Answer:
Step-by-step explanation:
I assume that you mean y = x²/(x²+1), not y = x²/x²+1.
x²+1 = 0
x² = -1
x = ±√(-1) = ±i
deleted: deleted by user
Convert 1.6 L to cubic centimeters
Answer:
1600
Step-by-step explanation:
multiply the volume value by 1000
if f(x)=3x²-7 and f(x+n)=3x²+24x+41, what is the value of n?
Answer:
n=4
Step-by-step explanation:
f(x+n)=3(x+n)^2-7=3x^2+24x+41
3x^2+3n^2+6xn-7=3x^2+24x+41
Comparing and we will get, n=4
Solve the polynomial by finding all roots.
X^3-6x^2-2x+12=0
Two trains are 500 miles apart when they first start moving towards each other. If in two hours the distance between them is 300 miles and one train goes 20 miles faster than another, find the speed of the faster train. (Note: there are two possible solutions. Could you please find both?)
Answer:
Step-by-step explanation:
They travel 500 - 300 = 200 miles in 2 hours so their combined speed is
100 mph.
If their respective speed are x and y mph then we have the system
x + y = 100
x - y = 20
Adding the 2 equations
2x = 120
x = 60
and y = 40.
The other solution is that y = 60 mph and x = 40 mph.
Let a submarine be at a constant depth of 5 km. It is headed in the direction of a lighthouse. If the distance between the submarine and the base of the lighthouse is decreasing at a rate of 24 km/h when the sub is 13 km away from the base, then what is the speed of the submarine
Answer:
24 km/h
Step-by-step explanation:
Given:
Constant speed of submarine = 24 km/h
Depth under sea = 5 km
Distance of submarine from lighthouse = 13 km
Find:
Speed of the submarine
Computation:
At steady speed, the distance between both the submarine and the lighthouse base decreases at a rate of 24 km/hr.
So, when it is 13 kilometres from its starting point, the speed remains constant at 24 kilometres per hour.
A variety of trigonometric functions are shown in the answer choices below.
Which trigonometric function has an inverse over the domain x2≤x≤3x2
A-f(x)=cos(x−1/2)+3/2
B-f(x)=cos(x+π/2)
C-f(x)=sin(x−1/2)+3/2
D-f(x)=sin(x+π/2)
A boat has a rip-hole in the bottom while 20 miles away from the shore. The water comes in at a rate of 1.5 tons every minute, and the boat would sink after 70 tons of water came in. How fast must the boat go in order to reach the shore before sinking?
Answer:
t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks
S = V * t
V = S / t = 20 mi * 5280 ft/mi / 2800 sec = 37.7 ft/sec
Since 88 ft/sec = 60 mph
the speed is 60 * 37.7 / 88 = 25.7 mph
Fixed costs are $3,000, variable costs are $5 per unit. The company will manufacture 100 units and chart a 50% markup. Using the cost-plus pricing method, what will the selling price be? (2 pts)
Your company has fixed costs of $150,000 per year. The variable costs per unit in 2018 were $3 per unit, and 30,000 units were produced that year. Your company uses cost-based pricing and has a profit margin of $3 per unit. In 2019, production increased and your team had more experience—variable costs went down to $2 per unit because of your team’s higher skill and 65,000 units were produced that year. What is the change in selling price from 2018 to 2019? (2 pts)
Fixed Costs are $500,000. Per unit costs are $75, and the proposed price is $200. How many units must be sold to break even? How many units must be sold to realize a $200,000 target return? (2 pts)
Congratulations! You you just decided to become the proud owner of a new food truck offering traditional Mediterranean cuisine. Kitchen and related equipment costs are $100,000. Other fixed costs include salaries, gas for the truck, and license fees and are estimated to be about $50,000 per year. Variable costs include food and beverages estimated at $6 per platter (meat, rice, vegetable, and pita bread). Meals will be priced at $10.
Answer:
1. Using the cost-plus pricing method, the selling price = $5.25
2. The change in selling price from 2018 to 2019 is $3.69 or 33.5% reduction.
3. To break-even, unit sales = 4,000 units
To realize a target return of $200,000, the unit sales = 5,600 units
4. Units to break-even = 12,500 meals
Sales revenue at break-even point = $125,000
Step-by-step explanation:
a) Data and Calculations:
Fixed costs = $3,000
Variable costs per unit = $5
Units manufactured = 100 units
Total variable costs = $500 ($5 * 100)
Total costs = $3,500 ($500 + $3,000)
Cost per unit = $3.50
Markup percentage = 50%
Using the cost-plus pricing method, the selling price = $5.25 ($3.50 * 1.5)
b) Fixed costs per year = $150,000
Variable costs per unit = $3
Production units = 30,000
Total variable costs = $90,000 ($3 * 30,000)
Cost-based pricing with a profit margin = $3 per unit
Total costs = $240,000 ($90,000 + $150,000)
Cost per unit = $8 ($240,000/30,000)
Selling price per unit = $11 ($8 + $3)
Variable cost = $2 per unit
Production units = 65,000 units
Total costs = ($2 * 65,000 + $150,000)
= $280,000 ($130,000 + $150,000)
Unit cost = $4.31 ($280,000/65,000)
Selling price = $7.31 ($4.31 + $3)
Change in selling = $3.69 ($11 = $7.31) = 33.5%
c) Fixed costs = $500,000
Per unit costs = $75
Proposed price = $200
Contribution margin per unit = $125 ($200 - $75)
To break-even, unit sales = $500,000/$125 = 4,000 units
To realize a target return of $200,000, the unit sales = $700,000/$125 = 5,600 units
d) Kitchen and related equipment costs = $100,000
Other fixed costs per year = $50,000
Variable costs = $6 per platter
Price per meal = $10
Contribution margin per meal = $4 ($10 - $6)
Units to break-even = $50,000/$4 = 12,500 meals
Sales revenue at break-even point = $50,000/40% = $125,000
Is it true that every whole number is a solution of x > 0? Use complete sentences to explain your reasoning.
Whole numbers are natural numbers, and natural numbers do not include negatives, decimals, fractions, or roots, so all whole numbers can indeed satisfy the inequality.
lim(x-0) (sinx-1/x-1)
lim ( sinx-1)/(x-1)
x=>0
apply x=0
(sin(0)-1)/(0-1)
(0-1)/(-1)
=1
The length of a rectangle is four more than three times the width. If the perimeter of this rectangle is at least 70 square centimeters. Write an inequality that can be solved to find the width of the rectangle
Answer:
Step-by-step explanation:
Let L represent the length of the triangle.
Let W represent the width of the triangle.
The length of a rectangle is four more than three times the width. This means that
L = 3W + 4
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
If the perimeter of this rectangle is at least 70 square centimeters, an inequality that can be solved to find the width of the rectangle is
2(L + W) ≥ 70
L + W ≥ 70/2
L + W ≥ 35
Answer:
6w +8 ≥70
Step-by-step explanation:
Let w be the width
The length is then 3w+4 ("the length is 4 more than 3 times the width")
Since a rectangle has opposite sides equal, the perimeter would be 2(l+w) or 2(w+3w+4) which would be 6w +8. If the perimeter is at least 70, that is, 70 or more, the inequality would be
6w + 8 ≥ 70.
The units, however, would not be SQUARE centimeters, just centimeters. If the question were asking for area, the units would be square units, but since perimeter is a linear measurement, the units would have to be linear.
Find the value of x. Round to the nearest tenth.
Answer:
1.6 ft
Step-by-step explanation:
If you use the Pythagorean Theorem to solve for x, you get:
[tex]x=\sqrt{2.1^2-1.4^2}[/tex]
[tex]x=\sqrt{2.45} = 1.56524758425[/tex]
Rounded to the nearest tenth, the answer is 1.6
I) Find the volume in terms of pie
ii) curved surface area in terms of pie
iii) capacity in litres (correct to nearest litre)
Answer:
i) pi×4500 cm³
ii) pi×600 cm²
iii) 14 liters
Step-by-step explanation:
in general : the diameter is 30 cm, the radius is half of that (15 cm)
i)
the volume of a cylinder is base area times height.
Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³
ii)
similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.
surface area of the cylinder mantle is
Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²
iii)
for this we need now to do the multiplication with pi and then convert the cm³ to liters.
1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³
pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of
$750. What was the rate charged per hour by each mechanic if the sum of the two rates was $105 per hour?
Step-by-step explanation:
let's convert the statement into equation..
let the charge of 1st mechanic be x and second be y..
by the question..
10x+5y=750...(i)
x+y=105..(ii)
from eqn(ii)..
x+y=105
or, x=105-y...(iii)
substituting the value of x in eqn (i)..
10x+5y=750
or, 10(105-y)+5y=750
or, 1050-10y+5y=750
or, 1050-750=5y
or, y=300/5
•°• y=60
substituting the value of y in eqn(iii).
x=105-y
or, x=105-60
•°• x= 45..
the rate charged by two mechanics per hour was 60$ and 45$
Car drove 2hours at a speed of 100km per hour & 3 hour at a speed of 50 km per hour . What was the average speed of the car during the trip?
Answer:
200 kilometers and 150 kilometers
I need help answering this ASAP
can you zoom in on my pic more or no does it say 1/z
Answer:
Option A. Reciprocal
Answered by GAUTHMATH
The 90% confidence interval for the mean one-way commuting time in New York City is
5.22 < < 5.98 minutes. Construct a 95% confidence interval based on the same data.
Which interval provides more information?
Answer:
95% provides more information
Step-by-step explanation:
The confidence interval is obtained by using the relation :
Xbar ± Zcritical * σ/√n
(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)
(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)
Adding (1) and (2)
2xbar = 5.22 + 5.98
2xbar = 11.2
xbar = 11.2 / 2 = 5.6
Margin of Error :
Xbar - lower C.I = Zcritical * σ/√n
Zcritical at 90% = 1.645
5.6 - 5.22 = 1.645 * (σ/√n)
0.38 = 1.645 * (σ/√n)
(σ/√n) = 0.38 / 1.645 = 0.231
Therefore, using the se parameters to construct at 95%
Zcritical at 95% = 1.96
Margin of Error = Zcritical * σ/√n
Margin of Error = 1.96 * 0.231 = 0.45276
C.I = xbar ± margin of error
C. I = 5.6 ± 0.45276
C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)
C. I = (5.147 ; 6.053)
Hence, 95% confidence interval provides more information as it is wider.
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9514 1404 393
Answer:
AC = 2.0 mm = 41.3 kgStep-by-step explanation:
The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.
__
a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).
The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)
These are equal, so we have ...
16(AC -1.5) = 7(3 -AC)
16AC -24 = 21 -7AC . . . . . eliminate parentheses
23AC = 45 . . . . . . . . . . . add 7AC+24
AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC
AC ≈ 2.0 meters . . . . rounded to 1 dp
__
b) The torques in this scenario are ...
M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m
M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M
M = 41.3 kg . . . . rounded to 1 dp
_____
Additional comment
Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.
Matematykakdbebox
Jaggbn
Answer:
theres no question....
Step-by-step explanation:
???
I need help guys thanks so much
I think its A) (f+g)(z)=|2x+4|-2
Step-by-step explanation:
If two people are splitting a total rent number of $1,120 a month, it would be $560 split evenly. However, if one roommate pays $60 more than the other, how much would that roommate be paying per month?
$560-$500
=$500
therefore, other roommate will be paying $500 per month
Can the three values represent the sides of a triangle?
7, 8, √113
Is this a triangle?
If so, what type?
Pythagorean Triple? (yes/no)
no the square root of 113 is rounded to 56x2
Every high school senior takes the SAT at a school in St. Louis. The high school guidance director at this school collects data on each graduating senior’s GPA and their corresponding SAT test score. The guidance director is conducting a _________ in this experimental design.
A. sample survey
B. census
C. sample poll
D. random sample
The guidance director is conducting a sample poll in this experimental design.
What is sample?Sample is a part of population. It does not comprises whole population. It is representatitive of whole population.
How to fill blank?We are required to fill the blank with appropriate term among the options.
The correct option is sample poll because the guidance director collects data in his school only.
Census collects the whole population of the country.
Sample poll means collecting data from small population.
Random sample means collecting data from a part of popultion without identifying any variable.
Hence we found that he was doing sample poll.
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3/8n+5(n-6)=1 7/8n-2
Answer:
n = 112/13 = 8.615
Step-by-step explanation:
(3/8) n + 5n - 30 = (17/8)n - 2
(3/8)n +5n - (17/8)n = 30-2
(13/4)n = 28
n = 28 * 4/13
n = 112/13
n = 8.615
7x to the power of 2 is a what is it
a) monomial
b) binomial
c) Trinomial
Please help on 25 it’s confusing me I need the correct answer
Answer:
X * 0.8 = $64
x = $80
Step-by-step explanation:
Answer:
$80 (D)
Step-by-step explanation:
If Richard is getting a discount and his final price is $64 that means the answer must be above 64. That eliminates A, B, and C.
Use the formula: 20% of x = $64 and substitute the other two options. 20 percent of 84 is 16.8. 84-16.8=67.2 (not the correct answer). 20 percent of 80 is 16. 80-16=64(The Correct Answer).The answer must be $80 (D)
Please help!!!!! Nowwww
Answer:
It has 1 term and a degree of 4.
Step-by-step explanation:
3j⁴k-2jk³+jk³-2j⁴k+jk³
= 3j⁴k-2j⁴k-2jk³+jk³+jk³
= j⁴k
So, in this expression, there is 1 term, and it has a degree of 4.
what is 6 3/5 - 4 3/10
Answer:
2 3/10
Step-by-step explanation:
3/5x2=6/10
6/10-3/10=3/10
Which expression is equivalent to the following complex fraction?
-25
245 5
+
y
3 2
у
Step-by-step explanation:
[tex] \longrightarrow \sf{ \dfrac{ \cfrac{ - 2}{x} + \cfrac{ 5}{y}}{\cfrac{ 3}{y} -\cfrac{ 2}{x} }} \\ \\ \longrightarrow \sf{ \dfrac{ \cfrac{ - 2y + 5x}{xy}}{\cfrac{ 3x - 2y}{xy} }} \\ \\ \longrightarrow \sf{ \cfrac{ - 2y + 5x}{xy}} \times{\cfrac{ xy}{3x - 2y} } \\ \\ \longrightarrow \boxed{ \sf{ \cfrac{ - 2y + 5x}{3x - 2y}}}[/tex]
Option A is correct!
The expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
[-2/x + 5/y] / [3/y - 2/x]
This expression could also be given by;
[-2y + 5x /xy] / [3 x- 2y /xy]
Now, we know that x would cancel out;
[-2y + 5x ] / [3 x- 2y]
Hence, the expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]
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help asap pleaseeee asap
