The final answer of the problem is -0.75.
What is the order of operations?
The order of operations is also known as the hierarchy of operations. The order of operations tells us the order in which we should perform mathematical operations in order to get the correct result. The order of operations is usually represented by the acronym PEMDAS:
P: Parentheses first
E: Exponents (ie Powers and Square Roots, etc.)
MD: Multiplication and Division (left-to-right)
AS: Addition and Subtraction (left-to-right)
We have,
-1 - (-0.25)
Using the order of operations, we can solve this problem as follows:
Parentheses: The first step is to perform any calculations inside parentheses. In this case, there are no parentheses, so we can move on to the next step.
Exponents: There are no exponents in this problem, so we can move on to the next step.
Multiplication and Division: There is no multiplication or division in this problem, so we can move on to the next step.
Addition and Subtraction: Finally, we can perform addition and subtraction in the problem. We start from left to right, so we start with the first operation: -1 - (-0.25). To subtract a negative number, we can use the rule that subtracting a negative number is the same as adding a positive number.
Therefore, we have -1 + 0.25.
The final step is to simplify the expression by performing the addition: -1 + 0.25 = -0.75.
Therefore, the final result of the problem is -0.75.
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please help and tell me what to put in
Using the two column proof, we have been able to prove that;
ΔPQR ≅ ΔTSR by AAS Congruency Postulate
How to solve two column proof problems?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
Thus, the two column proof required is as follows;
Statement 1: PR ≅ TR
Reason 1: Given
Statement 2: ∠PQR ≅ ∠TSR
Reason 2: Given
Statement 3: ∠PRQ ≅ ∠TRS
Reason 3: Opposite angles
Statement 4: ΔPQR ≅ ΔTSR
Reason 4: AAS Congruency postulate
AAS congruency postulate is one of the 5 major triangle congruency postulates that is defined as Angle-Angle-Side. This tells us that two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
We can also say that Opposite angles are defined as the angles that are directly opposite each other where two lines cross. The intersection point in this regards is called the vertex, which is the point where the lines connect to form the angle. Opposite angles are also referred to as vertical angles
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A professor wanted to know what proportion of college students believe in ghosts. She polled 200 students and found that 58% said they believe in ghosts. Create a 99% confidence interval for the true proportion of college students believing in ghosts. a. (0.5116, 0.64840 b. (0.2074, 0.3727) c. (0.4901, 0.6699) d. (0.2271,0.3529)
A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c) (0.4901, 0.6699)
According to the question,
A professor wanted to know what proportion of college students believe in ghosts.
For that he drawn a sample from the college.
Sample size : n = 200
Proportion of students that believed in ghosts in sample = 58%
=> p = 0.58
Proportion of students who does not believe in ghost : q = 1 - p
=> q = 0.42
We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts
Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200
=> 0.58 ± 2.576 √0.001218
=> 0.58 ± 2.576 × 0.035
=> 0.58 ± 0.08958
C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)
Hence, Option (c) is correct
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Answer:
41%
Step-by-step explanation:
Cost of goldfish: $3.45
Markup: 29%
What is the new cost?
After the markup in the price, the new cost of goldfish will be equal to $4.45.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Cost of goldfish = $3.45
Markup = 29%
So, the price increase will be,
(3.45 × 29)/100
= 100.05/100
= 1.0005
So, the new price is,
$3.45 + $1.0005
= $4.4505 ≈ $4.45
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find the value of the expression w2 + 1v for v=3 and w=3
Answer: 12
Step-by-step explanation:
Since we are given what v and w are, we can directly plug them in to solve the expression.
w²+1v [plug in v and w]
(3)²+1(3) [exponent]
9+1(3) [multiply]
9+3 [add]
12
The expression is equal to 12.
Milan is driving to San Francisco. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Milan has 68
milles to his destination after 37 minutes of driving, and he has 45.6 miles to his destination after 65 minutes of driving. How many miles will he have to his
destination after 81 minutes of driving?
After 81 minutes of driving the distance to destination is 32.8 miles.
What is linear function?Th function that has two variables with first order term is called linear function. While plotting on the XY coordinate system we get a straight line.
Why do we use linear equation in this problem?
as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.
given, distance to destination in miles is a linear function of total driving time in minutes.
y=mx+b
in the equation, y denotes the distance to destination in miles
x is the total driving time in minutes
m is the slope of linear equation
b is the y intercept
Milan has 68 miles to his destination after 37 minutes of driving
68 = mx37+b
he has 45.6 miles to destination after 65 minutes of driving
45.6=mX65+b
solving the two equations by addition method
slope, m= -0.8
from the above two equation
we get b=97.6
now, after 81 minutes of driving the distance to destination, y=mx+b
y= -0.8x81+97.6
distance = 32.8 miles
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Which expressions are equivalent to 20 divided by 1 plus 4
The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.
What are the rules of PEDMAS?The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.
The given statement for the problem is, " 20 divided by 1 plus 4".
It can be written in the form of expression as follows,
The sign of plus is given as '+'.
And, for divide it is '÷'.
Now, 20 divided by 1 plus 4 can be written as,
20 ÷ 1 + 4
Which is evaluated by BODMAS to give,
20 + 4 = 24.
Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.
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What is an equation of the parabola
Answer:
(c) x = -1/11(y -3)²
Step-by-step explanation:
You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).
EquationThe directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.
The vertex form of the equation is ...
x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)
ApplicationHere, we have ...
p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix
and
(h, k) = (0, 3)
so the equation is ...
x = 1/(4(-11/4))(y -3)² +0
x = -1/11(y -3)²
which of the following is not a valid property of circles? a rotateangle b none of these c left d width
There is no property named 'left' for the circle. So the answer is 'c'.
What is Circle?Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.
The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.
Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.
Width is another term for diameter of the circle, although it is not commonly used.
Left is the only term which does not have any role in the properties of circles.
Hence, the term 'left' is not a valid property of circles.
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Write each of these numbers in base five as a sum of multiples of powers of five (5):
(a). 1012⁵
(b). 101⁵
(c). 1.1⁵
(d). 10.21⁵
(e). 210⁵
Answer:
Step-by-step explanation:
a) 1012⁵ can be written as:
1012⁵ = 15¹² + 05¹¹ + 1*5¹º
= 5¹² + 5¹º
= 3125 + 625
= 3750
(b) 101⁵ can be written as:
101⁵ = 15⁴ + 05³ + 1*5²
= 5⁴ + 5²
= 625 + 25
= 650
(c) 1.1⁵ can be written as:
1.1⁵ = 15¹ + 15º
= 5¹ + 5º
= 25 + 5
= 30
(d) 10.21⁵ can be written as:
10.21⁵ = 15² + 05¹ + 25º + 15⁻¹
= 5² + 2*5º + 5⁻¹
= 25 + 10 + 0.2
= 35.2
(e) 210⁵ can be written as:
210⁵ = 25⁴ + 15²
= 2*625 + 25
= 1250 + 25
= 1275
Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college. The rate is 4.3%. How much interest accrued in the first four-and-a-half years
The interest accrued in the first four years is $1.69 and a half years is $0.21.
What is interest rate?
The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
Given:
Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.
The rate is 4.3%.
We have to find the interest accrued in the first four-and-a-half years.
First to find the interest for first four years.
p = $9.800, r = 4.3% = 0.043, t = 4
⇒ I = P x r x t
I = 9.800 x 0.043 x 4
I = 1.6856
I = $1.69
Now to find the interest for a half years.
p = $9.800 , r = 4.3% = 0.043, t = 1/2
I = p x r x t
I = 9.800 x 0.043 x 1/2
I = 0.2107
I = $0.21
Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.
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You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?
Kim decided that she wanted to go bowling. The bowling alley charges $2.75 per game and $10 for shoes. If Kim has $30, how many complete games can she bowl?
Write an equation and solve it.
Answer: 2 complete games
Step-by-step explanation:
add shoes and game charge
$10.00 + 2.75 = 12.75 <— that’s 1 complete game
subtract it from $30.00
$30.00 - 12.75 = 17.25.
A complete game costs 12.75. so, Kim had enough money for one more game.
17.25 - 12.75 = $4.50 remaining after 2 complete games
Answer: 7 games
Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.
Which number is a solution of the inequality?
x(7-x) > 8
x(7 - x) > 8
Steps for calculationFirst solve x(7 - x) = 8
x^2 - 7x + 8 = 0
x = 5.56, 1.44
If we plug in these values into the original equation we can see that solution is
1.44 < x < 5.56
Meaning and definition of systems of inequality:The value of the variable(s) that transforms the inequality into a true statement is the solution. Think about the example (x+3>5). If we provide any real value bigger than (2) for this inequality, it will be true (x). (therefore) This inequality's answer is (x>2)A collection of two or more inequalities in one or more variables is referred to as a system of inequalities. Systems of inequalities are utilized when a scenario calls for several solutions but also places multiple restrictions on those answers.The best answer is often found by solving a set of linear inequalities. This response could be as simple as calculating the number of products that need be produced in order to maximize profit or as complex as selecting the ideal medication regimen for a patient. The different kinds of inequalities and how to solve them will be covered in this article.To learn more about Systems of inequalities refer https://brainly.com/question/26119697
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Match the correct statement with the given information.
The correct statements regarding the transformations to the volumes are given as follows:
1. A cone's radius increases x 3: -> The cone's volume will increase x 9.
2. A cone's height increases x 3: -> The cone's volume will increase x 3
3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.
4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.
What are the volumes?The volume of a cone of radius r and height h is given as follows:
V = πr²h/3.
Then the scale factors are considered as follows:
If the radius is multiplied by 3, the volume is multiplied by 9, as the volume is squared.If the height is multiplied by 3, the volume is also multiplied by 3, as the power of the variable h is of h.The volume of an sphere of radius r is given as follows:
V = 4πr³/3.
Then when the radius is multiplied by 3, the volume is multiplied by 27, as 3³ = 27, and the radius is cubed in the equation.
The volume of a cylinder of radius r and height h is given as follows:
V = πr²h.
Then if the radius is multiplied by 6, the volume is multiplied by 36, as the variable r is squared in the equation for the volume.
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Find tan(0), if cot(0) = -2.6
According to Trigonometric Identity , tan(theta) = -5 / 13
What are Trigonometric Identities ?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.
Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.
According to the given information
We know that
tan(theta) = 1/cot(theta)
= 1 / -2.6
= -1 / 2.6
= -10 / 26
= -5 / 13
According to Trigonometric Identity , tan(theta) = -5 / 13
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expressions equivalent to 9 2/3
The equivalent expression for the given expression is 29/3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given mixed fraction [tex]9\frac{2}{3}[/tex].
There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.
Convert mixed fraction to improper fraction as follows
Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator
[(9×3)+2]/3
=[27+2]/3
= 29/3
Therefore, the equivalent fraction for the given mixed fraction is 29/3.
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Use a sign chart to solve the inequality. Express the solution in inequality notation and in interval notation. X2 - 5x - 36 < 0 The solution expressed in inequality notation is.
The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)
The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.
Here we have given the inequality (x² - 5)/ (x - 36) < 0
And we need to find the solution in inequality notation and in interval notation.
In order to find the inequality notation, we have to solve the given inequality, then we get.
(x² - 5)/ (x - 36) < 0
(x² - 5) < 0
x² < 5
x < √5
While we looking into the inequality we must know that the denominator must not be 0.
So, the interval notation can be written as,
=> (-∞ . -√5]∪[√5,36)
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Solve ABC using diagram and the given measurement A=64 a=7.4
Answer:
Hope this helps!
A magician's hat contains black rabbits and white rabbits. The magician selects two rabbits without replacement. If the probability of selecting a black rabbit and a white rabbit is 1/4, and the probability of selecting a black rabbit on the first draw is 5/12, find the probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit.
The probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit is 3/5.
P(B∩W) = 1/4 getting a black and a white rabbit
P(B) = 5/12 getting a black rabbit
P(W/B)
= P(B∩W) / P(B)
= (1/4) / (5/12)
= 12/20
= 3/5
Therefore, the conditional probability is 3/5.
Conditional probability is the chance of an event A occurring when another event B in relation to A has previously occurred. P(A|B) represents it. As seen in the picture above, S represents sample space, and A and B represent events.
The potential of an event or outcome occurring based on the existence of a preceding event or outcome is known as conditional probability. It is computed by multiplying the preceding event's probability by the renewed probability of the next, or conditional, occurrence.
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Which ordered pair lies on the graph of the function y = -2x + 1? (0, -2) (2, -2) (3, -5) (5, 2
So, the ordered pair which lies on the graph of the function y = -2x + 1 is (3,-5)
We will use the substitution method and check for all the ordered pair which are given
If the ordered pair lies on the graph, then it should satisfy the function.
So,
Given,
y = -2x+1
First check for (0,-2)
x=0, y=-2
Substitute the values,
y = -2x+1
-2=-2(0)+1
-2=1
It is false.
Next check for (2,-2)
x=2, y=-2
Substitute the values,
y = -2x+1
-2=-2(2)+1
-2=-3
It is false.
Next check for (3,-5)
x=3, y=-5
Substitute the values,
y = -2x+1
-5=-2(3)+1
-5=-5
It is true.
Next check for (5,2)
x=5, y=2
Substitute the values,
y = -2x+1
2=-2(5)+1
2=9
It is false.
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If a fair coin is tossed 9 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 tails?
Answer:
Below
Step-by-step explanation:
2^9 possibilities =512
9 possibles with only ONE tails (9 C 1)
36 possibles with TWO tails ( 9 C 2)
45 out of 512 45/512 = .088
Can someone help me?
Answer:
Y=6x-12
Step-by-step explanation:
whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.
For rhombus LMNO, m∠LON = 102° and NP = 5 units.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Use the diagram of rhombus LMNO to find the missing measures.
The measure of ∠LPM is
°.
The measure of ∠PMN is
°.
The length of LN is
units.
the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
Define Rhombus.
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.
For a Rhombus, LMNO
∠LON = 102°
NP = 5 units
By the properties of Rhombus, we know that
All sides of a rhombus are congruent (equal)
So, LM = MN = NO = OL
and
Opposite angles are equal and the opposite sides are parallel.
So, ∠LON = 102° = ∠LMN
Since Adjacent angles add up to 180°.
Therefore ∠L + ∠M = 180°
∠M + ∠N = 180°
∠N + ∠O = 180°
∠O + ∠L = 180°
So, ∠N = 180° - ∠O = 180° - 102° =78°
∠L = 180° - ∠O = 180° - 102° =78°
∠M = 180° - ∠L = 180° - 78° =102°
Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.
So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°
Thus, the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
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Answer:
Lpm= 90
PMN=51
LN= 10
Step-by-step explanation:
There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.
How long will it take (in days) for there to be 150 frogs in the pond?
Time to 150 frogs: days
The pond's ecosystem can support 1400 frogs. How long until the situation becomes critical?
Time to 1400 frogs: days
There are 21 days for there to be 150 frogs in the pond.
There are 37 days for there to be 1400 frogs in the pond.
What is exponential growth?
Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.
Given:
There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.
The exponential equation for the given problem is,
[tex]A(t) = Ar^t^/^1^0[/tex]
To find the number of days for there to be 150 frogs in the pond.
Here,
A(t) = 250, A = 25, r = 3
⇒
[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]
t ≈ 21
Hence, there are 21 days for there to be 150 frogs in the pond.
Now to find how long for there to be 1400 frogs in the pond, we solve:
[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]
t ≈ 37
Hence, there are 37 days for there to be 1400 frogs in the pond.
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An air traffic controller is tracking two planes. To start, plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitudes be when they’re at the same altitude?
44 seconds will pass before the planes are at the same altitude.
What do you mean by algebraic expression?
An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.
There are three main types of algebraic expressions:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression with only one term is called a monomial.
It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.
Let x seconds will pass before the planes are at the same altitude.
Plane A, 3500 + 45.5x
Plane B, 2609 + 65.75x
x is number of seconds of time
When altitudes equal
3500 + 45.5x = 2609 + 65.75x
3500 - 2609 = 65.75x - 45.5x
891 = 20.25x
891/20.25 = x
44 = x
Therefore, 44 seconds will pass before the planes are at the same altitude.
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MP MODELING REAL LIFE You sell instruments at a
Caribbean music festival. You earn $326 by selling 12 sets
of maracas, 6 sets of claves, and x djembe drums. Find the
number of djembe drums you sold.
The number of djembe drums you sold is 8
How to determine the number of djembe drums you sold.From the question, we have the following parameters that can be used in our computation:
Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.
Earning = $326
Also, we have:
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
So, we have
12 * 14 + 6 * 5 + x * 16 = 326
Evaluate the products
198 + 16x = 326
Evaluate the iike terms
16x = 128
So, we have
x = 8
Hence, the number of djembe drums is 8
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Complete question
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
Find the number of djembe drums you sold.
Which equation is the inverse of y = 2x^2 – 8?
Inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]
What do you mean by inverse function?
Let f and g be two functions. If
f(g(x)) = x and g(f(x)) = x,
g is the reciprocal of f, and f is the reciprocal of g.
Some functions don't have inverses Let f be a function.
If the horizontal line crosses the graph of f more than once, then f has no inverse.
If no horizontal line crosses the graph of f more than once, then f is the inverse.
Given equation:
y = [tex]2x^2-8[/tex]
To find the inverse of the function find the value of the x in terms of y
[tex]2x^2-8=y[/tex]
[tex]2x^2=y+8[/tex]
[tex]x^{2} =\frac{y+8}{2}[/tex]
x = [tex]\pm \sqrt{\frac{y+8}{2} }[/tex]
Therefore, inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]
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At a football game, a vender sold a combined total of 244 sodas and hot dogs. The number of hot dogs sold was 42 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
143 sodas101 hot dogsStep-by-step explanation:
Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.
SetupLet s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...
s +(s -42) = 244
SolutionAdd 42 and simplify
2s = 286
s = 143 . . . . . divide by 2
hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs
143 sodas and 101 hot dogs were sold.
Find the equation of a line that contains the points (−7,2) and (2,−2). Write the equation in slope-intercept form using fraction if necessary.
The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
What is the equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
The equation of the line's general form is:
y = MX + c
Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).
Determine the line's slope:
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2-2) / (2+7 )
Slope= -4/9
The y-intercept is determined as follows:
y = MX + c
2 = -4/9x 2+c
c = -8/9
The lines' equation:
y = MX + c
y = -4/9x - 8/9
Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
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Select the best answer. The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean (a) if the sample size is reasonably large (for any population). (b) if the population is Normally distributed and the sample size is reasonable large. (c) if the population is Normally distributed (for any sample size). (d) if the population is Normally distributed and the population standard deviation is known (for any sample size). (e) if the population size is reasonably large (whether the population distribution is known or not).
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
Given that,
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean,
In layman's words, the theorem asserts that regardless of the form of the initial population distribution, the sampling distribution of the mean tends to resemble a normal distribution as the sample size rises.
Statistics benefits from the Central Limit Theorem because it makes it safe to assume that the sampling distribution of the mean will be typically normal. As we will see in the next section, this means that we can benefit from statistical methods that presume a normal distribution.
The distribution of people's heights within a population is one illustration of how the central limit theorem is put to use. Even though the population's distribution of heights is not normal, when we sample this population, the distribution of the sample averages will be roughly normal.
Therefore,
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
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