Answers
a) By definition of standard form, a light-year is equal to 5.880 × 10¹² miles.
b) By simple rule of three, a magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.
How to convert miles to light-years and viceversa
In this problem we need to convert a magnitude in miles to an equivalent magnitude in light-years and another magnitud in light-years to an equivalent magnitude in miles. Standard form is a notation used to represent both large and small number with no significant loss of precision. This form is described by the following form:
a.b × 10ⁿ
Where:
a - Whole number between 0 and 10.b - Significant decimalsn - Order of magnitudea) A light-year is equal to 5.880 × 10¹² miles.
b) The equivalent magnitude in miles is found by the following simple rule of three:
x = 4.25 ly × (5.880 × 10¹² mi / ly)
x = 2.499 × 10¹³ mi
A magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.
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Related Questions
If x and y vary directly and y is 24 when x is 6, find y when x is 9.
Answers
Y is 2.25 when x is 9.
What is direct proportional?The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolized by the proportional sign (). According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. The generic form of the direct proportion equation is also y = kx. where k is the proportionality constant.
Given Data
If x and y vary directly and y is 24 when x is 6, find y when x is 9.
It is direct proportional
So,
y = kx
To find constant,
k = [tex]\frac{y}{x}[/tex]
x = 6 and y = 24
k = [tex]\frac{6}{24}[/tex]
k = [tex]\frac{1}{4}[/tex]
When x = 9,
k = [tex]\frac{1}{4}[/tex]
y = kx
y = [tex]\frac{1}{4}[/tex](9)
y = [tex]\frac{9}{4}[/tex]
y = 2.25
Y is 2.25 when x is 9.
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Which of the following is an arithmetic sequence?
A) 3, -3, 4, -4, 5, -5
B)1, 2, 4, 7, 10
C) 4, 7, 10, 13, 16
D)2, 4, 8, 16, 32
Answers
Answer:
The answer is C
Step-by-step explanation:
The increase between the numbers in a arithmetic sequence is always the same, in this case the number always increased by 3.
Here is a another example
3, 5, 7, 9
The difference between the consecutive terms is always 2
99 is what percent of 150 please help?
Answers
Answer:
66%
Step-by-step explanation:
99 of 150 is 66%
and 150 of 99 is 151%
What does the standard deviation measure?
Answers
The spread and consistency of data.
Which of the options below has a negative value?
Select all that apply.
A) - (-1/2)
B) - (-8)
C) - 7.5
D) -2/3
E) - 1.25
Answers
Answer: C, D, E
Step-by-step explanation:
A negative multiplied by a negative is a positive. In option A, for example, a one is implied in front of the first negative sign, thus: -1 * (-1/2) = 1/2. The same goes for option B, leaving C, D, and E as the only negative values.
a nursery decides to make a grass-seed blend by mixing rye seed that sells for $6.50 per pound with bluegrass seed that sells for $3.50 per pound. the final mix is 180 pounds and sells for $5.33 per pound. how much of each type was used?
Answers
The amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respective.
What exactly is the substitution method?The substitution method is an algebraic approach to solving simultaneous linear equations.As the name implies, the value with one variable from one equation is replaced in the other equation.In response to the given question;
Let's say the amount of rye seed is 'x.'
The cost of rye seed = $6.50 per pound
Let's say the amount of bluegrass seed is 'y.'
The cost of bluegrass seed = $3.50 per pound.
The total seeds are 180 pounds.
Thus,
x + y = 180
x = 180 - y .......eq 1.
The other equation for the total cost of $5.33 per pound is;
6.50x + 3.50y = 5.33×180
Put the value of x from eq 1.
6.50(180 - y) + 3.50y = 959.4
1170 - 6.50y + 3.50y = 959.4
3y = 210.6
y = 70.2
x = 180 - 70.2 = 109.8
Thus, the amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respectively.
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Sheila is a manager at the Adam's Mark hotel and has a yearly salary of $65,500. If Sheila pays
21% in taxes and gets paid on the 15th and last day of the month, how much is each paycheck?
Show your work.
Answers
Answer:
$2139.58
Step-by-step explanation:
First, you find how much each paycheck is worth with taxes excluded, since she is only keeping 79% of the money you multiply 65,000 by 0.79=51350. Since she is getting paid twice a month, she is getting 24 paychecks a year. So you diving 51350 by 24 to get 2139.58333 but round down to 2139.58
ANSWER ASAP
Select the correct answer from each drop-down menu.
Answers
Considering the concepts of the diameter and the radius of a circle, it is found that the correct statement is:
The ratio of the lengths of EF and AD is 2:1.
What are the diameter and the radius of a circle?The radius of a circle is given by the length of the line segment from the center of the circle towards an edge of the circle.The diameter of a circle is given by the length of the segment between two opposite edges of the circle, passing through the center, hence it is twice the radius.In the context of the circle given in this problem, we have that:
The center is of A.The radius is of AD.The diameter is of EF.hence:
EF = 2AD, meaning that the ratio is of 2:1.
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1
The equation of the line containing the points (1, 3) and (-1,2) is:
A y = 2x + 1
1 7
x+
2 2
-
By=
1 5
©y = ²√2² +²2²
Dy=-2x+5
Answers
The equation of the line containing the points (1, 3) and (-1,2) is [tex]y = \frac{1}{2}x + \frac{5}{2}[/tex].
So, Option(c) is the correct one.
What is the Equation of a Line?The slope of the line and a point on the line can be used to create the equation for a line. The slope of a line is the angle that the line creates with the positive x-axis and can be written as a numeric integer, fraction, or as tangent of that angle. The coordinate point with the x and y values is referred to as the point.Given points are (1, 3) and (-1,2).
The slope of the given line is = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
= [tex]\frac{2 - 3}{-1 -1}[/tex]
= [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
The equation of the line is given by,
y - y₁ = m(x - x₁)
[tex]y - 3 = \frac{1}{2} (x - 1)[/tex]
[tex]y = \frac{1}{2}x - \frac{1}{2}+3[/tex]
[tex]y = \frac{1}{2}x + \frac{5}{2}[/tex]
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Is my friend correct or incorrect
Answers
Answer:Your friend is incorrect
x=-2
Step-by-step explanation:
Add 6 to both sides
-6+2x=-10
+6 +6
2x=-4
Then divide each side
2x/2=-4/2
x=-2
explain how you solved for x in problem 12
btw x=2
Answers
The answer is x=2.
How to find the x?
[tex](6^{x}) ^{10} =(6^{12} )^{2} /6^{4}[/tex]
[tex]6^{10x} =(6^{12}) ^{2} -6^{4}[/tex]
10x=24-4
10x=20
x=20/10
x=2
A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. The way to express huge numbers in terms of powers is to multiply them by themselves n times, or mn, if m is a positive number and n is its exponent. An exponent is a sign that is printed above and to the right of a mathematical expression to indicate the action of raising to a power. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. This might be the number 64. In this case, the exponent is 4 and the base is 6.To more learn about exponents refers to:
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Write an equivalent expression for 10 6 power divided by 10 4 power
Answers
The equivalent expression for 10⁶ / 10⁴ will be equal to 10²
Given,
Exponents: 10⁶ and 10⁴
We have to find an equivalent expression for 10⁶ / 10⁴
Equivalent expression:
In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are plugged into the formula.
Here,
aˣ / aⁿ = x - n
So,
10⁶ / 10⁴ = 6 - 4 = 2
That is,
The equivalent expression for 10⁶ / 10⁴ will be equal to 10²
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please help asap for maatth
Answers
Answer:
B
Step-by-step explanation:
Reflection over x axis
This is a reflection over the x-axis (B)
find c for this equation!
ab + c = d
Answers
Answer:
c=d-ab
Step-by-step explanation:
ab+c=d
move over to the other side
change sides change signs
c=d-ab
Answer:
c=d−ab
Subtract ab from both sides of the equation
7.
4
-2698
13
=m/4 =26/13
Answers
The value of m is 104/13
What is Fraction?
A fraction, which also symbolizes a piece of a whole, is a mathematical symbol for any number of equal parts. When expressed in common English, a fraction, such as 1/2, 8/5, or 3/4, represents the number of components of a specific size.
The value of m must be determined.
As can be seen in light of the query
The formula is m/4 = 26 / 13
The equation will now be solved for m m/4 = 26 / 13
The result of multiplying 4 on both sides is
(m/4) x 4 = (26/13) x 4
m = (26 x 4)/13
m = 104/13.
Consequently, m has a value of 104/13.
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Kristen has 4 yard of ribbon that she wants to cut into 6 equal parts to make hair ribbons for her
daughter's 6 dolls. How long will each doll's hair ribbon be?
Answers
Each ribbon will be of 2/3 yards for her 6 dolls .
What is division ?Division is one of the four fundamental arithmetic operations, or the process by which two numbers may be joined to produce a new number. Addition, subtraction, and multiplication make up the remaining operations. A division in mathematics is the dividing of a sum into equal portions. One can divide a group of 20 people into four groups of five, five groups of four, and so on.
Calculationlength of each ribbon = 4 / 6 = 2/3 yards each
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pls help with these i need them quick
Answers
1. The transformation is: A. rotation 90° clockwise about the origin.
2. Based on the alternate exterior angles theorem, the value of x is: 2.
3. x = 10
4. The slope of the given line is: A. 2
How to Find the Slope of a Line?The slope of a line = change in y/change in x.
What is the Alternate Exterior Angles Theorem?The theorem states that alternate exterior angles are congruent if they each lie on lines that are parallel to each other.
1. The transformation that took UVWX to U'V'W'X' is: A. rotation 90° clockwise about the origin.
2. 26x - 2 = 50 [based on the alternate exterior angles theorem]
Solve for x
26x = 50 + 2
26x = 52
x = 52/26
x = 2
The value of x is: D. 2.
3. 9x + 15 + 6x + 15 = 180 [based on the same-side interior angles theorem]
Solve for x
15x + 30 = 180
15x = 180 - 30
15x = 150
x = 150/15
x = 10
The value of x is: C. 10
4. Using two points on the line, (1, 1) and (-1, -3), we have:
Slope of the line = (-3 - 1)/(-1 - 1) = -4/-2
Slope of the line = 2
The slope is: A. 2
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Select three names for the angle.
Answers
Answer:
Step-by-step explanation:
Here, what they're really saying is to find 3 different ways to rearrange the letters A, B, and C. Then, put them together to give the angle a combination of "names"
(1 ABC
(2 BAC
(3 CAB
Hope this helps! :D
Please help first person will get all the brainliest
Which equation does not represent a direct variation? *
O y = -x
O y = 3x + 2
O y=-3x
O y = 0.5x
Answers
y = -x equation does not represent a direct variation.
y = 3x + 2
y=-3x
y = 0.5x
equations are represent a direct variation
How can you tell if there is a direct variation?
Simply build ratios from a table of values if you have one and wish to determine whether the data indicate a direct variation. You have a straight variation if all the ratios are the same.
The constant of variation is k = = 3, for instance, if y varies straight as x and y = 6 when x = 2. So, y = 3x serves as the equation to describe this direct variation.
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Which system of inequalities is graphed below?
Answers
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. The system of inequalities graphed is y > x² - 4 and y < x² + 6.
What is meant by system of inequalities?A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are used.
A system of inequalities is one where the total number of inequalities is greater than or equal to the number of variables.
A system of inequalities may have,
Zero solutionOne solutionInfinite solutionThe equation of the vertical parabola with y-intercept -4 is equal to
y = x² - 4.
The solution of the inequality is the shaded area above the dashed line.
The inequality must be y > x² - 4
2) The equation of the vertical parabola with y-intercept 6 is equal to y = x² + 6.
The solution of the inequality exists the shaded area below the dashed line. The inequality must be y < x² + 6
The system of inequalities graphed is
y > x² - 4
y < x² + 6
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Write 360 as a product of primes.
Use index notation when giving your
answer
Answers
Answer:
2³ * 3² * 5
Step-by-step explanation:
Prime factorize 360 and find how many times each number is repeated and write in index notation.
360 = 36 * 10
= 6 * 6 * 2 * 5
= 2 * 3 * 2 * 3 * 2 * 5
= 2 * 2 * 2 * 3 * 3 * 5
= 2³ * 3² * 5
i could use the help thanks
Answers
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
19
Step-by-step explanation:
Answer:
9d :)
Step-by-step explanation:
So, we have the equation 5c + 9d - 5c
We combine our like terms which are 5c and -5c bc they both have the variable "c"
When we do 5c + -5c we get 0 since were adding a negative and a positive. This leaves us with just 9d, therefore, that's your answer!
Find the equation of the line through the point -7, 2 and parallel to y=2/5x-1/2
Y=
Answers
IT MEANS THE GRADIENT OF THE NEW EQUATION IS GOING TO BE
[tex] \frac{2}{5} [/tex]
TOO
WE CAN SUBSTITUTE IN THE GENERAL EQUATION OF A STRAIGHT LINE y=mx+c TO GET C[tex]2 = \frac{2}{5} ( - 7) + c \\ 2 = \frac{ - 14}{5} + c \\ c = 2 + \frac{14}{5} \\ c = \frac{24}{5} [/tex]
THE EQUATION PARALLEL TO THE ONE GIVEN NOW IS
[tex]y = \frac{2}{5} x + \frac{24}{5} [/tex]
billy had 15 apples. His mom took 2 and his dad took 5 for his cooking. How many apples does he have
Answers
Answer:
8
Step-by-step explanation:
Billy started with 15 apples.
Lost 2, and another 5, In total 7 apples were taken.
" Lost " Indicates subtraction.
The equation would look like this: 15 - 7.
Subtract.
Hence, your answer should be 8.
Hopes this helps!
Have a good day :).
Answer: 8
Step-by-step explanation: 15 - 2 = 13 and 13 - 5 = 8.
On a certain hot summer's day, 435 people used the public swimming pool. The daily prices are 1.25 for children and 2.00 for adults. The receipts for admission totaled 818.25 How many children and how many adults swam at the public pool that day?
Answers
The number of children and the number of adults that swam in the swimming pool that day are 69 and 366 respectively.
Given that:-
Total number of people that swam in the swimming pool = 435
Price for children = 1.25
Price for adults = 2
Total receipts = 818.25
We have to find the number of children and the number of adults that swam in the swimming pool that day.
Let the number of children that swam that day be x and,
the number of adults that swam that day be y.
Hence, we can write,
1.25x + 2y = 818.25 ...(1)
x + y = 435 ... (2)
Solving the linear equation in two variable by elimination method
Multiplying (2) by 2 , we get
2x + 2y = 870 ... (3)
(3) - (1)
0.75x = 870 - 818.25
0.75x = 51.75
x = 51.75/0.75
x = 69
From (2), we can write,
69 + y = 435
y = 435 - 69
y= 366
Hence, the number of children and the number of adults that swam that day are 69 and 366 respectively.
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A basketball player attempts 15 baskets in a game. He makes 9 out of the attempted baskets.
Which describes the number of the baskets the player made to the number of baskets the player attempted?
Answers
Answer: 3:5
Step-by-step explanation:
We are looking for the ratio of baskets made to baskets attempted
made: attempted
9:15
We can divide each number by 3
9/3: 15/3
3:5
The ratio of baskets made: attempted is 3:5
Given the functions f(x) = 3x - 1 and g(x) = 3x + 4, which operation results in the smallest coefficient on the x term?
Answers
The operation of Subtraction can be used to result in the smallest co-efficient term on the x term.
In the given question, Two functions are given f(x) = 3x - 1, and g(x) = 3x + 4. Now we have to find out which mathematical operation results in the smallest co-efficient term on x. We know that the basic Operations are:
AdditionSubtractionMultiplicationDivision=> Now, we use the operation of Subtraction for the two functions. Which can be calculated by: f(x) - g(x), Calculating we get:
=> (3x - 1) - (3x - 4)
=> 3x -1 -3x + 4
=> 3
Here we get the Coefficient of x = 0 which is the lowest.
Hence, Subtraction will be used
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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
32
Step-by-step explanation:
this expression cannot be simplified because there are no like terms to combine with the numbers in the expression.
the number that goes in the ? is 32
Please help me
I need this at least in 5 hours
Answers
The area of the parallelogram based on the given parameters is 0.0324 m²
The total cost of Lilian's apple if a pound cost $1.77 is $2.3364.Ethan is more correct because he moved the decimal point 4 places to the left.The total mass of the green rope given the length and weight is 3.146 kgThe product of 0.102 × 7.3 is 0.7446Area of a parallelogramHeight = 0.09mBase = 0.36 mArea of the parallelogram = Base × height
= 0.36 m × 0.09m
= 0.0324 m²
Cost of each pound of apple = $1.77Weight of Lilian's apple = 1.32 lbTotal cost of Lilian's apple = Cost of each pound of apple × Weight of Lilian's apple
= $1.77 × 1.32 lb
= $2.3364
Ethan:
3.045 × 1.3
= 3.9585
Anica:
3.045 × 1.3
= 39.585
Ethan is more correct because he moved the decimal point 4 places to the left.
Length of the green rope = 60.5 mMass of each meter of the rope = 0.052 kgTotal mass of the green rope = Length of the green rope × Mass of each meter of the rope
= 60.5 × 0.052
= 3.146 kg
0.102 × 7.3
= 0.7446
Therefore, the area of the parallelogram when calculated is 0.0324 m²
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