Answers
[tex] \huge\underline\mathcal{Answer \: - }[/tex]
Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.
therefore ,
[tex](25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0[/tex]
now using quadratic formula ,
[tex]x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]
here , a = 17 , b = 70 , c = -552
substituting the values in the equation above ,
[tex]x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ [/tex]
after simplifying we get ,
[tex]\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ [/tex]
since length can't be negative , therefore the other value will be neglected and hence ,
[tex]\boxed{value \: of \: x \: = \: 4 \: cm}[/tex]
hope helpful ;-;
======================================================
Work Shown:
As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.
[tex]a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\[/tex]
Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\[/tex]
Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.
This makes x = 4 the only possible solution.
----------------
If x = 4, then,
vertical leg = x+3 = 4+3 = 7horizontal leg = 4(x+2) = 4*(4+2) = 4*6 = 24This is a 7-24-25 right triangle.
We can confirm this using the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark[/tex]
Related Questions
a hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. if the sample consists of 41 observations and the correlation coefficient is 0.60, what is the computed value of the test statistic? round to two decimal places.
Answers
The computed value of the test statistic is 4.65 or 4.7
Information given in the query:
significance level = 0.05
Sample size is 41 observations, and the correlation value is 0.60.
Now,
Using the formula, the test statistic to determine whether the population correlation is zero is provided.
:
t =[tex]r\sqrt{n-2} /\sqrt{1-r^{2} }[/tex]
on substituting the respective values, we get
test statics , t = 4.65
or
t=4.7
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A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 12 granola bars. The camp bought a total of 9 boxes that have 100 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answers
The system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased is b + s = 9 and 10s + 12s = 100
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the small box be represented as s.
Let the big box be represented as b.
Each small box has 10 granola bars and each large box has 12 granola bars. The The camp bought a total of 9 boxes that have 100 granola bars altogether.
The equation will be:
b + s = 9
10s + 12s = 100
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Answer:
10x + 12y = 100
x + y = 9
Step-by-step explanation:
Define Variables:
Let x = the number of small boxes purchased
Let y = the number of large boxes purchased
Each small box has 10 granola bars, so small boxes have 10x granola bars.
Each large box has 12 granola bars, so large boxes have 12y granola bars. Therefore, the total number of granola bars 10x + 12y equals 100:
10x + 12y = 100
Since a total of 9 boxes were purchased, we know x + y must equal 9.
x + y = 9
What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)
Answers
By translating trapezoid S′T′U′V 7 using the same translation rule, the location of T′ in the image trapezoid S′T′U′V′ is: D. (13, -1)
The types of transformation.Generally, there are four (4) main types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.
By critically observing the graph (see attachment), we can logically deduce that rectangle JKLM was transformed to rectangle J'K'L'M' by translating it 7 units to the right and 5 units up.
Next, we would apply the same translation rule to T' which is located at point (6, -6) as follows:
(x, y) → (x + 7, y + 5)
Point T (6, -6) → Point T' = (6 + 7, -6 + 5) = (13, -1)
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Complete Question:
Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.
What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)
Cathy has 48m of fencing to make a rectangular pen for her pets. What is the
maximum area?
Answers
The area of the square will be 100 square meters. Then the dimensions of the pen of the rectangle will be 10 by 10 which is a square.
What is the area of the square?
Let a be the side length of the square.
Then the area of the square will be
Area of the square = a² square units
Cathy has 40 meters of fencing to build a rectangular pen for her pets.
For the maximum area of the rectangle, the length and width should be congruent.
40 = 4a
a = 10
Then the area of the square will be
A = 10²
A = 100 square meters
The dimensions of the pen of the rectangle will be 10 by 10 which is a square.
ANSWER ASAP For a ride on a rental scooter, Kevin paid an eight dollar fee to start the scooter +6 cents per minute of the ride. The total bill for Kevin’s ride was $14.36 for how many minutes did Kevin ride the scooter.
Answers
Answer:
106 seconds
Step-by-step explanation:
14.36-8=$6.36 $6.36=636 cents so 636/6=106 so 106 seconds
What is the operation rule from number of ounces of flour to number of cupcakes?
Please use the graph above.
(A.) Multiply by 3
(B.) Multiple by 2
(C.) Add 8
(D.) 2
Answers
Answer: (B) Multiply by 2
Step-by-step explanation:
For every ounce of flour, 2 cupcakes can be made.
Can someone help me with this please?
Answers
The output of the linear function is -n+3 when the input is n.
What is a slope?The slope of a line can be used to calculate its steepness. The slope or gradient of a line is a number that indicates its direction and steepness.The slope is calculated by dividing the vertical change by the horizontal change between any two distinct points on a line. The ratio is sometimes written as a quotient, which produces the same number for every two distinct points on the same line.How to find the output of the linear function?A linear equation is given by ,
f(x) = mx+ c ---(1)
From the table,
x value increases by 1
y value decreases by 1
The function's slope, or the coefficient that converts an increase in x to an increase in y, is represented by the letter m.So, the coefficient slope(m) magnifies the decrease by 1Substituting slope m = - 1 in (1)
f(x) = -x+ c ---(2)
Substitute (1, 2) in (2)
2 = -1 +c
c = 2 + 1
c = 3
Substitute slope m and c in (2)
f( x ) = - x + 3
When input is n output is given by,
f(n) = - n + 3
The output of the linear function is -n+3 when the input is n.
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0.8 divided by 0.6 then round to nearst hundredth
Answers
Answer: 1.33
Step-by-step explanation:
0.8 divided by 0.6= 1.33333333333
3 is in the hundredths place and 3 is in the thousandths place.
Since the digit in the thousandths place (3) is less than 5, the digit in the hundredths place (3) does not change.
The digits to the right of the hundredths place are dropped.
1.33333333 rounded to the nearest hundredth (two decimal places) = 1.33.
help on the ones you know
Answers
Answer:
2. y = x + 13
Step-by-step explanation:
Your points are: (-4, 9) and (2, 15)
To write an equation of a line from two ordered pairs, you first find the slope (m)
To find the slope, you do y2 - y1 / x2 - x1
(-4 is x1, 9 is y1) (2 is x2, 15 is y2)
Plug in the numbers:
15 - 9 / 2 - (-4) ----------------------> 6/6 ----------> 1, m = 1
The next equation we'll use is y - y1 = m(x - x1)
and slope intercept form is y = mx + b
Pick either ordered pair to plug in the coordinates, but this time I'll use
(2, 15) -----> 2 is x1, 15 is y1
y - 15 = m(x - 2)
Since we already know the slope, m, we can simplify the equation.
y - 15 = 1(x - 2)
Distributive property
y - 15 = x - 2
Add 15 on both sides,
y = x + 13
slope is rise/run. starting at (0,-4), i counted up 4 to the x-axis then over 6 to the point (6,0). this gives a slope of 4/6, which is then reduced to 2/3. our b in the y=mx+b is found by looking for where the line crosses the y-axis, which is at (0,-4). b is this y value. plugging everything in (m for slope, b for y-intercept) gives y=(2/3)x-4
2. the other commenter did a great job at explaining 2
3. the line with a slope of -3 is steeper
start this problem by solving for y in the equation given. -5x+2y=8 becomes 2y=5x+8, then y=(5/2)x+4. all we need from this is the slope 5/2 to compare to -3. a steeper slope is given by the larger absolute value. |5/2| is 5/2, and |-3| is 3. 5/2<3, so the line with the slope -3 is steeper.
4a. the lines are neither perpendicular or parallel.
the slopes are different, so they cannot be parallel. the slope of the first equation and second equation (-4 and 4) are not inverse reciprocals of each other, so they cannot be perpendicular.
4b. the lines are parallel.
to find the answer of this question, solve for y in the first equation. 5x+15y=-8 becomes 15y=-5x-8, then y=-(1/3)x-(8/15). the slopes of the lines are both -1/3 with different y-intercepts, so the lines are parallel.
5. y=(1/3)x-(14/3)
use point-slope form and simplify. plugging into point slope gives us y+2=m(x-8). m is found by taking the inverse reciprocal of the equation given to us. the inverse reciprocal of -3 is 1/3, so m=1/3. the equation is y+2=(1/3)(x-8). distribute to get y+2=(1/3)x-(8/3). solve for y. y=(1/3)x-(8/3)-2. y=(1/3)x-(8/3)-(6/3). y=(1/3)x-(14/3)
is 13 over 12 a proper or an improper fraction?
Answers
Step 1
An improper fraction is a fraction in which the numerator(top number) is greater than or equal to the denominator ( the bottom number)
Step 2
Conclude based on step 1
Hence
[tex]in\text{ }\frac{13}{12}\text{ the numerator 13 is bigger than the denominator 12, th}erefore\text{ it is an improper fraction}[/tex]Therefore the right answer is an improper fraction
a certain area of the eastern united states is, on average, hit by 6 hurricanes a year. find the prob- ability that in a given year that area will be hit by (a) fewer than 4 hurricanes; (b) anywhere from 6 to 8 hurricanes.
Answers
By applying probability method in a Poisson distribution, we find out that the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512 and the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.
It is given that -
On an average, Eastern United States is hit by 6 hurricanes in a year.
We have to find out -
(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes
(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes
This is a case of probability which relates to Poisson distribution that provides probability of any random event that occurs within a specific time interval.
Let us assume the number of hurricanes is represented by [tex]X[/tex]. The Poisson distribution can be represented as -
[tex]P(X) = \frac{(lambda)^{X}*e^{-lambda}}{X!}[/tex] -------(1)
Here, [tex]X\\[/tex] = 1,2,3,...
lambda = Average = 6 (in this question)
[tex]e[/tex] = 2.718
(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes
[tex]P(X < 4) = P(X=0) +P(X=1)+P(X=2)+P(X=3)\\= \frac{6^{0}*e^{-6}}{0!}+\frac{6^{1}*e^{-6}}{1!}+\frac{6^{2}*e^{-6}}{2!}+\frac{6^{3}*e^{-6}}{3!}\\=0.0025+0.0149+0.0446+0.0892\\=0.1512[/tex]
Thus, the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512.
(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes
[tex]P(6\leq X\leq 8)=P(X=6)+P(X=7)+P(X=8)\\=\frac{6^{6}*e^{-6} }{6!}+\frac{6^{7}*e^{-6} }{7!}+\frac{6^{8}*e^{-6} }{8!}\\=0.1606+0.1376+0.1033\\=0.4015[/tex]
Thus, the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.
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How to search question up on this?
Answers
Answer:
find search bar
Step-by-step explanation:
see answer
can someone tell me if im right?
Travis rents an apartment in a historic, all-brick building downtown. The value of the belongings in the apartment is about $11,000. If Travis wishes to insure his belongings while renting, how much will he have to pay for insurance per year? Use the table above to solve.
I did:
it fell under 0.39 for building and 0.43 for contents so I did
0.39 x 12=4.68 then added the 100 dollar bonus and got $104.68
Answers
The amount of insurance that Travis will have to pay for the year is of:
$47.3.
What is the amount of insurance that Travis has to pay?He is renting the apartment, in which the belongings are worth $11,000, hence the insurance will be paid over that amount.
The number of hundredths in $11,000 is given by:
11000/100 = 110.
He pays an insurance of $0.43 for each $100 in belongings, hence the total insurance is of:
0.43 x 110 = $47.3.
There is no information regarding the value of the building, hence we are going to consider that he does not pay insurance for the building.
This insurance was taken from the table, as the apartment is in the city (downtown), and all brick, hence the coefficient is of 0.43.
Missing informationThe table with the rates is given by the image at the end of the answer.
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use the properties of vector addition and scalar multiplication from the following theorem. properties of vector addition and scalar multiplication in rn let u, v, and w be vectors in rn, and let c and d be scalars.
Answers
The set R^2 with x ≤ 0 and y ≤ 0 is not a vector space.
The 10th axiom cv∈ V does not hold
Let u, v and w be vectors in the vector space V, and let c and d be scalars. A set S is defined as a vector space if it satisfies the following conditions:
1. u+ v ∈V
2. v + w = w + v
3. (u + v) + w = u + (v + w)
4. v + 0 = v = 0 + v
5. v + (−v) = 0
6. 1v = v
7. c(dv) = (cd)v
8. c(v + w) = cv + cw
9. (c + d)v = cv + dv
10. c v ∈V
Given the set of all vectors x, y in R^2 with x ≤ 0 and y ≤ 0
If the scalar c is such that c<0 then c v ∉R^2as cv>0
Therefore, the 10th axiom is not satisfied and thus the set R^2 with x ≤ 0 and y ≤ 0 is not a vector space.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
Submit
Answers
Answer:
1 / 121
Step-by-step explanation:
4^0 / 11^2
= 1 / 11^2
= 1 / 121
PLEASE HELP ME! QUICK!
Answers
The volume of the given triangular prism to the nearest tenth is; 171.5 in³
What is the Volume of the triangular prism?
The volume of a triangular prism of the kind given to us is expressed as;
Volume of a triangular prism = area of base triangle × length of the prism
Now, the formula for area of base triangle is;
Area = 1/2 * base * height
From the question, we have;
base = 9.8 in
height = 14 in
Now, the length of prism is 2.5 inches. Thus;
Volume of prism = (1/2 * 9.8 * 14) * 2.5
Volume of prism = 171.5 in³
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22 Which inequality is equivalent to 7x - 2y > 8?
Fy> / x+8
8
5 y> - ²/x + ²
Hy< ²x -
3
4
417
<-²/x-4/
32
Answers
Inequality which is equivalent to 7x - 2y > 8 x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex] and y <[tex]\frac{7x}{2} -4[/tex]
What is inequalities?Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
7x - 2y>8
-2y > 8 -7x
=y <[tex]\frac{7x}{2} -4[/tex]
or
7x >2y + 8
=x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex]
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Please help!! I’ve been struggling
Explain how to solve this question by multiplying, dividing, adding, or subtracting both sides by 2
Answers
Answer:
x=16
Step-by-step explanation:
x/2 = 8
Multiply both sides by 2
x=16
:] Hope this helps
the answer would be x=16
you would multiply both sides by 2
!!20 Points!! Solve using augmented matrices.
x+y=1
3x-y=7
Answers
y=-1
You have to do subtitution
13 people on a softball team show up for a game. how many ways are there to choose 10 players to take the field? (you must provide an answer before moving to the next part.)
Answers
858 combinations are there to choose 10 players to take the field.
Pick 10 people from 13,
[tex]C^{13} _{10}[/tex] = [tex](^{13} _{2} )[/tex]
Splitting the combination,
[tex]C^{13} _{10}[/tex] = (13 × 12 × 11) ÷ 2
[tex]C^{13} _{10}[/tex] = 1716 ÷ 2
[tex]C^{13} _{10}[/tex] = 858 ways to pick the 10 to play.
There are 858 different methods to select 10 players to take the pitch.
The permutations of a set are the vaguely defined community of its members in arrangement or linear order, or the permutation of its components if the set is already collected. The act or procedure of adjusting the linear ordering of a sorted set is often named "permutation".
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El valor de x que se cumple con 6x-10=2 es
Answers
Answer:
the answer is 2
What is an equation of the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10
Answers
The equation of the line that passes through the point (2,-3) and is parallel to the line 2x + 5y = 10 is y = - 2 / 5 x - 11 / 5
How to find the equation of a line?The equation of a line can be represented in various form such as point slope form, slope intercept form and standard form.
Therefore, let's find the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + 5y = 10.
Hence, parallel lines have the same slope.
5y = -2x + 10
y = - 2 / 5 x + 2
Therefore, the slope of the line is - 2 / 5.
Let's find the y-intercept using the slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptHence, (2, -3)
-3 = - 2 / 5(2) + b
-3 = - 4 / 5 + b
b = - 3 + 4 /5
b = - 11 / 5
Therefore, the equation of the line is y = - 2 / 5 x - 11 / 5
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The required equation of the line y = - (2/5)x - 11/5 passes through the point (2,-3) and is parallel to the line 2x + 5y = 10.
We have to determine the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10
Parallel lines are known to have the same slope.
Firstly, we have to find its slope by the given line
⇒ 5y = -2x + 10
⇒ y = - (2/5)x + 2
Thus, the slope of the line is - 2/5.
Let the required equation of the line is y - y₁ = m(x -x₁ )
Here x₁ = 3, y₁ = 1 and m = -2/5
y - 1 = (-2/5)(x - 3)
y - 1 = (-2/5)x + 3(-2/5)
y = - (2/5)x - 6/5 +1
y = - (2/5)x - 11/5
Therefore, the required equation of the line is y = - (2/5)x - 11/5.
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What is the absolute value of −1/4 ?
Plot your answer on the number line.
Answers
Answer:
1/4
Step-by-step explanation:
Hope this helps!
please answer question 98 please!
thanks
Answers
Steps: 3, 2, 2, 1, 1.5, 2. Add together; 9.5
divide; 9.5 / 6 = 1.583333
round up to nearest tenth; 1.6
Explanation: To calculate average (also called “mean”), you have to add all the numbers together, and divide that number by how many numbers there were. ex: 5, 2, 7, 4, 2. First you would add the numbers together: 20. There were 5 numbers I added together; 20 / 5 = 4. The average would be four.
98
7. A bag contains 100 marbles. Some are red and the rest are blue. If there are no
more than 12 times as many red marbles as blue marbles in the bag, at most how
re in the bag? At least, how many blue marbles are in the
many red marbles are
bag?
Answers
At least 84 blue marbles and 7 red marbles are there in the bag.
Let the bag contain x red marbles therefore there are 12x blue marbles.
Therefore according to the question,
12x + x = 100
13x = 100
= 100/13
=7.69 approx
Which is not possible as the no,of marbles cannot be in decimals therefore there must be atleast 7 marbles of red colour and 84 blue marbles.
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What is the slope shown below?
Answers
Answer:
5/8
Step-by-step explanation:
Slope = rise/run
In this problem:
rise = 5
run = 8
Therefore, Slope = 5/8
Maria runs of a mile every 8 minutes. Althea runs 2 miles every of an hour. Who runs ata faster 2 3 1 3 speed – Maria or Althea? Explain your reasoning.
Answers
The fact that Maria runs of a mile every 8 minutes means that we runs faster.
How to calculate the speed?The speed is measured as the distance with respect to the time. This will be illustrated thus:
Maria runs of a mile every 8 minutes. Althea runs 2 miles every of an hour. It should be noted that an hour is 60 minutes. That means the she runs 1 mile in (60 / 2) = 30 minutes.
In this case, Maria runs faster. This is because of her speed.
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standard to slope intercept form
Answers
Answer: y = 1/6x + 1
Step-by-step explanation:
12y - 2x= 12
+2x +2x
12y = 12 + 2x
DIVIDE BOTH SIDES BY 12
y = 1 + 1/6x
THEN PUT IN SLOPE INTERCEPT FORM
y = 1/6x + 1
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 12y - 2x = 12[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 2x + 12[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{12} x + \frac{12}{12} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{1}{6} x + 1[/tex]
Slope = 1/6, y - intercept = 1
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Draw a polygon with vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2). What is the perimeter, in units, of polygon RSTU? Draw a polygon with vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2). What is the perimeter, in units, of polygon RSTU?
Answers
Answer:
The perimeter of rectangle RSTU is 20 unitsStep-by-step explanation:
Given Vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2).To find The perimeter of the RSTUSolutionPlot the points, we see it is a rectangle.
Side lengths are:
RS = TU = 2 - (-4) = 6, the difference of x-coordinates,ST = RT = 2 - (-2) = 4, the difference of y-coordinates.The perimeter is:
P = 2(l + w)P = 2(6 + 4) = 2(10) = 20 unitsThe perimeter of polygon RSTU is
How to find distance between straight line?A straight line connects any two places with the smallest distance possible. The distance formula can be used to get this distance. It is possible to define the distance between two positions (x 1, y 1) and (x 2, y 2) as d=√(x2-x1)² + (y2 - y1)².
Distance between R and S is;
√(2+4)² + (2 - 2)²= 6 units
Distance between S and T is;
√(2-2)² + (-2 - 2)²= 4 units
Distance between T and U is;
√(-4+-2)² + (2 - 2)²= 6 units
Distance between T and U is;
√(-4+4)² + (2 + 2)²= 4 units
The total perimeter is of polygon is:
6+4+6+4 = 20 units
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a researcher separated the people in a population into three political categories: democrat, republican, or independent. she then selected a random sample from each of these three groups. what kind of sample did she select?
Answers
The researcher makes use of stratified sampling method to select a random sample from each of the three groups mentioned.
It is given to us that -
A researcher separated the people in a population into three political categories:
Democrat
Republican
or, Independent.
It is also mentioned that she then selected a random sample from each of these three groups.
We have to determine the kind of sample she selected.
In this case, stratified sampling is used by the researcher to select a random sample.
Stratified sampling is a type of probability sampling method where the total population is segmented into homogenous groups to successfully complete the sampling technique.
Here we see that the researcher has separated the total population into homogenous groups of democrat, republican, or independent.
From these homogenous groups, she selected random samples.
Thus, the kind of sample selected by the researcher is stratified sampling.
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