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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PLEASE HELP 50 POINTS
The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)
How to find an expression equivalent to another trigonometric expressionIn this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:
cos 3x / (sin x · cos x)
Second, use trigonometric formulas:
cos (x + 2x) / (sin x · cos x)
(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)
cos 2x / sin x - sin 2x / cos x
csc x · cos 2x - sec x · sin 2x
The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.
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a football team lost the same number of yards on each of three consecutive plays what is the total change in yards from where the team started
Answer:
-3x, where x is the number of yards lost on the first play.
Step-by-step explanation:
the sum of two number 12 when three times the first number is added to 5 times the second number the results is 44
Answer:
one number is 8 and other is 4
Step-by-step explanation:
So we can say x+y=12.
And 3x+5y=44
For x+y=12, we can subtract x to get: y=12-x
Plug that in to get 3x+5(12-x)=44
3x+60-5x=44
Subtract 44: -2x+16=0
2x=16
x=8
12-8=4.
If you roll a standard six-sided die a thousand times and add up the total number of pips, which approximate sum could you reasonably expect to end with?
1) 16.7% probability of rolling 10+.
2) 50% probability an odd number is rolled.
3) 7 is the most likely total result.
These are all the possible outcomes:
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes
1) what is the probability of rolling 10+?
There are 6 possible outcomes in which 10+ is rolled:
(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).
So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.
2) what is the probability of rolling an odd number?
There are 18 possible outcomes in which an odd number is rolled.
So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.
3) what is the total that is most likely to result?
There are 6 outcomes in which 7 is rolled.
So 7 is the most likely total result.
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2(x-4 1/2)=-6.1 hellllllppppp meeeee
Answer:
[tex]x=1.45[/tex]
Step-by-step explanation:
[tex]2\left(x-4 \frac{1}{2} \right)=-6.1 \\ \\ 2\left(x-\frac{9}{2} \right)=-6.1 \\ \\ 2x-9=-6.1 \\ \\ 2x=2.9 \\ \\ x=1.45[/tex]
1. Write two equivalent expressions to represent the area of this rectangle.
2. Write two equivalent expressions to represent the perimeter of this rectangle.
(pls add an explanation)
The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here, perimeter =2(x-2+5)
= 2(x+3)
= 2x+6 units
Area of a rectangle =length × width
= (x-2) × 5
= 5x-10 square units
Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
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Help please help help please help help me
Answer:
103
Step-by-step explanation:
angle 1 and angle 5 are the same as each other.
Answer to this question
In the picture
[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]
observations 1 2 3 4 5 6 num. of defects 10 18 13 15 9 12the number of runs up and down for the preceding data is:
The number of runs up and runs down for the preceding data is 5.
What is runs up ?Runs up refers to the number of observations that are higher than the number of observations before them.
What is runs down ?Runs down refers to the number of observations that are lower than the number of observations before them.
As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.
Therefore,
Runs up = 2nd + 4th + 6th observations
= 3
As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down
Therefore,
Runs down= 3rd +5th observations
=2
Therefore,
Runs up + Runs down =3+2
=5
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18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product? Circle the letter of the correct answer.
The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)
Writing an expression using the Greatest common factor and distributive propertyFrom the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.
The given expression is
18 + 24
First, we will determine the greatest common factor of 18 and 24
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Thus,
The greatest common factor is 2 × 3 = 6
Now, we will write the expression using the greatest common factor and the distributive property
18 + 24
6(3 + 4)
Hence, the expression is 6(3 + 4)
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visit your local library: on a recent saturday, a total of 1343 people visited a local library. of these people, 253 were under age 10, 466 were aged 10-18, 174 were aged 19-30, and the rest were more than 30 years old. one person is sampled at random. (a) what is the probability that the person is less than 19 years old? (b) what is the probability that the person is more than 10 years old? part 1 of 2 (a) what is the probability that the person is less than 19 years old? round your answer to four decimal places.
Probability of people less than 19 year old = 0.5343
Probability of people greater than 10 year old = 0.8116
What is probability?
Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.
People under age 10 = 253
People between the age of 10-18 = 466
People between the age of 19-30 = 174
People above the age of 30 = 450
Total no. of people = 1343
a) people less than 19 years old = 253+466 = 719
probability of people<19 year old = P(age<19) = 719/1343 = 0.5354
b) people of age greater than 10 = 466+174+450 = 1090
probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116
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A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is
Select one:
a. S = {$0, $1, $2, $3}
b. S = {$0, $3, $6, $9}
c. S = {-$2, $1, $4, $7}
The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.
What is cost?
A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.
Let, a game consists of drawing three cards at random from a deck of playing cards.
You win $3 for each red card that is drawn.
It costs $2 to play.
After deducting the cost of pay the amount will start from -$2.
For first red card drawn you win $3.
So, the amount becomes, -$2 + $3 = $1.
For second red card drawn you again win $3.
So, the next amount becomes $1 + $3 = $4.
For third red card drawn the amount becomes,
$4 + $3 = $7.
Hence, the sample space S for the net amount you win is
S = {-$2, $1, $4, $7}.
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Composition of functions worksheet
using f(x) = 8x squared and g(x) (2x+8), find:
The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.
We have,
i] f(x) = 8x and
g(x) = (2x+8)
(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16
(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) = 8x.
(f ∘ g) (x) = 8(2x+8)
= 16x + 64
ii] f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2
= 6x - 28
g [f(3)] = (6x + 2 ) - 5
= -30x - 10
Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
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If X is the midpoint of TV, TV bisects RS, and TR is parallel to VS, state five pairs of objects (segments or angles) that must be congruent and give a reason why for each pair.
According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Alternate Interior Angle Theorem?According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.Is it true or false that different interior angles are always congruent? Although untrue, this assertion is a typical misunderstanding. Keep in mind that when the lines are parallel, alternate inner angles are congruent.Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposing sides of the transversal when two lines are crossed by another line (referred to as the Transversal). These two pairs of alternate interior angles in this illustration are c and f.To learn more about Congruent refer to:
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Simplify. Rewrite the expression in the form y^n. y^5/y^3=
Answer:
y^2
Step-by-step explanation:
a^m/a^n = a^(m - n)
y^5/y^3 = y^2
The soccer field is 105 meters long. The football field is 120 yards long. Which is longer?
The football field is longer than soccer field.
What is a expression? What is a mathematical equation? What is unit conversion?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
We have a soccer field that is 105 meters long and a football field is 120 yards long.
In one yard, we have -
1 yard = 0.9144 meters
Then, in 120 yards, we will have -
120 x 0.9144 = 109.728 meters
Now, 109.728 meters > 105 meters.
Therefore, the football field is longer than soccer field.
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Brody loves to read, and he counts the number of books he reads each year. This year, he used a graph to keep track of the books he read. By his birthday, he read 15 books. The following graph shows how many books he read for the months following his birthday.
How many books does Brody read each month?
Brody reads 8 books each month.
What is the slope of a line?The slope of a line indicates the direction and the steepness of the line. The formula for the slope of a line passing through the points (x₁,y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁).
Give the graph of the line.
The graph of the line passes through points (0,15) and (5,55)
To find the number of books Brody read each month, find the slope of the line.
The slope of the line is:
m = (55 - 15)/ (5 - 0)
m = 8
Hence, Brody reads 8 books each month.
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2 websites sell the same type of headphone cost of headphone in website A is 49.95 and the postage is 4.39. The headphones in website B is 47.68 and the postage is 6.95. Including the postage which website is cheaper and by how much
Answer:
Website A is cheaper by 29 cents
Step-by-step explanation:
A
49.95 + 4.39 = 54.34
B
47.68 + 6.95 = 54.63
54.63 - 54.34 = 0.29
Answer:
the difference is 0.29 cents
website A is cheaper
Step-by-step explanation:
(47.68 + 6.95) - (49.95 + 4.39)
54.63 - 54.34 = 0.29
After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 1. 35te−2. 802t † models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). A. What is the maximum average BAC during the first 3 hours? (Round your answer to three decimal places. ) mg/mL b. When does it occur? (Round your answer to two decimal places. ) h
The maximum average BAC during the first 6 hours is about 0.177 mg/ml.
What is average ?
The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.
When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
The maximum is found where the derivative of C(t) is zero.
dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0
Solving for t gives ...
t = 1/2.802
So, the maximum C(t) is ...
C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL
The maximum average BAC during the first 6 hours is about 0.177 mg/mL.
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Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x
A)
(0, 0)
B)
(–4, 0) and (4, 0)
C)
(–4, 0) and (0, 0)
D)
(0, 0) and (4, 0)
Which expression is equivalent to (6x^-9x) - (2x - 3)?
The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3
What is an equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.
To find equivalent expression we can simplify the expression.
Therefore,
(6x² - 9x) - (2x -3)
open the brackets
6x² - 9x - 2x + 3
combine like terms
Therefore,
(6x² - 9x) - (2x -3) = 6x² - 11x + 3
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Bob bad $50. he spent $28.67 for a new backpack. How much money does he have left?
Answer: $21.33
Step-by-step explanation: 50 - 28.67 = 21.33
Scott bought a desktop computer and a laptop computer. Before finance charges and the laptop cost $350 more than the desktop. He paid for the computers using two different financial plans. For the desktop the interest rate was 6.5% per year and for the laptop it was 9% per year. The total finance charges for one year for $388. How much did each computer cost before finance charges
The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
What are mathematics operations?A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.
From the question , we are given that the laptop costs $350 more than the desktop, therefore,
let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .
The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;
388 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that the cost of desktop = x -350
therefore:
1,798- 350 = 1448
The cost of laptop = $1798
The cost of desktop = $1448
Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
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The length of a
rectangular garden is
three feet less than twice
its width. If the perimeter
of the garden is 42 feet,
what is its length?
Systems word problems
Answer:
The length will be 13 feet.
Step-by-step explanation:
Let the width be represented by w.
Based on the information given, the length will be:
= (2 × w) - 3
= 2w - 3
Therefore, the perimeter will be:
2(w) + 2(2w - 3) = 42
2w + 4w - 6 = 42
6w = 42 + 6
6w = 48
w = 48/6
w = 8
Therefore, the length will be:
L = 2w - 3
L = 2(8) - 3
L = 16 - 3
L = 13 feet
The length is 13 feet.
Answer:
The length will be 13 feet.
Step-by-step explanation:
Let the width be represented by w.
Based on the information given, the length will be:
= (2 × w) - 3
= 2w - 3
Therefore, the perimeter will be:
2(w) + 2(2w - 3) = 42
2w + 4w - 6 = 42
6w = 42 + 6
6w = 48
w = 48/6
w = 8
Therefore, the length will be:
L = 2w - 3
L = 2(8) - 3
L = 16 - 3
L = 13 feet
The length is 13 feet.
The interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. The sum S of the measures of the interior angles of a polygon with n sides can be found using the formula S = 180(n - 2). The sum of a polygon’s interior angle measures is 1260°. How many sides does the polygon have?
The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides
What is a polygon in geometry?A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.
The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;
S = 180·(n - 2)
Where;
n = The number of sides the polygon has
The sum of the interior angles in the specified polygon = 1,260°
The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;
When S = 1.260°, we get;
1,260 = 180·(n - 2)
Which indicates;
n - 2 = 1,260 ÷ 180 = 7
Therefore; n - 2 + 2 = 7 + 2 = 9
n = 9
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a punch recipe calls for 1 1/2 quarts of sparkling water and 3/4 of a quart of grape juice. how much of each ingredient would you need to make 75 quarts of punch?
50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.
The ratio of sparkling water to grape juice is,
1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) = 2 : 1
The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is
2/3 · 75quarts = 50 quarts
Then the grape juice content is,
1/3 · 75 quarts = 25 quarts
Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.
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Givenf(x)=4x^2 - 1, and g(x) = 2x - 1, find g(f(2)).
Given f(x) = x^2 and g(x)=x - 1, write each composite function.State the domain of each:2.f(g(x)) 3.g(f(x))
The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(x) = 4x² - 1. and g(x) = 2x - 1.
Now, g(f(2)) is the output of f(2) is the input of g(x).
∴ f(2) = 4(2)² - 1.
f(2) = 15.
Now, g(f(2)) = 2(15) - 1.
g(f(2)) = 29.
Also given,
f(x) = x² and g(x) = x - 1.
Now, 2.f(g(x)).
2.f(g(x)) = 2.f(x- 1).
2.f(g(x)) = 2(x - 1)².
2.f(g(x)) = 2(x² - 2x + 1).
2.f(g(x)) = 2x² - 4x + 2.
2.f(g(x)) = 2x² - 2x - 2x + 2.
2.f(g(x)) = 2x(x - 1) - 2(x - 1).
2.f(g(x)) = (x - 1)(2x - 2).
There is no restriction to the domain of this quadratic function.
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Give a number in the form of a/b o that when it i divided by 100, the reult would be 0. 014 (write in fraction in reduce form)
The reduced form of the fraction would be 2.8/2.
What is a fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
Given that a/b is a fraction and when it is divided by 100 it will result in 0.014.
So we can write,
[tex]\frac{\frac{a}{b} }{100}=0.014\\\\ \frac{a}{b}=0.014*100\\\\\frac{a}{b}=1.4\\[/tex]
Now 1.4 can be written as
a/b = 2.8/2
Hence, the reduced form of the fraction would be 2.8/2.
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A shopping mall has 226 stores on 4 levels. Each level of the mall has about the same number of stores. Which of the following are reasonable estimates for the number of stores on each level
The number of stores in each level of the shopping mall are 56 stores.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let x represent the number of stores on each level.
A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:
(4 × x) = 226
4x = 226
Divide
x = 226 / 4
x = 56.5
There are about 56 stores per level.
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Find the perimeter of a quadrilateral with the following vertices.
(−6, −2), (0, −10), (5, 2), (−1, 10)
a.40
b.52
c.23
d.46
The perimeter of the quadrilateral is 46 units, so the correct option is d.
How to find the perimeter of the quadrilateral?The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.
Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:
L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
The length between the first two vertices: (−6, −2), (0, −10)
L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10
The length between the second two vertices: (0, −10), (5, 2)
L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13
The length between the third two vertices: (5, 2), (−1, 10)
L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10
The length between the fourth two vertices: (−1, 10), (−6, −2)
L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13
Then the perimeter is:
P = 10 + 13 + 10 + 13 = 46
The correct option is D.
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