airplane leaves City A and flies 142 km due north to City B. It then turns through an angle of 57° and flies 108 km to City C. What angle 8 with respect to
due north could the pilot have used to fly directly from City A to City C? See the figure below.
City
108 km
Carry your intermediate computations to at least four decimal places.
Round your answer to the nearest tenth of a degree.

The annuity of the monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years is $333.71

An annuity is a series of payments made at equal period of time.

future value = annuity x [(1 + i)ⁿ - 1] / i

annuity = $125.30

i = 1.5% / 12 = 0.00125

n = 35 years x 12 months = 420

future value = $125.30 x [(1 + 0.00125)⁴²⁰ - 1] / 0.00125

future value = $69,156.049 ≈ $69,156.05

annuity = [i x (present value)] / [1 - (1 + i)⁻ⁿ]

i = 1.5% / 12 = 0.00125

n = 20 years x 12 months = 240

present value = $69,156.05

annuity = (0.00125 x $69,156.05) / [1 - (1 + 0.00125)⁻²⁴⁰]

annuity = $86.45 / 0.25904

= $333.71

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Answer: 424.12

Step-by-step explanation:

Answer:

38/45

Step-by-step explanation:

Answer:

38/45

Step-by-step explanation:

Hope it helps

m<COB

Our answer is 60°

Answer:

27°

Step-by-step explanation:

Answer:

∠OAC = 27°

Step-by-step explanation:

The radius of the circle is perpendicular to the tangent line.

Therefore, ∠ACO = 90°

The interior angles of a triangle sum to 180°

⇒ ∠OAC + ∠ACO ∠ COA = 180°

⇒ ∠OAC + 90° + 63° = 180°

⇒ ∠OAC + 153° = 180°

⇒ ∠OAC = 180° - 153°

⇒ ∠OAC = 27°

Answer:

A

Step-by-step explanation:

because g(x) is the opposite of f(x) minus three steps

Answer:

Yes it has infinity of solutions.

Step-by-step explanation:

If you plug in certain numbers it will make the statements true.

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=−6;4x+6y=−12

Step: Solve2x+3y=−6for x:

2x+3y=−6

2x+3y+−3y=−6+−3y(Add -3y to both sides)

2x=−3y−6

2x/2 = −3y−6/2

(Divide both sides by 2)

x= −3/2y−3

Step: Substitute −3/2y−3 for x in 4x+6y=−12:

4x+6y=−12 4(−3/2y−3)+6y=−12

−12=−12(Simplify both sides of the equation)

−12+12=−12+12(Add 12 to both sides)

0=0

Answer:

Infinitely many solutions.

The probability of drawing a two and another 2 is 1/72

Probability is the likelihood or chance that an event will occur

Pr(drawing a 2, then drawing another 2) = 1/72

Hence the probability of drawing a two and another 2 is 1/72

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Answer:

(0, - 3 )

Step-by-step explanation:

the solution to the system is at the point of intersection of the graphs.

the graphs intersect at (0, - 3 )

then solution is (0, - 3 )

Answer:

(0, -3)

Step-by-step explanation:

The solution is where the two lines intersect. The two lines intersect at the point (0, -3).

I hope it helped you!

We will see that the number of different combinations for each case are:

We have 5 selections for each password, we need to find the number of options for each one of these selections.

a) Here we can use only capitals an we can repeat, so for each selection (each letter), we have 26 options.

The total number of combinations will be equal to the product between the numbers of options:

C = 26*26*26*26*26 = 11,881,376

b)Now we can use either capitals or lower case, but we can't repeat. (Here I assume that A is different than a, so we can't use A two times, but we could use A and a).

Then we have 26*2 = 52 options.

For the first letter, we have 52 options.

For the second letter, we have 51 options (because one letter was already used).

For the third letter, we have 50 options, and so on.

The total number of combinations will be:

C = 52*51*50*49*48 = 311,875,200

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Answer:

12.56

Step-by-step explanation:

pi(r)^2

3.14(2)^2

12.56

Answer:

D. -20

Step-by-step explanation:

[tex]\frac{u}{5} +6=2[/tex]

[tex]\frac{u}{5} =-4[/tex]

[tex]u=-4(5)[/tex]

[tex]u=-20[/tex]

Hope this helps!

Answer:

D.

Step-by-step explanation:

u / 5 + 6 = 2

-20 / 5 + 6 = 2

-4 + 6 = 2

2 = 2

Answer:

I believe the answer is D.96

Step-by-step explanation:

well all rhombuses can be turned into a square or rectangle. and this looks like the sides are really close. just a guess don't get mad if it's wrong

1 mile = 1.6 kilometers

Multiply total miles by 1.6

9 miles x 1.6 = 14.4 kilometers

Answer: 14.4 kilometers

Answer:

14.4 kilometres

Step-by-step explanation:

Given that,

→ 1 mile = 1.6 kilometres

By using this information 9 miles will be,

→ 9 miles × 1.6 km

→ [ 14.4 km ]

Thus, the gas station is 14.4 km away.

Answer:

Step-by-step explanation:

Sum: addition

Difference: subtraction

Product: multiplication

Number                    Sum                    Difference                    Product

1, 4                         1 + 4 = 5                     4 - 1 = 3                       1 * 4 = 4

2, 8                       2 + 8 = 10                   8 - 2 = 6                      2 * 8 = 16

Hope this helps!

Answer:

B, C, D

Step-by-step explanation:

B, C, D

Answer:

A.12

Step-by-step explanation:

x²>100

square root both sides

it becomes x>10

x>10

from the options the only number greater than 10 is 12

Therefore the answer is A. 12

Answer:

10.7 cm

Step-by-step explanation:

V = (4/3)πr³

5128.8467 = (4/3)(3.14)r³

1225.043 = r³

r = 10.7

Answer:

Sticks of butter: 2 Number of cookies: 40

Step-by-step explanation:

the ratio begins with 3:24. if you were to divide 3 by 24 it could be 1:8 **2**x 8 =16 so sticks of butter would be 2. 5x8=40.

Answer:

about 181 or 180.96

Step-by-step explanation:

π·6.4·6.332+6.42≈180.9555

Answer:

x = [tex]-\frac{1}{2}a-\frac{1}{4}b+\frac{9}{4}[/tex]

Step-by-step explanation:

Answer:

$27.17

Step-by-step explanation:

Regular price of necklace = $44

If a discount of 35% is applied, then the new price of the necklace will be 65% of the regular price, as 100% - 35% = 65%

⇒ 65% of $44

= 0.65 × $44

= $28.60

If a second discount of 5% is then applied, the final price of the necklace will be 95% of the sale price, as 100% - 5% = 95%

⇒ 95% of $28.60

= 0.95 × $28.60

= $27.17

Therefore:

The sale price with a 35% discount is $28.60

The sale price with an additional 5% discount is $27.17

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

Given :-

The regular price of necklace = $44

Discount on necklace = 35%

Additional save from necklace = 5%

Solution :-

First we have to found the prize of necklace that Amantha had bought at 35% discount

To find this, there is a formula

[tex]new \: price = real \: price - (discount \: percentage \times real \: price) [/tex]

Now we will put our value in this formula

[tex] = 44 - ( \frac{35}{100} \times 44) \\ = 44 - ( \frac{7}{20} \times 44) \\ = 44 - ( \frac{7}{10} \times 22) \\ = 44 - \frac{154}{10} \\ = 44 - 15.4 \\ = 28.6 \:[/tex]

Now will deduct the additional discount from this price by using same formula

[tex] = 28.6 - ( \frac{5}{100} \times 28.6) \\ = 28.6 - ( \frac{1}{20} \times \frac{286}{10} ) \\ = 28.6 - ( \frac{1}{10} \times \frac{143}{10} ) \\ = 28.6 - 1.43 \\ = 27.17[/tex]

Result :-

She spend $27.17 on buying the necklace

The multiples of 8 from 1 to 100 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96.

To calculate the multiples of 8 we must multiply 8 by any number and the result will be a multiple of 8.

To identify the multiples of 8 that are between the number 1 and 100, we must multiply the number 8 by the number sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 .

So we will know properly are the multiples of 8 that are between 1 and 100 as shown below:

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The volume of a cone with diameter d (and hence radius d/2) and height h is

[tex]V_{\rm cone} = \dfrac\pi3 \left(\dfrac d2\right)^2 h[/tex]

so each scoop holds

[tex]V = \dfrac\pi3 \left(\dfrac{1\,\rm in}2\right)^2 \left(2\,\mathrm{in}\right) = \dfrac\pi6 \, \mathrm{in}^3[/tex]

of coffee.

The volume of a cylinder with base diameter d and height h is

[tex]V_{\rm cylinder} = \pi\left(\dfrac d2\right)^2 h[/tex]

so the coffee can contains

[tex]W = \pi \left(\dfrac{6 \, \rm in}2\right)^2 \left(6\dfrac14 \, \mathrm{in}\right) = 2025\pi \,\mathrm{in}^3[/tex]

of coffee.

One full scoop then uses up [tex]\frac VW = \frac1{12,150}[/tex] of the total amount of coffee in the can, so you can make 12,150 cups of coffee.

[tex]\sqrt 7 +\sqrt{28} - \sqrt{700}\\\\\\=\sqrt 7 +\sqrt{4 \times 7} - \sqrt{100 \times 7}\\\\\\=\sqrt 7 + 2\sqrt 7 - 10\sqrt 7\\\\\\=-7\sqrt 7[/tex]

Answer:

Yes, none of these are correct.

Step-by-step explanation:

We can easily see that none of these are correct just by looking at the second piece of criteria and substituting x and y for their respective numbers.

Answer:

$1.5

Step-by-step explanation:

9÷6= 1.5

1.5× 1 = 1.5

Mr. Brust needs 427 cans to cover the wall of dimensions 20 feet long and 9 feet tall.

Area of rectangle is the product of its sides

i.e., Area of rectangle = length  x breadth

The area of a circle is pi times the radius squared (A = π r²).

The circumference of a circle is defined as the linear distance around it.

( C= 2πr)

The can of red bull is in shape of cylinder.

If we open the cylinder it will have two circular surfaces( at bottom and top) and one rectangular sheet.

Like the given figure given.

It shows that the two circle will have the diameter 2.5 inches.

d= 2.5 inch

 = 0.208 ft

radius, r= [tex]\frac{d}{2}[/tex]

r= [tex]\frac{0.208}{2}[/tex]

r= 0.104 ft

Circumference of the circle be,

= 2πr

= 2 x 3.14 x 0.104

= 0.653 ft

The rectangular sheet will have,

length=  0.653 ft, breadth= 6.5 inches = 0.541 ft

      = length x breadth

      = 0.653 x 0.541

      =[tex]0.3532 ft^{2}[/tex]

       = 2 x π[tex]r^{2}[/tex]

       = 2 x 3.14 x 0.104 x 0.104

       = 6.28 x 0.010816

       = 0.0679 [tex]ft^{2}[/tex]

        = Area of rectangular sheet + Area of 2 circle( top and bottom of can)

        = 0.3532 + 0.0679

        = 0.4211 [tex]ft^{2}[/tex]

Now, we have the wall of dimensions

length= 9 ft, breadth= 20 ft

= length x breadth

=9 x 20

= 180 [tex]ft^{2}[/tex]

         =[tex]\frac{area \;of\; wall}{area \;of\; can}[/tex]

         =[tex]\frac{180}{0.4211}[/tex]

         = 427.45 cans

         ≈ 428 cans

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Answer:

829.4 m³

Step-by-step explanation:

Volume of cone:

        diameter = 12 m

                     r = 12 ÷ 2 = 6 m

                     h = 22 m

[tex]\sf \boxed{Volume \ of \ cone =\dfrac{1}{3} \pi r^2h}[/tex]

                           [tex]= \dfrac{1}{3}*\dfrac{22}{7}*6*6*22\\\\=\dfrac{22}{7}*2*6*22\\\\=\dfrac{5808}{7}\\\\= 829.4 \ m^3[/tex]

Answer: 76.8 mi²

Step-by-step explanation:

   The area of a parallelogram can be found be multiplying the base times the height.

       A = B * H

       A = 9.6 * 8

       A = 76.8 mi²

   Confused as to why this works? We use the same formula that we do for a rectangle because the "extra triangle" on the left can be moved to fill the empty space on the right. This then gives us a normal rectangle, which allows us to solve for the area

In this question we are provided with the base and height of a parallelogram and we are asked to calculate the area of the parallelogram using the formula.

It is given that the base is 9.6 mi and height is 8 mi.

We know,

[tex] \small\boxed{ \sf {Area_{(parallelogram)} = B × H}}[/tex]

Where,

Substituting the values we get

[tex] \small\sf{ Area_{(parallelogram)} = (9.6 × 8) mi} = 76.8 {mi}^{2} [/tex]