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Answer:

She should walk approximately 1,463.34369 feet along the sidewalk going to the east, then walk the remaining straight line distance along the grass.

====================================================

Explanation:

Refer to the diagram below.

Alaina starts at point A. If she stays on the sidewalk the entire time, then she can go from A to C to D in that order.

If she takes the direct line route, then she would go from A to D across the grass entirely.

The two paths have pros and cons. The optimal solution is a mix of the two routes. This means she'll be on the sidewalk for some amount of time, and then cut along the grass once reaching a certain point.

Let's say point B is the point where she decides to cut along the grass. In the diagram below, I made \(\text{BC} = x\) so that I could find \(\text{BD} = \sqrt{x^2+600^2}\) through the pythagorean theorem fairly quickly.

If \(\text{BC} = x\), then the remaining bit of the east/west side walk is \(\text{AB} = 2000-x\) since the two portions must add to 2000 feet.

----------------

If she travels along the side walk at a rate of 6 ft/sec, and travels 2000-x feet (from A to B), then it will take her

time = distance/speed = \(\frac{2000-x}{6}\) seconds

Then if she cuts across the grass to follow path BD, then she'll take another

time = distance/speed = \(\frac{\sqrt{x^2+600^2}}{4}\) seconds since she's traveling 4 ft/sec here.

----------------

If Alaina goes from A to B to D in that order, then she takes a total of

\(\text{(time from A to B)}+\text{(time from B to D)}\\ = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\)

That represents the total time taken when following this path at those specified speeds mentioned.

The goal is to find the minimum of that function. So we'll need to compute the derivative.

\(f(x) = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\\\\ f \ '(x) = -\frac{1}{6}+2x*\frac{1}{2*4\sqrt{x^2+600^2}}\\\\ f \ '(x) = -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}}\\\\\)

Set the derivative equal to zero and solve for x

\(f \ '(x) = 0\\\\ -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}} = 0\\\\ \frac{x}{4\sqrt{x^2+600^2}} = \frac{1}{6}\\\\ 6x = 4\sqrt{x^2+600^2}\\\\ (6x)^2 = \left(4\sqrt{x^2+600^2}\right)^2\\\\ 36x^2 = 16(x^2+600^2)\\\\ 36x^2 = 16x^2+16*600^2\\\\\)

\(36x^2 = 16x^2+5,760,000\\\\ 36x^2-16x^2 = 5,760,000\\\\ 20x^2 = 5,760,000\\\\ x^2 = 5,760,000/20\\\\ x^2 = 288,000\\\\ x = \sqrt{288,000}\\\\x \approx 536.65631\)

If you were to perform the first derivative test, you should find that the local min occurs at roughly x = 536.65631

This means she must walk a approximately 2000-x = 2000-536.65631 = 1,463.34369 feet when going from A to B such that to minimize the walking time.

Side note: you can use the minimum feature on your calculator to confirm the answer

The line that is perpendicular to y = 5 and passes through (3, - 4) is x = 3.

y = 5 is a horizontal line where all points on that line have a y-coordinate of 5.

This means for every x coordinates, the y value/coordinates is 5.

The y values are constant for every value of x .

A vertical line is perpendicular to a horizontal line.

Vertical lines pass through points that all share an x-coordinate.

Therefore, the line that is perpendicular to y = 5 and passes through (3, - 4) is x = 3.

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The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:

3.68 cm ^2

Step-by-step explanation:

A= b x h

A= 1.6 cm x 2.3 cm

A= 3.68 cm ^2

Answer: x = 13

Step-by-step explanation: When solving an equation like this, we are trying to get our variable which is our letter by itself.

So we first want to ask ourselves what is the 14 doing to x. Well, we can see that it's being added to x so to get x by itself, we will do the opposite of addition which is subtraction. So we subtract 14 from both sides of the equation.

The +14 -14 cancels out so we're left with x on the left.

On the right, we must subtract 14 from 27 to get 13.

So we have x = 13 which is the solution to this equation.

Answer:

\(x = 13\)

Step-by-step explanation:

\(x + 14 = 27 \\ x = 27 - 14 \\ x = 13\)

Answer:

x= 7

Step-by-step explanation:

\(\boxed{ \sinθ = \frac{opp}{hyp} }\)

\( \sin A = \frac{a}{c} \)

\( \frac{a}{c} = x + 2\)

\(\boxed{ \cosθ = \frac{adj}{hyp} }\)

\( \cos B = \frac{a}{c} \)

\( \frac{a}{c} = 2x - 5\)

Equating both expressions for a/c together:

x +2= 2x -5

Bring x terms to 1 side, constants to the other:

2x -x= 2 +5

x= 7

Answer:

X=7

Step-by-step explanation:

Hi, I took the quiz and the right answer is x=7.

we have that

The double angles formula is equal to

and remember that

therefore

substitute in the original expression

therefore

The law of large numbers is a fundamental concept in probability theory that describes the behavior of the average of a large number of independent random variables.

It states that as the sample size increases, the sample mean will converge to the true population mean, and the sample proportion will converge to the true population proportion.

In other words, the larger the sample size, the more reliable the sample mean and proportion will be as an estimate of the true population mean and proportion. This is because the variation in the sample mean and proportion decreases as the sample size increases, and the sample becomes more representative of the population. This principle is widely used in statistics, and it underpins many statistical methods and techniques.

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The first option is correct. There is no significant difference in the purchasing patterns across career types

In order for a dataset to be a valid representation of the total population, it needs to be collected in a way that ensures that it is a fair and accurate sample of the population.

One way to ensure this is through random sampling, where individuals are selected to participate in the study without any bias or preconceived notions about their characteristics. This helps to reduce the potential for selection bias and ensures that the sample is representative of the larger population.

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Answer:

Step-by-step explanation:

There are nine numbers on the spinner with 4 even and 5 odd numbers. Flipping a tail is just 1/2 so

P(ETO)=(4/9)(1/2)(5/9)

P(ETO)=20/162

P(ETO)=10/81

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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Answer: a=x represents sinks

b=the amount of money he will spend overall on the sink and sealent

c= 100x represents 100 sinks

d=joe will have to charge 85 dollars per sink

Step-by-step explanation:

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.

Let's define the decision variables:

Let C represent the number of chairs produced.

Let T represent the number of tables produced.

Objective function:

The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:

Profit = 150C + 750T

Constraints:

Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:

5C + 3T ≤ 240

Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:

4C + 20T ≤ 700

Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:

C ≥ 0

T ≥ 0

Now, we can solve the linear programming problem to find the optimal solution:

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

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Answer:

B

Step-by-step explanation:

we have to subtract the volume of the biggest one from the volume of the smallest one

for find the volume it is used the radius, not the diameter

Hello,

well I guess the correct answer is D

you can see the correct graph below

for all x<1 this is the line y = 1

and then this is the line defined by y = x

hope this helps

X and Y be discrete random variables with joint probability function is answer is (D) 11/9.

To find E[Y| X = 1], we need to use the conditional expectation formula:

E[Y| X = 1] = Σy y P(Y = y| X = 1)

Using the joint probability function, we can find P(Y = y| X = 1):

P(Y = y| X = 1) = f(1, y) / Σy f(1, y)

P(Y = y| X = 1) = ((1/54)(1 + 1)(y + 2)) / ((1/54)(1 + 1)(0 + 2) + (1/54)(1 + 1)(1 + 2) + (1/54)(1 + 1)(2 + 2))

P(Y = y| X = 1) = (y + 2) / 9

Substituting this into the formula for \(E[Y| X = 1],\) we get:

E[Y| X = 1] = Σy y P(Y = y| X = 1)

E[Y| X = 1] = (0)(1/9) + (1)(3/9) + (2)(5/9)

E[Y| X = 1] = 11/9

Therefore, the answer is (D) 11/9.

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Answer:

2.45 sec

Explanation:

use the equation:

a = (Vfy-Viy) / t a=-10m/sec sq

Viy = 30.1 Sin 24 = +12.24

Vfy = - Viy = -12.24

-10 = (-12.24-12.24)/t

t = 24.48/10= 2.45 sec

To determine whether there is a decrease in voter support for the candidate after the scandal, we can test the hypothesis using the proportions of the two polls. The first poll showed 54% support among 630 randomly selected voters, while the second poll showed 51% support among 1010 voters. By conducting a hypothesis test, we can determine if the difference in proportions is statistically significant.

To test the hypothesis, we can use the two-sample z-test for proportions. The null hypothesis (H0) assumes no difference in voter support, while the alternative hypothesis (H1) assumes a decrease in support. We can calculate the test statistic using the formula:

z = (p1 - p2) / √[(p(1 - p) / n1) + (p(1 - p) / n2)]

where p1 and p2 are the proportions from the two samples, and n1 and n2 are the respective sample sizes. p is the pooled proportion, calculated as (x1 + x2) / (n1 + n2), where x1 and x2 are the respective number of successes (votes for the candidate) in each sample.

By calculating the z-value, we can compare it to the critical value for the desired significance level (e.g., α = 0.05). If the z-value exceeds the critical value, we reject the null hypothesis in favor of the alternative hypothesis, indicating a statistically significant decrease in voter support.

After performing the calculations, if the z-value exceeds the critical value, we can conclude that there is evidence to support the claim of a decrease in voter support for the candidate after the scandal. Conversely, if the z-value does not exceed the critical value, we fail to reject the null hypothesis, suggesting that there is insufficient evidence to conclude a significant decrease in support.

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The slope - intercept form of a line is given by the equation:

In this case, we know that m=2 and y=5. So, the equation of this line will be:

To graph it, we need to plot two points and then join them both. These points could be:

Graphing:

The monster has 4 heads and 12 tails.

What is the ratio of the number?

A ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six .

We know that the ratio of the number of eyes to the number of heads is 5:1. If a monster has 20 eyes, we can set up the equation:

20 eyes = x heads

Where x is the number of heads.

We also know that the ratio of the number of heads to the number of tails is 2:6. We can set up the equation:

x heads = 2y tails

Where y is the number of tails.

We know the number of eyes is 20, therefore x = 20/5 = 4 heads

We also know the number of heads is 4, therefore y = 4*6/2 = 12 tails

Hence, the monster has 4 heads and 12 tails.

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Answer:

\(beinggreat78~is~here~to~help!\)

The equation should look something like this.

\(\frac{u(3)}{3}\)

Be careful with your use between cubing and multiplying; Cubing is multiplying the number by itself multiple times, while multiplying is like repeated adding, yet much easier.

In this case, if it says triple, I highly recommend multiplying by 3, which is what I did, it only looks different because it is in parentheses.

What have we learned?

The nurse should administer 19.958 mg of furosemide per dose to the toddler.

To use the unitary method, we need to convert the toddler's weight from pounds to kilograms, as the dose is given in mg/kg/day.

1 lb = 0.45359237 kg (conversion factor)

Therefore, the toddler's weight in kilograms is

22 lb x 0.45359237 kg/lb = 9.979 kg (rounded to three decimal places)

Now we can calculate the total daily dose of furosemide for the toddler

4 mg/kg/day x 9.979 kg = 39.916 mg/day (rounded to three decimal places)

Since the dose is divided into 2 equal doses daily, each dose would be half of the total daily dose

39.916 mg/day ÷ 2 = 19.958 mg/dose (rounded to three decimal places)

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The given function is f(x) = 2(3x) = 6x.

The domain of the function is all real numbers since there are no restrictions on the input x. Therefore, the correct answer is:

Domain: (-∞, ∞)

To find the range, we can consider the fact that the function is a linear function with a positive slope of 6. This means that the output values increase as the input values increase.

The lowest possible output value occurs when x = 0, which gives f(0) = 0. As x increases, the output values increase without bound. Therefore, the range of the function is:

Range: (0, ∞)

So, the correct answer is:

Domain: (-∞, ∞)

Range: (0, ∞)

The given set is {(x, y) | x ≠ −3}, open and connected. Option a and b are correct.

The set is open because for any point (x, y) in the set, we can find a small neighborhood around it (an open ball) that is entirely contained within the set. Specifically, we can choose a radius smaller than the distance from x to -3 to get an open ball around x that does not intersect -3.

The set is connected because any two points in the set can be connected by a continuous path within the set. This follows from the fact that the set is an open interval in the x-axis, which is a connected space.

The set is not simply connected because it has a "hole" at x = -3. Specifically, any closed curve in the set that encircles x = -3 cannot be continuously shrunk to a point within the set. This means that the set fails to satisfy the more stringent condition of simply connectedness, which requires that every closed curve in the set can be continuously shrunk to a point within the set. Option a and b are correct.

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The one value for x for which 2/7<x<1/3 is  (C)3/10 , the correct option is (C)3/10 .

In the question ,

the inequality is given as 2/7<x<1/3

Simplifying the fractions we get

2/7 = 0.2857

and

1/3 = 0.3333

Simplifying the options given  ,we get

(A) 1/12 = 0.0833

(B) 1/4 = 0.25

(C) 3/10 = 0.3

(D) 3/7 = 0.4285

(E) 5/9  = 0.5555

hence , the only value lying between 0.2857 and 0.3333 is option (C) 0.30

that is (C) 3/10.

Therefore , the one value for x for which 2/7<x<1/3 is (C)3/10 , the correct option is (C)3/10 .

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Answer:

$0.18 sales tax will be added to the purchase price.

Step-by-step explanation:

Given that:

Cost of cupcake = $3

Sales tax applied = 6%

Amount of sales tax = 6% of cost of cupcake

Amount of sales tax = \(\frac{6}{100}*3\)

Amount of sales tax = 0.06 * 3 = $0.18

Hence,

$0.18 sales tax will be added to the purchase price.

Answer:

\(|7m- 56| = 56 - 7m\)

Step-by-step explanation:

Given

\(|7m- 56|\)

\(m < 8\)

Required

Rewrite the expression without absolute values

The first step is to check if the expression in |...| is positive or negative;

The question says m < 8,

This means the value of m could be 7, 6 ...

Let's assume m is 7

\(7m - 56 = 7 * 7 - 56 = 49 - 56 = -7\)

This means that the expression \(|7m- 56|\) will give a negative value if \(m < 8\)

So,

\(|7m- 56| = -(7m - 56)\)

Open bracket

\(|7m- 56| = -7m + 56\)

Rearrange

\(|7m- 56| = 56 - 7m\)

The expression can't be further simplified

The difference between the 2 in the tens place and 2 to its left column in the given number 2,222.222 is 180.

According to the number system, a number can be written in its expanded form according to their pace value in the chart.

2,222.222 can be written as 2×1000+2×100+2×10+2X1+2×1/10+2×1/100+2×1/1000

The place value of 2 in the tens place in given number 2,222.222 = 20

The place value of 2 in its left column in the given number 2,222.22  = 200

Difference between the place of 2 in tens place and 2 in its left column

= 200 - 20

= 180

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