The equation that expresses the above situation is m/2 = 45
Linear Equation:The mathematical expression which is used to find the unknown number or value is known as Linear Equation. These are combinations of algebraic terms and constant terms. Here to represent the unknown we use different types of variables.
Here given that
Greg earned $45 dollars for washing cars this month.
He earned twice as much for washing cars than he did for moving lawns
Let us assume that he earned 'm' amount for moving lawns and 'c' be the amount earned by washing cars
From given data
=> m = 2 c
As we know The amount earned by washing cars = 45
=> m = 2(45)
Divide by 2 into both sides
=> m/2 = 45
Therefore,
The equation that expresses the above situation is m/2 = 45
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Find the olution to the following lhcc recurrence:
an=−6aₙ₋₁−5aₙ₋₂ for n≥3 with initial condition a0=28,a1=−76
aₙ = 6aₙ₋₁ - 5aₙ₋₂ then the values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.
How can the sequence's solution be found?
a = 2 and d = 3 decide the order. Using the method for locating the nth term, we can locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula an = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to find the nth term.Given:
a₁ = -76 ; a₀ = 28
aₙ = 6aₙ₋₁ - 5aₙ₋₂
Then the arithmetic sequence is followed by:
a₂= 6a₂₋₁ - 5a₂₋₂
= 6a₁ - 5a₀
= 6(-76) - 5 (28)
= -456 - 140
a₂ = -596
a₃ = 6a₃₋₁ - 5a₃₋₂
= 6a₂ - 5a₁
= 6(-596) - 5(-76)
= - 3576 + 380
a₃ = -3196
The values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.
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Multiple (3x+y) by (4x+2y)
Answer:
12x² + 10xy + 2y²
Step-by-step explanation:
(3x + y)(4x + 2y) =
= 12x² + 6xy + 4xy + 2y²
= 12x² + 10xy + 2y²
Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
The table below shows that the number of miles driven by Abigail is directly
proportional to the number of gallons she used.
Gallons Used Miles Driven
15
517.5
33
1138.5
36
1242
What is the constant of proportionality between the
number of miles driven and the number of gallons
used?
Answer: 34.5
Step-by-step explanation:
To find the constant of proportionality between miles driven and number of gallons used, we will divide the miles driven by the gallons used.
517.5 / 15 = 34.5
1138.5 / 33 = 34.5
1242 / 36 = 34.5
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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the cargo plane delivering the relief supplies must be at another location after dropping off the supplies at your site. this requires the unloading tasks to be completed in 70 minutes. the current process is taking 2 people to complete all tasks in 86 minutes
Total number of people required is 3 to complete it in 57.33 days.
What is indirect proportion ?Basically in this proportion, two quantities generally follow the opposite trend of each other like if one is increasing other one is decreasing.
As an example, if the time takes to run 10 m is inversely proportional to the speed you can run at - if you double your given speed, it takes you half as much long.
Initially,
Total People = 2
Total time taken = 86 minutes
Total time we have= 70 minutes
As people and time are inversely proportional to each other.
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{86}[/tex]
x = (86 × 2) / 3
x= 57.33
Hence, total number of people required is 3 to complete it in 57.33 days.
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m angle KHG= (4x+6) and m angle HGW= (6x-16) and m angle NGX=(y+9)
5. Find the value of x
6. Find the value of y
7. m angle KHG=
8. m angle HGW=
9. m angle NGX=
Question 5
Using the alternate interior angles theorem,
[tex]4x+6=6x-16\\\\6=2x-16\\\\22=2x\\\\x=11[/tex]
Question 6
Using the corresponding angles theorem,
[tex]4x+6=y+9\\\\4(11)+6=y+9\\\\50=y+9\\\\y=41[/tex]
Question 7
[tex]m\angle KHG=4(11)+6=50^{\circ}[/tex]
Question 8
[tex]m\angle HGW=6(11)-16=50^{\circ}[/tex]
Question 9
[tex]m\angle NGX=41+9=50^{\circ}[/tex]
If you vertically stretch the exponential function f(x) = 2x by a factor of 4, what is the equation of the new function?
The equation of the new function is g(x) = 4(2ˣ)
How to determine the equation of the new function?The exponential equation is given as
f(x) = 2ˣ
Then, we have the transformation to be:
Vertically stretch by a scale factor of 4
The scale factor can be represented as k
So, we have
k = 4
The rule of vertical stretch by a scale factor of k is represented a
g(x) = kf(x)
So, we have
g(x) = 4 * 2ˣ
This gives
g(x) = 4(2ˣ)
Hence, the equation is g(x) = 4(2ˣ)
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Why are factorial designs useful in testing theories?
a. They allow researchers to explore the construct validity of a theory.
b. Results from factorial designs are typically straightforward and easy to interpret.
c. They allow researchers to understand the nuances of how variables interact.
d. Results from factorial designs are always intuitive.
Factorial design are useful in testing theories because they enable researchers to investigate a theory's construct validity. so the correct answer is option (a).
What is factorial designs?A key technique for identifying the impact of numerous variables on a response is the factorial design. Traditionally, experiments are planned to ascertain how one variable affects just one response.
What is testing theories?The corpus of knowledge supporting the analysis and application of test results. The definition and measurement of reliability are of primary relevance. Classical test theory, generalizability theory, and item response theory are examples of theoretical frameworks.
a) They enable academics to investigate a theory's construct validity.
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Determine if the table how a proportional relationhip. X 25. 6 72. 8 77. 2 y 6. 4 18. 2 19. 3 Ye, it i proportional becaue all y over x ratio are equivalent to one fourth. Ye, it i proportional becaue all y over x ratio are equivalent to one third. No, it i not proportional becaue 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8. No, it i not proportional becaue 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Proportional relationship for the given table is true and is define as
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
As given in the question,
Value of x and y in the given table are :
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.
y / x for all the values of x and y:
First values:
y /x = 6.4 / 25.6
= 0.25
Second values:
y/x = 18.2/ 72.8
= 0.25
Third values :
y /x = 19.3/ 77.2
= 0.25
0.25 is equivalent to One fourth ( 1/4).
Constant of proportionality exist = 0.25 or One fourth.
Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.
The complete question is:
Determine if the table how a proportional relationship.
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
Yes, it is proportional because all y over x ratio are equivalent to one third.
No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.
No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
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Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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solve for x: x/7 < or equal to -6
Step-by-step explanation:
x
— - 6 = 0
7
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
6 6 • 7
6 = — = —————
1 7
x - (6 • 7) x - 42
——————————— = ——————
7 7
x - 42
—————— = 0
7
x-42
———— • 7 = 0 • 7
7
x-42 = 0
x = 42 Answer
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Write the equation of the line that passes through (4,2) and is parallel to y =3x + 1 in point-slope form
Answer:
y=3x-10
Step-by-step explanation:
y=mx+b
2=3(4)+b
2=12+b
b=-10
y=3x-10
Elephants sometimes damage trees in Africa. It turns out that elephants dislike bees. They recognize beehives and avoid them. Can this information be used to keep elephants away from trees? Will elephant damage be less in trees with hives? Will empty hives even keep elephants away? Researchers want to design an experiment to answer these questions using 72 acacia trees. Identify the experimental units, treatments, and the response variable.
a) The experimental units are the Acacia Trees.
b) The treatments carried used are; active beehives, empty beehives and no single beehive.
c) The response variable is the damage that the elephants caused to the trees.
How to interpret experimental research design?Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.
From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.
The treatments carried out here are the active beehives, empty beehives and no single beehive.
The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.
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The King family went out to eat. They ordered three combo meals, two sodas, and one iced tea. Write an expression representing their bill. Then, determine the cost of the dinner for the entire family.
½ Pound Cheeseburger - $3.50
Grilled Chicken Sandwich - $4.00 Combo Meal (with fries) - $5.25
Soda - $2.00
Iced Tea - $2.25
Milkshake - $3.75
Brownie a La Mode $4.00
The expression for their bill will be;
B = 3c + 2s + i
While the cost for the entire family for dinner will be $22.
What is a mathematical expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The structure of an expression is:
Expression is (Number/variable, Math Operator, Number/variable)
Types of Algebraic ExpressionsAlgebraic expressions are classified on the basis of the number of terms in the expression.
The various types of algebraic expressions are:
Monomial expressions contain only one term.Binomial expressions contain two unlike terms. Trinomial expressions contain only three unlike terms.Polynomial expressions have two or more terms. This includes binomials and trinomials too and all other expressions with four or more terms.Solution:
From the question;
Let c = Combo Meal (with fries) - $5.25
s = Soda - $2.00
i = Iced Tea - $2.25
The family ordered 3 combo meals, 2 sodas and 1 iced tea
So, expressing it;
Bill = 3c + 2s + i
Substituting the prices for the meals
Bill = 3(5.25) + 2(2) + 2.25
Bill = 15.75 + 4 + 2.25
Bill = $22
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The monthly rents (in dollars) paid by 9 people are given below. (Note that these are already ordered from least to greatest.)
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210
Suppose that one of the people moves. Her rent changes from $1210 to $1480.
Answer the following.
What happens to the mean=____ it decreases by __$
____ it increases by __$
____ it stays the same
What happens to the median=____ it decreases by __$
____ it increases by __$
____ it stays the same
The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.
In this problem, the data-set is given as follows:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.
Hence the mean is of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.
After the change, the data-set is of:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.
Hence the mean will be of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.
Then the increase will be of:
1065 - 1035 = 30.
What is the median of a data-set?The median of a data-set is the middle element of the data-set, the value which:
50% of the data-set is lesser than.50% of the data-set is greater than.The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.
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a military unit wants to pass through a forested arwa, but wants to check the area for possible enemy troops first. a team of speciaists will place 15 motion sensors throughout the area. each sensor has a probability of 0.95 of operating for a 24-hour period
By using Binomial distribution, it can be calculated that
a) Probability that the operation is successful = 0.8290
b) Number of sensors expected to operate during the 24 hour period = 14.25
What is Binomial Distribution?
Binomial Distribution is a discrete type probability distribution whose probability mass function is given by
P(X = x) = [tex]{n \choose x}p^xq^{n-x}[/tex]
p is the probability of success and q is the probability of failure.
a) This is a problem on Binomial Distribution
Probability that the operation is successful = P(X [tex]\geq[/tex] 14)
= P(X = 14) + P(X = 15)
P(X = 14) =
[tex]{15 \choose 14}(0.95)^{14}(1- 0.95)^{15 - 14}\\15 \times 0.95^{14}\times 0.05\\0.3657\\[/tex]
P(X = 15) =
[tex]{15 \choose 15} 0.95^{15}(1-0.95)^{15 - 15} = 0.4633[/tex]
Probability that the operation is successful = 0.3657+0.4633 = 0.8290
b) Number of sensors expected to operate during the 24 hour period = [tex]15 \times 0.95[/tex] = 14.25
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This graph shows the revenue, cost, and profit functions of a company. How can this company become profitable?
A graph shows the Price per Unit on the x-axis and dollars on the y-axis. A downward parabola revenue vertex at (25, 12,000) intercepts the origin and x-axis at (30, 0) linear function costs intercept the y axis at (0, 13,000).
A.
by increasing its production
B.
by increasing its prices
C.
by reducing its costs
D.
by reducing its prices
Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.
What is a profit?In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.
Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:
Profit = Revenue - Cost
In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.
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Question 8(Multiple Choice Worth 5 points) (Two-Step Linear Inequalities MC) A Solve the inequality and graph the solution. -3p+ 6.7> -4.4 (HELP ASAP!)
Answer: p < [tex]-\frac{11.1}{3}[/tex]
Step-by-step explanation:
To solve, we will isolate the p variable.
Given:
-3p + 6.7 > -4.4
Subtract 6.7 from both sides of the equation:
-3p > -11.1
Divide both sides of the equation by 3:
Note, you must switch the sign since you're dividing by a negative.
p < [tex]-\frac{11.1}{3}[/tex]
Answer:
p < 3.7
Step-by-step explanation:
-3p + 6.7 > -4.4
1- subtract 6.7 to leave -3p alone
-3p + 6.7 -6.7 > -4.4 - 6.7
-3p > -11.1
2- Divide both sides by -3. NOTE; u must change the > sign to < because u r dividing by a negative
-3p/-3 = p
-11.1/-3= 3.7
p < 3.7
The diameter of a dime is 17.91 mm. The diameter of a strand of human hair is
6.0 x 10-2 mm. How many times greater is the diameter of a dime than the diameter of
the strand of human hair?
The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.
What is DiameterThe diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.
In this problem, the diameter tells us about the length of the each quantity.
The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.
Comparing both values
Dime = 17.91mm
Hair = 6.0*10^-2
Divide both quantity together.
17.91 / 6.0*10^-2 = 298.5≅299
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The length of a rectangle i 4 inche more than it width. The area of the rectangle i equal to 4 inche le than 2 time the perimeter. Find l and w
12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.
Given that,
A rectangle's length is 4 inches longer than its width. The area of rectangle is equal to 4 inches less than 2 times the perimeter of rectangle.
We have to find what is the length and width of rectangle.
We know that,
Let take length as l and width as w.
l=4w
Area of rectangle is l×w
Perimeter of rectangle is 2(l+w)
So,
l×w=2(2(l+w))-4
l×w=4(l+w)-4
Take l as 4w
4w×w=4(4w+w)-4
4w²=4(5w)-4
4w²=20w-4
4w²-20w+4=0
w²-5w+1=0
w=3
So,
l=4w
l=12
Therefore, 12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.
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a marketing class polled 270 people at a shopping center to determine how many read the daily news and how many read the weekly gazette. they found the following: 124 read the daily news. 33 read both. 19 read neither. How many read the Weekly Gazette?
128 were Daily News readers. 19 read neither while 35 read both. Weekly Gazette A marketing class conducted a survey of 270 shoppers at a mall to find out how many of them read the Weekly Gazette and how many the Daily News.
What is News readers?
150 attendees were surveyed by a marketing class to find out how many read the Weekly Journal and how many the National News. In this section, word problems will be solved using Venn diagrams. The areas of a Venn diagram that indicate quantities as opposed to will have numbers in them. Confidence interval for difference of two formula You may have read statements like the ones below in newspapers, for instance. law in numerous nations.
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Three consecutive integers have a sum of â€""21. which equation can be used to find the value of the three numbers? x x x = negative 21 x 2 x 3 x = negative 21 x (x 1) (x 2) = negative 21
This equation x + (x + 1) + (x + 2) = negative 21 will be used.
Let the first Number is x.
We have to take 3 consecutive integers.
second Number is x+1
third Number is x+2.
Sum of these 3 consecutive integers is x+(x+1)+(x+2).
Sum of these 3 consecutive integers is given as negative21.
so we can write x+(x+1)+(x+2)=negative 21.
by using above equation we can find the value of 3 numbers.
So the final equation will be x + (x + 1) + (x + 2) = negative 21.
Given Question is incomplete, Complete Question here:
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21
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Leslie spent $43. 50 to purchase a combination of drinks, sandwiches, and chips for herself and her friends. A drink costs $1. 75, a sandwich costs $6. 25, and chips cost $1. 50. Identify the linear equation that represents this situation.
The linear equation that represents the given situation is 1.75x + 6.25y + 1.50z = 43.50
Total amount that she spent = $43.50
The cost of drinks = $1.75
The cost of sandwich = $6.25
The cost of chips = $1.50
The linear equation is defined as the equation in which the highest power of the variable is 1
The linear equation the represents this situation is
1.75x + 6.25y + 1.50z = 43.50
Where the number of drinks is x, number of sandwiches is y and the number of chips is z
Hence, the linear equation is 1.75x + 6.25y + 1.50z = 43.50
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Show me how to write a phrase as an expression then solve when x equals 5 and Y equals 26 more than the product of 8 and a number is X
The expression used to represent the given phrase is given by x =5 and
y = 26 + 8x and value of the given expression when x =5 is equal to
y = 66.
As given in the question,
Given phrase is:
x equal 5
y equals 26 more than the product of 8 and a number x
Required expression to represent the given phrase is:
x = 5
y = 26 + 8x
Value of the expression y = 26 + 8x when x = 5 is given by :
y = 26 + 8( 5 )
⇒ y = 26 + 40
⇒ y = 66
Therefore, the required expression for the given phrase is x =5 and
y=26 +8x , the value of the expression y = 66 when x = 5.
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In the context of hypothesis testing, what is a test statistic?
a. The confidence level that is to be used to except or reject the null hypothesis.
b. A parameter determine from a sample, such as mean or standard deviation, used to test a hypothesis.
c. A value, determined from sample information, used to test the null hypothesis.
In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.
How to Interpret Hypothesis Testing?Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables
The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.
Looking at the options and based on the definitions above, option C adequately describes the test statistic.
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Homework Progress
37/ 105 Marks
Gigi is going to buy 100 stickers.
Here is some information about the cost of stickers in two shops.
Stickers4u
Pack of 25 stickers for £2.25
World Stationery
Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack free
Gigi wants to buy the stickers for the best possible price.
Which shop should Gigi buy the 100 stickers from?
You must show how you get your answer.
Show your workin
Gigi should buy stickers from World Stationery.
Define Expressions.
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Let's see the information about Stickers4u
Here, pack of 25 stickers is = £2.25
1 sticker cost = 2.25 / 25
= £0.09 per sticker
Now, information about World Stationery
Here, pack of 10 stickers is = £1.75
1 sticker cost = 1.75/10
= £0.175 per sticker
In this shop, the offer is also there i.e, Buy 1 pack get 1 pack free.
Therefore, Gigi should go with this shop for best possible price.
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What error did the student make? in line 2, the student forgot to multiply the right side of the equation by 2. in line 3, the student should have subtracted the equations instead of adding them. in line 3, the student added the two equations incorrectly. in line 5, the student used an incorrect equation when solving for x.
Answer: the student forgot to multiple by right side of equation 2 in line 2
Step-by-step explanation: your welcome :)
Find the slope of the line.
The slope of the line is 5/7. So, option B is correct.
What is meant by slope?In mathematics, a line's slope or gradient is a number that specifies both its direction and its steepness. There is no obvious answer to why the letter m is used for slope, although its first use in English is in O'Brien (1844), who wrote the equation of a straight line .
The slope of a line is found by dividing the "vertical change" by the "horizontal change" between (any) two distinct places on the line. The ratio is sometimes stated as a quotient ("rise over run"), yielding the same value each time.
The points of the line on the graph are:
A(3,1), B(-4, 4)
Slope=(y₂-y₁)/(x₂-x₁)
=(-4-1)/(-4-3)
= -5/-7
=5/7
Therefore, the lines slope is 5/7
Hence option A is correct.
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