a certain star is 3.6 x 10^2 light years from the earth. one light year is about 5.9 x 10^12 miles how far from the earth in miles is the star

The word "to" comes before infinitives. Because they are unconstrained by time, like the idea of infinity, these verbs are known as infinitives.

In the given question, we have to explain why an infinitive called an infinitive.

The verb form known as an infinitive can be employed as a noun, adjective, or adverb. When describing acts without actually performing them, they are typically created by adding the term to before the base verb.

The word "to" comes before infinitives. Because they are unconstrained by time, like the idea of infinity, these verbs are known as infinitives. The conjugated forms of the verb, sometimes referred to as the finite forms of the verb, are derived from the infinitive.

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Answer:

12

Step-by-step explanation:

Using the properties of a 45-45-90 triangle, [tex]x=\sqrt{2}(6\sqrt{2})=12[/tex].

To prove that the triangles are similar by the SSS similarity theorem, we use MN corresponds to QR, also ∠S ≅ ∠O

Two triangles are comparable if the measurements of their corresponding sides are proportionate. Additionally, if the measurements of two sides in one triangle are proportional to the measurements of the corresponding sides in another triangle and the included angles are congruent, the triangles are similar.

Similar figures

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides is in the same proportion.

From the image, MN corresponds to QR, also ∠S ≅ ∠O

To prove that the triangles are similar by the SSS similarity theorem, we use MN corresponds to QR, also ∠S ≅ ∠O

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Answer: I pretty sure its 9 feet

Step-by-step explanation:

Sorry if Im wrong

The probability of getting heads is 3/8.

Probability:

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

Since 3 is a small number, let's list out all possible combinations.

H represents a head while T represents a tail.

3 Heads

HHH

2 Heads

HHT

HTH

THH

1 Head

HTT

THT

TTH

0 Head

TTT

The answer is

3/1+3+3+1=3/8

                                            OR

In general, we will find that the list resembles a particular row of the pascal's triangle.

If you want to know the probability of getting r heads (or tails) from n flips, it is the sum of the rth  elements in the n + 1 line. All elements of the series n+1.

[tex]\left[\begin{array}{ccc}N\\\\R\end{array}\right][/tex]/ 2ⁿ = [tex]\frac{n!}{r! * (n - r)!* 2^{n} }[/tex]

n this case,

N =3andR= 2

   3!/ 2!×1! × 2³

= 6/ 2× 1 × 8

= 3/8

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The expected area of a random square which has a side length that is uniform random variable is 1/3.

A family of symmetric probability distributions includes the continuous uniform distribution and rectangular distribution. The distribution describes an experiment with a random result that falls within predetermined bounds.

 The parameters, a and b, which represent the minimum and maximum values, define the bounds. The interval may be closed (for example, [a, b]) or open (for example, (a, b)). common abbreviation for the distribution is U (a, b), where U stands for uniform distribution. 

The length of the interval is defined by the difference between the bounds; intervals with the same length on the distribution's support are equally likely.

Let, side of the square = X

we know that the area of a square = side × side

                                                          =  X  ×  X

                                                          =  X^{2}

now, by using Continuous uniform distribution,

E[ X^{2} ] =  [tex]\int\limits^1_0 X^{2} \, dx[/tex]    

                =  [tex][\frac{1^{3} }{3} - \frac{0^{3} }{3} ][/tex]

                =  [tex]\frac{1}{3}[/tex]

Hence , the expected area of the square is [tex]\frac{1}{3}[/tex].

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There are 13340783196 ways to allocate marks to the questions.

It is given that the exam has 12 problems.

There are 11 questions that need to be assigned at least 5 marks while the last answer needs to be assigned at least 10 marks.

Hence the least marks to be assigned

= 11 X 5  + 10

= 65.

Hence are left with assigning 35 marks.

here,

n = 12

r = 35

In this type of problem, we need to use the formula

C(n + r -1 , r)

= ⁴⁶C₃₅

= 46! / (35! X 11!)

Hence no. of way to assign marks

= 13340783196 ways.

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Answer:

No, the solution to the equation 8x = 72 is x = 9. To solve this equation, you can divide both sides by 8 to obtain the value of x. This gives us x = 72/8 = 9.

It is discovered that the (1) graph represents a function whose inverse is also a function using the concept of an inverse function.

The set of ordered pairs is the graph of a function f in mathematics, where these pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph.

Since there is only one value of x in the first graph for any value of y, the inverse is also a function, making this the right answer.

The inverse is not a function in the second graph since, for instance, y = 0 when x = -1 and when x = 1.

For instance, in the third graph, the inverse is not a function because y = -3 when x = 0 and x = 2.

For instance, in the fourth graph, y = 1 for two different values of x, proving that the inverse is not a function.

Therefore, it is discovered that the (1) graph represents a function whose inverse is also a function using the concept of an inverse function.

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Correct question:

Which graph shows a function whose inverse is also a function?

The equation of a line that is perpendicular to 2y 3x 10 and passes through (- 6 1) is -3y + 2x -1 with slope.

1. Start by finding the slope of the given line by taking the coefficient of x and dividing it by the coefficient of y.

2. To find the slope of the line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.

Slope of the perpendicular line: m = -2/3

3. We know that the equation of a line in slope intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

4. So, the equation of the line perpendicular to 2y 3x 10 and passes through (-6 1) is:

y = -2/3x + b

5. To find the y-intercept, substitute the given point (-6 1) in the equation and solve for b.

-1 = -2/3(-6) + b

b = 1

6. Therefore, the equation of a line that is perpendicular to 2y 3x 10 and passes through (- 6 1) is -3y + 2x -1

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No, there is not a significant difference between these two values at the 95% confidence level.

The difference between the mean and literature values is 0.011 g/ml, which is less than the standard error of the mean (0.00387 g/ml). Therefore, the difference is not statistically significant. To reach a 95% confidence level, the difference must be greater than two standard errors of the mean. This would mean that the difference must be greater than 0.00773 g/ml, which it is not. Therefore, there is no significant difference between these two values at the 95% confidence level.

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Answer: 7/8?

Step-by-step explanation:

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Option-D is correct that is the larger the difference, the larger the value of chi-square, and the greater the probability of rejecting the null hypothesis.

Given that,

We have to find how will the results of a chi-square test be affected if there is a significant discrepancy between the expected and observed frequencies.

We know that,

If the observed values and expected values have a large difference then the chi-square value will be in large quantity that provides evidence against the null hypothesis and explain the huge difference between the sample data and null hypothesis.

The Chi-square statistic is,

X²=Σ i,j=0 to n (O i, j-E i,j)²/E i,j

Where,

O is the observed frequency value.

E is the Expected frequency value.

Therefore, Option-D is correct that is the larger the difference, the larger the value of chi-square, and the greater the probability of rejecting the null hypothesis.

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The system of inequalities that are graphed are:

y < (1/2)x + 4

y > 2x - 1

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Two coordinates from the graph of the green line.

(0, 4) and (2, 5)

The equation of the line.

y = mx + c

m = (5 - 4) / (2 - 0) = 1/2

m= 1/2

(0, 4) = (x, y)

4 = (1/2) x 0 + c

c = 4

y = (1/2)x + 4

Two coordinates from the graph of the Blue line.

(1, 1) and (2, 3).

The equation of the line.

y = mx + c

m = (3 - 1)/(2 - 1) = 2/1 = 2

m = 2

(1, 1) = (x, y)

1 = 2 + c

c = 1 - 2

c = -1

y = 2x - 1

Now,

The system of  linear inequalities that are graphed on the given graph are:

y < (1/2)x + 4

y > 2x - 1

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A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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Bonnie bought more jolly because the weight of her 2 bags is more than that of Linsey.

The pound or pound-mass is a unit of mass used in British imperial and United States customary systems of measurement.

If each Linsey's bag of jolly weighs 18 ounces then 3 bags would weigh 18 x 3 = 54 ounces

If each Bonnie's bag of jolly weighs 2 pounds then the 2 bags would weigh 2 x 2 = 4 pounds.

converting 4 pounds to ounces at the rate of 16 ounces per pound we have 16 x 4 = 64 ounces

So Bonnie bought more jolly than Linsey as the weight of the bags of Bonnie is heavier than that of Linsey.

In conclusion Bonnie bought more than Linsey as the weight of bags of Bonnie outweighs Linsey's

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The relationship between lines a and c, where both line a and c are perpendicular to line b is that line a and c are parallel, a ║ c

Please find attached an example drawing of the lines a and c created with MS Excel.

Parallel lines are coplanar lines that have a fixed distance between them and do not meet.

The specified information are;

the lines that are on the same plane = a, b, and c

The relationship between line a and b = a is perpendicular to b (a ⊥ b)

The relationship between line b and c = b is perpendicular to c (b ⊥ c)

The slope of a line perpendicular to another line with slope, m, is the negative inverse of m or -1/m

(The slope of parallel lines are the same)

Let the slope of line a = m, therefore;

The slope of the line b  which is perpendicular to a is -1/m

Therefore, the relationship between the lines b and c which are perpendicular (b ⊥ c) is as follows;

The slope of the line b = -1/m, therefore;

The slope of the line c, perpendicular to b is the negative inverse of the slope  of b

The slope of the line c = -1/(-1/m)) = 1/(1/m) = m

The slope of the line c = m

Therefore, the slope of the line c (m) is the same as the slope of the line a (m), which indicates that the lines a and c are parallel.

a ║ c.

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The proportion of the laptops is equal to 0.6 with the price range between 624 dollars to 768 dollars for the given mean and standard deviation.

As given in the question,

Given condition:

Price of of given laptops set are normally distributed:

Mean 'μ' is equal to 750 dollars

Standard deviation 'σ' is 60 dollars

let 'X' represents the price of laptops

Range of price is given by:

624 < X < 768

= (624 - μ)/σ < (X - μ)/σ < (768 - μ)/σ

= (624 - 750)/60 < (X - μ)/σ < (768 - 750)/60

= -126 /60 < (X - μ)/σ  <  18 /60

= -2.1 < Z < 0.3

From the table , value of z-score is equal to

z-score for -2.1 = 0.01786

z-score for 0.3 = 0.6179

Required proportion is equal to

0.6179 - 0.01786

= 0.6179 - 0.0179

= 0.6

Therefore, the proportion of laptops with the price between 624 and 768 is equal to 0.6.

The complete question is :

A set of laptop prices are normally distributed with a mean of 750 dollars and a standard deviation of 60dollars.

What proportion of laptop prices are between 624 dollars and 768 dollars?!

You may round your answer to four decimal places.

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Answer:

Step-by-step explanation:

To find the missing numbers, we must simplify the second half of the original proportion/fraction. Let's use number 2 as an example. First, we need to find out which number we are using to simplify. To do this, we divide 21 by 7. This gives us 3. Now, we divide 12 by 3 to get y, or 4. This strategy can be applied to all the problems.

The equation that Amy can use to find how many games of Balloon Bouncer, g, she played is; g = (35 - 2a)/3

We are told that Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score.

Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

Thus, the expression for the number of balloon bouncer games played at the arcade is :

2a + 3g = 35

Let :

Glimmer arcade, a = $2 per game

Balloon bouncer, g = $3 per game

Total game tokens = 35

Her spending could be represented using the expression :

2a + 3g = 35  

g = number of balloon bouncer games played

Thus, making g the subject of the formula we have;

g = (35 - 2a)/3

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Answer:

3g + 2 = 35 is the answer.

She played 11 games.

Step-by-step explanation:

Answer:

12 311 12 13 14142131 32 3341 42 4351 52 5361 62 6371 72 73 7481 82 83 84014 5 6 7 8 9 1015 16 17 18 19 2022 23 2424 25 26 27 28 29 3000 0935 36 37 38 39 4044 45444546 47 48 49 5055 56 57 58 59 6066 67 68 69 7075 76 77 78 79 8085 86 87 88 89 90343454 555464 6501

Step-by-step explanation:

The set of numbers are shaded on the hundred chart are,

⇒ Only the multiple of 33.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The set of numbers are shaded on the hundred chart.

Now, We get;

Shaded numbers are,

⇒ 33, 66, 99, ...

Thus, The set of numbers are shaded on the hundred chart are,

⇒ Only the multiple of 33.

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Answer:

I am so sorry but I dont see attachment

the answer of the question is -The current temperature and wind speed in Philadelphia

Weather describes the condition of the atmosphere, including how hot or cold, wet or dry, quiet or stormy, clear or cloudy, and so forth. The troposphere, the section of the planet's atmosphere immediately below the stratosphere, is where the majority of weather events on Earth take place.

Contrarily, climate refers to the weather patterns that can be determined by using data collected in a certain area over an extended period of time to produce adequate averages.

There are several weather conditions, such as cloudy, sunny, wet, windy, and snowy. Air masses are among the most important variables that impact the weather.

answer of the question is -The current temperature and wind speed in Philadelphia

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The equation of the line with slope [tex]1[/tex] and y-intercept is [tex]7[/tex] i.e. [tex]y=x+7[/tex]

The slope-intercept form is

[tex]y=mx+c[/tex]

Here, m is the slope and c is the y-intercept

y=x+7

The equation of the line is [tex]y=x+7\\[/tex]

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A study that compares two groups of people: people with the disease or condition being studied (cases) and a very similar group of people without the disease or condition.

A cohort study is a type of longitudinal study, an approach that follows study participants over a period of time, often over many years. Specifically, cohort studies recruit and track participants who share common characteristics such as:  Specific Occupational or Demographic Similarities.

Association measures quantify the relationship between exposure and disease between two groups.

A case-control study (also called a case-reference study) is a type of observational study in which two existing groups with different outcomes are identified and compared based on putative causal attributes. A case-control study is a study of a medical condition/disease by comparing patients with the condition/disease (“cases”) to otherwise similar patients (“cases”) who do not have the condition/disease. Commonly used to identify possible contributing factors. It requires fewer resources but provides less evidence for causal conclusions than randomized controlled trials. Case-control studies yield inferior odds ratios as a measure of the strength of association compared to relative risk.

A cohort study is a type of research design that tracks a group of people over time. Researchers use data from cohort studies to understand human health and the environmental and social factors that affect it. The word "cohort" means a group of people. Cohort studies can be prospective or retrospective.

A prospective cohort study is also known as a prospective cohort study. "Prospect" refers to the future.

A retrospective cohort study is also called a retrospective cohort study. "Retrospective" means to look into the past.

To conduct a prospective cohort study, researchers identify the population to study, plan the study in advance, and collect data over time. In retrospective her cohort studies, researchers use data already available in specific groups.

A statistical measure of association, one of several factors or coefficients used to quantify the relationship between two or more variables. Association measures are used in a variety of research fields, but are most widely used in the fields of epidemiology and psychology, where they are often used to quantify the relationship between exposure and disease or behavior.

Measures of association can be determined by one of several different analyses, such as correlation analysis or regression analysis. (The terms correlation and association are often used interchangeably, but in the narrower sense correlation refers to linear correlation and association for any relationship between variables. Used to determine strength of association How it is done depends on the properties of the data in each variable. Data can be measured on an interval/ratio scale, an ordinal/rank scale, or a nominal/category scale. These three characteristics can be displayed as continuous, integer, and qualitative categories respectively.

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The table that shows a function that is decreasing only over the interval (–1, ∞) is circled on the image given at the end of the answer.

The behavior of a function is classified as either increasing, decreasing or constant, as follows:

In this problem, we want a function that is decreasing only over the interval (–1, ∞), hence:

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Two ways in which the combination can be represented = 720 , 46656

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

According to the given information

Whether you can repeat numbers or not will determine which of two possibilities

First Way

If you cannot repeat the digits  

Then

You might perform 6 ! or 6x5x4x3x2x1 = 720

This is so that the initial digit, which can have up to six numbers, can never be repeated. As a result, one digit cannot be repeated, therefore

6 - 1 = 5. The third digit is the same, but since you've already used two of the six digits, you can only have 4.

The alternative

If you're able to repeat :

either [tex]6^{6}[/tex] or 6x6x6x6x6

= 46,656

This is due to the fact that each digit has six possible values.

Two ways in which the combination can be represented = 720 , 46656

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By Polynomial Addition, 1st,2nd equations goes to 3rd box; 3rd,4th equations goes to 2nd box; 5th,6th equations goes to 1st box.

Steps to solve polynomial addition:

1) Take the equation.

2) Arrange the polynomial such that common terms are placed at one place.

3) Group the like terms, Like terms are terms which has equal degree and equal  variables.

4) Simplify by combining like terms.

5) Solve the equation

1st equation:

[tex]x - 3 + 2x + 3 + 2x\\= 5x + 0\\= 5x[/tex]

goes to 3rd box

2nd equation:

[tex]6x - 9 - 5x +4 - x+5x+5\\= 5x +0\\=5x[/tex]

goes to 3rd box

3rd equation:

[tex]3x+5-2x-5x+9+8x\\= 4x + 5+9\\=4x + 14[/tex]

goes to 2nd box

4th equation:

[tex]4x+x-11-5x+25+4x\\=4x + 14\\[/tex]

goes to 2nd box

5th equation:

[tex]x+8+4x-3x-4\\=2x+4[/tex]

goes to 1st box

6th equation:

[tex]5+9x-7-4x-3x+6\\=2x+4\\[/tex]

goes to 1st box

By Polynomial Addition, 1st,2nd equations goes to 3rd box; 3rd,4th equations goes to 2nd box; 5th,6th equations goes to 1st box.

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