15/51+16/27-(-2/27-2/51)
Answer:
1
Step-by-step explanation:
USE PEMDAS OR ORDER OF OPERATIONS
1. Evaluate parenthesis.
-2/27 - 2/51 = - 52/459.
2. Add
15/51 + 16/27 = 407/459
3. Subtract to get the final answer
407/459 - -52/459 = 407/459 + 52/459 = 1
So, 15/51+16/27-(-2/27-2/51) = 1
1. The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.
(a) Write an equation to represent this relationship. Let x be the number of miles driven and y be the total cost for the day.
(b) What does the graph of this equation form on a coordinate plane? Explain.
(c) What is the slope and the y-intercept of the graph of the relationship? Explain
Answer:
a) y=0.50x+15
b) The graph of this equation form on a coordinate plane is a line.
c) Slope =0.50 and y-intercept = 15
Step-by-step explanation:
Let x = Number of miles driven by car
Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.
a) Total cost = 0.50x+15
If y =total cost of renting the car, then y=0.50x+15 (i)
b) Above equation is similar to y= mx+c (ii) [m = slope , xc=y-intercept] which a linear equation .
So the graph of this equation form on a coordinate plane is a line.
c) Comparing (i) and (ii)
m=0.50 , c=15
Hope this helps :)
Use the information in the table below to answer the following question. name of fund nav offer price upton group $18.47 $18.96 green energy $17.29 $18.01 tjh small-cap $18.43 $19.05 whi health $20.96 nl for which of the funds shown would you pay the most commission on the purchase of 100 shares? a. green energy b. tjh small-cap c. upton group d. whi health
WHI Health Fund pays the most commission on the purchase of 100 shares with a commission of $96.00. Thus, option d is correct.
Funds offer price for Upton Group = $18.96 - $18.47
Funds offer price for Green Energy fund = $18.01 - $17.29
Funds offer price for TJH Small-Cap fund = $19.05 - $18.43
Funds offer price for WHI Health fund = $20.96 - $20.00
To calculate the commission on purchasing shares, we need to find the allowance between the price ranges and then multiply the value by 100.
For the Upton Group fund, Commission = (Offer price - NAV) * 100
= ($18.96 - $18.47) * 100
= $49.00
For the Green Energy fund, Commission = (Offer price - NAV) * 100
= ($18.01 - $17.29) * 100
= $72.00
For the TJH Small-Cap fund, Commission = (Offer price - NAV) * 100
= ($19.05 - $18.43) * 100
= $62.00
For the WHI Health fund, Commission = (Offer price - NAV) * 100
= ($20.96 - $20.00) * 100
= $96.00
Therefore, we can conclude that the WHI Health fund pays the most commission of $96.00.
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Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 2x2 and the planes z = 0,2= 2 and y = 4.
Using the triple integral to find the volume of the solid bounded by the parabolic cylinder is 32/15 cubic units.
The given solid is bounded by the parabolic cylinder y = 2x², the plane z = 0, the plane z = 2, and the plane y = 4.
To find the volume of the solid using a triple integral, we can set up the integral as follows:
∫∫∫E dV
where E is the region of integration in three dimensions.
Region E can be described as:
0 ≤ z ≤ 2
0 ≤ y ≤ 4
0 ≤ x ≤ √(y/2)
Therefore, the triple integral can be written as:
∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz
Evaluating the integral gives us the volume of the solid:
V = ∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz = 32/15
Hence, the volume of the solid is 32/15 cubic units.
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Find the measure of the angle indicated. Assume that the lines which appear tangent are tangent.
Answer:
65°-----------------------------
The measure of the angle formed outside of circle is half the difference of major and minor arc measures.
It means the measure of angle T is:
m∠T = 1/2((360 - 115) - 115) = 180 - 115 = 65The measure of the angle indicated in the diagram is 50 degrees.
What is Tangent ?
In geometry, the tangent is a trigonometric function that relates the opposite side and adjacent side of a right triangle. More specifically, for a given angle θ, the tangent of θ (denoted by tan θ) is defined as the ratio of the length of the opposite side to the length of the adjacent side of the right triangle containing that angle.
In the given figure, the two lines are tangent to the circle with center O. Let's call the point where the two lines intersect point P.
We know that the angle formed by a tangent line and a radius of a circle is always 90 degrees. Therefore, we can draw a radius OP from the center of the circle to point P and we know that angle POQ (where Q is the point where the radius intersects the circle) is 90 degrees.
We also know that angle OPQ is 40 degrees (as given in the diagram).
Since the sum of the angles in a triangle is 180 degrees, we can find angle OQP as follows:
angle OQP = 180 - angle OPQ - angle POQ
= 180 - 40 - 90
= 50 degrees
Therefore, the measure of the angle indicated in the diagram is 50 degrees.
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Given that cos α = -8/17 and that 0° <= α <= 360°, find two values of α, to two decimal places.
Therefore, two possible values of α are approximately 138.19° and 221.81°.
What purpose does sin serve?Sin 180 has a precise value of zero. One of the fundamental trigonometric functions is sine, which is used to calculate the angle or sides of a right-angled triangle.
Given that cos = -8/17, we must determine two potential values for.
We can construct a right triangle with the adjacent side equal to -8 and the hypotenuse equal to 17, and then use the Pythagorean theorem to calculate the opposite side since cos = adjacent/hypotenuse.
The Pythagorean theorem gives us:
opposite² = hypotenuse² - adjacent²
opposite² = 17² - (-8)²
opposite² = 225
opposite = ±15
Both the x and y coordinates are negative in the second quadrant, resulting in:
cos α = -8/17
sin α = -15/17
Consequently, may have the following value: = 180° - arccos(-8/17) 138.19° (rounded to two decimal places)
The x coordinate is negative and the y coordinate is positive in the third quadrant, resulting in:
cos α = -8/17
sin α = 15/17
Therefore, another possible value of α is:
α = 360° - cos(-8/17)
≈ 221.81°
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Find the work done by the force field F(x,y) = x^2i – ryj in moving a particle along the F semicircle y = Sqrt(4 – x^2) from P(2,0) to Q(-2,0) and then back along the line segment from Q to P.
The work done by the force field F along the semicircle and the line segment is 32/3.
The work done by a force field F along a curve C from point A to point B is given by the line integral:
W = ∫ F dot dr
where dot represents the dot product and dr is the differential displacement vector along the curve C.
Let's divide the curve C into two parts: the semicircle from P to Q, denoted by C1, and the line segment from Q to P, denoted by C2.
For C1, the curve can be parameterized as x = 2cos(t) and y = 2sin(t) for t in [0, pi]. The differential displacement vector is then given by:
dr = (-2sin(t) dt)i + (2cos(t) dt)j
The force field F(x,y) = x^2i - ryj, so we have:
F(x,y) = (2cos^2(t))i - (2rsin(t))j
The dot product F dot dr is then:
F dot dr = (2cos^2(t))(-2sin(t) dt) + (2rsin(t))(2cos(t) dt)
= -4cos^2(t)sin(t) dt + 4rcos(t)sin(t) dt
= 4sin(t)cos(t)(r - cos(t)) dt
Therefore, the work done along C1 is:
W1 = ∫ C1 F dot dr
= ∫[0, pi] 4sin(t)cos(t)(r - cos(t)) dt
This integral can be evaluated using the substitution u = cos(t), du = -sin(t) dt:
W1 = -∫[1, -1] 4u(r - u) du
= 4r∫[1, -1] u du - 4∫[1, -1] u^2 du
= 0
Hence, the work done along C1 is 0.
For C2, the curve is simply the line segment from Q(-2,0) to P(2,0), which is parallel to the x-axis. Therefore, the differential displacement vector is given by:
dr = dx i
where i is the unit vector in the x-direction. The force field is the same as before, F(x,y) = x^2i - ryj. Along C2, y = 0, so the force field reduces to:
F(x,y) = x^2i
The dot product F dot dr is then:
F dot dr = x^2 dx
Therefore, the work done along C2 is:
W2 = ∫ C2 F dot dr
= ∫[-2, 2] x^2 dx
= 32/3
Hence, the work done along C2 is 32/3.
The total work done along the curve C is the sum of the work done along C1 and C2:
W = W1 + W2 = 0 + 32/3 = 32/3
Therefore, the work done by the force field F along the semicircle and the line segment is 32/3.
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f(x)=1/2x^4+2x^3 is concave up when f”(x) is
The function f(x) = (¹/₂)x⁴ +2x³ is concave up when f''(x) > 0, which is true when x > 0 or x < -2.
What is the concavity of the function?The concavity of a function is determined by taking the second derivative.
f'(x) = 2x³ + 6x²
f''(x) = 6x² + 12x
To find out when f(x) is concave up, we need to determine when f''(x) is positive;
f''(x) > 0
6x² + 12x > 0
6x(x + 2) > 0
When x > 0, both factors are positive, and the inequality is true.
When x < -2, both factors are negative, and the inequality is true.
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If a woman making $29,000 a year receives a cost-of-living increase of 2. 6%, what will her new salary be?
To find the new salary after a 2.6% increase, we need to add 2.6% of the original salary to the original salary.
2.6% of $29,000 can be calculated as:
(2.6/100) x $29,000 = $754
Therefore, the new salary will be:
$29,000 + $754 = $29,754
So the woman's new salary will be $29,754.
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A city's population in the year x=1953 was y=2,695,750. In 1971 the population was 2,694,850. Compute a slope of the population growth or decline and choose the most accurate statement
The negative slope indicates a decline in population over the 18-year period. The most accurate statement based on this information is that the city's population experienced a decline of approximately 50 people per year on average between 1953 and 1971.
To compute the slope of the population growth or decline, we need to use the formula:
slope = (y2 - y1) / (x2 - x1)
where y2 is the final population, y1 is the initial population, x2 is the final year, and x1 is the initial year.
Plugging in the values we have:
slope = (2,694,850 - 2,695,750) / (1971 - 1953)
slope = -900 / 18
slope = -50
The negative slope indicates a decline in population over the 18-year period.
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According to a simple physiological model, an athletic adult male needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer calories than those required to maintain his weight, his weight changes at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight; the constant of proportionality is 1/3500pounds per calorie. Suppose that a particular person has a constant caloric intake of HH calories per day. Let W(t)be the person's weight in pounds at time t (measured in days).
(a) What differential equation has solution W(t)? dWdt=
(Your answer may involve W, H and values given in the problem.)
(b) If the person starts out weighing 180 pounds and consumes 3200 calories a day. What happens to the person's weight as t→[infinity]? W→?
(a) The differential equation that has solution W(t) is:
dW/dt = (1/3500) * (HH - 20W)
This is because the rate of change of weight with respect to time is proportional to the difference between the person's constant caloric intake and the number of calories needed to maintain their current weight, which is 20 calories per day per pound of body weight. The constant of proportionality is 1/3500 pounds per calorie.
(b) To find out what happens to the person's weight as t→[infinity], we can look at the long-term behavior of the solution to the differential equation. As t gets very large, the weight W(t) approaches a limiting value W∞ such that dW/dt = 0. This means that the person's weight is no longer changing, and is therefore at a steady state.
To find this steady state weight, we set dW/dt = 0 in the differential equation:
(1/3500) * (HH - 20W∞) = 0
Solving for W∞, we get:
W∞ = HH/20
So as t→[infinity], the person's weight approaches W∞ = HH/20.
This means that if the person starts out weighing 180 pounds and consumes 3200 calories a day, their weight will eventually stabilize at W∞ = 3200/20 = 160 pounds.
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If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3 find the value of x.
If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3, then the value of x is 4 or 4.5
To solve this problem, we'll need to use some geometry and algebra.
Using the Pythagorean theorem, we can set up two equations:
OA² + AD² = OD² (for right triangle OAD)
OB² + BD² = OD² (for right triangle OBD)
In these equations, "OD" is the radius of the circle. We don't know this value yet, but we can express it in terms of "x" using the fact that "BD" = 4x-3.
Now, we can simplify these equations by substituting in the values we know. We get:
OA² + 13² = OD²
OB² + (4x-3)² = OD²
This means we can set up the equation:
OA = OB
Now we can substitute in the expressions we found for "OA" and "OB" earlier:
√(OD² - 13²) = √(OD² - (4x-3)²)
We can then square both sides to eliminate the square roots:
OD² - 13² = OD² - (4x-3)²
Simplifying this equation, we get:
169 = (4x-3)²
Taking the square root of both sides (and remembering to include the positive and negative solutions), we get:
4x-3 = ±13
Solving for "x," we get two possible values:
x = 4
x = 4.5
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Please help!!! Find the total surface area of the following cone. Leave your answer in terms of pi.
4 cm
3 cm
SA = [?]π cm²
Answer:
24π cm²
Concepts Applied:
SA (TSA) of a cone = π · r · ( l+r )
Relation between l, h, and r i.e. l²=h²+r²
(h: cone height, r: base radius, l: slant height)
Step-by-step explanation:
Calculating the Slant height:
l²=h²+r²
l = sqrt(h²+r²)
l = sqrt(16+9)
l = sqrt(25)
l = +5 cm (distance is a scalar quantity)
Calculating the TSA:
= π · 3 · (5+3)
= 24π cm²
Answer:
34π cm^2 is the correct answer
∫76 cos(29 x) cos(34 x) cos(4x) dx=
after integrating we get ∫76 cos(29 x) cos(34 x) cos(4x) dx= 1/150 [sin(75x) + 2sin(67x) + 2sin(59x)] + C
Using the identity cos(a)cos(b) = 1/2[cos(a+b) + cos(a-b)], we can rewrite the integrand as:
cos(29x)cos(34x)cos(4x) = 1/2[cos((29+34+4)x) + cos((29+34-4)x)]cos(4x)
= 1/2[cos(67x) + cos(59x)]cos(4x)
Now, using the same identity again, we can further simplify:
cos(67x)cos(4x) = 1/2[cos(71x) + cos(63x)]cos(4x)
cos(59x)cos(4x) = 1/2[cos(63x) + cos(55x)]cos(4x)
Substituting these back into the original integral, we get:
∫76 cos(29x)cos(34x)cos(4x) dx = 1/2 ∫76 [cos(71x) + cos(63x) + cos(63x) + cos(55x)]cos(4x) dx
= 1/2 ∫76 [cos(71x)cos(4x) + cos(63x)cos(4x) + cos(63x)cos(4x) + cos(55x)cos(4x)] dx
Now, using the identity ∫ cos(ax) dx = (1/a)sin(ax) + C, we can easily integrate each term:
1/2 [1/75 sin(75x) + 1/67 sin(67x) + 1/67 sin(67x) + 1/59 sin(59x)] + C
Therefore, the final answer is:
∫76 cos(29x)cos(34x)cos(4x) dx = 1/150 [sin(75x) + 2sin(67x) + 2sin(59x)] + C
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Terri is beginning a science experiment in the lab. The instructions call for 227 milligrams of potassium. Calculate the difference between this amount and 1 gram
The difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
The amount of potassium called for in the experiment is 227 milligrams. To convert milligrams to grams, we divide by 1000: 227/1000 = 0.227 grams.
The amount of 1 gram is larger than 0.227 grams. To find the difference between the two amounts, we subtract the smaller amount from the larger amount:
1 gram - 0.227 grams = 0.773 grams
Therefore, the difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
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The spinner at the right is spun 12 times. it lands on blue 1 time.
1. what is the experimental probability of landing on blue?
2. compare the experimental and theoretical probabilities of the spinner landing on blue. if the probabilities are not close, explain a possible reason for the discrepancy.
Experimental probability of landing on blue = 1/12 and experimental probability and theoretical probability are not close.
1.
To find the experimental probability of landing on blue, we need to divide the number of times it landed on blue by the total number of spins.
Experimental probability of landing on blue = Number of times landed on blue / Total number of spins
Here, the spinner was spun 12 times and landed on blue 1 time.
Experimental probability of landing on blue = 1/12
2.
The theoretical probability of landing on blue is the ratio of the number of blue spaces to the total number of spaces on the spinner. Since there is only one blue space out of four total spaces, the theoretical probability is 1/4 or 0.25.
The experimental probability = 1/12 = 0.083
So, the experimental probability and theoretical probability are not close.
A possible reason for the discrepancy is likely due to the small sample size of spins. With a larger number of spins, the experimental probability should converge closer to the theoretical probability. This is known as the law of large numbers in probability theory.
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HELP!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!
1. The value of d is 10
2. measure of angle BSR is 120°
3. measure of angle RSM is 60°
What are angles on a straight line?The sum of angles on a straight line is 180°. This angles are adjascent angles.
angle BSR and RSM are on a straight line, therefore;
10d+20+6d = 180
16d = 180-20
16d = 160
d = 160/16
d = 10
therefore the value of d is 10
angle BSR = 10d+20 = 10×10+20
= 100+20 = 120°
angle RSM = 6d = 6 × 10
= 60°
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Ryan buys some jumpers to sell on a stall.
He spends £130 buying 40 jumpers.
He sells 80% of the jumpers for £12 each.
He then puts the rest of the jumpers on a Buy one get one half price offer.
He manages to sell half the remaining jumpers using this offer.
How much profit does Ryan make?
Answer: £326
Step-by-step explanation:
Step 1: Calculate the cost per jumper
To find out how much Ryan spent on each jumper, we divide the total cost by the number of jumpers.
[tex]\frac{130}{40} = 3.25[/tex]
This gives us a cost of £3.25 per jumper.
Step 2: Calculate the revenue from selling 80% of the jumpers
Ryan sells 80% of the 40 jumpers, so:
[tex]\text{0.8 x 40 = 32}[/tex]
So he sold 32 Jumpers.
He sells each jumper for £12:
[tex]\text{32 x 12 = 384}[/tex]
So his revenue from selling these jumpers is £384
Step 3: Calculate the revenue from selling the remaining jumpers on the Buy one get one half price offer
Ryan has 8 jumpers left after selling 80% of them. He puts these on a Buy one get one half price offer, which means that for every jumper sold at full price, he sells another one at half price.
This means that he sells 4 jumpers at full price (£12 each) and 4 jumpers at half price (£6 each).
His revenue from selling these jumpers is:
[tex]\text{(4 x 12) + (4 x 6) = 72}[/tex]
Step 4: Calculate the total revenue
Ryan's total revenue is the sum of the revenue from selling 80% of the jumpers and the revenue from selling the remaining jumpers on the Buy one get one half price offer.
This is:
[tex]\text{384 + 72 = 456}[/tex]
So Ryan's total revenue is £456
Step 5: Calculate the total cost
Ryan's total cost is the amount he spent on buying the jumpers, which is £130.
Step 6: Calculate the profit
Ryan's profit is the difference between his total revenue and his total cost:
[tex]\text{456 - 130 = 326}[/tex]
Therefore, Ryan makes a profit of £326.
I need questions 3,4,5 with answers and explanations/work
The family with 8 pets cannot be used to represent the whole because it is an outlier
Bar chartCircle graphExplaining why the family with 8 pets cannot be used to represent the wholeGiven that we have
A dot plot that represents the display
On the dot plot, we have
Outlier = 8
This data value is considered an outlier because it is relatively far from other values
As a general rule, outliers cannot be used to represent the whole
The display that could be used to show trendHere, we have
Dot plotBar chartCircle graphOf the three displays, the bar chart is used to represent data such that users may readily recognize patterns or trends.
So, the bar chart is to be used
The display that could be used not to show trendHere, we have
Dot plotBar chartCircle graphOf the three displays, the circle graph does not show that users patterns or trends.
So, the circle graph is to be used
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HELP!!!
What is the unit rate of this graph?
BLUE: 200 beats/minute
TEAL: 75 beats/minute
YELLOW: 100 beats/minute
RED: 150 beats/minute
A spring with a 9-kg mass and a damping constant 7 can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value c2 – 4mk? m²kg / sec? Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form Great cos(Bt) + czert sin(8t)
The value of [tex]c2 – 4mk[/tex] in scenario is[tex]c2 – 0.748[/tex]m and the position of the mass after t seconds is x(t) = [tex]e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t)[/tex],which can be written in the general form Great [tex]cos(Bt) + czert sin(8t).[/tex]
The value of c2 – 4mk in this scenario can be found using the equation [tex]c2 – 4mk = c2 – 4mω02[/tex], where ω0 is the natural frequency of the spring. To calculate ω0, we can use the equation[tex]ω0 = sqrt(k/m)[/tex], where k is the spring constant and m is the mass.
Plugging in the given values, we get [tex]ω0 = sqrt(1.5/9) = 0.433[/tex]. Substituting this into the first equation, we get [tex]c2 – 4mk = c2 – 4m(0.433)2 = c2 – 0.748m.[/tex]
Using the given initial condition of the spring being stretched 1 meter beyond its natural length and then released with zero velocity, we can determine that A = 1 and B = 0.5. Plugging in all the values, we get [tex]x(t) = e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t).[/tex].
This equation represents the motion of the spring-mass system as it oscillates back and forth around its equilibrium position. The exponential term represents the damping of the system, while the sinusoidal terms represent the oscillation.
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X varies jointly as y and z.
Write an equation that express each relationship. Then solve the equation for y.
An equation that express each relationship for the joint variation is X = kyz. Solving for y will give the equation y = X/(kz)
What is joint variationJoint variation is a mathematical concept that describes the relationship between two or more variables.
If X varies jointly as y and z, we can express this relationship mathematically using the formula:
X = k × y × z
X = kyz
where k is a constant of proportionality.
We can solve for y by dividing both sides by kz follows:
X/kz = kyz/kz
X/(kz) = y
Therefore, the equation that express each relationship for the joint variation is X = kyz. And the equation solved for y is y = X/(kz).
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Find the maximum sum of two positive numbers (not necessarily
integers), each of which is in [1,450], and whose product is
450.
The maximum sum of two positive numbers in the range [1, 450] with a product of 450 is approximately 42.42.
How to find sum of two positive numbers?
1. Let the two numbers be x and y.
2. Given that their product is 450, we have the equation xy = 450.
3. To find the maximum sum, we will use the fact that the sum of two numbers is maximum when they are equal. So, x = y.
4. From the product equation, we get x * x = 450, which implies x^2 = 450.
5. Taking the square root of both sides, we have x = √450 ≈ 21.21 (approximately).
6. Since x = y, the maximum sum is x + y = 21.21 + 21.21 ≈ 42.42.
Therefore, the maximum sum of two positive numbers in the range [1, 450] with a product of 450 is approximately 42.42.
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Suppose you rent canoes to campers to go down the river for a living. Two summers ago you rented canoes for $35 a day and rented 150 canoes. To entice more campers last summer, you lowered the price by $5 and rented 25 more canoes. This summer you are considering lowering the price again based on the trend you noticed last summer. How much should you rent a canoe for to maximize revenue?
The optimal rental price to maximize revenue is $35, the same as two summers ago.
To determine the optimal canoe rental price to maximize revenue, we can use the concept of price elasticity of demand, which measures the responsiveness of demand to a change in price.
When the price of a product decreases, consumers tend to buy more of it, but the increase in demand may not be proportional to the decrease in price. The price elasticity of demand can help us estimate the percentage change in demand for a given percentage change in price.
In this case, we can use the data from the previous two summers to estimate the price elasticity of demand for canoe rentals. From the data provided, we know that a $5 decrease in price led to an increase of 25 canoes rented.
This means that the price elasticity of demand is approximately -5 (25/5). In other words, for every 1% decrease in price, we can expect a 5% increase in demand.
To determine the optimal rental price, we need to find the point where the marginal revenue from renting an additional canoe is equal to the marginal cost of renting it out. Assuming that the marginal cost of renting out an additional canoe is constant, we can use the price elasticity of demand to estimate the change in revenue due to a change in price.
If we increase the rental price by $1, we can expect to lose 5% of customers (assuming the same elasticity as last summer). This means that for every $1 increase in price, we will lose 7.5 (150*5%) customers. On the other hand, we will gain $35 in revenue for each of the remaining 142.5 canoes rented, resulting in a total revenue of $4,987.5.
If we decrease the rental price by $1, we can expect to gain 5% more customers, resulting in 157.5 canoes rented. However, we will also lose $30 in revenue for each of the 150 original customers who decide to rent at the lower price.
This means that for every $1 decrease in price, we will gain 7.5 customers but lose $4,500 in revenue. The total revenue at a rental price of $34 will be $4,827.5.
This price will result in the same number of customers as two summers ago but with a slightly higher revenue due to inflation.
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Lulu has 10 feet of ribbon she uses 1 1/3 feet ribbon for a project she uses the rest of the ribbon to make bows she uses 8 inches of ribbon for each bowl how many does lulu make?
The number of bows Lulu can make from the remaining ribbon is 13 bows.
To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.
10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.
She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:
(26/3) * 12 = 104 inches of ribbon remaining.
Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:
104 / 8 = 13 bows.
Lulu can make 13 bows with the remaining ribbon.
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Use an integer to describe the situations.
6 meters above sea level ___
sea level ___
Answer:
An integer to describe 6 meters above the sea level would be meters.
As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".
We assume that sea level is the datum line and anything above that would be positive and below that would be negative.
So 6 meters above the sea level can be described as .
Integers: Set of whole number containing both positive and negative values of it.
PLS MARK BRAINLIEST
Step-by-step explanation:
Term 1: 1 + 1×4 = 5 Term 2: 1 + 2x4 = 9 Term 3: 1 + 3x4 = 13 1.4.1. Term 4: 144x4 = 17 1.4.2. Term 5: 1 +5XL = 21 1.4.3. Term 10:+10X4=4/ 1.4.4. Term 50: 1450 xy = 201 1.5. What stays the same in the pattern in (1.4.1. - 1.4.4.) and what varies? (2)
The polynomial x²+xy+y² has 3 terms. Option C is correct.
We have,
A polynomial is an algebraic statement made up of variables and coefficients.
Variables are sometimes known as unknowns. We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.
Given polynomial;
⇒x²+xy+y²
The three terms are as follows;
x²
xy
y²
The polynomial x²+xy+y² has 3 terms.
Hence, option C is correct.
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complete question:
How many terms does the polynomial x² + xy y2 have?
1 term
2 terms
3 terms
4 terms
1. Un ciclista ha recorrido 145. 8 km en una etapa, 136. 65 km en otra etapa y 162. 62 km en una tercera etapa. ¿Cuántos kilómetros le quedan por recorrer si la carrera es de 1000 km?
Esta es una y la segunda es otra ayúdenme
2. Una clinica dental tiene una tarifa de $ 19,99 para las calzas de piezas dentales. Si en un mes se registraron 109 calzas realizadas, ¿ que cantidad de dinero ingreso a la clinica?
1) The distance left in the race is 554.93km
2) The total amount earned is $2,178.91
How many kilometers remain in the race?We know that the total race is of 1000km, to find the distance missing, we need to take that total distance and subtract the amounts that the cyclist already traveled.
Then we will get:
distance left = 1000km - 145.8km - 136.65km - 162.62 km
distance left = 554.93km
That is the distance left in the race.
2) We know that each piece costs $19.99, and 109 pieces are sold, then the amount earned is the product between these two numbers.
Earnings = 109*$19.99 = $2,178.91
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Which of the equations shown have infinitely many solutions? Select all that apply. A. 3x – 1 = 3x + 1 B. 2x – 1 = 1 – 2x C. 3x – 2 = 2x – 3 D. 3(x – 1) = 3x – 3 E. 2x + 2 = 2(x + 1) F. 3(x – 2) = 2(x – 3)
The two equations with infinite solutions are D 3(x – 1) = 3x – 3 and E2x + 2 = 2(x + 1)
Which equations have infinite solutions?An equation has infinite solutions if we can remove the dependence of the variable, and we end with a true equation.
For example, option D is:
3(x - 1) =3x - 3
Expanding the left side:
3x - 3 = 3x - 3
Subtract 3x in both sides:
-3 = -3
That is true for any value of x.
The other correct option is E:
2x + 2 = 2(x + 1)
2x + 2 = 2x + 2
2 = 2
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Let F(X) = - 8 - x^2, find the following:
(f(7) - f(3))/ 7 -3
A relation is a set of ordered pairs that define the relationship between two sets. And, a function is a relation in which each element of the domain is connected to a single element of the codomain. The evaluated function is -10.
To find the expression (f(7) - f(3))/ 7 -3, we need to first find f(7) and f(3).
Using the given function F(X) = - 8 - x^2, we can find:
f(7) = -8 - 7^2 = -57
f(3) = -8 - 3^2 = -17
Now, we can substitute these values into the expression:
(f(7) - f(3))/ 7 -3 = (-57 - (-17))/ (7-3) = -40/4 = -10
Therefore, the answer is -10.
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