Sonya made a resolution to walk 2.5 kilometers a day. On Tuesday she walked 4 times around the running track at the local high school (each lap is 0.4 kilometers.) How many additional kilometers does Sonya need to walk? (HINT: this is a multi-step problem with 2 operations...)

Answer:

2,3

Step-by-step explanation:

Answer:

(2,3) if the distance between each line is 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer 10 inches

To find how many inches will equal 25 miles on the the map use the info they have already given u.

4in=10

8in=20

10in=25

The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.

The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.

Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.

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Answer:

17^2 or 289

Step-by-step explanation:

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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The correct answer is D) The flow capacity of the parallel system will remain the same.  In a parallel pipeline system, increasing the length of the parallel pipes will not have a significant impact on the flow capacity, and the capacity will remain the same.

In a parallel pipeline system, increasing the length of the parallel pipes does not directly impact the capacity of the system. The capacity of the system is primarily determined by the diameters of the pipes and the overall hydraulic characteristics of the system.

When pipes are connected in parallel, each pipe offers a separate pathway for the flow of fluid. The total capacity of the system is the sum of the capacities of each individual pipe. As long as the pipe diameters and the hydraulic conditions remain the same, increasing the length of the parallel pipes will not affect the capacity.

The length of the pipes may introduce additional frictional losses, which can slightly reduce the flow rate. However, this reduction is usually negligible compared to the effects of pipe diameter and other factors that determine the capacity of the system.

Therefore, in a parallel pipeline system, increasing the length of the parallel pipes does not directly impact the capacity of the system. The capacity of the system is primarily determined by the diameters of the pipes and the overall hydraulic characteristics of the system.

Thus, the appropriate option is "D".

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Answer:

a=4

Step-by-step explanation:

a)  The combination of units that results in the minimum cost to supply a load of 200MW is Combination 1, with Unit 1 generating 130MW, Unit 2 generating 39MW, and Unit 3 generating 31MW. b) the optimal dispatch remains the same as before, which is Combination 1: Unit 1 generating 130MW

a) To determine how the units should be dispatched to supply a load of 200MW at minimum cost, we need to compare the costs of operating each unit within their respective output limits.

Unit 1 cost calculation:

At minimum output (50MW):

Cost = 5000 + 215P + 0.5P^2

      = 5000 + 215(50) + 0.5(50^2)

      = 5000 + 10750 + 0.5(2500)

      = 5000 + 10750 + 1250

      = 17000 + 1250

      = 18250 [C]

At maximum output (130MW):

Cost = 5000 + 215P + 0.5P^2

      = 5000 + 215(130) + 0.5(130^2)

      = 5000 + 27950 + 0.5(16900)

      = 5000 + 27950 + 8450

      = 32950 + 8450

      = 41400 [C]

Unit 2 cost calculation:

At minimum output (39MW):

Cost = 5000 + 270P + 1.0P^2

      = 5000 + 270(39) + 1.0(39^2)

      = 5000 + 10530 + 1.0(1521)

      = 5000 + 10530 + 1521

     = 16051 [C]

At maximum output (128MW):

Cost = 5000 + 270P + 1.0P^2

      = 5000 + 270(128) + 1.0(128^2)

      = 5000 + 34560 + 1.0(16384)

      = 5000 + 34560 + 16384

      = 55944 [C]

Unit 3 cost calculation:

At minimum output (40MW):

Cost = 9000 + 160P + 0.7P^2

      = 9000 + 160(40) + 0.7(40^2)

      = 9000 + 6400 + 0.7(1600)

      = 9000 + 6400 + 1120

      = 16520 [C]

At maximum output (149MW):

Cost = 9000 + 160P + 0.7P^2

      = 9000 + 160(149) + 0.7(149^2)

      = 9000 + 23840 + 0.7(22201)

      = 9000 + 23840 + 15540.7

      = 48380.7 [C]

To supply a load of 200MW at minimum cost, we need to determine the combination of units that results in the lowest total cost.

To find the optimal dispatch, we'll compare the costs of different combinations:

Combination 1: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 31MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 41400 + 16051 + 16520

               = 73971 [C]

Combination 2: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 40MW

Total cost = Cost(Unit 1) + Cost(Unit

2) + Cost(Unit 3)

               = 41400 + 16051 + 16520

               = 73971 [C]

Combination 3: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 41MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 41400 + 16051 + 18307.7

               = 75758.7 [C]

Based on these calculations, the combination of units that results in the minimum cost to supply a load of 200MW is Combination 1, with Unit 1 generating 130MW, Unit 2 generating 39MW, and Unit 3 generating 31MW.

b) If the company has the opportunity to buy energy on the spot market at the price of 300 d/MWh and 220 c/MWh, respectively.

To determine the new dispatch, we compare the costs of operating the units with the market prices:

Unit 1 cost with spot market price: 300 d/MWh

Cost = 5000 + 215P + 0.5P^2

      = 5000 + 215(300) + 0.5(300^2)

      = 5000 + 64500 + 0.5(90000)

      = 5000 + 64500 + 45000

      = 114500 [C]

Unit 2 cost with spot market price: 220 c/MWh

Cost = 5000 + 270P + 1.0P^2

      = 5000 + 270(220) + 1.0(220^2)

      = 5000 + 59400 + 1.0(48400)

      = 5000 + 59400 + 48400

      = 112800 [C]

Unit 3 cost with spot market price: 220 c/MWh

Cost = 9000 + 160P + 0.7P^2

      = 9000 + 160(220) + 0.7(220^2)

      = 9000 + 35200 + 0.7(48400)

      = 9000 + 35200 + 33880

      = 78080 [C]

To determine the new optimal dispatch, we compare the costs considering the spot market prices:

Combination 1: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 31MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 114500 + 112800 + 78080

               = 305380 [C]

Combination 2: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 40MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 114500 + 112800 + 78080

               = 305380 [C]

Combination 3: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 41MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 114500 + 112800 + 79912

               = 307212 [C]

Based on these calculations, even with the spot market prices, the optimal dispatch remains the same as before, which is Combination 1: Unit 1 generating 130MW.

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The result of the division based on the exponent will be C. −5x6y2 + 3x3y.

When dividing with the same base, you subtract the exponents. So, for the x terms, you subtract the exponent of x in the denominator (-2) from the exponent of x in the numerator (8 - 5 = 3). Similarly, for the y terms, you subtract the exponent of y in the denominator (1) from the exponent of y in the numerator (3 - 2 = 1).

Therefore, the result is -5xy²+ 3x(5-2), which simplifies to -5xy² + 3x³y.

Thus, the correct answer is −5x6y2 + 3x3y.

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Given:

The equation is

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)

To find:

The solutions of given equation over the interval \([0,2\pi]\).

Solution:

We have,

The equation is

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\sin \dfrac{\pi }{3}\)

\(\sin\left(x+\dfrac{7\pi}{2}\right)=\sin (-\dfrac{\pi }{3})\)

If \(\sin x=\sin y\), then \(x=n\pi +(-1)^ny\).

Over the interval \([0,2\pi]\).

\(x+\dfrac{7\pi}{2}=4\pi-\dfrac{\pi }{3}\) and \(x+\dfrac{7\pi}{2}=5\pi+\dfrac{\pi }{3}\)

\(x=\dfrac{11\pi }{3}-\dfrac{7\pi}{2}\) and \(x=\dfrac{16\pi}{3}-\dfrac{7\pi}{2}\)

\(x=\dfrac{22\pi-21\pi }{6}\) and \(x=\dfrac{32\pi-21\pi }{6}\)

\(x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\)

Therefore, the two solutions are tex]x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\).

Answer:

C. π/6 & 11π/6

Step-by-step explanation:

If you graph the equation ( Sin (x+7π/2)=-√3/2) and look between 0 & 2π, you'll see that the lines intersect the x-axis at π/6 & 11π/6.

Total number of deaths = 883 (Given in question)

Deaths because of accidents = 24 (Given in question)

Deaths because of cancer = 182 (Given in question)

Deaths because of heart disease = 333 (Given in question)

The empirical formula of probability is given as:

Number of chosen observations/ Total number of observations of the event

Let deaths because of accidents be represented as A

Let the Total number of deaths T

Then the empirical formula for the probability of deaths caused due to accidents is:

P(E)= A/T (Where P(E) represents empirical probability)

P(E)= 24/883

Thus the probability of deaths caused due to automobile accidents using the empirical approach is a) 24/883

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Ok the first thing we have to do is calculate the approximate values of each number's probability. That probability tells how often will the dice land on a certain number. To approximate it you have to divide every frequency by the total amount of times the dice was tossed. Let's do that for every number:

Now we can solve the question. For example if you want to know how many times the dice is expected to land on 4 you just need to multiply the probability for that number, which I called P(4), for the total amount of times the dice was tossed, which are 180 times:

And that's the answer for a.

For item b we need to make more operations. We are being asked how many times the dice is expected to land on a number greater than 3. For this we'll have to use the probability for all the numbers on the dice that are greater than 3: 4, 5 and 6. We'll need to add all these probabilities and multiply the result od that sum by 180:

Since 92.88 isn't a whole number we round it to 93 and that's the answer for item b.

We can repeat our calculations for item c but using the probabilities of the even numbers instead. Said numbers are 2, 4 and 6:

Rounding 83.88 we have 84, the solution to item c.

According to probability, 8 ± 4 heads in 16 tosses is about as likely as 32 ±  8 heads in 64 tosses.

For 8 ± 4 heads in 16 tosses, we can calculate the probability of getting either 4 or 12 heads as follows:

P(X = 4) = ¹⁶C₄ x (1/2)⁴ x (1/2)¹² = 0.088

P(X = 12) = ¹⁶C₁₂ x (1/2)¹² x (1/2)⁴ = 0.088

So, the probability of getting either 4 or 12 heads in 16 tosses is about 0.176 or 17.6%.

In the second part of the question, we are asked to find the number of heads in 64 tosses that is about as likely as 8 ± 4 heads in 16 tosses. To do this, we need to find the mean and standard deviation of the binomial distribution for 64 tosses:

Mean = np = 64 x 1/2 = 32

Standard deviation = √(np(1-p)) = √(64 x 1/2 x 1/2) = 4

Since we are looking for a value that is about as likely as 8 ± 4 heads in 16 tosses, we can use the standard deviation of the binomial distribution to determine the range of values that are likely to occur:

Lower range = 32 - 4 x 2 = 24

Upper range = 32 + 4 x 2 = 40

So, the number of heads in 64 tosses that is about as likely as 8 ± 4 heads in 16 tosses is 32 ± 8. This means that the number of heads could be anywhere between 24 and 40 with about the same probability as getting 8 ± 4 heads in 16 tosses.

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Complete Question:

According to probability, 8 ± 4 heads in 16 tosses is about as likely as 32 ±  _____ heads in 64 tosses.

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

931 Days

Step-by-step explanation:

Answer:

931 days pls brainliest

Step-by-step explanation:

Answer:

12 is an acute angle that is less than 90 degrees and 6 is an obtuse angle which is more than 90 degrees.

Analysis of Variance (ANOVA) is used to investigate the differences between two or more sample means. ANOVA is used to compare the means of two or more groups of data.

It does this by comparing the variance between the groups to the variance within the groups. The null hypothesis in ANOVA is that all group means are equal. This hypothesis is tested using an F-test.

The F-test is used to determine if the variation between groups is significantly greater than the variation within groups. If the F-test is significant, it indicates that at least one of the means is significantly different from the others. To calculate the F-test, we need to find the mean square for the between-groups variance (MSB) and the mean square for the within-groups variance (MSW).

We can use the following formula: F = MSB / MSW,

where

MSB = SSb / dfb, MSW = SSw / dfw,

SSb = the sum of squares between groups, SSw = the sum of squares within groups, dfb = the degrees of freedom for the between-groups variance, and dfw = the degrees of freedom for the within-groups variance. In this case, the Flesch Reading Ease scores were obtained from each page of three different novels. The TI-83/84 Plus calculator results from analysis of variance are not provided.

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Using mathematical expression to solve the word problem, the height of the tree is calculated as: 11.5 ft.

To solve a word problem like the one given above, translate each of the statements into mathematical expressions using numbers and operation signs.

Height of the house = 52 ft

Height of the tree = (2(52) + 7.5) ft

Thus, to find the actual height of the tree, simplify the expression formed from the word problem above:

Height of the tree = (2(52) + 7.5) ft = (104 + 7.5) ft

Height of the tree = 111.5 ft

Thus, by solving the word problem using mathematical expression, the height of the tree is calculated as: 11.5 ft.

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Answer:

B: 0.50x + 3 = 4.50

Step-by-step explanation:

James needed an additional 3 scoops so the x would have to be on $0.50. the $3 is what the cone cost so it has to be with the scoop price. $4.50 is the total price of the ice cream so that would be on the other side of the equal sign, resulting in 0.50x + 3 = 4.50

The speed of the boat in still water is 5 km/h.

Let's denote the speed of the boat in still water as "v" (in km/h). Since the boat travels 2 km upstream and 2 km downstream, we know that the total distance traveled is 4 km.

Let's first calculate the time taken to travel 2 km upstream. We know that the current is flowing at 2 km/h, so the effective speed of the boat relative to the river is (v - 2) km/h (since it is going against the current). Therefore, the time taken to travel 2 km upstream is

time taken = distance / speed = 2 / (v - 2) hours

Similarly, the time taken to travel 2 km downstream is

time taken = distance / speed = 2 / (v + 2) hours

The total time taken for the round trip (2 km upstream and 2 km downstream) is given as 11 minutes, which is equivalent to (11/60) hours. Therefore, we can write

2 / (v - 2) + 2 / (v + 2) = 11/60

Multiplying both sides by (v - 2)(v + 2) gives

2(v + 2) + 2(v - 2) = (v - 2)(v + 2)(11/60)

Simplifying the right-hand side gives

(v - 2)(v + 2)(11/60) = (11/3)v^2 - 44/3

Substituting this expression into the previous equation and simplifying gives

22v = (11/3)v^2 - 44/3

Multiplying both sides by 3 gives

66v = 11v^2 - 44

Rearranging and solving for v using the quadratic formula gives

v = (11 ± √(11^2 + 4×44))/22

Taking the positive solution (since v must be positive) gives

v = 5 km/h

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Answer:

T. S. A. =2πrh+2πr2

V=Bh

V = Base×h

V= (lw) × h

V= lwh

Answer: i belive its B but im not 100%

Step-by-step explanation:

Answer:

5,000.

¡Espero que ayude!

Step-by-step explanation:

Answer: 3480 seconds and 5420 feet

Step-by-step explanation:

We can set an equation for both Keith and Erica. Let t = time in seconds.

Keith's BalloonHeight = 1.5*t+200ft

Erica's Balloon Height = 1.4*t+548ft

We want to know when E=K (same height)

1.4*t+548ft = 1.5*t+200ft

348 = 0.1t

t = 3480 seconds

Use this time in either Keith's or Erica's Height formula:

Keith Balloon Height: 1.5*t+200ft for t=3480

1.5*(3480)+548

Keith's Height in 3460 sec: 5420 feet

Erik's Balloon Height: = 1.4*t+548ft

= 1.4*(3480)+548ft

Erik's Height in 3480 sec: 5420 feet

The two lines intersect at (3460,5420). At 3460 seconds both balloons will be at 5420 feet.

Answer:

-1/2

Step-by-step explanation:

y = mx + c

y = -1/2x + 3 (rearranged from question)

slope = m

Answer:

- 1/2

Step-by-step explanation:

Answer:

w = ±3

Step-by-step explanation:

(w - 1) (w + 1) = 8

FOIL the left hand side.

w^2 -w+w-1 = 8

w^2 -1 =8

Add 1 to each side.

w^2 -1+1 = 8+1

w^2 = 9

Take the square root of each side.

sqrt(w^2) = sqrt(9)

w = ±3

Answer........

Step-by-step explanation:

Answer:

$90

Step-by-step explanation:

Given that:

Number of mobile phones = 450

Cost per mobile phone = $30

Number of mobile phones purchased = 3

The total cost of 3 mobile phones = amount paid remaining :

(Cost per mobile phone * number of mobile phones purchased)

= $30 * 3

= $90

Answer:

68 members

Step-by-step explanation:

80% of 85 =

10% = 8.5

8.5 x 8 = 68.

Hope this helps

Answer:

9x - 11

Step-by-step explanation:

4x - 3 + 5x - 8

4x + 5x - 3 - 8

9x - 11