False, that is if the number of data observations is even, the median is generally considered to be the average of middle values not the first and last values.
The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.
At least half of the observations are equal to or smaller than the median, and at least half of the measurements are equal to or greater than the median. The median divides the bottom half of observations from the upper half.
Even Number of Observations :
Suppose we have the monthly wages of 4 employees of a company. How would you find the median wage?
wages are 120,240,500,400
we have arranged their wages above from lowest to highest. This ranking will help us to determine the median. Using the method introduced earlier, the median is computed by taking the simple average of the (n/2)ᵗʰ = (4/2)ᵗʰ = 2ⁿᵈ and
(n/2 + 1)ᵗʰ = (2+1)ᵗʰ = 3ʳᵈ observations.
Therefore, the median is 240+500/2
= 370.
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Complete question
True/false
if the number of data observations is even, the median is generally considered to be the average of the first and last values
Two friends, Pedro and Oliver, took summer jobs. Pedro earned $521.40 in 22 hours. The graph below represents Oliver's earnings in dollars and cents, yy, for working xx hours.
How much more does Pedro earn per hour than Oliver?
Pedro earns $5.1 per hour more than Oliver
How to determine the extra amount that Pedro earn per hour than Oliver?From the question, we have the following parameters that can be used in our computation:
Pedro earned $521.40 in 22 hours. Oliver's earnings in dollars and cents are represented by the graphThe hourly rate of Pedro is calculated using
Hourly rate = Amount earned/Number of hours
Substitute the known values in the above equation, so, we have the following representation
Hourly rate = 521.40/22
Evaluate
Hourly rate = 23.7
Using the points on Oliver's graph
The hourly rate of Oliver is calculated using
Hourly rate = Amount earned/Number of hours
Substitute the known values in the above equation, so, we have the following representation
Hourly rate = 186/10
Evaluate
Hourly rate = 18.6
The difference between these rates is
Difference = 23.7 - 18.6
Evaluate the difference
Difference = 5.1
Hence, the difference is $5.1
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Find the sixth number in this sequence. (a.) The fourth number is equal to 3x10. (b.) The second number is equal to 10+6. (c.) The Third number is halfway between the second and fourth numbers. (d.) The fifth number is 7 more than the fourth number.
The sixth number of the arithmetic progression is 44
What is arithmetic progression?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
For example 3, 8 , 13, 18, 23 is an arithmetic progression with common difference of 5
The nth term of a sequence is given as a1+(n-1)d
where a1 is the first number
Therefore
a5= 37
a4= 30
a2= 16
a3 = (30+16)÷2 = 46÷2= 23
therefore common difference = 23-16 = 7
a1 = 16-7= 9
therefore a6 = fifth number + common difference
a6= 37+7= 44
therefore the sixth number is 44
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Write the equation in slope-intercept form.
y+2=1/6(x−4)
Answer:
Step-by-step explanation:
First: You do PEMDAS.
Second: you do what in your parentheses
A couple just had a baby. How much should they invest now at 5.5% compounded weekly in order
to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest
dollar. (Assume there are 52 weeks in a year.)
Answer:
To find the amount that the couple needs to invest now, we can use the following formula:
investment = education cost * (1 + interest rate / number of compounding periods per year) ^ (number of years * number of compounding periods per year)
Plugging in the given values, we get:
investment = $40,000 * (1 + 0.055 / 52) ^ (17 * 52)
Solving this equation, we find that the couple needs to invest $11,226.31 now to have $40,000 for the child's education in 17 years. Rounded to the nearest dollar, this is $11,226.
Step-by-step explanation:
Which equation can be used to find V the volume of the cylinder in cubic inches?; What is the dimensional formula of cylinder?; Which equation can be used to find V the volume of the silo in cubic meters?; Which equation can be used to find the surface area of the cylinder?
The equation of the volume of the cylinder is V = A× h where a is base area and h is height.
Given that,
We have to find the equation of the volume of the cylinder.
We know that,
Given that a cylinder and a prism have similar shapes, but a cylinder differs from a prism in that it has a curved side face, we can determine a cylinder's volume using the same formula. We are aware that the formula, which is used to determine a prism's area,
Where V = A× h
A = the base's area
height is h.
Using the formula above, the volume (V) of a right circular cylinder is,
V = πr²h
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two dice are rolled. find the probability of the following event. the first die is 3 or the sum is 6.
The probability of the following event. The first die is 3 or the sum is 6 would be 1/4.
What is the probability?
Probability refers to a possibility that deals with the occurrence of random events.
All events must have a probability of occuring at least once, or 1.
The proportion of positive outcomes to all outcomes is referred to as the probability formula.
Let's assume that the blue die came up first among the two.
A = the amount of times we roll a first-die and get a 3.
B is the quantity of times a total of six occurs.
Now Locate 3 on the blue die and notice there are 6 occurrences when this happens which corresponds to the 6 other possibilities for the red die. So we have A = 5.
Also,there are 5 occurrences of the sum "6" in the table. So B = 5.
We have A+B = 5+5 = 10 occurrences of either the first die is 3 or the sum is 6.
However, we have to subtract off 1 because we double counted "6" when adding A and B.
So in reality we have 10-1 = 9 times this happens.
This is out of 36 total ways to roll two dice.
Therefore, the probability of the following event.
The first die is 3 or the sum is 6 would be 9/36 = 1/4
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general: what is represented on the x and y axis in this graph? what does the black observed line represent in each graph?
The given question is incomplete as the graph is missing.
But, considering a line graph, the following parameters can be represented on the x-axis and y-axis:
X-Axis Y-Axis
Year Population
Time Number of employees hired
Identical items purchased Total cost in dollars
What does the blank observed line represent in each graph?
The blank observed line represents the time. A line graph is basically used to connect the quantitative values over the different time intervals. The change in values over time is easier to estimate, by the help of the line graph. For example: in a graph showing the year on the x-axis and the population on the y-axis, the blank line represents the change in population over the years, the increase or decrease or the rate of change.
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Find the angle θ , in radians, in the given right triangle. The length of the side adjacent to θ is 16 and the length of the side opposite θ is 10. A right triangle with height 10 opposite from angle theta and base 16 adjacent to angle theta. 10 16 Round your answer to the nearest hundredth
Angle θ is equal to 0.56 radian.
What do you mean by inverse trignometry?
Inverse trigonometric functions are just the sine, cosine, tangent, cotangent, secant, and cosecant functions of the fundamental trigonometric functions. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions.
It is given that in right angle triangle, base of the triangle is 16 and height of the triangle is 10.
Now to find θ, from the given right angled triangle. Using the formula for tanθ
tanθ = P/B = 10/16 = 5/8
θ = [tex]tan^{-1}(5/8) = tan^{-1}(0.625) = 0.56[/tex] radian.
Therefore, angle θ is equal to 0.56 radian.
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An electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day. The model can be written as follows:
ŷ = 103.38 + 2.45x
where ŷ is in thousands of dollars.
What would you predict the sales to be on day 60?
Using the regression model you predict the sales to be $ 250.38 on day 60.
What is a regression model?A regression model is an equation used to ascertain the relationship between two variables.
How to find what you would predict the sales to be on day 60?Given that an electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day.
The model can be written as follows:
ŷ = 103.38 + 2.45x
where ŷ is in thousands of dollars.
Since we require the sales gtowth after 0 days, substituting x = 60 into the equation for the regression model, we have that
ŷ = 103.38 + 2.45x
ŷ = 103.38 + 2.45(60)
ŷ = 103.38 + 2.45(60)
ŷ = 103.38 + 147
ŷ = 250.38
So, you predict the sales to be $ 250.38 on day 60.
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the function relates the length of a skid mark measured in feet at an accident scene to the speed of the car in miles per hour. that means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. if a skid mark with a length of 82.5 ft was found, find the speed of the car. round your answer to the nearest tenth.
If a skid mark with a length of 82.5 feet was found, then the speed of the car is 13.59 miles per hour
The function is
l(s) = 0.46s^2 - 0.199s + 0.264
Where l is the length of a skid mark measured in feet at an accident scene
s is the speed of the car in miles per hour
Given that the skid mark length = 82.5 feet
Then the equation will be
0.46s^2 - 0.199s + 0.264 = 82.5
Rearrange the terms
0.46s^2 - 0.199s + 0.264 - 82.5 = 0
0.46s^2 - 0.199s - 82.236 = 0
Use the quadratic equation
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the equation
= [tex]\frac{0.199+/-\sqrt{(-0.199)^2-4(0.46)(-82.236)} }{2(0.46)}[/tex]
= (0.199 ± 12.30) / 0.92
Then
(0.199 + 12.30) / 0.92 = 13.59
(0.199 - 12.30) / 0.92 = -13.15
Therefore, the speed of the car is 13.59 miles per hour
The complete question is:
The function l(s) = 0.46s^2 - 0.199s + 0.264 relates the length of a skid mark measured in feet at an accident scene to the speed of the car in miles per hour. that means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. if a skid mark with a length of 82.5 ft was found, find the speed of the car. round your answer to the nearest tenth.
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What is the statement of triangle?
The statement of triangle is that it has three corresponding sides and three corresponding angles.
What are the theorems about triangles?There are at least 3 theorems about triangles, those are: the total of the three interior angles in any triangle is 180 degrees; when a triangle side is constructed, the exterior angle formed is equal to the sum of the interior opposite angles; and, the base angles of an isosceles triangle are equivalent.
Scalene, isosceles and equilateral triangle are the types of triangles which differ from each other based on their side-length. If all the three sides are different in length, then its scalene triangle. If any two sides are equal in length, then it is an isosceles triangle.
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Solve the problem.
The formula P = 14.7e-0.21x gives the average atmospheric pressure, P, in pounds per square inch, at an altitude x, in miles above sea level. Find the average atmospheric pressure for an altitude of 2.3 miles. Round your answer to the nearest tenth.
A) 9.1 lb/in.²
B) 8.4 lb/in.²
C) 11.0 lb/in.²
D) 7.8 lb/in.²
Answer: 9.1 lb/in.^2
Step-by-step explanation:
To begin, plug in your X value to get P=14.7e^(-0.21(2.3)).
With this you can solve for P=9.1 lb/in.^2
Suppose the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi ), for i =1, . . . , n, is 1. Which of the following statements do you think would be INCORRECT? Evaluate each expression and give reasons
(a) Ëεi =Yi âËYi =0, for all i =1, . . . , n.
(b) Mean Squared Error =0.
(c) The coefficient of determination R^2 =1.
(d) nâ i=1 (Yi âYbar)^2 = nâ i=1 (ËYicap âYbar ^)2
(e) SE(Ëμ(x))=1.
Option (e) SE(u(x)) = 1 is incorrect about the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi )
The examination of the relationship between two variables is possible using bivariate analysis, which also has many real-world applications. It seeks to determine whether there is a link between the variables and how strong it is.
You can examine an association or causality hypothesis using bivariate analysis. It also aids in the prediction of dependent variable values based on changes in an independent variable.
The correlation coefficient (R) is a numerical value that ranges from -1 to 1. It reveals the strength of the linear relationship between the two specified variables.
The coefficient is referred to as Pearson's correlation coefficient when used to describe a linear regression.
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Answer please! Will give 5 star. Need explanation
The greatest common factor for the fraction is 26.
What is fraction?
A fraction represents a district of an entire or, additional typically, any range of equal components. once spoken in everyday English, a fraction describes what number components of an exact size there area unit.
Main body:
According to the question,
fraction = 52/78
to find its common factor , we need to write it in form of multiples of its factors,
52 = 2*2*13
78 = 2*3*13
from this it is clear that both 52, 78 has factor as 2*13
Hence the greatest common factor for the fraction is 26
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A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function =Cx+−0.7x2168x17,557. What is the minimum unit cost? Do not round your answer.
The minimum unit cost is given as 7477
How to solve for the minimum unit costWe have a = 0.7
b = - 168
c = 17557
We have to find the vertex for the minimum value
-b / 2a
where we would have
-(-168) /2* 0.7
= 168 / 1.4
= 120
We have to put this value in the original function
x stands for the machines
c(120) = 0.7x² - 168x + 17,557
= 0.7(120)² - 168 * 120 + 17,557
= 10080 - 20160 + 17557
= 7477
The minimum unit cost from the calculation that has been done above is given as 7477
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Which of the following is not a regular polygon? A) equilateral triangle
B) square
C) rectangle
D) None of these
Answer: D.) None of these
Step-by-step explanation: A polygon is regular when all angles are equal and all sides are equal (otherwise it is "irregular").
Which of the following is most likely to be a relative maximum for this graph? the points are (-1,0) (2,0) and (4,0)
The relative maximum for this graph is zero
Maximum of the graph is defined as the highest value of y-coordinate. This means the highest value on the y-axis. There are two types of maximums on the graph. Absolute maximum and the relative maximum.
Absolute maximum is the highest value of the y-coordinate on the graph. Whereas, relative maximum is the point where the graph changes its nature e.g. positive to negative.
Since, the given graph has all the points plotted on the x-axis e.g. value of y-coordinate is zero. That is why the value of relative maximum is also zero.
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model cutting and sewing finishing packaging and shipping profit/glove regular model 1 1/2 1/8 $5 catcher's model 3/2 1/3 1/4 $8
The inequality of each model cutting, sewing finishing packaging and shipping profit
The maximum value = 5x + 8y
1R + 3/2 C ≤ 900
1/2 R + 1/3 C ≤ 300
1/8 R + 1/4 C ≤ 100
R, C ≥ 0
Consider x be the number of regular model of gloves to be produced
y be the catcher’s model of gloves to be produced
The maximum value = 5x + 8y
Then the inequality will be
The inequality of Cutting and Sewing
1R + 3/2 C ≤ 900
The inequality of Finishing
1/2 R + 1/3 C ≤ 300
The inequality of Packaging and Shipping
1/8 R + 1/4 C ≤ 100
R, C ≥ 0
Therefore, the inequality of each model cutting, sewing finishing packaging and shipping profit has been found
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7. After paying $5.00 for a salad, Taylor has no more than $27.00 left. How
much money did she have before buying the salad?
(Set up inequality!)
Answer:
32.00 dollars before she bought the salad
T/F alma corp. issues 1,000 shares of $10 par common stock at $14 per share. when the transaction is journalized, credit(s) are made to
Cash is debited for increasing assets and credited for increasing stockholder equity by crediting common stock and paid-in capital.
Given,
Alma corp. issues 1,000 shares of $10 par common stock at $14 per share.
We have to find the credits made to when the transaction is journalized;
The journal entry is displayed below;
Cash; 1,000 shares at $14 = 1000 × 14 = $14,000
To Common Stock ; 1,000 shares at $10 = 1000 × 10 = 10,000
To Paid in capital in excess of par value; 3,000 shares at $4 = 14,000 - 10,000 = 4,000
Being documented as the common stock's issue
Here, cash is debited because it increased assets and credited because it increased stockholder equity by purchasing common shares and paying for capital.
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let be a diagonalizable matrix. if is the solution to the system , then check all the possible values of and below. (a); (b) ; (c) ; (d) ; (e) ; (f) .
Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system
x⃗' (t) = A x⃗ ( t )
the possible values of c₁ is 1 and c₂ is 2 .
So, the correct option is option(a) and (e).
We have given that A is 2 × 2 diagonalizable matrix and x⃗ (t) = ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) is a solution of system, x⃗ '(t) = A x⃗(ᵗ) .
A Solution of system always satisfied the equation of system.
Now, Differenating x⃗ (t) wih respect to t we get, x⃗' (t)=( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)
So, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)= A ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) where A is diagonalizable and A = [a 0 0 b].
Then, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ) = ( 3aeᵗ + aeᶜ₁t , 3be²ᵗ + b eᶜ₂ᵗ)
equating the coefficients on both sides we get, 3eᵗ + c₁ eᶜ₁t = 3aeᵗ + aeᶜ₁t 6e²ᵗ + c₂ eᶜ₂ᵗ = 3be²ᵗ + b eᶜ₂ᵗ
after equating the corresponding equations , 3 = 3a and c₁ = a and 6 = 3b and c₂ = b after solving all we get a = 1 and b = 2 which implies c₁ = 1 and c₂ = 2. Hence, the possible values are c₁ = 1 and c₂ = 2.
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Complete question:
Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system x⃗ (t) = A x⃗
then check all the possible values of c₁ and c₂ and below.
(a) c₁ = 1
(b) c₁ = 3
(c) c₁ = 2
d) c₂ = 1
(e)c₂ =2
(f) c₂ = 3
The heights of a boys and girls track team are shown. Find the range of the heights
for each team. Compare your results.
Boys' heights (inches) 84 75 77 82
82
Girls' heights (inches) 70 66 68
72
72
80 80
80 81 78 79 80
70
67 70 72 67
75
75
Answer:
For the boys' team, the tallest kid is 84 inches while the shortest is 75 inches making the range 9.
For the girls, the tallest is 75 inches tall while the shortest is 66, making the range 9.
Both the boys and the girls have a range of 9 but together, with the tallest boy and the shortest girl, the range is 18 inches.
Hope this helps! Have a nice day!
Raquel is playing a game where she throws a ball that paper called a trash ball into her trashcan the diameter of the top of the trashcan is 20 inches Raquel once the trash ball to have a diameter that is 1/4 the diameter of the top of the trashcan what should the timing of Raquel trash Be?
The diameter of the top of the trash ball is 5 inch.
What is a diameter?The diameter is the distance along the circle's center that must travel in order to touch two points on its periphery.
solution:
Given that the diameter of top of the trash can is 20 inch.
And the diameter of trash ball is 1/4th of the diameter of trash can.
The diameter of trash ball = 1/4 ( the diameter of trash can )
The diameter of trash ball = 1/4 (20 inch)
The diameter of trash ball = 20/4
The diameter of trash ball = 5 inch.
Therefore, the diameter of the top of the trash ball is 5 inch.
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1. Select all expressions that are equivalent to 8 +16i.
(A.) 2(4 + 8)
(B.) 2i(8-4)
4(21-4)
4i(4-21)
(E.) -2i(-8-4i)
The equivalent expression for the given expression is -2i(-8+4i).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 8 +16i.
The given expression can be written as 8(1+2i)
-2i(-8+4i)
= -2i×(-8)-(-2i)×4i
= 16i-8i²
= 16i-8(-1)
= 8+16i
Therefore, the equivalent expression is -2i(-8+4i).
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y <= -15x + 3000y <= 5xIn the xy plane, if a point with coordinates (a,b) lies in the solution set of the system of inequalities above, what is the maximum possible value for b?
B can have a maximum value of 750.
Given info,
y ≤ - 15x + 3000
y ≤ 5x
What is the highest possible value of b in the XY plane if a point with the coordinates (a,b) is found in the system of inequalities above?
The maximum value of b occurs when taking equality.
⇒ - 15x + 3000 = 5x
⇒ - 20x = - 3000
⇒ - 20x = - 3000
⇒ x = 150
Therefore, y = 5 * 150
= 750
Hence, the maximum possible value of b = 750
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Question 9 (4 points)
Chee is saving up to buy a new phone. The situation is represented by the equation y = 5.45x +
70 where x is the number of weeks and y is the total saved. How much total money would
Chee have after 6 weeks of saving?
A) $81.45
OB) $32.70
OC) $75.45
D) $102.70
Answer:
$102.70
Step-by-step explanation:
since x is weeks to find 6 weeks we replace x with 6
y=5.45(6)+70
y=32.7+70
y=102.7
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What is a credit card trap?
Reminder: Assume all dimensions are feet.
Task: Cover the given figure with flooring. Estimate that you will need 5% more than the actual area in case of mistakes.
Cost: $20 for 12 square feet of flooring.
Cost of Task =
The cost of the flooring task is $35
How to determine the cost of the task?
Consider the image I attached:
Actual area of floor = Area of rectangle A + Area of rectangle B
Actual area of floor = (6×3) + (2×1) = 18 + 2 = 20 ft²
With Estimate of 5% more than the actual area in case of mistakes:
Area = 20 + (5/100 × 20)
Area = 20 + 1 = 21 ft²
Since Cost: $20 for 12 square feet of flooring. Thus:
Cost of task = 21/12 × 20 = $35
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Which of the following is coterminal to 500 degrees in radians?
5pi/6
8pi/9
2pi/3
7pi/9
Answer:
7pi/9
Step-by-step explanation:
subtract 360 from 500 as many times as you can
number left should be converted to radians
500 - 360 = 140
140 * (pi/180) =
140Pi/180 =
simplify by dividing by 20 top & bottom
7Pi/9
varsitytutors
Find the value of X, need help ASAP
The value of x is 17
Define Angle
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Define Mid-line in Triangle
In a triangle, a midline (or a midsegment) is any of the three lines joining the midpoints of any pair of the sides of the triangle.
We know, the x+6 is mid-line of 46.
So, according to that make it a half of 46 is 23
Now, equate the value and find x
23 = x + 6
23 - 6 = x
17 = x
swap the sides
x = 17
Hence, the value of x is 17
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