Sam is skiing down a mountain. He starts at the peak 97 yards above sea level and skis down the mountain at a rate of 1.5 yards per second. If it takes him 3 minutes to reach flat ground at sea level, what is the measure of the angle that the mountain slope forms with the ground at sea level to the nearest degree?

Answer:

-3 is the gradient.

BONUS: y-interspet is -1

Step-by-step explanation:

The gradient is what you mean by slope I am guessing?

well, the line that contains those points will more or less look  like the one in the picture below, and we can use any two points from that set to get its slope, say hmmmmm let's use (-5,7) and (1,-2)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}}\implies \cfrac{-9}{1+5}\implies \cfrac{-9}{6}\implies -\cfrac{3}{2}[/tex]

Given:

Principal = $54,000

Time = 9 years

Rate of compound interest = 12% per annum.​

To find:

The compound interest.

Solution:

The formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest in decimal, n is the number of time interest compounded and t is the number of years.

The interest is compounded annually, so [tex]n=1[/tex].

Substituting [tex]P=54000,\ t=9,\ n=1,\ r=0.12[/tex] in the above formula, we get

[tex]A=54000\left(1+\dfrac{0.12}{1}\right)^{1(9)}[/tex]

[tex]A=54000\left(1.12\right)^{9}[/tex]

[tex]A=149746.252902[/tex]

[tex]A\approx 149746.25[/tex]

The amount after 9 years is $149746.25.

Now, the compound interest is:

[tex]C.I.=A-P[/tex]

Where, C.I. is compound interest, A is amount and P is principal.

[tex]C.I.=149746.25-54000[/tex]

[tex]C.I.=95746.25[/tex]

Therefore, the compound interest is $95746.25.

Answer:

n = 8

Step-by-step explanation:

Continuing the sequence using

[tex]x_{n}[/tex] + [tex]x_{n+1}[/tex]

x₄ = x₂ + x₃ =1 + 2 = 3

x₅ = x₃ + x₄ = 2 + 3 = 5

x₆ = x₄ + x₅ = 3 + 5 = 8

x₇ = x₅ + x₆ = 5 + 8 = 13

x₈ = x₆ + x₇ = 8 + 13 = 21

x₉ = x₇ + x₈ = 13 + 21 = 34

x₁₀ = x₈ + x₉ = 21 + 34 = 55 ← with n = 8

Answer:

The Fibonacci numbers are

1

1

2

3

5

8

13

21

34

55

The eighth Fibonacci Number  is 21, the  ninth  is 34 and the tenth is 55.

So Fibonacci # 8 + Fibonacci Number #9 = Fibonacci# 10

21 + 34 = 55

If you want to read a little bit more about Fibonacci numbers, try this page: http://www.1728.org/fibonacci.htm

that's my website :-)

Step-by-step explanation:

Answer:

4 and 16

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

slope = (y2-y1)/(x2-x1)

(-4-2)/(-4--2)

-6/-2

3

Answer:

to find slope we use the following methods

Step-by-step explanation:

given

X1 -2

X2= -4

Y1= 2

Y2= -4

slope=y2-Y1 ÷X2-X1

= -4-2÷ -4-(-2)

=-6 ÷-4+2

= -6÷-2

= 3

slop of (-2,2) (-4,-4) = 3

Answer:

Men = 660

Women = 550

Step-by-step explanation:

Say the total number of people = x = 1210

Then men = 6/11 x = 660

And women = 5/11x = 550

Solution :

It is given that a company named  "Sugary Sweet" wishes to test about the sweet and the flavorful that their participants like the candy.

There are Two levels of the flavor and three levels of sugar.

Thus it is a Two Way ANOVA test.

A two-way ANOVA test is used to test the effect of any two independent variables on the dependent variable.

[tex]$H_{01} : \text{Mean effect of the sugar are equal}$[/tex]

[tex]$H_{02} : \text{Mean effect of the flavor are equal}$[/tex]

[tex]$H_{01} : \text{There is no interaction between the sugar and the flavor}$[/tex]

Answer:

45000 cubic cm

Step-by-step explanation:

Capacity of the fuel tank

= 45 litres

= 45/1000 = 0.045 cubic meters

Or 45* 1000 = 45000 cubic cm

Answer:

[tex]{ \bf{factor : x + 2}} \\ { \tt{divisor = - 2 }} \\ { \bf{f(x) = {x}^{3} + 1 }} \\ { \bf{f( - 2) = {( - 2)}^{3} + 1}} \\ { \bf{remainder = - 7}}[/tex]

Answer:

The correct answer is B. Long-term.

Step-by-step explanation:

Since Zach has bought a car for $ 20,000 paying a down payment of $ 5,000 and monthly payments of $ 450 per month for 5 years, he will be paying a total of $ 32,000 for that car (5,000 + 450 x 12 x 5). Thus, the responsibility that Zach has incurred forces him to maintain his monthly payment obligation for 5 years, thus becoming a long term liability.

Answer:

[tex]\text{C. }\pm \frac{1}{2}[/tex]

Step-by-step explanation:

Start by moving the 2 to the right (so we can multiply both sides by the denominator):

[tex]\frac{1}{2x^2-1}=-2[/tex]

Multiply both sides by [tex]2x^2-1[/tex]:

[tex]1=-2(2x^2-1),\\1=-4x^2+2[/tex]

Move everything to one side:

[tex]4x^2-2+1=0,\\4x^2-1=0,\\4x^2=1,\\x^2=\frac{1}{4},\\x=\boxed{\pm\frac{1}{2}}[/tex]

Answer:

the answer for this is C.

Answer:

[tex]{ \tt{on \: x - axis : 3}} \\ { \tt{on \: y - axis : 0}} \\ = > \: { \tt{x, \: y}} \\ { \boxed{ \bf{substitute \: for \: x \: and \: y}}} \\ \therefore \: { \boxed{ \bf{answer : } \:{ \tt {(3, \: 0)}}}} \\ \\ { \underline{ \blue{ \tt{⚜becker \: jnr}}}}[/tex]

Answer:

15

Step-by-step explanation:

u add up that then u get the answet

Answer:

Step-by-step explanation:

x^2 －6x-8=0

Answer:

6x + 3

Step-by-step explanation:

3(2x + 1)

=3*2x + 3*1

=6x + 3

Answer:

1

2

0.5

Step-by-step explanation:

Answer:

The answer is x = -6

Step-by-step explanation:

Answer:

 =  − 6

Step-by-step explanation:

Answer:

x = 3/2

The axis of symmetry is located at the vertex,

which is the also the highest point in this problem...

the x component of the vertex can be calculated as -b/2a = -48/-32 = 24/16 = 6/4 = 3/2

x = 3/2

Step-by-step explanation:

Answer:

610$

Step-by-step explanation:

According to the Question,

Thus , Mr. Cruz Consumes 50kwh in this month .

Given, the minimum charge for the first 10 kWh is $210 . & the succeeding consumed kWh costs $10 .

The Total Bill Of Mr. Cruz is ⇒ 210 + (50-10)×10 ⇔ 610$

Answer:

B. 3408pi

Step-by-step explanation:

formula volume of cone = 1/3 x pi x r x r x h

volume = 1/3 x pi x 12 x 12 x 71

= 3408pi

The volume of the cone is approximately 10,224 cubic units.

Option C is the correct answer.

It is a shape of a christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is V = (1/3)πr²h,

We have,

The formula for the volume of a cone is V = (1/3)πr²h,

where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.

Substituting the given values, we get:

V = (1/3)π(12²)(71)

V = (1/3)π(144)(71)

V = (1/3)(3.14)(144)(71)

V = 10,223.04

Rounding this answer to the nearest whole number, we get:

V ≈ 10,224

Therefore,

The volume of the cone is approximately 10,224 cubic units.

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ7

Answer:

493.29[tex]cm^2[/tex]

Step-by-step explanation:

Multiply all values (6.72, 5.78, and 12.7) together, then round to the nearest tenth.

Answer:

2x + 5

ok.. slightly silly question...

you will eventually learn that this formula is the

formula for the "derivative" in calculus....

A[tex]x^{b}[/tex] becomes (a*b)  [tex]x^{b-1}[/tex]

2x + 5

Step-by-step explanation:

Answer:

x=50, y=20

Step-by-step explanation:

50-20=30, 50+20=70

Answer:

34

Step-by-step explanation:

let x = number of stamps ranu gives out and the number of stamps cathy receives

200 - x = 132 + x

combine like term s

200 - 132 = 2x

68 = 2x

x = 34

Answer:

Copper = x= 36.19

Step-by-step explanation:

The number of copper is unknown

Gold = 1/3

Silver = 1/5

Bronze =2/7

Copper = x

Total coins = 200

Gold = 1/3 of 200

= 1/3 × 200

= 200/3

= 66.67

Silver = 1/5 × 200

= 200/5

= 40

Bronze = 2/7 × 200

= 400/7

= 57.14

Total = gold + silver + bronze + copper

200 = 66.67 + 40 + 57.14 + x

200 = 163.81 + x

200 - 163.81 = x

x = 36.19

Copper = x= 36.19

Answer:

A

Step-by-step explanation:

Lines are parallel...

Answer:

Step-by-step explanation:

rather than doing all of the sums, you should just learn the formula (for the pattern)

it is n(highest + lowest) where n is number of numbers

             2

for example 2+3+4+5+6 = 20

5(6+2) =  20

  2

~~~~~~~~~~~~~~~~~~~~

1+2+3+4+5+6+7+8 = 36

8(9) = 72/2= 36

2

Answer:

11.2

Step-by-step explanation:

(AB) ^2 - (BC) ^2 = b^2 (Pythogoras Theorem)

(15)^2 - (10)^2 = (b) ^2

b^2=225-100

b^2=125

b=root (125)

b=11.18

b=11.2

Answer:

In A Premier League there are 20 soccer teams.

(a)In One Round How Many Games Are There?

20 choose 2 = 20C2 = 190

(b) If five of the teams represent one company, find the

number of ways pairs of teams representing different companies

can play the game.

So there are 4 companies, each having 5 teams.

4 companies choose 2 = 4C2 = 6 ways

Choose a team of the company that's, say, been in business the

longest.

5 teams choose 1 = 5C1 = 5 ways

Choose a team of the other company,

5 teams choose 1 = 5C1 = 5 ways

Answer 6*5*5 = 150 ways.