Answer:
Assuming the length to be x and the width to be y.
Since the area is 64cm, hence
x*y = 64 (equation 1)
Since the perimeter is 40cm, hence
x + x + y + y = 40
2x + 2y = 40
2(x + y) = 2(20)
x + y = 20 (equation 2)
Hence by using simultaneous equation,
x = 20 - y (equation 3)
Substituting equation 3 into equation 1, we get
(20-y)*y=64
20y-y^2=64
Tidying up the equation,
y^2 - 20y + 64 = 0
By using factorisation,
(y-16)(y-4)=0
y=16 or y=4
By substituting y=16 into equation 1,
x*16=64
x = 4
By substituting y = 4 into equation 1,
x*4=64
x=16
Therefore,
The length is 4 cm while the width is 16 cm.
OR
The length is 16 cm while the width is 4cm.
Hope this helps!!
Grafting, the uniting of the stem of one plant with the stem or root of another, is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with a hardy root system. For example, most sweet oranges grow on trees grafted to the root of a sour orange variety. Suppose each graft fails independently withprobability 0.3. Five grafts are scheduled to be performed nextweek. Let X deonte the number of graftes that will fail nextweek.
a. The random variable x is (choose one): binomial, hypergeometric, negative binomial, poisson.
b. Give the sample space and pmf of x.
c. give the expected value and variance of x.
d. Suppose that the cost of each failed graft is $9.00. Find:
i. The probability that the cost from failed grafts will exceed $20.00.
ii. The expected and the variance of the cost from failed grafts.
Step-by-step explanation:
a. The random variable is a binomial distribution.
b. the sample space, X = {0, 1, 2, 3, 4, 5}
the pmf
we solve for this using
nCx * P^x * (1-p)^n-x
n = 5
p = 0.3
for x = 0
5C0 * 0.3⁰(1-0.3)^5-0
= 1 * 1* 0.7⁵
= 0.16807
for x = 1
5C1*0.3¹(1-0.3)^5-1
= 5*0.3(0.7)⁴
= 5x0.3x0.2401
= 0.36015
for x = 2
5C2 * 0.3² * (1-0.3) ^5-2
= 0.30870
for x = 3
5C3 * 0.3³ * (1-0.3) ^ 5-3
= 10 * 0.027 * 0.7²
= 0.1323
for x = 4
5C4 * 0.3⁴ (1-0.3) ^ 5-4
= 5 * 0.0081 * 0.7
= 0.02835
for x = 5
5C5 *0.3⁵ (1- 0.3) ^5-5
= 1*0.00243*0,7⁰
= 0.00243
c. E[X] = N*p = 5*0.3 = 1.5
var[X] = np(1-p) = 5*0.3*0.7 = 1.05
d. 20/9 = 2.222
so we have that if x is greater than or equal to 3, cost will exceed 20
p(x=3) + p(x=4) + p(x=5)
= 0.1323 + 0.02835 + 0.00243
probability = 0.16308
E[C] = 1.5 * 9 = 13.5
VAR[C] = 1.05 * 9 = 9.45
Consider the following IP problem.
Max z = 5x1+x2
s.t. − x1 + 2x2 ≤ 4
x1 − x2 ≤ 1
4x1 + x2 ≤ 12
x1,x2 ∈Z+
1. Solve graphically
2. Solve the LP relaxation of the problem graphically. Round this solution to the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i.e., by rounding each non-integer value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate z. Are any of these feasible rounded solutions optimal for the IP problem?
Answer:
See Annex
Step-by-step explanation:
The relaxation of any Linear Programming problem, consists of eliminating the integer constraint condition, keeping the original constraint and the objective function, solving the problem as continuous variables. If in such new condition we find that optimal solution consist of integer solution we have found optimal solution already, if not we need to go ahead with the branching procedure of making variables integer above and down of the fractional values.
In this particular case ( see GeoGebra graphic solution attached changing x₁ and x₂ by x and y respectively ), and Objective Function in red we got integer solution :
z(max) = 11
x₁ = x = 2
x₂ = y = 1
Simplify : -sqrt(9+y)^2 if y<-10
Answer:
−y−9
Step-by-step explanation:
Answer:
9+y is the correct answer
Step-by-step explanation:
Write an equation, and solve. Round your answer to the nearest cent.
If 3 oz of granola costs $3.03, find the cost of 16 oz of granola.
The cost of 16 oz of granola should be $
Answer:
The cost of 16 oz of granola should be $16.16
Step-by-step explanation:
Given that,
The cost of 3 oz of granola is $3.03
We need to find the cost of 16 oz of granola..
As 3 oz = $3.03
1 oz = (3.03/3) = $1.01
The cost of 16 oz will be :
16 oz = 16×1.01
= $16.16
Hence, the cost of 16 oz of granola should be $16.16.
8b + 32
b=7
also an expression equivalent to 8b + 32 and why
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter .to the nearest meter ,how many meters are in 241 inches ?
Answer:
6.12 meters
Step-by-step explanation:
find the cost of fencing a rectangular field 250m long and 130m wide at rupees 30 per meter
Answer:
length of rectangular =250m
breath =130m
perimeter of rectangular field =(130*250)
=32500m
cost of fencing a rectangular field at the rate of 30 per meter
cost of the rectangular field =32500*30
=rupees 975000
hope it helps
[tex]if x^2 = 17x + y \: and \: y {}^{2} = 17y + x \: then \: find \sqrt{x {?}^ + {y { }^{2} + 1 } } [/tex]
Answer:
Bro wat
Step-by-step explanation:
3 units to the right of 8 answer
Answer:
11
Step-by-step explanation:
If you're at 8 and move 3 to the right in a number line, you would end up at 11.
Triangle ABC is inscribed in a circle O. What is the measure of Angle A?
Answer:
answer is 40 degree
Step-by-step explanation:
hope it helps!!!
What number in Arabic numerals is Roman numeral MCMXLI
(Enter numeric value only.)
Answer:
1941
Step-by-step explanation:
Hope this helped!!!
1,1,1,2,2,2,2,3,4,4,5,7,8,12,14 what's the median mode and the and range for these numbers
Answer:
median: 3
mode: 2 (appeared 4 times)
range: 13
Step-by-step explanation:
What is the decimal equivalent of the fraction 8/15?
0.53
_
0.53
Show work!!
9514 1404 393
Answer:
0.533... (repeating)
Step-by-step explanation:
You will notice that the division problem repeats when the quotient digit is 3. The decimal equivalent is a repeating decimal with a 1-digit repeat. That digit is 3.
[tex]\dfrac{8}{15}=0.5\overline{3}[/tex]
Answer:
0.5333333…. (3 repeated)
Step-by-step explanation:
8 goes on the inside of the house and 14 on the outside
*Not my handwriting. A friend wrote it and I did the math*
The supermarket sells juice in 16- and 32-ounce bottles. If Warren wants to bring home 144 ounces of juice in 7 separate bottles, which system of equations should he solve to determine how many 16- and 32-ounce bottles to buy? (Let x represent the number of 16-ounce bottles and y represent the number of 32-ounce bottles.)
A. 32x+16y=144 x+y=7
B. 16x+32y=144 x+y=7
C. 32x+16y=144 x+y=144
D. 16x+32y=7 x+y=32
Refer to the table below to answer problems 25-27.
(TABLE) Mark's Personal Running Records Distance Time (minutes:seconds)
1/4 mile: 0:58
1/2 mile: 2:12
1 mile: 5:00
If Mark set his 1-mile record by keeping a steady pace, then what was his 1/2 -mile time during the 1-mile run?
Answer:
it will be 2:50
Step-by-step explanation:
Measuring your fitness level regularly is one way to find out if you're making progress. Most fitness centers have trained staff who can evaluate your body composition, muscular strength and endurance, flexibility, and cardiovascular endurance, but it can be pricey. If you don’t have access to all the toys and tools of your gym, don’t panic. You have everything you need to measure your fitness level in your own house!
This One-Mile Walking Test measures your aerobic (cardiovascular) fitness level based on how quickly you are able to walk a mile at a submaximal (moderate) exercise intensity.
Assume that it is equally likely for a child to be born a boy or a girl, and that the Lin family is planning on having three children. List the elements of the event that the Lins have at least one girl. (Use B to represent boy, and G to represent girl. For example, if there are three girls born, it would be represented as GGG).
Answer:
[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]
Step-by-step explanation:
Given
[tex]Children = 3[/tex]
Required
List all cases of having at least 1 girl
We have:
[tex]B = Boy[/tex]
[tex]G = Girl[/tex]
For 1 girl, we have:
GBB; BGB; BBG
For 2 girls, we have:
GGB; BGG; GBG
For 3 girls, we have:
GGG
Hence, the list is:
[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]
Will give the brainliest answer and 20 points to anyone who can give a complete answer and not a scam link or a joke answer or begging for points (those 3 types of answers will be reported)
A grocery store manager notices that this month her store sold a total of 571 gallons of ice cream, which represents a decrease of 18% from last month. How much ice cream did the store sell last month? Round your answer to the nearest integer.
The store sold ____________ gallons of ice cream last month.
Answer:
673.8
Step-by-step explanation:
Need some help on this question
Answer:
9.We know that
6 × 3 = 2 × x
18 = 2x
x = 9
I will give the BRAINEST
State how many solutions each equation has.
x2
-100
5x2
1
6x2 + 17 = 11
7 (x² + 6)
42
Answer:
-100x4xx=17xStep-by-step explanation:
goodluck
The percentage of students in the school that attended the talent show for the years 2008 to 2013 are shown
2008: 86%
2009: 89%
2010: 93%
2011: 85%
2012: 92%
2013: 95%
This year, the school has a total of 360 students. How many students will attend the talent show this year (in %)
The school has a total of 360 students. The number of students that would attend this year is 357.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
The percentage of students in the school that attended the talent show for the years 2008 to 2013 is shown
2008: 86%
2009: 89%
2010: 93%
2011: 85%
2012: 92%
2013: 95%
Number of students that would attend this year
= percentage of students that attended in 2013 x total number of students
[tex]= \frac{94}{100} \times 380\\= 357.2[/tex]
Thus, 357 to the nearest whole number.
Learn more about percentages;
https://brainly.com/question/13450942
#SPJ2
Change to slope-intercept form. Then find the y-intercept, first point, and second point.
x + 3y > 9
slope intercept form
y -Intercept
first point (let x=0)
second point
Answer:
[tex]x + 3y > 9 \\ 3y > - x + 9 \\ y > - \frac{1}{3} x + 3 \\ y - intercept \: is \: 3 \\ first \: point = 3 \\ second \: point \: = 9[/tex]
4x+2y=16
3x+4y=17
i need help
Answer:
x = 3 , y = 2
Step-by-step explanation:
Pls answer fast and will mark brainliest.
Answer: b 5 calories per minute
Step-by-step explanation: you can see that the graph starts at 0 and at the one at the bottom it goes to 5 and then 10 for 2 minutes and so on
Which expression is equivalent to..
plz help for a brainly
Answer:
364yd^2
Step-by-step explanation:
LxWxH
Answer:
its 364
Step-by-step explanation:
you do length times width times height
A bag contains 5 red marbles, 8
green marbles, 6 orange marbles, and
11 yellow marbles. What is the
probability of randomly choosing
an orange marbles
Answer:
1/5
Step-by-step explanation:
First you need to find the total amount of marbles
5+8+6+11= 30
There are 6 orange marbles
So the probability is 6/30 which reduces to 1/5
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answer:
.764
Step-by-step explanation:
do it on a calculator (TI84)
Answer:
45.6°
Step-by-step explanation:
take the inverse cosine of 7/10: [tex]cos^{-1}(\frac{7}{10})[/tex]
plug it into a graphing calc and you get ≈ 45.573°, they want 1 decimal place so it would be ≈ 45.6°
This trapezoid-based right pyramid has a volume of 48 m3 what is the area?
Answer:
18m^3
Step-by-step explanation:
Khan Academy, It shows how to do the steps
VWXY is a parallelogram. Find the value of n.
Help meeee
Answer:
3.5
Step-by-step explanation:
n+7=3n
7=2n
n=3.5
Answer:
n=7/2
Step-by-step explanation:
n+7=3n
-n -n
7=2n
/2 /2
7/2=n
Which phrase is a description of 7t-3?
