 A = 2400 + 20e - e^2 Now looking at those 2 "e" terms is interesting. It's pretty obvious that any negative value of e will cause those term to result in a value less than 0, and decrease the available area. Also any value of e greater than 20 will also cause those 2 values to sum to a negative value and decrease the area. But a value of e in the range of 0 to 20 will result in a positive value and cause the area enclosed to be larger. So it's obvious that 40 feet isn't optimal. Let's pick the middle of the e values that result in something positive (0+20)/2 = 10 and add that to our initial guess, getting a length of 50 and replace length by (50+e) and see what happens. A = 100L -L^2 A = 100(50+e) -(50+e)^2 A = 5000+100e -(2500+100e + e^2) A = 5000+100e - 2500 - 100e - e^2 A = 2500 - e^2 This looks quite promising. Any non-zero value of e will result in the area enclosed being smaller. So the idea value of e is 0. That means that the idea length of the rectangle is 50 feet. And that makes the width 50 feet as well. Mind, this problem could have been also solved using the first derivative of the equation A = 100L -L^2, which would have been A' = 100 - 2L, and then solving for 0. But I did this problem to demonstrate that you don't need to resort to calculus for every maximum type of problem.
Step-by-step explanation:
Will a fluoride mouthwash used after brushing reduce cavities? Twenty sets of twins were used to investigate this question. One member of each set of twins used the mouthwash after each brushing, the other did not. After six months, the difference in the number of cavities of those using the mouthwash was compared with the number of cavities for those who did not use the mouthwash. This experiment uses:
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is b
Step-by-step explanation:
The correct option is matched pair design the reason for this is because in the experiment individual(elements) are group into pairs based on a characteristics that they have in common (in this question the characteristics being a twin) and then within each group the subject a placed on different treatment , in the case of this question each twin in each group are placed on different treatment (i.e one is given the mouthwash while the other is not ).
This process which I have explained is how a matched pair design is carried out
Simplify the polynomial, then evaluate for x=-3
-x^2+2x-2x^2-3x+4+x^2
Step-by-step explanation:
Let's simplify step-by-step.
−x2+2x−2x2−3x+4+x2
=−x2+2x+−2x2+−3x+4+x2
Combine Like Terms:
=−x2+2x+−2x2+−3x+4+x2
=(−x2+−2x2+x2)+(2x+−3x)+(4)
=−2x2+−x+4
Answer:
=−2x2−x+4
What is the equation of the line of best fit that Samir drew? OA. y = -x + 12 OB. O C. y = - + 18 y = -x + 12 y = -x + 18 OD.
Answer:
Answer: Choice A
y = (-2/3)x + 12
================================================
Work Shown:
We will only focus on the two points that are on the regression line.
Those two points are (3,10) and (12,4)
Let (x1,y1) = (3,10) and (x2,y2) = (12,4)
Find the slope of the line through (x1,y1) = (3,10) and (x2,y2) = (12,4)
m = (y2 - y1)/(x2 - x1)
m = (4 - 10)/(12 - 3)
m = -6/9
m = -2/3
Plug m = -2/3 and (x1,y1) = (3,10) into the point slope formula
Solve for y.
y - y1 = m(x - x1)
y - 10 = (-2/3)(x - 3)
y - 10 = (-2/3)x + (-2/3)(-3) ... distribute
y - 10 = (-2/3)x + 2
y - 10 + 10 = (-2/3)x + 2 + 10 .... add 10 to both sides
y = (-2/3)x + 12
This matches up with what the graph shows because the regression line intersects 12 on the y axis, so the y intercept is 12.
y = (-2/3)x + 12 is in the form y = mx+b with m = -2/3 as the slope and b = 12 as the y intercept.
Trevor is preparing dinner plates. He has 18 pieces of chicken and 14 rolls. If he wants to make all the plates identical without any food left over, what is the greatest number of plates Trevor can prepare?
Answer:
split the four extra pieces into smaller pieces to were it will give each plate the same amount.
Step-by-step explanation:
Complete the following table with the properties used to solve 4 (x + 3) = 20
#1) 4x + 12 = 20
#2) 4x = 8
#3) x = 2
If it not a good description, I'll put this as an example
4 (x + 3) = 20 is a Given Property
Answer:
Step-by-step explanation:
4 (x + 3) = 20 Distributive
#1) 4x + 12 = 20 Addition property of equality
#2) 4x = 8 Division Property of Equality
#3) x = 2 Answer
Mark used a number line to model dividing į by 3. He
divided the number line from 0 to 1 in 3 equal sections,
and then divided each of those sections into 2 equal
parts. Mark says ſ = 3 is į
Is his answer correct? Explain why or why not.
No, he is incorrect. Using a number line to model thirds means that each space that is 1/3 should be divided into 3 parts, not 2 parts. 6 parts divided into 3 groups gives 2 parts out of 9 parts total, so the answer is 2/9.
Answer:
No, he is incorrect. Using a number line to model thirds means that each space that is 1/3 should be divided into 3 parts, not 2 parts. 6 parts divided into 3 groups gives 2 parts out of 9 parts total, so the answer is 2/9.
Step-by-step explanation:
sample responce
5 2/3 divided by 2 1/8
Answer:
[tex]2 \frac{2}{3} [/tex]
ANSWER PLEASE NEED HELP ASAP
Answer: 43 should be divided into 0.37 to find “x”.
Step-by-step explanation:
Question 3
65% of 700
Question 4
25% of 84
Answer:
question 3The answer for 65% of 700 is 455
Answer:
3= 455
4= 21
Explanation:
700 x .65
84 x .25
If the points P(5,2),Q(0,7) and R(-5,2) are drawn on coordinate plane,where must point S be located so that figure PQRS is square.
Answer:
(0, -7) i think
hope this helps :3
sorry if im wrong
he pulse rates of 179 randomly selected adult males vary from a low of 43 bpm to a high of 115 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 90% confidence that the sample mean is within 3 bpm of the population mean. Complete parts (a) through (c) belo
Answer:
97
Step-by-step explanation:
Given that:
Low = 43bpm
High = 115 bpm
Error = 3
α = 90%
To find the range estimate :
Standard destviation = (high - low) / 4
Standard deviation = (115 - 43) / 4
Standard deviation = 72/4 = 18
The sample size,(n) :
n = [(Zα/2 * sd)/E] ²
2 - tail = (Zα/2) = 1.645
[(Zα/2 * sd)/E] ² = [(1.645 * 18) / 3]² = (29.61/3)²
= 97.41
Sample size = 97
3. How many solutions are there to the
equation 2x^2 - 3x +12=0? Tell how
you know.
Answer:
If you're talking about solutions in general (real and imaginary solutions), there is 2, because the fundamental theorem of algebra says that the number of roots of any polynomial is the degree if it's highest power, which is 2.
If you're talking about only real solutions, there is 0. To show that, we can take the discriminant (b^2-4ac) part of the quadratic equation, and plug in the know values. We then get:
(-3)^2-4*2*12
=9-96
=-87
Remember, the discriminant will be taken the square root. Since this is negative, the answer will be imaginary. Therefore, there is no real solution.
Double line graphs are used to compare two sets of data over the same period of time.
-True
-False
Answer:
the answer is true! :)
Step-by-step explanation:
Find each quotient in the table below.
Write your answer as a fraction or a mixed number.
Problem
Quotient
6 1/4 divided by 2
10 1/7 divided by 5
8 1/2 divided by 11
Find the solution for the equation. 3 (n - 4) = -12
Answer:
0
Step-by-step explanation:
3n-12=-12
-3n=-0
n=0
Answer:
n=0.0
Step-by-step explanation:
3(n-4) = -12
3n-12 = -12
3n = 0
n = 0
The area of a parallelogram is 24 square units. One side of the parallelogramis
36 units long. The other side is 4 units long. Which could be the parallelogram's
height? Choose all the correct answers.
A.1/6
B.2/3
C.3/2
D.6
E.9
The required height of the parallelogram is 2/3. Option B is correct.
Given that,
The area of a parallelogram is 24 square units. One side of the parallelogramis 36 units long. The other side is 4 units long. Which could be the parallelogram's height is to be determined.
A parallelogram is a quadrilateral consisting of pairs of parallel side.
Here,
We have given the area of the parallelogram and the measure of its base. So,
Area of the parallelogram = base * height
24 = 36 * height
height = 2 / 3
Thus, the required height of the parallelogram is 2/3. Option B is correct.
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If L||m find the value of X
Please help me :)
Answer:
x= 12
Step-by-step explanation:
(9x -4)° +(5x +16)° = 180° (int. ∠s, L//m)
9x -4 +5x +16= 180
14x +12= 180 (simplify)
14x= 180 -12 (-12 on both sides)
14x= 168
x= 168 ÷14 (÷14 on both sides)
x= 12
It takes Daphne 25 minutes to assemble a model plane. During her work
minutes for lunch and one 15 minute break. Which inequality could Daphne use to determine the number
of model planes, p, she can assemble in her 8 hour work day?
A. 25p – 45 > 8
B. 25p + 45 2 8
C. 25p – 45 < 480
D. 25p + 45 < 480
Answer: 25p+45>= 8
Step-by-step explanation:
The qoutient of 9 3/4 and 5/8?
Answer:
do you mean 9 3/4 divided by 5/8, if so, it gives you 78/5
Step-by-step explanation:
answer:
it is 15 3/5
your welcome
Let V be the volume of the pyramid of height 11 whose base is a square of side length 6. Find a formula for the area A of the horizontal cross section at a height y.
Answer:
Base area = 36
Volume of the pyramid = 132
Step-by-step explanation:
Volume of a pyramid = Base Area × Height/3
Base area = Length × Length (since base of the pyramid is a square)
Given the side length of the square = 6
Base area = 6×6
Base area = 36
Given height of pyramid =11
Volume of the pyramid = 36×11/3
Volume of the pyramid = 12×11
Volume of the pyramid = 132
help please ?!??!!????
Answer:
2 hours 80 miles I believe is the answer hope this helps
Step-by-step explanation:
What is the length of the line segment with endpoints (−3, 8) and (7, 8) ?
Answer:
length/distance = 10 units
Step-by-step explanation:
Use the distance formula for both points / length / magnitude, d = √((x2-x1)^2+(y2-y1)^2).
Given endpoints (-3,8) [(x1,y1)], and (7,8) [(x2,y2)], plug in the corresponding y, and x values of both coordinates, and simplify.
√((8-8)^2+(7-(-3))^2) = √(0^2+10^2) = √100 = 10
*This may be in units if the unit used is unspecified.*
_______________________________
Also since the y values of both coordinates are the same, you can just subtract the x values in the coordinates, and take the absolute value since distance/length cannot be negative.
Step-by-step explanation:
[tex]|AB | = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]
[tex] = \sqrt{( - 3 - 7)^{2} + (8 - 8)^{2}} \\ = \sqrt{100 + 0} = 10[/tex]
A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 8 face cards. Leave your answer as a reduced fraction.
Answer: [tex]\dfrac{9}{66892280}[/tex]
Step-by-step explanation:
Number of combinations of r things from n things = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Number of combinations of choosing 9 cards out of 52 = [tex]^{52}C_9=\dfrac{52!}{9!(52-9)!}=3679075400[/tex]
Total face cards = 12
Number of combinations of choosing 8 face cards = [tex]^{12}C_8=\dfrac{12!}{8!(12-8)!}=495[/tex]
Required probability = [tex]\dfrac{495}{3679075400}=\dfrac{9}{66892280}[/tex]
Hence, the probability that the hand contains exactly 8 face cards. = [tex]\dfrac{9}{66892280}[/tex]
Jayden's family watched 8 hours of TV last week. This week, they watchec
25% more than that. How many hours of TV did they watch this week? *
Answer:
I THINK that it is 10 hours
Step-by-step explanation:
(Sorry if I am wrong)
25% = 1/4 SO 8 divided by 4 = 2
Since they watched 25% MORE you add 2 to 8 and get 10
resta y suma de valor absoluto
Answer: Éstos son los pasos para usar la estrategia del valor absoluto. Para sumar dos enteros con el mismo signo, suma sus valores absolutos. Luego, coloca el mismo signo de los dos enteros originales a la respuesta. Para sumar dos enteros con signos diferentes, resta el valor absoluto menor al valor absoluto mayor.
Step-by-step explanation: Ojalá esto ayude !
Answer:
El valor absoluto de un número consiste en su valor, sin importar su signo. Cuando tomamos el valor absoluto de un número, éste es siempre positivo o cero. ... Por ejemplo, el valor absoluto de 5 es 5. El valor absoluto de -5 es también 5.
Step-by-step explanation:
The cost to build an amusement park ride by a certain contractor is represented by the function: Cost = 2*x2 – 10/x + 36*y + 25 where x is the number of people able to be on the ride at once. For what value of x would unit cost be minimized? What is the minimum cost for this number of passengers? Show mathematically that the value found is truly a minimum and discuss whether this solution is feasible.
Answer:
The minimum cost for this number of passengers is Rs.36.05
Step-by-step explanation:
The cost to build an amusement park ride by a certain contractor is represented by the function:
[tex]Cost = 2x^2 - \frac{10}{x}+ 36y + 25[/tex]
x : Number of people able to be on the ride at once.
Differentiate the function w.r.t x
[tex]\frac{\partial cost}{\partial x}=4x-(\frac{-10}{x^2})=0[/tex]
[tex]x^3=\frac{-5}{2}[/tex]
x=-1.3572
Differentiate the function w.r.t y
[tex]\frac{\partial cost}{\partial y}=36=0[/tex]
Minimum cost =[tex]2x^2 - \frac{10}{x}+ 36y + 25[/tex]
Minimum cost = [tex]2(-1.3572)^2 - \frac{10}{(-1.3572)}+ 36(0) + 25[/tex]
Minimum cost = 36.05
Hence the minimum cost for this number of passengers is Rs.36.05
A model of the American flag was made out of 1,776 colored tiles. The star field took 444 blue tiles. The rest of the tiles were split evenly to form the red and white stripes. Choose the correct answer that represents the number of red or white tiles.
A. 540
B. 444
C. 1,332
D. 666
Answer:
D
Step-by-step explanation:
The number of red and white stripes = 666
Given, A model of the American flag was made out of 1,776 colored tiles.
The star field took 444 blue tiles.
The rest of the tiles were split evenly to form the red and white stripes.
Number of red or white stripes = (Total number of colored tiles - number of blue tiles)/2
= (1776 - 444)/2
= (1332)/2
= 666
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A number is divided by 4, and the quotient is added to 3. The result is 24. What is the number? (Please show how you got it)
(n/4) + 3 = 24
Answer:
84
Step-by-step explanation:
(x/4) + 3 = 24
so in this case try and make x the subject or in other words try to leave x on one side of the equation.
(x/4) = 24 - 3
(x/4) = 21
now multiply 21 by 4 using cross multiplication
so x= 84
Durant and Westbrook are playing a three-point challenge game to improve long
distance shooting. Each time each of them makes a basket, 3 points are added to
their respective scores. Durant has 18 points and Westbrook has 12 points.
Which of the following options has the pair of explicit formulas that represents the
number of points for each player as an arithmetic sequence?
A: Durant: 18 +(n-1)(3)
B: Durant: 18-(n-1)(3)
C: Durant 18+(n-3)
D: Durant 18+3n
Answer:
I THINK ITS A
Step-by-step explan I TOOK THE TEST TODAY I DONT NOW NOTHING
If(2p+3)(p+5)=p2 +p+,whatisthevalueof++?
Answer: (p - 1) • (5p + 3)
Step-by-step explanation: Changes made to your input should not affect the solution:
(1): "p2" was replaced by "p^2".
STEP
1
:
Equation at the end of step 1
(5p2 - 2p) - 3
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 5p2-2p-3
The first term is, 5p2 its coefficient is 5 .
The middle term is, -2p its coefficient is -2 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 5 • -3 = -15
Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is -2 .
-15 + 1 = -14
-5 + 3 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 3
5p2 - 5p + 3p - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
5p • (p-1)
Add up the last 2 terms, pulling out common factors :
3 • (p-1)
Step-5 : Add up the four terms of step 4 :
(5p+3) • (p-1)
Which is the desired factorization
