Find x
round your answer to the nearest tenth of a degree

See below for the proof that the areas of the lune and the isosceles triangle are equal

The area of the isosceles triangle is:

\(A_1 = \frac 12r^2\sin(\theta)\)

Where r represents the radius.

From the figure, we have:

\(\theta = 90\)

So, the equation becomes

\(A_1 = \frac 12r^2\sin(90)\)

Evaluate

\(A_1 = \frac 12r^2\)

Next, we calculate the length (L) of the chord as follows:

\(\sin(45) = \frac{\frac 12L}{r}\)

Multiply both sides by r

\(r\sin(45) = \frac 12L\)

Multiply by 2

\(L = 2r\sin(45)\)

This gives

\(L = 2r\times \frac{\sqrt 2}{2}\)

\(L = r\sqrt 2\)

The area of the semicircle is then calculated as:

\(A_2 = \frac 12 \pi (\frac{L}{2})^2\)

This gives

\(A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2\)

Evaluate the square

\(A_2 = \frac 12 \pi (\frac{2r^2}{4})\)

Divide

\(A_2 = \frac{\pi r^2}{4}\)

Next, calculate the area of the chord using

\(A_3 = \frac 12r^2(\theta - \sin(\theta))\)

Recall that:

\(\theta = 90\)

Convert to radians

\(\theta = \frac{\pi}{2}\)

So, we have:

\(A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))\)

This gives

\(A_3 = \frac 12r^2(\frac{\pi}{2} - 1)\)

The area of the lune is then calculated as:

\(A = A_2 - A_3\)

This gives

\(A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)\)

Expand

\(A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2\)

Evaluate the difference

\(A = \frac 12r^2\)

Recall that the area of the isosceles triangle is

\(A_1 = \frac 12r^2\)

By comparison, we have:

\(A = A_1 = \frac 12r^2\)

This means that the areas of the lune and the isosceles triangle are equal

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The paired t-test results suggest that there is no significant improvement in students' learning after the new unit on factoring, based on a 90% confidence level.

To determine if there has been an improvement in students' learning after a new unit on factoring, we can perform a paired t-test on the pre-test and post-test scores of the five randomly selected students.

The differences between the pre-test and post-test scores for each student are: 3, 3, 4, 8, 0.

The mean of the differences is 3.6, and the sample standard deviation is 2.39.

The t-value for a 90% confidence interval with 4 degrees of freedom is 2.776. Since the calculated t-value of 2.68 (calculated as the mean of the differences divided by the standard error of the mean of the differences) is less than the critical t-value of 2.776, we fail to reject the null hypothesis that there is no improvement in students' learning.

Therefore, there is not enough evidence to conclude that the new unit on factoring has helped students learn based on the sample data.

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The limit of the expression (3x) multiplied by \(x^7\) as x approaches infinity is infinity.

To evaluate the limit as x approaches infinity, we consider the behavior of the expression (3x) * \(x^7\) as x becomes larger and larger. As x approaches infinity, the term 3x grows without bound since x is increasing without limit. Additionally, the term\(x^7\)also increases without bound as x becomes larger. When we multiply these two terms together, we have a product of two functions that both tend to infinity.

More specifically, the term 3x grows linearly with x, while \(x^7\) grows exponentially. Since the exponential growth dominates linear growth as x becomes larger, the product of \((3x) * x^7\) approaches infinity as x approaches infinity. This means that as x gets larger and larger, the value of the expression \((3x) * x^7\) also gets larger without bound. Therefore, the limit of\((3x) * x^7\)as x approaches infinity is infinity.

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Answer:Yes

Step-by-step explanation:

Both angles are the same. Meaning they are congruent with each other

Answer:

the area is 289

Step-by-step explanation:

the formula for calculating the perimeter of a square is the side*4

68/4=17

the formula for calculating tha area is side*side

17*17=289

The equation models the median monthly cost for the rent of a one bedroom apartment in San Fransisco.

If the year 2013 can be counted as t=0

Then the next year 2014 will be t=1

And the next year, 2015, will be t=2

To determine how much less would James pay if he moved in 2014 instead of 2015, you have to calculate the median cost for both yeanrs and calculate their difference.

Median cost for 2015 (t=2)

Median cost for 2014 (t=1)

Subtract the median cost of 2014 to the median cost of 2015:

He woul have paid $250 less if he rented the place in 2014.

To find the answers, we need to calculate the number of steps each player takes before they are unable to continue:

For Amar:

5 stairs up and 2 stairs down per turn

Net gain of 3 stairs per turn

It will take 32 turns to reach 96 stairs (32 * 3 = 96)

In the 33rd turn, Amar will climb 5 stairs and reach 100 stairs.

For Akbar:

7 stairs up and 2 stairs down per turn

Net gain of 5 stairs per turn

It will take 19 turns to reach 95 stairs (19 * 5 = 95)

In the 20th turn, Akbar will climb 7 stairs and reach 100 stairs.

For Anthony:

10 stairs up and 3 stairs down per turn

Net gain of 7 stairs per turn

It will take 14 turns to reach 98 stairs (14 * 7 = 98)

In the 15th turn, Anthony will climb 10 stairs and reach 100 stairs.

I) The players will meet on the same stair whenever they end up on a stair whose number is the same for any two players. To find out the number of times they meet on the same stair, we need to calculate the lowest common multiple (LCM) of the number of turns taken by each player to reach 100 stairs.

Amar takes 33 turns

Akbar takes 20 turns

Anthony takes 15 turns

LCM(33,20,15) = 660

Therefore, they will meet on the same stair 660/33 + 660/20 + 660/15 = 20 + 33 + 44 = 97 times.

II) Anthony takes the least number of steps to reach near hundred, as he only needs 15 turns to reach 98 stairs.

The maximum displacement of the tuning fork is 0.4 mm

The equation of the function is given as:

d = 0.4 sine (1760 pi t)

The above equation is a sine equation.

A sine equation is represented as:

f(t) = A sin(Bt + C) + D

Where A represents the maximum/amplitude

By comparison, we have:

A = 0.4

Hence, the maximum displacement of the tuning fork is 0.4 mm

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Answer:

0.4 mm

Step-by-step explanation:

The answer above is correct.

Answer  x = -10

Step-by-step explanation:

 Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     10-4*x-(50)=0 

STEP1:Pulling out like terms

 1.1     Pull out like factors :

   -40 - 4x  =   -4 • (x + 10) 

Equation at the end of step1:

STEP2:

Equations which are never true:

 2.1      Solve :    -4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

 2.2      Solve  :    x+10 = 0 

 Subtract  10  from both sides of the equation : 

                      x = -10

One solution was found :

 x = -10

Answer:

The angle SQR is half the intercepted arc SR which is 43°

True. Post-implementation evaluation refers to the process of evaluating the performance and effectiveness of a new system after it has been implemented.

It involves assessing the extent to which the system meets the intended objectives, as well as its overall quality and impact on the organization. The evaluation can be carried out through various methods such as user feedback, performance metrics, and system testing.

Therefore, post-implementation evaluation is primarily concerned with assessing the quality of a new system and its ability to deliver the expected benefits to the organization.

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When x is a uniformly distributed random variable on [0,1], it divides the interval [0,1] into two subintervals: [0,x] and [x,1]. This division exhibits symmetry, as explained in the following paragraphs.

Consider a uniformly distributed random variable x on the interval [0,1]. The probability density function of x is constant within this interval. When x takes a particular value, it acts as a dividing point that splits [0,1] into two subintervals.

The first subinterval, [0,x], represents all the values less than or equal to x. Since x is randomly distributed, any value within [0,1] is equally likely to be chosen. Therefore, the probability of x falling within the subinterval [0,x] is equal to the length of [0,x] divided by the length of [0,1]. This probability is simply x.

By symmetry, the second subinterval, [x,1], represents all the values greater than x. The probability of x falling within the subinterval [x,1] can be calculated as the length of [x,1] divided by the length of [0,1], which is equal to 1 - x.

The symmetry arises because the probability of x falling within [0,x] is the same as the probability of x falling within [x,1]. This symmetry is a consequence of the uniform distribution of x on the interval [0,1].

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The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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The SAA (Side-Angle-Angle) criterion is not a triangle similarity theorem.

Triangle similarity theorems are used to determine if two triangles are similar. Similar triangles have corresponding angles that are equal and corresponding sides that are proportional.  There are three main triangle similarity theorems:  AA (Angle-Angle) Criterion.

SSS (Side-Side-Side) Criterion: If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. SAS (Side-Angle-Side) Criterion.

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Answer:

0.290

Step-by-step explanation:

You just have to divide 3.49/12

Answer:

GUESS: 55ft

Step-by-step explanation:

55 ft is my guess, not 100 percent sure but the math i did was 50% of 110

Answer:

84 ft

Step-by-step explanation:

The ground and the two ropes form a right triangle.

For the 50-deg angle, the height, h, is the opposite leg. The hypotenuse is the 110-ft side.

sin A = opp/hyp

sin 50° = h/110

h = 110 sin 50°

h = 84

Answer: 84 ft

The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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The absolute value inequality that represents the number of hours spent on doing homework is 2 ≤ x ≤ 5

Let us assume that one spends x hours doing homework on a typical weekday. Then we can write

The inequality expression for a slow weekend is given as;

X ≥ 2

In the same vein, the inequality expression for a busy weekend is given as;

X ≤ 5

Pooling the two inequalities expression we have;

2 ≤ x ≤ 5

Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality and is often written in the form a ≤ f (x) ≤ b

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Answer:

Volume left = 16π cm³ or 50.265 cm³

Step-by-step explanation:

Let's first find the surface area of the tennis ball.

S.A = (4/3)πr³

Radius of a ball = 2 cm

Thus;

S.A = (4/3)π(2)³

S.A = 32π/3

Since there are 3 radius balls that will make the cylinder full, then;

Surface area of 3 balls = 3 × 32π/3 = 32π

Now, formula for volume of cylinder is;

V = πr²h

r = 2 cm

h = 4 × 3 = 12 (since diameter of tennis ball is 4 cm)

Thus;

V = π × 2² × 12

V = 48π

Thus;

Volume left = Volume of cylinder - surface area of 3 balls = 48π - 32π = 16π cm³ or 50.265 cm³

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

The exponential distribution is a continuous probability distribution that describes the time between two consecutive events that occur randomly and independently of each other. This distribution is useful in the fields of reliability, physics, and finance, among others.

The exponential distribution has a single parameter known as the scale parameter, which is denoted by lambda (λ) and is typically expressed in terms of the mean time between failures.The mean, median, and standard deviation are three of the most common summary statistics used to describe a probability distribution.

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester can also be calculated using the exponential distribution.

Mean: The mean of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the mean is 1/λ = 1/0.143 = 6.993.

Median: The median of the exponential distribution is equal to ln(2)/λ.λ = 1/7 = 0.143

Therefore, the median is ln(2)/λ = ln(2)/0.143 = 4.837.

Standard deviation: The standard deviation of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the standard deviation is 1/λ = 1/0.143 = 6.993.

Probability: P(X > 16) = e^(-λx)λ = 1/7 = 0.143X = 16P(X > 16) = e^(-0.143 * 16) = 0.230

Therefore, the probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

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Start by putting the possible integers your friend can select

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A= Be more than 6

B= The number is odd

The probability of the union of two events can be calculated as:

Then,

Finally,

Answer:

the probability that the number will be more than 6 or odd is: 7/10

Answer:

true

Step-by-step explanation:

if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:

\(sec\left(\frac{\pi }{2}\:-x\right)\)    \(=\frac{1}{\sin \left(x\right)}\)

\(\frac{1}{\sin \left(x\right)}\)  \(=\csc \left(x\right)\)

so, yes,  \(sec\left(\frac{\pi }{2}\:-x\right)\)  \(=\csc \left(x\right)\)

hope this helps!!

Answer: $22.50

Step-by-step explanation:

Let x be the cost per pound of the secret-formula coffee beans.

The total cost of the secret-formula beans is 12x dollars.

The total cost of the other beans is 15 × 18 = 270 dollars.

The total cost of the mix is (12 + 15) × 20 = 540 dollars.

Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.

We can set up an equation based on the total cost of the mix:

12x + 270 = 540

Subtracting 270 from both sides:

12x = 270

Dividing both sides by 12:

x = 22.5

Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.

Answer:

The correct option is;

c. The horizontal axis labeled Hours Driven goes from 0 to 15 in increments of 1 and the vertical axis labeled Miles Remaining goes from 0 to 150 in increments of 10. The line starts at left parenthesis (0, 0), and passes through (1, 65) and (2, 130)

Step-by-step explanation:

The given parameters are;

The speed of the truck = 65 miles per hour

The length of the highway = 130 miles

Therefore, from the given information, we have;

The time, t, it will take the truck to arrive at the end of the highway is given as follows;

Time = Distance/speed = 130/65 = 2 hours

Therefore, if the truck timing starts from the point (0, 0), we have;

The points on the straight line (constant) speed graph are;

(0, 0), (1, 65), and (2, 130)

Answer:

C

Step-by-step explanation:

Answer: 5y + 2x - 3

(In simplest form)

The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

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