Answer:
a) A(x) = 360*x - 3*x²
b) The Domain of the function is ( 0 : ∞ )
c) x = 60 yards
y = 180 yards
c) A(max) = 10800 yd²
Step-by-step explanation:
Two rectangular corrals, with sides y and x ( y is the side parallel to the river) having a river as one side of the corrals means:
L length to be fenced
L = y + 3*x 360 = y + 3*x y = 360 - 3*x
The total areaof the two corrals as a function of x is
A(t) = x*y as y = 360 - 3*x by substitution we get
A(x) = x * ( 360 - 3*x)
A(x) = 360*x - 3*x²
Tacking derivatives on both sides of the equation we get:
A´(x) = 360 - 6*x A´(x) = 0 360 - 6*x = 0
x = 60 yards
and y = 360 - 3*x y = 360 - 180 y = 180 yards
A(max) = 60*180 = 10800 yd²
To find out if the value x = 60 is the x value for a maximum of A we go to the second derivative
A´´(x) = - 6 A´´(x) < 0 then there is a maximum value for function A in x = 60
The Domain of the function is ( 0 : ∞ )
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'?
Answer:
The length of BC is 14 units.Step-by-step explanation:
[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]
The length of B'C' is 0 units.
What is translation?It is the movement of the shape in left, right, up, and down direction.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The length of AD = 5 units.
Since the rectangle translates down by 4 units,
The length of A'D' =5 units.
The width of the original rectangle is AB, which is 3 units.
Since the rectangle translates to the right by 2 units,
The width of the new rectangle = 3 units.
Now,
The length of B'C' is the same as the length of AD', which is 5 units.
Subtracting 5 units from 5 units gives us a length of 0 units.
Thus,
The length of B'C' is 0 units.
Learn more about translation here:
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4 pillows and 5 quilts cost £53, 6 pillows and 5 quilts cost £57, find the cost of one each
Answer:
p=2
q=9
Step-by-step explanation:
4p+5q=53
6p+5q =57
Need help finding the end behavior !
Let's focus on f(x) = |x| for now.
Recall that the absolute value of any number is never negative.
Some examples: |-7| = 7 and |5| = 5
So as x gets bigger in the positive direction, so does y. That explains the notation [tex]x \to \infty, \ f(x) \to \infty[/tex]. Informally, we can say "the graph rises to the right".
Similarly, we have [tex]x \to -\infty, \ f(x) \to \infty[/tex] which means it "rises to the left". Both endpoints rise to positive infinity. The left side of the graph goes up forever because again the result of any absolute value function is never negative. So if we plug in say negative a million, then the result is positive a million. In a sense, the V shape absolute value function is almost like a parabola. Both have the exact same end behavior on both sides.
---------------------------------------------------------------------------------------
Now let's move onto g(x) = 2x^2+4
The only thing that matters when determining the end behavior is the leading term. The leading term here is 2x^2
The even exponent means the endpoints either A) go up together or B) go down together. We go with case A because the leading coefficient is positive. Like I mentioned earlier, this parabola mimics the V shaped absolute value graph in terms of the end behaviors being the same.
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Lastly, let's focus on h(y) = 3y^4-2
I'm not sure why your teacher is using y when the others were using x. I'll just swap y for x to get h(x) = 3x^4-2
Like the g(x) function, the largest exponent is even, so the left and right end behaviors go in the same direction. The positive leading coefficient means we have the endpoints going upward toward positive infinity.
What is the probability that they both choose a card labeled dog?
Answer:
0.16
Step-by-step explanation:
As it is stated that the card having the label of a dog has a probability of 0.4. Hence, the probability that they both choose a card labeled dog is 0.16.
What is the quotient of the fractions below? 2/3÷5/4
answer:
2/3÷5/4 is equal to 8/15
A book store had 30816 exercise books which were paclced in cartons each carton contained 24 exercise books the mass of an empty carton was 2kg and a full carton 12kg
30,816 books would go into 1,284 containers which would weigh 15,408kg with all the books in them or 2,568kg with the books not in them.
Which angle is coterminal with a 130° angle? A. An angle measuring –130° O B. An angle measuring 310° C. An angle measuring 490° O D. An angle measuring 480°
Answer:
Option C
Step-by-step explanation:
Positive coterminal angle of 130° is
(130+360)°
= 490°
Answered by GAUTHMATH
Answer:
An angle measuring 490
Step-by-step explanation:
it was right
Whats the equavalent to log8 64+log8 8
One of the questions Rasmussen Reports included on a 2018 survey of 2,500 likely voters asked if the country is headed in right direction. Representative data are shown in the DATAfile named Right Direction. A response of Yes indicates that the respondent does think the country is headed in the right direction. A response of No indicates that the respondent does not think the country is headed in the right direction. Respondents may also give a response of Not Sure.
(a) What is the point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction?
(b) At 95% confidence, what is the margin of error for the proportion of respondents who do think that the country is headed in the right direction?
(c) What is the 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction?
(d) What is the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction?
(e) Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Why?
The confidence interval in part (c) has a (Smaller or Larger) margin of error than the confidence interval in part (d). This is because the sample proportion of respondents who do think that the country is headed in the right direction is (closer to .5 / closer to 1 / farther from .5 / farther from 1) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Dataset:
553 - No
70 - Not Sure
384 - Yes
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
553 - No
70 - Not Sure
384 - Yes
Total = (553 + 70 + 384) = 1007
Proportion who do think country is headed in the right direction :
P = yes / total = 384/1007 = 0.381
b.) Error margin at 95%
Margin of Error = Zcritical * √p(1-p)/n
1-p = 1 - 0.381 = 0.619
Zcritical at 95% = 1.96
Margin of error = 1.96 * √0.381(0.619)/1007
Margin of error = 0.030
C.)
95% confidence interval for heading in the right direction:
P ± margin of error
P ± 0.030
Lower boundary = 0.381 - 0.030 = 0.351
Upper boundary = 0.381 + 0.030 = 0.411
(0.351 ; 0.411)
D.)
Confidence interval for people who don't think :
P = 553 / 1007 = 0.549
Confidence interval = P ± margin of error
Error margin at 95%
Margin of Error = Zcritical * √p(1-p)/n
1-p = 1 - 0.549 = 0.451
Zcritical at 95% = 1.96
Margin of error = 1.96 * √0.549(0.451)/1007
Margin of error = 0.031
P ± margin of error
P ± 0.031
Lower boundary = 0.549 - 0.031 = 0.518
Upper boundary = 0.549 + 0.031 = 0.580
(0.518 ; 0.580)
E.)
The interval with smaller error margin is ; 0.030 (those who think country is headed in the right direction because sample proportion is farther from .5 / farther from 1)
The value of the expression
2x²
+ x(100 - 15x) when x = 5 is
Х
0 119.
0 129.
135.
0 145.
Answer:
f(5) = 75
Step-by-step explanation:
The function is f(x) = 2x^2 + x(100 - 15x).
Evaluate this function at x = 5: replace each instance of x with 5:
f(5) = 2(5)^2 + 5(100 - 15·5)
Order of operations rules require evaluating the expression enclosed in parentheses first. We get:
f(5) = 2(5)^2 + 5(100 - 15·5)
= 50 + (100 - 75), so that:
f(5) = 50 + 25 = 75
f(5) = 75
Answer:
175?
Step-by-step explanation:
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
The sample space,S,of a coin being tossed three times is shown below, where H and T denote the coin landing on heads and tails respectively.
Answer: Bottom left corner
=======================================================
Explanation:
There are only four possible outcomes here
A) we get all tails, ie getting 0 headsB) we get exactly one head (the rest tails)C) we get exactly 2 headsD) we get all three headsBased on this so far, the answer is either the table in the bottom left corner or in the top right corner. It's not possible for X = 4 since we only flipped 3 coins.
The probability of case A happening is 1/8 since we have 1 scenario that's all tails (TTT) out of 8 items in the sample space. Similarly, the probability for case D is the same probability. We only have one HHH out of 8 total items.
The probabilities of cases B and C are the same. Both are 3/8. Note that for case B, we have HTT, THT, TTH which is three occurrences in which we get exactly 1 head. So that explains the 3/8.
Given that E is the universal set and that A and B are subsets of E. simplify An(B-A)
Answer:
Answer a h bro ok bye bro good luck
Find the volume. Help please it’s due tomorrow
Answer:
2cm
Step-by-step explanation:
vbjufdxcvhjjkknvxzdhjkbcxdf
In the figure, ∆ALM ≅ ∆BLM by Side-Angle-Side (SAS). Which angles are congruent by CPCTC?
Answer:
C. L LAM = L LBM
Step-by-step explanation:
__________
Find the volume and surface area of the rectangular solid. The length is 4 meters, the width is 6 meters, and the height is 3 meters.
Answer:
Volume = h * w * l (height, width, length)
Volume = 4* 6 * 3
Volume = 72 cube meters
Surface area is finding the are of every 2D plane on the solid.
2(w * h) + 2(l*h) + 2(w * l)
Surface are = 108 square meters
12 Jy
10
Which statement is true regarding the graphed
functions?
g
18
f(
4
Of(0) = 2 and g(-2) = 0
Of(0) = 4 and g(-2) = 4
Of(2)= 0 and g(-2) = 0
Of(-2) = 0 and g(-2) = 0
2
3 4
5 6 x
t6 -5 -3 -2 -12
-4
16
8
10
-121
Mark this and retum
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Given:
The graphs of the function f(x) and g(x).
To find:
The correct statement for the given graph.
Solution:
From the given graph it is clear that, the function f(x) passes through the points (0,4) and (2,0). So,
[tex]f(0)=4[/tex]
[tex]f(2)=0[/tex]
[tex]f(-2)\neq 0[/tex]
The graph of the function g(x) passes through the point (-2,0). So,
[tex]g(-2)=0[/tex]
Since [tex]f(2)=0[/tex] and [tex]g(-2)=0[/tex], therefore the correct option is C.
The graphs of the given functions, f(x), and g(x), bounces off the x-axis.
Correct response:
The true statement regarding the graphed function is the option;
[tex]\underline{f(2) = 0 \ and \ g(-2) = 0 }[/tex]Method used to find the true statementThe properties of the graph of f(x) and g(x) are;
When x = 0, the value of f(x) is; f(0) = 4
Therefore;
f(0) = 4
When x = 2, the value of f(x), which is the point on the graph corresponding to a x-value of 2 is; [tex]\underline{f(2) = 0}[/tex]
When x = 0, g(x) value is g(0) = 4
When x = -2, g(x) is; g(-2) = 0
The correct option is therefore;
[tex]\underline{f(2) = 0 \ and \ g(-2) = 0}[/tex]Learn more about functions here:
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Identify the pairs of congruent angles and proportional corresponding side lengths
Answer:
∠B=∠D, ∠C=∠E, ∠A=F.
Step-by-step explanation
FE/AC=6/8=3/4, FD/AB=9/12=3/4,DE/BC=13.5/18=3/4. Since all proportions are equal to 3/4, the corresponding side lengths are proportional.
what is the slope of this graph?? :,)
Answer:
1/2
Step-by-step explanation:
This line is going up towards the right- that makes it positive. It is increasing. So it can't be negative or going "down"
The question wants to see if you know the direction of the line.
need help with algebra question ‼️
Answer:
c
Step-by-step explanation:
There are three types of variations.
1. Direct
2. Inverse
3. Joint
There is positive proportionality is two variables are positively related to each other.
The equation for direct proportionality =
y = bx
where y = dependent variable
b = constant
x = independent variable
if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
the equation that represents inverse proportion :
where b = constant of proportionality
Joint variation occurs when the dependent variables value is determined by two or more values
For example, the volume of a cylinder is dependent on the value of the radius and height
f h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g circle h) (5)?
Answer:
here is your answer
Step-by-step explanation:
here is your answer
What additional information do you need to prove triangle ABC ~ triangle JKL
Answer:
no additional information will help because the triangles are not similar
Step-by-step explanation:
Similar triangles have 3 pairs of congruent, corresponding angles.
Let's look at triangle ABC. Two angle measures are given: 51 deg and 63 deg.
180 - 51 - 63 - 66
The measure of the thrid angle is 66 deg.
One anlgle measure of triangle JKL is given. It is 66 deg.
Since <J is not congruent to any angle of triangler ABC, the triangles are not similar.
Answer: no additional information will help because the triangles are not similar
Which of the following statement is incorrect? .
a.Closure property is true for subtraction of Rational numbers
b.Commutative property is true for subtraction of Rational numbers
c.Closure property is true for addition of Rational numbers
d.Closure property is true for multiplication of Rational numbers
If you answer the question I will follow you
answer fast
Answer:
b.Commutative property is true for subtraction of Rational numbers
Step-by-step explanation:
Option B is the correct answer as it is the incorrect statment in the given options.which of the following does not describe a rigid motion transformation
Answer:
The answer to this question is dilating the figure by a scale factor of one half.
Arithmetic or geometric 18,13,8
Answer:
That is Arithmetic
Step-by-step explanation:
Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity. Which is -5 in this case.
Hope this helps
WILL MARK YOU IF YOU ANSWER SO PLEASE HELP
Answer:
x= 83
first take vertical opposite angle then take corresponding angles then you're done
Answer:
x value is 83 degree
because they both are alternate exterior angle
question- pls help me find the answer
Answer:
(d) -1
Step-by-step explanation:
Hope you have good grades and study well..btw make me as brainliest....ty sweetie
What's the area
5.1 5.1 5.1 ?
Answer:
Are you talking about the are of a 3d cube? then it would be 156.06 because you take the length times width to get the area of one side then multiply it by 6 to gets all the sides.
I need help with this problem
Answer:
x = 21, y = 40
Step-by-step explanation:
The angle above (7x - 13) is (2x + 4 ) ← alternate angle
(7x - 13) and (2x + 4) are adjacent angles and sum to 180° , then
7x - 13 + 2x + 4 = 180
9x - 9 = 180 ( add 9 to both sides )
9x = 189 ( divide both sides by 9 )
x = 21
Then
2x + 4 = 2(21) + 4 = 42 + 4 = 46
(2x + 4) and (3y + 14) are adjacent angles and sum to 180° , so
46 + 3y + 14 = 180
60 + 3y = 180 ( subtract 60 from both sides )
3y = 120 ( divide both sides by 3 )
y = 40
20 POINTS- Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
A 4-column table with 5 rows titled Vacation Preferences. Column 1 has entries beach, big city, camping, skiing, total. Column 2 is labeled spring with entries 35, 7, 14, 4, 60. Column 3 is labeled summer with entries 10, 2, 8, 10, 30. Column 4 is labeled total with entries 45, 9, 22, 14, 90.
Complete each statments.
About ____% of the students surveyed prefer a spring camping vacation.
About ____% of the students surveyed prefer a big city vacation.
Answer:
The answers for edge 2021 is
Step-by-step explanation:
16 and 10
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 108 disks are summarized as follows: Shock Resistance Scratch Resistance High Low High 55 10 Low 13 30 Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance. If a disk is selected at random, determine the following probabilities. P(A)=86/100P(B)=79/100P(A')=7/50P(A U B)=95/100P(A' U B)= ???
Answer:
i) 0.63
ii) 0.37
iii) 0.37
iv) 0.77
v) 0.51
Step-by-step explanation:
Total resistance value = 108
A = high shock resistance
B = high scratch resistance
when a disk is selected at random
i) P(A) = P ( high shock resistance )
= ( 55 + 13 ) / 108
= 68/108 = 17/27 = 0.63
ii) P( B ) = P ( high scratch resistance )
= ( 10 + 30 ) / 108
= 40 / 108 = 10/27 = 0.37
iii) P(A') = 1 - P(A)
= 1 - 17/27 = 10/27 = 0.37
iv) P( A U B ) = P(A) + P(B) - P( A n B )
= 0.63 + 0.37 - 0.233
= 0.766 ≈ 0.77
v) P( A' U B ) = P(A') + P(B) - P(A n B )
= 0.37 + 0.37 - 0.233
= 0.507 ≈ 0.51