"the time since dinosaurs became extinct is roughly equal to _____ average human lifespans"

average human lifespan: 2.4 x 10^4
time since dinosaurs became extinct: 2.4 x 10^10

Answer:

A,D,E

Step-by-step explanation:

A:

14/4 = 3.5

D:

7/2 = 3.5

E: 14/4 = 3.5

The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.

To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.

Now, we need to find the relationships that have the same constant of proportionality.

For example, if we have a table with the following values:

x1 y1

x2 y2

x3 y3

and the constant of proportionality is k, then we have the following equations:

x1/ y1 = k

x2/ y2 = k

x3/ y3 = k

So, any other table that satisfies these equations will have the same constant of proportionality as the given table.

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The value of x and z are x° = 6.71°, z° = 75.26° simulataneously,

What is the linear pair angles?

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

We have,

Angles:

6x° + 35°

z°

8x° + 51°

To find the values of x and z

from the given figure

Linear pair angles:

6x° + 35° + 8x° + 51° = 180

14x° + 86° = 180

14x° = 180° - 86°

14x° = 94°

x° = 94°/14°

x° = 6.71°

Vertically opposites angles are equal

6x° + 35° = z°

z° =  6( 6.71°)° + 35

z° = 40.26 + 35

z° = 75.26°

Hence, the value of x and z are x° = 6.71°, z° = 75.26° simulataneously.

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Answer:

80 kg

Step-by-step explanation:

To find the mass of the skater, you can use the formula for centripetal force:

F_centripetal = m * v^2 / r

Where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.

Plugging in the values you know, you get:

720 N = m * (15 m/s)^2 / 25 m

Solving for m, you find that the mass of the skater is:

m = 720 N * 25 m / (15 m/s)^2

= 720 N * 25 m / 225 m^2/s^2

= 80 kg

So the mass of the skater is approximately 80 kilograms.

If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.

What is bisector of an angle?

In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..

Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.

Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.

AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.

Consider △ABD and △DBC:

∠ABD = ∠DBC

∠ADB = ∠BDC

Therefore, △ABD ≅ △DBC

According to CPCT, AD ≅ CD.

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The equivalent expression could be 4×3·4×4−s

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.

Let's now have a look at some expressions with variables, such 5x+2.

It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.

The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.

When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.

Here, 4×3=12 and 4×4=16

therefore, 4×3·4×4−s is equal to the expression 12⋅16−s

4×3·4×4−s and 12⋅16−s  are equivalent expressions.

Hence, The equivalent expression could be 4×3·4×4−s

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The equivalent expression could be 4×3·4×4−s.

Here, 4×3=12 and 4×4=16

therefore, 4×3·4×4−s is equal to the expression 12⋅16−s

4×3·4×4−s and 12⋅16−s  are equivalent expressions.

Hence, The equivalent expression could be 4×3·4×4−s

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Answer:

0.043

Step-by-step explanation:

I hope this helps you! Let me know if you have any questions! :)

The proportions for this problem are given as follows:

a) Took echinacea: 0.27.

b) Having a cold in the last 30 days, of those who took Vitamin C: 0.2679.

c) Took zinc, of those having a cold: 0.1923.

The proportions are calculated as the division of the number of desired outcomes by the number of total outcomes.

The survey is composed by 100 adults, and of those, 27 took echinacea, hence the proportion is of:

27/100 = 0.27.

56 adults took vitamin C, and of those, 15 reported a cold in the last 30 days, hence the proportion is of:

15/56 = 0.2679.

26 students had a cold in the last 30 days, and of those, 5 took zinc, hence the proportion is calculated as follows:

5/26 = 0.1923.

The table is given by the image shown at the end of the answer.

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So, it will take the rider 5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.

The circumference of the ferris wheel is equal to the diameter times pi, or 50*pi=157.08 ft. Since the ferris wheel makes one revolution every 40 seconds, the speed of the ferris wheel is 157.08/40=3.92 ft/sec.

Since the rider starts at a height of 30 ft above the ground and ends up 50 ft above the ground, the total change in height is 50-30=20 ft. Since the speed of the ferris wheel is 3.92 ft/sec, it will take the rider 20/3.92=5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.

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Answer:

81

Step-by-step explanation:

y = -9

y² = (-9)² = 81

The number which can be raised by 3 to give the value of 11 is 2.224.

The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

Given:

The exponent to which 3 must be raised to obtain 11,

Assume the number is x then, According to the statement,

x³ = 11

x  = ∛11

x = 2.224

Thus, the number is 2.224.

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Answer: 1

Yessssssssssssssss

The value of baseball card has increased by 160(%) percentage.

What is the percentage?

A number or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word per cent means. The letter "%" stands for it.

Increase = New Number - Original Number

Then: we divide the increased number by the original number and multiply by 100.

Therefore, % increase = (Increase ÷ Original Number)× 100.

Given, the new price of a baseball card = $13

The original price of a baseball card = $5

Then from the above definition,

Increase = 13-5 = 8

% increase = (8/5)*100 = 160%

Hence, its value has increased by 160 percentage.

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Explanation:

x = amount she travels on each of those three remaining days

3x = total amount traveled over those three remaining days

3x+24 = total amount traveled over the four days

3x+24 = 120 miles total

This equation is in the form px+q = r where:

Let's solve for x. We follow PEMDAS in reverse to undo what's happening to x, so we can isolate it.

3x+24 = 120

3x+24-24 = 120-24 .... subtract 24 from both sides

3x = 96

3x/3 = 96/3 .... divide both sides by 3

x = 32

Triana must travel 32 miles per day for those remaining three days.

Doing so means she travels 3x = 3*32 = 96 miles over those three remaining days. Then add on those 24 miles traveled on the first day to get 96+24 = 120 miles total. This helps confirm the answer.

Another way to confirm the answer is to plug x = 32 into 3x+24 = 120. After simplifying both sides, you should get 120 = 120 which is a true statement.

The total number of books completed by 2:45 pm will be 42.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that when the librarian starts downloading new books at 11:00 am, there are 15 already loaded. When she checks at noon, there are 25 books completely loaded.

The number of books loaded in 1 hour is calculated as,

N = 25 - 15

N = 10 books

Now from 12 noon to 2:45 pm, the time in hours will be,

T = 165 minutes or 165 / 60 = 2.75 hours

The equation for the number of books loaded will be written as,

y = 15 + 10T

y = 15 + ( 10 x 2.75)

y = 15 + 27.5

y = 42.5 or 42

The completely loaded books are 42 in number.

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The remainder of polynomial g(x) divides (x - 3) that is  g(x) / (x - 3) is 0.

What is polynomial?

A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.

Given: g(x) = 2x^3 + 5x^2 - 28x - 15

(x - 3) is a factor of g(x).

We have to find the remainder of g(x) / (x - 3).

Consider,

                 2x^2 + 11x + 5

         [tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]

          -    2x^3 -6x^2

____________________________

                      11x^2 - 28x

               -      11x^2 - 33x

____________________________

                               5x - 15

                          -    5x - 15

_______________________________

                                      0

Hence, the remainder of polynomial g(x) divides (x - 3) that is

g(x) / (x - 3) is 0.

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Answer:

41° and 49°

Step-by-step explanation:

Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:

2x + 8 = 90

Solving for x, we get:

2x = 82

 x = 41

Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.

Therefore, the two angles have measures of 41 and 49 degrees.

A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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Answer: (6, -1)

Step-by-step explanation:

<3

Sample is biased. Based on her findings, Arianna revealed the percentage in her state after polling 600 residents of her city. Thus, the sample fails to accurately reflect the population. Option (4) is correct.

When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. What makes sampling bias significant? Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population. When some population members have a higher or lower sampling probability than others, the sample is biased.

This includes choosing or sampling people according to their hobbies, gender, or age. Therefore, a fair or impartial sample must be representative of the entire population under investigation. When a research study design fails to gather a representative sample of a target population, the phenomenon known as sampling bias takes place. This usually happens as a result of the respondents' selection criteria not capturing a broad enough sampling frame to include all points of view.

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Correct Question:

Arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. Based on the results, she reports that 44% of the people in her state bike to work. Why is this statistic misleading?

Select the correct answer below:

1. The statistic contains a calculation error.

2. The sample is self-selected.

3. The data contains an outlier.

4. The sample is biased.

The matrix that can be multiplied to the left of a vector matrix to produce another vector matrix given as follows:

A. [2;5].

A matrix is also called a vector matrix when it has either only one row or only one column.

In multiplication of matrices, the rows of the left matrix are multiplied by the columns of the right matrix, and the dimensions are given as follows:

The matrix in this problem that we are going to multiply is the right matrix, meaning that we want a matrix with one column, and more than one row, which is given by option A.

(a matrix with only one element, as is the case for option D, is not considered a vector matrix).

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C (5,24) ordered pair represents the ratio that is not equivalent to the others.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Consider first pair A, the ratio is given  by

2/12 = 1/6

Consider next pair B, the ratio is given  by

3/18 = 1/6

Consider next pair C, the ratio is given  by

5/24 is not equat to 1/6

Consider next pair D, the ratio is given  by

6/36 = 1/6

Hence, the ordered pair represents a ratio that is not equivalent to the others is C (5,24).

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The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }

What is Domain of function?

A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.

According to question

⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]

⇒ x² + y² - 1 ≥ 0

 ⇒ x² + y² ≥ 1

Hence, the Domain of f(x, y) is  { (x, y) ∈ R² | x² + y² ≥ 1 }

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Answer: ( -56 - 45t ) / 72t

Step-by-step explanation:

attached a picture for explaination.

hope that helps...

Answer:

Step-by-step explanation:

Dallas = 1 x 10^6

Los Angeles = 3 times Dallas = 3 [ 1 x 10^6] = 3 x 10^6

Pittsburgh / Dallas = [ 3 x 10^5 ] / [ 1 x 10^6] = 3 / 10 that of Dallas

The expression which represents the correctly rewritten form of the given expression; 20x⁴y³ - 30x³y⁴ is; 5x³y³ ( 4x - 6y ).

It follows from the task content that the expression which correctly represents the rewritten form of the given expression be determined.

On this note, since the given expression is;

20x⁴y³ - 30x³y⁴

The greatest common factor of both terms in the expression is; 10x³y³ .

On this note, the expression can be factorised completely as follows;

10x³y³ ( 2x - 3y )

However, the expression which is equivalent to the expression above among the answer choices is;

5x³y³ ( 4x - 6y )

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The domain of the relation is {4,8} and the range of the relation is {n,q,m}.

A function or relation's domain is the set of all potential independent values that it can have.

Suppose that the relation S is defined as follows.

S= {(4,n), (8,q), (4,m)}

The first term at the point represents the input and the second term at the point represents the output.

So,

the input values are 4,8 and 4 and their respective outputs are n, q and m,

The collection of all conceivable independent values that a function or relation may take is known as its domain.

So, the domain is {4,8}.

The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.

So, the range is {n,q,m}

Therefore, the domain is {4,8} and the range is {n,q,m}.

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Answer:We may rewrite f(x) = (x-1)^2

We stretch by having 3(x-1)^2

We reflect about the y axis by changing x to -x:   3(-x-1)^2 = 3(x+1)^2

We  move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2

Step-by-step explanation:A way to verify this:  Consider y = x^2 to be the unit parabola.  f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1;  moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2

We may write g(x) = 3x^2 + 18x + 27, also.

Answer:

x = -1

Step-by-step explanation:

To solve this equation, you can use the process of polynomial algebra.

First, you can rearrange the terms on the left side of the equation so that all the terms with an x^2 coefficient are on one side and all the other terms are on the other side. You can do this by adding x^2 to both sides of the equation:

5x^2 - 2x - 6 + x^2 = -x^2 + 6x + x^2

This gives you:

6x^2 - 2x - 6 = 6x

Now, you can rearrange the terms on the right side of the equation in the same way:

6x^2 - 2x - 6 = 6x^2 - 6x

To solve for x, you can now use the process of polynomial algebra to combine like terms on each side of the equation. This gives you:

6x^2 - 2x - 6 = 6x^2 - 6x

Combining like terms on the left side of the equation gives you:

6x^2 - 6x - 6 = 6x^2 - 6x

Combining like terms on the right side of the equation gives you:

6x^2 - 6x - 6 = 6x^2 - 6x

Now, you can subtract 6x^2 - 6x from both sides of the equation to obtain:

-6x - 6 = 0

Dividing both sides of the equation by -6 gives you:

x + 1 = 0

Finally, you can solve for x by subtracting 1 from both sides of the equation, which gives you:

x = -1

Therefore, the solution to the original equation is x = -1.

The depth of the submarine after 8 minutes is -123.6 feet below sea level.

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,

Depth of the submarine after y minutes.

= -270 + 18.3y

The depth of the submarine after 8 minutes.

= -270 + 18.3 x 8

= -270 + 146.4

= -123.6

Thus,

The submarine is at -123.6 feet below sea level.

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