A plane's airspeed is 400 miles per hour on a heading of 45 degrees south of east (compass: 135 degrees, babylonian 315 degrees). if a wind is blowing from the west with a speed of 50 miles per hour, what is the ground speed and direction of the plane?

Answer:

Option b. width = 16.5 inches and length = 24 inches

Step-by-step explanation:

Tim enlarged a picture wit a width of 5.5 inches and a length of 8 inches.

He enlarged the picture by a scale factor of 3.

We have to find the new dimensions of the picture.

Since, New dimension of the picture = Scale factor × dimensions before enlargement

So new width = 3×5.5 = 16.5 inches

new length = 3×8 = 24 inches

Therefore, option b. is the answer.

Answer:

I think Table C - Corralle

Answer:

c

Step-by-step explanation:

52 cards in a deck

 4 kings

 4 queens

 King = 4/52 reduces to 1/13

Queen = 4/52 reduces to 1/13

1/13 *1/13 = 1/169

 so none of the above

87-3x>165

-3x> (165-85)

-3x>80

80/-3 = -26.666

check;

87-3*(-26)=165

so x < -26

To find the location of point R on the number line, you can use the formula for finding a point on a line segment given the endpoints and the ratio. In this case, the ratio is 3:5 and the endpoints are -14 and 2.

To find the location of point R, you can use the formula for finding a point on a line segment given the endpoints and the ratio. In this case, the formula is:

R = Q + r(QS)

where Q is the starting point, S is the ending point, r is the ratio between Q and S, and QS is the displacement vector from Q to S. In this problem, Q is -14, S is 2, and the ratio is 3:5. So we can substitute these values into the formula and solve:

R = -14 + (3/8)(2 - (-14)) = -14 + (3/8)(16) = -14 + 6 = -8

Therefore, the location of point R is -8 on the number line.

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The location of point R is -8. The correct answer is option a. [tex]\frac{3}{3+5}(2-(-14))+(-14)[/tex]

To find the location of point R which partitions the directed line segment from Q to S in a 3:5 ratio, we use the section formula. The formula is:

[tex]R =\frac{m}{m+n}(x_2-x_1)+x_1[/tex]

Here, m = 3 and n = 5, while Q is at [tex]x_1 =[/tex] -14 and S is at [tex]x_2 =[/tex] 2.

Plugging in the values, we have:

Therefore, the location of point R is at -8 on the number line and it is calculated by the expression [tex]R =\frac{3}{3+5}(2-(-14))+(-14)[/tex].

The complete question is:
On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula [tex]R =\frac{m}{m+n}(x_2-x_1)+x_1[/tex] to find the location of point R?

a. [tex](\frac{3}{3+5})(2-(-14))+(-14)[/tex]

b. [tex](\frac{3}{3+5})(-14-2)+2[/tex]

c. [tex](\frac{3}{3+5})(2-14)+14[/tex]

d. [tex](\frac{3}{3+5})(-14-2)-2[/tex]

Answer:

128 lawn mowers

Step-by-step explanation:

Given,

The overhead cost = $ 34,816,

The cost for one lawn mower = $ 388,

Let x be the number of lawn mowers manufactured,

So, the total cost of x lawn mowers = 34816 + 388x,

Now, if the average cost of x mowers = $ 660,

So, the total cost = 660x

[tex]\implies 660x = 34816 + 388x[/tex]

[tex]660x - 388x = 34816[/tex]

[tex]272x= 34816[/tex]

[tex]\implies x = \frac{34816}{272}=128[/tex]

Hence, 128 lawn mowers were manufactured.

Answer:  The required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]  

Step-by-step explanation:  We are given to find the fourth term of a geometric sequence with the following first term and common ratio :

[tex]a=15,~~r=\dfrac{1}{3}.[/tex]

We know that

the nth term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

Therefore, the forth term of the given geometric sequence is

[tex]a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.[/tex]

Thus, the required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]  

to calculate the vertical height multiply the hypotenuse ( 5280) by the sin of the angle (5)

5280 x sin(5) = 460.1823

round off to 460 feet

2

2x2 = 4

2+2 =4

0

0x0=0

0+0=0

Answer:

Part 1) [tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]

Part 2) [tex]TA=(104+16\sqrt{13})\ in^{2}[/tex]

Step-by-step explanation:

Part 1) Find the lateral area of the prism

we know that

The lateral area of the prism is equal to

[tex]LA=Ph[/tex]

where

P is the perimeter of the base

h is the height of the prism

Applying the Pythagoras Theorem

Find the hypotenuse of the triangle

[tex]c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in[/tex]

Find the perimeter of triangle

[tex]P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in[/tex]

Find the lateral area

[tex]LA=Ph[/tex]

we have

[tex]P=(10+2\sqrt{13})\ in[/tex]

[tex]h=8\ in[/tex]

substitutes

[tex]LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}[/tex]

Part 2) Find the total area of the prism

we know that

The total area of the prism is equal to

[tex]TA=LA+2B[/tex]

where

LA is the lateral area of the prism

B is the area of the base of the prism

Find the area of the base B

The area of the base is equal to the area of the triangle

[tex]B=\frac{1}{2}bh[/tex]

substitute

[tex]B=\frac{1}{2}(6)(4)=12\ in^{2}[/tex]

Find the total area of the prism

[tex]TA=LA+2B[/tex]

we have

[tex]B=12\ in^{2}[/tex]

[tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]

substitute

[tex]TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}[/tex]

Final answer:

The function y = 2,000 - 90x shows Bradley's distance from home decreases by 90 meters for every minute walked, starting from 2,000 meters away. The graph of this equation is a straight line with a negative slope, indicating constant speed.

Explanation:

The equation y = 2,000 - 90x represents Bradley's distance from home in meters, y, as a function of the time x in minutes that he walks. This equation is a linear function where the initial value 2,000 meters represents the distance from home at the start, and -90 meters/minute is the rate at which this distance decreases as Bradley walks home. As time increases by 1 minute, the distance from home decreases by 90 meters. This relationship shows that Bradley travels at a constant speed since the slope of the line representing the equation (which is the rate of change of distance with respect to time) is constant.

If we graph this function, we would get a straight line that starts at 2,000 meters on the y-axis when t=0 and has a negative slope of 90. Therefore, the graph shows that as time passes, Bradley gets closer to home at a steady pace. This also reflects that the total distance Bradley would walk is 2,000 meters, and the time it would take for him to return home can be found by setting the function equal to zero and solving for x.

The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.

To calculate simple interest, you can use the formula:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Where:

- Principal (P) is the initial amount of the loan.

- Rate (R) is the annual interest rate (in decimal form).

- Time (T) is the number of years.

In this case:

- Principal (P) = $850

- Rate (R) = 7.5% = 0.075 (decimal form)

- Time (T) = 8 years

Now, plug these values into the formula:

SI = $850 × 0.075 × 8

SI = $510

The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.

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Let us say that the total amount paid in the first dealer is P1 and the total amount paid to the second dealer is P2. So that:

P1 = 2500 + 150 t

P2 = 3000 + 125 t

Where t is the total number of months

Now we are asked when the total amount paid would be equal for the two dealers, this means P1 = P2, therefore equating the two:

2500 + 150 t = 3000 + 125 t

25 t = 500

t = 20 months

Therefore the total amount paid for both dealers would be equal after 20 months.