One of the brightest stars in the sky is Sirius ​, which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. How​ far, in​ miles, is Sirius ​?

At a standard deviation of $15,000, the probability that the condominium will sell at a price below $200,000 is 0.2525 and above $240,000 is 0.02. At a standard deviation of $20,000, the probability that the condominium will sell at a price below $200,000 is 0.3085 and above $240,000 is 0.0668.

From the given question;

Let the average sale price(μ)=210,000

Standard Deviation(σ)=$15,000

(a) We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/15,000

Z= −10,000/15000

Z= −0.67

Now finding P(x<200,000) is same as finding P(Z<−0.67) using the standard table of z.

P(Z<−0.67) = 0.2525

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/15,000

Z= 30,000/15000

Z= 2

Now finding P(x>240,000) is same as finding P(Z>2) using the standard table of z.

P(Z>240,000)=P(Z>2)

P(Z>240,000)=1−P(Z<2)

P(z>240,000)=1−0.98

P(z>240,000)=0.02

(b) Now the average sale price(μ)=210,000

Standard Deviation(σ)=$20,000

We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/20,000

Z= −10,000/20000

Z= −0.5

Now finding P(x<200,000) is same as finding P(Z<−0.5) using the standard table of z.

P(Z<−0.5) = 0.2085

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/20,000

Z= 30,000/20000

Z= 1.5

Now finding P(x>240,000) is same as finding P(Z>1.5) using the standard table of z.

P(Z>240,000)=P(Z>1.5)

P(Z>240,000)=1−P(Z<1.5)

P(z>240,000)=1−0.93319

P(z>240,000)=0.0668

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The median will be greater than 10 and less than 15.

Given,

The mean of the skewed distribution = 15

The mode of the skewed distribution = 10

We have to find the potential range of the median for a positively skewed distribution;

Here,

The empirical relationship between mean, median, and mode for a frequency distribution that is positively skewed is mean > median > mode. Based on this, the range of the median is 15 > median > 10 if the mean is 15 and the mode is 10.

Therefore,

The median will  be higher than 10 and lower than 15.

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The problem is based on laws of exponents and answer to this Question is a = 2 and b = 14

What are laws of exponents?

Laws which are used to solve the problems including the exponents are called laws of exponents

Solution:

As we can clearly see in whole expression 2 is present in every term

By laws of Exponents we can take 2 common out and we can easily express this thing in given form that a multiplied 2 rays to power b

When we solve this expression we get

this expression equal to 2^15

which we can write 2×2^14

hence on comparing we get a = 2 and b = 14

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Answer:

7

Step-by-step explanation:

649-531=118

We know that there are 118 more guests per hour.

Divide 826 by 118 to get 7.

Answer: 7

Step-by-step explanation:

The first line of the table is 2 and 236 if you divide 236 by 2 you get 118

Then after that you times it by any number after 5.5 until you get 826.

Answer:

(-2,-4)

Step-by-step explanation:

3x+2=-2x-8

+2x.    +2x

5x+2=-8

   -2. -2

5x=-10

/5.  /5

x= -2

y=3(-2)+2

y=-6+2

y= -4

(-2,-4)

Hopes this helps please mark brainliest

Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B

A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.

On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.

From the graph the actual heart rate=150

but calculated heart rate from best fit line=148

Difference between actual and calculated=150−148=2

Option B is correct.

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Consta8of proportionality is 1/9

Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good

Step-by-step explanation:

7(x-1)=3x+2

Distribute through the parentheses

7x-7=3x+2

Move the variable to the left-hand side and change its sign

7x-7-3x=2

or Move the constant to the right-hand side and change its sign

7x-7-3x=2

Collect like terms

4x=2+7

And then Add the numbers

4x=9

Divide both sides of the equation by 4

x=9/4

Mixed number is 2 1/4

The expression 5(x + 7) has a sum of two terms 5x and 35.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, an expression 5(x + 7).

Now distributing 5 to x and 7 we get 5x + 35.

So, The expression 5(x + 7) has the sum of two terms.

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Answer:

hi do you mind making the question a bit clear? where is the table?

Step-by-step explanation:

Answer:

x=mp-n

Step-by-step explanation:

Switch sides:

(n+x)/p=m

Then multiply both sides by p:

n+x=mp

Move n to the other side:

x=mp-n

The proper way that you can prove that the square of an odd number is always one more than a multiple of eight is by using an example.

An example is a term that refers to a tool that is intended to explain, illustrate, or prove a general statement. When we want to explain a procedure we can give an example (that we have previously chosen) to seek to clarify the understanding of a phenomenon or process.

To prove that the square of an odd number is always a multiple of eight, the first step is to find the square of any odd number. Subsequently, we must subtract 1 from the result. Finally we must divide the previous result by 8 and it must give us an exact number (not a decimal).

3 * 3 = 9

9 - 1 = 8

8 / 8 = 1

123 * 123 = 15,129

15,129 - 1 = 15,128
15,128 / 8 = 1,891

9 * 9 = 81

81 - 1 = 80

80 / 8 = 10

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The propagated error in the measurement of the side of the cube is 0.001.

We know that,

the volume of a cube is dependent on the length of the edge, s, which is given by the equation,

V = [tex]s^{3}[/tex].

With this we determine that the given cube has an edge of 27 = [tex]s^{3}[/tex]

⇒ s = 3 inches.

Now we can acquire the differential of the equation for the volume of the cube with the following equations.

V = [tex]s^{3}[/tex]

dV = d([tex]s^{3}[/tex])

dV = 3[tex]s^{2}[/tex] ds

We have given that volume of the cube is 0.027.

That is dV = 0.027 and s = 3

we simply plug in the given and then solve for ds to determine the error in the measurement of the edge of the cube.

dV = 3[tex]s^{2}[/tex] ds

0.027 = 3(3)²ds

0.027 = 27ds

0.001 = ds

Therefore, there is an error in measurement of the edge of the cube up to 0.001 inches.

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The quadratic function which models the motion of the penny is

h(t) = -4.9t² -0.327761 t + 52.6  

and the maximum height reached is 57.43

h(t) = - 0.5gt² + vt + h

g = 9.8 m/s²

h = 52.6 m

v = ?

For v,

h(t) = -0.5gt² + vt + 52.6

h(t) = - 4.9t² + vt + 52.6

Time when penny hits the ground ; t = 3.31

h(3.31) = 0

0 = -4.9(3.31)² + v(3.31) + 52.6

0 = -53.68489 + 3.31v +52.6

3.31v = -1.08489

v = -1.08489/3.31

v = -0.327761 m/s

Therefore,

h(t) = -4.9t² -0.327761 t + 52.6

2.) Maximum height of the penny above the ground

t = 0.85 seconds

h(0.85) = -4.9(0.85^2)-0.327761 (0.85) + 52.6

Maximum height reached =  57.43 meters

Therefore, the maximum height reached is 57.43 meters.

An object changing its position with regard to time is referred to as motion. Motion is mathematically characterised in terms of displacement, distance, velocity, acceleration, and speed as well as the observer's frame of reference and the measurement of the change in the body's position with respect to that frame over time. Kinematics is the area of physics that studies how motion is affected by forces, whereas dynamics is the area that studies how motion is affected by forces.

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The relations which are functions as required to be identified in the task content are;

It follows from the task content that the relations which are functions among the given answer choices are to be identified.

Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.

Put simply, a function has only one output value for each input value.

Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.

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The expression that can be use to represent the amount owned on rental is 0.1x + 25y

Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven.

The expression that can be use to represent the amount owned on rental can be represented as follows:

let

x = number of miles driven

y = number of days

Let's convert cent to dollars

100 cents  = 1 dollars

10 cents = ?

cross multiply

amount in dollars = 10 / 100 = 0.1 dollars

Therefore,

the expression = 0.1x + 25y

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Answer:

Domain: {9, 13, 21}

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-------------------------------

Find y:

Number of kids ticket is 40

What do you mean by system of linear equation?

A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.

Total number of tickets = 60

Cost of 1 kid ticket = $3

Cost of 1 adult ticket = $5

Total profit = $220

Let number of kid tickets = x

number of adult tickets = y

According to question:

x + y = 60 ......(1)

3x + 5y = 220 ........(2)

Substitute the value of x from eq(1) to eq(2)

3(60 - y) + 5y = 220

180 - 3y + 5y = 220

180 + 2y = 220

2y = 220 - 180

2y = 40

y = 40/2

y = 20

Substitute this value of y in eq(1)

x + 20 = 60

x = 60 - 20

x = 40

Therefore, number of kids ticket is 40

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Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:

y = f(0) = 1.

Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:

y = g(0) = -1.

From the information provided above, we have the following function:

g(x) = f(x) + k

g(0) = f(0) + k

Making k the subject of formula, we have:

k = g(0) - f(0)

k = -1 - 1

k = -2.

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Work Shown:

[tex](x_1,y_1) = (-5,-3) \text{ and } (x_2,y_2) = (8,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{8 - (-5)}\\\\m = \frac{-1 + 3}{8 + 5}\\\\m = \boldsymbol{\frac{2}{13}}\\\\[/tex]

A slope of 2/13 means we go up 2 units and to the right 13 units. If starting at (-5,-3) and following this movement pattern of "up 2, right 13", then we arrive at (8,-1).

The sampling technique used in the given scenario is Systematic sampling technique.

Systematic sampling technique

Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.

Types of Systematic sampling technique

A systematic sample can be generated in three ways:

Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.

Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.

Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.

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The speedup of a parallel algorithm will eventually reach some limit.

What is parallel algorithm?

An algorithm is a set of instructions that takes input from the user and, after doing some calculations, generates an output. A parallel algorithm is one that can carry out multiple operations simultaneously on various processing units and then combines all of the separate outputs to get the desired outcome.

An algorithm that can execute several instructions concurrently on various processing devices and then aggregate all of the individual outputs to produce the final result is known as a parallel algorithm.

Because a parallel algorithm's speedup is never equal to the number of processors, it ultimately reaches a limit beyond which it can no longer be accelerated. At that point, the algorithm will no longer be accelerated and the speedup will stop.

Hence, the speedup of a parallel algorithm will eventually reach some limit.

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Answer:

attached in the file

Answer:

Step-by-step explanation:

Answer= use 2 eggs per 1 cup of flour to make 1 serving.

Using polar coordinates, the result for integral is - 0.448[tex]\pi[/tex]

What is polar co-ordinates?

In arithmetic, the polar coordinate system may be a two-dimensional organization within which every purpose on a plane is set by a distance from a indicator and an angle from a reference direction.

Main body:

The most used relation for polar coordinates is:

[tex]x^{2} +y ^{2} =r^{2}[/tex]

An integral in Cartesian coordinates is converted to polar using:

[tex]\int\int{f(x,y)} \, dA = \int\int{ f(r, \beta )d\beta[/tex]

In this problem:

f(x,y) = sin [tex]x^{2} +y^{2}[/tex]

thus

f(r,[tex]\beta[/tex]) = sin[tex]r^{2}[/tex]

Region between the circles with center at the origin and radii 1 and 3, thus the inner limits of integration are r =1  and r =3.

First quadrant, thus, the outer limits of integration are: [tex]\beta[/tex] = 0,[tex]\beta[/tex] = [tex]\pi /2[/tex].

The polar integral is:

I = [tex]\int\limits^3_1 {sinr^{2} r} \, dr[/tex]

Using substitution:

u =[tex]r^{2}[/tex] ⇒ du = 2rdr⇒ dr = du /2

I = 1/2[tex]\int\ {sin u} \, du[/tex]

 = -[tex]cos r^{2[/tex] /2     where limits are 3, 1

Applying the fundamental theorem of calculus:

I = [tex]-cos 5^{2} /2[/tex][tex]-cos1^{2}/2[/tex]

I = - 0.996

Then, the outer integral is:

O =[tex]\int\limits^\pi _0 {-0.996} \, d\beta[/tex]

O=  - 0.448[tex]\pi[/tex]

Hence the result for integral is - 0.448[tex]\pi[/tex]

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The angles in the intersected lines are as follows:

When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.

Angle a is vertically opposite to angle b.

Vertically opposite angles are congruent.

Therefore,

∠a ≅ ∠b

Hence,

x + 8 = 100(vertically opposite angles)

x = 100 - 8

x = 92

b + x + 8 = 180(sum of angles on a straight line)

b + 92 + 8 = 180

b = 180 - 100

b = 80 degrees.

Hence,

a = 80 degrees

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The minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738

A company's unit cost is the cost of producing, storing, and selling one unit of a specific product. Unit costs encompass all fixed and variable production costs. A cost unit is a quantity measuring unit for a product or service.

A unit cost is the overall cost incurred by a business to manufacture, store, and sell one unit of a specific product or service. Unit costs are the same as cost of goods sold (COGS). This accounting metric incorporates all fixed and variable expenses related with the manufacture of a good or service.

Given,

C(x)=1.2x²-600x+82,738

Minimum value [tex]C_{min}[/tex]=c-(b²/4a)

Where a=1.2, b=-600, c=82738

[tex]C(x)_{min}[/tex]=82738-((-600)²/4(1.2))

=82738-(360000/4.8)

=7738

Therefore, the minimum unit cost is 7738.

Hence, the minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738

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The response variable in this study is

Yield of crop.

"Information available from the question"

In the question:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil.

Now, According to the question:

Let's know:

What is called fertilizer?

A fertiliser is a natural or artificial substance containing chemical elements (such as Nitrogen (N), Phosphorus (P) and Potassium (K)) that improve growth and productiveness of plants. Some synonyms include the terms "enrichment" or "plant nutrient".

The answer is:

Yield of crop.

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The complete question is this:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is