Two factories blow their whistles at exactly the same time. If a man hears the two blasts exactly


4. 2 seconds and 5. 9 seconds after they are blown and the angle between his lines of sight to the two


factories is 40. 8°, how far apart are the factories? Give your result to the nearest meter. (Use the fact


that sound travels at 344 m/sec. )


A) 2903 meters


B) 3263 meters C) 1329 meters D) 1997 meters

Answer:

total area = 132 units²

Step-by-step explanation:

Area of largest rectangle = 4 x 15 = 60 units²

Area of smallest rectangle = 4 x 6 = 24 units²

Area of largest triangle = 1/2 x (15 - 6) x (4 + 4) = 36 units²

Area of smallest triangle = 1/2 x 6 x 4 = 12 units²

Total area of the figure = sum of areas of 2 rectangles and 2 triangles

⇒ area = 60 + 24 + 36 + 12 = 132 units²

Answer:

739

Step-by-step explanation:

a sub 92 = 11 + (92 - 1) * 8

a sub 92 = 11 + 728

a sub 92 = 739

The coordinates of the image after the translation is as follows

B' (-2, 5)

V' (-1, 3)

H' (-3, 0)

The rule for the transformation as given by the problem is

(x, y) → (x-4, y + 5)

This is applied to the coordinates of the preimage as follows

B (2, 0) → (2 - 4, 0 + 5) → B' (-2, 5)

V (3, -2) → (3 - 4, -2 + 5) → V' (-1, 3)

H (1, -5) → (1 - 4, -5 + 5) → H' (-3, 0)

The image is attached

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Answer: Approximately 5.21

Step-by-step explanation:

Given that the survey of US adults ages 18-24 found that 34% get the news on an average day, we can assume that the probability of an 18-24 year old getting news on an average day is p = 0.34. We also know that we have randomly selected 200 adults in this age group.

The mean of a binomial distribution is given by:

μ = np

where n is the sample size and p is the probability of success. Substituting the given values, we get:

μ = 200 x 0.34 = 68

Therefore, the mean number of adults ages 18-24 who get news on an average day is 68.

The standard deviation of a binomial distribution is given by:

σ = sqrt(np(1-p))

Substituting the given values, we get:

σ = sqrt(200 x 0.34 x 0.66) ≈ 5.21

Therefore, the standard deviation of the number of adults ages 18-24 who get news on an average day is approximately 5.21. Since the sample size is large (n=200), we can use the normal distribution to approximate the binomial distribution.

Answer:

The mean and standard deviation of the number of adults out of 200 who get news on an average day are mu = 68 and sigma = 5.36, respectively, assuming we can use the normal distribution to approximate the binomial distribution.

So the probability that at least 85 people say they get no news on an average day is approximately 0.0013 or 0.13%.

Step-by-step explanation:

Since the survey found that 34% of US adults ages 18-24 get news on an average day, we can assume that the probability of a randomly selected adult in this age group getting news on an average day is p = 0.34. Therefore, the number of adults out of 200 who get news on an average day follows a binomial distribution with parameters n = 200 and p = 0.34.

To use the normal distribution to approximate this binomial distribution, we need to check if the conditions for doing so are met. These conditions are:

np >= 10

n(1-p) >= 10

Here, np = 200 x 0.34 = 68 and n(1-p) = 200 x 0.66 = 132. Both of these values are greater than 10, so the conditions are met.

Now, we can approximate the binomial distribution with a normal distribution with mean mu = np = 68 and standard deviation sigma = sqrt(np(1-p)) = sqrt(200 x 0.34 x 0.66) = 5.36.

Therefore, the mean and standard deviation of the number of adults out of 200 who get news on an average day are mu = 68 and sigma = 5.36, respectively, assuming we can use the normal distribution to approximate the binomial distribution.

Using the previous information, to find the probability that at least 85 people say they get no news on an average day.

Let X be the number of people out of 200 who say they get no news on an average day. We want to find the probability that X is greater than or equal to 85.

Since the probability of any one person saying they get no news on an average day is q = 1 - p = 0.66, we can use the binomial distribution with parameters n = 200 and p = 0.34 to model the number of people who say they get news on an average day.

The probability of at least 85 people saying they get no news on an average day can be calculated using the complement rule:

P(X >= 85) = 1 - P(X < 85)

To use the normal distribution to approximate the binomial distribution, we need to standardize the variable X.

Z = (X - mu) / sigma

where mu = np = 68 and sigma = sqrt(npq) = 5.36, as calculated in the previous question.

Using the continuity correction, we can adjust the upper bound to P(X < 84.5) since we want the probability of at least 85 people saying they get no news.

Z = (84.5 - 68) / 5.36 = 3.00

Using a standard normal distribution table or calculator, we can find that P(Z < 3.00) = 0.9987.

Therefore, the probability of at least 85 people saying they get no news on an average day is:

P(X >= 85) = 1 - P(X < 85)

≈ 1 - P(Z < 3.00)

= 1 - 0.9987

≈ 0.0013

So the probability that at least 85 people say they get no news on an average day is approximately 0.0013 or 0.13%.

The perimeter of the floor of the office building  which was given as 127.5 feet is equal to 42.5 yards.

Perimeter of the floor in an office building is equal to 127.5 feet.

Convert perimeter of the floor of the given office building in feet into yards:

Number of feet in one yard = 3 feet

3 feet = 1 yard

⇒ 1 feet = ( 1 / 3 ) yard

⇒ 127.5 feet = ( 127.5 ) ×   ( 1 / 3 ) yards

⇒127.5 feet = ( 127.5 / 3 ) yards

⇒127.5 feet = ( 42.5 ) yards

Therefore, the perimeter of the floor of the given office building is equal to 42.5 yards.

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Answer: y = (1/2)x + 8

Step-by-step explanation:

Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2

y = (1/2)x + b

7 = (1/2)-2 + b

7 = -1 + b

8 = b

y = (1/2)x + 8

Answer:

Step-by-step explanation:

The angles of that 5-sided polygon add up to equal 540 degrees. So we add up all the angles and solve for x, then plug x back in to angle N to get our answer.

17x + 4 + 10x - 10 + 18x + 6 + 90 + 90 = 540 and

45x + 180 = 540 and

45x = 360 so

x = 8

Now we'll fill 8 back in for x to get the measure of angle N:

18(8) + 6 = 150, the last option listed

Answer: 8 groups is the largest number of groups he can make

Answer:

Step-by-step explanation:

3*5=15

8*16=128

10*7=70

4*3/2=6

15+6+70+128=219

Answer:

219 yd²

area of rectangle

area of 2nd rectangle

area of rectangle

area of triangle

total area:

Answer:

The formula to calculate pressure at an altitude in this case is:

P = original pressure x (1 + rate of change)^(number of changing)

in which,

original pressure = 101 kilopascals

rate of change = -11.9% = - 0.119

number of changing = 2000/1000 = 2

=> P = 101 x (1 - 0.119)^2 = 78.39 kilopascals

Hope this helps!

:)

Answer:

The y intercept of Function A is less than the y intercept of Function B.

Step-by-step explanation:

To find the y-intercept of the equation for A set x=0 and solve for y

Y=4(0)+1 therefore the y intercept for equation A is y=1

To find the y intercept for graph B you find the point where the graph intercepts the y axis which in this case it looks like it intercepts(crosses) the y axis at y=2

Therefore equation A y- intercept(y=1) < equation B y-intercept (y=2)

Hopefully this helps! If it did please mark brainliest! Feel free to ask me any other questions :)

Answer:

Step-by-step explanation:

Find area and perimeter of square of side 5cm

P = 4 × side

A = l x l

Perimeter

5 * 4 = 20 cm

Area

5 * 5 = 25 cm²

Answer:

true

Step-by-step explanation:

A correlation is symmetrical;x is as correlated with y as y is with x. The Pearson product-moment correlation can be understood within a regression context,however.

The number on round off to each place will be 45,621.

The decimal number is rounded to any place by the following concept -

We look at the number to the right of concerned digit. If that number is more than five or exactly five, then we add 1 to our number. However, if it is less than five, then the number remains same.

For instance, if we round 45.621 to nearest tenth, we will get 45.6. This is because on right to it, the number 2 is less than 5. Now, in the mentioned digit which is 45,621, we see there is no decimal and number after that. So, as the digits are 0 which is less than 5, the number will remain as it is.

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When examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

What is statistical validity?

Statistical validity is defined as a procedure or an extent of drawing conclusions to which research works or studies can be considered precise and accurate which are derived from the already existing or reliable statistical tests.

It can also be the statistics which are derived from the research works or studies.

What is frequency in statistics?

Frequency in statistics can be defined as the number of times an observation or a record or a value occurred in the duration of the research work. The frequencies of different records are represented in a tabular form.

For a given set of data the frequency can either be 0 or more than that.

Frequency of a given record or an observation cannot be negative as the least number of times the instance of an object can appear is zero.

What is margin of error estimate?

The margin of error estimate is a percentage figure which can be some percentage more or less than the actual or ideal value.

The margin of error is the range of values greater or lesser than the sample outcome statistic in the accuracy or confidence region or the  interval.

Hence, when examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

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The given statement "To change the contents of a macro, you must use the Record Macro button to step into the macro" is false because one can use other options such open the Visual Basic Editor .

To change the contents of a macro,

It is not necessary we have to use the Record Macro button to step into the macro.

Here one can also open the Visual Basic Editor instead of record Macro button.

In the Visual Basic Editor Project Explorer window.

First we have to open the project folder

And then in the Modules folder we have to select Recorded.

Finally select the module that has the name of the macro.

Here the recorded macro code is going to displayed in the code window.

First one can find the macro in the project window, and then edit the code directly.

Alternatively, one can use the Macro dialog box to have a view and to edit the macro.

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Two linearly independent vectors are perpendicular to v→=[4 −5 −3].

To find two linearly independent vectors perpendicular to v→=[4 −5 −3], we can use the following approach:

Let's apply this approach step by step:

1. The dot product of v→=[4 −5 −3] with an arbitrary vector w→=[x y z] is: v→⋅w→=4x−5y−3z

2. Equating the dot product to zero, we get: 4x−5y−3z=0

Solving for y, we obtain: y=(4/5)x-(3/5)z

3. Choosing a value for z, we can obtain a specific vector that is perpendicular to v→. Let's set z=5 to obtain:

y=(4/5)x-3

We can choose any value for x, say x=5, to obtain the vector:

u→=[5 (4/5)(5)-3 5]

Simplifying, we get:

u→=[5 17 5]

4. To obtain a second vector that is linearly independent from u→, we repeat the same process using a different value for z. Let's set z=0 to obtain:

y=(4/5)x

We can choose any value for x, say x=5, to obtain the vector:

w→=[5 4 0]

Now we have two linearly independent vectors u→=[5 17 5] and w→=[5 4 0] that are perpendicular to v→=[4 −5 −3].

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Answer:

shelter B

Step-by-step explanation:

I think im so sorry if im wrong but it seems B is correct

No, when finding the upper and lower quartiles, the median is not included in the calculations.

When finding the upper and lower quartiles of a data set, the median (or second quartile) is not included in the calculations. The quartiles divide the data set into four equal parts, with the median representing the second quartile.

To find the lower quartile (Q1), one needs to determine the median of the lower half of the data set, excluding the median itself. This includes the data points below the median.

Similarly, to find the upper quartile (Q3), the median of the upper half of the data set is determined, excluding the median. This includes the data points above the median.

The inclusion of the median in the calculation of quartiles can cause confusion, but it is important to note that the median is separate and distinct from the quartiles.

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The vertices of the ellipse are (12, -1) and (4, -1), and the co-vertices are (8, 1) and (8, -3).

To find the vertices and co-vertices of the given ellipse, we can use the equation of an ellipse in standard form:

((x-h)²/a²) + ((y-k)²/b²) = 1

Comparing this with the given equation ((x-8)²/(16)) + ((y+1)²/(4)) = 1, we can identify the values of h, k, a, and b.

From the equation, we can see that the center of the ellipse is at (h, k) = (8, -1). The value of a is the square root of the denominator of the x-term, which is 4, so a = 4. Similarly, the value of b is the square root of the denominator of the y-term, which is 2, so b = 2.

The vertices of the ellipse are located at a distance of a units from the center along the major axis, which is the x-axis. Therefore, the vertices are (8+a, -1) and (8-a, -1), which simplifies to (12, -1) and (4, -1).

The co-vertices of the ellipse are located at a distance of b units from the center along the minor axis, which is the y-axis. Therefore, the co-vertices are (8, -1+b) and (8, -1-b), which simplifies to (8, 1) and (8, -3).

Hence, the correct answer is: The vertices are (12, -1) and (4, -1). The co-vertices are (8, 1) and (8, -3).

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The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

Percentage change = (14000-11200) / 11200 * 100

= 280000 / 11200

= 25%

So, your final answer is 25%

Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

52.5 miles

Step-by-step explanation:

5 miles = 8 km

→ Find how many miles in 1 km

8 km = 5 miles

1 km = 0.625 miles

→ Multiply both sides by 84

84 km = 52.5 miles

Answer:

$35.53

Step-by-step explanation:

25% of 12.92 is 3.23

so 12.92-3.23=9.69

now plus the 2 shirts 9.69+12.92+12.92=35.53

Answer:373248

Step-by-step explanation:

72^3 = 373248