What postulate proves triangle congruence?
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AAS
SAS
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ASA

Answer:

Although nuclear is not renewable, it is clean energy

Step-by-step explanation:

Nuclear power is presently a sustainable energy source but could become completely renewable if the source of uranium changed from mined ore to seawater.

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Part a:  What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost

The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)

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The correct answer is A. Test statistic t = 2.1213 is a value greater than the critical value to = +2.110. Hence, the test value is clearly in the critical region. Thus, we decide to reject the null hypothesis.

To determine whether there is sufficient evidence to reject the null hypothesis that the true average time of the athlete's 100-meter sprint is 98 seconds, we need to perform a hypothesis test using the given data.

The test statistic for this scenario is calculated using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case, the sample mean is 98.2 seconds, the hypothesized mean is 98 seconds, the sample standard deviation is 0.4 seconds, and the sample size is 18.

Substituting the values into the formula, we get:

t = (98.2 - 98) / (0.4 / sqrt(18)) ≈ 2.1213

To make a decision, we compare the test statistic to the critical value at the given significance level of 0.05. The critical value for a two-tailed test with a significance level of 0.05 and 17 degrees of freedom is approximately ±2.110.

Since the test statistic (2.1213) is greater than the critical value (+2.110), it falls into the critical region. Therefore, we reject the null hypothesis.

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Answer:

median:30 mode:42 range:36

Step-by-step explanation:

i did the math on my netpad and i dont want to type it but there you go goodluck.

Answer:

Well I'm not a girl soo No.

Step-by-step explanation:

By using formula volume of cone, When the pile is 5 feet high, the height of the pile is increasing at a rate of 0.0169 feet per minute.

What does volume mean in plain terms?

A solid shape's capacity is measured using volume, a three-dimensional quantity.

                   It implies that a closed figure's volume determines how much three-dimensional space it can fill.

Volume of cone = 1/3πr²h

          If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

  volume of the cone = πh/3 (h/2)²

            v = πh³/12

  Rate of Change of the Volume, dV/dt = 3πh²/12  dh/dt

  Since gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. Therefore, the Volume of the cone is increasing at a rate of 10 cubic feet per minute.

      dV/dt = 4ft³/min

 We want to determine how fast is the height of the pile is increasing when the pile is 5 feet high.

We have

         3πh²/12  dh/dt   = 4

 when  h = 5 feet

   3π * 5²/12  dh/dt  = 4

 75π dh/dt  = 4

 dh/dt = 4/75π

  dh/dt = 0.0169 feet per minute.

When the pile is 5 feet high, the height of the pile is increasing at a rate of 0.0169 feet per minute.

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Answer:

idu it, the question but the euqation is x= -2y - 433 / 2 -5

Step-by-step explanation:

The radius of the circle is 4 units

The equation of the circle is given as:

(x + 5)^2 + (y - 3)^2 = 4^2

The general equation of a circle is given as:

(x - a)^2 + (y - b)^2 = r^2

Where r represents the radius

By comparing both equations, we have:

r^2 = 4^2

Take the square root of both sides

r = 4

Hence, the radius of the circle is 4 units

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The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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The approximate values triangle for angle B, angle C, and side b are B ≈ 54.4 degrees, C ≈ 96.6 degrees, and b ≈ 36.8 units, respectively, rounded to the nearest 10th.

Given data:

Side a = 18

Side c = 27

Angle A = 29 degrees

Step 1: Find angle B using the law of sines:

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

sin(B)/27 = sin(29°)/18

sin(B) = (27sin(29°))/18

B = arcsin((27sin(29°))/18)

Step 2: Find angle C using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

C = 180° - 29° - B

Step 3: Find side b using the law of sines:

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

sin(C)/27 = sin(29°)/18

sin(C) = (27 × sin(29°))/18

b = (sin(C) × a)/sin(A)

Step 4: Substitute the given values into the equations and calculate the approximate values using a calculator:

B ≈ arcsin((27 × sin(29°))/18) ≈ 54.4 degrees

C ≈ 180° - 29° - 54.4° ≈ 96.6 degrees

b ≈ (sin(96.6°)*18)/sin(29°) ≈ 36.8

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The question is -

Solve the triangle. Angle A is opposite side a, Angle B is opposite side b and Angle C is opposite side c. Round final answers to the nearest 10th

Given data: side a = 18, side c = 27, angle A = 29 degrees.

According to the 1991 census, there are about 43406932 people in our country who speak Urdu. Which of the following is the closest approximation of this number?

A 4 lakhs

B 43 lakhs

C 4 crores

D 43 crores

→ C 4 crores

Explaination :

2 - Unit place

3-tens place

9- hundred place

6 - thousand place

0- ten thousand place

4 - lakh place

3 - ten lakh place

4 - crore place

hence , closest approximation of this number is 4 crores.

Approximation of number is 4 crores.

Anything that is similar to something else but not exactly equal to it is an approximation. By rounding, a number can be approximated. By rounding the values contained within a calculation prior to performing the operations, it can be approximated.

Given census of a country is 43406932

Adjusting numbers to the closest 10, 100, 1,000

To rough to the closest ten, check out at the digit during the tens section.

Look at the digit in the hundreds column to approximate to the nearest hundred. Take a look at the digit in the thousands column to determine the nearest thousand.

so the number to the closest is crore

Hence the closest approximation of this number is 4 crores.

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Answer:

here

Step-by-step explanation:

18000 divided by 360, then multiply that new number with 48. i believe that is the correct math...

Answer:

240

Step-by-step explanation:

48/360*1800

240

(A) n3+10*2n expressed in big-O notation is O(n3).

(B) n2+3log2⁡n expressed in big-O notation is O(n2).

(C) 5nlog2⁡n+2n2 expressed in big-O notation is O(n2).

(D) 1+2+3+…+(n−1)+n can be simplified as 1+2+3+…+n and using the formula for the sum of an arithmetic series, we have n(n+1)/2. Therefore, its big-O notation is O(n2).

(E) The code fragment can be written as:

                               for(int i=0;i< n;i++){for(int j=0;j< n;j++){ans++;}}

This code fragment has two nested loops.

The outer loop executes n times, while the inner loop also executes n times for each iteration of the outer loop.

Therefore, the code fragment has a time complexity of O(n2) in the Worst case.

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The dimensions of the poster with the smallest area are 48 cm by 16 cm.

Let the width of the printed material be x cm and the height be y cm. Then the total width of the poster including the margins is (x + 16) cm, and the total height is (y + 24) cm.

The total area of the poster is the area of the printed material plus the area of the margins:

(x + 16)(y + 24) = 1536

Expanding the left side, we get:

xy + 16y + 24x + 384 = 1536

Rearranging terms, we get:

xy = 1152 - 16y - 24x

To find the dimensions of the poster with the smallest area, we want to minimize the product xy subject to the constraint given by the equation above.

One way to do this is to use the method of Lagrange multipliers. Let L = xy + λ[(x + 16)(y + 24) - 1536] be the Lagrangian, where λ is a Lagrange multiplier. Setting the partial derivatives of L with respect to x, y, and λ equal to zero, we get:

y + 16λ = 0

x + 24λ = 0

(x + 16)(y + 24) = 1536

From the first two equations, we get:

x = -24λ

y = -16λ

Substituting these into the third equation, we get:

(-24λ + 16)(-16λ + 24) = 1536

Simplifying, we get:

-6λ + 4 = 0

Therefore, λ = 2/3. Substituting this into the expressions for x and y, we get:

x = -16

y = -32

These values give the dimensions of the printed material. To find the dimensions of the poster, we add the margins:

width = x + 16 + 16 = 48 cm

height = y + 24 + 24 = 16 cm

Therefore, the dimensions of the poster with the smallest area are 48 cm by 16 cm.

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I believe the difference is 5 degrees Fahrenheit.

Answer:

please be more specific

Answer:

3 pounds

Step-by-step explanation:

a pound is 16oz so 3x16=48

Answer:

$1.25 dollars per day added to the coin jar

Step-by-step explanation:

the given equation is: 56 – 4y = –5x

we can rewrite it:

4y = 56 + 5x

y = (56 + 5x) / 4

y = 14 + ⁵/₄x

the slope of the equation is ⁵/₄, which gives us how much money is added into the coin jar every day. We can write ⁵/₄ as 1.25 or $1.25 dollars per day added to the coin jar

a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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SOLUTION

We want to solve the question below

We are told to find the length of arc RS.

We will use the formula for length of an arc that says

Substituting the values into the formula, we have

Hence the answer is 17.0 to the nearest tenth

Therefore, the two events are not proportional because

At 9am, she would run 1 mile in 24minutes, Whereas

At 6 pm, she ran 1 mile in 12minutes.

If the p-value less than the significance level then we have a type i error.

We know that if your P-value is less than the chosen significance level then you reject the null hypothesis i,e. accept that your sample gives reasonable evidence to support the alternative hypothesis.

Im statistics, a type i error means rejecting the null hypothesis when it's actually true, while type ii error means failing to reject the null hypothesis when it's actually false.

The chance that you commit type i errors is known as the type i error rate or significance level (p-value). This number is conventionally and arbitrarily set to o.o5 or 5%. Type ii errors are like "false negatives", an incorrect rejection that a variation in a test has made no statistically significant difference.

The probability of making a type i error is represented by alpha level, which is the p-value below which you reject the null hypothesis.

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Answer: 19 coins

Step-by-step explanation:

38-19=19

To check, take any one of the nubers and replace it with x, and when you solve for x. you'll get that number back. For example:

Let x represent the amount used to buy a notebook

19+x=38

x=38-19

x=19

First of all, we need to know what the units are in this problem.

We can see that there is yards, inches, and feet.

(Keep in mind that yd = yard, ft = feet, and in = inches)

1yd = 3ft

1ft = 12in

Let's figure out how many inches are in a yard.

If we know that 3 feet are in every yard, and 12 inches are in every foot, we can make an equation that looks like this:

(1yd × 3ft) × 12 = 36

This means that there are 36 inches in every foot.

Now that we know how many inches are in a yard, lets figure out how many inches are in 10 yards.

36 × 10 = 360

There are 360 inches in 10 yards.

Now, let's figure out how much 360 inches exceeds 192 inches.

360 - 192 = 168

To convert this to feet, we need to use an equation that looks like this:

168 ÷ 12 = 14

Therefore, the amount of feet that the length of the room exceeds the width is 14 feet.

The problem involves finding the dimensions of a rectangular page with a fixed area of 92 square inches of print while minimizing the amount of paper used by minimizing the dimensions of the page.

The margins on each side are fixed at 1 inch. This is an optimization problem.

To solve the problem, we need to set up an equation that relates the area of the page to its dimensions. Let the width of the page be x, and the length be y. Then, we have:

Area of print + Margins = Total Area of page

92 + (1)(2x) + (1)(2y) = (x + 2)(y + 2)

Simplifying this equation, we get:

92 + 2x + 2y = xy + 2x + 2y + 4

92 = xy + 4

Now, we want to minimize the dimensions of the page, which is the same as minimizing the area. Using the equation above, we can express one variable in terms of the other. For instance, we can solve for y:

y = (92 - 4) / x

y = 88 / x

Now, we can substitute this expression for y into the equation for the area of the page:

A(x) = xy

A(x) = x(88 / x)

A(x) = 88

We can see that the area of the page is a constant, 88 square inches, which means that the dimensions of the page that use the least amount of paper are the ones that minimize the perimeter. The perimeter of the page is given by:

P(x) = 2x + 2y + 4

P(x) = 2x + 2(88/x) + 4

To minimize the perimeter, we can differentiate with respect to x:

P'(x) = 2 - 176/x^2

Setting P'(x) = 0, we find:

2 - 176/x^2 = 0

x = sqrt(88) = 2sqrt(22)

Thus, the dimensions of the page that use the least amount of paper are 2sqrt(22) inches by 88 / (2sqrt(22)) = sqrt(88) inches.

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Answer:1564cm cube

Step-by-step explanation: v=\(\pi\)r2h

v=22/7*6*6*14=1564.containter b volume of water is the total volume in container a so you just have to find container a volume

Answer: The correct answer is 1583.4

Step-by-step explanation:

Answer:

leave at  1:30 PM

Step-by-step explanation:

10 mph 40 hours 6600/1200 5.5 hr  40/15 2 hr 40 mins 5.5 -.5 =

After two hours there at the meeting place, the helicopter must depart at 1:30 pm to join the boat.

Speed is the rate an object travels in a predetermined period of time.

Its speed is expressed in km/h. 

As per the given information in the question,

If the boat goes to the station ,

Speed of the boat = 10mph

it will take 400/10 = 40 hours.

The helicopter has, 6600 lbs of fuel.

It will take 30 minutes to clean the fisherman and an additional hour to get enough fuel.

1.5 × 1200 = 1800 lbs of fuel.

So, the amount of fuel helicopter now has

6600 - 1800

= 4800 lbs of fuel.

This will allow it to fly for 4 hours as:

4800 lbs/1200 lbs per hour, It can only travel at 150 mph for two hours one way.

= 300 miles distance from the station.

The boat is available at 400 miles, and its maximum flight time at 150 mph is two hours going one way, which is 100 miles from where it is now,

So,

100/10 = 10 hours, the journey to the meeting location will take the boat ten hours.

To reach the boat, which will require 10 hours, the chopper must take off after 8 hours since it will take 2 hours.

So 8 hours of time from 5:30 am will be equal to 1:30 pm.

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Your question seems incomplete, probably the complete question is:

A crewman on a fishing boat was injured and needs to be treated in a hospital right away. You are with a Coast Guard station nearest to the boat, but you are 400 miles away. The boat travels at a rate of 10 mph. It is 5:30 A.M. You have a helicopter that can hold 6600 lbs. of fuel, consumes 1200 pounds of fuel an hour, and travels 150 mph. However, you need to save a minimum of 1 hour worth of fuel for landing problems at the Coast Guard station, and you need to have 30 minutes’ worth of fuel to remove the crewman from the boat. You have to create a plan for extracting the crew member. When would you leave and why? Fully explain your answer.