As Mercury revolves around the sun, it travels at a speed of approximately 30 miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will Mercury travel in 15 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.

The entry to record this payment when the company’s estimated taxes for the first quarter total $50,000 will be:

Debit Income taxes payable $50000

Credit Cash $50000.

A journal is a book in which all of a company's transactions are recorded for the first time. Journaling is the process of recording transactions in a journal. Every transaction has two effects: one is debited and the other is credited.

The act of keeping or making records of any transaction, economic or non-economic, is referred to as journal entry. An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry may include multiple recordings, each of which is either a debit or a credit. A journal entry's purpose is to physically or digitally record every business transaction properly and accurately.

The journal entry based on the information is illustrated.

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Answer:

C) y=1/2x-2

Step-by-step explanation:

In the graph we have to identify the slope and y-intercept.

Y-intercept = -2 (In the graph it goes down two units)

To find the slope I identified the next nearest point, which was (2,-1).

From my y-intercept, -2, I had to go up one unit and two units to the right.

That makes my slope = 1/2

You need to remember slope intercept form is: y=mx+b

When plugging in the numbers you get:

y=1/2x-2

The equation of the verticallly-oriented ellipse is x²/4 + y²/25 = 1

The equation of a vertically-oriented ellipse centered at the origin with major axis y axis is given by

x²/b² + y²/a² = 1 where a > b

Given that the vertically-oriented ellipse centered at (0,0) with a full major y-axis length of 10 units and a full minor x-axis length of 4 units.

We have that the length of major axis 2a = 10

⇒ a = 10/2

⇒ a = 5

Also, the length of minor axis 2b = 4

⇒ a = 4/2

⇒ a = 2

So, given the equation of the vertically-oriented ellipse,

x²/b² + y²/a² = 1 where a > b

Substituting the values of the variables into the equation, we have that

x²/b² + y²/a² = 1 where a > b

x²/2² + y²/5² = 1

x²/4 + y²/25 = 1

So, the equation is x²/4 + y²/25 = 1

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Benjamin's walk described as a composition of two translations is (8, 0) and (2, 3) respectively.

The translation walks from his house directly to school is (10, 3)

A translation is a type of transformation that moves every point in a figure by a fixed distance in a certain direction. This can be thought of as sliding the figure along a straight line.

Looking at the image:

The coordinate of  Benjamin's house is (5,4) and he walks to Timothy's house (13, 4) and then to school (15, 7)

The displacement vector from Benjamin's house to Timothy's house is (13, 4) - (5, 4) = (8, 0), which represents an 8 unit move to the right.

The displacement vector from Timothy's house to school is (15, 7) - (13, 4) = (2, 3), which represents a 2 unit move to the right and a 3 unit move up.

Thus, Benjamin's walk can be described as a composition of two translations can be represented using displacement vectors as (8, 0) and (2, 3) respectively.

If Benjamin walks from his house directly to school:

The displacement vector from Benjamin's house directly to Timothy's house is (15, 7) - (5, 4) = (10, 3), which represents 10 units move to the right and 3 units up.

Thus, the translation describes his walk is (10, 3)

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By solving a linear equation, it can be calculated that the value of 3x - 4 is 8

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

[tex]\frac{3}{4}x - 2 = 1\\\frac{3}{4}x = 1 + 2\\\frac{3}{4}x = 3\\x = \frac{3 \times 4}{3}\\x = 4\\[/tex]

Value of 3x - 4  = [tex]3 \times 4 - 4 \\[/tex]

                          = 12 - 4

                          = 8

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The geometric figure above has been dilated by a scale factor of 4/3 centered at the origin and plotted in the graph attached below.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 4/3 centered at the origin as follows:

Coordinate X (-3, -6) → Coordinate X' (-3 × 4/3, -6 × 4/3) = Coordinate A' (-4, -8).

Coordinate Y (3, 3) → Coordinate Y' (3 × 4/3, 3 × 4/3) = Coordinate A' (4, 4).

Coordinate Z (-3, 6) → Coordinate Z' (-3 × 4/3, 6 × 4/3) = Coordinate A' (-4, 8).

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Simple linear regression is a model that assesses the relationship between a dependent variable and an independent variable. The simple linear model is expressed using the following equation:

Where:

1. Y– Dependent variable

2. X– Independent (explanatory) variable

3. a– Intercept

4. b– Slope

Statistical Analysis Regression uses the statistics methods such as mean, median, normal distributions to figure out the relationships between the dependent and independent variables, to access the relationship strength between the variables and for modelling the new relationship among them, as it involves various variations such as simple linear, multilinear and non-linear where the non-linear regression is mainly used for complicated datasets in which the independent and dependent variables shows the nonlinear relationship.

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

[tex]\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}[/tex]

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.  

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

[tex]\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}[/tex]

A vertical shift is a movement up or down the y-axis, and it's represented by a change in the value of the y-intercept. A horizontal shift is a movement left or right along the x-axis, and in the equation of a function it's a change in the value of x before it's multiplied by the slope.

Vertical Shifts

One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input. For a function  

g(x) =f(x)+k,  the function  f(x)  is shifted vertically  k  units.

Horizontal Shifts

We just saw that the vertical shift is a change to the output, or outside, of the function. We will now look at how changes to input, on the inside of the function, change its graph and meaning. A shift to the input results in a movement of the graph of the function left or right in what is known as a horizontal shift,

Given a function  f, a new function  g(x)=f(x−h) , where  h  is a constant, is a horizontal shift of the function  f . If  h is positive, the graph will shift right. If  h is negative, the graph will shift left.

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The residuals e1, e2,..., en will always have a zero mean in least squares regression. fake group starts

False. The residuals may not have a zero mean, depending on the data used in the regression.

Least squares regression is a type of linear regression that is used to determine the best fit line for a given set of data points. The residuals in this type of regression are the differences between the actual values of the data points and the predicted values of the data points based on the model. While the sum of the residuals should be zero, the mean of the residuals may not necessarily be zero, depending on the data used in the regression.

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a) The approximate mean shipping time: X{bar} = 1.64

b) The approximate variance and standard deviation:

S² = 27.03, σ = 5.2

In this question, we have been given the frequency distribution of shipping times (number of hours between the time an order is placed and the time the order is shipped) for a random sample of 40 orders.

We need to find the approximate mean shipping time, variance and standard deviation.

Number of Hours        fi                midpoint

      4 < 10                  8                    7

     10 < 16                15                  13

     16 < 22                10                  19

     22 < 28                  7                   25

       SUM:                  40

a) the approximate mean shipping time:

X{bar} = (7.8 + 13.15 + 19.10 + 25.7)/40

X{bar} = 65.75/40

X{bar} = 1.64

b) the approximate variance:

S² = [(7.8 - 1.64)² + (13.15 - 1.64)²+(19.10 - 1.64)²+(25.7 - 1.64)²] / 39

S² = 1054.16/39

S² = 27.03

And the standard deviation:

σ = √S²

σ = √27.03

σ = 5.2

Therefore, for given frequency distribution,

a) mean = 1.64

b) variance = 27.03 and standard deviation = 5.2

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The given confidence interval is correct and it is between 22% to 38%.

The formula for calculating the confidence interval of population proportion is

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

Here the sample proportion is represented by [tex]\bar{p}[/tex].

It is given that,

The 95% confidence interval has a sample size of n = 120 and the number of successes = 36.

So, the sample proportion [tex]\bar{p}[/tex] = 36/120 = 0.3

For the 95% confidence interval, α = 1 - 0.95 = 0.05

And α/2 = 0.05/2 = 0.025

Then, the z-score for α/2 = 0.025 is [tex]z{\alpha/2|=1.96[/tex].

And the standard deviation, [tex]\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }=\sqrt{\frac{0.3(1-0.3)}{120} }[/tex] = 0.0418

So, the interval is in between

C.I = 0.3 ± 1.96 × 0.0418

Upper limit = 0.3 + 1.96 × 0.0418 = 0.38 = 38%

Lower limit = 0.3 - 1.96 × 0.0418 = 0.218 = 0.22 = 22%

Therefore, the given confidence interval is correct.

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The number with the given features in this problem is given as follows:

36.

First we consider that the number is a square number, meaning that it has a perfect square root.

The number is between 10 and 99, hence the possible square numbers between 10 and 99 are given as follows:

The numbers with a sum of the digits of 9 are given as follows:

The factors of each number are given as follows:

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Answer:

43 Is half

Step-by-step explanation:

86/2=43

I need you to promise me you will do good on the homework

The market equilibrium of the demand and the supply functions is

x = 88.69 bushels and p = $2.67

From the question, we have the following parameters that can be used in our computation:

Supply Function: p = 1.41 + 0.00016x2

Demand Function: p = (2.343 − 0.008x)2

These equations can be properly expressed

So, we have the following representation

Supply Function: p = 1.41 + 0.00016x²

Demand Function: p = (2.343 − 0.008x)²

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

This is so because the market equilibrium is the point of intersection of the graphs for x > 0.

From the graph, the lines and curves intersect at the point (88.685, 2.668)

Approximate

(88.69, 2.67)

This means that the market equilibrium is (88.69, 2.67)

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The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.

Volume of a solid plain:

The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.

Given in the question:

y = 2 - 1/2x

y = 0 , x = 1 and x = 2

As we know that:

[tex]\int\limits^2_1 {\pi (2 - \frac{1}{2}x - 0 })^2 \, dx[/tex]     ------------------------------ (1)

Simplifying,

      [tex]\pi \int\limits^2_1 {(2 - \frac{x}{2} )}^2 \, dx[/tex][tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]

⇒ [tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]

⇒ [tex]\pi [ 4x - x^2 + \frac{x^3}{12}]_1^2[/tex]

⇒ [tex]\pi [(8 - 4+ \frac{8}{12} ) - ( 4 - 1 + \frac{1}{12} )[/tex]

⇒ [tex]\pi (1 + \frac{7}{12})[/tex]

⇒ [tex]\frac{19\pi }{12}[/tex]

We can write 19π / 12 as

   (19× 22/7 )÷ 12

=  209/ 42

= 4.97 ≈ 5 cm³

Therefore, the volume is 5 cm³

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Let V be a finite-dimensional vector space and let B ={α 1…,α n } be a basis for V . Let ( | ) be the inner product of V. If c 1,...,c n , are n is a scalar, then show that there exist one vector α∈ V such that (α∣αj)=cj, j=1 ,…,n.

We have given that V is a finite dimensional vector space.

Consider α∈ V defined as

α = α₁β₁ + α₂β₂ + -----+ αₙβₙ where,

β₁ = α₁

β₂= α₂ - (α₁ |β₁)/β₁/β₂ |(β₁)

similarly, __

βⱼ = αⱼ - ( ∑ (αⱼ|βⱼ) / βᵢ|(βᵢ) βᵢ ) , j = 2,n bar

As defined aᵢ, i = 1, j bar

α₁ = c₁/ (β₁ )|β₁

___

α₂ = c₁/ (β₁ )|β₁ - a₁ ( α₂|β₂/β₁|β₂)

proceeding like as we get

_______

αⱼ = 1/β₁|(β₁) (cⱼ - ∑ αⱼ ( αⱼ |βⱼ)

then conider

(α|αⱼ )= ( α₁β₁ + α₂β₂ + -- + αₙβₙ |αⱼ )

= α₁β₁ + α₂β₂ + -- + αₙβₙ |βⱼ ) + ∑ α₁β₁+ α₂β₂ +---+αⱼβᵢ /βᵢβᵢ)

______

(α|αⱼ) =αⱼ(βⱼ |βⱼ) + (cⱼ - ∑ αⱼ ( αⱼ |βⱼ) βⱼ |βⱼ

__ ___

= (cⱼ - ∑ αᵢ ( αⱼ |βᵢ) + ∑αⱼ |βᵢ

(α|αⱼ) = cj, j = 1,n

Hence proved.

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Everything else is being equal, but we prefer an unbiased estimator mostly compare to a biased estimator because a biased estimator may be used for a variety of reasons, such as the difficulty of computing an unbiased estimator (as in the case of estimating standard deviation).

The fact that a biased estimator may be unbiased with respect to different measures, and the fact that an unbiased estimator does not exist without further assumptions about a population. Thus, it's miles scientifically now no longer accurate to apply a biased estimator for a parameter while there may be an independent estimator for it.

Only in unavoidable situation, it's miles cautioned to apply a biased estimator (which need to be consistent) for a parameter while there may be no independent estimator for it. It could be anticipated that a terrific estimator need to bring about an estimate this is near the real cost of the parameter. Because in exercise the parameters are unknown, it isn't always viable to evaluate the estimate with the real cost. Unbiasedness serves as a degree of closeness among an estimator and the parameter.

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The histogram that represents the data-set in this problem is given by the image shown at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, the elements are divided in ranges, hence the histogram will give the number of elements in each range that was observed.

The ranges for this histogram are given as follows:

The number of elements in each range is given as follows:

Meaning that the third histogram, from the top down, is the correct option.

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Range is the measure of variability which is not dependent on the exact value of each score.

In terms of variability, range is independent of the exact value of each score, and in terms of central tendency, median is the measure that is independent of the exact values of each score.

What is a range?

Range is basically the difference of the highest and the lowest value of a series. The range has nothing to do with the exact value of each score. It just considers the highest and the lowest values of any given class for its calculation.

Range= highest value- Lowest value

That is the reason, why, Range is the independent measure of variability.

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The measure of the angle ∠BDC is 68°.

What is the straight line angle?

A straight angle in geometry is one that is 180 degrees in length. It looks like a straight line, which is why it is known as a straight angle. In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.

We have,

∠BDA is a straight angle

so ∠BDA = 180°

We need to find the ∠BDC

∠CDA = -8x + 48°

∠BDC = -7x + 12°

∠BDA = ∠BDC + ∠CDA = 180°

(-8x + 48°) + (-7x + 12°) = 180°

-15x + 60° = 180°

-15x = 120°

x = -8°

∠BDC = -7x + 12°

= -7(-8°) + 12°

= 56° + 12°

= 68°

Hence, the measure of the angle ∠BDC is 68°.

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Answer:

15.06

Step-by-step explanation:

Substituting this value into the first equation gives us b + 2.94 = 18, so b = 15.06 hours. Since Karen can only work whole hours, she must have worked 15 hours babysitting and 3 hours giving music lessons.

Answer: 3 pieces

Step-by-step explanation:

This problem can be solved by modeling the problem using equivalent fractions.

We know Stephanie put icing on 9 of her 15 pieces, this gives us a fraction of [tex]\frac{9}{15}[/tex].

Tammy cut her cake in 5 pieces, but we do not know how many were iced, the pieces of iced cake will be our variable, x, so her fraction is [tex]\frac{x}{5}[/tex].

Both of the fractions need to be equivalent so [tex]\frac{9}{15} =\frac{x}{5}[/tex], which can be solved for x = 3 pieces.

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

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The new interval for mu becomes narrower, If the number of observations stays the same, but the confidence is reduced to 90%.

The population mean 95% confidence interval is calculated to be between 65.32 and 73.54. The confidence interval for mu will get narrower if the range is trimmed to 90%. This is because the margin of error has decreased. The mean's potential values would be reduced as a result.

The probability that the confidence interval contains the actual population mean is known as the confidence level. You would anticipate that the true value would fall within these ranges 95% of the time if the study were to be repeated and the range computed each time. The more confident you may be that the interval contains the true mean, the greater the confidence level.

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a) The relationship of the graph is drawn by using the above table is attached below:

b) Since, the time is increasing the pay of increasing is more. By this we have known the graph.

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph. Though it is frequently helpful to think about functions as mappings, which also include which set is the domain and which set is the codomain, it is also important to note that mappings do not just refer to the relationship between input and output. A codomain should be considered, for instance, while determining if a function is onto (surjective) or not. The codomain is not determined by the graph of a function alone.

Given, equation of pay is:

p=8.25t

Here p represents the pay and t represents the time he works.

The table is:

20          10       0       30         4           5             6

165       82.5     0      247.5    330   412.5         495

a) The relationship of the graph is drawn by using the above table:

b) Since, the time is increasing the pay of increasing is more. By this we have known the graph.

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The angles in order from the smallest to the largest are ∠E < ∠D < ∠F.

Option D is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

∠D is opposite to the side length 15.

∠E is opposite to the side length 14.

∠E is the smallest angle.

∠F is opposite to the side length 23.

∠F is the largest angle.

Thus,

∠E < ∠D < ∠F

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Answer:

6

Step-by-step explanation:

3 is 3/5 of 5 therefore 6 would be 3/5 of 10 and the triangles are similar so

Answer: 9x

Step-by-step explanation:

-4x+y=5x

solve for x

y=9x