Answer:
Let the width of the garden =x meter
Then length=(x+4) meter
Half perimeter =36 m
So perimeter of garden =(2×36)=72 meters
According to the question
⇒2(l+b)=72
⇒2(x+x+4)=72
⇒2x+2x+4=74⇒4x=64⇒x=16 meters
Hence,the width of the garden =16 meters
The length of the garden =(16+4)=20 meters
Which expression is equivalent to 3 square root of x^5*y
Answer:
√3 x^5y
First, let's do √3
√3=1.7
1.7 • x^5 • y
if you want
1.7 • X^4• x• y.
There are tons of equivalent's!
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend
Bean Regular DeCaf
Brazilian Natural 75% 40%
Columbian Mild 25% 60%
Romans sells the regular blend for $3.60 per pound and the Decaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Columbian coffee beans that will enable the production of 1000 pounds of Romans Regular coffee and 500 pound of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Columbian Mild that will maximize the total contribution to profit. What is the optimal solution and what is the contribution profit?
Answer:
z(max) = 2996.13 $
x₁ = 968 x₂ = 430 ( quantities of regular and Decaf coffee respectevely)
Total quantity of BN = 898 pounds
Total quantity of CM = 500 pounds
Step-by-step explanation:
Cost of the beans
Brazilian natural = Price market + 10 % = 0.47 + 0.047
BN Cost = 0.517 $/lb
Clombian Mild = Price market + 10 % = 0.62 + 0.062
CM Cost = 0.682 $/lb
Composition of the coffee blend
Regular coffee 0.75 BN + 0.25 CM
De Caf coffee 0.40 BN + 0.60 CM
PRICES
Regular Roman = 3.60 $
Decaf = 4.40 $
Production costs:
Regular Roman = 0.80 $/lb
Decaf = 1.05 $/lb
Packaging costs: 0.25 $/Lb both
Profit = Price - cost
Profit of regular coffee = 3.60 - 0.80 - 0.25 -Cost of bean
for regular coffee cost of BN + CM
BN is : 0.75*BN cost = 0.75*0.517 = 0.38775 and
CM is : 0.25*0.682 = 0.1705
Profit of regular coffee = 1.99175 $
Profit for Decaf coffee = 4.4 - 1.05 - 0.25 - ( 0.517*0.4 + 0.6*0.682)
Profit for Decaf coffee = 4.4 - 1.30 - 0.616
Profit for Decaf coffee = 2.484 $
Let´s call x₁ pounds of regular coffee and x₂ pounds of Decaf coffee then:
Objective Function is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
Availability of beans for 1000 pounds of Regular coffee means:
750 pounds of BN + 250 pounds of CM
Availability of beans for 500 pounds of Decaf coffee means
200 pounds of BN + 300 pounds of CM
Then 750 + 200 = 900 pounds of BN
And 250 + 300 = 550 pounds of CM
Availability of beans for 1000 pounds of Decaf coffee correspond to
0.75 *x₁ + 0.40*x₂ ≤ 900
Availability of beans for 500 pounds of Regular coffee correspond to
0.25*x₁ + 0.60*x₂ ≤ 500
Then the model is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
0.75 *x₁ + 0.40*x₂ ≤ 900
0.25*x₁ + 0.60*x₂ ≤ 500
General constraints x₁ ≥ 0 x₂ ≥ 0 both integers
After 6 iterations optimal solution ( maximum z) is
z(max) = 2996.13 $
x₁ = 968 x₂ = 430
x₁ and x₂ are quantities of Regular and Decaf coffee respectively, to find out quantities of Brazilian Natural and Colombian Mild
we proceed as follows
Regular coffee is : 0.75*968 = 726 pounds of BN
Decaf coffee is : 0.40*430 = 172 pounds of BN
Total quantity of BN = 898 pounds
Regular coffee is : 0.25*968 = 242 pounds of CM
Decaf coffee is : 0.6*430 = 258 pounds of CM
Total quantity of CM = 500 pounds
What conclusion can be made based on this multiplication problem?
8 × 6 = 48
Eight is 6 times greater than 48.
Eight is 8 times greater than 48.
Forty-eight is 6 times greater than 8.
Forty-eight is 8 times greater than 8.
The linear equation Y = a + bX is often used to express cost formulas. In this equation:_________
a) the b term represents variable cost per unit of activity.
b) the a term represents variable cost in total.
c) the X term represents total cost.
d) the Y term represents total fixed cost.
What is the image point of (1,-2) after a translation right 4 units and down 4units
Answer:
(-4, -1)
Step-by-step explanation:
14 Calculate the mode from the following data: 7,8, 6, 5, 10, 11, 4, 5,2 b. 5: а. 3.' 4 6 с. d: 6
MODE IS THE NUMBER THAT IS REPEATED THE HIGHEST TIME..
HERE, IN YOUR QUESTION 5CAME 2 TIMES i.e. it is repeated highest time .so mode=5....
Four times a number is 88 less than 6 times the number. Find the number.
Answer:
44
Step-by-step explanation:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
The number is 44.
To find the number.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).
Given that:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
Learn more about arithmetic here:
https://brainly.com/question/24163536
#SPJ2
The diagram below is divided into equal parts. Which fraction of the parts is white?
A diagram is divided into 4 blue parts and 3 white parts.
Three-sevenths
Four-sevenths
Three-fourths
Four-thirds
Answer: This problem is a fraction since we have several equal parts that make up one whole. The problem asks us to talk about the relationship of white pieces to the whole. Since we know the whole is made up of 7 pieces (4 blue parts and 3 white parts = 7 total parts), then 7 will be our denominator (number on the bottom of the fraction).
Now that we have our number on the bottom, we need to look back at the question to carefully decide what parts of the whole we are looking at. The question wants to know how many of the parts are white. We know that 3 of the parts are white, so that is our numerator (number of the top of the fraction).
Our final answer is 3/7 or "three-sevenths." Said another way, three of the seven pieces are white.
Step-by-step explanation:
if f(x)=x+8 and g(x)=-4x-3 find (f+g)(x)
Answer:
for this case we have the following functions:
f (x) = x + 8
g (x) = -4x - 3
Subtracting the functions we have:
(f - g) (x) = f (x) - g (x)
(f - g) (x) = (x + 8) - (-4x - 3)
Rewriting:
(f - g) (x) = x + 8 + 4x + 3
(f - g) (x) = 5x + 11
Answer:
D. (f - g) (x) = 5x + 11
How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?
Answer:
The fabric needs 196.4 ft²
Step-by-step explanation:
∵ The tent formed formed from 4 faces
two equilateral triangles with side length 7 ft
two rectangles with dimensions 11 ft and 7 ft
∵ Area equilateral Δ = 1/4 S²√3
∵ Area rectangle = L × W
∴ The area of the prism = 2 × 1/4 × (7)²√3 + 2 × 7 × 11
= 196.4 ft²
Note:
If you find the area of the triangle by the rule 1/2 × base × height
∴ Area Δ = 1/2 × (7) × 6 = 21 ft²
∴ Area tent = 2 × 21 + 2 × 77 = 196 ft²
Two answer very closed
Answer:
273 ft^2 (apparently you have to cover the ground)
Step-by-step explanation:
The quadratic function f(x) = -x2 - 6x - 8 is graphed.
What are the solutions of the quadratic equation 0 =
x2 - 6x - 8?
Ту
2
O 2 and 4
0-2 and 4
0-2 and 4
O: 2 and 4
6 5 A
-3
-1
X
-2
ون
Answer:
-2 and -4
Step-by-step explanation:
When the quadratic equation equals 0, that means when y = 0.
By looking at the graph, whenever y = 0 is when the graph crosses the x-axis.
The graph crosses the x-axis at only two points:
(-4, 0) and (-2, 0)
So the solutions to the graph when -x^2 - 6x - 8 equals 0 is -2 & -4.
Hope it helps (●'◡'●)
Answer:
-2 and -4
Step-by-step explanation:
if you'll notice the function goes through the x axis at -2 and -4
In a random sample of 26 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.23 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value that should be used in constructing the confidence interval is T = 1.316.
The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 26 - 1 = 25
80% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.8}{2} = 0.9[/tex]. So we have T = 1.316
The critical value that should be used in constructing the confidence interval is T = 1.316.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds
The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.
The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.
About 9% of the population has a particular genetic mutation. 900 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 900.
Answer:
The standard deviation is of 8.586.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have a genetic mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
About 9% of the population has a particular genetic mutation.
This means that [tex]p = 0.09[/tex]
900 people are randomly selected.
This means that [tex]n = 900[/tex]
Find the standard deviation for the number of people with the genetic mutation in such groups of 900.
[tex]\sqrt{V(X)} = \sqrt{900*0.09*0.91} = 8.586[/tex]
The standard deviation is of 8.586.
(sec theta - tan theta)²
Answer:
(sec θ - tan θ)²
= sec² θ –2 sec θ tan θ + tan² θ
A decorative wall in a garden is to be built using bricks that are 5 1/2 inches thick and mortar joints are 1/4 inch thick. What is the height of the wall?
Step-by-step explanation:
how many layers of bricks are used ?
also, I assume, the thickness of bricks means actually their height when laid.
but still, I cannot answer that, as nothing indicates if there is only one layer of bricks or 2 or 3 or 4 or ...
The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month constantly for its first year.
a) Find the linear function that models the baby’s weight, W, as a function of the age of the baby, in
months, t.
b) Find a reasonable domain and range for the function W.
c) If the function W is graphed, find and interpret the x- and y-intercepts.
d) If the function W is graphed, find and interpret the slope of the function.
e) When did the baby weight 10.4 pounds?
f) What is the output when the input is 6.2? Interpret your answer.
Warren drives his car 330 miles and has an average of a certain speed. If the average speed had been 3 mph more. he could have traveled 352 miles in the same length
of time. What was his average speed?
Keypad
Answer:
45 miles per hour
Step-by-step explanation:
d=distance in miles
r=rate miles/hr
t = time in hours
t = 352/(r+3)
330/r = 352/(r+3)
352r = 330r + 990
22r = 990
r = 45
A committee raised 7/9 of their target goal last year and another 1/9 of the goal this year. What fraction of their goal has been raised
First, find 40% of 3,000:
0.40 * 3000 = 1200
So they raised 1200 so far.
Now subtract 1200 from the total they want to raise:
3000 - 1200 = 1800
So they need $1,800 more to meet their goal.
Answer:
8iriiruruj
Step-by-step explanation:
u4u the UK. We have a good idea to advertise the UK. I have been a
Think about tossing two coins.
What is
P (H on first coin)? ………………………….
P (H on second coin)? ……………………..
List the paired outcomes for tossing two coins: ………………………………
How many ways are there for two coins to land? ………………………
What is P (HH)? …………………………
Given:
Two coins are tossed.
To find:
1. P(H on first coin)?
2. P(H on second coin)?
3. List the paired outcomes for tossing two coins.
4. How many ways are there for two coins to land?
5. What is P(HH)?
Solution:
If a a coin is tossed, then we have to possible outcomes, i.e., heads (H) and tails (T).
It is given that two coins are tossed.
1. The probability of getting a heads on first coin is:
[tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]
2. The probability of getting a heads on second coin is:
[tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]
3. If two coins are tossed, then the total possible outcomes are:
[tex]\{HH,HT,TH,TT\}[/tex]
4. The number of ways for two coins to land is 4.
5. The probability of the heads on both tosses is:
[tex]P(HH)=\dfrac{1}{4}[/tex]
Therefore, the required solution are:
1. [tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]
2. [tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]
3. List of possible outcomes is [tex]\{HH,HT,TH,TT\}[/tex].
4. Number of possible outcomes is 4.
5. [tex]P(HH)=\dfrac{1}{4}[/tex]
What is the measure of angle b
Answer:
51 ?
Step-by-step explanation:
90-39= 51. I hope its correct
Answer:
51 degrees
Step-by-step explanation:
Well if you look at the picture angle b and the 39 degrees angle together must make a 90 degree angle
90-39 is 51 so therefor angle b must be 51 degrees
Plz get me the correct answer or u will be reported. 15 points for correct answer. Thx.
Answer:
D
Step-by-step explanation:
correct answer, thanks for 15 pts
Answer:
Option D is correct
Step-by-step explanation:
Hope it is helpful....
Sidney's retirement party costs $28, plus an additional $1 for each guest she invites. What is the maximum number of guests there can be if Sidney can afford to spend a total of $44 on her retirement party?
Answer:
16 guests
Step-by-step explanation:
Firstly, we know Sidney's retirement party costs a starting amount of $28. We also know that she can only spend $44 on her retirement party. The easiest way to do it in my opinion is subtract 28 from 44, giving you 16. Since we know that each guest is only $1, we know that the maximum number of guests Sidney can afford is 16 guests. I hope this helped and please don't hesitate to ask for clarification!
$44-$28=$16
$16÷$1=16 guests at most
Question 3
A 70kg patient has approximately 8 pints of blood. The patient donates 470mL of blood.
Approximately what fraction of his body's blood is this? (one pint = 568mL)
Step-by-step explanation:
Given that,
The mass of a patient = 70 kg
A 70kg patient has approximately 8 pints of blood.
The patient donates 470mL of blood.
We know that,
1 pint = 568 mL
8 pints = 4544 mL
Required fraction,
[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]
So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].
Coliform bacteria are randomly distributed in a river at an average concentration of 1 per 20cc of water. What is the variance of the number of Coliform bacteria in a sample of 40cc of water
Answer:
[tex]Var = 1.9[/tex]
Step-by-step explanation:
Given
[tex]p = \frac{1}{20}[/tex] i.e. 1 per 20cc of water
[tex]n = 40[/tex] -- sample size
Required
The variance
This is calculated using:
[tex]Var = np(1 - p)[/tex]
So, we have:
[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]
[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]
[tex]Var = 2 * \frac{19}{20}[/tex]
[tex]Var = \frac{38}{20}[/tex]
[tex]Var = 1.9[/tex]
At the 6th grade school dance, there are 132 boys, 89 girls, and 14 adults. What is the ratio of adults to boys at the school dance?
Answer:
14 to 132
Step-by-step explanation:
We are given that there are 132 boys and 14 adults. Since the question is only asking for the ratio of adults to boys, we don't have to worry about the number of girls in this question. From here, we see that the question is asking for the ratio of adults to boys, so we put it in that exact order. Our answer is 14 to 132. I hope this helps and please don't hesitate to reach out with more questions!
The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? (Round your answer to two decimal places.) x1 = 10 cos(2t), y1 = 6 sin(2t) First object x2 = 4 cos(t), y2 = 4 sin(t) Second object t = π/2
Answer:
- [tex]\frac{4}{\sqrt{29} }[/tex]
Step-by-step explanation:
The equations for the 1st object :
x₁ = 10 cos(2t), and y₁ = 6 sin(2t)
2nd object :
x₂ = 4 cos(t), y₂ = 4 sin(t)
Determine rate at which distance between objects will continue to change
solution Attached below
Distance( D ) = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]
hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]
a linear model is appropriate for the data in which scatterplot.?
Answer: (b) or 2
Step-by-step explanation: its the only one linear to the best possibility.
The solution set of the inequality 1 + 2y
Answer:
is it four I am not quite sure
Mark purchashed 3 giant jawbreakers at 75cents each.he also bought 1/4 pound of hot tamales.which sell for $2.76 a pound.he gave the clerk a $5 bill.how much change did mark recieve? Whith his change,mark decided to buy 1/2 pound of m&ms at $3.24 a pound.how much money does mark have left?
Answer: $0.44
Step-by-step explanation: a) (3 * 0.75) + ((1/4)*2.76) = 2.25 + 0.69 = 2.94
Pays with $5 - $2.94 = $2.06 Change
((1/2) * 3.24) = $1.62
Money left = 2.06 - 1.62 => $0.44
(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 2 to each of the following.
(i) 2 to 3
(ii) 2 to 2.5
(iii) 2 to 2.1
(b) Find the instantaneous rate of change when r =2.
Answer:
ai) 5pi
aii) 4.5pi
aiii) 4.1pi
b) 4pi
Step-by-step explanation:
a) Area of a circle is given by pi×r^2.
The average rate of change of the area of a circle from r=b to r=a is (pi×b^2-pi×a^2)/(b-a).
Let's simplify this.
Factor pi from the terms in the numerator:
pi(b^2-a^2)/(b-a)
Factor the difference of squares in the numerator:
pi(b-a)(b+a)/(b-a)
"Cancel" common factor (b-a):
pi(b+a).
So let's write a conclusive statement about what we just came up with:
The average rate of change of the area of a circle from r=b to r=a is pi(b+a).
i) from 2 to 3 the average rate of change is pi(2+3)=5pi.
ii) from 2 to 2.5 the average rate of change is pi(2+2.5)=4.5pi.
from 2 to 2.1 the average rate of change is pi(2+2.1)=4.1pi.
b) It looks like a good guess at the instantaneous rate of change is 4pi following what the average rate of change of the area approached in parts i) through iii) as we got closer to making the other number 2.
Let's confirm by differentiating and then plugging in 2 for r.
A=pi×r^2
A'=pi×2r
At r=2, we have A'=pi×2(2)=4pi. It has been confirmed.
