11. An airplane flying against the wind travels 140 miles in the same amount of time it would take the same plane to travel 160 miles with the wind. If the wind speed is a constant 20 miles per hour, how fast would the plane travel in still air? ​

Answer:

$1 per lb

Step-by-step explanation:

If you divide the cost by the amount you are getting, then you get the unit rate. So, since 7 divided by 7.00 is 1.00, then the cost per pound is $1.00

The diner sold $600 worth of French fries in May

The diner sold $2400 worth of French fries in June. This amount sold in June

is 4 times as much as was sold in May.

Therefore, the dollars worth of French fries sold in May can be computed as follows:

Let

x = amount sold in May

Therefore,

divide both sides by 4

4x / 4 = 2400 / 4

x = $600

Therefore, the diner sold $600 worth of French fries in May

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Answer:

35/16      2 2/16

Step-by-step explanation:

1 1/4 = 5/4

1 3/4 = 7/4

5 * 7 = 35

4 * 4 = 16

35/16

Answer:

2 3/16

Step-by-step explanation:

First, we have to convert our mixed numbers to improper fractions, so our new equation is:

5/4 x 7/4 = 35/16

35/16 = 2 3/16

We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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There were 50 questions on her exam.

To find this answer, first make the percentage a decimal by dividing 72 by 100. This will give you 0.72, which you divide into 36 (36 ÷ 0.72). Doing so reverses the percentage, and gives you the total amount of questions. Thus meaning your answer is 50.

I hope this helps!!

Answer:

The probability is \(P(|p-\^{p}| >  0.03)  =   0.0040\)

Step-by-step explanation:

From the question we are told that

   The population proportion is \(p =  0.07\)

   The mean of the sampling distribution is   \(\mu_p =  0.07\)

   The sample size is n = 600

Generally the standard deviation is mathematically represented as

     \(\sigma_p  =  \sqrt{\frac{p (1 -p)}{n} }\)

=>    \(\sigma_p  =  \sqrt{\frac{0.07(1 -0.07)}{600} }\)    

=>    \(\sigma_p  =  0.010416 \)    

Generally the probability that the proportion of airborne viruses in a sample of 600 viruses would differ from the population proportion by greater than 3% is mathematically represented as

      \(P(|p-\^{p}| >  0.03) =  1 - P(|p -\^{p}| \le 0.03)\)

=>   \(P(|p-\^{p}| >  0.03)  =  1 -  P(-0.03 \le p -\^{p} \le 0.03 )\)

Now  add p  to  both side of the inequality

=>   \(P(|p-\^{p}| >  0.03)  =  1 -  P( 0.07-0.03  \le \^{p} \le 0.03+ 0.07 )\)

=>   \(P(|p-\^{p}| >  0.03)  =  1 -  P(0.04 \le \^{p} \le 0.10 )\)

Now  converting the probabilities to their respective standardized score

=> \(P(|p-\^{p}| >  0.03)  =  1 -  P(\frac{0.04 - 0.07}{0.010416}  \le Z \le \frac{0.10 -0.07}{0.010416}  )\)

=> \(P(|p-\^{p}| >  0.03)  =  1 -  P(-2.88  \le Z \le 2.88 )\)

=>   \(P(|p-\^{p}| >  0.03)  =   1 - [P(Z \le 2.88) - P(Z \le -2.88)]\)

From the z-table  

       \(P(Z \le 2.88)  =  0.9980\)

and

       \(P(Z \le -2.88)  = 0.0020\)

So

     \(P(|p-\^{p}| >  0.03)  =   1 - [0.9980 - 0.0020]\)

=>   \(P(|p-\^{p}| >  0.03)  =   0.0040\)

Answer:

x=34

Step-by-step explanation:

a^2 + b^2 = c^2

16^2 + 30^2 = c^2

256 + 900 = c^2

1156 = c^2

sqrt1156 = c

34 = c

34 = x

Checked work with a calculator. Hope this helps. Have a nice day. May it be filled with joy and happiness. Please, be safe and wash your hands. Happy Holidays.

Answer:

x = 34

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to find the missing side.

Step 2: Identify Variables

Leg a = 30

Leg b = 16

Hypotenuse c = x

Step 3: Solve for x

a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:

Distance between point A and C:

d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]

    = sqrt[(14 - 2)^2 + (9 - 4)^2]

    = sqrt[144 + 25]

    = sqrt(169)

    = 13

Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.

Distance between point B and C:

d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]

    = sqrt[(7 - 2)^2 + (16 - 4)^2]

    = sqrt[25 + 144]

    = sqrt(169)

    = 13

Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.

Therefore, points A and B are on the circle with center C(2, 4) and radius 13.

b) The midpoint of line segment AB can be found using the midpoint formula:

M = [(x_A + x_B)/2, (y_A + y_B)/2]

 = [(14 + 7)/2, (9 + 16)/2]

 = [10.5, 12.5]

The slope of line segment AB can be found using the slope formula:

m_AB = (y_B - y_A)/(x_B - x_A)

    = (16 - 9)/(7 - 14)

    = -7/-7

    = 1

The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:

m_CM = -1/m_AB

    = -1/1

    = -1

The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:

y - y_C = m_CM(x - x_C)

y - 4 = -1(x - 2)

y = -x + 6

The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.

Hence, we have shown that line segment CM is perpendicular to line segment AB.

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A function's domain is the set of all possible inputs to the function. Domains can be limited if the function is rational and the denominator is 0 for some x value or values.

What are the 3 domain restrictions?

The square root function, log function, and reciprocal function are the three functions with limited domains. Because you cannot take square roots of negative numbers and produce real numbers, the square root function has a limited domain.

To find the domain restriction of an expression, take the expression's denominator. Put that denominator to zero. Solve the resulting equation for the denominator zeroes. The domain consists of all other x-values.

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The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

Given: height of helicopter = 300√3 feet from the ground.

To find: Distance between zoo and library.

Finding:

(Refer to the image attached.)

Let the distance from the plane to the zoo and library be d1 and d2 respectively.

Then, with the help of concepts of applications of trigonometry,

\(tan(60) = \frac{300\sqrt{3}}{d1}\)

=> \(\sqrt{3}=\frac{300\sqrt{3}}{d1}\)

=> d1 = 300 feet

\(tan(30) = \frac{300\sqrt{3}}{d2}\)

=> \(\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}\)

=> d2 = 300 (3) = 900 feet

The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.

Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

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Answer:

slope = - 14

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 92, 21 ) and (x₂, y₂ ) = (- 93, 35 )

m = \(\frac{35-21}{-93-(-92)}\) = \(\frac{14}{-93+92}\) = \(\frac{14}{-1}\) = - 14

Answer:

B. 1.828 meters

Step-by-step explanation:

You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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Answer:

green brown green brown brown green brown green YAY YOUR FAILING GOOD JOB green brown brown green  I KNOW THE ANSWER BUT IM NOT TELLING YOU brown green green brown

Step-by-step explanation:

The estimated volume of the solid bounded by the given surface and planes using the midpoint rule with m = 4 and n = 2 is 6 cubic units.

Here, we have,

To estimate the volume of the solid using the midpoint rule, we divide the region into small rectangular boxes and approximate the volume of each box.

Given that m = 4 and n = 2, we divide the region into 4 intervals along the x-axis and 2 intervals along the y-axis.

The width of each subinterval along the x-axis is:

Δx = (2 - 1) / 4 = 1/4

The width of each subinterval along the y-axis is:

Δy = (2 - 1) / 2 = 1/2

Now, let's estimate the volume using the midpoint rule.

For each subinterval, we evaluate the function at the midpoint of the interval and multiply it by the area of the corresponding rectangle.

The volume of each rectangular box is given by:

V_box = f(x*, y*) * Δx * Δy

where (x*, y*) is the midpoint of each rectangle.

Let's calculate the volume:

V_total = Σ V_box

V_total = ∑ f(x*, y*) * Δx * Δy

Since f(x, y) = 4x + 2y + 8x, we have:

f(x, y) = 4x + 2y + 8x = 12x + 2y

We can evaluate the function at the midpoints of each subinterval and calculate the corresponding volumes.

Substituting the values into the formula, we have:

V_total

= [(12(1/8) + 2(1/4)) * (1/4) * (1/2)] + [(12(3/8) + 2(1/4)) * (1/4) * (1/2)] + [(12(5/8) + 2(1/4)) * (1/4) * (1/2)] + [(12(7/8) + 2(1/4)) * (1/4) * (1/2)]

= [(3/2 + 1/2) * (1/4) * (1/2)] + [(9/2 + 1/2) * (1/4) * (1/2)] + [(15/2 + 1/2) * (1/4) * (1/2)] + [(21/2 + 1/2) * (1/4) * (1/2)]

= [(2) * (1/4) * (1/2)] + [(5) * (1/4) * (1/2)] + [(8) * (1/4) * (1/2)] + [(11) * (1/4) * (1/2)]

= (1/4) + (5/4) + (4) + (11/4)

= 6

Therefore, the estimated volume of the solid bounded by the given surface and planes using the midpoint rule with m = 4 and n = 2 is 6 cubic units.

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Given a metal rod of length 31 cm placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, you need to consider the following:

1. The metal rod is 31 cm in length.
2. The magnetic field strength is 2.3 T (tesla).
3. The rod is positioned perpendicular to the magnetic field, which means that the angle between the rod and the magnetic field is 90 degrees.

In this scenario, the rod is placed in such a way that it experiences the full effect of the magnetic field due to its perpendicular orientation.

When a metal rod of length 31 cm is placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, it will experience a force. The force on the rod will be given by the formula F = BIL, where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod.

Since the rod is not connected to a circuit, there is no current flowing through it. Therefore, the force on the rod will be zero. However, if a current is passed through the rod, it will experience a force perpendicular to both the magnetic field and the direction of the current flow. The magnitude of the force will depend on the strength of the magnetic field, the current flowing through the rod, and the length of the rod.

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The length of the rectangle is 15 inches, and the width is 9 inches.

Let's denote the length of the rectangle as L and the width as W.

According to the given information, the width is 6 inches less than the length, which can be expressed as:

W = L - 6

The perimeter of a rectangle is calculated by adding the lengths of all sides. In this case, the perimeter is given as 48 inches:

2(L + W) = 48

Substituting the value of W from the first equation into the perimeter equation:

2(L + L - 6) = 48

2(2L - 6) = 48

4L - 12 = 48

4L = 48 + 12

4L = 60

L = 60 / 4

L = 15

Now, substitute the value of L back into the first equation to find the width:

W = L - 6

W = 15 - 6

W = 9

Therefore, the length of the rectangle is 15 inches, and the width is 9 inches.

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Answer:

Option C

Step-by-step explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.  

Let's try this with option C. To make things easier, convert -4.5 into decimal form: \(-4\frac{1}{2}\). Substitute \(-4\frac{1}{2}\) for x and 10 for y in the equation, then solve:  

\(y = -\frac{2}{3} x+7\\\\10 = -\frac{2}{3} (-4\frac{1}{2} )+7\\10 = -\frac{2}{3} (-\frac{9}{2})+7\\10 = 3+7\\10 = 10\)

10 does equal 10, so this is a true statement. Option C is the right answer.

Answer:

5.5

Step-by-step explanation:

Answer:

option A 1/5, 3/10, 1/15, 4/15, 1/6

The probability distribution for the 30 pieces of fruit is,

A. 1/5, 3/10, 1/15, 4/15, 1/6.

A probability distribution is a mathematical function used in probability theory and statistics that estimate the likelihood that various possible outcomes of an experiment will occur.

Given, Every week a company provides fruit for its office employees and the total number of fruits is 30 and the number of different types of food is

listed in the table.

Therefore, The probability distribution of apple (A) is 6/30 = 1/5.

Similarly, P(B) = 9/30 = 3/10.

P(L) = 2/30 = 1/15.

P(O) = 8/30 = 4/15.

P(P) = 5/30 = 1/6.

So, The distribution table is 1/5, 3/10, 1/15, 4/15, 1/6.

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A) The probability of selecting a tomato soup can on the first draw = 4/10

The probability of selecting another tomato soup can on the second draw (without replacement) = 3/9

The probability of selecting a pumpkin soup can on the first draw = 6/10

The probability of selecting another pumpkin soup can on the second draw (without replacement) = 5/9

B) Probability of selecting one tomato soup can and one pumpkin soup can = probability of (i) + probability of (ii)

= 2/15 + 1/3

= 1/3

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Answer:

(18 + 36 + 27) = 9 x (2+4+3)

(88 + 66 + 22) = 22 x (4+3+1)

(36 + 96 + 12) = 12 x (3+8+1)

(126 + 28 + 14) = 14 x (9+2+1)

(54 + 81 + 27) = 27 x (2+3+1)

(16 + 28 + 48) = 4 x (4+7+12)

Step-by-step explanation:

The equations in the solution represent each expression as a multiple of a sum of whole numbers with no common factor.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

As per the given question, the required solution would be as:

(18 + 36 + 27) = 9 × (2+4+3)

This equation represents each expression as a multiple of a sum of whole numbers with no common factor.

Similarly further equations like as :

(88 + 66 + 22) = 22 × (4+3+1)

(36 + 96 + 12) = 12 × (3+8+1)

(126 + 28 + 14) = 14 × (9+2+1)

(54 + 81 + 27) = 27 × (2+3+1)

(16 + 28 + 48) = 4 × (4+7+12)

Thus, the above equations represent each expression as a multiple of a sum of whole numbers with no common factor.

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Using an exponential function, it is found that her total profit for the first ten years is of $422,426.72.

An increasing exponential function is modeled by:

\(A(t) = A(0)(1 + r)^t\)

In which:

In this problem, we have that the initial value and the growth rate are given as follows:

A(0) = 31124, r = 0.06.

Hence the profit function is given by:

\(P(t) = 31124(1.06)^t\)

Then, the total profit over the first 10 years is given by:

\(\int_{0}^{10} P(t) dt\)

\(\int_{0}^{10} 31124(1.06)^t dt\)

\(\frac{31124}{\ln{1.06}} \times (1.06)^t|_{t = 0}^{t = 10} = 422,426.72\)

Thus, her total profit for the first ten years is of $422,426.72.

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In this scenario, the population consists of the multiple choices provided in the instructions. These choices represent the various categories or options that the respondents can select when expressing their beliefs about wearing face masks in public as an important public health measure.

The researcher plans to poll a random sample of 2,000 adults from this population in order to gather data and test the null hypothesis against the alternative hypothesis.

By examining the responses of this sample, the researcher aims to make inferences about the larger population and draw conclusions regarding the proportion of people who believe in the importance of wearing face masks in public.

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Answer:

200 FEET

2 units/5 feet = x units/200 feet

x = 2/5 (200) = 400/5 = 80 units

Cross Multiplication

5x = 2(200)

x = 400/5 = 80 units

Step-by-step explanation:

A situation that could follow a binomial distribution is the number of heads that occur when flipping a "fair-coin" multiple times.

A "Binomial-Distribution" is defined as a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, flipping a "fair-coin" is an independent trial with two possible outcomes (heads or tails), and the probability of getting a heads on any given flip is 0.5.

Each "coin-flip" is independent of the others, and the probability of getting a heads on any given flip is always the same which is "0.5",

So, this situation fits the requirements for a binomial distribution.

The "binomial-distribution" can then be used to calculate the probability of getting a certain number of heads out of a fixed number of flips. For example, if we flip a coin 10 times, the probability of getting exactly-5 heads can be calculated using the binomial distribution formula.

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The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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