Instructions: Write the equation of the line in Point-Slope Form given the information below. Hint: The y-intercept is the
coordinate point (0,b)

Slope= -6/5
Y-Intercept = 2
Point-Slope Form:

The linear speed of a point on the circumference is approximately 9895 feet per minute.

(a) To find the angular speed in radians per minute, we need to convert the given rotational speed from rpm (revolutions per minute) to radians per minute. Since there are 2π radians in one revolution, we can use the conversion factor:

Angular speed (in radians per minute) = Rotational speed (in rpm) * 2π

Given that the rotational speed is 2100 rpm, we can calculate the angular speed:

Angular speed = 2100 rpm * 2π ≈ 13194 radians per minute

Therefore, the angular speed of the wheel is approximately 13194 radians per minute.

(b) To find the linear speed of a point on the circumference in feet per minute, we can use the formula:

Linear speed = Angular speed * Radius

Given that the radius of the wheel is 9 inches, we need to convert it to feet:

Radius = 9 inches * (1 foot / 12 inches) = 0.75 feet

Now, we can calculate the linear speed:

Linear speed = 13194 radians per minute * 0.75 feet ≈ 9895 feet per minute

Therefore, the linear speed of a point on the circumference is approximately 9895 feet per minute.

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The percent tip is 13.2%.

To find out what percentage Patrick gave as tip, we need to divide the tip amount by the total bill amount and then convert the result into a percentage.

For this question:

Patrick left an $7 tip on a $53 restaurant bill. What percent tip is that?

Solution:The percentage of tip can be found using the following formula:

% = (Tip amount / Total bill amount) x 100

Plugging in the given values we get:

% = (7 / 53) x 100% = 0.132 x 100% = 13.2 %

Therefore, Patrick gave a 13.2% tip on his restaurant bill.

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Answer:

4.5

Step-by-step explanation:

The given functions f(n) = 11 and g(n) = (3/4)^(n-1) can be combined to create a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term is given as 11, and the common ratio is (3/4).

The nth term of a geometric sequence is calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the position of the term. By substituting the values into the formula, we can find the 9th term.

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Answer:

92/37

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

Answer: 50, 60, Less.

Step-by-step explanation: The theoretical probability of the coin landing heads up is 50%

Based on​ Liz's results, the experimental probability of the coin landing heads up is 60

The theoretical probability is less than the experimental probability in this experiment.

Hope this helped have a nice day!

This indicates that vector 2AB has a length of 165.

Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), and E, let's determine the length of the vector 2AB. To begin, we must determine the distance that separates points A and B. The distance formula is as follows: Equation for distance: We can calculate d as [(x2 - x1)2 + (y2 - y1)2] using the distance formula: Spot = [(6 - (- 2))2 + (16 - 0)2] = [(6 + 2)2 + (16)2] = [(8)2 + (16)2] = [(64 + 256) = 320 = 8] Now, we can deduct the directions of point A from guide B toward decide the vector Stomach muscle:

To find 2AB, simply multiply each part of AB by 2: AB = (6 - (-2)i + (16 - 0)j = 8i + 16j 2AB = 2(8i + 16j) = 16i + 32j. Last but not least, we must ascertain the magnitude of 2AB. The extent recipe is as per the following: Size formula: Using the magnitude formula, we get: ||v|| = (v12 + v22). ||2AB|| = (162 + 322) = (256 + 1024) = (1280 + 165). This indicates that vector 2AB has a length of 165.

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Answer:

The angle of elevation is 17°.

Step-by-step explanation:

Let's draw the scenario to better understand the problem:

Focusing on the right triangle formed, it appears that we get measures of the two sides of the right triangles.

Opposite Side = 3 Ft.

Adjacent Side = 10 Ft.

To find the angle of elevation, we will be using the Targent Function:

[tex]targent \: 0 = \frac{opposite \: side}{adjacent \: side} \\ targent \: 0 = \frac{3}{10} \\ 0 = {targent}^{ - 1} ( \frac{3}{10} ) \\ 0 = 16.69924423399 = 17[/tex]

Therefore, the angle of elevation is 17°.

Each satisfies the wave equation.

We are given the functions as follows:

(a) (x+at)², (b) 2e-(x-at) ², 7 satisfy the wave equation J²u(x, t) Ət² = (c) 5 sin[3 (x - at)] + (x + at).

₂d²u(x, t) dx²

Let us prove that they satisfy the wave equation using the formula of the wave equation. Wave equation is given by;

J²u(x, t) Ət² = ₂d²u(x, t) dx²

Applying the partial derivative to

(a) with respect to time, t, we obtain:

2a(x+at)

The second partial derivative with respect to x is as follows:

2a

By substituting these results into the wave equation, we have:

J²u(x, t) Ət² = ₂d²u(x, t) dx²

(2a(x+at)) = 2aJ²u(x, t) Ət² = 2a

Ət² = 1/J².

Thus, (a) satisfies the wave equation.  

For part (b), let us begin by taking the partial derivative of the function with respect to time, t. This is given by:

-4a e^-(x-at) ²

By taking the second partial derivative with respect to x, we get:4a e^-(x-at) ²

Similar to above, we substitute these results into the wave equation as follows:

J²u(x, t) Ət² = ₂d²u(x, t) dx²

-4a e^-(x-at) ² = 4aJ²u(x, t) Ət² = -4a e^-(x-at) ²/J²

Ət² = -1/J²e^-(x-at) ².

Thus, (b) satisfies the wave equation.

For part (c), let us calculate the partial derivative with respect to t as follows:

5a cos[3(x-at)] + a

The second partial derivative with respect to x is given by:-

15a sin[3(x-at)]

By substituting these results into the wave equation, we have:

J²u(x, t) Ət² = ₂d²u(x, t) dx²

(5a cos[3(x-at)] + a) = -15a

sin[3(x-at)]J²u(x, t) Ət² = -15a

sin[3(x-at)]/(5a cos[3(x-at)] + a)

Ət² = -3 sin[3(x-at)]/(cos[3(x-at)] + 1/5).

Thus, (c) satisfies the wave equation.

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Answer:

“Mean for both bakeries because the data is symmetric.”

Step-by-step explanation:

This is correct because the numbers shown in this problem is all in the same range. Meaning that on bakery A and B there are no stray numbers, also known as outliers. No outliers means that the data is symmetric. If you search up, you can see that when the data is symmetric, you use “mean.”

also I got it right on my test

Answer:

Mean for both bakeries because the data is symmetric.

Step-by-step explanation:

Answer:

Answer and work is in the pdf

Step-by-step explanation:

75+75+80+80+80+80+80+80+85+85+90+90+90+90+90+90+95+95+95+100+100+100+100+100+100

=2,425

2+6+2+6+3+8

=27

2,425/27=89.81

The mean is 89.81

Answer:

1.3 ounces, 1.3*5 =6.5

Answer: A

Step-by-step explanation:

Answer:

The two triangles are related by angles, so the triangles are similar but not proven to be congruent.

Step-by-step explanation:

Because the triangles have the same angles, they are congruent. The definition of congruence is if you take a shape and scale it up or down (or keep it the same) therefore, they are congruent.

Hope this helped, have a nice day

EDIT: I screwed up, I thought it was supposed to be similar.  These triangles are SIMILAR not congruent. The actual answer is they are related by AAA similarity but they are similar, but they are not proven to be congruent. Hope this clears it up, and sorry.

~cloud

Answer:

10 feets

Step-by-step explanation:

Given that:

Angle, θ = 4π/3

Radius, r = 2.5 feets

To obtain how Far Reagan traveled, we calculate the Length of the arc, s

s = r*θ

s = 2.5 feets * 4π/3

s = 10π/3

s = 10.4719

To the nearest foot ; distance traveled by Reagan is 10 feets

Answer:

61

Step-by-step explanation:

Givens

Let the pizzas = x

Let the sodas = y

Equation

y = 3x + 2

Part A

y = 3*8 + 2

y = 24 + 2

y = 26

Part B

Sodas = 26* 1.25 = 32.50

Pizzas =9.50 * 3  = 28.50

Total for both = 32.50 + 28.50 = 61

Answer:

33

Step-by-step explanation:

6 * 3 = 18

8-3 = h

h = 5

A = 5 * 3 = 15

Combined:

15 + 18

33

Answer:

B and D.

Step-by-step explanation:

A p e x

The following are among the five basic postulates of Euclidean geometry

The five basic postulates of Euclidean geometry

The five (5) basic postulates are:

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Answer:

900 cm = 9 m

Step-by-step explanation:

9 m = 900 cm

Therefore, 9 m equals 900 cm.

Step-by-step explanation: *First, decide which volume formula to use:     v = lwh

*Next, substitute in for what you do know (leave variable for unknown):  288 = 12 · w · 6

*Then simplify the side of the equation with the variable: 288 = 72 · w

*Now divide each side of the equation by 72 to solve for w:

288 ÷ 72 = w

4 in = w

Answer:

Add up all of the numbers, and divide by the number of digits. To put it another way, the total is divided by the count.

Step-by-step explanation:

so ... 2,4,4,2

2+4+4+2= 12

12 divided by 4=3

i think 3 is the mean....

hope this helps.....

1) The solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.

2) The difference quotient as a function of Δr is -4.

3)  f'(-1) = -4 and f'(5) = -4.

To solve the equation system using Cramer's rule, we need to find the determinant of the coefficient matrix A and the determinants of the matrices obtained by replacing each column of A with the column on the right-hand side.

The given equation system is:

8x₁ + 9x₂ = 2

11x₁ + 2x₂ = 3

7x₁ + 6x₂ = 1

Step 1: Calculate the determinant of the coefficient matrix A.

A = |8 9|

|11 2|

|7 6|

|A| = (8 * 2) - (9 * 11)

    = -78

Step 2: Calculate the determinant of the matrix obtained by replacing the first column of A with the column on the right-hand side.

A₁ = |2 9|

|3 2|

|1 6|

|A₁| = (2 * 2) - (9 * 3)

     = -22

Step 3: Calculate the determinant of the matrix obtained by replacing the second column of A with the column on the right-hand side.

A₂ = |8 2|

|11 3|

|7 1|

|A₂| = (8 * 3) - (2 * 11)

     = 14

Step 4: Calculate the solutions x₁ and x₂ using Cramer's rule.

x₁ = |A₁| / |A|

   = -22 / -78

   = 11/39

x₂ = |A₂| / |A|

    = 14 / -78

    = -7/39

Therefore, the solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.

Now, let's move on to the second part of your question regarding the function f(r) = 57 - 4r.

(a) To find the difference quotient as a function of Δr (Δr represents the change in r):

Difference quotient = (f(r + Δr) - f(r)) / Δr

Expanding and simplifying the expression:

Difference quotient = (57 - 4(r + Δr) - (57 - 4r)) / Δr

                                = (57 - 4r - 4Δr - 57 + 4r) / Δr

                                = -4Δr / Δr

                                = -4

Therefore, the difference quotient as a function of Δr is -4.

(b) To find f'(-1) and f'(5), we need to find the derivative of f(r) with respect to r.

f'(r) = d/dx (57 - 4r)

     = -4

Substituting r = -1 and r = 5 into f'(r), we get:

f'(-1) = -4

f'(5) = -4

Therefore, f'(-1) = -4 and f'(5) = -4.

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89 inches!

Because each foot is 12 inches and 12*7=84 and 84+5=89!

Answer:

Step-by-step explanation:

x = 87.2ft

Hope that helps :)

7 TURKEY AND 13 HAM

I USED CALCULATOR BTW

Answer:

p) = 17/30 or 0.56

q) = 191/60 or 3 11/60

Answer:

I think it's 21. .........