Consider vectors u = ⟨2, 1⟩ and v = ⟨4, –1⟩ with the angle between them equal to 40°. What are the scalar projections uv and vu?

a) uv = 1.33 and vu = 1.33
b) uv = 1.33 and vu = 3.16
c) uv = 1.71 and vu = 1.33
d) uv = 1.71 and vu = 3.16

Answer:

(3,-2)

Step-by-step explanation:

I used a graphing calculator to get the solution, attached is what I got with the graphing calculator.

hope this helps.

Answer: ₱40,909.1

Step-by-step explanation:

Given data:

Rate for first year = 4%

Rate for next two years = 6%

Rate for the next 3 years = 7.5%

Interest paid back after 5years = ₱ 15,750

Solution:

How much did she borrow.

= let the sum borrowed be P

= P * 4 / 100

= 4P/100

= 1P/25.

For the next two years

= P* 6 * 2/100

= 12P/100

= 3P/25

For the next 3years

= P* 7.5*3/100

= 22.5P/100

= 9P/40.

1P/25 + 3P/25 + 9P/40 = 15750

77P/200 = 15750

P = 15750 * 200 / 77

P = 315,0000/77

P = ₱40,909.1

The amount borrowed is ₱40,909.1

Answer:

x - intercept = 5

y- intercept = 2

Step-by-step explanation:

2x + 5y = 10

Write the equation in   [tex]\frac{x}{a}+\frac{y}{b}=1[/tex]  form

So, divide the equation by 10

[tex]\frac{2x}{10}+\frac{5y}{10}=\frac{10}{10}\\\\\frac{x}{5}+\frac{y}{2}=1[/tex]

x - intercept = 5

y- intercept = 2

Answer:

(5,0) and (0,2)

Step-by-step explanation:

Basically, all we need to do is enter 0 for both variables. We can do this because the y-value of an x-intercept will always be 0, and the x-value of a y-intercept will always be 0.

So, to find the x-intercept we can set y equal to 0 and then solve for x.

[tex]2x+5(0)=10\\2x=10\\x=5[/tex]

So the x-intercept will be (5,0).

We can do the same thing to find the y-intercept.

[tex]2(0)+5y=10\\5y=10\\y=2[/tex]

The y-intercept is (0,2)

Hope this helps!

Answer:

6. The distance Rampy Ronald would have travelled horizontally is approximately 48.428 feet for an actual maximum height of 21.486 feet

7. Rampy Ronald is going to make the jump

Please find attached the graph of the motion of Rampy Ronald, created with Microsoft Excel

Step-by-step explanation:

6. The given parameters are;

The width of the ravine = 80 ft

The inclination of the ramp with which Rampy Ronald will jump = 30°

The distance from the edge of the ravine the ramp ends = 5 feet

The speed with which Rampy Ronald will make the jump = 60 mph

The maximum height he will reach = 30 feet

Therefore, we have;

The height of the end of the ramp = 15 × sin(30°) = 7.5

The height of the end of the ramp = 7.5 feet

The height of the jump = 30 - 7.5 = 22.5

The vertical velocity = 60 × sin(30°) = 30

The vertical velocity = 30 mph

The horizontal velocity = 60 × cos(30°) = 30·√3

The horizontal velocity = 30·√3 mph

From the kinematic equation, v² = u² - 2gh, we have;

u² = 2gh

h = u²/2g = 900/(2 × 32.17405) ≈ 13.986

The maximum height reached 13.986 + 7.5 = 21.486

From v = u - gt

t = u/g = 30/32.17405 ≈ 0.932

t  ≈ 0.932 s

The distance Rampy Ronald would have travelled horizontally = 30·√3 × 0.932 ≈ 48.428

The distance Rampy Ronald would have travelled horizontally ≈ 48.428 feet

7. The time before Rampy Ronald reaches ground level again, is given by the following relation;

h = 1/2·g·t²

21.846 = 1/2 × 32.17405 × t²

t = √(21.846/16.087025) ≈ 1.165

t ≈ 1.366 s

The horizontal distance traveled is therefore;

The horizontal distance traveled from maximum height is 30·√3 × 1.165 ≈ 60.535

The horizontal distance traveled from maximum height is ≈ 70.979 feet

The total horizontal distance traveled ≈ 48.428 + 60.535 = 108.963

The total horizontal distance traveled ≈ 108.963 feet

The total horizontal distance required to make it across the ravine = 5 feet + 80 feet = 85 feet

Therefore, Rampy Ronald is going to make the jump

Question d:

(D) Find the probability of F'nA'

Answer:

0.4140

0.7619

0.2381

0.9576

Step-by-step explanation:

Given that :

Female in fatal accident P(F) = 0.2805

Driver is 24 years or less P(A) = 0.1759

Driver is female and 24 years or less P(FnA) = 0.0424

A.) Find the probability of FUA.

P(FUA) = P(F) + P(A) - P(FnA)

= 0.2805 + 0.1759 - 0.0424

= 0.4140

(b) Find the probability of F'UA.

P(F'UA) = 1 - P(F) + P(FnA)

= 1 - 0.2805 + 0.0424

= 0.7619

C.) P(FnA') = 1 - P(F'UA)

= 1 - 0.7619

= 0.2381

(d) Find the probability of F'nA'

P(F'nA') = (FnA)' = 1 - (FnA)

= 1 - 0.0424

= 0.9576

Answer:

5

Step-by-step explanation:

Answer:

y=2x+1

Step-by-step explanation:

y=mx+c

y-intercept is 1

y=mx+1

gradient= rise/run= 2/1= 2

y=2x+1

Answer:

Aunt drove  4 hours

Uncle drove 6 hours.

Step-by-step explanation:

Equations:

580 = 55/x + 60/y

600 = 55x + 60y

Happy Holidays!

Possibly B but i'm not sure..

Answer:

Absolute Minimum: (3,−29)

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Given that:

Number of yellow notepads = 6

Number of Blue notepad = 6

Number of green notepads = 6

Number of pink notepads = 6

Samole space for experiment :

(Number of different distinct notepads * Number of notepads in each)

(4 * 6) = 24

Answer:

3 dollars 6 cents or 3.6

Step-by-step explanation:

you need to divide the 30 percent by the twelve dollars to get your answer

Answer: 81, 664 is the total!

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The answer is 5 because it just is

Answer:

Step-by-step explanation:

__________________________________________________________

Hannah gave her friend 5, so now she has 5!

__________________________________________________________

We can solve this by subtracting!

__________________________________________________________

10 - 1 = 9

10 - 2 = 8

10 - 3 = 7

10 - 4 = 6

10 - 5 = 5

__________________________________________________________

Hope this helps! uwu

__________________________________________________________

Answer:

32%

Step-by-step explanation:

at least twenty caters long

Answer:

$20.87

Step-by-step explanation:

Divide 1.03 into 21.50

Answer:

47

Step-by-step explanation:

(26+5) • 2-15

Follow Pemdas

P.E.M.D.A.S

Parenthesis first

31•2-15

Multiplication next

62-15

47

Answer:

A.

Step-by-step explanation:

Answer:

The equation of a linear function is:

Step-by-step explanation:

Given the table

x                    y

-10               -16

-3                 -2

1                    6

2                   8

Determining the slope between the points (-10, -16), (-3, -2)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-10,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)[/tex]

[tex]m=\frac{-2-\left(-16\right)}{-3-\left(-10\right)}[/tex]

[tex]m=2[/tex]

Determining the slope between the points (-3, -2), (1, 6)

[tex]m=\frac{6-\left(-2\right)}{1-\left(-3\right)}[/tex]

[tex]m=2[/tex]

Determining the slope between the points (1, 6),(2, 8)

[tex]m=\frac{8-6}{2-1}[/tex]

[tex]m = 2[/tex]

As the slope between the points is the same. Thus, the table represents the linear function.

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

substituting the values m = 2 and any point let say (1, 6)

[tex]y - 6 = 2(x-1)[/tex]

[tex]y-6 = 2x-2[/tex]

[tex]y = 2x-2+6[/tex]

[tex]y = 2x+4[/tex]

Therefore, the equation of a linear function is:

Andy is correct! Andy has the function 4, his leading coefficient is negative, and his functions contains zeros. Hope this helps!

Answer: From top to bottom of the chart: -13, -6, 1, 8, 15

Step-by-step explanation:

You can solve the equation by putting the numbers in the graph (under the letter x) into the equation. Meaning when it says "-2", you can write 7(-2)+1, or 7 times negative 2 minus one, which equals -13. Do the same thing with the rest :]

Answer:

I belive the answer is 5

Step-by-step explanation:

$12- $2 for ppl= $10

$10÷$2 per mile = 5

Answer:

7

Step-by-step explanation:

-2 x 6 = -12

-6/1 ÷ -3/1 = 2

-12 - 2 = -14

-14 ÷ -2 = 7

Answer:

x=10 and y=−9

Step-by-step explanation:

Answer:

(x,y) = (10,-9)

Step-by-step explanation:

x=-3y-17

2x+3y=-7

2(-3y-17)+3y=-7

y=-9

x=-3(-9)-17

x=10

Answer:

D) y= -2X+1

Step-by-step explanation:

All of the lines are perpendicular to the line 2x+y=6 except for D) y= -2X+1.

Answer:

60%

Step-by-step explanation:

Answer:

6 1/6

Step-by-step explanation:

A fraction that is equivalent to 3/8 is 6 1/6