The point on the line is (-4, 3) and the slope of the line is m=3
What is meant by slope?Divide the "vertical change" by the "horizontal change" between (any) two distinct points on the line to find the slope.
The slope's absolute value is used to calculate the steepness, incline, or grade of a line. A line's direction can be increasing, decreasing, horizontal, or vertical.
If a line runs up from left to right, it is growing. The slope is positive, implying that m>0.
If a line falls from left to right, it is diminishing. m<0 is the slope.
A horizontal line has a slope of zero. This is a function that never changes.
Given,
y=3+3(x+4)
y-3=3(x-(-4))
Here, the point on the line is (-4, 3)
And the slope of the line is m=3
Hence, the point on the line is (-4, 3) and the slope of the line is m=3
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An arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 60 students?
1. The students that the academy have per teacher is 18.
2. The students per tutor will be 10.
3. The tutors that the academy need if it has 60 students is 6 tutors.
How to calculate the number of students?Given that the arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students.
The students that the academy have per teacher will be:
= Number if students / Teacher
= 72/4
= 18 students per teacher.
The students per tutor will be:
= 30/3
= 10 students per tutor
The number of tutors for 60 students will be:
= 60 / 10
= 6 tutors.
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suppose a department store wants to estimate the average age of the customers of its contemporary apparel department, correct to within 2 years, with level of confidence equal to 0.95. management believes that the standard deviation is 8 years. the sample size they should take is .
By using the formula for sample size, it can be calculated that the sample size is 62
What is sample?
At first it is important to know about population.
Population is the group of items from where samples are taken for study and research and for statistical purpose
A subset of population is called sample.
Here, margin of error E = 2
Value of z for 95 % confidence interval = 1.96
Standard deviation = 8
Sample size = [tex](\frac{1.96 \times 8}{2})^2[/tex] [tex]\sim[/tex] 62
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Ian's home is represented by the point (4, 4) on the coordinate grid. Joe's home is represented by the point (10, 6) on the coordinate grid. They want to meet at a diner is halfway between their houses (i. E. , divides the line from ian's house to joe's house in a 1:1 ratio). What are the coordinates of the diner?.
(7, 5) are the required coordinates of the diner.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
You do the reverse to determine a point's coordinates in a coordinate system.
Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there.
To find the y-coordinate, repeat the previous step while adhering to a horizontal line.
So, we must discover the halfway point between Lan's house and Joe's house in order to get the diner's coordinates.
The following equation will determine the midway between any two points:
M(x1 + x2/2, y1 + y2/2)
There are (4, 4), the point, and the point replaces the specified values:
M(4+10/2, 4+6/2)
M(7, 5)
Therefore, (7, 5) are the required coordinates of the diner.
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Which equation could generate the curve in the graph below?
Answer:
(Not accurate because I'm estimating amounts) y = ((x-2)/2)^2 + 4
Step-by-step explanation:
Scales horizontally by 2, Shifts up 4, right 2
Find the Base & Height of the triangle
Area =42 in^2
Answer:
Height: 6
Base: 14
Step-by-step explanation:
Area=42 in^2
height=x-1
base=2x
bh/2=42
Substitute in the values:
2x(x-1)/2=42
The 2s cancel out each other.
x(x-1)=42
x^2 - x =42
x^2 - x - 42=0
When we factor that, we get:
(x-7)(x+6)=0
x=7 or x=-6
We will take the positive answer.
height= x-1 = 7-1 = 6
base= 2x = 2(7) = 14
Now let's double check if we are correct.
6(14)/2
=84/2
=42
We are correct!
Answer:
Base: 14 and height: 6 OR Base: -12 and height -7
Step-by-step explanation:
First, set up a proportion. (base x height) divided by 2 on one side and 42 over 1 on the other.
[tex]\frac{2x(x-1)}{2}=\frac{42}{1}[/tex] Next, cross multiply. This involves taking the numerator of
one side (top) and multiplying it by the denominator
(bottom) of the other side.
84=2x(x-1) 42*2=84 and anything multiplied by 1 equals itself. Next,
distribute (multiply) the 2x by each term in the
parentheses.
84=2[tex]x^2[/tex]-2x 2x*x=2[tex]x^2[/tex]. 2x*-1=-2x. Next, subtract 84 from both sides.
0=2[tex]x^2[/tex]-2x-84 Now, you can simplify this by dividing by 2 on both sides.
0=[tex]x^2[/tex]-x-42 This is a quadratic equation, which means you have to
factor or use the quadratic formula. In this case, you can
factor by using product and sum. You have to find what
multiplies to -42 and adds to -1. Those numbers would be
-7 and 6. -7*6=-42 and -7+6=-1 Therefore, you will have
x-7 and x+6
0=(x-7)(x+6) Next, solve each equation with each binomial set equal
to 0. For x-7=0, x=7 because you add 7 to both sides. For
x+6=0, x=-6 because you subtract 6 from both sides.
x=7 x=-6
You can check if these values work by plugging them into the formula.
[tex]\frac{2x(x-1)}{2}- > \frac{2*7(7-1)}{2}- > \frac{14(6)}{2}- > \frac{84}{2}- > 42[/tex]. x can be 7.
[tex]\frac{2x(x-1)}{2}- > \frac{2*-6(-6-1)}{2}- > \frac{-12(-7)}{2}- > \frac{84}{2}- > 42[/tex] x can be -6
The base and height are the numbers in the numerator of the equation after the 3rd arrow for both processes.
What is the equation of a line that has a
3/4
slope of and an x-intercept of 0?
A y=0
B y=3/4
C y=3/4x
D y=x+3/4
Answer: C
Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.
A particle of mass mm moves in the plane with coordinates ( x ( t ) , y ( t ) )(x(t),y(t)) under the influence of a force that is directed toward the origin and has magnitude k / \left( x ^ { 2 } + y ^ { 2 } \right)k/(x 2 +y 2 )—an inverse-square central force field.
An inverse-square central force field is [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].
From Newton's second law of motion,
mass × acceleration = Force acting on the mass
Resolving the force F along x and y directions and applying Newton's second law of motion,
Using,
[tex]r = \sqrt{x^2+y^2}[/tex]
Therefore,
[tex]m\frac{d^2x}{dt^2} =-|F|cos \theta[/tex]
[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]
Where [tex]r = \sqrt{x^2+y^2}[/tex]
and cosθ = [tex]\frac{x}{\sqrt{x^2+y^2} }[/tex]
Similarly using,
[tex]r = \sqrt{x^2+y^2}[/tex]
we get,
[tex]m\frac{d^2y}{dt^2} = -|F|sin\theta[/tex]
[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]
Where [tex]r = \sqrt{x^2+y^2}[/tex]
and sinθ = [tex]\frac{y}{\sqrt{x^2+y^2} }[/tex]
Therefore we showed that holds
[tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex]
Hence the answer is an inverse-square central force field is [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].
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Can someone help? Solve for a given that the height of the triangle is 3 centimeters and each of the legs are 6 centimeters. I also need the centimeters please !!
Answer:
6√3 centimeters
Step-by-step explanation:
This is an isosceles triangle because two of the sides are the same. We can divide this into two triangles to make two right triangles, and use the Pythagorean theorem. The base (a) will be divided by 2.
Pythagorean theorem: a^2 + b^2 = c^2
a and b are the legs of the triangle. c is the hypotenuse.
Let's replace the variables with the given information we know.
The hypotenuse is 6. One of the legs is 3. the other leg is a/2.
3^2 + b^2 = 6^2
9 + b^2 = 36
b^2 = 27
b = √27 = 3√3
Since this was for half of the base, we will multiply it by 2.
3√3 x 2 = 6√3
That is our answer.
I hope this helps.
Ernesto guesses there are 69 marbles in a jar, but there are actually 60.
What is the percent error in Ernesto's guess?
Answer:
15%
Step-by-step explanation:
Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:
60 = 100%
68 = x
x = 69x100/60
x = 115
That means 69 is 115% of 60, which means that the error is of:
115 - 100 = 15%
Hope this helps, have a great day! :D
The sum of 4 times a number and 2 is two times the number minus 8. What is the number?
Answer:
Step-by-step explanation:
The word "Sum" = addition.
"A number" = the unknown, aka 'x'.
"Is equal to" is =.
Go piece by piece. I will set your equation exactly as it is worded as you read it. Follow along:
4x + (-2) = 5x + (-2)
Imagine there is a "1" infront of the parenthesis around the -2. A positive * a negative always = negative. So.
let m be the number of five-element subsets that can be chosen from the set of the first 14 natural numbers so that at least two of the five numbers are consecutive. find the remainder when m is divided by 1000.
We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.
The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .
According to our question-
Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,
with at least two of the five numbers being consecutive.
I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).
Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.
Hence, multiplication principle we come to know that there are 13×(123).
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I got the rest of the answers just stuck on these two
The slope for the first table will be;
⇒ m = - 4/3
The slope for the second table will be;
⇒ m = 1 / 4
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
There are two table is shown in figure.
Now,
For first table;
Two points are,
⇒ (x, y) = (3, -6) (0, - 2)
Since, The slope of the line passing through the points (x₁ , y₁) and
(x₂, y₂) will be;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Hence, Slope for first table;
⇒ m = (- 2 - (-6)) / (0 - 3)
⇒ m = (- 2 + 6) / (-3)
⇒ m = - 4/3
And, For second table;
Two points are,
⇒ (x, y) = (0, -3) (4, - 2)
Since, The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) will be;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Hence, Slope for second table;
⇒ m = (- 2 - (-3)) / (4 - 0)
⇒ m = (- 2 + 3) / (4)
⇒ m = 1 / 4
Thus, The slope for the first table will be;
⇒ m = - 4/3
The slope for the second table will be;
⇒ m = 1 / 4
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how is the year 2029 written as a roman numeral?
The year 2029 written as a roman numeral is MMXXIX.
What are Roman numerals?Roman numerals are mathematical representations of numbers in the Roman alphabet. Roman numerals are a numeral system that originated in ancient Rome and remained the standard way of writing numbers in Europe until the late Middle Ages.
Roman numerals are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, which stand for 1, 5, 10, 50, 100, 500, and 1,000, respectively.
In this case, it should be noted that 2029 is MMXXIX.
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blackhawk tech gives four presidential scholarships. if there are 58 nominees, in how many ways can the scholarships be awarded?
If there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
If there are 58 nominees, and Blackhawk can give only four scholarships then the number of ways is =
[tex]=^nC_r\\\\=^{58}C_4\\\\=\frac{58!}{4!*54!}\\\\=\frac{58 * 57 * 56 * 55}{4 * 3 * 2 *1}\\\\=4,24,270[/tex]
Hence, if there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.
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what is the sum of the infinite geometric series?25 minus 10 plus 4 minus eight fifths plus continuing the series diverges.
Answer:
Geometric Sequence
Finding the sum
The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.
Solution:
Geometric Series Sum Formula: S = a₁/1 - r
Given: a₁ = 3/4
a₂ = -9/16
a₃ = 27/64
a₄ = -81/256
1. Find the common ratio.
a_n = a₁r ⁿ ⁻ ¹
a₂ = a₁r ⁿ ⁻ ¹
-9/16 = 3/4 r ² ⁻ ¹
-9/16 = 3/4 r
2. Divide both sides of the equation by 3/4 to find r.
-9/16/3/4 = 3/4 r/3/4
(-9/16)(4/3) = r
-36/48 = r
-3/4 = r
3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...
S = a₁/1 – r
S = 3/4/1 – (-3/4)
S = 3/4/1 + ¾
S = 3/4/4/4 + 3/4
S = 3/4/7/4
S = (3/4)(4/7)
S = 12/28
S = 3/7
4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.
Definition:
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.
Code: 10.3.1.1
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Step-by-step explanation:
In triangle LMN, the measure of angle L is 50° and the measure of angle M 70°. What is the measure of the exterior angle to angle N?
Answer:
120°
Step-by-step explanation:
The 3 angle measures of a triangle will always equal 180.
Since we've already got two angles, all we need to do is a simple equation to get our missing angle:
180-(50+70)=60
Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:
180-60=120
And there's your answer, 120°
There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!
Please answer! Question is below! Thanks!
Answer:
y=4x+4
Step-by-step explanation:
slope intercept form is y=mx+b
m is slope
B is y intercept
To find slope we use y2-y1/x2-x1
16-(-4)/3-(-2)
20/5
4 is the slope
We can fill this in
y=4x+b
To find b we fill in any coordinates
-4=4(-2)+b
-4=-8+b
+8. +8
4=b
Now we can fill it in
y=4x+4
Hopes this helps please mark brainliest
Identify each of the following as rational or
irrational.
√23
104.42
√64
49.396
10.97846727460
Answer:
Irrational, rational, rational, rational, rational.
Step-by-step explanation:
√23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.
104.42 this is a rational number! An irrational number has repeating values or just random numbers after the decimal point.
Here's an example...
Tell, does this number look rational?
4.2359712309458730495870192354870394587234098657293085412364781236409584790853467923456790324785098234570923845702398547 (and it goes on forever...and ever...and ever......)
√64 is a rational number. As we know that √64 = 8, a rational number.
49.396 with the 6 repeating is rational because we can express 49.39 as:
49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with
49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.
10.97846727460 is rational because the decimal places stop, it is rational. Remember, an Irrational number is non-repeating and non-terminating. Since the number terminates, it is rational
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
In a city with an 8.5% tax rate, what would be the total cost for a $66.00
(9 * 6) * 1 = 3 operations
Answer:
53
Step-by-step explanation:
PEMDAS
Parenthesis
multiply the numbers
Divide
Add
Subtract
5pts and who ever get this right gets brainliest
Answer:D is incorrect
Step-by-step explanation:
D is the only one that is incorrect because D is 9x-81
Answer:
(d) 9(x -9)
Step-by-step explanation:
You want the expression that is not equivalent to the other three.
Simplified expressionsThe simplified versions of the expressions are ...
9(x -1) = 9x -99x -92x -4 +7x -5 = (2+7)x +(-4 -5) = 9x -99(x -9) = 9x -81 . . . . . . . not equivalent to the othersThe expression not equivalent to the other three is 9(x -9).
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an english reading list has 9 american novels and 7 english novels. a student must read 4 from the list, and at least 2 must be american novels. in how many different ways can the 4 books be selected?
The total ways in which the student can readd the books are 1512 ways.
What is Combination?
A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant (unlike permutations).
Solution:
Since reading 2 american novels is compulsory
The student therefore needs to read only two more novels
It can be either American Novels or English Novels
Ways to read American Novel = 7C2
Ways to read English Novel = 7C2
Total Ways = 9C2 * (7C2 + 7C2)
Total Ways = 36 * (42)
Total Ways = 1512 ways
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x, 3, 1, 12, 8 if x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers? (1) x > 6 (2) x is greater than the median of the 5 numbers.
if x is an integer it does not show the median of the 5 numbers to be greater than the average of the 5 numbers
What is a median in math?The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
How do you find the median?Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the center, making it the median of 4, 1 and 7.
(1) x must be higher than one or three. It will be the median if it is 8 or fewer.
Consequently, if x = 7, then the list is 1, 3, 7, 8, 12, and median is 7, while the average is 31/5, which equals 6.2, and the answer is YES.
The list is 1, 3, 8, 8, 12, and the median is 8 if x = 8. Average = 32/5 = 6.4; if x = REALLY BIG, the list is 1, 3, 8, 12, and x; and the median is 8; the answer is YES. The answer to the question is NO since the average is REALLY BIG.
insufficient
(2) According to the aforementioned findings, x must be at least 9.
Depending on the amount of x, the list is either 1, 3, 8, x, 12, or 1, 3, 8, x.
The median and mean expressions are the same, regardless of whether order is appropriate:
Mean (average): 8 median = (1 + 3 + 8 + 12 + x)/5 = (24 + x)/5 mean (average):
The mean is at least (24 + 9)/5 = 33/5 = 6.6 since x is at least 9.
This is not convincing because the mean might be either millions or 6.6 (if x = 9) (if x is huge).
insufficient
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It is -4 in Iceland at 7 am. The temperature then
increases by 6 Degrees. What is the new temperature?
Answer:
Step-by-step explanation:
kakaka
Answer: 2 degrees.
Step-by-step explanation: If it is -4 degrees in Iceland at 7 am and the temperature increases by 6 degrees, the new temperature would be -4 + 6 = 2 degrees.
Write an equation in point-slope form of the line that passes through the given point and with the given slope (-7,2); m =7
Answer:
Y = 7x + 51
Step-by-step explanation:
Point-slope form is in this form: y = mx + b where b is the y-intercept and m is the slope. We have the slope, and we already have a point that must be on the line. The only thing we need is the y-intercept, so we can plug in the given point and the slope to solve for b.
Plug in (-7, 2) for x and y and the slope(7) for m. This gives: [tex]2 = 7*-7 + b[/tex], or [tex]2 = -49 + b[/tex]. Now add 49 to both sides to isolate x, and we get that [tex]b = 51[/tex]. We have everything we need for the equation now, so plug in the slope and y-intercept for m and b, giving us y = 7x + 51.\
Hope this helps!
Fill in the table using this function rule.
y=3x+1
X
2
3
6
7
X
y
0
0
0
S
Answer:
y={7,10,19,22}
Step-by-step explanation:
3(2)+1 = 6+1 = 7
3(3)+1 = 9+1 = 10
3(6) + 1 = 18+1 = 19
3(7) + 1 = 21+1 = 22
Can someone please help me with, best answer will be marked brainiest.
A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.
The value of x is 47
The value of y is 10.6
The four angles for the given quadrilateral are,
96, 94, 76, and 94.
What is quadrilateral?A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.
We have,
A an isoceles trapezium.
Where one pair of sides are equal and parallel.
Two angles are equal.
Now,
94 = 2x
x = 47
Now,
The four angles sum is 360.
94 + 94 + 96 + 3y + 44 = 360
328 + 3y = 360
3y = 360 - 328
3y = 32
y = 32/3
y = 10.7
Now,
3y + 44 = 3 x 10.7 + 44 = 32 + 44 = 76
Thus,
The four angles for the given quadrilateral are,
96, 94, 76, and 94.
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Determine the distance covered by a car traveling 80 km/h each unit and given time round answers to the nearest unit.
A. Kilometers in on hour?
B. Meters in one hour?
C. Meters in one minute?
D. Meters in one second?
Determine the distance covered by a car traveling 80 km/h for each unit and time given. The answer should be in meter in one hour.
What is a kilometer?
1,000 meters is one metric unit of measurement (approximately 0.62 miles).
The car is travelling at the speed of 80 kilometers per hour.
One hour is 60 minutes.
So car will travel in ideal conditions 80 kilometers in one hour which is 60 minutes.
So just convert the kilometers into meters.
1 kilometer = 1000 meters,
Thus,
80 kilometers = 80,000 meters.
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Elouise and Marcus are 20km apart.
There is a lake due west of Elouise that is also 10√3 km due north of Marcus.
Work out the bearing of Marcus from Elouise
Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.
At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.
Given that,
Elouise and Marcus are 20 km apart (AB)
There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)
Now, according to a Pythagoras theorem,
(AC)² + (AB)² = (BC)²
or, (AC)² = (BC)²- (AB)²
or, (AC)² = (10√3)² - (20)²
or, AC = [tex]\sqrt{500}[/tex]
or, AC = 22.36 km
So, distance bearing of Marcus from Elouise is 22.36 km.
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true or false: the most common level of confidence used in creating confidence intervals is 90%. group of answer choices true false
It is true, that the most level of confidence used in creating confidence intervals is 90%.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
We have given,
Given n = 93, u =24, x' = 23, α=5.5
z = x'- u / α(/√n) = 1.645
Hence the answer choice is true.
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