a searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how deep should the searchlight be?

Answers

Answer 1

A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.

As per the given information,

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.

Here we have to Find: How deep should the searchlight be.

First of all, we need to find the equation of the paraboloid of revolution.

Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).

So, the equation of the paraboloid is given by:

y² = 4ax

Where, a = 2 feet (distance of light source from vertex)

So, the equation of the paraboloid is:

y² = 8x ..... (1)

The opening of the paraboloid is given to be 5 feet across.

We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.

The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)

The equation of the plane is given by x = -2.5

Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.

We can substitute x = -2.5 in equation (1) to get:

y² = -20

Squaring both sides, we get:

y = ±√(-20)

Since y can only be positive (since we are considering the upper half of the paraboloid),

y = √(-20) = i√20 = 2√5 i

So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)

The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet

Hence, the depth of the searchlight should be 2.5 feet.

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Related Questions

4 cleaner can clean all the rooms in a hotel in 7 1/2 hours. How long will it take 6 cleaners working at the same rate to clean all the rooms in the hotel?

Answers

it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.

If 4 cleaners can clean all the rooms in a hotel in 7 1/2 hours, we can start by using the concept of work rate. Work rate is a measure of how much work is completed in a certain amount of time. If we assume that the work rate of each cleaner is constant, we can set up a proportion to find how long it will take 6 cleaners to clean the same amount of rooms:

4 cleaners can clean all the rooms in 7 1/2 hours.

Therefore, 1 cleaner can clean all the rooms in (4 x 7 1/2) hours = 30 hours.

So, if 1 cleaner takes 30 hours to clean all the rooms, then 6 cleaners working at the same rate will take:

(time for 1 cleaner) / (number of cleaners) = (30 hours) / (6 cleaners) = 5 hours

Therefore, it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.

It is important to note that this assumes that the work rate of each cleaner is constant and that there are no factors that may affect the cleaning time, such as interruptions or changes in the number of rooms to be cleaned. Additionally, the optimal number of cleaners may vary depending on the size of the hotel and the specific cleaning needs.

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A 0.2-kilogram softball is thrown toward a catcher’s mitt. The ball is accelerating at a rate of 8 meters per second squared. With what force will the ball hit the catcher’s mitt?


A.7.8N

B.40N

C.1.6N

D.8.2N

Answers

Refer to the attached image.

Help please it’s urgent

Answers

The system of equation with the same solution with 2x + 2y = 16 3x  - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.

How to solve system of equation?

System of equation can be solved using different method such as elimination method, substitution method and graphical method.  Therefore, let's solve the system of equation as follows;

2x + 2y = 16

3x  - y = 4

multiply equation(ii) by 2

2x + 2y = 16

6x - 2y = 8

add the equations

8x = 24

x = 24  / 8

x = 3

y = 3x - 4

y = 3(3) - 4

y = 9 - 4

y = 5

Therefore,

2x + 2y = 16

6x - 2y = 8

add the equation

8x = 24

x = 24  / 8

x = 3

Therefore,

2(3) + 2y = 16

6 + 2y = 16

2y = 16 - 6

2y = 10

y = 5

Therefore, the equation with the same solution is 2x + 2y = 16

6x - 2y = 8.

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The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate

Answers

The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.

The time Jasmine spends biking is indeed a function of the distance she bikes.

The formula to calculate the time Jasmine takes to bike a certain distance is equal to,

time = distance / speed __(1)

Here the speed is the rate at which Jasmine bikes = 18 miles per hour.

Let us consider 'd' be the distance representing the number of miles Jasmine bikes.

This implies,

The function that represents the time Jasmine spends biking in terms of the distance .

Function f(d)  representing the time Jasmine spends biking for a distance of d miles

Substitute all the values in the formula (1) we get,

⇒ f(d) = d / 18

Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.

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The above question is incomplete , the complete question is:

The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.

Write the function representing the time Jasmine spends biking in terms of the distance?


Hint
Use the Pythagorean Theorem to solve for the missing sides

Answers

Answer: Shape one: 5, Shape 2: 13

Step-by-step explanation:

shape one
12^2+x^2=13^2

shape two
5^2+12^2=x^2

Answer:

PLEASE MARK ME AS BRAINLLIEST

Step-by-step explanation:

p=12

h=13

b=?

p²+b²=h²

12²+b²=13²

144+b²=169

b²=169-144

   = 25

b=root25

b=5m

b=5

p=12

h=?

p²+b²=h²

12²+5²=h²

144+25=h²

h²=169

h=root169

h=13

How many unique triangles are there in the regular hexagon?

Answers

From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.

Answer:

Step-by-step explanation: There are 6 equilateral triangles in a regular hexagon by connecting the opposite vertices of a regular hexagon.

a bag of elven counters
5 of the counters are white
a counter is taken out of the bag at random and not replaced
a second counter is taken out of the bag
calculate the probality that only one of the counters is white

Answers

Answer: 6/11P (A) = [tex]\frac{6}{11}[/tex]

Step-by-step explanation:

Probabilities

The question describes an event where two counters are taken out of a bag that originally contains 11 counters, 5 of which are white.

Let's call W the event of picking a white counter in any of the two extractions, and N when the counter is not white. The sample space of the random experience is Ω = {WW, W N, NW, N N}

We are required to compute the probability that only one of the counters is white. It means that the favorable options are A = {W N, NW}

Let's calculate both probabilities separately. At first, there are 11 counters, and 5 of them are white. Thus, the probability of picking a white counter is 5/11.

Once a white counter is out, there are only 4 of them and 10 counters in total. The probability to pick a non-white counter is now 6/10.

Thus, the option WN has the probability P(WN) = 5/11 x 6/10 = 30/110 = 3/11

Now for the second option NW. The initial probability to pick a non-white counter is 6/11.

The probability to pick a white counter is 5/10

Thus, the option NW has the probability P(WN) = 6/11 x 5/10 = 30/110 = 3/11

P(A) = 3/11 + 3/11 = 6/11.

SO THE ANSWER IS 6/11!!

If this helped you. Could I have a brainliest by any chance? And tell me if I am wrong! :D Bye now! :D And you are welcome.

Write an equation for the function g whose graph is the graph f(t) = -100(1.05)^t translated to the right 5 units and up 50 units.

Answers

g(t) = -100 * [tex](1.05)^t[/tex] +[tex](1.05)^(-5)[/tex] 50 is equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated to the right 5 units and up 50 units.

Starting with the function f(t) = -100[tex](1.05)^t[/tex], to translate it 5 units to the right and 50 units up, we can replace t with (t - 5) to shift it to the right, and add 50 to the whole function to shift it up. This gives us:

g(t) = f(t - 5) + 50

g(t) = -100[tex](1.05)^(t - 5)[/tex]+ 50

Simplifying this equation, we can use the properties of exponents to rewrite [tex](1.05)^(t - 5)[/tex] as [tex](1.05)^t[/tex] * [tex](1.05)^(-5)[/tex]:

g(t) = -100[tex](1.05)^t[/tex] *[tex](1.05)^(-5)[/tex]+ 50

g(t) = -100[tex](1.05)^(-5)[/tex] * [tex](1.05)^t[/tex] + 50

So the equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated 5 units to the right and 50 units up is:

g(t) = -100[tex](1.05)^(-5)[/tex]* [tex](1.05)^t[/tex]+ 50

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It takes Nancy 12/3 mins to read 1 page in her social studies book. It took her 221/2 mins to complete her reading assignment. How long was the assignment let n represent the number of pages she has read

Answers

Step-by-step explanation:

well, we need to see how often 12/3 minutes (for one page) fits into 221/2 minutes (for all pages) :

n = 221/2 / 12/3 = (221×3) / (12×2) = 221 / (4×2) = 221/8

the book had n = 221/8 pages = 27.625 ≈ 27 pages.

as parts of a page do not make sense, we only count full pages.

Exact value of sec 5pi/6

Answers

By trigonometric formula, the trigonometric function sec (5π / 6) has the exact value - 2√3 / 3.

How to determine the exact value of a trigonometric function

In this problem we find the case of a trigonometric function, whose exact value can be found by means of trigonometric formula and tables of values:

sec θ = 1 / cos θ

sec (5π / 6) = 1 / cos (5π / 6)

sec (5π / 6) = - 1 / cos (π / 6)

sec (5π / 6) = 1 / (- √3 / 2)

sec (5π / 6) = - 2 / √3

sec (5π / 6) = - 2√3 / 3

The exact value of the trigonometric function sec (5π / 6) is equal to - 2√3 / 3.

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by how much must the sample size n be increased if the width of the ci (7.5) is to be halved? if the sample size is increased by a factor of 25, what effect will this have on the width of the interval? justify your assertions.

Answers

The width of the interval will be reduced to 1.5 if the sample size is increased by a factor of 25.

To find how much the sample size n must be increased if the width of the confidence interval is to be halved, use the following formula:

W = (zα/2 x σ/√n)W/2 = (zα/2 x σ/√n')

Where W is the initial width of the confidence interval,

zα/2 is the critical value of the standard normal distribution that corresponds to the level of significance α and the appropriate two-tailed area,

σ is the population standard deviation,

n is the initial sample size, and

n' is the new sample size needed to halve the width of the interval.

Rearranging the second equation to solve for n', we get:

n' = n(4)

So the sample size needs to be increased by a factor of 4, or 300% if the width of the confidence interval is to be halved.

If the sample size is increased by a factor of 25, the effect it will have on the width of the interval can be found using the following formula:

W' = (zα/2*σ/√25n) = (zα/2*σ/5√n)

The width of the interval will be divided by 5, or reduced to one-fifth of its initial value.

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the radius of a circle is changing at .5 cm/sec. find the rate of change of the area when the radius is 4 cm.

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The rate of change of the area of a circle when the radius is 4 cm is 4π cm2/sec.

This can be calculated using the formula for the area of a circle (A = πr2) and the chain rule for derivatives. The chain rule states that when the radius (r) changes, the area of a circle (A) is equal to 2πr times the rate of change of the radius (dr/dt).

Therefore, the rate of change of the area of a circle when the radius is 4 cm is equal to 2π(4 cm) × (0.5 cm/sec) = 4π cm2/sec.

Note that if the rate of change of the radius were different, the rate of change of the area would also be different. This formula can be used to calculate the rate of change of the area of a circle at any given radius, as long as the rate of change of the radius is known.

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Solve the given equation for z and right the correct answer 4z + 9 = 29

Answers

4z+9=29 we would have to get rid of the 9 so we would have subtract 9 from both sides which would leave us with 4z=20 to get rid of the z we would have to divide 20 by 4z which the answer would be 5

Jada is training for a swimming race. The more she practices, the less time it takes for her to swim one lap. Name the independent and dependent variables.​

Answers

Answer:Independent = Her practice time. Dependent= Her lap time.

Step-by-step explanation: The more she practices the faster she can swim.

please help asap look at the screen shot to help

Answers

The mean class size at Mountain View School is 4.4 and at Seaside School is 4.2.

The median class size is 5 for both schools.

The range for Mountain View School is 12 and for Seaside School is 8.

The IQR for Mountain View School is 6 and for Seaside School is 3.

How do we solve this?

To find the measures of center, we can calculate the mean and median for both schools.

Mountain View School:

Mean = (2+1+0+5+8+6+9+8+2+0+1+0+6)/15

Mean = 4.4

Median = 5

Seaside School:

Mean = (0+1+2+5+6+8+8+7+6+5+5+4+4+3+1+0)/15

Mean = 4.2

Median = 5

Part B:

To find the measures of variability, we can calculate the range and interquartile range (IQR) for both schools.

Mountain View School:

Range = largest value - smallest value = 12 - 0

Range = 12

IQR = Q3 - Q1 = 8 - 2 = 6

Seaside School:

Range = largest value - smallest value = 8 - 0

Range = 8

IQR = Q3 - Q1 = 7 - 4 = 3

Part C:

If we are interested in a smaller class size, Seaside School would be the better choice. The median class size is the same at both schools, but Seaside School has a smaller mean, which suggests that on average, class sizes are smaller.

Additionally, the range and IQR are both smaller for Seaside School, indicating less variability in class size.

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If a regular polygon had 360 side, what would each exterior angle measure? What would each interior angle measure?

Answers

Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.

what is angle ?

In mathematics, an angle is a figure made up of two rays that share a shared endpoint and are referred to as the sides of the angle and the vertex of the angle, respectively. Angles are typically measured in degrees, radians, or other angle measurement units. Angles can be categorized based on how wide they are. An acute angle is one that is less than 90 degrees, an obtuse angle is one that is higher than 90 degrees but less than 180 degrees, and a right angle is one that is 90 degrees. A reflex angle is greater than 180 degrees but less than 360 degrees, and a straight angle is precisely 180 degrees.

given

Since a polygon with that many sides would have sides that are extremely tiny in relation to the radius, if a regular polygon has 360 sides, it is a circle. Since every group of points in a regular polygon has an equal exterior angle and the sum of all exterior angles in a circle is 360 degrees, each exterior angle in a regular polygon would be measured as follows:

360 edges / 360 degrees = one degree.

Each interior angle of a regular polygon with n sides can be determined using the following formula:

Inner angle is equal to (n-2) x 180 / n.

When we enter n = 360 into this algorithm, we obtain:

(360-2) x 180 degrees / 360 = 178 degrees is the interior angle.

Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.

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a study indicates that the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs. what is the probability that a randomly selected adult weights between 120 and 165 lbs?

Answers

The probability that a randomly selected adult weighs between 120 and 165 lbs is approximately 0.8186.

Since the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs, we can use the standard normal distribution to calculate the probability.

We first need to standardize the values using the formula: z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.

For x = 120 lbs, z = (120 - 140) / 25 = -0.8, and for x = 165 lbs, z = (165 - 140) / 25 = 1.0. We can then use a calculator to find the probability between -0.8 and 1.0, which is approximately 0.8186.

Thus, the chance of picking an adult at random who weighs between 120 and 165 lbs is roughly 0.8186.

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PLEASE HELP, DUE TODAY,

Which of the following tables represents a linear function?



x −4 −1 0 1 2

y −4 2 −4 0 2


x 1 1 1 1 1

y −3 −2 −1 0 1


x −6 −1 0 2 3

y −7 negative sixteen thirds −5 negative thirteen thirds −4


x −2 −1 0 2 4

y −4 negative two thirds −1 two thirds 1

Answers

The table that represents a linear function is table 2.

How to explain the linear function

A linear function is a function whose graph is a straight line, and the equation of such function has the form y = mx + b, where m is the slope of the line and b is the y-intercept. To determine which table represents a linear function, we can calculate the slope between any two points in the table, and see if the slope is the same for all pairs of points.

Table 1:

The slope between (0,-4) and (1,0) is (0 - (-4)) / (1 - 0) = 4/1 = 4.

The slope between (-1,2) and (0,-4) is (-4 - 2) / (0 - (-1)) = -6/1 = -6.

The slope between (1,0) and (2,2) is (2 - 0) / (2 - 1) = 2/1 = 2.

The slopes are not the same for all pairs of points, so this table does not represent a linear function.

Table 3:

The slope between (-1, negative sixteen thirds) and (0,-5) is (-5 - (-16/3)) / (0 - (-1)) = -1/3.

The slope between (0,-5) and (2,-13/3) is (-13/3 - (-5)) / (2 - 0) = -8/3.

The slopes are not the same for all pairs of points, so this table does not represent a linear function.

Table 4:

The slope between (-1,negative two thirds) and (0,-1) is (-1 - (-2/3)) / (0 - (-1)) = -1/3.

The slope between (0,-1) and (2,2/3) is (2/3 - (-1)) / (2 - 0) = 5/6.

The slopes are not the same for all pairs of points, so this table does not represent a linear function.

Therefore, the correct option is table 2.

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Doing missing work and I don’t remember how to do these

Answers

The value of x in ΔPQR is 12 and value of x and y are 17.5 and 19.2 respectively, with the scale factor 8 : 5.

What is scale factor?

Scale Factοr is used tο scale shapes in different dimensiοns. In geοmetry, we learn abοut different geοmetrical shapes which bοth in twο-dimensiοn and three-dimensiοn. The scale factοr is a measure fοr similar figures, whο lοοk the same but have different scales οr measures. Suppοse, twο circle lοοks similar but they cοuld have varying radii.

The scale factοr states the scale by which a figure is bigger οr smaller than the οriginal figure.  It is pοssible tο draw the enlarged shape οr reduced shape οf any οriginal shape with the help οf scale factοr.

4. The scale factor is in the ratio of 2:5

x = QR ≅ VS

x ≅ 30

Now, we have

2/5 = x/30

x = 2/5 × 30

x = 12

Thus, The value of x is 12 when scale factor is 2:5.

5. As ΔABC ≅ ΔAVW

WA = x ≅  CA

x ≅  28

And in the same way

y ≅  12

Now, Scale factor is

CB/VW

= 16/10

= 8/5

= 8 : 5

Now,

8/5 = 28/x

x = 28 × 5/8

x = 28 × 5/8

x = 35/2

x = 17.5

And for y

8/5 = y/12

8/5 × 12= y

y = 8/5 × 12

y = 96/5

y = 19.2

Thus, The value of x in ΔPQR is 12 and value of x and y are 17.5 and 19.2 respectively, with the scale factor 8 : 5.

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true or false (and state why): if a sample from a population is large, a histogram of the values in the sample will be approximately normal, even if the population is not normal.

Answers

By the central limit theorem, with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.

The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.

Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.

The complete question is-

true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.

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johnny makes an initial deposit into a bank account that earns compound interest annually. what's the initial deposit? whats the common ratio? whats the interest rate? how much money is there after 8 years? please help me and please be specific!! thank youuu

Answers

1. The initial deposit is $10,000 since John deposited this amount to open the savings account.

2. The common ratio can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt)

3. After 8 years, the amount will be $13,685.70 in the savings account.

How do we get how much money in account after 8 years?

The formula which will be used to calculated the compound interest is A = P(1 + r/n)^(nt). For this problem, the interest is compounded annually, so n = 1.

The annual interest rate is 4%, or 0.04 as a decimal. Plugging these values into the formula, we get:

A = $10,000*(1 + 0.04/1)^(1*8)

A = $10,000*(1.04)^8

A = $10,000*1.36857

A = $13,685.70

Therefore, after 8 years, there will be $13,685.70 in the savings account.

Full question "John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded interest. What's the initial deposit? whats the common ratio? whats the interest rate? how much money is there after 8 years?"

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john conducts emissions inspections on cars. he finds that 6% of cars fail inspection. let the random variable x be the number of cars that john inspects until a car fails an inspection. assume independence. the random variable x is:

Answers

The random variable x in this case is a binomial random variable, representing the number of cars that need to be inspected until a car fails an inspection. A binomial random variable is defined as the number of successes, “s”, in “n” independent trials. In this case, “s” would be 1 (the single failure) and “n” would be the number of cars that John inspects until a car fails inspection.

The probability of success, “p”, in this case is 0.06 since 6% of cars fail inspection. The probability of failure is “q”, which would be 0.94 in this case (1 - 0.06). The mean, “μ”, of the random variable x is equal to n * p, or the total number of trials times the probability of success. In this case, the mean would be equal to n * 0.06, or 6%.

The variance, “σ2”, of the random variable x is equal to n * p * q, or the total number of trials times the probability of success times the probability of failure. In this case, the variance would be equal to n * 0.06 * 0.94, or 5.64%.

The binomial random variable x can be used to calculate the expected number of inspections it will take John until a car fails an inspection, as well as the probability of a car failing an inspection. By knowing the probability of success, the number of trials, and the probability of failure, we can calculate the mean, variance, and expected value of the binomial random variable x.

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GIVING BRAINLIEST FOR THE CORRECT ANSWER (i need a proof that what you’re saying is right bc ppl are giving me the wrong answers)

Answers

Answer:

x [tex]\geq[/tex]2

Step-by-step explanation:

Since the arrow is pointing to the right, we know that it is greater than two. We also know that it could be equal to 2 because the dot is filled in on the number line. So, the answer is x is greater than or equal to 2.

Help explain how to solve

Answers

The value of the angle U in the triangle is 92.10 degrees.

How to find the angle in a triangle?

The angle U in the triangle can be found using cosine rule as follows:

Let's use cosine formula to find the angle U

c² = a² + b² - 2ab cos C

Hence,

Therefore,

a = 58.8

b = 38.4

c = 71.4

Hence,

71.4²  = 58.8² +  38.4² - 2(58.8)(38.4) cos U

5097.96 = 3457.44 + 1474.56 - 4515.84 cos U

5097.96 - 4932 =  - 4515.84 cos U

165.96 = - 4515.84 cos U

divide both sides by - 4515.84

cos U = 165.96 / - 4515.84

cos U = - 0.03675063775

U = cos⁻¹ - 0.03675063775

U = 92.1032274244

Therefore,

U = 92.10 degrees

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Find the surface area of the volume generated when the following curve revolves around the y-axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. (Round your answer to four decimal places.) y = x2 from x = 0 to x = 2 36.7

Answers

To find the surface area of the volume generated when the curve y = x^2 revolves around the y-axis from x = 0 to x = 2, we will use the surface area formula for revolution:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from x = 0 to x = 2.

First, find the derivative dy/dx:
y = x^2
dy/dx = 2x

Now, plug in the derivative and simplify the expression inside the integral:
sqrt(1 + (2x)^2) = sqrt(1 + 4x^2)

Now, set up the integral with the surface area formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + 4x^2)] dx from x = 0 to x = 2.

Next, we will approximate the integral using a calculator:
Approximate Integral ≈ 9.8433

Finally, multiply by 2 * pi:
Surface Area ≈ 2 * pi * 9.8433 ≈ 61.9362

So, the surface area of the volume generated when the curve revolves around the y-axis is approximately 61.9362 (rounded to four decimal places).

Figure ABCD is reflected across the x-axis.

What are the coordinates of A' , B' , C' , and D'

Answers

Answer: A'(-1,-4)B'(-5,-8)C'(-5,-4)D'(-4,-2)

Step-by-step explanation:

We have been given a graph of a quadrilateral and we are asked to find the coordinates of our quadrilateral after reflecting it across the x-axis.We can see that coordinates of quadrilateral ABCD are:A (-1,4),B (-5,8),C (-5,4),D (-4,2).

Since we know that rule for reflecting an image across x-axis is . This means that y-coordinates of our given image will be negative.So after reflecting our given quadrilateral across x-axis, coordinates will be:

A'(-1,-4)B'(-5,-8)C'(-5,-4)D'(-4,-2)

4
Mrs. Donley's math class has a total of 25 students. On Friday, the class was given an eight question quiz on fractions. The numbe
of incorrect answers given by the students is shown below.
Incorrect Answers Number of Students
What is the relative frequency of students that missed 1 question on the quiz?

Answers

Answer: To find the relative frequency of students that missed 1 question on the quiz, we need to first determine the total number of students who missed 1 question. From the table, we see that 9 students missed 1 question.

The relative frequency of students that missed 1 question can be calculated as:

Relative frequency = (Number of students who missed 1 question) / (Total number of students)

Relative frequency = 9 / 25

Relative frequency = 0.36

Therefore, the relative frequency of students that missed 1 question on the quiz is 0.36 or 36%.

Step-by-step explanation:

g in a study, the sample is chosen by separating all cars by size, and selecting 10 of each size grouping what is the sampling method?

Answers

The sampling method used in the study where the sample is chosen by separating all cars by size, and selecting 10 of each size grouping is known as stratified random sampling.

Stratified random sampling is a method of sampling that involves dividing the population into smaller sub-groups known as strata. In this method, each stratum is composed of elements that have similar characteristics.

The strata could be based on demographic characteristics such as age, sex, education, and so on. Once the strata have been created, the next step is to select a sample from each of the strata to make up the final sample. The selection is done randomly, and the number of elements selected from each stratum is proportional to the size of the stratum. This ensures that the sample is representative of the entire population in terms of the different characteristics of the population.

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consider the following table. what is the probability of red? red blue total yes 15 21 36 no 38 13 51 total 53 34 87 g

Answers

The probability of red is 0.1724, given the following table.

The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.

The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.

The probability of Red can be calculated using the formula;

P(Red) = (Frequency of Red) / (Total Frequency)

Using the values provided in the table

,P(Red) = 15/87P(Red) = 0.1724

Hence, the probability of red is 0.1724.

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help please i dont get this

Answers

● < P=R " angles opp =sides"

●PQ =QR " Angles opposite = sides"

therefore PQR is an isosceles " 2 opp angles and sides are equal "

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