The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).
The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.
The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.
In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.
The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.
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In December, Mr. Dillon opened a checking account and made deposits of $1530, $896, $571, and $472. He also wrote checks for $32, $918, $825, $661, and $224. What was his balance at the end of the month?
Mr. Dillon balance at the end of month is $809.
What is checking account?In a financial institution, a checking account is a deposit account that permits both deposits and withdrawals.
What is deposit?Money kept or held in any bank account is referred to as a deposit.
What is withdrawal?A withdrawal entails taking money out of a trust, pension, savings plan, or bank account.
As Mr. Dillon opened a checking account, so balance is $0 in starting.
When he deposits $1530, $896, $571, $472
Total deposit= $1530+$896+$571+$472
= $ 3,469
Check is a kind of withdrawal.
He wrote check of $32 , $981 , $825 , $661 , $224
Total withdrawal= $32+$981,$825+$661+$224
= $2,660
Balance= Total deposit - Total withdrawal
= $3,469 - $2,660
= $809
Therefore, balance is $ 809.
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A horse eats 10 kg of hay each day. she is for equal sized meals each day how many grams are in each meal ?
Answer:
For the problem with the horse: 10,000 grams
For the problem with the hiker labeled 11: 2 feet
I hope these answers are of use to you!
Step-by-step explanation:
Okay, for the horse problem I understood that it was a horse eating exactly 10 kg per day. If she does, then you just convert 10 kilograms to grams. To do this, you multiply the amount of kilograms by 1,000, since that is how it works.
10 x 1,000 = 10,000 grams.
For the problem labeled 11 with the hiker, you divide 120 ft by 60 since there are 60 seconds in a minute.
120 divided by 60 = 2 feet
{y:y is an integer AND Y>10
{y:y is an integer AND y>10} is a set of integers that are greater than 10. Some examples of elements that would be included in this set are 11, 12, 13, 14, and so on.
A plane flying horizontally at an altitude of 2 km and a speed of 600 km/h passes directly over a radar station. Find the rate (in km/h) at which the distance from the plane to the station is increasing when it is 3 km away from the station. (Round your answer to the nearest whole number.)
Answer:
When the plane is 2mi away from the radar station, its distance's increase rate is approximately 433mi/h.
Step-by-step explanation:
Sketch a right triangle with one leg going vertically a length of 3 miles above the station, and the other leg x going horizontally from the top of the first leg. Distance r from plane to station is related by r2 = x2 + 32. Differentiate: 2r dr/dt = 2x dx/dt, which rearranges to the desired dr/dt = x/r dx/dt. When r = 4, x2 = 42 - 9 and x = √7. So dr/dt = (√7 / 4) * 520 mph = 344 mph.
Line q passes through the points (3,5) and (-2,4).
10. Give a second pair of coordinates on the line parallel to q that passes through (0,1).
11. Give a second pair of coordinates on the line perpendicular to q that passes through (3,5).
The second pair of coordinates on the line parallel to q that passes through (0,1) is (1,-4/5) and that of (3,5) is (1,7).
How to solve equation of a line?The general form of the equation of a line is y=mx+c
where
m=slope
c is a constant
The equation of the line is
m= [tex]\frac{y-y_{1} }{x-x_{1} }[/tex]
M=[tex]\frac{5-4}{3+2}[/tex]
m=1/5
From the slope formula
m = -1/5
X₎=0
y₎=1
substitute these in the formula for slope
[tex]\frac{-1}{5} =\frac{y-1}{x-0}[/tex]
x=5y-5
x-5y=5
Now, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.
when x=1,
x-5y=5
1-5y=5
-5y=5-1
y=[tex]\frac{-4}{5}[/tex]
The other coordinate is (1,-4/5)
11. In the second line (3,5)
Using the slope formula
m=[tex]\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]
[tex]\frac{-1}{5} =\frac{y-5}{x-3}[/tex]
x-3=-y+2
x+y=5+3
x+y=8
Also, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.
when x=1,
x+y=8
1+y=8
y=8-1
y=7
Therefore the second coordinate is (1,7)
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True or false If the sample size is at least 30, we use the z-critical value
Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. The given statement is true.
Does critical value depend on sample size?
The sample size and the crucial value that the researcher employed must be connected. The variations in critical values between the t-distribution and the normal-shaped sampling distribution, however, are minimal for sample sizes bigger than 30.
Z-tests and t-tests are closely related, but t-tests work best with small sample sizes of data, or those with fewer than 30 participants. Additionally, whereas z-tests assume that the standard deviation is known, t-tests assume that it is unknown.
You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.
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The sum of a number and six is four less than six times the number
4 - 6x is linear equation .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
A linear equation's graph almost always takes the shape of a straight line.
Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
let the number be =x
4 - 6x
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if 2x - 4y = 0 is written as a directly proportional function, where y is a function of x, then what is k?
a. 2
b. 1/2
c. 4
d. 1
Answer:
b
Step-by-step explanation:
4y = 2x
y = 2/4 x
y = 1/2 x where y = kx then k = 1/2
“24 hours per day” translate the algebraic expression
Answer:
24*X or 24X
Step-by-step explanation:
24X or 24*X or 24 multiplied by X days
The variable "X" represents the number of days.
Max baked 5 pies for the bake sale. He cut each pie into 8 equal slices. In the first 30 mins of the bake sale, Max sold 19 slices of pie. How many pies did max sell in that time? Give your answer in 2 ways
Answer: He sold 19/40 of his pies or 0.475% of his pies
Step-by-step explanation: There are 40 total slices of pie and if he sold 19, then the fraction is 19/40. Additionally the fraction 19/40 as a decimal is 0.475 so it would be 0.475% of the pies.
(Evaluate a function for a given domain and a domain value for a given range.)
If f(x)=3-5x, then find the value of each of the following. Show your work/thinking.
a) f(2)
b) f(-4)
c) f(0)
can you please explain
Answer:
a) 3-5*2=-7
b)3-5*-4=23
c)3-5*0=3
Step-by-step explanation:
you would plug each of them into the equation because they give you x so
a) 3-5*2=-7 x=2
b) 3-5*-4=23 x=-4
c) 3-5*0=3 x=0
Can someone help me simplify 4(3x^2y^4)3 / (2x^3y^5) ^4??? Actually answer, give explanation. How did you arrive to the answer??
The simplified form of the given expression, 4(3x^2y^4)3 / (2x^3y^5) ^4, is 27/x⁶y⁸
Simplifying an expressionFrom the question, we are to simplify the given expression
From the given information,
The expression is
4(3x^2y^4)3 / (2x^3y^5) ^4
First, we will write the given expression properly
The given expression written properly is
4(3x²y⁴)³ / (2x³y⁵)⁴
Simplifying the expression
4(3x²y⁴)³ / (2x³y⁵)⁴
4 × (3x²y⁴)³ / (2x³y⁵)⁴
4 × (3)³(x²)³(y⁴)³ / (2)⁴(x³)⁴(y⁵)⁴
4 × (3)³ × (x²)³ × (y⁴)³ / (2)⁴ × (x³)⁴ × (y⁵)⁴
4 × 27 × x⁶ × y¹² / 16 × x¹² × y²⁰
108 × x⁶ × y¹² / 16 × x¹² × y²⁰
This can be further expressed as
108/16 × x⁶/x¹² × y¹²/y²⁰
27/4 × 1/x⁶ × 1/y⁸
= 27/x⁶y⁸
Hence, the simplified expression is 27/x⁶y⁸
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Need answer asap don’t know
The length of the JU would be 60 units.
What is the Basic Proportionality Theorem?
The basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.
In the given figure side TU is parallel to side LK
If JK = 64 and JU = -4 + 4x
then UK = JK - JU
= 64 - (-4 + 4x)
=68 - 4x
Similarly,if JL = 72 and JT = 27
then TL = JL - JT
= 72 - 27
= 45
Now by using the property of the basic proportionality theorem, we can write
[tex]\frac{JT}{TL} =\frac{JU}{UK}\\\\ \frac{27}{45} =\frac{-4+4x}{68 - 4x}\\\\\frac{3}{5} = \frac{-4+4x}{68 - 4x}\\\\3(68-4x) = 5(-4+4x)\\\\204 - 12x=-20+2x\\\\204+20=14x\\\\x=\frac{224}{14}\\\\x=16[/tex]
Now we can calculate the length of JU = -4 + 4x
= -4 + 4(16)
= -4 + 64 = 60
Hence, the length of the JU would be 60 units.
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A parking garage bases its prices on the number of hours that a vehicle parks in the garage.
The first two hours cost $2 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
b
The first two hours cost $2 per hour, between two and four hours cost $1 per hour, and all hours after that cost $0.50.
c
The first two hours cost $4, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
d
The first two hours cost $4, between two hours and six hours cost $1 per hour, and all hours after that cost $0.50.
Answer:
c The first two hours cost $4, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
Step-by-step explanation:
You want an interpretation of the graph that is a constant 4 up to x=2, has a slope of 2 for 2 ≤ x < 6, and a slope of 1 for x ≥ 6. The vertical axis is labeled dollars, and the horizontal axis is labeled hours.
Graph interpretationThe constant value of y = 4 for x < 2 means the cost of parking is $4 for the first two hours.
The slope of 2 from x=2 to x=6 means the cost of parking is $2 per hour between 2 and 6 hours.
The slope of 2 for x ≥ 6 means the cost of parking is $1 per hour for more than 6 hours.
The description of c applies.
__
Additional comment
The slope, or "unit rate", is the ratio of "rise" to "run". It can be simpler to choose a "run" of 1 and look at the corresponding "rise".
From x=2 to x=3, the cost rises from $4 to $6, a rise of 2 for the run of 1. That is why we say the slope is 2, or the "unit rate" in dollars per hour is $2 per hour.
A 16 foot long ladder is placed against a 12 foot high wall, reaching the top exactly. (Round your answer to the nearest hundredth if necessary.)
7th/8th math quick it is a test
pwese quick
The distance of the foot of the ladder from the wall is 10.58m, the distance can find using pythagoras theorem states that in a right-angled triangle.
What is Pythagoras Theorem?A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two points.
Let AC be the ladder and A be the window.
Given: AC=15m, AB=12m, CB=am
In right angled triangle ACB,
(Hypotenuse) ² =(Base)² +[Perpendicular)² [By Pythagoras theorem]
⇒(AC)² =(CB)² +(AB)²
⇒(16)² =(a)² +(12)²
⇒256 = a² + 144
⇒ a = √112 = 10.58cm.
The distance of the foot of the ladder from the wall is 9m.
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
2.0 acres
Step-by-step explanation:
C(x) = 270 ln(x+1) + 1900 = 2200
270 ln(x+1) = 300
ln(x+1) = 10/9
x+1 = e^(10/9)
x = e^(10/9) - 1 = 2.0377
Find the volume of the figure below. Round your answer to the nearest tenta
A. 5870.8 ft³
B. 6575.3 ft³
C. 4559.3 f³
D. 5017.8 ft
12 ft
11 ft
Please help!!!!
What is AC?
Answer:
Step-by-step explanation:
I think its 40
The triangle is isosceles so the left and right side are equal in length.
you would equal 4x+4=6x-14 and solve, getting 18=2x the 9=x
A sales representative can take one of 3 different routes from City Upper C to City Upper D and any one of 6 different routes from City Upper D to City Upper G. How many different routes can she take from City Upper C to City Upper G, going through City Upper D?
The number of different routes she can take from City Upper C to City Upper G is 18
How to determine the number of different routes can she take from City Upper C to City Upper G?From the question, we have the following parameters that can be used in our computation:
Routes from City Upper C to City Upper D = 3 routes
Routes from City Upper D to City Upper G = 6 routes
The number of different routes she can take is calculated as
Routes = Routes from City Upper C to City Upper D x Routes from City Upper D to City Upper G
Substitute the known values in the above equation, so, we have the following representation
Routes = 3 * 6
Evaluate
Routes = 18
Hence, the number of routes is 18
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every answer i have put is wrong can someone help
The mathematical model that gives the stopping distance d in terms of speed v is
d = 1/(40 x 5280²) v²
The stopping distance when v is 59 miles per hour is 87.03 feet.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
The stopping distance d is directly proportional to the square of the speed v.
This can be written as,
d ∝ v²
Now,
Converting 40 miles into feet.
1 mile = 5280 feet
40 miles = 40 x 5280 feet
40 miles = 211200 feet
Now,
40 feet ∝ 211200 feet per
Now,
The stopping distance is 40 feet when the speed is 40 miles per hour
d = 40 and v = (40 x 5280) feet per hour
d = k v²
k = d/v²
k = 40/(40 x 5280)²
k = 1/(40 x 5280²)
The mathematical model that gives the stopping distance d in terms of speed v is
d = 1/(40 x 5280²) v²
The stopping distance when v is 59 miles per hour
v = (59 x 5280) feet per hour
d = 1/(40 x 5280²) x (59 x 5280)²
d = (59 x 59) / 40
d = 87.03 feet
Thus,
The mathematical model that gives the stopping distance d in terms of speed v is
d = 1/(40 x 5280²) v²
The stopping distance when v is 59 miles per hour is 87.03 feet.
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Maria is going to purchase cranberry juice and lemon-lime soda for a new fruit punch recipe. The recipe calls for 3.5 times as many bottles of lemon-lime soda as cranberry juice. If she has $17.40, what is the most bottles of cranberry juice she can buy if cranberry juice costs $3.80 per bottle and lemon-lime soda costs $1.40 per bottle?
Answer:
Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.
Step-by-step explanation:
Setting up the SolutionFor this problem, we can set up an algebraic expression to represent the price, and this will help us solve the problem.
So firstly, let's assign the number of cranberry juice bottles to the variable "C". We could technically represent this as the variable name "cranberry juice bottles", but "C" is a bit more easier to write when writing an algebraic expression while still making it easy to distinguish. Let's also assign the number of lemon-lime soda to the variable "L".
Now let's find a way to express the price of each. The price of buying a certain amount of items, can generally be expressed as: [tex](\text{items bought})*(\text{item price})[/tex], since you have to pay the item price for each item bought, also known as, multiplication.
Since we know that the price of a cranberry juice bottle is $3.80 then that means the total amount used towards cranberry juice can be expressed as: [tex]3.80C[/tex]. We're just multiplying the number of cranberry juice bottles times the price. Likewise, we can represent the total amount used towards lemon-lime soda as: [tex]1.40L[/tex]. The same logic is being applied here.
Now if we add both of these, we get the total amount that will be spent which is: [tex]3.80C + 1.40L = T[/tex], and in this case I just set it equal to "T" which just represents the total spent.
Now there's two more things to do. Generally we can't really solve two-variable equations and we want to express one variable in terms of the other, so that we can rewrite the equation as a one-variable equation.
There is one piece of information given that allows us to do this. "The recipe calls for 3.5 times as many bottles of lemon-lime soda as cranberry". So we can represent the numbers of lemon-lime soda bottles as 3.5 times the amount of cranberry juice bottles. We can express it as: [tex]L=3.5C[/tex]
So now let's plug this into the equation, instead of "L". This gives us: [tex]3.80C + 1.40(3.5C) = T[/tex]
let's multiply the 1.40 by the 3
[tex]3.80C + 4.9C= T[/tex]
now let's add up the values.
[tex]8.7C=T[/tex]
Now lastly, this represents the total amount that is going to be spent. Since Maria only has $17.40, we want this total to be less than or equal to 17.40 (assuming there is no sales tax, but this was never given). this gives us our final expression we will be using: [tex]8.7C\le 17.40[/tex]
Solving the ProblemFrom here solving the problem is actually pretty easy. Think of the inequality as a linear equation, we can still apply the same (for the most part) algebraic manipulations we apply to linear equations. We just divide both sides by 8.7 to isolate the C
[tex]\frac{8.7C}{8.7}\le\frac{17.40}{8.7}\\\\C\le 2[/tex]
So Maria can buy a maximum of 2 bottles of cranberry juice. From this we can actually determine the number of lemon-lime soda bottles.
So we know that:
[tex]C=2[/tex]
From this we can determine what L is, since remember the equation we set up earlier?
[tex]L = 3.5C[/tex]
Let's just plug C into the equation, and we get:
[tex]L=3.5(2)[/tex]
Multiply
[tex]L=7[/tex]
So Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.
Is ( − 3, 2) a solution of 7 x + 9 y > − 3
Answer:
No
Step-by-step explanation:
x > -9y-3/7 (Solve for X)
_____________________________________________________
y > -7x/9 - 1/3 (Solve for Y)
_____________________________________________________
Therefore, (-3, 2) is not a solution.
Please help! I really don't understand this, and if I could get the answer along with a really simple way to solve next questions like this it would be rlly helpful !!!!!!!
A fruit company packages its fruit into two types of boxes: large and small. This morning, the company made two deliveries. The table below shows the number of boxes in each delivery and the total weight (in kilograms).
1st delivery 2nd delivery
number of large boxes 3 9
number of small boxes 5 7
total weight (in kilograms) 116 238
Let x be the weight (in kilograms) of each large box.
Let y be the weight (in kilograms) of each small box.
(a) Write a system of equations that could be used to find the weight (in kilograms) of each type of box.
[ ]x + [ ]y = [ ]
[ ]x + [ ]y = [ ]
(b) How much does each type of box weigh (in kilograms)?
Weight of each large box: [ ] kilograms
Weight of each small box: [ ] kilograms
I know how to solve part a of the problem, at least. But part b is so difficult for me to understand, and I don't get it at all.
(a) The system of equations that could be used to find the weight (in kilograms) of each type of box is
3x + 5y = 116
9x + 7y = 238
(b)
Weight of each large box: 15.75 kilograms
Weight of each small box: 13.75 kilograms
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Given that, the weight of 3 large boxes and 5 small boxes is 116 kilograms.
The weight of 9 large boxes and 7 small boxes is 238 kilograms.
Let x be the weight (in kilograms) of each large box.
Then the weight of 3 large boxes is 3x kilograms.
Then the weight of 9 large boxes is 9x kilograms.
Let y be the weight (in kilograms) of each small box.
Then the weight of 5 large boxes is 5y kilograms.
Then the weight of 7 large boxes is 7y kilograms.
The weight of 3 large boxes and 5 small boxes is 3x + 5y kilograms.
The weight of 9 large boxes and 7 small boxes is 9x + 7y kilograms.
Therefore,
3x + 5y = 116 .....(i)
9x + 7y = 238 .....(ii)
Solve equation by using elimination method:
Multiplying equation(i) by 3 and subtract equation (ii) from it:
9x + 15y = 348
9x + 7y = 238
(-) (-) (-)
_____________
8y = 110
y = 13.75
Putting y = 13.75 in equation (i)
3x + 5×(13.75) = 116
3x = 47.25
x = 15.75
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Anna, Sandra, and Jessy take Graduate Management Admission Council’s GMAT examinations. Their scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 90. What is the probability that Anna obtains the highest grade?
On a team, 3 girls and 2 boys scored a total of 41 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 13. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answer:
each girl scored 9 points
each boy scored 7 points
Step-by-step explanation:
41-13=28
28/2=14
14 is the number scored by boys
14/2
one boy scored 7 points
14+13=27
27 is the number scored by girls
27/3=9
each girl scored 9 points
An ounce of gold costs $1310 and an ounce of silver costs $20. Find all possible weights of
silver and gold that make an alloy (combination of metals) that costs less than $900.
s = number of ounces of silver
g = number of ounces of gold
Find the inequality for this question
By using linear inequation it can be calculated that-
The shaded region right of the y axis and above the x axis gives all possible solution.
The required linear inequation is
1310g + 20s < 900
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤
A one degree inequation is known as linear inequation
Let the alloy has g ounces of gold and s ounces of silver
An ounce of gold costs $1310 and an ounce of silver costs $20.
Cost of the alloy should be less than $900
The required linear inequation is
1310g + 20s < 900
The graph has been attached
The shaded region right of the y axis and above the x axis gives all possible solution.
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write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence be determined.
According to the task content, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
Consequently, the required expression is an arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
Ultimately, The required expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the nth term of the arithmetic sequence is given by the expression; T (n) = 1 + 7 (n -1).
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Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars. What fraction of a cup of nuts does Brielle use for 1 cup of oatmeal?
Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.
What is unitary method?
The unitary method is a process of finding the value of a single unit, and based on this value finding the required solution.
According to the given question:
Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars.
To find the fraction cup of nuts required for 1 cup of oatmeal, using unitary method
2 cups ----- 2/3 cup of nuts
1 cup ------- [tex]\frac{2/3}{2}[/tex] cup of nuts = 1/3 cup of nuts
Therefore Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.
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[tex]x+\frac{8x}{x-7} =\frac{56}{x-7}[/tex]
The equation has two solutions, on is extraneous and x = 7, and the real solution is x = -8.
How to solve the equation?Here we have the following equation:
x + 8x/(x - 7) = 56/(x - 7)
This is the original equation, notice that if x = 7, we will have a zero on the denominators, and we can't divide by zero, thus, x can't be equal to 7.
Now let's multiply all the equation by (x - 7)
(x - 7)*x + 8x = 56
Now we have a quadratic equation:
x^2 - 7x + 8x - 56 = 0
x^2 + x - 65 = 0
Using the quadratic formula we will get the two solutions:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-56} }{2*1} \\\\x = \frac{-1 \pm15}{2*1}[/tex]
Then the two solutions are:
x = (-1 + 15)/2 = 7 (this one is an extraneous solution, we can discard this one)
x = (-1 - 15)/2 = -8
This is our solution.
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TRIGONOMETRY HELP!!
The measure of the arc length of the sector will be 1.047 units. Then the correct option is A.
What is the arc length of the sector?Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
The radius of the sector is 1 unit and the central angle is π/3. Then the measure of the arc length of the sector will be given as,
Arc = [(π/3)/2π] 2π(1)
Simplify the equation, then we have
Arc = [(π/3)/2π] 2π(1)
Arc = (1/6) × 2π
Arc = π/3
Arc = 1.047 units
The proportion of the circular segment length of the area will be 1.047 units. Then, at that point, the right choice is A.
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