Answers
By SAS congruence triangle MLN and triangle OLN are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, LM≅LO, ∠MLN≅∠OLN.
LM≅LO (Given)
∠MLN≅∠OLN (Given)
LN≅LN (Reflexive property of congruence)
ΔMLN≅ΔOLN (SAS congruence)
∠M≅∠O (CPTC)
MN≅ON (CPTC)
Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.
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Related Questions
(8-12) x (8 x 4) +7²
Answers
Step-by-step explanation:
[tex](8 - 12) \times (8 \times 4) + {7}^{2} \\ [/tex]
[tex]( - 4) \times (32) + 49[/tex]
[tex] -12 8 + 49 =79 [/tex]
Solve the following
X=?
Y=?
Answers
The value of x = 3.8 cm and y = 3.44 cm
What are some examples of consistency?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.
What are the five different types of congruence?
Two triangles are congruent if they satisfy all five conditions for congruence. Right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).
This can be solve by congruence
these two triangle can be congruent by AAS
so x = 3.8 com
in this triangle we have all angle 60 degree
so this is an equivalent triangle
hence down side = 3.8 cm
hence y = (3.8)^2-(1.6)^2 = 14.44 - 2.56 = √11.88 = 3.44
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help meeeeeeeeeee pleaseee
Answers
The pressure of 28 inches of mercury occurs at 6.03 miles from the eyes of the hurricane
How to determine the distance?From the question, we have the following pressure function that can be used in our computation:
f(x) = 0.48 ln(x + 2) + 27
Also from the question, we have
Pressure = 28 inches
This means that
f(x) = 28
So, we have the following equation
0.48 ln(x + 2) + 27 = 28
Subtract 27 from both sides
0.48 ln(x + 2) = 1
Divide 0.48 from both sides
ln(x + 2) = 2.083
Take the exponent of both sides
x + 2 = 8.03
So, we have
x = 6.03
Hence, the distance is 6.03 miles
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6 Find the value of the unknowns in each of the following.
(a) 2(w 2 5 z)+3(2 x -2 -6)=4(4 7 y 3)
Answers
The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.
Given,
To determine the value of the unknowns in the matrix,
A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.
Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,
2z -18 = 12
z = 15
10 - 6 = 4y
y = 1
Thus, the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.
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Van is 12 yrs older than john. Two yrs ago. Van was twice as old as john. Find thier present age.
Answers
Answer:
John = 14 ; Van = 26
Step-by-step explanation:
V = 12 + J
V - 2 = 2(J-2)
12 + J - 2 = 2J - 4
J + 10 = 2J - 4
2J - J = 10 + 4
J = 14
V = 12 + 14
V = 26
if you were conducting an upper tailed test where the level of significance was 0.05 and the population standard deviation was not known, then which of the following excel commands would give you the critical value? the sample size is 26.
Answers
The following excel commands would give you the critical value is T.INV(0.95,25)
What is excel commands?
The following describe the commands in Excel: They carry out tasks the same way users do. They can change Excel settings, open, close, and edit documents, start recalculations, and other actions that users may perform (within the bounds of the interface being utilized). Excel's command menu interface is called the Ribbon. It logically and visually groups together frequently used actions. These make up the Ribbon's principal components. Related groupings of commands are grouped together by tabs.
Population sd is not available so we have to use t test.
0.95 is for upper bound and 25 is df of t test.
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A line segment on a coordinate plane representing the
distance a bicyclist is from home has a slope of 35/2
On the line segment, x represents the time, in hours,
that the bicyclist has been riding and y represents the
bicyclist's distance, in miles, from home. The bicyclist
began his ride at home and rides his bicycle at a
constant rate. How long will it take until the bicyclist is
140 miles from home?
A. 2 hours
B. 4 hours
C. 7 hours
D. 8 hours
Answers
Time taken by the bicyclist is 8 hours.
What is slope?Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Given slope = 35 / 2 = 17.5
Distance = 140 miles.
then time is calculated by 140 /17.5
= 8 hours
The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.
As x grows, there are 4 different sorts of slopes: negative, positive, zero, and undefined. The "average rate of change" can also be thought of as the slope of a line.
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What does (5x2−14x+24)÷(x−4) equal?
I dont need explanation or anything just answer pls
Answers
The value of (5x2−14x+24)÷(x−4) is 5x + 6
How to calculate value of (5x2−14x+24)÷(x−4)?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given ,
5x2 - 14x - 24
x - 4
5x2 multiplied by 14x, then 24.
The first term is 5x2, and 5 is its coefficient.
The coefficient of the middle term, which is -14x, is -14.
"The constant," the final term, is -24.
Step 1: Multiply the first term's coefficient by the constant 5 • -24 to get a result of -120.
Find two factors of -120 whose combined value is equivalent to the middle term's coefficient, which is -14, in step two.
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 6
5x2 - 20x + 6x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x-4)
Add up the last 2 terms, pulling out common factors :
6 • (x-4)
Step-5 : Add up the four terms of step 4 :
(5x+6) • (x-4)
Therefore The value of (5x2−14x+24)÷(x−4) is 5x + 6
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Simplified term is 5x + 6. Simplification is the process of reducing an expression/fraction/problem to a simpler form.
What is simplification method?A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.
Mathematical expressions are made up of different numbers and operations. To simplify them, we must first understand the rule known as the order of operations. It specifies the order in which operations must be performed when simplifying a mathematical expression.
Factoring 5x2 - 14x - 24
The first term is, 5x2 its coefficient is 5 .
The middle term is, -14x its coefficient is -14 .
The last term, "the constant", is -24
Multiply the coefficient of the first term by the constant 5 • -24 = -120
Find two factors of -120 whose sum equals the coefficient of the middle term, which is -14 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 6
5x2 - 20x + 6x - 24
Add up the first 2 terms, pulling out like factors :
5x • (x-4)
Add up the last 2 terms, pulling out common factors :
6 • (x-4)
Add up the four terms of step 4 :
(5x+6) • (x-4)
Which is the desired factorization
Cancel out (x-4) which appears on both sides of the fraction line.
5x + 6
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Which expression has the smallest value?
a
|-34|
b
|-19|
c
|11|
d
|47|
Answers
Answer:
c. |11|
Step-by-step explanation:
When it comes to absolute value, we're talking about the distance from 0. Even though 11 is greater than -19 and -34, the distance from 11 and 0 is smaller than the distance from -19 and 0 and the distance from -34 and 0.
|11-0|=11
|0-19|=19-0=19
|0-34|=34-0=34
A paint store makes two batches of a color called Ocean Teal using the recipe shown.
Each batch contains a different amount of paint.
Drag numbers to show how much of each color should be used in each batch of Ocean Teal.
Answers
For the third part of the batch, 1 :1/2 gallon of yellow is needed and for the second batch part 1/4 gallon is needed.
How to illustrate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Since we know that there should be the same amount of yellow and green (they are each 1/4 of the recipe) and there is a half a gallon of green there should same amount the yellow. Hence, the answer is 1/2 gallon.
For the second part of the question, we know that 2 gallons is 1/4 of the recipe, and we know that 1/4 * 2= 1/2 (2/4) we just have to multiply 2 by 2 and get 4, our answer.
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Answer:
third part of the batch 1 :1/2 gallon of yellow Second batch part 1: 4
Step-by-step explanation:
have a nice day.
5 customers entered a store over the course of 15 minutes. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
THE CORRECT ONE GETS BRAINLIEST
Answers
2. 2:6
when 5 customers entered the store, 15 minutes elapsed. the ratio here is 5:15, which simplifies to 1:3. (5/5 = 1; 15/5 = 3 —> 1:3)
when the minutes elapsed is 3, that means the customer amount must be 1, and when there are 2 customers, the amount of minutes that go by is 6. 1:3 —> 2:6 (multiply both numbers by 2). hope this helps.
6 people equally share 1/2 a pan of macaroni and cheesse draw a diagram to represent the situation
Answers
Share of the each person is 1/12. And the above situation can be represented in the given picture.
Fractions and diagrams:Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.
When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.
To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.
First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.
Here we have
6 people equally share 1/2 a pan of macaroni and cheese
As we know 1/2 means half
By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts
=> (1/2) ÷ 6 = [tex]\frac{ \frac{1}{2} }{6}[/tex] = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]
Therefore,
Share of the each person is 1/12. And the above situation can be represented in the given picture.
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Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= -2, x=7
P(x)=_____
(Type an expression using x as the variable. Do not factor.)
Answers
The polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the zeroes of the polynomial are, x= -2, x=7
The polynomial expression is obtained as,
=(x+2)(x-7)
=x²-7x+2x+14
=x²-5x+14
Thus, the polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14.
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Could someone help??
Answers
Answer:
C.
Step-by-step explanation:
For the first letter there are 26 choices, then, since one has been used, for the second letter there are only 25 choices left. And so on. You multiply them to get the total number of combinations.
For the digits, the initial choice is from 10 digits (0..9), which invalidates answer B.
(2x-123):3=33 ;200-8.(2x+7)=112
Answers
Answer:
x = 222:2 and x = 2
Step-by-step explanation:
(2x-123):3=33
(2x – 123):3 = 33
2x – 123 = 33.3
2x – 123 = 99
2x = 99 + 123
2x = 222
x = 222:2
x = 111
200-8.(2x+7)=112
200 – 8.(2x + 7) = 112
-8.(2x + 7) = 112 – 200
-8.(2x + 7) = -88
2x + 7 = (-88):(-8)
2x + 7 = 11
2x = 11 – 7
2x = 4
x = 4:2
x = 2
I hope my answer helps you.
The city council voted on a new tax. 38 council members voted in favor of the tax. The council has 76 members. What percentage of the council members voted in favor of the tax
Answers
The percentage of the council members who voted in favor of the tax is 50%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the council has 76 members out of which 38 members voted in favor of the tax.
The percentage amount of members who favor the tax is:
(38/76) × 100%
= 50%
Hence, the percentage of the council members who voted in favor of the tax is 50%.
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Suppose that the efficacy of a certain drug is 0.35. Consider the sampling distribution (sample size n = 156)
for the proportion of patients cured by this drug.
What is the mean of this distribution?
What is the standard error of this distribution?
(Round answer to four decimal places.)
Answers
a) The mean of this distribution is of: 0.35.
b) The standard error of this distribution is of: 0.0382.
How to define the sampling distribution of p?The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has mean and standard deviation defined as follows:
Mean: equals to proportion p.Standard deviation: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex](the standard deviation can also be called standard error).
The sample size and the proportion for this problem are given as follows:
n = 156, p = 0.35.
Then the standard error for this distribution is calculated as follows:
s = square root(0.35 x 0.65/156) = 0.0382.
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Write as a logarithmic equation. 2^1/2= square root 2
Answers
Answer:
1
log₂√2 = ------
2
Step-by-step explanation:
I'm assuming the equation looks like this:
2¹⁽² = √2
1
log₂√2 = ------
2
I hope this helps!
How is a system of two linear inequalities in two variables similar to a system of two linear equations in two variables?
a. point of intersect
b. overlaps
c. boundary lines
d. points that are not boundary lines
which one
Answers
Answer:
q. point of intersection
Step-by-step explanation:
Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.
A(2, 5), B(2, -3), and D(-6, 5) are three vertices of square ABCD. What are the coordinates of the fourth vertex, C?
Answers
Answer:
C(-6, -3)
Step-by-step explanation:
In a square, all four sides have the same length and all four angles have the same measure (90 degrees). Therefore, the line segments connecting the vertices of a square are all perpendicular to each other and all have the same length.
Since the line segment AB has a length of 8 (the difference in the y-coordinates is 8) and a horizontal component (the difference in the x-coordinates is 0), the line segment CD must also have a length of 8 and a horizontal component of 0. This means that the x-coordinate of point C is the same as the x-coordinate of point A, which is 2.
The line segment CD also has a vertical component equal to the difference in the y-coordinates of points D and A, which is 5 - (-3) = 8. Therefore, the y-coordinate of point C is the same as the y-coordinate of point D minus 8, or -3.
Therefore, the coordinates of point C are (-6, -3).
Write the missing numbers
2. 200 300
-600 +400
_____ _____
3. 3 hours= ____minutes
_____hours= 1 day
_______months= 2 years
Answers
The missing numbers are 3 hours = 180 minutes 24 hours = 1 day
24 months = 2 years
What are numbers ?
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.
An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and these are four.
1. 5 × x = 45
45 / 5 = x
x = 9
45 ÷ 5 = 9
2. 200 + 600 = 800
300 + 400 = 700
3. 3 hours = 180 minutes
3 * 60 minutes
24 hours = 1 day
24 months = 2 years
12 * 2 = 24
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Find the exact values when 4cos x + 2 = 0 where 0 ≤ x ≤ π
Answers
By using trigonometry, it can be calculated that
Value of x is [tex]\frac{2\pi}{3}[/tex]
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
Trigonometry is a very important tool in mathematics.
Trigonometry has a very good application in heights and distance.
Trigonometry has also a very good application in calculus and differential equation and also in physics, trigonometry plays a very vital role
Here,
The trigonometric equation is
4cos x + 2 = 0 where 0 ≤ x ≤ π
4cos x = -2
cos x = [tex]-\frac{2}{4}[/tex]
cos x = [tex]-\frac{1}{2}[/tex]
cos x = cos [tex]\frac{2\pi}{3}[/tex]
x = [tex]\frac{2\pi}{3}[/tex]
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Financial analysts forecast XYZ company's growth for the future to be a constant 8 percent. XYZ's recent dividend was $0.88. What is the value of XYZ stock when the required return is 12 percent?
Answers
$23.76 is the value of XYZ stock when the required return is 12 percent.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let the price per share be P
growth rate, g = 8% = 0.08
D = Next years dividend = $0.88 × 1.08 = $0.9504
Required rate of return r = 12% = 0.12
P=D/r-g
P=0.9504/0.12-0.08
P=$23.76
Hence,$23.76 is the value of XYZ stock when the required return is 12 percent.
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a) Work out the minimum number of dogs that could have a mass of more than 24kg}
b) Work out the maximum number of dogs that could have a mass of more than 24kg
Answers
The minimum number of dogs that have a mass of more than 24kg is 6 and the maximum number of dogs that could have a mass of more than 24kg is 18
Maximum and Minimum values of a function:Using fundamental algebraic principles, rearrange the function to get the value of x at the derivative value of 0. The maximum or minimum will be at the vertex of the function, which is indicated by the response's x-coordinate. Rewrite the answer into the original function to determine the minimum or maximum.
Here we have
The given shows the masses of various dogs
Mass (x) kg frequency
0 ≤ x < 10 2
10 ≤ x < 20 7
20 ≤ x < 30 12
30 ≤ x < 40 6
a) The minimum number of dogs that have a mass of more than 24kg.
If we observe the given table the mass of 24 kg will lie in class intervals 20 ≤ x < 30, 30 ≤ x < 40
In class interval 20 ≤ x < 30, mass ranges from 20 kg to 30 kg there is a possibility that the mass of dag will be less than 24 since it started from 20 kg,
In class interval 30 ≤ x < 40, mass ranges from 30 kg to 40 here there is no possibility that the mass will be less than 24 kg.
So here we can take the frequency of class interval 30 ≤ x < 40 as the Minimum value or number of dogs that could have a mass of more than 24 kg
Therefore,
The minimum number of dogs that have a mass of more than 24kg is 6
b) The maximum number of dogs that have a mass of more than 24kg.
In the above case since we are calculating minimum value, we didn't consider class interval 20 ≤ x < 30.
In this case, to get the maximum value or a maximum number of dogs we will consider class interval 20 ≤ x < 30 as there is a possibility that the mass could be more than 24 kg
In class interval 30 ≤ x < 40 the mass will always be more than 24 kg.
Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18
Therefore,
The maximum number of dogs that could have a mass of more than 24kg is 18
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which is the correct answers ??????
Answers
I literally have no idea how to do this someone help meplease
Answers
Answer:
Step-by-step explanation:
Although the answer is correct, the Step 3 is not correct.
express 2/(1-(x^2)) into partial fractions
Answers
2/ ( 1 + x) ( 1 - x) is express into partial fractions.
With an example, what is a partial fraction?
The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].
The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.
= 2/(1-(x^2))
= 2 / (1)² - (X)²
= 2/ ( 1 + x) ( 1 - x)
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Pls answer its for my final
Answers
The equivalent expression is (x + 2√3i) (x - 2√3i).
What is a Polynomial Equation?
The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.
Given polynomial is,
x² + 12
We need to find it's equivalent expression for that see the options
Solve the option (a)
(x + 2√3i) (x - 2√3i)
Now, solve this if we get equal to x² + 12 that means that option is answer
x(x - 2√3i) + 2√3i(x - 2√3i)
x² - 2xi√3 + 2xi√3 - 2√3i * 2√3i
x² - 12 i²
we know, i² = -1
so, we get
x² + 12
We get the answer by 1st option. If you solve other options you'll get different answer.
Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).
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omari buys a computer for $1099. He makes a down payment of 20%. His monthly payments for the computer are $144. How many months will it take omari to finish paying off the computer
Answers
It will take Omari 7 months to pay off the computer.
What is a percentage?
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.
To find the amount of the down payment, multiply the price of the computer by the down payment percentage:
down payment = $1,099 * 20% = $219.80
The remaining balance on the computer after the down payment is:
remaining balance = $1,099 - $219.80 = $879.20
To find the total number of months it will take Omari to pay off the computer, divide the remaining balance by the monthly payment:
total months = $879.20 / $144/month = 6.1 months
Since it is not possible to have a fraction of a month.
Hence, it will take Omari 7 months to pay off the computer.
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An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answers
The decision for rejecting the null hypothesis is μ = 8.4
In statistics the term hypothesis refers a tentative statement about the relationship between two or more variables.
Here we have given that engineer designed a valve that will regulate water pressure on an automobile engine and he is designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. Then it is believed that the valve performs above the specifications. Where the valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 Here the level of significance of 0.05 will be used.
Here we have to determine the decision for rejecting the null hypothesis.
While we looking into the the given question we have identified the following values,
Standard deviation = 1.0
Mean pressure = 8.4 pounds/square
Level of significance = 0.05
Sample size = 24
According to these values the null and alternative hypothesis is written as,
H0 = μ = 8.4
Hx = μ ≠ 8.4
Therefore, H0 = μ = 8.4 is the decision for this one.
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