cos(x/3)cos(x/3=1/2[1+cos(2x/3)] true or false

Where the following triangle problem is given, note that:

A) α [tex]\approx[/tex] 11.0

β  β [tex]\approx[/tex] 9.4

B) 25.59 yrds

C) 0.38 yrds

A) To determine the near post angle and the far post angle when the striker is 24 yards from the near post

1/2 (24²) + 1/2 (28²) - 1/4(10²) = 655 (central line length formula)

Cos  α = (24² + 655 - 5²)/ (2 x 24 x √655)

= 0.98171498561

α = Cos ⁻¹ 0.98171498561

α = 10.973603643623608717848651724941

α [tex]\approx[/tex] 11.0° (Cosine Law)

For   28 yards from the far post.

Cos   β   = (28² + 655 - 5²)/ (2 x 28 x √655)

= 0.98659913977

 β  = Cos ⁻¹ 0.98659913977

 β  = 9.3905311636838307510867912796592

 β  [tex]\approx[/tex] 9.4°

B)  Distance between the goalie from the ball is

√655 = 25.592967784139454896443137575823

Distance  [tex]\approx[/tex] 25.59 yrds

C)  5-10 * ((24)/(24+28)) = 0.38 yrds (Angular Bisector Theorem)

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Answer:

In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.

A = (1/2)Pa

= (1/2)(2)(8/√3)(6)(8)

= (384√3)/3 = 128√3 = 221.7 units^2

The total amount owed, to the nearest cent A = $ 3,283.44

Simple interest is interest that is only calculated on the initial sum (the "principal") borrowed or deposited. Generally, simple interest is set as a fixed percentage for the duration of a loan. No matter how often simple interest is calculated, it only applies to this original principal amount.

A = P + I where

P (principal) = $ 2,950.00

I (interest) = $ 333.44

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

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Correct question:

Find the total amount owed, to the nearest cent, for a simple interest loan with a principal of $2950, an interest rate of 7.4% and a time period of 1.5 years. Show​

Answer:

-4.7854909e+52

Step-by-step explanation:

how do i know

cuz i used a calculator

what evevn is your equation

Answer:

x = -1/12

Step-by-step explanation:

It is actually a rather simple proof. Before we get to that, it’s important to understand a couple of other things. Let’s consider the following infinite summation:

X = 1 - 1 + 1 - 1 + 1 - 1 ...

Rearranging the above equation a little bit, we get:

X = 1 - (1 - 1 + 1 - 1 + 1 - 1 ...)

If you look at the term inside the brackets, it in fact equals X. So let’s substitute that:

X = 1 - X

2X = 1

X = 1/2

Now let’s consider another sum.

Y = 1 - 2 + 3 - 4 + 5 - ...

Writing it in another way, we get:

Y = 0 + 1 - 2 + 3 - 4 + 5 + ...

Adding the above two equations:

Y + Y = (1 - 2 + 3 - 4 + 5 ...) + (0 + 1 - 2 + 3 - 4 + 5 ...)

Grouping the corresponding terms within the brackets, we get:

2Y = 1 + 0 - 2 + 1 + 3 - 2 - 4 + 3 + 5 - 4 ...

2Y = 1 - (2-1) + (3-2) - (4-3) + ...

2Y = 1 - 1 + 1 - 1 + 1 - 1 ...

But the summation on the right hand side is X. Let’s substitute it:

2Y = X

2Y = 1/2

Y = 1/4

Finally, let’s consider our original question at hand i.e. the sum of all natural numbers:

S = 1 + 2 + 3 + 4 + ...

We defined Y earlier as:

Y = 1 - 2 + 3 - 4 + ...

Subtracting Y from S:

S - Y = 1 - 1 + 2 + 2 + 3 - 3 + 4 + 4 + ...

S - Y = 4 + 8 + 12 + 16 + ...

We just calculated the value of Y to be 1/4. So let’s substitute it:

S - 1/4 = 4 x (1 + 2 + 3 + 4 + ...)

S - 1/4 = 4S

3S = -1/4

S = -1/12

The greatest common factor is 2z^2

How you find it is first you find the greatest common factor of the two numbers, which is 2 (2 is the greatest number that can be multiplied into 2 and 10; 2 times 1 = 2 and also 2 times 5 = 10)

Then you find the greatest common factor of the variables, which is z^2.

(z^2 is the largest that can go into z^3 and z^2 because z^2 times z = z^3 and z^2 = z^2)

After that, you just multiply them together to get 2z^2

The two values which are located at the same point on a number line as required to be determined are; 4/1 and 4.

It follows from the task content that the answer choice which represents two values located at the same point on the number line be determined.

On this note, such two values must be equivalent.

Hence, by observation; the answer choice which represents two equivalent values is; 4/1 and 4 and they represent values located at the same point on the number line.

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The probability that exactly 2 of them say job applicants should follow up within two weeks is 33.02%.

We can use the binomial probability formula:

P(x) = C ( n, x ) × p ^ x × ( 1 - p ) ^ ( n - x )

Solving then gives:

P ( 2 ) = C ( 7, 2 ) x 0.49 ^ 2 x ( 1 - 0. 49 ) ^ ( 7 - 2)

P ( 2 )  = 21 x 0. 49 ^ 2 x ( 1 - 0. 49) ^5

=  21 x 0. 2401 x 0. 078109

=  0. 3302

In conclusion, the probability that 2 of the 7 human resource managers say job applicants should follow up within two weeks is approximately 0.3302 or 33.02%.

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so, we know the diameter is 8, so that means its radius is half that, or 4.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2[/tex]

The height of the building when the surveyor is standing that far is D.)41ft​

The tangent function would be best to use to find the height because we would be able to use the adjacent and and opposite.

Assuming that 5 feet is the height and the angle of elevation is 41. 7 degrees, and the distance of 40 feet, we have :

tan ( A ) = (h - x) / D

tan ( 41. 7° ) = ( h - 5 ) / 40

h - 5 = 40 x tan ( 41. 7 ° )

h - 5 = 40 x 0.8895

h = 35.58 + 5

= 40.58

= 41 feet

The height of the building is 41 feet.

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Answer:

25

Step-by-step explanation:

range = largest number - smallest number

38-13=25

The answer is option A. That is, the time taken in hours if the train traveled 13 miles in 30 minutes is 4.5 hours.

The relation between distance traveled and time is given by the formula:

Distance = Speed x Time

where distance is the total distance traveled, speed is the rate at which the distance is covered, and time is the duration for which the distance is covered. This formula applies to any type of motion, whether it is linear or circular, and it is often used to calculate the distance covered by an object given its speed and the time it traveled. Alternatively, the formula can also be used to calculate the time required to travel a certain distance given the speed at which the object is traveling.

Given that the total distance = 117 miles. We need to find the time taken in hours if the train traveled 13 miles in 30 minutes.

For that we can use the equation, distance = rate x time

Now, rate = distance/time

Distance = 13 miles, time = 30 minutes = 30/60 hours = 0.5 hours

Therefore, rate = 13 miles / 0.5 hours = 26 miles per hour

Now to find the time it took to travel the entire 117 miles:

time = distance/rate

time = 117 miles/ 26 miles per hour

time = 4.5 hours

Therefore, the answer is (A) 4.5 hours.

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Correct answer is option A. If the height of the pyramid on the drawing was 3 1/2 inches, then the height of the actual pyramid is 98 feet

When a scale drawing or model is made, the actual object is typically much larger than the drawing or model. In order to represent the object in a smaller size, a ratio is used to scale down the dimensions. This ratio is can be in a fraction form or 'is to' form. We can use this ratio to easily calculate the dimensions of a replica from the actual object or vice versa.

To find the height of the actual pyramid, we need to use both scales given in the problem.

We can start by finding the height of the replica using the first scale:

1 inch on the drawing = 2 feet on the replica

So, 3.5 inches on the drawing = (3.5 * 2) feet on the replica = 7 feet on the replica

Now, using the second scale we can find the height of the actual pyramid:

1 foot on the replica = 14 feet on the actual pyramid

So, 7 feet on the replica = (7 * 14) feet on the actual pyramid = 98 feet

Therefore, the height of the actual pyramid is 98 feet.

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Answer:

arc PTR = 277°

Step-by-step explanation:

PS is the diameter of the circle , then arc PS = 180°

arc PTR = PS + SR = 180° + 97° = 277°

Answer:

arc PTR = 277°

Step-by-step explanation:

PS is the diameter of the circle , then arc PS = 180°

arc PTR = PS + SR = 180° + 97° = 277°

Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

[tex](10x - 20) + (6x + 8) = 180[/tex]

First, combine like terms. Like terms are terms that share the same amount of the same variables:

[tex](10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\[/tex]

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

[tex]16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192[/tex]

Next, divide 16 from both sides of the equation:

[tex]\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12[/tex]

12 is your answer.

~

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the number of gallons of water it can pump inn 45 minutes is

The given parameters that will help us to determine the quantity are

Powejet pumps 420 gallons of water per hour

how many gallons of water will it pump in 45 minutes  = ?

1 hour = 60 minutes

This means = 450/60  = 7 gallons

Therefore in  45 minutes it can pump 7*45 = 315 gollons

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The end behavior of f(x) is described as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:

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To find the margin of error, we can use the formula: E = z√((p(1-p))/n)

where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.

From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.

Plugging in the values, we get:

E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385

So the margin of error is 0.0385.

To find the confidence interval, we can use the formula:

p ± E

where p is the sample proportion and E is the margin of error.

Plugging in the values, we get:

0.696 ± 0.0385

So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].

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4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral ​.

What do math quadrilaterals mean?

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.

                                   There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.

2X + 2 = 4

   2X = 4 -2

      2X = 2

        X = 1

2x + 2 = 2 * 1 + 2  = 4

4x + 3 = 4 * 1 + 3 = 7

2x = 2 * 1 = 2

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4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral ​.

What do math quadrilaterals mean?

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.

                                   There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.

2X + 2 = 4

   2X = 4 -2

      2X = 2

        X = 1

2x + 2 = 2 * 1 + 2  = 4

4x + 3 = 4 * 1 + 3 = 7

2x = 2 * 1 = 2

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The balance at the end of the month was $7046.93.

To determine the balance at the end of the month, we need to:

Data

Starting balance = $9145.87

Deposits = $2783.71

Interest earned = $11.15

Checks written = $4871.90

Maintenance fee = $12

Balance at the end of the month will be:

= Starting balance + Deposits + Interest earned - Checks written - Maintenance fee

= $9145.87 + $2783.71 + $11.15 - $4871.90 - $12

= $7046.93.

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The distance for boat is,

=  43.2 miles

Given that;

Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour

Now, For Walk DATA:

Rate = 2 mph ; time = x hrs.

Then, distance = 2x miles

For Boat DATA:

Rate = 10 mph ; time = 5 - x hrs

Then, distance = 10 (5 - x) miles

Hence, We can formulate;

distance + distance = 12 miles

2x + 10 (5 - x) = 20

2x + 50 - 10x = 20

30 = 8x

x = 3.6

Hence, Boat time ,

5 - x = 5 - 3.6 = 1.4 hr (boat time)

And, The value of Boat distance = 12x = 12 x 3.6 = 43.2 miles

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Step-by-step explanation:

If Sarah buys the oil and oil filter separately, she would spend:

Cost of oil = $37.54

Cost of oil filter = $9.47

Total cost = $37.54 + $9.47 = $47.01

Therefore, Sarah can save:

Coupon price - Total cost = $49.95 - $47.01 = $2.94

So, Sarah can save $2.94 by doing the oil change herself instead of using the coupon.

Answer:

x + 5 + 7x - 5 + x = 180

9x = 180

x = 20

So the measure of angle M is x + 5 = 20 + 5 = 25°

The minimum variance unbiased estimator of the parameter,λ of a poisson population is λ = Σxi/n.

Variance is a measure of how spread out a set of data is. In statistics, it is the average of the squared differences from the mean of a set of values. It is calculated by taking the sum of the squared deviations from the mean and dividing it by the number of data points.

Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean λ. The likelihood function is given by:

[tex]L(\lambda | x) = \pi[e^{(-\lambda)} \lambda^{(xi)} / xi!][/tex]

Taking the natural logarithm and differentiating with respect to λ:

ln L(λ | x) = -nλ + ln(λ) Σxi - Σln(xi!)

d/dλ ln L(λ | x) = -n + Σxi/λ

Setting the derivative equal to zero and solving for λ, we get:

λ = Σxi/n

This is the sample mean of the Poisson distribution, which is an unbiased estimator of λ. Moreover, using the Cramer-Rao lower bound, we can show that it is also the minimum variance unbiased estimator of λ.

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The probability that the sample mean would be greater than 70.8 kilograms is given as follows:

0.1762 = 17.62%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 70, \sigma = 8, n = 87, s = \frac{8}{\sqrt{87}} = 0.8577[/tex]

The probability is one subtracted by the p-value of Z when X = 70.8, hence:

Z = (70.8 - 70)/0.8577

Z = 0.93

Z = 0.93 has a p-value of 0.8238

1 - 0.8238 = 0.1762.

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