The theoretical mean and standard deviation is 22 and 38 respectively
np>5 and n(1-p)>5 for normal approximation
p=0.77
np>5 n×0.77>5=6.49
n(1=0.77)>5
n>5/0.23
n=21.7
The standard error of the mean for a sample size of 153 is 25 . In quest to reduce the SE of the mean in half(to 12.5 )
Standard error of sample maean is se=sd/sqrt n
se=sd/sqrt 153
Taking four times of sample size we get 4×153=612
The required sample size is 612
The mean of an infinite population is 73 and a standard deviation of 38 . The sample size of 121 is taken randomly from the given population. The SE of the sample mean equals:
standard error of the sample mean =38/sqrt121=3.4545
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Solve 6 + a = 3 for a.
Answer:
subtract 6 from 3 and a is -3
Step-by-step explanation:
Answer:
a= -3
Step-by-step explanation:
a=3-6
a=-3
Juilan divided his savings equally between two charities. If its Julian's savings, evaluate the expression when s=$125
The expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
WE have been given that Juilan divided his savings equally between two charities. then Julian's savings as 's' =$125
First, we will write the expression;
s/2
Second, substitute the value 125 in for the variable s.
Then simplify by dividing 125 and 2.
=$125 / 2
= $62.50
Hence the expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.
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Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
Answer:
2 and 12
Step-by-step explanation:
2x3=6
12 x 6=72
6 and 72 is 78
Answer:
2 and 12
Step-by-step explanation:
Y= 1/2x -2
y= 3/4x +3
an isosceles triangle has an angle that measures 40 what measures are possible for the other two angles
The measures are possible for the other two angles are 70 degrees respectively
Isosceles triangleAn isosceles triangle is a triangle that has 2 of its sides and angles to be equal.
Let the measure of the other possible angles be x and y such that x = y
Since the sum of angle in a triangle is 180 degrees, hence;
x+y +40 = 180
x+x+40=180
2x+40=180
2x=180-40
2x = 140
x = 70
x = y = 70 degrees
Hence the measures are possible for the other two angles are 70 degrees respectively
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A=√15.5(15.5-14) (15.5-11) (15.5-6)
The value of A is 31.5.
The square root of any number is the factor that we can be multiplied by itself to get that given number. The symbol for square root is √.
Here, we are given an equation as follows-
A=√[15.5(15.5-14) (15.5-11) (15.5-6)]
Let us simplify it step by step. Firstly, we will perform the operations inside the brackets as follows-
A = √[15.5(1.5) (4.5) (9.5)]
Now, multiplying the terms we get-
A = √[15.5(1.5) (4.5) (9.5)]
A = √[(23.25) (42.75)]
A = √[(993.9375)]
Now, we calculate the square root of the number obtained above-
A = 31.5
Thus, the value of A in the equation A=√15.5(15.5-14) (15.5-11) (15.5-6) comes out to be 31.5.
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someone PLEASE help me with this asap.
The description and definition and values of the sequence are;
a. Each term of sequence A is produced from the previous term by multiplying the previous term by 2
b. Each term of sequence B is produced from the previous term by adding 10 to the previous term
c. [tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]
d. B(n) = 2 + (n-1) × 10
e. B(9) > A(9)
What is a sequence of numbers?A sequence is series of objects that follow each other in a particular order.
a. The terms of sequence A are;
1/4, 1/2, 1, 2, 4
Therefore, each term is produced from the previous term by multiplying the previous term by 2 as follows;
1/4 × 2 = 1/2,
1/2 × 2 = 1
1 × 2 = 2
2 × 2 = 4
b. The values in sequence B are;
2, 12, 22, 32, and 42
Therefore, each term is produced from the previous term by adding 10 to the previous term as follows;
2 + 10 = 1212 + 10 = 2222 + 10 = 3232 + 10 = 42c. The definition of the nth term of sequence A is found using the formula for a geometric progression as follows;
nth term of a GP is; A(n) = a•r^(n-1)
Where;
a = The first term = 1/4
r = The common ratio = 1/2/(1/4) = 2
The nth term of sequence A is therefore;
[tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]d. The definition of the nth term of sequence B is found using the formula for a arithmetic progression as follows;
nth term of a AP is; B(n) = a + (n-1)•d
Where;
a = The first term = 2
d = The common difference = 12 - 2 = 10
The nth term is therefore
B(n) = 2 + (n-1) × 10
e. The value of A(9) is therefore;
[tex] A(9) = \frac{1}{2} \times 2^{(9-1)} = 64 [/tex]
Which gives; A(9) = 64
The value of B(9) = 2 + (9-1) × 10 = 82
B(9) = 82
Which gives;
B(9) = 82 > A(9) = 64
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer: 3/4
Step-by-step explanation:
Q. If 140 students want to go on the Mackinac Island field trip and are ALL riding together, how many
cars will they need if each car holds 6 people?
answer choices
Answer:
24
Step-by-step explanation:
140/6 = 23.3333333333333
You can’t have .3 of a car, so you would need to round up.
23.333333333333333 rounds up to 24
The first step in solving 7 + 3(x - 2) = 2x + 10 is to
Answer:
x=9
Step-by-step explanation:
Simplify 7+3x−67+3x−6 to 3x+13x+1.
Subtract 11 from both sides
Simplify 2x+10−12x+10−1 to 2x+92x+9.
Subtract 2x2x from both sides.
Simplify 3x−2x3x−2x to xx.
Answer: x=9
Step-by-step explanation:
7+3(x-2)=2x+10
7+3x-6=2x+10
1+3x=2x+10
1+3x-2x=2x-2x+10
1+1x=10
1x=9
x=9
HELP ME PLEASE I need this now
question 1 first picture is to this question
As x decreases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y = - 4.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 4.
question 2 the second picture to this question
As x decreases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) increases without bound.
Answer:
Question 1:
As x decreases without bound, f(x) increases without bound. TRUEAs x increases without bound, f(x) approaches the line y = - 4. TRUEAs x decreases without bound, f(x) approaches zero. FALSEAs x decreases without bound, f(x) approaches the line y = 4. FALSEQuestion 2:
As x decreases without bound, f(x) approaches the line y = 6. TRUEAs x increases without bound, f(x) approaches the line y = 6. FALSEAs x increases without bound, f(x) increases without bound. TRUEAs x decreases without bound, f(x) increases without bound. FALSEAs x decreases without bound, f(x) approaches the line y = 6.Step-by-step explanation:
Question 1:
options
As x decreases without bound, f(x) increases without bound.As x increases without bound, f(x) approaches the line y = - 4.As x decreases without bound, f(x) approaches zero.As x decreases without bound, f(x) approaches the line y = 4.Solving notes:
As x decreases without bound, f(x) does NOT approach zero.
As x decreases without bound, f(x) does NOT approaches the line y = 4.
_________________________________________________
Question 2:
options
As x decreases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) increases without bound.As x decreases without bound, f(x) increases without bound.Solving notes:
As x increases without bound, f(x) does NOT approach the line y = 6.
As x decreases without bound, f(x) does NOT increase without bound.
daisy is making solid spikes for her halloween costume. the spikes are shaped like right circular cones with base radius of 2222 inches and height of 6666 inches. if daisy has 360360360360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make?
Question :- Daisy is making solid spikes for her Halloween costume. the spikes are shaped like right circular cones with base radius of 2 inches and height of 6 inches. if daisy has 360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make ?
Answer:- She can only create a maximum of 14 spikes.
Step-by-step explanation:
Given that :-
Daisy is making solid spikes for her Halloween costume.The spikes have a base radius of 2 inches and a height of 6 inches. They are formed like right circular cones.For creating the spikes, Daisy has 360 cubic inches of material.To find :-
maximum number of spikes made by her.According to Question,
We have,
base radius of the spikes = 2 inchheight of the spikes = 6 inchFor finding the maximum number of spikes,
We have to divide the volume of the material by the volume of the cone, for producing a maximum number of spikes.
So,
Maximum spikes = Volume of the material / volume of the cone
Now,
Volume of the material = 360 cubic inches
Volume of the cone = [tex]\frac{1}{3}[/tex] πr²h
Where:
r = radius = 2 in
h = height = 6 in
π = pi = 22/7
= [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × [tex]2^{2}[/tex] ×6
= 3.14 × 4 × 2
= 25.12
So,
Maximum spikes = Volume of the material / volume of the cone
= [tex]\frac{360}{25.12}[/tex]
= 14.33
∴ The number of spikes must be an integer.
∵ Maximum spikes = 14.
Answer:- She can only create a maximum of 14 spikes.
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Which of the following intervals is equivalent to -2
A. [-2, 3]
B. [-2, 3)
C. (-2, 3]
D. (-2, 3)
Answer:
the answer is A
each of the following statements can be recast in the if-then form. please rewrite each of the following sentences in the form "if a, then b." a. the product of an odd integer and an even integer is even. b. the square of an odd integer is odd. c. the square of a prime number is not prime. d. the product of two negative integers is negative. (this, of course, is false.) e. the diagonals of a rhombus are perpendicular
According to the given statements:
a. If the integers x and y are, respectively, even and odd, then xy is even.
b. When x is odd, x2 is also odd.
c. If p is a prime number, p2 is not a prime number.
d. If the integers a and b are negative, then ab is also a negative number.
e. If AC and BD are diagonally arranged in a rhombus, then AC is perpendicular to BD.
What is number system in math's?A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or even other symbols to represent the numbers in a given set in a standardized way. The same set of symbols can represent various numbers in various numeral systems.
According to the given statement:A. if a, then b the product of an odd integer and an even integer is even.
If the integers x and y are, respectively, even and odd, then xy is even.
B. if a, then b the square of an odd integer is odd.
When x is odd, x2 is also odd.
C. if a, then b the square of a prime number is not prime.
If p is a prime number, p2 is not a prime number.
D. the product of two negative integers is negative. (this, of course, is false.)
If the integers a and b are negative, then ab is also a negative number.
E. the diagonals of a rhombus are perpendicular.
If AC and BD are diagonally arranged in a rhombus, then AC is perpendicular to BD.
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I understand that the question you are looking for is:
Each of the following statements can be recast in the if-then form. please rewrite each of the following sentences in the form "if a, then b."
a. the product of an odd integer and an even integer is even.
b. the square of an odd integer is odd.
c. the square of a prime number is not prime.
d. the product of two negative integers is negative. (this, of course, is false.)
e. the diagonals of a rhombus are perpendicular
Please help asap!!!!
Answer:
A.2
explanation:
the equation to find circumference is [tex]2\pi (radius)[/tex]
the circumference of A is [tex]2\pi 8 = 50.27[/tex]
the circumference of B is [tex]2\pi 4 = 25.13[/tex]
50.27/25.13 = 2/1
Which is the graph of g(x) = (two-thirds) Superscript x – 2?
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)
the correct option is:
"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"
Which is the graph of the given function?
Here we have the exponential function:
g(x) = (2/3)^x - 2
Now, remember that for any real number different than zero, we have that:
x^0 = 1
So if we evaluate our function in x= 0 we will get:
g(0) = (2/3)^0 - 2 = 1 - 2 = -1
Then the function passes through the point (0, -1)
With this in mind, we conclude that the correct option is:
"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"
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Answer:
C: The third graph
Step-by-step explanation:
on edge
Her teacher asked her to write the correct equation or inequality that matches the
graph. Laurie wrote the following: y ≤ 2x - 4. Her teacher marked her answer
incorrect. Explain the error that Laurie made and then write the correct solution.
The correct solution of Laurie's inequality expression is y ≥ 2x – 4
Given,
The inequality expression wrote by Laurie = y > 2x - 4
The graph of the inequality expression that completes this question is added as an attachment
From the attached graph, we can see that the line of the inequality is a thick or closed line
Thick and closed line are represented by the inequality signs ≤ and ≥
Since the upper region is shaded, we make use of ≥ inequality sign
Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4
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2a-18 in algebraic form
Answer: 2(a-9)
Step-by-step explanation:
2a-18
then factor
which leads to 2(a-9)
Answer: 2(a-9)
Step-by-step explanation: Factor out 2 from the expression 2(a-9)
what is the simplest form of 14/27 divided by 7/1
Answer:
2/27
Step-by-step explanation:
i think this is the answer.
Simplify
√5 x √12 x √50
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3} \times \sqrt{2 \times {5}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \times 2 \sqrt{5 \times 3 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 10 \sqrt{30} [/tex]
Alex has twice the number of hats that Joey has, plus 2 more. The number
of hats Alex has is also 4 times the difference of the number of hats and 5
that Joey has. Find how hats many each of them has.
From the given Alex and Joey hats equation we got Alex has 24 hats Joey has 11 hats.
Given that,
Joey only has 2 times more hats than Alex, who has 2 more. The difference between the amount of hats Alex has and the 5 that Joey has is also 4 times the number of hats Alex has.
We have to discover how many hats each one of them has.
Let Alex has x hats Joey has y hats.
From the given
We get
x=2y+2 ------> equation (1)
x=4(y-5) --------> equation (2)
Equating equation (1) and equation (2)
2y+2=4(y-5)
2y+2=4y-20
2y-4y=-20-2
-2y=-22
y=-22/-2
y=11
Take y=11 in equation (1)
x=2(11)+2
x=22+2
x=24
Therefore, Alex has 24 hats Joey has 11 hats.
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Find the product. Simplify your answer. (3f–1)(4f+1)
definition of differentiation in mathematics
Answer:
This is also known as "Derivative"." in mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus."! hope this helps!
PLEASE HELP!! 80 PTS!! You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. What is the equation for a line of best fit? How much would you expect to pay for a tank of gas in the year 2019? Let x be the number of years after 1998.
Answer: Because the initial value is $26.40, the line must pass through this when x is 0. Thus, the answer is either the first or the second equation.
Next, we calculate the difference between the year 2019 and 1998 and substitute it into the value of x.
2019 - 1998 = 21.
Substituting this into the equation:
y = 1.006(21) + 26.40
y = $47.52
Thus, the first option is correct.
three houses are located on a straight road. house A is at the end of the road. house b is 4 miles from house a. house c is at least 1 mile from house b. write and solve an inequality to show the possible distances of house a from house c
The inequality that shows the possible distances of house A from house C is x ≥ 5
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.
We are given that;
Distance= 4miles
Let x be the distance of house A from house C. Since house B is 4 miles from house A, and house C is at least 1 mile from house B, we can write an inequality that relates x, 4, and 1:
x ≥ 4 + 1
This inequality means that the distance of house A from house C is greater than or equal to the sum of the distances of house A from house B and house B from house C.
To solve this inequality, we need to simplify it by adding 4 and 1:
x ≥ 5
Therefore, by inequality the answer will be x ≥ 5.
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write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (−13, −14)
The standard equation of the circle will be (x+5)²+(y+5)²= 145
The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.
formula for the midpoint
= ((x1+x2)/2, (y1+y2)/2)
Given points are - (3, 4), (−13, −14)
The circle's center is at (-5,-5)
Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.
The distance between a point on the circle and the circle's center in order to get the radius.
Therefore, let's calculate the distance between (-5, -5) and (-13,-14)
Radius R = √((-13+5)²+(-14+5)²) using the distance formula.
= 12.04
equation will be -
(x+5)²+(y+5)²= 145
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A small theater had 8 rows of 26 chairs each. an extra 8 chairs have just been brought in. how many chairs are in the theater now ?
After 8 chairs have been bought in there are now 216 chairs in the theater.
What is unitary method ?A unitary method is a mathematical technique for first finding the value of a single unit and then deriving the required units by multiplying with it.
According to the given question, a small theater had 8 rows of 26 chairs each.
∴ The total number of chairs in the theater is (8×26) chairs = 208 chairs.
Later an extra 8 chairs have bought in.
∴ The total no. of chairs in the theater now is (208+8) = 216 chairs.
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A rectangular section of a field is to be fenced. Because one side of the field is bordered by a creek, only 3 sides need to be fenced. The fenced section should have an area of 60 m². Determine the minimum perimeter and dimensions of the fenced area.
The minimum perimeter is 23.24m and dimensions of the fenced area is 15.5m x 3.8m.
Let us assume the length of the fenced area to be L and breadth of the fenced area to be W. As we know, only three sides are to be fenced,
So, the perimeter P of the fenced would be,
P = L + 2W
Also, it is given that, area of the fence is 60m²,
So, the are should be,
60m² = LW
60m²/L = W
Now, to minimize the perimeter,
P = L + 2W
P = L + 120/L
Differentiating both sides with respect to "L",
d(p)/dL = 1 - 240/L²
To find the value of "L", putting dp/dL equal to 0,
d(P)/dL = 0
1 - 240/L² = 0
L = √240m
Now, from the first derivative test, we know that, the perimeter will be maximum or minimum if value of L>√240 or L<√240 respectively,
For minimum, L should be,
L = √240m
L = 15.5m
Now we know from area,
area = LW
60 = 15.5 x W
W = 60/15.5
W = 3.8m
Hence, the minimum perimeter will be,
L + 2W = 23.24m
The dimensions are,
L = 15.5m
W = 3.8m
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What is another way to write the absolute value inequality |p|<12
Another way to write the absolute value inequality |p|<12 is
-12 < p < 12
What is absolute values?
This is a term in mathematics that refers to numbers considered regardless of the sign. The concept of absolute values is well appreciated in a number line. In a case where the signs helps on to position the number but do not have influence in the magnitude or size of the number.
Since absolute values considers the magnitude of the number and not the sign. We can see the equation given to represent values from zero to a point just less than 12 as this will have same magnitude to the point from zero to a point just less than negative 12. The sign just gives the direction.
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Find the distance between each pair of points. Round to one decimal place. A(-4, 6) and B(3, -7), and E(-6, -5) and F(2, 0).
AB=(
EF=
To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.
Given that,
To one decimal place, round.
Points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
We have to find the distance between two points that are AB and EF.
1. The distance between 2 points A and B.
A(-4, 6) and B(3, -7).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-1,x₂=3 and y₁=6,y₂=-7
After substituting we get,
[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]
[tex]\sqrt{16 +163}\\[/tex]
[tex]\sqrt{185}[/tex]
13.601
Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.
2.The distance between 2 points E and F.
E(-6, -5) and F (2, 0).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-6,x₂=2 and y₁=-5,y₂=0
After substituting we get,
[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]
[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]
[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]
[tex]\sqrt{64 +25}\\[/tex]
[tex]\sqrt{89}[/tex]
9.433
Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.
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