Answer:
It will take 800seconds to you to run 5000m
Step-by-step explanation:
Let time taken to run 5000m is x
Using ratio and proportion
200:32=5000:x
200/32=5000/x
200*x=5000*32
200x=160000
x=800seconds
A box is with a square base and open top is to be constructed and a total volume of 720 cubic inches is required. The cost of material for the base is 8 dollars per square inch and the cost of material for the sides is 6 dollars per square inch. Express the total cost of the box as a function of the length of the base.
Answer:
total cost = 8x^2 +17280/x
Step-by-step explanation:
Let x represent the base length. Then the area of the base is x^2, and the height is h = 720/x^2.
The area of the four sides is ...
(4x)(h) = (4x)(720/x^2) = 2880/x
The cost of the base is ...
base cost = 8x^2
And the cost of the sides is ...
side cost = 6(2880)/x = 17280/x
The total cost of the box is ...
total cost = base cost + side cost
total cost = 8x^2 +17280/x
_____
Comment on the cost function
You will find this function has a minimum at x=∛1080 ≈ 10.260 in. The total cost is about $2526.35, and the box is 2/3 times as tall as wide. That aspect ratio makes any pair of opposite sides cost the same as the base, the generic solution to a cost optimization problem of this sort.
If 5=3+2,then 3+2=5. What is the truth value
Answer:
true
Step-by-step explanation:
Analyze the diagram below and answer the question that follows.
Answer:
B. Complements of congruent angles are congruent.
Step-by-step explanation:
Angles <DCF and <FEG have angles measures that are complementary to to angles E and C.
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
odd numbers always end in 1,3,5,7 and 9
odd numbers - 51,23,95,11,67,75,83, and 29
even numbers - 16,32,38,76,62,40 and 80
19p 25p 16p
9 - 2p , 1 - 1p 12- 2p, 1- 1p 5- 2p, 6- 1p
19 - 1p 10 - 2p, 5- 1p 6 - 2p, 2- 1p
7- 2p , 5- 1p 8- 2p, 9- 1p 4- 2p, 8- 1p
9- 2p, 6- 1p 6- 2p, 4- 1p
Which side will require the use of the distance formula to find the length?
Answer:
CD
Step-by-step explanation:
For all sides except CD, you do not need the distance formula, since they are vertical or horizontal, meaning that you can find their length simply through subtraction. However, with side CD, since it is diagonal, you need to form a right triangle with to solve its length. Hope this helps!
Given that (- 2, 7) is on the graph of f(x) , find the corresponding point for the function f(x + 4).
Answer:
[tex]\boxed{\ the \ corresponding\ point\ is \ (-6,7)\ }[/tex]
Step-by-step explanation:
We know that f(-2)=7
x+4 = -2 <=> x = -6
so f(-6+4) = f(-2)=7
then the corresponding point is (-6,7)
John works 21 hours a week and earns $157.50. How much does john earn per hour?
Answer:
D. $7.50
Step-by-step explanation:
$157.50 / 21 hours = $7.50 per hour
Eli uses 1/4 pound of apples to make 4 servings of fruit salad. He uses the same amount of apples for each serving. What amount of apples does he use for each serving of fruit salad?
Answer:
1/16 pound
Step-by-step explanation:
1/4 ÷ 4 = 1/4 x 1/4 = 1/16
Please help! Correct answer only, please! Consider the matrix shown below: What are the dimensions of A. A. 3 X 4 B. 4 X 3 C. 12 D. A and B
Answer: A) 3 x 4
Step-by-step explanation:
The dimensions of a matrix are ROWS x COLUMNS.
The given matrix has 3 rows and 4 columns,
therefore the dimensions are: 3 x 4
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
Answer:
V ≈ 382 inches ³
Step-by-step explanation:
V = 4/3πr³
V = 4/3(3.14)(4.5)³
V = 1145.11/3
V = 381.7
V ≈ 382 inches ³
Suppose you want to buy a new car and are trying to choose between two models: Model A: costs $16,500 and its gas mileage is 25 miles per gallon and its insurance is $250 per year. Model B: costs $24,500 and its gas mileage is 40 miles per gallon and its insurance is $450 per year. If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:
1. Find a formula for the total cost of owning Model A where the number of years you own the car is represented by x.
2. Find a formula for the total cost of owning Model B where the number of years is the independent variable.
3. Find the total cost for each model for the first five years. If you plan to keep the car for 4 years, which model is more economical?
4. Find the number of years in which the total cost to keep the two cars will be the same.
5. Identify the number of months where neither car holds a cost of ownership advantage.
6. What effect would the cost of gas doubling have on cost of ownership?
7. If you can sell neither car for 40% of its value at any time, how does the analysis change?
Answer:
1. CA=16,500+5,050x
2. CB=24,500+3,450x
3. CA(x=5)=CB(x=5)=41,750
If keeped 4 years, Model A is more economical.
4. 5 years
5. From month 49 to 61.
6. The cost of ownership of Model A increases more than Model B, as it is less gas efficient. The break-even point for x is reduced from x=5 to x=2.35.
7. The fixed cost are reduced by a 40%, so the variable cost, the ones that depend on time of ownership, are increased in importance.
Step-by-step explanation:
We can express the cost of ownership as the sum of the purchase cost, gas cost and insurance cost.
1. For model A we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$4,800x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$5,050x[/tex]
2. For model B we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$3,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$3,450x[/tex]
3. If x=5, the costs for each car are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(5)=16,500+25,250=41,750\\\\\\\text{CoOwn B}=24,500+3,450\cdot(5)=24,500+17,250=41,750[/tex]
5 years is the break-even point for the cost of ownership between these two cars.
If you plan to keep the car for 4 years, the costs are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(4)=16,500+20,200=36,700\\\\\\\text{CoOwn B}=24,500+3,450\cdot(4)=24,500+13,800=38,300[/tex]
For a 4 year period ownership, the model A is more economical ($36,700).
4. This happens for 1 year, the fifth year, in which the two models have the same cost of ownership.
5. At the 5th year, the cost for both models are the same.
Then, this corresponds to the months 4*12+1=48+1=49 and 5*12+1=61.
6. If the cost of gas doubles, the cost of ownership would rise for both model, but more for the Model A, which is less gas efficient and hence has a higher gas cost.
Model A
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$9,600x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$9,850x[/tex]
Model B
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$6,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$6,450x[/tex]
The breakeven point goes from x=5 (for $3 per gallon) to x=2.35 (for $6 per gallon).
[tex]16,500+9,850x=24,500+6,450x\\\\(9,850-6,450)x=24,500-16,500\\\\x=8,000/3400=2.35[/tex]
7. If we can sell any car for 40% of its value at any time, the cost of ownership becames:
Model A:
[tex]\text{Cost of ownership}=16,500+5,050x-0.4\cdot16,500\\\\\text{Cost of ownership}=9,900+5,050x[/tex]
Model B
[tex]\text{Cost of ownership}=24,500+3,450x-0.4\cdot24,500\\\\\text{Cost of ownership}=14,700+3,450x[/tex]
The fixed costs are lowered by 40%, so the variable costs (the ones that depend on time) became more important.
Shiva brought $39.00 to the state fair. She bought a burger, a souvenir, and a pass. The burger was 1/3 as much as the souvenir, and the souvenir cost 1/2 the cost of the pass. Shiva had $4.00 left over after buying these items.
Pass = $21 , Souvenir = 2x/3 = $14 , Burger = x/6 =$3.5 .
A study published in 2010 showed that city dwellers have a higher risk of developing anxiety disorders and a higher risk of developing mood disorders than those who live in the country. A follow-up study published in 2011 used brain scans of city dwellers and country dwellers as they took a difficult math test.1 To increase the stress of the participants, those conducting the study tried to humiliate the participants by telling them how poorly they were doing on the test. The brain scans showed very different levels of activity in stress centers of the brain, with the urban dwellers having greater brain activity than rural dwellers in areas that react to stress.
Required:
a. Is the 2010 study an experiment or an observational study?
i. Experiment
ii. Observational study
b. Can we conclude from the 2010 study that living in a city increases a person's likelihood of developing an anxiety disorder or mood disorder?
i. Yes
ii. No
c. Is the 2011 study an experiment or an observational study?
i. Experiment
ii. Observational study
d. Can we conclude from the 2011 study that living in a city increases activity in stress centers of the brain when a person is under stress?
i. Yes
ii. No
Step-by-step explanation:
a.It is a controlled experiment because it is clearly seen that an established hypothesis or study is being verified through an experiment, now in this case the hypothesis is tested through an experiment where excessive stress is placed on the Participants during their math exam to effectively verify that people in urban or city areas live with more stress than people in rural areas.
2..As now that the previously established hypothesis has been verified, it is concluded that people who live in the city live with more anxiety and stress than people who live in rural areas.
Find the nth term and the 150th term of the following sequence 7,11,15,19,23,...
Answer:
for the 9th it is 39 for the 150th it is 607
Suppose 44% of a large sample of a population favor a tax increase. If there
are 95,000 people in the population about how many people in the population
favor a tax increase?
A. 13,300
B. 22,800
C. 41,800
D. 32,300
Answer:
C. 41,800
Step-by-step explanation:
Multiply 0.44 by 95,000.
0.44 x 95,000 = 41,800
What’s the correct answer for this question?
Answer:
3724 in^3
Step-by-step explanation:
19 times 14 times 14 = 3724
Answer:
3724 inches ³
Step-by-step explanation:
Volume of cooler = whl
Where w is width, h is height and l is length
V = (19)(14)(14)
V = 3724 inches³
If A={A,15,E,17,18, B,20} and B={ X,22, F,42, Y,62,72}, then what is n(A∪B)?
Answer:
14
Step-by-step explanation:
There are 7 elements in each set, and no elements are shared. The number of elements in the union of the sets is then ...
n(A∪B) = 7+7 = 14
Score: 0 of 1 pt
7.4.41
From a standard 52-card deck, how many 5-card hands consist entirely of black cards?
Answer:
so halve the deck is black and halve the deck is red so you have 26 black cards then divide by 5 and you get 5 with 1 card leftover
How much will a person pay for 12.2 pounds of bananas at a price of $2.24 per pound
Answer:
It would be 27.328 but since it is money, we have to leave the 8 out.
So the answer is 27.32
Step-by-step explanation:
Answer:
$27.33
Step-by-step explanation:
You multiply 12.2 and 2.24 and the answer is 27.328. You then round it to the nearest tenth which is 27.33.
What are the next two numbers in the pattern of numbers; 45, 15, 44, 17, 40, 20, 31, 25, ...
Answer:
15, 33
(if I'm not wrong, it should work this way)
What’s the correct answer for this?
Answer:
B and F
Step-by-step explanation:
When we'll slice a triangular prism, a square and triangle would be formed
Given: AB || DE , AD bisects BE.
Prove: ABC = DEC using the ASA postulate.
Answer:
As per ASA postulate, the two triangles are congruent.
Step-by-step explanation:
We are given two triangles:
[tex]\triangle ABC[/tex] and [tex]\triangle DEC[/tex].
AD bisects BE.
AB || DE.
Let us have a look at two properties.
1. When two lines are parallel and a line intersects both of them, then alternate angles are equal.
i.e. AB || ED and [tex]\angle B[/tex] and [tex]\angle E[/tex] are alternate angles [tex]\Rightarrow[/tex] [tex]\angle B = \angle E[/tex].
2. When two lines are cutting each other, angles formed at the crossing of two, are known as Vertically opposite angles and they are are equal.
[tex]\Rightarrow \angle ACB = \angle DCE[/tex]
Also, it is given that AD bisects BE.
i.e. EC = CB
1. [tex]\angle B = \angle E[/tex]
2. EC = CB
3. [tex]\angle ACB = \angle DCE[/tex]
So, we can in see that in [tex]\triangle ABC[/tex] and [tex]\triangle DEC[/tex], two angles are equal and side between them is also equal to each other.
Hence, proved that [tex]\triangle ABC[/tex] [tex]\cong[/tex] [tex]\triangle DEC[/tex].
Which is the graph of f(x) = 2(3)^x?
Answer: The graph is:
Find values of a. b. and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
X + y = 6
y + z = 6
x + z = 6
ax + by + cz = 0
a) a unique solution (a. b .c)=([])
b) no solution (a. b .c)=([])
c) infinitely many solutions (a. b, c) = ([])
Answer:
Step-by-step explanation:
The given equations are
x + y = 6- - - - - - - - -1
y + z = 6- - - - - - - -2
x + z = 6- - - - - - - - - 3
From equation 2, y = 6 - z
Substituting y = 6 - z into equation 1, it becomes
x + 6 - z = 6
x - z = 6 - 6
x - z = 0
x = z
Substituting x = z into equation 3, it becomes
z + z = 6
2z = 6
z = 6/2
z = 3
x = 3
Substituting x = 3 into equation 1, it becomes
3 + y = 6
y = 6 - 3
y = 3
ax + by + cz = 0
3a + 3b + 3c = 0
3(a + b + c) = 0
Therefore, it is impossible
Which is an irrational number?
Answer: THE SECOND ONE
Step-by-step explanation:
Answer: the second one
Step-by-step explanation:
determine the slope of a line with the equation 6x+2y-4=0
find the quotient of 25.5÷0.5
Answer:
[tex]51[/tex]
Step-by-step explanation:
[tex]\frac{25.5}{0.5}[/tex]
[tex]\frac{255}{5}[/tex]
[tex]=51[/tex]
Eleanor can drive an average of 374 Miles on one tank of gas. How many miles can she drive on 15 tanks of gas
Answer:
5,610 Miles
Step-by-step explanation:
To solve this you would need to multiply the average miles by how many tanks of gas she will use.
374 * 15 = 5,610
So, Eleanor can drive 5,610 miles with 15 tanks of gas.
need answers to 34 35 and 36
Answer:
34) 75
35) 60
36) 210
Step-by-step explanation:
34) Area of a rectangle:
L x B
= 15 x 5
= 75
35) Area of a trapezium :
½ h (sum of || sides)
= ½ x 6 x (12+8)
= 3 x 20
= 60
36) Area of a regular hexagon:
3BH
= 3 x 7 x 10
210
Hope it helps....
Answer:
Step-by-step explanation:
35. 75
area of rectangle : A = b x h
= 15 X 5
= 75
36. 60
area of trapezoid : A = (b1 + b2) x h
2
= (8+12) x 6
2
= 60
37. 210
area of regular polygon : A = P x a (P no. of sides) (a is apothem)
2
= (6 x 10) x 7
2
= 210
A hose fills a hot tub at a rate of 3.15 gallons per minute. How many hours will it take to fill a 322-gallon hot tub? It will take nothing hours to fill the hot tub. (Simplify your answer. Round to two decimal places as needed.)
Answer:
So we find how many of 3.15 units of gallons will fit into the tub.
That means we need to divide. 311/3.15 is about 98.73 minutes
That means that it takes 1 hour and 38.73 mins
Step-by-step explanation: