A 90-degree tan is referred to as infinity. Thus, 90 degrees is the value for tan-1.
It is given that, tan⁻¹∞
We have to find the value of tan⁻¹∞.
Now,
The value of tan⁻¹∞ is π/2.
By using the trigonometric concepts, we can find the value of tan⁻¹∞
we already know that, tan π/2 = ∞
we have to apply tan⁻¹ on both sides
we get,
tan⁻¹ tan π/2 = tan ∞
π/2 = tan⁻¹∞
Hence, the value of tan⁻¹∞ is π/2.
The trigonometric function "tangent" is represented by the inverse function "inverse tan." The opposing side of the right triangle is divided by the adjacent side, and this relationship is utilized to compute the angle by using the tangent ratio of the angle. All inverse trigonometric functions must be named with the prefix "arc," so inverse tangent is abbreviated as "arctan."
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A plane rises from take-off and flies at an angle of 14 with the horizontal runway. When it has gained 950 feet, find the distance, to the nearest foot, the plane has flown.
The distance, to the nearest foot, the plane has flown is 3926.887 feet.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Angles are usually measured in degrees or radians
The horizontal runway, the distance plane flied and the height gained forms a right angled triangle.
Let x be the distance plane flied.
Height gained = 950 feet
Angle that plane makes with the horizontal runway = 14°
Sin 14 = Opposite side / Hypotenuse
Sin 14 = 950 / x
x = 950 / sin 14
x = 3926.887 feet
Hence the distance plane flied is 3926.887 feet.
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a+b=b-a
what are some numbers to make this equation true?
Answer:
b =0nand a =0 simple beacaes3 0-0=0and 0+0=0
The ratio of peanuts to raisins is 2:8. What percent of the peanuts and the raisins are peanuts? I need this ASAP.
Answer:
20%
Step-by-step explanation:
2+8=10
10*10=100
2*10=2
Please can you give me brainliest?
Select the correct answer
Nia wants to check whether the finance charge applied in her credit card statement is correct. To do this, she needs to calculate the average daily
balance in her account for the previous billing cycle. She made a table to do the calculation. The billing cycle is 31 days
What was Nia's average daily balance in this billing cycle?
Balance
Days
7
10
$745. 00
$585. 15
$245 20
$90. 75
A. $13,420. 00
B. $13,418. 00
c. $800. 00
D. $432. 84
E. $430. 48
The Nia's average daily balance in this billing cycle was equals to the $432.85. So, correct choice is option(D).
Nia wants to check whether the finance charge applied in her credit card statement is correct or not. For this she made a table to do this calculation. The billing cycle is 31 days is present in above figure. We have to calculate the Nia's average daily balance in billing. Average daily balance of Nid is represented by:
Average mean = (Days x Balance)/Total Number of days
So, Days × balance = (745.0 x 7) + (1555. 15 × 10) + (245.20 × 7) + (90.75 × 7)
= 5215 + 5851.5 +1716.4 + 635.25
= $13418.15
Total number of days = 7+ 10 + 7 + 7 = 31 days
Hence, the Average = 13418.15/31
= $432.84
Hence, required average daily balance is $432.84.
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Simplify 2/3+1/6 in the simplest form
Answer: answer is 5/6, check my photo to understand
Answer: 5/6
Step-by-step explanation:
The ratio of markers to crayons in an artist's collection is 4:3. Which of the following ratios is equivalent to 4:3?
Answer:
A
Step-by-step explanation:make brainiest
Is the inverse of a function always a function example?.
Every function has an inverse, but not every inverse will be a function.
A function takes a starting value, performs some operation on this value, and creates an output answer.
The inverse function takes the output answer, performs some operation on it, and arrives back at the original function's starting value.
An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
A function is a one-to-one function if and only if each second element corresponds to one and only one first element.
Example:
consider the inverse of the function an f(x)=2x-4.
y=2x-4
x=y-4
x+4=y
f⁻¹(y)=x+4
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Jayden invests $2,644.93 in a retirement account with an interest rate of 8% compounded annually. What will the account balance be after 5 years?
The balance in the account of Jayden after 5 years will be $3,886.27.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Jayden invests $2,644.93 in a retirement account with an interest rate of 8% compounded annually. Then the amount after 5 years is calculated as,
A = $2,644.93 x (1 + 0.08)⁵
A = $2,644.93 x (1.08)⁵
A = $2,644.93 x 1.469
A = $3,886.27
The balance in the account of Jayden after 5 years will be $3,886.27.
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Which equation is true?
A.
3
4
=
9
16
B.
6
8
=
4
3
C.
3
5
=
8
10
D.
12
16
=
36
48
Answer: a and c
Step-by-step explanation:
What is range and X range?.
The range of a set of numbers is the difference between the maximum and minimum values in the set. X range is a type of range chart used to identify patterns in data points over a period of time.
The Range of a dataset is determined by subtracting the smallest value from the largest value in that dataset, providing an indication of the total spread of the data points. Range is a useful metric for understanding the variability of data points and for comparing different datasets.
X Range is a type of range chart used to identify patterns in data points over a period of time. It is a graphical representation of the range of data points and can help to identify trends and seasonal patterns. X Range charts are particularly useful for understanding how data points fluctuate over time, and can be used to identify any outliers in the data that may require further investigation.
X Range charts can be used to identify any clusters of data points, and to compare different data sets. X Range charts are also useful for understanding the overall volatility of a dataset and for making predictions about future data points.
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Use 4 of the 5 numbers shown to make the equations true.
Each number can be used only once.
The answers to the two blank portions are, √64 = 8 and ∛1000 = 10.
What are surds and indices?We are aware that there are two different sorts of radicals. Surds are created when a number is raised to a power that makes it greater than zero but less than one. Indices are created when a number is raised to a power that makes it bigger than one.
We know 10×10 = 100.
10¹×10¹ = 100.
10² = 100.
√100 = 10.
Similarly ∛1000 = 10.
As ∛1000 = ∛(10×10×10) = ∛10³ = 10.
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Can some please help I need to get this answer?
The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the two shorter sides, according to the Pythagorean theorem.
Pythagoras, a Greek philosopher who was born around 570 BC, is honored in the name of the theorem. Perhaps more than any other mathematical theorem, the theorem has been demonstrated numerous times using a variety of techniques. There are many different types of proofs, some of which go back thousands of years, including both geometric proofs and algebraic proofs.
The Pythagorean relation holds true when Euclidean space is represented by a Cartesian coordinate system in analytical geometry: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points.
[tex]c=\sqrt{ a2+b2}= \sqrt{ 3.92+82}=8.9[/tex]
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A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form. Select all the true statements about this relation. Number of squares, x 1 2 3 4 perimeter, y 8 12 16 20.
Perimeter is directly proportional to number of squares, x and is 4x where x is the number of squares.
What is perimeter ?
Perimeter is the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of a shape. It is commonly used to measure the size of a closed shape such as a square, rectangle, or circle. The formula for perimeter depends on the shape in question.
The statements that are true about the relation between the number of squares and the perimeter of the rectangles they form are:
As the number of squares increases, the perimeter of the rectangle also increases.
The perimeter of the rectangle is 4 times the number of squares.
The perimeter increases by 4 for every increase in 1 square.
The perimeter is calculated by multiplying the number of squares by 4.
The perimeter is directly proportional to the number of squares.
Perimeter is directly proportional to number of squares, x and is 4x where x is the number of squares.
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What is the solution to y 6 =- 3y 26?.
The solution to y+6 =- 3y-26 is 8.
The solution to the equation y+6 =- 3y-26 is to solve for y. This can be done by rearranging the equation and combining like terms. The equation can be rearranged to -3y-y+6 = -26.
Combining the like terms yields -4y+6 = -26.
To solve for y, subtract 6 from both sides.
These yields -4y = -32.
Finally, divide both sides by -4 to obtain y = 8.
Therefore, the solution to the equation y+6 =- 3y-26 is y = 8.
Understanding the solution to an equation is a critical part of algebra and can be used to solve a variety of problems. There are many methods for solving equations, and it is important to understand each type and how to employ them appropriately. Solving equations like y+6 =- 3y-26 requires rearranging the equation and combining like terms to obtain the solution. Once the equation is in a simpler form, the solution can be found by applying basic math operations.
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Pls help me with this question (#4) !
I’m learning abt similar figures in math and I don’t know what this one is
Tysm!
Answer:
x = 17, y = 8
Step-by-step explanation:
Answer:
y-8
X-17
Step-by-step explanation:
Look at the ratio. If BC is 2x of ZY, then multiply the sides of XZ and YX by 2
A bracelet has two colors of beads. The ratio of green beads to blue beads is 2:7. There are 18 green beads. How many beads are there in total?
Answer:
81 Bead in total
Ratio: 18:63
Step-by-step explanation:
2*9 = 18
7*9 = 63
The cost of 250 bricks, delivered to a worksite, is $170. The cost of 400 bricks delivered is $245. How much would it cost to have 320 bricks delivered
The cost of 250 bricks, delivered to a worksite, is $170. The cost of 400 bricks delivered is $245 and the cost to have 320 bricks will delivered $217.6 .
How much would it cost to have 320 bricks delivered?The cost of 250 bricks, delivered to a worksite, is $170.
So , we can calculate the single brick cost need to divide 170/250=0.68
Single brick cost is 0.68
The cost of 400 bricks delivered is $245. In this case a single brick cost is 0.6125
The answers is different from the first answer we can calculate 320 brick cost 320×0.68=217.6
The following equation is used to calculate the Cost Per Brick. To calculate the cost per brick, divide the total cost of the bricks by the number of bricks. Bricks in 1 cubic Feet (cft) = Volume of brickwork/ Volume of one brick with mortar. Thus, thumb rule formula: No. of bricks in wall per Cubic Feet= (Area in Cft × 14).
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In a certain tate about 3/5 of regitred voter particated in 2016 election what fraction of regitred voter did not
The fraction of registered voter that did not participate was 2/5
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
To solve this exercise we have to perform a mathematical operation with fractions:
Information about the problem:
Total = 1Registered voter participated= 3/5No. did not participate = ?Calculating the fraction of the registered voter that did not vote we get:
No. did not participate = Total - Registered voter participated
No. did not participate = 1 - 3/5
No. did not participate = (5 - 3) /5
No. did not participate = 2/5
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Subtract 33 1/3% of 36 from 50% of 88.
Add explanation.
The value of the expression is 32.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
50% of 88 - 33(1/3)% of 36
This can be written as,
= 50/100 x 88 - (100/3)/100 x 36
= 44 - 12
= 32
Thus,
The value is 32.
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18. The table shows the amount of time you work and your total wages. Write an equation in
slope intercept form that gives your wage at any time. What do the slope and y-intercept
represent?
Time worked, x Wages earned,
. y($)
1. 9.25
3. 27.75
7. 64.75
The slope and y-intercept represent, time worked, x Wages earned,
y($) is 9.25.
Give a brief account in slope?In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.
From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.
The point-slope form of a linear equation is y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
We can use the data from the table to find the slope of the line.
m = (y2 - y1) / (x2 - x1)
We can use the first two data points (x1 = 1, y1 = 9.25) and (x2 = 3, y2 = 27.75) to find the slope:
m = (27.75 - 9.25) / (3 - 1) = 18.5/2 = 9.25
Now we have the slope, we can use the point (x1 = 1, y1 = 9.25) to find the y-intercept, b
9.25 = 9.25 * 1 + b
we can find b is 0
So, the equation of the line in slope-intercept form is y = 9.25x + 0
The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.
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The slope and y-intercept represent, time worked, x Wages earned, y($) is 9.25.
Give a brief account of slope.In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.
From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.
The point-slope form of a linear equation is y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is a point on the line.
We can use the data from the table to find the slope of the line.
m = (y₂ - y₁) / (x₂ - x₁)
We can use the first two data points (x₁ = 1, y₁ = 9.25) and (x₂ = 3, y₂ = 27.75) to find the slope:
m = (27.75 - 9.25) / (3 - 1)
= 18.5/2
= 9.25
Now we have the slope, we can use the point (x₁ = 1, y₁ = 9.25) to find the y-intercept, b
9.25 = 9.25 * 1 + b
We can find b is 0
So, the equation of the line in slope-intercept form is y = 9.25x + 0
The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.
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Use the Distributive Property to simplify the expression.
9(2n+1) =
PLs help me fast .
A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects' symptoms are studied and compared. Answer parts (a) through (c) below.
After six months, the subjects' symptoms are studied and compared. Answer parts are given below.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
A pharmaceutical company wants to test the effectiveness of a new allergy drug.
The company identifies 250 females 30–35 years old who suffer from severe allergies.
The subjects are randomly assigned into two groups.
One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.
After six months, the subjects' symptoms are studied and compared.
Here, 30-35 year-old girls are used to test the new allergy medication's effects.
(a)
Females between the ages of 30 and 35 who are the test subjects are the experimental units.
The new allergy medication, whose results are being studied, is the remedy.
It's best to choose C.
(b)
A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.
In this case, choice B is preferable.
(c)
If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.
In this case, choice A is preferable.
Therefore, all the correct choices are given above.
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The complete question is given in the image.
For what values of k is the quadratic equation 9x2?.
The possible values of k for the quadratic equation 9x² - 5kx + 1 = 0 has equal roots are 6/5 and -6/5.
The standard form of an quadratic equation is, ax² + bx + c = 0, a ≠ 0 and a,b,c --> constants. The quadratic formula for solution of above equation is, x = ( - b ±√b² - 4ac)/2a , where Discriminate, D is equals to b² - 4ac . We have an quadratic equation, 9x² - 5kx + 1 = 0 --(*)
Step 1 : Determining the discriminant of the quadratic equation : After comparing the equation (*) with standard one , a = 9 , b = - 5k and c = k . So, discriminate formula , D = b² - 4ac
=> D = (- 5k)² - 4×9×1
=> D = 25 k² - 36
Step 2: Determining the values of k : We have equation (*) has equal roots then according to the nature of the roots of an quadratic equation When the value of discriminant, D = 0, then the quadratic equation has real and equal roots.
So, 25 k²- 36 = 0
=> 25 k² = 36
=> k² = 36/25
=> k = ±√36/25
=> k = ± 6/5
Hence, the values of k are ± 6/5.
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Complete question:
For what values of k is the quadratic equation 9x² - 5kx + k = 0, has equal roots?
What are the 5 steps in solving equations by substitution?.
The 5 steps in solving equations by substitution are
Solve one equation for either x or y.Substitute the expression from step one into the 2nd equation.Solve the second equation for the given variable.Plug you solution back into the first equation.Write your solution as a point.If we take an example ,
Equation 1: 3x + 2y = 11Equation 2: -x + y = 3Substituting y = 3+x in equation 1 we get,
3x + 2(3 + x) = 11
3x + 6 + 2x = 11
5x = 5
x = 1
Put the value of x = 1 in the equation -x + y = 3
we get -1 + y = 3
so y = 4
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a pet store gives away 3 dog treats with every food bowl sold. write an expression to represent this situation please help asap tysm
A manufacturer of new smart phones purchases screens from two different suppliers. The company receives 55% of its screens from Corning Inc. And remaining screens from Philips. The quality of the screens varies between the suppliers: Corning Inc. Supplies 1% unsatisfactory screens while 4% of the screens from Philips are unsatisfactory. Given that a randomly chosen screen is unsatisfactory, what is the probability it came from Philips
The probability that a randomly chosen unsatisfactory screen came from Philips is approximately 0.4444.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Let's call the probability that a screen came from Philips "P".
know that 55% of the screens came from Corning Inc. and the rest came from Philips, so:
P = 1 - 0.55 = 0.45
We also know that the probability of getting an unsatisfactory screen from Corning Inc. is 1%, while the probability of getting an unsatisfactory screen from Philips is 4%:
P(unsatisfactory | Corning Inc.) = 0.01
P(unsatisfactory | Philips) = 0.04
Using Bayes' theorem, the probability that a randomly chosen unsatisfactory screen came from Philips can be calculated as:
P(Philips | unsatisfactory) = P(unsatisfactory | Philips) * P(Philips) / [P(unsatisfactory | Philips) * P(Philips) + P(unsatisfactory | Corning Inc.) * P(Corning Inc.)]
Substituting the values we have:
P(Philips | unsatisfactory) = 0.04 * 0.45 / [0.04 * 0.45 + 0.01 * 0.55] = 0.444444... or approximately 0.4444
Therefore, the probability that a randomly chosen unsatisfactory screen came from Philips is approximately 0.4444.
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The probability that a randomly chosen unsatisfactory screen came from Philips is 46.48%.
Let's call P(Philips) the probability that a randomly chosen screen came from Philips, and P(Unsatisfactory | Philips) the probability that a screen is unsatisfactory given that it came from Philips. Then we can use Bayes' theorem to find P(Philips | Unsatisfactory), the probability that a screen came from Philips given that it is unsatisfactory.
Bayes' theorem states:
P(A | B) = P(B | A) * P(A) / P(B)
where A and B are events, P(A | B) is the conditional probability of A given B, P(B | A) is the conditional probability of B given A, P(A) is the probability of A, and P(B) is the probability of B.
In this case,
A = "the screen came from Philips"
B = "the screen is unsatisfactory"
So:
P(Philips | Unsatisfactory) = P(Unsatisfactory | Philips) * P(Philips) / P(Unsatisfactory)
We are given:
P(Unsatisfactory | Philips) = 4% = 0.04
P(Philips) = 45% = 0.45 (since 55% came from Corning Inc.)
P(Unsatisfactory) = P(Unsatisfactory | Corning Inc.) * P(Corning Inc.) + P(Unsatisfactory | Philips) * P(Philips)
= 1% * 55% + 4% * 45% = 0.55% + 1.8% = 2.35%
So:
P(Philips | Unsatisfactory) = 0.04 * 0.45 / 0.0235 = 46.48%
So the probability that a randomly chosen unsatisfactory screen came from Philips is 46.48%.
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How do you solve systems by elimination with multiplication?.
To solve the given system of equations using elimination method following steps need to follow:
Equate the coefficient in opposite sign by multiplying the equation by required number for the variable you want to eliminate.
As given in the question,
Steps required to solve the given system of equations by elimination method with multiplication:
To eliminate x-term equate the coefficient of x in opposite sign.
4x + 3y = 1 __(1)
3x + 4y = 1 __(2)
1. Multiply 3 to (1) and -4 to (2) to eliminate the x-term.
12x + 9y = 3 __(3)
-12x - 16y = -4 __(4)
2. Now add (4) from (3) and eliminate x-term.
12x + 9y = 3
-12x - 16y = -4
0x -7y = -1
⇒ y = 1 / 7.
Therefore, solution of the system of equation using elimination method with multiplication is:
Equate the coefficient in opposite sign by multiplying the equation by required number for the variable you want to eliminate.
The above question is incomplete , the complete question is :
How do you solve systems of equations by elimination method with multiplication?.
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How do i solve this?
Answer:
x = 45/2 or 22.5
Step-by-step explanation:
Since we are given CDE ~ KLM, we know that C is similar to K, D is similar to L, and E is similar to M. The problem asks to find DE, so by comparison, it is known that DE is similar to LM.
From the two triangles, KM is similar to CE, and we can see that the ratio between the two is 8:15. We are given LM, which is 12, so we can find x using this equation to compare the smaller triangle to the bigger one:
KM/CE = LM/DE
Plug in your given values:
8/15 = 12/x
Find x:
x = 45/2 or 22.5
Which data set could be represented by the boxplot shown?
A. {6, 6, 8, 8, 9, 12, 13, 13, 14}
B. {6, 6, 7, 9, 9, 12, 13, 14, 16}
C. {6, 7, 8, 9, 10, 11, 12, 13, 14}
D. {6, 7, 9, 9, 9, 12, 13, 14, 14}
A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.
What is a box-and-whisker plot?In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 6First quartile = 7.Median = 9.Third quartile = 13.Maximum = 14.For the median, we have:
Median = 6, 6, 8, 8, 9, 12, 13, 13, 14
Median = 9.
In conclusion, we can logically deduce that the median of the given data set is equal to 9 while the first quartile is 7 and the third quartile is 13.
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The average temperature during the winter in the Arctic tundra i -34C. You can convernt Celete C to degree farenhite F uing the formula F=9\5C 32
The average temperature during the winter in the Arctic tundra i -34C which is also 93.2 degrees Fahrenheit
The difference between the freezing point of water and its boiling point at normal atmospheric pressure is divided into exactly 100 equal parts to determine the temperature in degrees Celsius (degrees). Water has a freezing point set at 0° and a boiling point set at 100°.
Therefore, a 100°C difference is precisely equivalent to a 180°F difference. As a result, each degree in Celsius is equivalent to 1.8 degrees Fahrenheit.
The 34 Celsius to Fahrenheit formula is a linear function:
[°F] = ([34] x 9 ⁄ 5) + 32.
Therefore, we get:
34 C to F = 93.2 °F
34 °C in °F = 93.2 Fahrenheit
34 C in F = 93.2 degrees Fahrenheit
Know more about Celsius to Fahrenheit
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