A googol is the number 1 followed by 100 zeros. Earths mass is 5.972 x 10 to the 24 power kilograms. How many earths are needed to have a total mass of 1 googol kilograms?

The triangle's conclusion is that the two triangles are equal because they are congruent.

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Answer:

Step-by-step explanation:

2a + 4b = 12c

4b = 12c - 2a

b = 3c - 1/2a

or

b = (6c - a)/2

A two-column method be that can used to prove that segment QR is parallel to segment PS is presented as follows;

Statement                      [tex]{}[/tex]                 Reasons

1. [tex]\overline{QP}[/tex] ≅ [tex]\overline{RS}[/tex]                                     1. Given

2. [tex]\overline{QP}[/tex] ║ [tex]\overline{RS}[/tex]   [tex]{}[/tex]                                 2. Given

3. ∠PRQ ≅ ∠RPS [tex]{}[/tex]                          3. Alt. int. angles theorem

∠QPR ≅ ∠PRS    [tex]{}[/tex]                      

4. ∠PRQ = ∠RPS        [tex]{}[/tex]                    4. Definition of congruency

∠QPR = ∠PRS

5. ∠QRS = ∠PRQ + ∠PRS [tex]{}[/tex]            5. Angle addition postulate

∠QPS = ∠QPR + ∠RPS

6. ∠PRQ + ∠PRS = ∠QPR + ∠RPS [tex]{}[/tex] 6. Substitution property

7. ∠QRP = ∠QPS   [tex]{}[/tex]                          7. Transitive property

8. [tex]\overline{PR}[/tex] ≅ [tex]\overline{PR}[/tex]             [tex]{}[/tex]  [tex]{}[/tex]                    8. Reflexive property

9. ΔQRP ≅ ΔSPR  [tex]{}[/tex]                        9. ASA congruency rule

10. ∠PQR ≅ ∠PSR  [tex]{}[/tex]                       10. CPCTC

11. ∠PQR = ∠PSR [tex]{}[/tex]                          11. Definition of congruency

12. QRSP is a parallelogram [tex]{}[/tex]       12. Parallelogram opp. int. ∠s theorem

13. [tex]\overline{QR}[/tex] ║ [tex]\overline{PS}[/tex]              [tex]{}[/tex]                   13. Properties of a parallelogram

A parallelogram is a quadrilateral that has opposite parallel sides.

The details of the reasons used to prove that the segment [tex]\overline{QR}[/tex] is parallel to segment [tex]\overline{PS}[/tex] are as follows;

Alt. int. angles theorem

The alternate interior angles theorem states that the alternate interior angles formed between two parallel lines and their common transversal are congruent

Definition of congruency

Two geometric figures are congruent if they have the same measurements.

Angle addition postulate

The angle addition postulate states that the measure of an angle ∠A, which is formed by two adjacent angles ∠B and ∠C, is the same as the sum of the measures of the two angles, ∠A = ∠B + ∠C

Substitution property

The substitution property of equality states that if a variable, a = another variable, b, a = b, then b can be plugged into expressions and equations to substitute for a and the values of the expressions and sides of equations remain the same.

Transitive property

The transitive property of equality states that if a = b, and b = c, then a = c

Reflexive property

The reflexive property of congruency states that a geometric figure is congruent to its self

ASA congruency rule

The Angle-Side-Angle congruency rule states that if two angles and the included side of one triangle are congruent to the two angles and included side of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent

Parallelogram opp. int. ∠s theorem

The parallelogram opposite interior angles theorem states that the opposite interior angles of a parallelogram are congruent.

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The required proof is completed by proving that triangle FCA and triangle DBE are congruent hence sides FA ≅ ED

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

In the problem, since FG can safely be extended to FC also EG to EB so that

FC ≅ EB this is one side of the triangle

Similarly, AB can be extended to AC and DC to DB such that

AC ≅ DB another side of the triangle

Given that < C ≅ < B the required sides for congruency by the SAS rule is completed and thus FA = ED

The SAS rule have it that when two sides and the included angle of angle of a triangle is equal to that of another triangle then all the sides and the angels are equal therefore they are congruent triangles

since ΔFCA ≅ ΔEBD the corresponding sides are equal to each other

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The length of line segment LB is equal by definition of bisector to 6 feet.

In this question we find a geometric system with two right triangles generated by bisector AL, that is, a side that divides line segment CL into two segments of equal length. Then, the length of line segment LB is equal to:

CL = LB

Where CL and LB are measured in feet.

If we know that CL = 6 ft, then the length of line segment LB is 6 feet.

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Answer:

the value of x is 1

Step-by-step explanation:

2x+3(4x-3)=8-3x

2x+12x-9=8-3x

2x+12x+3x=8+9

17x=17

17x/17=17/17.......... divide both side by 17 to get the value of x

x=1......so, the value of x is 1

The coordinates of P and Q are

PQ have equal slope with BC so they are parallel

The coordinates of P and Q is found using the midpoint formula

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

solving for P (X, Y) Using points A(2, -1), B(-3, 4)

(X, Y) = ((2 + -3)/2, (-1 + 4)/2)

= (-1/2, 3/2)

solving for Q (X, Y) points A(2, -1), C(-5,-7)

(X, Y) = ((2 + -5)/2, (-1 + -7)/2)

= (-3/2, -4)

Parallel lines have equal slopes

Using BC = (4 - -7) / (-3 - -5) = 11/2

Using PQ = (-4 - 3/2) / (-3/2 - -1/2) = (-11/2) / (-1) = 11/2

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The quotient of the given division is (x + 9).

What is synthetic division?

Synthetic division is a technique for performing manual Euclidean division of polynomials in algebra that requires less writing and calculation than long division. Although it is typically taught for division by monic linear polynomials, the technique can be applied to division by any polynomial.

Given:  x^2 - 81 / (x - 9)

We have to find the quotient for the given division.

We can find the quotient using synthetic division.

                       x + 9

                 [tex]\sqrt[x-9]{x^2-81}[/tex]

                 -    x^2 - 9x

              _______________

                            9x - 81

                       -    9x - 81

                 _____________

                                    0

Hence, the quotient of the given division is (x + 9).

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Perpendicular lines have slopes that are opposite signs and reciprocals.

Since the line y = -1/4x + 10 has a slope of -1/4, the slope of the perpendicular line will be + 4/1 or 4.  So any line with a slope of 4 will be perpendicular to  y = -1/4x + 10.

This means A and D will be your answers.

Answer:

-1

Step-by-step explanation:

This line is already in slope, intercept form of   y = mx + b   <===='b' is the y-axis intercept   =  -1

Answer:

Below

Step-by-step explanation:

e^(-kt) = 1/2     when t = 11.43

so  k = .060642797

e^ (- .060642797 * 1) = .9411  <====   is left after one year

             which means the decay in one year is

                  1 - .9411 = .05884 = 5.88% per year

The required circumference of the pool is given as 95.1 feet.

Perimeter is the measure of the figure on its circumference. where the circumference of the circle is given as 2πr.

Here,
The Linton family has a swimming pool as of the circular profile.
The radius of the circular swimming pool is 15 feet
π = 3.17

Now,
Circumference of the swimming pool is given as,
= 2πr

Substitute the value in the above formula,
Circumference of the swimming pool = 2 × 3.17 × 15
                                                         = 95.1 feet.

Thus, the circumference is 95.1 feet.

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Answer:

21°

Step-by-step explanation:

Answer: 0.4

Step-by-step explanation:

The question is asking for the probability to own a dog.

40% own a dog.

If you add all of the percentages you get 100%

40/100

=0.4

The probability is 0.4 times to randomly select a resident that only owns a dog.

Answer: (6,-6),(0,1) plot these 2 points

Step-by-step explanation:

The Range of the length of a rectangle having fixed width and area increasing linearly is  = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers,

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

The width of the rectangle is fixed, and the length is changing.

The line is formed when connected through the graph.

The area of the rectangle = [tex]length\times width[/tex]

So when the width is fixed, the area would increase linearly and directly proportional to length.

Calculate the range of function y = cx,

y = area as shown in the graph, x is the length, and width is constant c.

Range = {y ∈ R : c ≠ 0 or y ≠ 0}

Calculate the domain,

It can be any real number, as the area can't be negative.

Domain = All real numbers.

Therefore, Range = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers.

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Answer:

66mph i belive

Step-by-step explanation:

The probability that in tonight's game he misses for the first time on his 6th attempt = 0.2244

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The Probability that the basketball player made a foul shot = 0.66 or 60%

Then the probability of good shot is = 1-0.66

= 0.34

probability that in tonight's game he misses for the first time on his 6th attempt = (1-p) 5(p)

= ( 1- 0.34)⁵ (0.34)

= 0.2244

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Answer:

[tex]\huge\boxed{\sf y = \pm 13}[/tex]

Step-by-step explanation:

Given that,

y² = 169

Take sq. root on both sides

√y² = √169

So,

y = 13    OR    y = -13

[tex]\rule[225]{225}{2}[/tex]

Answer:

b) y = + 13

Step-by-step explanation:

Now we have to,

→ find the required value of y.

The problem is,

→ y² = 169

Let's solve the problem,

→ y² = 169

→ y = √(169)

→ [ y = + 13 ]

Hence, the answer is + 13.

Answer:

do you need help with anything if not hello

Step-by-step explanation:

If Two signs that scores are significantly different then (a) the error bars of group will not overlap

Error bars are graphical representations of data variability that are used to indicate the error or uncertainty in a reported measurement on graphs.

The estimated error in a measurement is indicated by error bars. In other words, an error bar represents the degree of uncertainty in a value.

When the standard deviation error bars overlap significantly, it is an indication that the difference is not statistically significant. To reach a conclusion, you must conduct a statistical test.

When the standard deviation error bars overlap even less, it indicates that the difference is unlikely to be statistically significant.

For significantly different group , we also have p-value greater than 0.05

So, Option (b) is incorrect.

Hence, (a) The error bars of the groups will not overlap is correct

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The formula is Y=kx.

the financial gain experienced when the income from a commercial activity is greater than the costs, taxes, and other costs associated with maintaining the activity in question.

When laying sod, the equation to determine sakeem's profit is Y= KX, where y represents profit, x is the number of square feet of sod, and k is a constant.

His supplier bills him $0.43 per square foot for sod when he builds a lawn.

For laying the sod, Sakeem's costs his clients $2.00 per square foot.

The amount of sod used to create a lawn directly affects how much money Sakeem's makes.

The profit will then be

Earnings = 2 - 0.43 ,Earnings = $1.57 per square foot

The formula is Y=KX.

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We know that Julian has $8.75 using mathematical operations.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.

The five basic operations in mathematics are addition, subtraction, multiplication, division, and modular forms.

So, we know that:

Juan has $3.50.

Julian has 2½ times Juan.

So, the money Julian has is:

First, calculate 2½:

2½

4+1/2

5/2

2.5 times

The money Julian has is:

3.50 * 2.5

$8.75

Therefore, we know that Julian has $8.75 using mathematical operations.

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The population after 5 years if the starting population is 3000 is 75,000.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The population after 5 years.

= n x 25

Where n is the starting population in thousands.

The expression can be considered as.

= nx²

Where x is the number of years.

Now,

n = 3000

The population after 5 years.

= 3000 x 25

= 75,000

Thus,

The population is 75,000.

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Answer: Sale price: $254.15 , Discount: $44.85

Step-by-step explanation:

15% off indicates that the stereo will now cost 85% of what it did originally:

$299(100% – 15%) = $299(85%)

Decimalizing the percentage results in = $299(0.85) = $254.15

Discount= $299 - $254.15 = 44.85

Answer:

12

Step-by-step explanation:

He is running 12

If according to the American Veterinary Medicine Association, 72% of households in Wyoming owned a pet in 2018. There were 278,595 households in Wyoming in 2018. The number of those households that owned a pet is:  200,588.

We would be making use of the given data to find the number of household that owned a pet.

Using this formula

Number of household with pet = Percentage of household × Number of household

Let plug in the formula

Number of household with pet = 72% × 278,595

Number of household with pet = 200,588 household

Therefore the Number of household with pet  is 200,588.

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The inequality model of given problem is |5x-4|≤80.

In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. In mathematics, an inequality depicts the connection between two non-equal values in an algebraic expression. Inequality signs can indicate that one of the two variables is larger than, greater than or equal to, less than, or less than or equal to another value. An inequality is a mathematical connection between two expressions that is represented by one of the following symbols:: "less than or equal to": "less than": "not equal to"

Here,

The provided problem's inequality model is |5x-4|≤80.

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The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times then the table 4 represents a linear function.

An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx + b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

The slope-intercept form of the equation for a linear function. As a result, it is written as f(x) = mx + b, where b is the line's y-intercept and m is the slope. Tables with a constant rate of change are represented by linear functions.

Table 4 represents a linear function

From the given tables, only table 4 represent a linear function.

As x's values change by 1, the matching y's values change by 5. This is why.

The table exists represented as:

x     y

1     -5

2     0

3     5

4     10

Therefore, table 4 represents a linear function.

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