Using the median concept, it is found that the statement is true.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, we have that the 50th percentile is of 33.2 hours, hence the 54th percentile has to be above 33.2 hours = above 31 hours, hence the statement is true.
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Pls help! Geometry!
How long is the other side?
Answer: 18 feet
Step-by-step explanation:
The area of a rectangle is given by [tex]A=lw[/tex], which means that the length of the unknown side is [tex]\frac{216}{12}=18[/tex] feet.
You are one of 16 finalists on a game show.
One finalist is randomly selected to answer
a trivia question for a prize. What is the
probability that you will be selected?
Write your answer as a percent.
If one finalist is randomly selected for a prize then the probability that person will be selected is 6.25%.
Given A person is one of 16 finalists and one finalist is randomly selected for a prize.
Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability is number of events possible/total outcomes.
The value of probability lies between 0 and 1. It cannot be negative because there might be chances of something and sometimes not so the value be 0.
Total finalists=16
Probability=1/16
When we convert it in percentage it will be 1*100/16
=6.25%
Hence the probability that person will be selected is 6.25%.
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Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.
The center of mass is mathematically given as
[tex]\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]
What is the center of mass.?Determine the center of mass in one dimension:
Represent the masses at the respective distances.
[tex]\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end[/tex]
We calculate the total mass of the system.
[tex]\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}[/tex]
Step 03: Calculate the moment of the system.
[tex]\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}[/tex]
we calculate the center of mass.
[tex]\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]
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Can someone please help me
Answer:
Vertex form: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]
Standard Form: [tex]y=0.50x^2-2x-1[/tex]
Step-by-step explanation:
Well the vertex form of an equation is given in the form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you: [tex]y=a(x-2)^2-3[/tex]. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in
Plug in (0, -1) as (x, y)
[tex]-1 = a(0-2)^2-3[/tex]
calculate inside the parenthesis
[tex]-1 = a(-2)^2-3[/tex]
square the -2
[tex]-1 = 4a-3[/tex]
Add 3 to both 3 to both sides
[tex]2 = 4a[/tex]
divide both sides by 4
[tex]a=\frac{1}{2}[/tex]
This gives you the equation: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]
To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to: [tex](a+b)^2=a^2+2ab+b^2[/tex].
Original equation:
[tex]y=\frac{1}{2}(x-2)^2-3[/tex]
expand square binomial:
[tex]y=\frac{1}{2}(x^2-4x+4)^2-3[/tex]
Distribute the 1/2
[tex]y=0.50x^2-2x+2-3[/tex]
Combine like terms:
[tex]y=0.50x^2-2x-1[/tex]
How many terms of the G.P 3 , 3/2,3/4 are needed to give the Sum 3069 /512
Answer: 10
Step-by-step explanation:
The first term is 3 and the common ratio is 1/2.
Using the sum of a geometric series formula,
[tex]\frac{3069}{512}=\frac{3(1-(1/2)^{n}}{1-(1/2)}\\\\\frac{3069}{1024}=3(1-(1/2)^{n})\\\\\frac{1023}{1024}=1-(1/2)^{n}\\\\-(1/2)^{n}=-\frac{1}{1024}\\\\(1/2)^n=\frac{1}[1024}\\\\2^{-n}=2^{-10}\\\\n=10[/tex]
The scale of a map says that 4 çm represents 5 km.
What distance on the map (in centimeters) represents an actual distance of 4
kilometers?
Answer:
Distance on the map (in centimeters) represents an actual distance of 4 kilometers is 3,2 cm.
Step-by-step explanation:
The scale of a map = 4 cm : 5 km
The scale of a map = 4 : 500.000
So, 0,000008 times the actual distance is the distance on the map.
0,000008 × 400.000 = 3,2 cm
A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders and randomly assigns each second grader to participate in the reading intervention program or not participate in the program. The researcher knows that the standard deviation of the reading comprehension scores among all second graders is σ = 25.24.
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8. Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.
Of the plots that follow, which best represents a plot of these results?
The brackets or error bars shown at the top of each bar extend _______ above and below each of the group means. For group 1, the error bar extends _______units above and below the mean for group 1.
The brackets or error bars shown at the top of each bar extend one standard error above and below each of the group means. For group 1, the error bar extends 3.9 units above and below the mean for group 1.
A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8.
Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.
Error bar, are the line through a point on a graph,axes, which emphasizes the uncertainty or variation of the corresponding coordinate of the point.
We have the data,
σ = 25.24, n₁ = 52 M₁ = 36.8.
n₂ = 56 M₂ = 52.4.
Error bar = M2-M1/n2-n1
= (52.4-36.8)/(56-52)
= 3.9
Thus, the required value that will be put in black space is 3.9
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Fthis other one but this is cheesing hard
A is zero
B) D
C) x= - 1 & x= 4
Hope this helps!
Solve: 4x−1>7 or 5x−1<−6
Answer and Explanation:
First, solve for x in both inequalities:
4x − 1 > 7 5x − 1 < −6
4x > 8 5x < −5
x > 2 x < −1
Because this is an OR problem, determine if there is any overlap. (See the attached image for details.) There is not, so the answer is no solution or Ø.
Find the angle [OA] makes with the positive x-axis if the x-coordinate of the point A on the unit circle is 0.222
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
How to find an angle in an unit circle
Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:
[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]
tan θ ≈ 77.173°
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
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The radius of a circle is 17 inches. What is the circumference? Round your
answer to the nearest tenth.
OA. 106.8 inches
OB. 907.9 inches
OC. 53.4 inches
OD. 289 inches
Answer: A
Step-by-step explanation:
[tex]C=2\pi r=2(\pi)(17) \approx 106.8[/tex]
LC)A polygon is shown:
A polygon MNOPQR is shown. The top vertex on the left is labeled M, and rest of the vertices are labeled clockwise starting from the top left vertex labeled, M. The side MN is parallel to side QR. The side MR is parallel to side PQ. The side MN is labeled as 5 units. The side QR is labeled as 7 units. The side MR is labeled as 3 units, and the side NO is labeled as 2 units.
The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)
The area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
How to determine the area of the rectangleFrom the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ
With a perpendicular line drawn from point O on the side RQ, which intersects with line RQ at point S.
We can then divide the polygon into two different rectangles
MNSR with A₁ as its area
OPQS with A₂ as its area
For rectangle MNSR, line MN is 5 units and line MR is 3 units
The formula for area of a rectangle is given as;
A₁ = (length)×(width)
Substitute the values
A₁ = 5 × 3
A₁ = 15 square units
For rectangle MNSR, line MN= line RS and line MR = line NS,
We have RS= 5 units and NS= 3 units
So, line SQ= RQ- RS = 7-5 = 2 units
Also, OS= NS - NO = 3- 2 = 1 unit
Let's substitute the values
A₂ = 2 × 1
A₂ = 2 square units
Therefore, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
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which number would be equivalent to the expression: 3 times 4 to the second power plus 6 divided by 2
The given expression is equivalent to the number 147.
We have given that,
[tex](3\times4)^2+\frac{6}{2}[/tex]
We have to determine the value of the given expression.
What is the expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
[tex]=(12)^2+\frac{6}{2} \\=144+3\\=147[/tex]
Therefore the given expression is equivalent to the number 147.
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You are in charge of planning a reunion party for your high school alumni. The food will cost $12 per person. The rental fee for the room is $650. The entertainment fee is $730. Other miscellaneous expenses costs $1,000. If 120 alumni are expected to come then what will be the total cost? How much must each alumnus contribute to cover the cost of the reunion (round to the nearest whole number)?
Answer:
$3820 total, $32 per alumnus.
Step-by-step explanation:
The total cost will be [tex]12\times120+650+730+1000=3820[/tex]
Each alumnus pays [tex]\frac{3820}{120} =31\frac{5}{6}[/tex]
Rounding to nearest whole number = $32 per alumnus.
Factor completely.
Y^2-12y+32
A. (y+4)(y+8)
B. (y-4)(y-8)
C. (y+18)(y + 2)
D. (y-18)(y-2)
Answer:
B
Step-by-step explanation:
y² - 12y + 32
consider the product of factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)
the factors are - 4 and - 8 , since
- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then
y² - 12y + 32 = (y - 4)(y - 8)
Answer:
B. (y-4)(y-8)
Step-by-step explanation:
Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.
1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.
They are: -8 and -4.
2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.
y² - 8y - 4y +32
y(y - 8) - 4(y - 8)
(y - 4)(y -8)
What additional information would allow you to prove the quadrilateral is a parallelogram?
The additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ
How to prove a Parallelogram?The six basic properties of parallelograms are primarily;
Both pairs of opposite sides are parallelBoth pairs of opposite sides are congruentBoth pairs of opposite angles are congruentDiagonals bisect each otherOne angle is supplementary to both consecutive angles (same-side interior)One pair of opposite sides are congruent AND parallel.Now, looking at the parallelogram properties above and comparing with the given image of the quadrilateral attached, we can say that the additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ
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The diagonal of the square is 10 cm. The length of the sides in cm is:
A. 5
B. 5sqrt2
C. 10sqrt2
D. 20
E. 100
*sqrt = square root I can't put the icon in
The length of a square with diagonal of 10 cm is 5√2 cm.
How to find the length of a square?Each angle in a square is 90 degrees.
Therefore, the diagonal form a right triangle with the length of the square.
The length of the square are equal.
Hence, using Pythagoras theorem,
let
x = length of square
x² + x² = 10²
2x² = 100
x² = 50
x = √50
x = 5√2
Therefore, the length of a square with diagonal of 10 cm is 5√2 cm.
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(02.02 MC)
Given the function g(x) = 8x − 2, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values.
Group of answer choices
The value of g(−2) is larger than the value of g(4).
The value of g(−2) is the same as the value of g(4).
The value of g(−2) is smaller than the value of g(4).
The values of g(−2) and g(4) cannot be compared.
Answer:
The value of g(-2) and g(4) cannot be compared because they are two different functions with two completely different values.
Step-by-step explanation:
So, you plug in -2 in the function of the x in g(x) = 8x - 2
Then, you multiply 8 by -2 in g(-2) = 8x - 2
8 × -2 would be -16
Afterwards you subtract -16 by 2 in g(-2) = -16 - 2
The function of g(-2) is -14 in g (x) = -14
You plug in 4 in the function of x in g(4) = 8x - 2
g(4) = 8 (4) - 2
Then, You multiply 8 by 4 which will give you 32 in
g(4) = 32 - 2
Lastly, you subtract the 32 by 2 and the function of the answer would be 30 in g(x) = 30
Question
Find the x- and y-intercepts of the parabola y
=
=-3x²
-
10x 10.
-
Answer:
-100/3,0
Step-by-step explanation:
substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
if that makes sense Hope this helps pls brainliest have a nice day :>
Answer:
100- 3X
Step-by-step explanation:
SLAY
Anil is a married teacher in a college. He has monthly salary of Rs 45,000
dearness allowance Rs 4,000. His life insurance premium paid by his college is
Rs 15,000. Dashain allowance is equals to one month's basic salary. Anil has contributed
in Employee Provident Fund 10% of basic salary. The college also contributed same amount.
Tax rate for first 450000 1% , next 100000 10% and 25% above that
The amount paid in tax based on the information is Rs 13500.
How to compute the tax?From the information given, the monthly salary is 45000. Therefore, the yearly salary will be:
= 45000 × 12
= 540000
Also, it's stated that the tax rate for first 450000 is 1% and next 100000 is 10%. Therefore, the amount that will be paid in tax will be:
= (450000 × 1%) + (90000 × 10%)
= 4500 + 9000
= 13500
Therefore, the amount paid in tax will be Rs 13500.
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The answer for this math problem because I don’t really understand it
Answer:
See below
Step-by-step explanation:
Start by subtracting 5.2 from both sides of the equation
so "subtraction property of equality " I suppose ......
then the next step would be divide both sides by 2.5
which would be division property of equality
Answer: Subtraction Property of Equality
Step-by-step explanation:
- the subtraction property of equality is the rule that when you subtract the same number to or from both sides of an equation and get an equivalent equation
__________________________________________________________
- for this equation you would subtract 5.2 from the left-side of the equation and subtract it from 35.2 on the right side of the equation
- this is to isolate n
- basically 2.5n = 30 since n is a variable and that number multiplied by 2.5 will equal 30
- so the new equation would be 2.5n = 30
- so then: [tex]\frac{n}{2.5}[/tex] = [tex]\frac{30}{2.5}[/tex] so n = 12
hope this helps :)
A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 222 inches and a height of 666 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 444 inches.
What will the height of the new cones be?
Based on the given parameters about old cone, the height of the new cone is 12 inches
Equivalent ratioOld cone:
Radius, r = 2 inchesHeight, h = 6 inchesNew cone:
Radius, r = 4 inchesHeight, h = hequate ratio of radius to height in old and new cone
2 : 6 = 4 : h
2/6 = 4/h
cross product
2 × h = 6 × 4
2h = 24
h = 24/2
h = 12 inches
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Work out the height of this
triangle with base, b = 4.9mm
and area, A = 108.29mm².
Answer: 44.2
Step-by-step explanation:
108.29*2/4.9=44.2
QUESTION IS DOWN BELOW
Using proportions, the ratios are given as follows:
a) 9:196.
b) 27:2744.
c) 3:14.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the standard ratio of 3:14 units, we have that:
The area is given in units squared, hence the ratio will be of [tex]\left(\frac{3}{14}\right)^2 = \frac{9}{196}[/tex].The volume is given in cubic units, hence the ratio will be of [tex]\left(\frac{3}{14}\right)^3 = \frac{27}{2744}[/tex]. The width is also given in units, hence the ratio is also of 3:14.More can be learned about proportions at https://brainly.com/question/24372153
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Two trains leave a station at the same time. One train is heading south at a rate that is 1.5 times faster than the other train, which is heading north. After 5 hours, the trains are 750 miles apart.
1) At what speed, in mph, are the two trains getting farther away from each other?
2) What is the speed, in mph, of the faster train?
3) Suppose the trains simultaneously leave stations that are 450 miles apart and travel toward each other. In how many hours will the trains meet?
Answer:
1) 150 mph
2) 90 mph
3) 3 mph
Explanation:
1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150
2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.
3) We know that both trains combined travel 150 mph. 450/150=3.
Based on the data given, the speeds and time taken are as follows:
The combined speed of the two trains is 150 mphThe speed of faster train 150 x 3/5 = 90 mphThe time taken by the trains to cover 450 miles = 3 hoursWhat is speed?Speed is the ratio of distance covered and time taken.
Speed = distance/time1)The distance covered by the two trains in 5 hours = 750 miles.
The trains move at a constant speed and their combined speed will be:
Combined speed = 750/5
Combined speed = 150 mph
2) The train heading south has a speed 1.5 times faster than the other train heading north.
Ratio of speeds = 3 : 2
Speed of faster train 150 x 3/5 = 90 mph
3) The combined speed of the trains = 150 mph
Distance to be covered = 450 miles
Time taken = 450/150
Time taken = 3 hours
In conclusion, the speed of the two trains are determined from the distance travelled and time taken.
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To solve the division problem, multiply
by the reciprocal of the divisor.
1/9 divided by 3=1/9X1/? Solve the question mark.
Answer:
?=3
Step-by-step explanation:
3=3/1
Flip 3/1 and you get
1/3
Two rules for creating a pattern are given below. Each rule begins with a number called the input and creates a number called the output.
Rule 1: Divide the input by 2 to get the output.
Rule 2: Subtract by 10 to get the output.
Which input and output table works for both rules?
The input and output table that works for both rules is input = 20 and output = 10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the output and x represent the input.
From the first rule:
y = x/2
From the second rule:
y = x - 10
To work for both rules:
x/2 = x - 10
x = 2x - 20
x = 20
y = 20 - 10 = 10
The input and output table that works for both rules is input = 20 and output = 10.
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Determine the slope of a line that is perpendicular to the equation 3x + 6y =18
Rewriting the equation of the given line in slope-intercept form,
[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]
This means the slope of the given line is -1/2.
As perpendicular lines have slopes that are negative reciprocals, the answer is 2.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Determine the slope of the line perpendicular to 3x+6y=18
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form
[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x
[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].
[tex]\cline{1-2}[/tex]
Now, perpendicular lines' slopes are opposite inverses of each other.
The opposite inverse of -1/2 is
= 2
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=2}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]
Find the distance between the two points.
(-8,-8) and (-14, -16)
Answer:
the distance between both points is 10
Step-by-step explanation:
Distance (d) = √(-14 - -8)2 + (-16 - -8)2
= √(-6)2 + (-8)2
= √100
= 10
The distance between the two points (-8, -8) and (-14, -16) is 10 units.
We have,
To find the distance between two points in a coordinate plane, you can use the distance formula:
Distance = [tex]\sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
In this case, the two points are (-8, -8) and (-14, -16).
Let's plug the values into the distance formula:
Distance = √[(-14 - (-8))² + (-16 - (-8))²]
Distance = √[(-14 + 8)² + (-16 + 8)²]
Distance = √[(-6)² + (-8)²]
Distance = √[36 + 64]
Distance = √100
Distance = 10
Thus,
The distance between the two points (-8, -8) and (-14, -16) is 10 units.
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Use the logarithm lays to simplify this expression
log2 8x^3/2 = log2 8x^3 - log2 2y
By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.
How to simplify a logarithmic expressions
Herein we must simplify an expression that uses logarithms by applying any of the following three laws:
[tex]\log_{a} (b \cdot c) = \log_{a} b + \log_{a} c[/tex] (1)
[tex]\log_{a} \left(\frac{b}{c} \right) = \log_{a} b - \log_{a} c[/tex] (2)
[tex]\log_{a}{b^{c}} = c \cdot \log_{a} b[/tex] (3)
Now we proceed to simplify the expression:
[tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex]
[tex]\log_{2} 2\cdot y = \log_{2} 8\cdot x^{3} - \log_{2} \frac{8\cdot x^{3}}{2}[/tex]
[tex]\log_{2} 2 \cdot y = \log_{2} \frac{\frac{8\cdot x^{3}}{1} }{\frac{8\cdot x^{3}}{2} }[/tex]
[tex]\log_{2} 2\cdot y = \log_{2} 2[/tex]
By the relationship between logarithms and powers of same base:
2 · y = 2
y = 1
By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.
To learn more on logarithms: https://brainly.com/question/20785664
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