Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, d
represents the distance from a start to the Sun. Using a technique called "stellar parallax," astronomers determined θ
is 0.00001389 degrees.

b) Write an equation to calculate d
for any star.

(Your response must include an equal sign, and the variables d
and θ.)

Angle EBI and angle BCJ are congruent is proved as follow.

To prove that corresponding angles are congruent, we can use the transformation that takes angle EBI to angle BCJ.

Therefore, we can conclude that corresponding angles are congruent.

Alternatively, we can use the fact that if two lines are parallel, then the alternate interior angles are congruent and corresponding angles are congruent. Since AI and GJ are parallel, angle EBI and angle BCJ are congruent.

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Answer:

Step-by-step explanation:

-Hope this helps!

Answer: x = 16

Step-by-step explanation:

To solve for x, add 5 and 11.

5 + 11 = 16

16 - 5 = 11

x = 16

Using the information in the issue and the formulas for the total surface area and volume of a rectangular solid, we can determine the volume of the rectangle solid in detail.

First, we calculate the rectangular solid's overall surface area using the following formula:

2(lw + lh + wh) = 972

Where the rectangular solid's dimensions are l for length, w for width, and h for height.

We can describe the three sides in terms of x, so that l = 10x, w = 4x, and h = x, since the ratio of the length to the breadth to the height is 10:4:1.

Now, we change the variables in the equation for the total surface area to match these values:

The formula is 2(lw + lh + wh) = 2(10x * 4x + 10x * x + 4x * x) = 972.

The equation will become more precise and give us:

80x^2 = 972

x^2 = 12.15

x = 3.5

Now that we have one side's value (height), we can use the following formula to get the solid's volume:

V = lwh

V = (10x)(4x)(x)

V = 40x^3

V = 40 * (3.5)^3

V = 40 * 42.875

V = 1715 cubic units

As a result, the rectangular solid has a volume of 1715 cubic units.

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Answer: Since AFGH is a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. We can use this property, known as the triangle inequality theorem, to determine the angles of AFGH in order from largest to smallest.

We are given that the perimeter of AFGH is 87, so we know that:

FG + GH + FH = 87

6x + 7 + 8x - 5 + 10x - 11 = 87

24x + 1 = 87

24x = 86

x = 3.5

Now that we know that x = 3.5, we can use the given lengths of the sides to find the values of the sides:

FG = 6x + 7 = 6(3.5) + 7 = 23

GH = 8x - 5 = 8(3.5) - 5 = 25

FH = 10x - 11 = 10(3.5) - 11 = 29

We can now use these values to determine the angles of AFGH in order from largest to smallest.

We can use the triangle inequality theorem to determine that:

FH>FG+GH

29>23+25

Therefore, the angle that is opposite to side FH is the largest angle in the triangle, and the angles opposite to FG and GH are the smaller angles.

So, the angles in the triangle AFGH are ordered from largest to smallest:

The angle opposite to side FH, angle A, is the largest.

The angles opposite to side FG and GH are the smaller angles.

Step-by-step explanation:

Using the congruency of the top-right angles, it is found that the value of y is of 130.

What are parallel lines ?

Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.

When two parallel lines are cut by a transversal, the top-right angles are congruent, that is, they have the same measure.

In this question, their measures are of (2x + 18)º and (4x - 14)º. Thus, with this, we can find x:

4x-14 = 2x+18

4x-2x = 18+14

2x = 32

x = 32/2

x = 16

Thus, the measure of the top right angles is given by, in degrees:

4x-14 = 4*16 - 14 = 64 - 14 = 50

The top-right and the bottom-right angles are supplementary, that is, the sum of their measures is 180º.

The measure of the top-right angle is of 50º.

The measure of the bottom-right angle is of y.

Thus:

y + 50 = 180

y = 180 - 50

y = 130

Hence, The value of y is of 130.

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Answer: b ≤ 17/10

Step-by-step explanation:

7/2 ≥ b + 9/5

7/2 - 9/5 ≥ b

17/10 ≥ b

b ≤ 17/10

Answer:

To find an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1, we know that the slope of the line we are looking for must be the same as the slope of the line 4x-y = 1. We can find the slope of 4x-y = 1 by rearranging it to the slope-intercept form y = mx + b.

4x - y = 1

y = -4x + 1

The slope of this line is -4

Now that we know the slope of the line we are looking for is -4, we can use the point-slope form of a linear equation, which is:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line, and m is the slope.

We know that the point (-2, -3) is on the line we are looking for, so we can substitute these values into the point-slope form:

y - (-3) = -4 (x - (-2))

y + 3 = -4x + 8

y = -4x + 5

So an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1 is y = -4x + 5.

Answer: 167.7

Step-by-step explanation:

Step 1:

Substitute

11.5(7) + 10.9(8)

Step 2:

Multiply:

80.5 + 87.2

Step 3:

Add:

167.7

167.7

Variables are letters within math that represent numbers.

The Expression

The question above is written as an expression. An expression is a mathematical statement that does not contain an equal sign. This is an expression because it's an addition statement without an equal sign.

Within the expression, there are 2 variables. Both x and y are variables because they're letters within the expression that are intended to represent numbers.

Solving the Expression

Now, to solve the expression we can plug the numbers we were given for each variable.

So, the answer to the expression 167.7.

The value of the expression is 28

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

2 square root 98 times square root 2

Express properly

So, we have the following representation

2√98 * √2

Evaluate the products

This gives

2√196

Take the square root of 196

2 * 14

So, we have

28

hence, the solution is 28

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Part A) According to the the scatter plot r = 0.01 is not an accurate value for this data

Part B) We have to describe a scenery where a variable is the cause of the number of strawberries picked.

The term scatter plot in math is known as  a horizontal and a vertical axis in the attempt to show how much one variable is affected by another

As we all know that the correlation coefficients r and it measure the strength of the correlation of two variables and they can have values from - 1 to  1.

Here we have know that r = - 1 is  a perfect negative correlation and the points will adjust perfectly to a line with negative slope.

Where as r =  + 1 is a perfect positive correlation and the points will adjust perfectly to a line with positive slope.

Where as r = 0 means that the variables are not correlated at all.

Hence the calculated value of r = 0.01 is not accurate for t his scatter plot.

As we all know that the causal relationship means that the explanatory variable is the cause of the dependent variable.

Therefore here we know we have to find a reasonable variable that can be the cause of the number of strawberries picked.

As the amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.

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Answer:

16.281 rounded to the nearest whole number is 16.

This is because since 2 in the tenths place is bellow 5, the 16 will not round up to 17, and remain the same.

Step-by-step explanation:

Hope it helps! =D

The value of g(-6) is 42

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

For example if f(x) = 3x-2, the value of f(3) is derived by substituting 3 for x In the function. Therefore f(x) = 3(3) -2 = 9-2 = 7

Similarly to solve g(-6) we substitute -6 for x in the function

g(-6) = -6² -(-6)

g(-6) = 36 + 6

g(-6) = 42

therefore the value of g(-6) = 42

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a. Each shoebox has a volume of 288 cubic inches.

b. Each crate has a volume of about 5,760 cubic inches.

c. If the crate could hold 27 shoeboxes, the total volume would be of about 7,776 cubic inches.

The volume of a rectangular prism is obtained by the multiplication of the dimensions of the prism.

Hence the volume of the box in this problem is of:

6 x 4 x 12 = 288 cubic inches.

For the crates, we have that:

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Answer:

A.288

B.5,760

C.27 shoeboxes

Step-by-step explanation:

Given that a = 8 cm and b = 21 cm, the value of A is 20.9 degrees

The complete question is added as an attachment

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

a = 8 cm and b = 21 cm

Using the tangent function, we have

tan(A) = a/b

So, we have

tan(A) = 8/21

Evaluate

tan(A) = 0.3810

Take the arctan of both sides

A = 20.9 degrees

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Answer:

3

Step-by-step explanation:

Experimental probability is based on the actual outcomes of an experiment (gathered by experimenting repeatedly).  

Theoretical probability is based on the possible outcomes (expected outcomes).

Probability formula

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Theoretical probability of flipping a head

A coin has two sides: one side is a "head", the other side is a "tail".

The number of ways flipping a head can occur is 1.

The total number of possible outcomes is 2.

Therefore, the theoretical probability of flipping a head is 1/2.

Theoretical probability of rolling a number less than 3

The cube has six sides labelled 1, 2, 3, 4, 5 and 6.

The number of ways that rolling less than 3 can occur is 2 (rolling 1 or 2).

The total number of possible outcomes is 6.

Therefore, the theoretical probability of rolling a number less than 3 is 2/6 = 1/3.

Therefore, the theoretical probability of flipping a head and rolling a number less than 3 is:

[tex]\sf P(head)\; and\; P(X < 3)=\dfrac{1}{2} \times \dfrac{1}{3}=\dfrac{1}{6}[/tex]

To calculate the number of actual outcomes and expected outcomes after 90 trials, multiply the number of trials by the probability for each outcome:

[tex]\textsf{Number of actual outcomes}=90 \times \dfrac{2}{15}=12[/tex]

[tex]\textsf{Number of expected outcomes}=90 \times \dfrac{1}{6}=15[/tex]

Therefore, the difference between the number of expected outcomes and the number of actual outcomes is:

[tex]\implies 15-12=3[/tex]

Note: If Olivia continued to flip the coin and roll the number cube, as the number of trials increased, we would expect the experimental probability of 2/15 to get nearer to the theoretical probability of 1/6 and so the difference between the number of actual and expected outcomes would become smaller.

In parallelogram lmno measure of angle m m∠M = 80°

In a parallelogram, opposite sides and opposite angles are congruent to each other.

⇒ m∠N = m∠L and m∠M = m∠O ..........(1)

Also, the sum of any two consecutive angles of a parallelogram is supplementary that is 180°

⇒ m∠M + m∠L = 180°  ...........(2)

Now, using equation (1)

m∠N = m∠L

⇒ 5x = 3x + 40

⇒ 5x - 3x = 40

⇒ 2x = 40

⇒ x = 20

⇒ m∠N = m∠L = 5x = 100°

Now, from equation (2)

m∠M + m∠L = 180°

⇒ m∠M + 100 = 180

⇒ m∠M = 80°

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The probability of scoring more than 45 ixe is 0.91. P(X<=45) = (240C0 * (1/2)^0 * (1/2)^240) + (240C1 * (1/2)^1 * (1/2)^239) + (240C2 * (1/2)^2 * (1/2)^238) + ... + (240C45 * (1/2)^45 * (1/2)^195)

P(X<=45) = 0.0909

The probability of scoring more than 45 ixe can be calculated by using the Binomial Probability formula.

The formula is:  P(X>45) = 1 - P(X<=45)

Where P(X<=45) is the probability of scoring 45 or less ixe.

P(X<=45) = (240C0 * (1/2)^0 * (1/2)^240) + (240C1 * (1/2)^1 * (1/2)^239) + (240C2 * (1/2)^2 * (1/2)^238) + ... + (240C45 * (1/2)^45 * (1/2)^195)

P(X<=45) = 0.0909

Therefore, P(X>45) = 1 - 0.0909 = 0.9091

The probability of scoring more than 45 ixe is 0.91 (to 2 d.p.).

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The z-score is greater in the case of Amber than in Roger so Amber had a better year relative to their peers.

First for Roger:

We have

Mean, μ = 4.371

Standard deviation, s = 0.787

so z-score for X = 3.14 will be

z = (X-μ)/s = (3.14 - 4.371)/0.787

or z = -1.564

Now In the case of Amber:

We have

μ = 4.363

s = 0.869

X = 3.38

so z = (X-μ)/s =  (3.38 - 4.363)/0.869

or z = -1.131

Therefore, The z-score is greater in the case of Amber than Roger so Amber had a better year relative to their peers.

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The probability that the student will be a student who lives on campus is 0.24

In math the term probability is referred as the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Here we have given that one full-time student who is a freshman or sophomore is selected at random.

Here we need to find the probability that the student will be a student who lives on campus.

Here we know that the probability that a student is a sophomore is calculated as,

=> P(S) = 19/42 = 0.45.

Whereas the probability that a student has a freshman is calculated as,

=>P(H)=25/42=0.6.

Then the probability that the student will be a student who lives on campus is calculated as,

=> P(H∩S)=P(S)+P(H)−P(S∪H)

Apply the values then simplify this one then we get,

=> 0.45+0.6−(42−8)/42=0.24

Complete Question:

Suppose that a certain college class contains 42 students and then if one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?

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The solution to the equation is 23

From the question, we have the following parameters that can be used to solve the question

7 - 5p + 3q

Also, we have the following values

p = 1 and q = 7

Substitute the know values in the given expression, so we have the following representation

7 - 5(1) + 3(7)

Evaluate the products

This gives

7 - 5 + 21

Evaluate the like terms

23

Hence the solution is 23

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[tex]\overline{AB}[/tex]1) The proof for to show that ΔJKN ≅ΔMKL is given as follows:

Given:

∠N≅∠L

[tex]\overline{JK}[/tex] ≅ [tex]\overline{MK}[/tex]

Thus,

ΔJKN ≅ΔMKL:

Reason: Angle - Angle - Side Theorem

Note that Vertical ∡s are ≅ (Congruent)

2) Given:

[tex]\overline{DE}[/tex] || [tex]\overline{FG}[/tex]

∠E ≅ ∠G

Since

[tex]\overline{DE}[/tex] || [tex]\overline{FG}[/tex], it means that ∠EDF ≅ ∠GFD, is because Alternate Angles of parallel lines are ≅ (Congruent). Given that ∠E ≅ ∠G. On the basis of reflexive property, [tex]\overline{DF}[/tex] ≅ [tex]\overline{FD}[/tex].

Hence, by the rule of Angle - Angle - Side, ΔFDE ≅ΔDFG.

In geometry, the reflexive property of congruence asserts that every angle, line, and figure/shape is congruent to itself.

This characteristic is commonly utilized in proofs such as establishing two triangles are congruent and parallel lines are parallel.

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A population is a person or object that is a member of the sample being studied while a sample is the entire group that is being studied.

In a research study, a sample is a relatively small group of people from whom data is collected. The population is the bigger group to whom the information is then generalized.

All citizens, whether they are living there permanently or are only visiting, are referred to as the "people."

This indicator shows the average population density of a given area. The annual population fluctuations brought on by births, deaths, and net migration are known as growth rates.

A population is any large group that has at least one attribute in common. Not all populations are made up of people.

Populations can include, but are not limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.

Of the 7.8 billion people on the planet, 1%, or around 78 million individuals, would be there. One percent of the 7.8 billion people on the planet, or 78 million people, live there.

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Complete question -

A person or object that is a member of the group being studied is called ______.

a. The scale factor is: 3/2

b. The pairs of corresponding angles are, <J and <P; <K and <Q; <L and <R.

c. The ratios are: JK/PQ = KL/QR = JL/PR.

The scale factor, also known as the ratio of similitude, is used to describe the relationship between the size of two similar figures. It is the ratio of the corresponding measurement of the new figure to the original figure.

a. scale factor from triangle JKL to triangle PQR = PQ/JK

= 9/6

= 3/2

b. The pairs of corresponding angles are:

<J and <P

<K and <Q

<L and <R

c. The ratios of the corresponding side lengths in a statement of proportionality will be: JK/PQ = KL/QR = JL/PR.

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The association between the two sets of data in the scatterplot is; Positive.

A scatter plot is a graph that shows the association that exists between two variables. A scatter plot matrix shows all the pairwise scatter plots for a lot of  variables.

Now, If the variables tend to increase and decrease together, the association is said to be positive. However, If one variable tends to increase as the other decreases, then the association is said to be negative. Finally, If there is no pattern, then the association is said to be zero.

When a straight line is used to describe the relationship between the variables, then the association is said to be linear. When a constantly increasing or decreasing nonlinear function describes the relationship, the association is monotonic.

The scatterplot given shows us that the association is positive as increasing x values lead to increasing y values.

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The analysis of the data in the table, which is a linear relationship between the pages Jake reads to the number of days is as  follows;

1. Please find attached the graph of the data in the table created with MS Excel

a. The variable x represents the number of days Jake reads the book

b. The variable y represents the number of pages Jake reads

c. The slope is the rate of change of the pages Jake reads to the number of days he has been reading the book

d. The slope is 27 pages per day

A linear relationship is a relationship that has a straight line graph when plotted on the coordinate plane.

1. The data in the table are presented as follows;

Days[tex]{}[/tex]             Pages Read

0[tex]{}[/tex]                   0

2[tex]{}[/tex]                   54

4[tex]{}[/tex]                   108

6[tex]{}[/tex]                   162

8[tex]{}[/tex]                   216

Please find attached the graph created with the above data in the table for the Days and the number of Pages Jake read, created with MS Excel.

a. The input variable is normally represented by x, while the output variable is normally represented by y.

The input variable, which is the variable that determines or indicates the number of pages Jake reads is the number of days, therefore;

The value of x represents the number of days

b. The output variable obtained from the input variable which is the number of days is the number of books Jake reads, therefore;

The output variable, y, represents the number of books Jake reads

c. The slope is the rate of change of the number of pages Jake reads per unit time. Therefore, the slope represents the number of pages Jake reads per day.

d. The graph of the data in the table indicates that the relationship is a straight line relationship,the slope can therefore be obtained using two points as follows;

Slope, m = (108 - 0)/(4 - 0) = 27

The slope of the line is 27 pages per day

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For making of 60 biscuits the quantity and packs of butter required by Helen is :

a. The exact amount of butter is 480 grams to make 60 biscuits.

b. Number of packs of butter Helen needs to buy is 2 packs.

Amount of sugar need to make 15 biscuits = 60 grams

Flour is three time of sugar to make 15 biscuits = 60 × 3

                                                                               = 180 grams

Amount of flour to make 60 biscuits = 180 × 4

                                                            = 720 grams

Butter is two times as sugar  to make 15 biscuits= 60 × 2

                                                                                = 120grams

a. Exact amount of butter to make 60 biscuits is:

Butter required to make 60 biscuits = 120 × 4

                                                            = 480 grams

b. One pack is of 250 grams

Number of packs of butter she need to buy = 480 / 250

                                                                         = 1,92

                                                                         ≈ 2packs

Therefore, the quantity of butter and number of packs of butter is given by :

a. The exact amount of butter required to make 60 biscuits is 480 grams.

b. The number of packs she needs to purchase is 2 packs.

The above question is incomplete, the complete question is :

Helen has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250g packs.

(i) What is the exact amount of butter she needs?

(ii) How many packs of butter will she have to buy?

Figure is attached.

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Answer:

rate = 7%

Step-by-step explanation:

From the question

Principal = $1,800

Time = 7 years

simple interest = $882

Rate = ?

rate = 100 × ST

P × T

rate = 100 × $882

$1,800 × 7

rate = $88200

12,600

rate = 7%

Answer:

72.8

Step-by-step explanation:

52*1.4=72.8

Answer: $70.80

Step-by-step explanation:

This is a two-step equation. First, you need to find what 40% of 52 is. You do this by multiplying 52 by 0.40. Then you would get the answer 20.8, but that isn't the final answer. Next, you add 52 and 20.8 together to get the final solution.