the projected benefit obligation was $300 million at the beginning of the year. service cost for the year was $34 million. at the end of the year, pension benefits paid by the trustee

The rounded values to the nearest tenth are:

Angle A ≈ 22.8°

Angle B ≈ 56.9°

Angle C ≈ 100.3°

Side a = 20.2 cm

Side b (opposite angle B) and side c (opposite angle C) remain the same at 44.2 cm.

Given the values:

B = 56.9°

a = 20.2 cm

c = 44.2 cm

To find the missing side or angle, we can use the Law of Sines, which states:

sin(A)/a = sin(B)/b = sin(C)/c

We have B = 56.9°, a = 20.2 cm, and c = 44.2 cm.

Using the Law of Sines, we can find the value of angle A:

sin(A)/20.2 = sin(56.9°)/44.2

To find sin(A), we can rearrange the equation:

sin(A) = (20.2 * sin(56.9°))/44.2

Now we can calculate sin(A):

sin(A) ≈ (20.2 * 0.831)/(44.2)

sin(A) ≈ 0.383

To find angle A, we can take the inverse sine (sin^(-1)) of 0.383:

A ≈ sin^(-1)(0.383)

A ≈ 22.8°

Now, we can find angle C by subtracting angles A and B from 180°:

C = 180° - A - B

C = 180° - 22.8° - 56.9°

C ≈ 100.3°

Therefore, the rounded values to the nearest tenth are:

Angle A ≈ 22.8°

Angle B ≈ 56.9°

Angle C ≈ 100.3°

Side a = 20.2 cm

Side b (opposite angle B) and side c (opposite angle C) remain the same at 44.2 cm.

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The answer to the correct number of significant digits is 167.

Maximum digits in the question is Three so we have to keep final answer to three significant figures

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures.

Now by doing simple addition (105+62.4) = 167.4

On rounding off our final answer to three ,digit 4 after decimal will be dropped.

Therefore, the answer to the correct number of significant digits is 167.

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the answer is 22 hope this helps

To find the critical numbers A and B of the function f(x) = -2x^3 + 39x^2 - 216x + 2, we need to determine the values of x where the derivative of the function is equal to zero or undefined.

First, let's find the derivative of f(x):

f'(x) = -6x^2 + 78x - 216

To find the critical numbers, we set f'(x) equal to zero and solve for x:

-6x^2 + 78x - 216 = 0

We can factor out -6 from the equation:

-6(x^2 - 13x + 36) = 0

Now, we solve the quadratic equation x^2 - 13x + 36 = 0:(x - 4)(x - 9) = 0

So, the solutions are x = 4 and x = 9.

Therefore, the critical numbers of the function f(x) = -2x^3 + 39x^2 - 216x + 2 are A = 4 and B = 9.

To find the second derivative of f(x), we differentiate f'(x):

f''(x) = -12x + 78

Now, we can find f''(A) and f''(B):

f''(A) = -12(A) + 78

= -12(4) + 78

= 30

f''(B) = -12(B) + 78

= -12(9) + 78

= -6

f''(A) = 30 and f''(B) = -6.

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The complete question is:

Consider the function f (x) = -2x^3 +39x^2- 216x + 2. This function has two critical numbers A < B:

A=?

B = ?

f " (A) = ?

f " (B) = ?

To the right of z = -0.65, the area under the standard normal curve can be found using a standard normal distribution table. The exact value can be obtained from the table without rounding.

A standard normal distribution table provides the area under the standard normal curve to the left of a given z-score. To find the area to the right of z = -0.65, we need to subtract the area to the left of -0.65 from 1. Looking up the z-score of -0.65 in the table, we find the corresponding area to the left of -0.65 is 0.2578. Subtracting this value from 1 gives us the area to the right of -0.65, which is 1 - 0.2578 = 0.7422. Therefore, to the right of z = -0.65, the area under the standard normal curve is 0.7422. This represents the proportion of the population that falls to the right of -0.65 standard deviations from the mean.

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The area of the circle is 452.16 square inches

Area is the the total surface that is occupied by a two dimensional shape

The radius of the circle = 12 inch

The radius of a circle is the distance between the center and any point on the circumference of the circle

The area of the circle A = π×\(r^2\)

Where A is the area of the circle

r is the radius of the circle

π = 3.14

substitute the values in the equation

The area of the circle = 3.14 × \(12^2\)

= 3.14 × 144

= 452.16 square inches

Hence, the area of the circle is 452.16 square inches

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Answer:

3/18, or simplified, he has a 1/6 chance of grabbing an adventure book.

Step-by-step explanation:

6 + 5 + 4 + 3 = 18. There's 3 adventure books, which makes it so that he has a 3/18 chance of it being an adventure book. How did I simplify? 18 ÷ 3 = 6, 3 ÷ 3 = 1.

The value of the coefficient a must be different than 0 .

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula: \(x= \frac{-b\pm\sqrt{\Delta} }{2a}\).

From definition for the coefficients of quadratic function, the coefficient a must be different than 0 (a≠0).

The given expression is a(x-3)²-1, therefore the coefficient a must be different than 0.

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The limit of the given Riemann sum is 256.

The given expression represents a Riemann sum for the function f(x) = 3x^3 - 9x over the interval [2, 6], where xi* is any point in the ith subinterval, and δx = (b-a)/n is the width of each subinterval.

Using the formula for the Riemann sum with right endpoints, we have xi* = 2 + iδx for i = 1, 2, ..., n. Substituting these values, we get:

n i=1 [3(xi*)^3 − 9xi*]δx = δx [3(2 + δx)^3 - 9(2 + δx) + 3(2 + 2δx)^3 - 9(2 + 2δx) + ... + 3(2 + nδx)^3 - 9(2 + nδx)]

= δx [3(2^3 + 3(2^2)δx + 3(2)(δx^2) + (δx)^3) - 9(2 + δx) + 3(2^3 + 3(2^2)(2δx) + 3(2)(4δx^2) + (8δx)^3) - 9(2 + 2δx) + ... + 3( (2 + nδx)^3) - 9(2 + nδx)]

= δx [3(8 + 12δx + 6δx^2 + δx^3) - 9(2 + δx) + 3(8 + 24δx + 24δx^2 + 8δx^3) - 9(2 + 2δx) + ... + 3((2 + nδx)^3) - 9(2 + nδx)]

= δx [3(8 + 12δx + 6δx^2 + δx^3) + 3(8 + 24δx + 24δx^2 + 8δx^3) + ... + 3((2 + nδx)^3) - 9(nδx)]

= δx [3(8n + 12δx(n(n+1)/2) + 6δx^2(n(n+1)(2n+1)/6) + δx^3(n^2(n+1)^2/4)) - 9(nδx)]

Taking the limit as n tends to infinity, we have δx = (6-2)/n = 4/n and nδx = 4. Therefore, the expression simplifies to:

lim n→[infinity] n i=1 [3(xi*)^3 − 9xi*]δx = lim n→[infinity] 4 [3(8n + 12(4/n)(n(n+1)/2) + 6(4/n)^2(n(n+1)(2n+1)/6) + (4/n)^3(n^2(n+1)^2/4)) - 9(4)]

= lim n→[infinity] 4 (96n + 64 + 64 + 64) - 144 = 256

Therefore, the limit of the given Riemann sum is 256.

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Answer: Lines a and b are parallel

Step-by-step explanation:

The slope of line a is \(\frac{13-10}{4-2}=\frac{3}{2}\).

The slope of line b is \(\frac{12-9}{6-4}=\frac{3}{2}\).

The slope of line c is \(\frac{10-9}{2-4}=-\frac{1}{2}\).

Since lines a and b have the same slope, they are parallel.

Answer: 52.94

Step-by-step explanation:

Length of train A = 480m

Tunnel length = 1320m

Time taken to cross tunnel = 2 mins = 120sec

Length of train B = 420m

Train B is slower than train A

Difference between their speed = 18km/hr

18km/hr = (18×1000)/3600 = 5m/s

Speed of train A :

Speed = distance / time

Speed = 1320 / 120 = 11m/s

Therefore, speed of train B :

(11 - 5)m/s = 6m/s

Relative speed of the two trains is therefore;

(Speed of A + speed of B)

Note : they are moving in opposite direction

( 11 + 6)m/s = 17m/s

Therefore time taken to cross each other :

(Sum of the length of both trains / relative speed of the trains)

Time taken = (480m + 420m) / (17m/s)

Time taken = 900m / 17m/s

Time taken = 52.94s

Answer:

3*3*44.14$

That's the answer

Use a calculator

Answer:

(y-1)

Step-by-step explanation:

simplified you split y^2-1y+-4y+4 this is further simplified by splitting equation into y(y-1)   -4(y-1) this leaves you with (y-4)(y-1)/(y-4) y-4 will cancel out and you are left with y-1

Question:

Write an algebraic statement that represents all the ways your player will win. Be sure to define your variable

Answer:

Erica:

\(0 \leq |x - y| < 10\)

Nita:

\(10 < |x - y| \leq 20\)

Step-by-step explanation:

Given

Players: Erica & Nita

Range: 0 to 20

Represent Erica with x and Nita with y

For Erica to win;

The difference between x and y must be less than 10 but greater than or equal to 0

i.e.

\(0 \leq x - y \leq 10\) or \(0 \leq y - x \leq 10\)

These two expressions can be merged together to be:

\(0 \leq |x - y| < 10\)

For Nita to win;

The difference between x and y must be greater than 10 but less than or equal to 20

i.e.

\(10 < x - y \leq 20\) or \(10 < y - x \leq 20\)

These two expressions can be merged together to be:

\(10 < |x - y| \leq 20\)

Answer:

It is C

Step-by-step explanation:

Khan Academy I use it trust me

The slope formula is:

\(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Let:

\((x_{1} , y_{1}) = (5 , 7)\\(x_{2} , y_{2}) = (3 , 4)\)

Plug in the corresponding numbers to the corresponding variables:

\(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{(4) - (7)}{(3) - (5)} = \frac{-3}{-2} = \frac{3}{2}\)

Your slope is:

\(m = \frac{3}{2}\)

Answer:

m= 3/2

Step-by-step explanation:

Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

Answer:

The solution to the inequality is 0.

The divisions is rewritten as a fraction dividing integers as follows

-16 ÷ -2 = 16 / 2 = 8

The calculation can be done simply by calculator however to so it manually the decimal is converted to fraction

The fractions are set of numbers classified as numerators and denominators

The numerator refers to the numbers in the upper part while the denominators are the numbers below

converting to fraction

-16 ÷ -2

= - 16 / - 2

= 16/2 fraction

dividing gives

= 8

The quotient which is the result of division is calculated to be equal to 8

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Answer:

39 miles per hour.

Step-by-step explanation:

780/20 = 39

The electric force exerted by particle A on C is 1.35 × 10^-11 N in the downward direction. The y-component of the force exerted by B on C is 0. The magnitude of the resultant force is 1.72 × 10^-11 N and the direction is 50.48° clockwise from the +x-axis.

Given:
Charge on Particle A, q1 = 3.05 × 10^-4 C

Charge on Particle B, q2 = -6.15 × 10^-4 C

Charge on Particle C, q3 = 1.25 × 10^-4 C

Position of Particle A = (0,0)

Position of Particle B = (4.02,0)

Position of Particle C = (0,3.74)

Formula used:
The electric force between two charges, F12 = K × (q1 × q2) / r^2

where K = Coulomb's constant = 9 × 10^9 Nm^2/C^2

q1 and q2 = Charges of particle 1 and particle 2 respectively

r = distance between the two particles

(a) The electric force between particle A and particle C is given by: F13 = K × (q1 × q3) / r^2

F13 = (9 × 10^9 Nm^2/C^2) × [(3.05 × 10^-4 C) × (1.25 × 10^-4 C)] / (3.74 m)^2

F13 = 1.35 × 10^-11 N

The electric force exerted by particle A on C is 1.35 × 10^-11 N in the downward direction.

(b) Electric force F13 is directed downwards. Therefore, the y-component of this force is given by: Fy = F13 * sin θ

where θ is the angle made by the force F13 with the horizontal.

Fy = F13 * sin θ = F13 * sin (90°) = F13 * 1 = 1.35 × 10^-11 N

The y-component of the force exerted by A on C is 1.35 × 10^-11 N.

(c) The electric force between particle B and particle C is given by:F23 = K × (q2 × q3) / r^2

where r is the distance between particle B and particle C

.F23 = (9 × 10^9 Nm^2/C^2) × [(6.15 × 10^-4 C) × (1.25 × 10^-4 C)] / (4.02 m)^2

F23 = 2.41 × 10^-11 N

(d) The force F23 is directed towards particle A. Therefore, the x-component of the force F23 is given by: Fx = F23 * cos θ

where θ is the angle made by the force F23 with the horizontal.

Fx = F23 * cos θ = F23 * cos (180°) = F23 * (-1) = -2.41 × 10^-11 N

The x-component of the force exerted by B on C is -2.41 × 10^-11 N

(e) The force F23 is directed towards particle A. Therefore, the y-component of the force F23 is given by:Fy = F23 * sin θwhere θ is the angle made by the force F23 with the horizontal. Fy = F23 * sin θ = F23 * sin (180°) = F23 * 0 = 0

The y-component of the force exerted by B on C is 0.

(f) The x-component of the electric force acting on C is given by the vector sum of the x-components of the forces F13 and F23. Fx,net = F13 + F23

Fx,net = (1.35 × 10^-11 N) + (-2.41 × 10^-11 N)

Fx,net = -1.06 × 10^-11 N

(a) The y-component of the electric force acting on C is given by the vector sum of the y-components of the forces F13 and F23.

Fy,net = F13 + F23

Fy,net = (1.35 × 10^-11 N) + (0)

Fy,net = 1.35 × 10^-11 N

(h) The magnitude of the resultant force acting on C is given by:

Fnet = √(Fx,net^2 + Fy,net^2)

Fnet = √[(-1.06 × 10^-11 N)^2 + (1.35 × 10^-11 N)^2]

Fnet = 1.72 × 10^-11 N

The direction of the resultant force acting on C is counterclockwise from the +x-axis. The angle that the force makes with the +x-axis is given by:

θ = tan^-1 (Fy,net / Fx,net)θ = tan^-1 [(1.35 × 10^-11 N) / (-1.06 × 10^-11 N)]θ = -50.48°

The magnitude of the resultant force is 1.72 × 10^-11 N and the direction is 50.48° clockwise from the +x-axis.

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Answer:

Step-by-step explanation:

Jane's caldles:

Chris's candles:

Profit, if equal per x candles is:

Each will have profit of $10 if 10 candles sell

Answer:

x = \(\sqrt{120}\) ≈ 10.95

Step-by-step explanation:

Use Pythagorean Theorem a²+b²=c²

6²-4²=a²

36-16=a²

a²=20

a=\(\sqrt{20}\)

\(\sqrt{20\)²+10²=c²

20+100=c²

c²=120

c= \(\sqrt{120}\) ≈ 10.95

If a lines is parallel to the x-axis so the slope would be m=0,

Then, by the slope-intercept form:

Here is the answer! Hope it helps! (C.)