In the scale drawing of the base of a rectanglar swimming pool, the pool is 8.5 inches long and 4.5 inches wide. If 1 inch on the scale drawing is equivalent to 4 meters of actual length, what are the actual length and width of the swimming pool

Answer : a ) Variance = (21 - 6.5)^2/12 = 13.7708, b) 1, 21 <= x, c) Probability = 0.5862, D) Probability = 0.8552

The uniform distribution on the interval (6.5, 21) can be represented as U(6.5, 21).
(a) The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b)/2
Variance = (b - a)^2/12
where a and b are the lower and upper bounds of the distribution, respectively.
For the given distribution, a = 6.5 and b = 21.
Therefore, the mean and variance of depth are:
Mean = (6.5 + 21)/2 = 13.75
Variance = (21 - 6.5)^2/12 = 13.7708

(b) The cdf of a uniform distribution can be calculated using the following formula:
F(x) = (x - a)/(b - a)
For the given distribution, F(x) = (x - 6.5)/(21 - 6.5) for 6.5 <= x < 21.
Therefore, the cdf of depth is:
F(x) = {
0, x < 6.5
(x - 6.5)/14.5, 6.5 <= x < 21
1, 21 <= x

(c) The probability that observed depth is at most 10 can be calculated using the cdf:
P(X <= 10) = F(10) = (10 - 6.5)/14.5 = 0.2414
The probability that observed depth is between 10 and 15 can be calculated using the cdf:
P(10 <= X <= 15) = F(15) - F(10) = (15 - 6.5)/14.5 - (10 - 6.5)/14.5 = 0.5862

(d) The standard deviation of a uniform distribution can be calculated using the following formula:
Standard deviation = sqrt(Variance)

For the given distribution, the standard deviation is:
Standard deviation = sqrt(13.7708) = 3.7118
The probability that the observed depth is within 1 standard deviation of the mean value can be calculated using the cdf:
P(13.75 - 3.7118 <= X <= 13.75 + 3.7118) = F(13.75 + 3.7118) - F(13.75 - 3.7118) = (13.75 + 3.7118 - 6.5)/14.5 - (13.75 - 3.7118 - 6.5)/14.5 = 0.5118
The probability that the observed depth is within 2 standard deviations of the mean value can be calculated using the cdf:
P(13.75 - 2*3.7118 <= X <= 13.75 + 2*3.7118) = F(13.75 + 2*3.7118) - F(13.75 - 2*3.7118) = (13.75 + 2*3.7118 - 6.5)/14.5 - (13.75 - 2*3.7118 - 6.5)/14.5 = 0.8552

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Therefore, DM = 0, which means that the plane is directly above point D. Pythagorean theorem The vertical distance from the plane to point D is simply the altitude of the plane.

The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides.

drawing a diagram

  A ------ 3 miles ------ D ----- x miles ------ C

  |                                               |

  |                                               |

  6 miles                                         6 miles

  |                                               |

  |                                               |

  B -----------------------------------------------

[tex]AC^2 = AD^2 + DC^2\\BC^2 = BD^2 + DC^2\\AD^2 + DC^2 = BD^2 + DC^2\\AD^2 = BD^2[/tex]

So, the plane must be directly above the midpoint of AB. Let's call this point M:

  A ------ 3 miles ------ D ----- x miles ------ C

  |                                               |

  |                                               |

  6 miles                           3 miles        6 miles

  |                                               |

  |                                               |

  B -----------------------------------------------

                     |

                     |

                     M

Now, let's use Pythagoras' theorem again to find the distance from the plane to point D:

[tex]DM^2 = AD^2 - AM^2\\DM^2 = AD^2 - 3^2\\DM^2 = 3^2 - 3^2\\DM^2 = 0[/tex]

Therefore, DM = 0, which means that the plane is directly above point D. The vertical distance from the plane to point D is simply the altitude of the plane.

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In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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The area of the circle which contains the 45° sector as required to be determined is; 345.4 cm².

As evident from the task content; A 45° sector in a circle has an area of 13.75π cm².

Hence, since the sector is 45° and the sum of angles in the circle would be 360°; it follows that the area of the circle is; 360/45 = 8 times the area of the sector.

Area of circle = 8 × 13.75π

= 8 × 13.75 × 3.14

= 345.4 cm².

Ultimately, the area of the circle is; 345.4 cm².

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The length of the silver rod when heated to 500°C is approximately 48.47 cm.

To solve this problem, we can use the formula:

L₂ = L₁ (1 + αΔT)

where L₁ is the original length of the rod at temperature T₁, L₂ is the new length of the rod at temperature T₂, α is the coefficient of linear expansion of the material, and ΔT = T₂ - T₁ is the change in temperature.

We are given that the original length of the silver rod is L₁ = 48 cm at temperature T₁ = 13°C. The coefficient of linear expansion for silver is α = 2x10^(-5) °C^(-1). The change in temperature is ΔT = 500°C - 13°C = 487°C.

Substituting these values into the formula, we get:

L₂ = 48 cm (1 + 2x10^(-5) °C^(-1) x 487°C)

= 48 cm (1 + 0.00974)

= 48 cm (1.00974)

= 48.47 cm

Therefore, the length of the silver rod is approximately 48.47 cm.

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_____The given question is incorrect, the correct question is given below:

A silver rod measures 48 cm at 13°C. What is its length when heated to 500°C? (α=2x10^(-5) °C^(-1)).

Answer:

-180

Step-by-step explanation:

The measure of the angle on the attached figure is

There are two ways to measuring it

1. Counterclockwise: In this the sign is positive

So,

We can write

180°,

180°+360° = 540°,

180° + 2(360°) =180°+720° =900°,

2. Clockwise: In this, the sign is negative

So,

We can write

-180°,

-180° - 360° = -540°,

-180° - 2(360°) = -180° - 720° = -900°

the correct option is A.

The probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.

Drawing cards from a standard deck of 52 cards is a random process, and the probability of getting 2 kings out of 25 cards depends on the total number of possible outcomes.

There are 4 kings in a deck of 52 cards,

So, The probability of drawing a king on the first draw = 4/52.

Since the deck is not replaced,

The probability of drawing another king on the second draw = 3/51.

Therefore,

The probability of getting 2 kings out of 25 cards can be calculated by combining these two probabilities.
The probability of drawing 2 kings = [tex](4/52) * (3/51) * (25C2)[/tex]

Where,

25C2 = The number of ways to select 2 cards out of 25.

After calculating this expression, the probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.

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The percentage of of the shaded region is 74.8%

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The enclosed body of a circle is called the circumference.

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in squared units.

The area of a circle is expressed as :

πr²

The area of the shaded part = area of big circle - area of small circle

= 3.14(8.01²-4.02²)

= 3.14(64.16-16.16)

= 3.14( 48)

= 150.72in²

area of the big circle = 3.14 × 64.16 = 201.46

therefore the percentage of the shaded region of the point = 150.72/201.46 × 100

= 74.8% ( nearest tenth)

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An equation that represents this situation include the following: D. y = -2x + 9.50.

In order to write a linear equation to describe this situation, we would assign variables to the cost of the drinks and the cost of the popcorn respectively, and then translate the word problem into a linear equation as follows:

Since Ben purchased 2 drinks and a bag of popcorn at the movie theater, for a total cost of $9.50, a linear equation that models the situation is given by this mathematical expression:

2x + y = 9.50

By making y the subject of formula, we have:

y = -2x + 9.50

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It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

Calculating the time required to fill the bucket:

To solve this problem, use the concept of proportionality to calculate the time required. Use the concept of percentage increase to find the volume of the larger bucket, which was 67% larger than the 3-gallon bucket.

Here we have

A hose fills a 3-gallon bucket in 9 seconds.

The volume of the bucket which is 167% more than 3 gallons

= 167% of 3 gallons = [167/100] × 3 = 5.01 gallons

It took 9 seconds to fill 3 gallons

The time required to fill 5.01 gallons = 9/3 × [5.01]

= 15.03 seconds

Therefore,

It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

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Based on the information provided in the question, The expected value of the sample mean is approximately 497.92 million dollars.

To calculate the expected value of the sample mean, first calculate the mean of the population ($10.82 million) and then multiply it by the sample size (46).
Mean of Population * Sample Size = Expected Value of Sample Mean
$10.82 million * 46 = $497.92 million
Expected Value of Sample Mean = $497.92 million

A sample mean is a statistical measurement that shows the mean value of the data in a sample. It is determined by summing all of the values in the sample and dividing the total by the number of observations.

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In the given functions  [tex]5^x[/tex] function is increasing because 5>1.

Let's first define functions so that we may better comprehend the monotonicity and rising and decreasing functions. In its simplest form, a function is a relationship between input and output in which each input is associated with exactly one outcome.

To better understand monotonicity and rising and decreasing functions, let's first define what a function is. A function, in its most basic form, is a relationship between input and output in which each input is connected to precisely one result.

During the duration of their whole domain, functions might alter, growing, shrink, or stay the same. Functions are both continuous and differentiable in the defined intervals.

Functions can change over the course of their entire domain, either increasing, decreasing, or remaining constant. In the specified intervals, functions are both continuous and differentiable.

We have all the functions that are exponential

So when we shall check all the given function

We observe that we have functions of the form:

f (x) = A[tex]b^x[/tex]

When

b > 1 The function grows

b <1 Function decreases

Hence [tex]5^x[/tex] function is increasing.

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The amount more that Alex earn per hour more than Sam is $2.

A linear equation is an equation that has a single variable that is raised to the power of one. The general form of a linear equation is

y = mx + c

Where:

The linear equation that represents the amount that Alex earns is y = 20x. This means that for every hour worked, Alex earns $20. Looking at the table, Sam earns $18 for every hour worked. This can be represented with the equation : y = 18x

The difference in the amount earned = 20 - 18 = $2

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According to proportionality, the virus will spread at a rate of 12475 students per day.

If five college students with the flu return to an isolated campus of 2500 students, and the rate at which the virus spreads is proportional to both the number of students infected and the number of students not infected, then we can use the following formula to find the rate of spread:

Rate of spread = (number of students infected) x (number of students not infected)

In this case, the number of students infected is 5 and the number of students not infected is 2500 - 5 = 2495. So, the rate of spread is:

Rate of spread = 5 x 2495 = 12475

This means that the virus will spread at a rate of 12475 students per day, assuming that the rate of spread is proportional to both the number of students infected and the number of students not infected.

It is important to note that this is a simplified model and does not take into account other factors that may affect the rate of spread, such as the effectiveness of quarantine measures or the individual immune systems of the students. However, it does give us an idea of how quickly the flu can spread in a population of 2500 students.

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The fixed charge for a taxi ride is Rs. 5 and the charge per km is Rs. 7.

Given that the charge for a 12 km ride is Rs. 89 and for a 20 km ride is Rs. 145, we can form two equations in terms of the fixed charge (c) and the charge per km (x).

Solving these equations, we get c = 5 and x = 7. Therefore, the fixed charge for a taxi ride is Rs. 5 and the charge per km is Rs. 7. To find the charge for a 30 km ride, we can substitute these values in the formula

c + 7x, which gives us 5 + 7x30 = Rs. 215.

89 = c + 12x ---------------(1)

145 = c + 20x -------------(2)

Solving equations 1 and 2, we get,

8x = 56

x = 7.

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Complete Question:

The car hire charges in a city comprised of a fixed charge together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs 89 and for a journey of 20 km, the charge paid is Rs 145. What will a person have to pay for traveling a distance of 30 km?

sale price=$30

discount price=0.05

Taking it $30*0.05=600$

after applying 0.08

600*0.08=48$

, so 48$ is the final price of the wind chime.

The force exerted by the brick on the window is equal in magnitude but

opposite in direction to the force exerted by the window on the brick.

When a brick hits a window and smashes it, there are two forces

involved: the force exerted by the brick on the window and the force

exerted by the window on the brick.

According to Newton's third law of motion, for every action, there is an

equal and opposite reaction.

The magnitude of the forces involved depends on several factors,

including the mass of the brick, its velocity, the angle of incidence, and

the strength of the window. The force exerted by the brick on the

window will be the impact force, which is the force applied over a short

period of time during the collision.

The impact force will depend on the momentum of the brick, which is

the product of its mass and velocity.

It's not possible to say which force is larger because the two forces are

equal in magnitude but opposite in direction, according to Newton's third

law of motion.

The strength of the window will also play a role, as a stronger window

will be able to resist a higher impact force before breaking.

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Answer:

To rewrite a mixed number as an improper fraction, you need to multiply the whole number by the denominator of the fraction, then add the numerator. The resulting sum is the numerator of the improper fraction, while the denominator remains the same.

For example, to rewrite the mixed number 3 1/2 as an improper fraction, you would:

Multiply the whole number 3 by the denominator 2: 3 x 2 = 6

Add the numerator 1 to the product: 6 + 1 = 7

Write the sum 7 as the numerator of the improper fraction, with the denominator 2: 7/2

So, the improper fraction equivalent of the mixed number 3 1/2 is 7/2.

Step-by-step explanation:

The z-values of the sampling distributions are;

A sampling distribution is a probability distribution obtained through the repeated sampling of a specified population.

The z-value for a sampling distribution can be obtained using the formula;

[tex]z = \frac{\bar{x} -\mu}{\frac{\sigma}{\sqrt{N} } }[/tex]

Where;

[tex]\bar{x}[/tex] = The sample mean

μ = The population mean = 156

σ = The population standard deviation = 23

N = The sample size

The z-values for the sampling distributions are therefore;

1) The number of observations selected from the population, is 76, and the sample mean is; [tex]\bar{x}[/tex] = 162, we get the following z-value.

When, N = 76 and [tex]\bar{x}[/tex] = 162

2) The selected observations is 92, and the sample mean is; [tex]\bar{x}[/tex] = 151, we get the following z-value.

When, N = 92 and [tex]\bar{x}[/tex] = 151

3) The number in the random sample, N = 102 and the sample mean is; [tex]\bar{x}[/tex] = 151, we get;

When, N = 102 and [tex]\bar{x}[/tex] = 151

4) The number of observations in the random sample, N = 120 and the sample mean is; [tex]\bar{x}[/tex] = 149, we get;

When, N = 120 and [tex]\bar{x}[/tex] = 149

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Answer:

plot it on -4

Step-by-step explanation:

Answer: -3

Step-by-step explanation:

The approximate change in cost corresponding to an increase in sales of one unit is 8.50. and actual change in cost is 8.25.

To answer this question, we need to use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. To do this, we need to calculate the derivative of the given cost function C = 0.075x^2 + 6x + 7.

The derivative of this function is dC/dx = 0.15x + 6. We can now use this derivative to approximate the change in cost when x is increased by one unit. This is given by dC/dx = 0.15(10) + 6 = 8.5.

To compare this with the actual change in cost, we can calculate the change in cost when x is increased from 10 to 11. This is given by C(11) - C(10) = (0.075x^2 + 6x + 7) | 11 - (0.075x^2 + 6x + 7) | 10 = 0.075(121) + 66 + 7 - 0.075(100) - 60 - 7 = 8.25.

Therefore, the approximate change in cost when x is increased by one unit (calculated by differentials) is 8.50 and the actual change in cost is 8.25. This shows that the approximate change in cost calculated by differentials is an accurate estimation of the actual change in cost.

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Austin needs to cover 15 square inches of surface area with paint in order to finish the task.

The area of the pennant is the length times the width, which is 3 inches times 5 inches. This gives us 15 square inches of surface area to be covered. To calculate the amount of paint needed, we first need to calculate the area of the pennant. The formula for area is area = length x width. Plugging in the measurements for the base and height of the pennant, we get 15 square inches of surface area. This means that Austin needs to cover 15 square inches of surface area with paint in order to finish the task.

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By speed fοrmula, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

We can use the fοrmula:

time = distance/speed

where distance is the distance frοm the star tο Earth, and speed is the speed οf light.

Putting the values, we get:

time = (3.9 x 10¹⁴ km) / (3.0 x 10⁵km/s)

Simplifying, we can divide the distances and divide the pοwers οf ten:

time = 1.3 x 10⁹ s

Therefοre, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

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Therefore , the solution of the given problem of probability comes out to be -y^(β-1)/[(β-1)Β(1, β)] .

The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.

Here,

We are aware that X's PDF is provided by:

If x is between 0 and 1 and 0 otherwise, f(x) Equals 1/B

where represents the size factor.

The formula for Yn's cumulative distribution function (CDF) is

=> F(y) = P(Yn ≤ y) = [P(Xi > y)]ⁿ = [1 - P(Xi ≤ y)]ⁿ

Using the CDF of the beta distribution, we have:

=> F(y) = [1 - Β(1, β; y)]ⁿ

We can approximate Yn by a normal distribution with mean and variance given by the following formulas using the continuity adjustment and central limit theorem:

=> E(Yn) = Β(2, β; 1)/Β(1, β) and Var(Yn) = E(Yn) - [Β(1, β; 1)/Β(1, β)]²

Therefore, we have:

=> (Yn - E(Yn))/sqrt(Var(Yn)) → N(0,1)

With the formulas for E(Yn) and Var(Yn) substituted, we obtain:

=> (Yn - Β(2, β; 1)/Β(1, β))/sqrt[Β(2, β; 1)/Β(1, β) - [Β(1, β; 1)/Β(1, β)]²] → N(0,1)

We need to work out the solution to determine b:

where is the CDF's usual standard value.

After applying the limit and taking the logarithm of both sides, we obtain:

=> F(y) = lim n log[n] = lim n n log

=> [1 - B(1, β; y)] = lim n -n (y, n)/(1, n)

L'Hopital's law gives us:

=> lim n -d/dy [n -(1, y)/n -(1, y)] = lim nn y(-1), ((1, )) ^2Β(2, β; y)

=> -y^(β-1)/[(β-1)Β(1, β)]

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Answer:

2.50 p + 1.50p

Step-by-step explanation:

if you buy an item x amount of times you would times the two to figure out the total cost of that type of item then add with the other

Answer: go look on yt there’s a good video on this one

Step-by-step explanation:

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\stackrel{ y-intercept }{(\stackrel{x_1}{0}~,~\stackrel{y_1}{4})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{12}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 8 }{ 4 } \implies 2[/tex]

Answer:

y = 2/3x + 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know

m = 2/3

Y-intercept is located at (0, 6)

So, our equation is y = 2/3x + 6

Option #1: point-slope form: y - y1 = m ( x - x1 )

y - 4 = 2/3 ( x - (-3) )     or     y - 4 = 2/3 ( x + 3 )

Option #2: slope-intercept form: y = mx + b

Take the point-slope and solve for y:

     y - 4 = 2/3 ( x + 3 )

     y - 4 = 2/3 x + 2

          y = 2/3 x + 6  

The percent of carbon remaining after 30642 years if, the half-life of carbon is 5730 years would be 3.1%

Total time is given: 30642 years

Half-Life of carbon-14 : 5730 years

After 1 half-life of the carbon-14 remaining carbon: 1/2

After 2 half-lives the carbon-14 remaining carbon : 1/4

After 3 half-lives the carbon-14 remaining carbon : 1/8

...

...

After n half-lives the carbon-14 remaining carbon : (1/2)^n

Number of half-lives in 30642 years: 30642 / 5730 ≈ 5 approx.

Amount of carbon remaining after 5 half-lives: 1/32

1/32 ≈ 0.031 = 3.1%

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Answer:

Step-by-step explanation:

[tex]a[/tex] is the amount earned on the first day.

She earnt $[tex]$a[/tex] dollar on day 1, $55.50 on day 2, and $65.50 total in the 2 days.

So we get

                  [tex]a+55.50=65.50[/tex]