A jet is flying with an air speed of 480 miles per hour at a bearing of N82 °E. Because of the wind, NE° . the ground speed of the plane is 518 miles per hour at a bearing of 79°E.
a- What are the speed and direction of the wind?
b- If the pilot increased the air speed of the plane to 500 miles per hour, what would be the resulting ground speed and direction of the plane?

Given:

Initial number of bacteria = 3000

With a growth constant (k) of 2.8 per hour.

To find:

The number of hours it will take to be 15,000 bacteria.

Solution:

Let P(t) be the number of bacteria after t number of hours.

The exponential growth model (continuously) is:

[tex]P(t)=P_0e^{kt}[/tex]

Where, [tex]P_0[/tex] is the initial value, k is the growth constant and t is the number of years.

Putting [tex]P(t)=15000,P_0=3000, k=2.8[/tex] in the above formula, we get

[tex]15000=3000e^{2.8t}[/tex]

[tex]\dfrac{15000}{3000}=e^{2.8t}[/tex]

[tex]5=e^{2.8t}[/tex]

Taking ln on both sides, we get

[tex]\ln 5=\ln e^{2.8t}[/tex]

[tex]1.609438=2.8t[/tex]                  [tex][\because \ln e^x=x][/tex]

[tex]\dfrac{1.609438}{2.8}=t[/tex]

[tex]0.574799=t[/tex]

[tex]t\approx 0.575[/tex]

Therefore, the number of bacteria will be 15,000 after 0.575 hours.

Answer:

40

Step-by-step explanation:

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The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

what is triangle ?

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

Given, side length, a = 12 units.

the height of equilateral triangle, h = (a√3)/2.

Substituting the value of 'a',

h = (12√3)/2 = 6√3 =

10.39 units.

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

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Answer:

12.6 ft

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

let h be height up the side of the building , then

h² + 6² = 14²

h² + 36 = 196 ( subtract 36 from both sides )

h² = 160 ( take the square root of both sides )

h = [tex]\sqrt{160}[/tex] ≈ 12.6 ft ( to the nearest tenth )

The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.

We can rewrite the equations as:

3x + 5y = 3

6x + ky = 8

To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:

6x + 10y = 6

-18x - 3ky = -24

Now we can add the two equations together and get:

-12x - 3ky = -18

Since the coefficient of x is 0, this equation does not have any solution for any value of k.

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Answer:

11 grades of 85 did Brenda, Robert, and Timothy receive altogether.

Step-by-step explanation:

Let 6x be the number of 85 received by Brenda.

The number of 85 received by Robert is 1/3 of Brenda= 2x

The number of 85 received by Timothy is 1/2 of Brenda= 3x

Then according to the given conditions

6x+ 2x+ 3x

= 11x

So  the number of total 85s received by all the three is 11.

11 grades of 85 did Brenda, Robert, and Timothy receive altogether.

The answer is yes since there are no repeating x values.

Step-by-step explanation:

a) Attached at the end.

b) Strong positive linear correlation.

c) The length of time is 220 minutes.

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).

Given:

a) The Scatter plot Associated with data is attached below.

b) The Scatter plot shows the positive linear correlation between number of pieces in a jigsaw puzzle and time required for a person to complete it.

c) To complete the puzzle with 650 pieces it will take 220 minutes.

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Answer:

a)  See attachment.

b)  Strong positive correlation.

c)  247 minutes

Step-by-step explanation:

Plot the points from the given table on the given coordinate plane.

Draw a line of best fit.

(See attachment).

As the line of best fit has a positive gradient, the two variables are positively correlated.

As the line of best fit lies close to most of the points, this indicates there may be a strong correlation.

To predict the length of time it will take Dave to complete a 650-piece puzzle, locate 650 on the x-axis of the scatter plot, trace up to the line of best fit and read the y-value:

Therefore, it will take Dave approximately 247 minutes to complete a 650-piece puzzle.

Answer: 6

Step-by-step explanation:

y = -3x + 6 is the linear equation of the form y = mx + c

where m is the gradient of the graph and c is the y-intercept of the graph.

Hence,

m = -3

c = 6

y-intercept of the graph = c

                                        = 6

The residual value of coordinate is 0.24.

A residual is the discrepancy between a data point's actual value and the value predicted by a regression or trend line.

Trend lines provide the approximate shape of the data and display the general shape the data takes. The most precise trend lines are those that best suit the data.

Given equation y = 1.18x + 5.4

and coordinates (2, 8)

y at x = 2

y = 1.18x + 5.4

y = 1.18(2) + 5.4

y = 7.76

residual value = actual y axis value - predicted y axis value

residual value = 8 - 7.76 = 0.24

Hence the residual value is 0.24.

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Answer:

8x+14

Step-by-step explanation:

The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.

1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.

2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.

3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.

4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.

5) Intercepts: The points where the graph of a function crosses the x- and y-axes.

6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.

7) Continuity: A function is continuous if its graph has no breaks or gaps.

8) Smoothness: A function is smooth if its graph has no sharp corners or links.

9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.

10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.

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Answer:

100 minutes / [tex]1 \frac{2}{3}[/tex] hours

First, we need to do 40 ÷ 12 = 3 1/3

Next, multiply 3 1/3 by 30 = 100

So, it is 100 minutes. But wait! We can simply it...

100 minutes = 1 2/3 hours

You can always convert it into different time labels. I think this is the most popular.

Answer:

Step-by-step explanation:

1. Substitute the number for the variable in the equation.

Hey Buddy,

Answer:

343 cm³

Step-by-step explanation:

Total Surface Area of the cube = 294 cm²

Surface Area = 6a²

6a² = 294

a² = 49

a = square root of 49

  = 7

Volume of a cube =  a³

Thus, the volume of the cube = 7³

                                                 = 7*7*7

                                                 = 343 cubic centimeters

Hope it helps :)

Answer:

$8.28

Step-by-step explanation:

0.18*46=8.28

Answer:

X < -7

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

11 and 12

Step-by-step explanation:

this is because the square root of 121 is 11 and the square root of 144 is 12 so the answer will lie between 11 and 12

It will take you 6.5 hours to read a 312-page book

From the question, we have the following parameters that can be used in our computation:

Rate = 12 pages of a book in 15 minutes

This means that

Rate = 12 pages/15 minutes

Convert to per hour

Rate = 12 pages/0.25 hour

Evaluate

Rate = 48 pages per hour

For a 312-page book, we have

Time = 312 pages/48 pages per hour

Evaluate

Time = 6.5 hours

Hence, the time is 6.5 hours

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The linear regression equation that represents the given set of data is y=0.2x+865.

Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.

The line of best fit is in the form y=bx+a

The slope is b= [tex]\frac{\sum (x-\bar x)\sum (y-\bar y)}{\sum (x-\bar x)^2}[/tex]

Here, [tex]\bar x[/tex] =(0+1+2+3+4)/5

= 1.8

[tex]\bar y[/tex] = (856+871+924+961+961)/5

= 914.6

∑(x-[tex]\bar x[/tex])=(0-2.5)+(1-2.5)+(2-2.5)+(3-2.5)+(4-2.5)

= -2.5-1.5-0.5+0.5+1.5

= -2.5

∑(y- [tex]\bar y[/tex]) =(865-914.6)+(871-914.6)+(924-914.6)+(961-914.6)+(961-914.6)

= -49.6-43.6+9.4+46.4+46.4

= 9

So, slope b= 1.8×9/9²

b=0.2

Substitute b=0.2 and (0, 865) in y=bx+a, we get

865=0.2×0+a

a=865

Substitute b=0.2 and a=865 in y=bx+a, we get

y=0.2x+865

Therefore, the linear regression equation that represents the given set of data is y=0.2x+865.

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"Your question is incomplete, probably the complete question/missing part is:"

The number of newly reported crime cases in a county in New York State is shown in the accompanying table; where X represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected number of new cases for 2003, rounded to the nearest whole number: Years since 1995 (x) New Cases (y) 856 871 924 961 961

Two identical set squares with angles 30-60-90 degree Placed adjacently to form a parallelogram  

Answer:

1)

17/20 will have the same value as 1D.

To get this

given D=1

Substitute that into the equation..

you have

E=17/20

To verify this... input E=17/20 into the original equation to see if you will get 1D

17/20 =17/20D

Multiply through by 20/17

You'll have D=1.

So

17/20E will have the same value as 1U.S dollar.

2)

20/17US dollar will Equal 1E.

Solving arithmetically

Given E=1.

Find D subject

your have

D=20E/17

E=1

D=20/17

To verify this answer

substitute D=20/17 and see if you'll get 1E

E=17/20D

E=17/20 x 20/17

E=1.

Conclusion

20/17D will have the same value as 1E

Making

Answer:

Step-by-step explanation:

12h + 15(4) = 444

12h + 60 = 444

12h = 444 - 60

12h = 384

h = 384/12

h = 32 <===== Hector worked 32 hrs

Answer:

11) I haven't done these yet don't go by my answers wait for more responses.

So if TR looks exactly half way from the middle and it says its 11, and if PS is basically two of TR then it would be 22. It looks to me that TR is 11 which is exactly half way I think, and PS looks double of TR so 2 x 11 = 22. Please go by the way you learned i don't know if I'm right.

12) If MK is exactly straight and its 10, half of 10 would be 5. I did half of 10 because L to M looks as if it is 10 already but since its L to the point in the middle that would be half way of the total line from L to M. So L to the point must be 5, MK is already given which is 10 so now we add 5 since L to the point in the middle is half way of 10 which is 5.

10(MK) + 5(L to the point in the middle of the circle) = 15

I don't want to be the one who brings your grades down so do by the way you learned.

Answer:

12

Explanation:

40/100 = 0.4

0.4 * 30 = 12

I hope this helps you!

American nickels are issued as currency. A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).

A dime is worth ten cents and a nickel five cents. In other words, one dime is equivalent to two nickels.

In light of this, we might state that a nickel is worth half what a dime is worth.

Despite having a higher value than a nickel, the dime is smaller.

n + d = 22 <— d = 22-n

Amount in pennies: 5n + 10d = 170

5n + 10(22 - n) = 170

5n + 220 - 10n = 170

220 - 5n = 170

220 - 170 - 5n = 0

50 - 5n = 0

50 = 5n

n = 10

A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).

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Answer:

[tex]\small\mathfrak\green{2x + 10 + 46 = 180 \: = linear \: pair} \\ \\ \small\mathfrak\red{hope it helps...}[/tex]