Answer:
Step-by-step explanation:
Nelson grows tomatoes and sells them at a nearby farmers roadside stand.
Let x = number of tomatoes sold
Let m = amount of money made for selling x tomatoes.
He sells them for $2.50 each. This means that he sells x tomatoes for 2.5×x = $2.5x
The farmer charges him $15 a day to use the stand. This means that he pays a constant amount of $15 each day.
Amount of money that Nelson will make will be total amount made in selling x tomatoes minus the constant amount being paid for rent. It becomes
m = 2.5x - 15 This is the general form. In the factored form, it will be
m = 2.5(x+6)
A Hospital/Surgical Expense policy was purchased for a family of four in March of 2013. The policy was issued with a $500 deductible and a limit of four deductibles per calendar year. Two claims were paid in September 2013, each incurring medical expenses in excess of the deductible. Two additional claims were filed in 2014, each in excess of the deductible amount as well. What would be this family's out-of-pocket medical expenses for 2013?
Answer:
The answer is $1000.
Step-by-step explanation:
The policy was issued with a $500 deductible and a limit of four deductibles per calendar year.
As given that two claims were paid in September 2013, each incurring medical expenses in excess of the deductible.
So, the family's out-of-pocket medical expenses for 2013 will be :
[tex]500+500=1000[/tex] dollars
As the limit was up to 4 deductibles in a calendar year, and in 2013, there were 2 claims, so that sums up to be $1000.
The family's out-of-pocket medical expenses for 2013 would be $1000, as they paid the $500 deductible for each of the two claims made that year, with their health insurance policy limiting to four deductibles per year.
Explanation:The subject of the question involves calculating the out-of-pocket medical expenses for a family under their health insurance policy, which includes understanding how deductibles work. In the scenario given, the family purchased a policy with a $500 deductible and a limit of four deductibles per calendar year. In 2013, they made two claims where each exceeded the deductible amount. Therefore, their out-of-pocket expenses for 2013 would be two times the deductible amount, since the policy has a limit of four deductibles per year but only two claims were filed and paid within that year.
Mathematically, this can be calculated as:
Claim 1 in September 2013: $500 (deductible)Claim 2 in September 2013: $500 (deductible)Total out-of-pocket expenses for 2013: $500 + $500 = $1000.
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For each cost function (given in dollars), find (a) the cost,average cost, and marginal cost at a production level of 1000units; (b) the production level that will minimize the averagecost; and c) the minimum average cost.C(x)= 16,000x + 200x+ 4x3/2
Answer:
a) $342,491
$342.491
$389.74
b) $400
c) $320
Step-by-step explanation:
the cost function = C(x)
C(x) = 16000 + 200x + 4x^3/2
a) when we have a unit of 1000 unit, x= 1000
C(1000) = 16000 + 200(1000) + 4(1000)^3/2
= 16000 + 200000 + 126491
= 342,491
Cost = $342,491
Average cost= C(1000) / 1000
= 342,491/1000
= 342.491
The average cost = $342.491
Marginal cost = derivative of the cost
C'(x) = 200 + 4(3/2) x^1/2
= 200 + 6x^1/2
C'(1000) = 200 + 6(1000)^1/2
= 389.74
Marginal cost = $389.74
Marginal cost = Marginal revenue
C'(x) = C(x) / x
200 + 6x^1/2 = (16000 + 200x + 4x^3/2) / x
200 + 6x^1*2 = 16000/x + 200 +4x^1/2
Collect like terms
6x^1*2 - 4x^1/2 = 16000/x + 200 -200
2x^1/2 = 16000/x
2x^3/2 = 16000
x^3/2 = 16000/2
x^3/2 = 8000
x = 8000^2/3
x = 400
Therefore, the production level that will minimize the average cost is the critical value = $400
C'(x) = C(x) / x
C'(400) = 16000/400 + 200 + 4(400)^1/2
= 40 + 200 + 80
= 320
The minimum average cost = $320
If a cup of coffee has temperature 95∘C in a room where the temperature is 20∘C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t)=20+75e−t/50. What is the average temperature (in degrees Celsius) of the coffee during the first half hour?
Answer:
61°C
Step-by-step explanation:
Newton's Law of cooling gives the temperature -time relationship has:
T (t) = 20 + 75 е⁻(t/50)-------------------------------------------------------- (1)
where Time is in minutes (min) & Temperature in degree Celsius (°C)
During the first half hour, t = 30 mins
Substituting into (1)
T = 20 + 75 е⁻(30/50)
= 20 + 75(0.5488)
= 20 + 41.16
= 61.16°C
≈ 61°C
Plz explain and prove the triangles congruence.
Answer:
(3) ∠BCA ≅ ∠DAC
Step-by-step explanation:
BC and AD are parallel. AC is a transversal line passing through both lines. That means ∠BCA and ∠DAC are alternate interior angles. Therefore, they are congruent.
2 questions geometry :) thanks if you answer
Answer:
Part 1) An expression for the x-coordinate of T is (a+2)
Part 2) The value of x=39 ft (see the explanation)
Step-by-step explanation:
Part 1)
step 1
we know that
The rule of the reflection of a point across the x-axis is equal to
[tex](x,y) -----> (x,-y)[/tex]
Apply the rule of the reflection across the x-axis to the Q coordinates
Q (a,b) ----------> Q'(a,-b)
step 2
The translation is 2 units to the right
so
The rule of the translation is
(x,y) ----> (x+2,y)
Apply the rule of the translation to the Q' coordinates
Q'(a,-b) -----> T(a+2,-b)
therefore
An expression for the x-coordinate of T is (a+2)
Part 2)
we know that
A reflection is a rigid transformation, the image is the same size and shape as the pre-image
In this problem the floor plan house A and the floor house B have the same size and shape
That means that its corresponding sides and corresponding angles are congruent
therefore
The value of x=39 ft
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent
Answer: These events are dependent.
Step-by-step explanation: The probability of the second woman getting a pink rose is affected by the first woman getting a pink rose as the pink rose obtained by the first woman was not replaced. Hence there are less pink roses in the flower vase and hence lower probability that the second woman gets a pink rose. These events are thus dependent.
Answer:
Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
Step-by-step explanation:
A particle whose mass is 4 kg moves in xyplane with a constant speed of 2 m/s in the positive x-direction along y = 6 m. Find the magnitude of its angular momentum relative to the point (x0, y0), where x0 = 0.9 m and y0 = 10 m. Answer in units of kg m2 /s.
The magnitude of the angular momentum of the particle relative to the point (0.9 m, 10 m) is [tex]{\text} 32.8 kg m^2/s[/tex].
Angular momentum is a physical quantity that measures the rotational motion of an object or system.
Given:
Mass = 4 kg,
velocity = 2 m/s
The following equation provides the particle's angular momentum (L):
L = mvr
where:
m = mass
v = velocity of the particle
r = perpendicular distance
To find the magnitude of the angular momentum relative to the point point [tex](x_0, y_0)[/tex], where [tex]x_0[/tex] = 0.9 m and [tex]y_0[/tex] = 10 m.
To find the perpendicular distance (r), use the distance formula:
[tex]r = \sqrt{((x - x0)^2 + (y - y0)^2)[/tex]
Substituting the values [tex]x_0[/tex] = 0.9 m and [tex]y_0[/tex] = 10 m in above formula
[tex]r = \sqrt{((0 - 0.9)^2 + (6-10)^2)[/tex]
= [tex]\sqrt{((-0.9)^2 + (-4)^2)[/tex]
= √(0.81 + 16)
= √16.81
= 4.1 m
Now, the angular momentum (L) using the formula:
L = mvr
L = 4 kg x 2 m/s x 4.1 m
L = 32.8 kg
As a result, the particle's angular momentum is [tex]{\text} 32.8 kg m^2/s[/tex].
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The magnitude of the angular momentum relative to a point (x0, y0) depends on the moment of inertia and angular velocity of the particle. However, in this case, the angular velocity is undefined, so the magnitude of the angular momentum is also undefined.
Explanation:The angular momentum of a particle can be calculated by multiplying its moment of inertia with its angular velocity. In this case, the particle has a mass of 4 kg and moves with a constant speed of 2 m/s in the positive x-direction. To find the magnitude of its angular momentum relative to the point (x0, y0), we need to calculate the moment of inertia and angular velocity. Since the particle is moving in the xy-plane, we can calculate the distance of the particle from the point (x0, y0) and use it to find the angular momentum. The magnitude of the angular momentum can be calculated by dividing the cross product of the position vector and linear momentum with the mass of the particle.
First, let's calculate the moment of inertia (I) of the particle. The moment of inertia can be calculated using the formula I = mr², where m is the mass of the particle and r is the distance of the particle from the axis of rotation. In this case, the particle is moving in the xy-plane, so the distance of the particle from the point (x0, y0) can be calculated using the distance formula: d = sqrt((x-x0)² + (y-y0)²). Substituting the values, we have d = sqrt((0-0.9)² + (6-10)²) = sqrt(13.21) = 3.63 m. The moment of inertia can be calculated as I = 4 kg * (3.63 m)² = 52.60 kg*m².
Next, let's calculate the angular velocity (ω) of the particle. The angular velocity can be calculated using the formula ω = v/r, where v is the linear velocity of the particle and r is the distance of the particle from the axis of rotation. In this case, the particle has a constant speed of 2 m/s in the positive x-direction along y = 6 m, so the distance of the particle from the axis of rotation is the distance from the point (0, 6). Substituting the values, we have r = sqrt((0-0)² + (6-6)²) = sqrt(0) = 0 m. The angular velocity can be calculated as ω = 2 m/s / 0 m = undefined. Since the angular velocity is undefined, the magnitude of the angular momentum relative to the point (x0, y0) is also undefined.
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After a storm damages the community center, Shanika and her friends hold fundraising events to help pay for repairs. After the first event, they raise $240, which is 10% of the total amount that they want to raise. What is the total amount of money that Shanika and her friends want to raise?
Answer:Shanny and her friends wanted to raise $2400
Step-by-step explanation:
Fundraising events were held by Shanika and her friends to help pay for repairs.
Let x = the total amount of money that Shanika and her friends want to raise during the fund raising events. After the first event, they raise $240,which is 10% of the total amount that they want to raise. This means that after the first event, they raised 10/100 ×x = 0.1x
This 0.1x that they raised is equal to $240. Therefore,
0.1x = 240
x = 240/0.1 = 2400
Shanny and her friends wanted to raise $2400
Answer:
$2,400 is the correct answer
Step-by-step explanation:
A manufacturer knows that their items have a normally distributed length, with a mean of 7.1 inches, and standard deviation of 1.7 inches.Round your answer to four decimals.If 24 items is chosen at random, what is the probability that their mean length is less than 6.2 inches?
Answer: 0.0047
Step-by-step explanation:
Given : A manufacturer knows that their items have a normally distributed length, with a mean of 7.1 inches, and standard deviation of 1.7 inches.
i.e. [tex]\mu=7.1\text{ inches}[/tex]
[tex]\sigma=17\text{ inches}[/tex]
Sample size : n= 24
Let [tex]\overline{X}[/tex] be the sample mean.
Formula : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Then, the probability that their mean length is less than 6.2 inches will be :-
[tex]P(\overline{x}<6.2)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{6.2-7.1}{\dfrac{1.7}{\sqrt{24}}})\\\\\approx P(z<-2.6)\\\\=1-P(z<2.6)\ \ [\because\ P(Z<-z)=1-P(Z<z)]\\\\=1-0.9953=0.0047\ \ \ [ \text{Using z-value table}][/tex]
hence,. the required probability = 0.0047
Answer:
0.0047
step-by-step explanation
pls help me finna mark brainliest
The right answer is Option D.
Step-by-step explanation:
Given,
Total people surveyed = 250
Total people who prefer sports channel= 62
Percent of people who prefer sports channel;
Percent = [tex]\frac{people\ who\ prefer\ sports\ channel}{Total\ no.\ of\ people\ surveyed}*100[/tex]
[tex]Percent=\frac{62}{250}*100\\\\Percent=\frac{6200}{250}\\\\Percent= 24.8\%[/tex]
24.8% of everyone surveyed preferred sports channel.
The right answer is Option D.
Keywords: percentage, division
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Find the area of a triangle with the given vertices.
Part I: Graph the following points on the coordinate grid below.
(1, -3), (3, -1), (5, -3)
Part II: Find the area of the triangle. Show your work.
Answer:
the area of the triangle is 4 square units.
Step-by-step explanation:
Plotting the points, we can see that the triangle is isosceles lying in the 4th quadrant of graph.
we can break the triangle in 2 similar right angled triangles,
each with base 2 and height 2 units.
area of triangle is given by the formula,
A= [tex](\frac{1}{2})(base)(height)[/tex]
thus, A= [tex](\frac{1}{2})(2)(2)[/tex]
A=2 square units.
there are 2 such triangles,
thus total area is 4 square units.
No yes no @ 90, 9, 0,-90,-9 @ 25, 11, -8, -7, -15 @ 4, 2, 0, -2, -4, -42 MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E Em56 O Creative Publications 4-R - 34-M
Answer:
Step-by-step explanation:
what?
orest fire covers 2008 acres at time t equals 0. The fire is growing at a rate of 8 StartRoot t EndRoot acres per hour, where t is in hours. How many acres are covered 24 hours later? Round your answer to the nearest integer.
Answer: There are 2635 acres covered 24 hours later.
Step-by-step explanation:
Since we have given that
At time t = 0, number of acres forest fire covers = 2008 acres
We first consider the equation:
[tex]A=\int\limits^t_0 {8\sqrt{t}} \, dt\\\\A=8\dfrac{t^{\frac{3}{2}}}{\frac{3}{2}}+C\\\\A=\dfrac{16}{3}t^{\frac{3}{2}}+C[/tex]
At t=0, A= 2008
So, it becomes,
[tex]2008=C[/tex]
So, now it becomes,
[tex]A=\dfrac{16}{3}t^{\frac{3}{2}}+2008\\\\At\ t=24,\\\\A=\dfrac{16}{3}(24)^{\frac{3}{2}}+2008\\\\A=2635.06[/tex]
Hence, there are 2635 acres covered 24 hours later.
A manufacturer knows that their items have a normally distributed length, with a mean of 10.9 inches, and standard deviation of 1.2 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?
Answer:
The probability that their mean length is less than 11.2 inches is 0.5987
Step-by-step explanation:
Mean = 10.9 inches
Standard deviation = 1.2 inches
We are supposed to find If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches
Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]
We are supposed to find P(x<11.2)
[tex]Z=\frac{11.2-10.9}{1.2}[/tex]
[tex]Z=0.25[/tex]
Refer the z table for p value
p value = 0.5987
Hence the probability that their mean length is less than 11.2 inches is 0.5987
A submarine let Hawaii two hours before an aircraft carrier. The vessels traveled in opposite directions. The aircraft carrier traveled at 25 mph for nine hours. After this time the vessels were 280 miles apart. Find the submarines speed.
Answer: the speed of the submarine is 5miles per hour
Step-by-step explanation:
The submarine left Hawaii two hours before the aircraft carrier.
Let x = the speed of the submarine
The aircraft carrier traveled at 25 mph for nine hours.
After this time the vessels were 280 miles apart. This means that when they became 280 miles apart, the aircraft carrier has travelled for 9 hours. If the submarine was ahead of the aircraft carrier with 2 hours, that means that the submarine travelled 9 + 2 = 11 hours
Distance travelled = speed × time
Distance travelled by submarine will be 11 × x = 11x miles per hour
Distance travelled by aircraft carrier will be 25 × 9 = 225 miles per hour
If they are 280 miles apart, this would be their total distance. Therefore,
225 + 11x = 280
11x = 280 - 225 = 55
x = 55/11 = 5miles per hour
To find the submarines speed, we can set up an equation using the given information and solve for the unknown variable. The speed of the submarine is found to be 5 mph.
Explanation:To solve this problem, we need to set up an equation using the information given. Let's denote the speed of the submarine as 's'. The submarine traveled for two hours longer than the aircraft carrier, so the total time traveled by the submarine is '9 + 2 = 11' hours. The total distance between the vessels is given as 280 miles.
To find the speed of the submarine, we can use the formula: Distance = Speed * Time. Plugging in the given values, we can write the equation as: 280 = (25 mph * 9 hours) + (s mph * 11 hours).
Simplifying the equation gives us: 280 = 225 + 11s. Subtracting 225 from both sides gives us: 55 = 11s. Dividing both sides by 11 gives us: s = 5.
Therefore, the speed of the submarine is 5 mph.
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Give the coordinates for the image of R (0, -5) E (4, -3) C (6, -5) T (2, -7) when it is reflected across the line y = x.
Answer:
Below.
Step-by-step explanation:
The x and y coordinates flip with this reflection e, g (2, 1) goes to (1, 2).
So R (0, -5) ---> R' (-5, 0).
E (4, -3) ---> E' (-3, 4).
C (6, -5) ---> C' (-5, 6).
T (2, -7) ---> T' (-7, 2).
can anyone help me? I've been stuck with this problem for hours
Answer:
336.02 square centimeters
Step-by-step explanation:
The surface area is the area of all the surfaces of the prism shown.
The prism has 7 surfaces.
Top and Bottom are pentagons with side lengths of 5.
The other 5 side surfaces are rectangles with length 10 and width 5.
Note the formulas of area of pentagon and area of rectangle below:
Area of Rectangle = Length * Width
Area of Pentagon = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2[/tex] , where a is the side length
Lets find area of each of the surfaces:
Top Surface (Pentagon with side length 5) = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2=\frac{1}{4}\sqrt{25+10\sqrt{5} }* (5)^2=43.01[/tex]
Bottom Surface = same as Top Surface = 43.01
Side Surface (rectangle with length 10 and width 5) = 10 * 5 = 50
There are 5 side surfaces that are each 50 sq. cm. so area would be:
Area of 5 Side Surface = 5 * 50 = 250
Total Surface Area = 250 + 43.01 + 43.01 = 336.02 square centimeters
A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% CI for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.
Answer:345
Step-by-step explanation:
Final answer:
To construct a 99% confidence interval for the calorie content of the energy bars, calculate the standard error, find the appropriate t-value, then compute the margin of error, and add and subtract it from the sample mean. The resulting 99% CI for the true mean calorie content is approximately (214.59, 245.41) calories.
Explanation:
To construct a 99% confidence interval (CI) for the true mean calorie content of the chocolate energy bars, we will use the sample mean, the sample standard deviation, and the t-distribution since the sample size is small. Given are the sample mean (×) is 230 calories, the sample standard deviation (s) is 15 calories, and the sample size (n) is 10.
Steps to follow:
Identify the appropriate t-value for the 99% CI, which corresponds to a two-tailed test with 9 degrees of freedom (n-1). From the t-distribution table, this value is approximately 3.25.
Calculate the standard error (SE) of the mean by dividing the standard deviation by the square root of the sample size: SE = s / √n = 15 / √10 ≈ 4.74.
Multiply the t-value by the SE to get the margin of error (ME): ME = t * SE ≈ 3.25 * 4.74 ≈ 15.41.
Finally, subtract and add the ME from the sample mean to get the lower and upper bounds of the CI: (× - ME, × + ME) = (230 - 15.41, 230 + 15.41) = (214.59, 245.41).
Therefore, the 99% confidence interval for the true mean calorie content is approximately (214.59, 245.41) calories.
Explanation of a 95% CI: A 95% confidence interval means that if we were to take 100 different random samples from the population and construct a CI for each using the same method, approximately 95 of these intervals would contain the true population mean.
There were 90 people at a party. There were four more men than women and there were 10 more children than adults now many men women and children were at the party?
Answer:
288
Step-by-step explanation:
Answer: 50 children
18 women
22 men
Step-by-step explanation:
There were 90 people at a party. The persons consists of men, women and children. The men and women are adults.
Let m = number of men at the party
Let w = number of women at the party
Let c = number of children at the party
There were four more men than women. It means
w = m - 4
There were 10 more children than adults. It means
m + w + 10 = c
c = m + w + 10
Substituting w = m- 4 into the above equation, it becomes
c = m + m- 4 + 10 = 2m+ 6
Note: adults = sum of men and women
There were 90 people at a party. It means
m + w + c = 90
Substituting c = 2m+6 and w = m-4, it becomes
m + m-4 + 2m+6 = 90
4m = 90 - 18 = 88
m = 88/4= 22
w = m- 4 = 22-4
w = 18
c = 2m + 6 = 44 + 6 = 50
c = 50
The first term of an arithmetic sequence is equal to four and the common difference is three. find the formula for the value of the nth term
The formula for the value of nth term is [tex]a_{n}[/tex] = 3n + 1
Step-by-step explanation:
The formula of the nth term in the arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first term of the sequenced is the common difference between each two consecutive terms∵ The first term of an arithmetic sequence is equal to four
∴ a = 4
∵ The common difference is equal to three
∴ d = 3
- Substitute these values in the rule of the nth term
∵ [tex]a_{n}=a+(n-1)d[/tex]
∴ [tex]a_{n}=4+(n-1)3[/tex]
- Simplify it
∴ [tex]a_{n}=4+3n-3[/tex]
∴ [tex]a_{n}=1+3n[/tex]
The formula for the value of nth term is [tex]a_{n}[/tex] = 3n + 1
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A 150 km trip was covered by a motorcycle going at an average speed of 75 km/h, by a bus doing 60 km/h, by a truck doing 50 km/h, and by a bicycle doing 20 km/h. What is the constant of variation?
Answer:
Step-by-step explanation:
Motrcycle: 2 hours 150/75 = 2 hours
Bus: 150/60= 2.5 hours
Truck:150/50= 3 hours
Bike:= 150/20= 7.5 hours
On a drive from one city to another, Victor averaged 5151 mph. If he had been able to average 7575 mph, he would have reached his destination 88 hrs earlier. What is the driving distance between one city and the other?
Answer:
d=1.416.525 mile
Step-by-step explanation:
V1=5151m/h, t1=t, V2=7575m/h, t2=t-88h
d1=d2 Because it is same distance; V1=d1/t and V2=d2/(t-88) but d1=d2
d=V1t=V2(t-88) → 5151t=7575(t-88) → 5151t=7575t-666.600 → 7575t-5151t=666.600 → 2424t=666.600 → t=666.600/2424 → t=275h so
[tex]d=5151\frac{mile}{h}.275h = 1.416.525mile[/tex]
A farmer wants to build a rectangular pen enclosing an area of 100 square feet. He will use wooden fencing on one side, which costs $20 per foot. He will use a chain-link fence on the 3 other sides, which costs $10 per foot. What should the dimensions of the pen be to minimize the cost?
Answer:
The dimensions of the pen that minimize the cost of fencing are:
[tex]x \approx 12.25 \:ft[/tex]
[tex]y \approx 8.17 \:ft[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the width and [tex]y[/tex] the length of the rectangular pen.
We know that the area of this rectangle is going to be [tex]x\cdot y[/tex].The problem tells us that the area is 100 feet, so we get the constraint equation:
[tex]x\cdot y=100[/tex]
The quantity we want to optimize is going to be the cost to make our fence. If we have chain-link on three sides of the pen, say one side of length [tex]y[/tex] and both sides of length [tex]x[/tex], the cost for these sides will be
[tex]10(y+2x)[/tex]
and the remaining side will be fence and hence have cost
[tex]20y[/tex]
Thus we have the objective equation:
[tex]C=10(y+2x)+20y\\C=10y+20x+20y\\C=30y+20x[/tex]
We can solve the constraint equation for one of the variables to get:
[tex]x\cdot y=100\\y=\frac{100}{x}[/tex]
Thus, we get the cost equation in terms of one variable:
[tex]C=30(\frac{100}{x})+20x\\C=\frac{3000}{x}+20x[/tex]
We want to find the dimensions that minimize the cost of the pen, for this reason, we take the derivative of the cost equation and set it equal to zero.
[tex]\frac{d}{dx} C=\frac{d}{dx} (\frac{3000}{x}+20x)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\C'(x)=\frac{d}{dx}\left(\frac{3000}{x}\right)+\frac{d}{dx}\left(20x\right)\\\\C'(x)=-\frac{3000}{x^2}+20[/tex]
[tex]C'(x)=-\frac{3000}{x^2}+20=0\\\\-\frac{3000}{x^2}x^2+20x^2=0\cdot \:x^2\\-3000+20x^2=0\\-3000+20x^2+3000=0+3000\\20x^2=3000\\\frac{20x^2}{20}=\frac{3000}{20}\\x^2=150\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{150},\:x=-\sqrt{150}[/tex]
Because length must always be zero or positive we take [tex]x=\sqrt{150}[/tex] as only value for the width.
To check that this is indeed a value of [tex]x[/tex] that gives us a minimum, we need to take the second derivative of our cost function.
[tex]\frac{d}{dx} C'(x)=\frac{d}{dx} (-\frac{3000}{x^2}+20)\\\\C''(x)=-\frac{d}{dx}\left(\frac{3000}{x^2}\right)+\frac{d}{dx}\left(20\right)\\\\C''(x)=\frac{6000}{x^3}[/tex]
Because [tex]C''(\sqrt{150})=\frac{6000}{\left(\sqrt{150}\right)^3}=\frac{4\sqrt{6}}{3}[/tex] is greater than zero, [tex]x=\sqrt{150}[/tex] is a minimum.
Now, we need values of both x and y, thus as [tex]y=\frac{100}{x}[/tex], we get
[tex]x=\sqrt{150}=5\sqrt{6}=12.25[/tex]
[tex]y=\frac{100}{\sqrt{150}}=\frac{10\sqrt{6}}{3}\approx 8.17[/tex]
The dimensions of the pen that minimize the cost of fencing are:
[tex]x \approx 12.25 \:ft[/tex]
[tex]y \approx 8.17 \:ft[/tex]
determine whether the graph is the graph of a function
yes or no?
Answer:
yes
Step-by-step explanation:
The graph passes the vertical line test, so is the graph of a function (yes). Each input value has exactly one output value.
I= nE/nr+R , solve for n
For this case we have the following equation:
[tex]I = \frac {nE} {nr + R}[/tex]
We must clear the variable "n", for them we follow the steps below:
We multiply by [tex]nr + R[/tex] on both sides of the equation:
[tex]I (nr + R) = nE[/tex]
We apply distributive property on the left side of the equation:
[tex]Inr + IR = nE[/tex]
Subtracting [tex]nE[/tex] from both sides of the equation:
[tex]Inr-nE + IR = 0[/tex]
Subtracting IR from both sides of the equation:
[tex]Inr-nE = -IR[/tex]
We take common factor n from the left side of the equation:
[tex]n (Ir-E) = - IR[/tex]
We divide between Ir-E on both sides of the equation:
[tex]n = - \frac {IR} {Ir-E}[/tex]
Answer:
[tex]n = - \frac {IR} {Ir-E}[/tex]
In parallelogram ABCD
What is BD
Answer: BD = 108
Step-by-step explanation:
In a parallelogram, the opposite sides are congruent and the diagonals bisect each other. It means that they bisect at a midpoint that divides them equally.
Therefore,
AB = DC
AD = BC
BD = AC
Also BE = ED. This means that
7x - 2 = x^2 - 10
x^2 - 10 +2 - 7x = 0
x^2 - 7x -8 = 0
Solving the quadratic equation with factorization method,
x^2 + x - 8x -8 = 0
x(x + 1) -8(x + 1) = 0
x - 8 = 0 or x + 1 = 0
x = 8 or x = -1
Since x cannot be negative,
x = 8
BE = 7×8 - 2 = 54
ED = 8^2 - 10 = 54
BD = BE + ED = 54 +54 = 108
A textbook search committee is considering 19 books for possible adoption. The committee has decided to select 7 of the 19 for further consideration. In how many ways can it do so?
It can be done in 50388 ways
Step-by-step explanation:
When the selection has to be made without order, combinations are used.
The formula for combination is:
[tex]C(n,r) =\frac{n!}{r!(n-r)!}[/tex]
Here
Total books = n =19
Books to be chosen = r = 7
Putting the values
[tex]C(19,7) = \frac{19!}{7!(19-7)!}\\\\=\frac{19!}{7!12!}\\\\=50388\ ways[/tex]
It can be done in 50388 ways
Keywords: Combination, selection
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PLZ HELP!!
The revolving restaurant on top of a hotel in San Francisco, California takes 45 minutes to complete a full counterclockwise rotation. A table that is 30 ft from the center of the restaurant starts at position (30, 0). What are the coordinates of the table after 9 minutes? Round to the nearest tenth.
A. (9.3, 28.5)
B. (28.5, 9.3)
C. (23, 19.3)
D. (11.3, 17.3)
Answer:
Step-by-step explanation:
In 9 minutes it would make 9/45 = 1/5 th of a revolution.
360(1/5) = 72 degrees
Coordinates:
(30cos72, +/- 30sin72) [+ for counterclockwise, - for clockwise)
(9.3ft, +/- 28.5ft)
https://answers.yahoo.com/question/index?qid=20100518113431AAvVZGM&guccounter=1&guce_referrer=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_sig=AQAAADh3so85ELjMHYh-Bs4EBfWYXngnX6lb_DUJTEV63qEAk8V25pxPyGr-fVlMatpwaXP-ke4TzkPe-OvBlV2WAwZ7iw3e4lBodLi1bt5txsrb6ccIGmS2tQHRymY0UsEqHUDfdNuDJKZRsnZ_gUPM1ChwoRTmeHDtRf2vrisw_B_e
The coordinates of the table after 9 minutes are approximately (9.3, 28.5).
What are Coordinates?Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane.
Since the restaurant takes 45 minutes to complete a full counter clockwise rotation, its angular velocity is:
ω = (2π radians) / (45 minutes)
≈ 0.1396 radians per minute
If we let θ be the angle between the position of the table and the positive x-axis at time t, then the position of the table can be expressed as:
x = 30 cos(θ)
y = 30 sin(θ)
To find the position of the table after 9 minutes, we can use the angular velocity to determine the angle that the restaurant has rotated. After 9 minutes, the angle of rotation is:
θ = ωt = 0.1396 radians/minute x 9 minutes
≈ 1.256 radians
Using the values of θ and the radius of 30 ft, we can find the coordinates of the table:
x = 30 cos(1.256) ≈ 9.3
y = 30 sin(1.256) ≈ 28.5
Learn more about Coordinates here:
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Clara has driven 70,000 miles in her car. On average, she drives 26 miles every day. Write a rule that represents her miles driven m as a function of time d.
Answer:
[tex]m(d)=26\ d[/tex]
where [tex]m[/tex] represents miles driven
and [tex]d[/tex] represents number of days driven.
Step-by-step explanation:
Given:
Total distance driven in miles = 70,000
Average distance driven each day = 26 miles
Taking average as unit rate of miles covered per day.
∴ we can say the car covers 26 miles per day.
Using unitary method to find miles driven in [tex]d[/tex] days.
In 1 day miles driven = 26
In [tex]d[/tex] days miles driven = [tex]26\times d =26\ d[/tex]
So, to find [tex]m[/tex] miles driven the expression can be written as:
[tex]m(d)=26\ d[/tex]
Usually, Dolores has to stock the shelves by herself and it takes her 7.2 hours. Today Camille helped Dolores and they were able to finish the task in 2.8 hours. How long would it have taken Camille if she were working alone?
Step-by-step explanation:
Let w be the work of stock the shelves and t be the time for Camille to the worl alone.
Dolores takes 7.2 hours.
[tex]\texttt{Rate of Dolores = }\frac{w}{7.2}[/tex]
[tex]\texttt{Rate of Camille = }\frac{w}{t}[/tex]
If they combine work is completed in 2.8 hours.
That is
[tex]2.8=\frac{w}{\frac{w}{7.2}+\frac{w}{t}}\\\\2.8=\frac{7.2t}{t+7.2}\\\\2.8t+20.16=7.2t\\\\4.4t=20.16\\\\t=4.58hours[/tex]
It takes 4.58 hours to stock the shelves if Camille were working alone