Tom has 120 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. As shown below, one of the sides has length x (in meters).
Find a function:
What is the side length?
What is the maximum area?
Answer:
a) Function A(x) = (60*x - 1/2*x²)
b)Side length x = 60 m the other side y = 30 m
c) A (max) = 1800 m²
Step-by-step explanation:
Area of rectangular garden with length " x " and wide "y"
A = x*y
Perimeter of rectangular area ( only three sides 2*y and 1*x)
P(r) = 2*y + x
P(r) = 120 = 2*y + x
y = ( 120 - x ) /2
Area of the garden as function of x is
A(x) = [( 120 - x ) /2]*x ⇒ A(x) = (60*x - 1/2*x²)
Taking derivatives on both sides of the equation:
A´(x) = 60 - x
A´(x) = 0 60 - x = 0
x = 60 m
Then
y = ( 120 - x ) / 2 ⇒ y = (120 - 60 )/2
y = 30 m
A(max) = 30 * 60
A(max) = 1800 m²
The side length (x) is 30 m each
The maximum area is 1800 m².
He has 120 meters for fencing . He use it to form 3 sides of a rectangular garden.
Therefore,
let
the side parallel to the house = y
the sides perpendicular to the house = x (2 sides)
Therefore,
perimeter = 2x + y
120 = 2x + y
y = 120 - 2x
area = x(120 - 2x)
area = 120x - 2x²
area = -2x² + 120x
The leading coefficient is less than zero, therefore, the parabola is facing downward. The maximum area is at (h, k).
where
h = - b / 2a
a = -2
b = 120
h = - 120 / 2 × -2
h = 120 / 4 = 30
The sides perpendicular to the building = 30 meter
The side parallel to the building = 120 - 2(30) = 60 meters
The maximum area = 60 × 30 = 1800 m²
read more: https://brainly.com/question/8602676?referrer=searchResults
Construct a table of values for the following functions using the integers from -4 to 4.
a. F(x)=6/x-2
b. r(x)=6x+12/x^-4
Step-by-step explanation:
Find the table attached
a) Given
F(x) = 6/x-2
When x = -4
F(-4) = 6/-4-2
F(-4) = 6/-6
F(-4) = -1
F(x) = 6/x-2
When x = -3
F(-3) = 6/-3-2
F(-3) = 6/-5
F(-3) = -1.2
F(x) = 6/x-2
When x = -2
F(-2) = 6/-2-2
F(-2) = 6/-4
F(-2) = -1.5
F(x) = 6/x-2
When x = -1
F(-1) = 6/-1-2
F(-1) = 6/-3
F(-1) = -2.0
F(x) = 6/x-2
When x = 0
F(0) = 6/0-2
F(0) = 6/-2
F(0) = -3
F(x) = 6/x-2
When x = 1
F(1) = 6/1-2
F(1) = 6/-1
F(1) = -6
F(x) = 6/x-2
When x = 2
F(2) = 6/2-2
F(2) = 6/0
F(2) = infty
F(x) = 6/x-2
When x = 3
F(3) = 6/3-2
F(3) = 6/1
F(3) = 6
F(x) = 6/x-2
When x = 4
F(4) = 6/4-2
F(4) = 6/2
F(4) = 3
b) Given
r(x)=6x+12/x^-4
When x = -4
r(-4) = 6(-4)+12/(-4)^-4
r(-4) = -24+12/(1/256)
r(-4) = -12(256)
r(-4) = -3072
When x = -3
r(-3) = 6(-3)+12/(-3)^-4
r(-3) = -18+12/(1/81)
r(-3) = -6(81)
r(-3) = -486
When x = -2
r(-2) = 6(-2)+12/(-2)^-4
r(-2) = -12+12/(1/16)
r(-2) = -0(16)
r(-2) = 0
When x = -1
r(-1) = 6(-1)+12/(-1)^-4
r(-1) = -6+12/(1)
r(-1) = -6+12
r(-1) = 6
When x = 0
r(0) = 6(0)+12/(0)^-4
r(0) = 0+12/0
r(0) = 12/0
r(0) = infty
When x = 1
r(1) = 6(1)+12/(1)^-4
r(1) = 6+12/1
r(1) = 18(1)
r(1) = 18
When x = 2
r(2) = 6(2)+12/(2)^-4
r(2) = 12+12/1/16
r(2) = 24(16)
r(2) = 384
When x = 3
r(3) = 6(3)+12/(3)^-4
r(3) = 18+12/1/81
r(3) = 30(81)
r(3) = 2430
When x = 4
r(4) = 6(4)+12/(4)^-4
r(4) = 24+12/1/256
r(4) = 36(256)
r(4) = 9216
We want to construct tables of values for the two given functions.
The tables are:
a)
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b)
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
A table will be something like:
[tex]\left[\begin{array}{ccc}x&y\\-4&\\-3&\\-2&\\-1&\\0&\\1&\\2&\\3&\\4&\end{array}\right][/tex]
Where the values of x go from -4 to 4.
To complete the tables, we just need to evaluate the functions in each one of the x-values at the left, and the outcome will be placed at the right.
a) f(x) = 6/x - 2
Now we just need to evaluate the function in all the given points:
f(-4) = 6/(-4) - 2 = -3/2 - 4/2 = -7/2
f(-3) = 6/-3 - 2 = -4
f(-2) = 6/-2 - 2 = -5
f(-1) = 6/-1 - 2 = -8
f(0) is undefined, as we can't divide by zero, here we can write NaN (Not a number).
f(1) = 6/1 - 2 = 4
f(2) = 6/2 - 2 = 1
f(3) = 6/3 - 2 = 0
f(4) = 6/4 - 2 = -1/2
Now we put all of these in the correspondent place of the table:
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b) We do the same thing, here we have:
r(x) = 6*x + 12/x^-4 = 6*x + 12*x^4
Now we evaluate this in the given values:
r(-4) = 6*(-4) + 12*(-4)^4 = 3,048
r(3) = 6*(-3) + 12*(-3)^4 = 954
r(-2) = 6*(-2) + 12*(-2)^4 = 180
r(-1) = 6*(-1) + 12*(-1)^4 = 6
r(0) = 6*0 + 120^4 = 0
r(1) = 6*1 + 12*1^4 = 18
r(2) = 6*2 + 12*2^4 = 204
r(3) = 6*3 + 12*3^4 = 990
r(4) = 6*4 + 12*4^4 = 3,096
Now we place these values in the correspondent place on the table:
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
These are our two tables.
If you want to learn more, you can read.
https://brainly.com/question/8629807
123x78=
how much it equals too?
Answer:9,594 thats tha answer
a rectangular prism is 12 inches long, 6 inches wide and 10 inches tall. what is the length of it's longest diagonal?
Answer:
15.620
Step-by-step explanation:
use pythagorean theorm :)
(the 6 is pointless for this problem)
Determine whether the following graph represents a function.
Answer:
function
Step-by-step explanation:
Answer:
Its a Function
Step-by-step explanation:
Its a function because no vertical line Its intersect the curve more than once.
Area of shaded region of a rectangle
u forgot to add the pic lma.o.
Please answer correctly, will give brainlist.
Answer:
the answer is 77
Step-by-step explanation:
A measures 32 and B measures 109 so you subtract 109 and 32 and your answer will be 77
9.831 rounded to the nearest tenth
Answer:
9.8
Can i get brainliest please?
Answer:
9.8
Step-by-step explanation:
Hoped that helped :)
Use inductive reasoning to predict the next three numbers in the pattern.
Home
3, 5, 8, 13, 21, 34, ...
nents
Predict the next three numbers in the pattern.
3, 5, 8, 13, 21, 34,
Answer:
The next three terms are 55,89 and 144
Step-by-step explanation:
We want to predict the next three numbers in the pattern
3, 5, 8 , 13 , 21 , 34
The difference between two successive terms is written between them.
Thus, we have
3 2 5 3 8 5 13 8 21 13 34
So the rule here is to add the next term to the previous so as to get the next coming term
Thus, we have;
34 + 21 = 55
55 + 34 = 89
89 + 55 = 144
What's the slop of ( 2.5),(6,13)
Answer:
2
Step-by-step explanation:
m=y2-y1/x2-x1
13-5=8
6-2=4
8/4=2
hope this helps :3
if it did pls mark brainliest
[tex](15+23)+7=15+(_______+7)[/tex]
Can someone who knows Pre Calculus help me on these questions.
Answer:
the answer should be B:12/5
What property is if x=12 , then 3x=36
Answer:
3x=x+12 This is not quadratic. This is linear in x. (3x-x) = 12 (bringing x from the right to the left, change side then change sign, in other words add - x to both the sides.
Step-by-step explanation:
3.1 to the nearest tenth
Answer:
3.1 to the nearest tenth is 3.1.
Step-by-step explanation:
The first decimal place is the tenths place. Hope this helps!
3.1 because 1 can't be raised to the next number
The Acme Battery Company has developed a new cell phone battery. On average, the battery lasts 60 minutes on a single charge. The standard deviation is 4 minutes. Suppose the manufacturing department runs a quality control test. They randomly select 7 batteries. The standard deviation of the selected batteries is 6 minutes. a. What would be the chi-square statistic represented by this test? b. What are the degrees of freedom for the chi-square statistic? c. Suppose they repeated the test with a new random sample of 7 batteries. What is the probability that the standard deviation in the new test would be greater than 6 minutes? (Use the applet)
Answer:
X² = 13.5
Degree of freedom = 6
0.04
Step-by-step explanation:
Give the following :
Number of samples (n) = 7
Population standard deviation (σ) =.4 minutes
Sample standard deviation (s) = 6
Mean battery life = 60 minutes
A) Chisquare (X²) :
X² = ((n - 1) * s²) / σ²
X² = ((7 - 1) * 6²) / 4²
X² = (6 * 6²) / 4²
X² = (6 * 36) / 16
X² = 216 / 16
X² = 13.5
B.) The degree of freedom:
degree of freedom = n - 1
Degree of freedom = 7 - 1 = 6
C.) using a chisquare distribution calculator :
With degree of freedom (df) = 6
X² = 13.5
Hence,
P(X² > 13.5) = 0.04 ( from calculator)
I really need help 1260 divided by 17
6699 divided by 72
Answer:
1) 7.118 (rounded to the nearest thousandth)
2) 93.042 (rounded to the nearest thousandth)
Step-by-step explanation:
1260 divided by 17 = 7.118 (rounded to the nearest thousandth)
6699 divided by 72 = 93.042 (rounded to the nearest thousandth)
(I don't really know how to explain this in detail. Sorry.
Hope I helped :)
Please consider Brainliest :)
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]
Compute the probability that a randomly selected peanut M&M is not yellow.
Compute the probability that a randomly selected peanut M&M is brown or red.
Compute the probability that three randomly selected peanut M&M’s are all brown.
If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
P(brown) = 12% = 0.12
P(Yellow) = 15% = 0.15
P(Red) = 12% = 0.12
P(blue) = 23% = 0.23
P(orange) = 23% = 0.23
P(green) = 15% = 0.15
A.) Compute the probability that a randomly selected peanut M&M is not yellow.
P(not yellow) = P(Yellow)' = 1 - P(Yellow) = 1 - 0.15 = 0.85
B.) Compute the probability that a randomly selected peanut M&M is brown or red.
P(Brown) or P(Red) :
0.12 + 0.12 = 0.24
C.) Compute the probability that three randomly selected peanut M&M’s are all brown.
P(brown) * P(brown) * P(brown)
0.12 * 0.12 * 0.12 =0.001728
D.) If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
P(3 blue)' = 1 - P(3 blue)
P(3 blue) = 0.23 * 0.23 * 0.23 = 0.012167
1 - P(3 blue) = 1 - 0.012167 = 0.987833
If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
P(1 blue) + p(2 blue) + p(3 blue)
(0.23) + (0.23*0.23) + (0.23*0.23*0.23)
0.23 + 0.0529 + 0.012167
= 0.295067
Sophia earned $18 for working 2 1/4 hours. How much did she earn per hour?
Answer:
It is price between 1~100 lol
Step-by-step explanation:
A scientist observes and counts 155 bacteria in a culture. Later, the scientist counts again and finds the number has increased by 40%.How many bacteria are there now?
Answer:
217
Step-by-step explanation:
155 + 40% = 217
I need help with this! Right nowww I will brainliest
Answer:
2 and 7: Alternate exterior
3 and 7: Corresponding
3 and 5: Same side interior
3 and 6: Alternate interior
please help, I can't get it
What is a single discount rate and how does it apply to chain discounts?
Answer:
Single discount rates are one off discounts which are given by seller on certain products with certain conditions which most be met for it to apply such conditions can be for buyers who pay in cash, buyers who buy in bulks e.g buy 10 get one free, or for every 5 bought you get a 5% discount e.t.c.
This is related to chain discount because its also a series of discount which is allowed for list price of products or services.
Jose's savings account pays 3.25% interest.
He has $1,200 in his account. How much
interest will he earn in 9 months?
Answer:
He will earn $2025
Step-by-step explanation:
1200*3.25=3900
3900-1200=2700
2700/12=225
225*9
Answer:
His interest is $3,900 earn for 9 months.
If m<3 =54°. find each measure.
Answer/Step-by-step explanation:
Given:
m<3 = 54°
m<2 = right angle
a. m<1 + m<2 + m<3 = 180° (angles in a straight line)
m<1 + 90° + 54° = 180° (substitution)
m<1 + 144° = 180°
m<1 = 180° - 144°
m<1 = 36°
b. m<2 = 90° (right angle)
c. m<4 = m<1 (vertical angles)
m<4 = 36° (substitution)
d. m<5 = m<2 (vertical angles)
m<5 = 90°
e. m<6 = m<3 (vertical angles)
m<6 = 54°
f. m<7 + m<6 = 180° (same side interior angles)
m<7 + 54° = 180° (substitution)
m<7 = 180 - 54
m<7 = 126°
g. m<8 = m<6 (alternate interior angles are congruent)
m<8 = 54°
h. m<9 = m<7 (vertical angles)
m<9 = 126°
i. m<10 = m<8 (vertical angles)
m<10 = 54°
j. m<11 = m<4 (alternate interior angles are congruent)
m<11 = 36° (substitution)
k. m<12 + m<11 = 180° (linear pair)
m<12 + 36° = 180° (substitution)
m<12 = 180° - 36°
m<12 = 144°
l. m<13 = m<11 (vertical angles)
m<13 = 36°
m. m<14 = m<12 (vertical angles)
m<14 = 144° (substitution)
find the sum of 2x ÷ x-1 and x÷x-1
Answer with step-by-step explanation:
First of all, ORDER OF OPERATIONS!! 2x/x is 2/1, which is 2. Then, subtract 1, which is 1.
2x ÷ x - 1 = 1
Same thing: x/x = 1. Subtract 1 from 1, which is 0.
x ÷ x - 1 = 0
1 + 0 = 1
Hope this helped!
Jodi bought a new sofa for $1,430, plus fees and insurance. She made paid off the balance in 18 months at $89 per month. How much did she pay in insurance and fees?
Answer:
$172
Step-by-step explanation:
Ok, So $1430 is the total amount PLUS fees and insurance. So 18 months at $89 per month. so do 18*89=1602. $1602-$1430=$172.
So She paid insurance and fees $172.
Zachary bought a baseball for $9.96, a bat for $10.05, and a glove for $19.75. About how much did he pay for the three
items?
$50
$40
$30
$20
Answer:
About 40 DollarsStep-by-step explanation:
9.96 + 10.05 = 20.01
20.01 + 19.75 = 39.76
About 40 Dollars
Hope this helps! <3
Answer:
40$
Step-by-step explanation:
If u add it all together u get 39.76$ and if u round it u get 40$ so 40$
Order from least to greatest.
1/3 ,5/4, 0.85
Answer:
I believe it should be; 1/3, 0.85, 5/4
Answer:
The order from least to greatest of 1/3,5/4,0.85 is. ANSWER: 1/3,0.85,5/4
7th grade math help me plzzzz
Answer:
a. -14
b. -13
c. -5
d. -3
e. -12
f. 0
Step-by-step explanation:
hope it helps
Answer:
A is -14.
B is -13
C is -5
D is -3
E is -12
F is 0
Step-by-step explanation:
A, B, E both numbers are negative so you just add them together and add a negative sign.
C would read 4-9
D 10-7 and add a - to the answer
F is 6-6
The normal distribution An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that x, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months. Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.)
1. If the manufacturer's assumptions are correct, it would reed to replace _______ of its batteries free.
2. The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of ____ results in a 1.07% replacement rate.
3. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
Answer:
1) if the manufacturer's assumptions are correct, it would reed to replace 0.62% of its batteries free.
2) a standard deviation of 6.0843 results in a 1.07% replacement rate
3) using the revised standard deviation for battery life, 91.9% of the manufacturer's batteries don't get free replacement but qualifies for the prorated credit
Step-by-step explanation:
based on the given data;
x will represent the random variable such that the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months
so
x → N( U = 45, ∝ = 5.6)
Under the warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charges to the consumer.
if the battery fails after 31 months but within 54 months, the manufacturer provides a prostrated credit towards the purchase of anew battery
1) If the manufacturer's assumptions are correct,
p(x < 3) = p( [x-u / ∝ ] < [ 31-45 / 5.6] )
= p( z < -2.5 )
using the standard normal table,
value of z = 0.0062 ≈ 0.62%
so if the manufacturer's assumptions are correct, it would reed to replace 0.62% of its batteries free.
2)
The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect, so a standard deviation of ? results in a 1.07%
so lets say;
p ( x < 31 ) = ( 1.07%) = 0.0107
p ( [x-u / ∝ ] < [ 31-45 / ∝] ) = 0.0107
now from the standard table
-2.301 is 1.07%
so
( 31 - 45 / ∝ ) = -2.301
-14 / ∝ = -2.301
∝ = -14 / - 2.301
∝ = 6.0843
therefore a standard deviation of 6.0843 results in a 1.07% replacement rate
3)
Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
p( 31 < x < 54 ) = p ( [31 - u / ∝ ] < [ x-u / ∝] < [ 54 - 45 / ∝] )
= p ( [31 - 45 / 6.0843 ] < [ x-u / ∝] < [ 54 - 45 / 6.0843] )
= p ( -2.301 < z < 1.4792 )
= p(Z < 1.5) - p(Z < -2.3)
= 0.9393 - 0.0108
= 0.919 ≈ 91.9%
therefore using the revised standard deviation for battery life, 91.9% of the manufacturer's batteries don't get free replacement but qualifies for the prorated credit
