Answers
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
Related Questions
√(1- x²) y' = xy
Calculus, please help
Answers
In the given differential equation, the general solution to the differential equation is: y = Ae^(√(1 - x²)), where A is any non-zero constant.
How to solve Differential Equation?To solve this differential equation, we can start by using separation of variables.
√(1 - x²) y' = xy
We can rewrite this equation as:
y' / y = x / √(1 - x²)
Now we can integrate both sides:
∫ (y' / y) dy = ∫ (x / √(1 - x²)) dx
ln|y| = -√(1 - x²) + C
where C is the constant of integration.
Taking the exponential of both sides:
|y| = e^(-√(1 - x²) + C) = e^C / e^(√(1 - x²))
Since we only care about the magnitude of y, we can drop the absolute value signs and write:
y = Ae^(√(1 - x²))
where A = ± e^C is another constant of integration.
Therefore, the general solution to the differential equation is:
y = Ae^(√(1 - x²))
where A is any non-zero constant.
Note that the solution only holds for |x| ≤ 1, since otherwise the expression inside the square root would become negative, and the solution would not be real-valued.
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Find the measure of x.
Answers
Answer:
x = 25
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
71° is an exterior angle of the triangle , then
x + 46 = 71 ( subtract 46 from both sides )
x = 25
the local farmers market has many different booths selling cabbage below are different advertisements for cabbage calculate the cost for 1 pound of cabbage from each booth and determine which booth is the least expensive and which is the most expensive
Answers
Answer:
Step-by-step explanation:
A carpenter has a box of nails of various
different lengths. You decide to practice your
weighted averaging skills to figure out the
average length of a nail in the box. You grab
two handfuls of nails and count out the
number of each type of nail. You record your
data in the table below.
Sample
Type
Short nail
Medium nail
Long nall
Number
of Nails
67
18
10
Abundance
(%)
[7]
Nail Length
(cm)
2.5
5.0
7.5
What is the percent abundance of the
medium nails in your sample?
Med Nail % Abund.
Enter
Answers
According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.
Explain medium?Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.
To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:
Total number of nails = 67 + 18 + 10 = 95
Next, we can calculate the percent abundance of the medium nails using the formula:
Percent abundance = (number of medium nails / total number of nails) x 100%
Using the values from of the table as inputs, we obtain:
Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%
As a result, the sample's average percentage of medium nails is roughly 18.95%.
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6. This is an example of a O reflection O rotation O translation transformation.
Answers
Answer:
translation
Step-by-step explanation:
becuz it can't be rotation as it isn't rotated in any way.
it also cant be reflection as it isnt facing the other way.
so its translation
The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.
Answers
The Correct answer is D) Most students read more often than they draw.as the median of the "read" plot is lower than the median of the "draw" plot.
Based on the box plots, we can see that:
The median for the "read" data is around 8 days per month, and the interquartile range (IQR) is between 4 and 12 days.
The median for the "draw" data is around 12 days per month, and the IQR is between 8 and 16 days.
So, we can conclude that:
A) Most students read less than 12 days a month. This is true, since the median for the "read" data is below 12 days per month, and the box plot shows that most of the data is concentrated in the lower half of the range.
B) Most students draw at least 12 days a month. This is not true, since the median for the "draw" data is around 12 days per month, and the box plot shows that there is a considerable amount of data below that median.
C) Most students draw more often than they read. This is not true, since the median for the "read" data is lower than the median for the "draw" data.
D) Most students read more often than they draw. This is true, since the median for the "read" data is lower than the median for the "draw" data, and the box plot shows that most of the "read" data is concentrated in the lower half of the range, while most of the "draw" data is concentrated in the upper half of the range.
The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.
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A charity organization has to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets they were still at a net loss of $800 (due to the production costs). They sold each tickets for $70.
Answers
the organization needs to sell at least 22 tickets to break even.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let C be the total production cost and n be the number of tickets sold.
From the problem, we know that the organization had a net loss of $800 after selling 10 tickets, so we have:
10(70) - C = -800
Simplifying, we get:
C = 1500
This means that the total production cost was $1500.
The revenue from selling n tickets at $70 per ticket is given by:
R = 70n
Substituting the values of R and C, we get:
70n = 1500
Solving for n, we get:
n = 1500/70 = 21.43
Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number.
Therefore, the organization needs to sell at least 22 tickets to break even.
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Find the speed a car will travel with a gear ratio of 3.2 with 27 inch diameter tires , 2690 RPM engine.
Answers
To find the speed of the car, we need to use the formula:
speed = (RPM * tire diameter * pi * gear ratio) / (336 * 12)
where:
RPM is the engine speed in revolutions per minute
tire diameter is the diameter of the tires in inches
pi is the mathematical constant pi (approximately 3.14)
gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear
336 is a constant representing the number of inches per minute that a car will travel at 1 mile per hour
12 is a constant representing the number of inches in a foot
Plugging in the given values, we get:
speed = (2690 * 27 * 3.14 * 3.2) / (336 * 12)
simplifying the equation, we get:
speed = 63.8 mph (rounded to one decimal place)
Therefore, the car will travel at a speed of approximately 63.8 miles per hour
Will give brainiest need Help go to my profile for other part
Answers
Answer:
Yes, there is a linear relationship between height and volume.
V = (12π)h. 12π is a constant.
If you rewrite this as y = (12π)x and graph it, you will notice that the graph is a line which goes through the origin.
A health club surveyed its members to determine if they worked out alone or with a personal trainer. The survey shows that 111 members work out alone, 67 work out with a personal trainer, and 41 sometimes work out alone and sometimes work out with a personal trainer.
Answers
The probability that a randomly selected member always works out alone or always works out with a personal trainer is 0.5393.
What is probability?
The idea of probability can be used to determine if an event is possible. It is solely useful for calculating the likelihood that an event will occur. a scale from 0 to 1, where 0 represents impossibility and 1 represents a specific occurrence.
We are given that 111 members work out alone, 67 work out with a personal trainer, and 41 sometimes work out alone and sometimes work out with a personal trainer.
So, the number of members who always work out alone is 111 - 41 = 70.
Similarly, the number of members who always work out with a personal trainer is 67 - 41 = 26.
Therefore, 96 members are there who either exercise alone or always exercise with a personal trainer.
Number of people surveyed = 111 + 67 - 41 = 137
Let A be the event where a member always exercises alone and B be the event where a member always exercises with a personal trainer.
From this, we get
P (A) = [tex]\frac{70}{137}[/tex]
P (B) = [tex]\frac{26}{137}[/tex]
P (A and B) = [tex]\frac{26}{137}[/tex]
So,
⇒ P(A or B) = P(A) + P(B) - P(A and B)
⇒ P(A or B) = [tex]\frac{70}{137}[/tex]+ [tex]\frac{26}{137}[/tex]- [tex]\frac{26}{137}[/tex]
⇒ P(A or B) = [tex]\frac{70}{137}[/tex]
Hence, the probability that a randomly selected member always works out alone or always works out with a personal trainer is 0.5393.
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Question:
A health club surveyed its members to determine if they worked out alone or with a personal trainer. The survey shows that 111 members work out alone, 67 work out with a personal trainer, and 41 sometimes work out alone and sometimes work out with a personal trainer. Find the probability that a randomly selected member always works out alone or always works out with a personal trainer.
a. 0.03714
b.0.5393
c.0.6342
d.0.6531
e.0.8128
Select the MEAN, MEDIUM, MODE and RANGE for the data below and how you worked it out
Employment status of parents in couple families
Labour force, parents or partners aged 15 years and over in Warragul
Both employed, worked full-time
580
Both employed, worked part-time
134
One employed full-time, one part-time
853
One employed full-time, other not working
471
One employed part-time, other not working
217
Both not working
799
Other (includes away from work)
193
Labour force status not stated (by one or both parents in a couple family)
185
Answers
Answer:
Measures of Central Tendancy
Mean: 429
Median: 344
Mode: 134,185,193,217,471,580,799,853
Range: 719
Step-by-step explanation:
Mean:The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{3432}{8} = 429[/tex]
Median:The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:
[tex]134, 185, 193, 217, 471, 580, 799, 853[/tex]
Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 217 and 471. The median is the average of these numbers. We have
[tex]{\frac{ 217 + 471 }{2}}[/tex]
Therefore, the median is
[tex]344[/tex]
Mode:The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are
[tex]134,185,193,217,471,580,799,853[/tex]
What is the most appropriate measure of center for the data set? A line plot showing number of siblings for seventh graders. There are 2 dots above zero, four dots above one, two dots above two, two dots above three, no dots above 4, 5, 6, or 7, one dot above eight, and no dots above 9. Savass easybridge btw 30 pts
Answers
Median is most appropriate since it is not affected by outliers or extreme values, and gives a more representative estimate of the typical number of siblings for seventh graders. Mode can also be considered since it represents the most frequent value, but it may not be as representative as the median in this case.
What is mean?
In statistics, the mean is a measure of central tendency that is calculated by adding up all the values in a dataset and dividing by the total number of values.
It is commonly referred to as the "average." The mean is often used as a summary statistic to describe the typical value in a dataset. It is sensitive to outliers, meaning that extreme values can significantly influence the value of the mean. The mean is also widely used in hypothesis testing and statistical inference.
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stal Find the Product (X+3÷x)²
Answers
the product of (x + 3/x)² is x² + 6 + 9/x².
Why it is and what is Algebra?
To find the product of (x + 3/x)², we can use the formula for squaring a binomial:
(a + b)² = a² + 2ab + b²
In this case, we have a = x and b = 3/x, so we can substitute these values into the formula and simplify:
(x + 3/x)² = x² + 2(x)(3/x) + (3/x)²
= x² + 6 + 9/x²
Therefore, the product of (x + 3/x)² is x² + 6 + 9/x².
Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent numbers and quantities in equations and expressions. The primary goal of algebra is to solve mathematical problems and equations using various operations such as addition, subtraction, multiplication, and division.
Algebraic concepts can be applied to a wide range of mathematical and real-world problems, including geometry, physics, engineering, economics, and statistics.
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Complete question:
Find the product of (x + 3/x)²2.
2. Zara stores in the United States stocks a particular type of designer denim jeans in the United States. It stores 500 pairs of jeans each month from its two suppliers. The Hong Kong supplier charges Zara $11 per pair of jeans, and the Colombian supplier charges $16 per pair (and then Zara marks them up almost 1,000%). Although the jeans from Hong Kong are less expensive, they also have more defects than those from Colombia. Based on past data, Zara estimates that 7% of the Hong Kong jeans will be defective compared to only 2% from Colombia and Zara does not want to import any more than 5% defective items. However, Zara does not want to rely on a single supplier, so it wants to order at least 20% from each supplier every month. a. Formulate a linear programming model for this problem. b. Solve the linear programming model graphically. Use either iso-line or corner point method. How many of each should Zara buy? c. How much will Zara pay for them? d. If the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to %5, what would be the effect on the solution. Solve c in a separate sheet. First copy the sheet you solved a, b and c. Then change the necessary line and re-solve.
Answers
Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia for a total cost of $6,000.
See below for other solutions
Formulation of the linear programming model:Let x be the number of pairs of jeans ordered from Hong Kong and y be the number of pairs ordered from Colombia.
Objective function:
Maximize profit, C(x, y) = 11x + 16y
Subject to the following constraints:
The total number of jeans ordered cannot exceed 500: x + y ≤ 500Zara wants to order at least 20% from each supplier: x ≥ 0.2(x+y) and y ≥ 0.2(x+y)Zara does not want to import more than 5% defective items: 0.07x + 0.02y ≤ 0.05(x+y)Non-negativity constraint: x, y > 0Graphical solution using the corner point method:See attachment for the graph, where we have the following corner points
(x, y) = (100, 400), (300, 200), (400, 100)
By substitution, we have
C(100, 400) = 11(100) + 16(400) = 7500
C(300, 200) = 11(300) + 16(200) = 6500
C(400, 100) = 11(400) + 16(100) = 6000
The minimum cost above is $6000
So, Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia.
The amount paid for themThe amount paid for them is $6,000
Reducing the percentage of defective pairsIf the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to 5%, we would need to update the constraint accordingly:
0.05x + 0.02y ≤ 0.05(x+y)
The new optimal solution would be to order 425 pairs of jeans from the Hong Kong supplier and 75 pairs of jeans from the Colombian supplier, for a total cost of $5875
i.e. C(425, 75) = 11(425) + 16(75) = 5875
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there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
Answers
The constant of proportionality for vanilla to chocolate ice cream is 2/3.
Constant of Proportionality for Vanilla to Chocolate Ice CreamThe constant of proportionality represents the fixed relationship between two quantities in a proportional relationship.
In this case, we are given that there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream.
To find the constant of proportionality in terms of vanilla to chocolate, we need to express this relationship as a fraction with the same units.
We can start by setting up the ratio of vanilla to chocolate ice cream, which would be 2:3.
This can then be expressed as
2/3
Therefore, the constant of proportionality for vanilla to chocolate ice cream is 2/3.
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Pls help thanks!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = 20.4
Step-by-step explanation:
cos(32) = adjacent/ hypotenuse
24 cos (32) = x
x = 20.4
Solve for X
x^2+ y^2=25 and y=x
Answers
The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.
Define Equation?
An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.
In the initial equation, we get: by substituting y=x:
[tex]x^2[/tex] +[tex]y^2[/tex]= 25
[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)
2[tex]x^2[/tex] = 25
[tex]x^2[/tex] = 12.5
When the two sides are square, we get:
x = ±[tex]\sqrt{12.5[/tex]
Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]
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I WILL GIVE BRAINLIEST
What is the height of the plant if less than 3 weeks have passed? Express your answer as an inequality in terms of h.
(look at photo)
Answers
Answer:
The height of the plant is less than 10 centimeters if less than 3 weeks have passed.
Step-by-step explanation:
If less than 3 weeks have passed, then the value of t is less than 3. We can express this as t < 3.
Using the formula h = 3t + 1, we can substitute t < 3 to get:
h = 3t + 1 < 3(3) + 1
h < 10
A store pays $2.50 per pound for cat liter. One cubic foot of cat liter weighs about 48 pounds. What is the selling price of cat liter in the container shown when the markup is 20%?
Answers
Answer: The selling price of cat litter in the container shown when the markup is 20% is $3.00 per pound.
Step-by-step explanation:
One cubic foot of cat litter weighs about 48 pounds, so the weight of one pound of cat litter is 1/48 cubic feet.
The store pays $2.50 per pound for cat litter, so the cost of one pound of cat litter is $2.50.
To find the selling price with a 20% markup, we add 20% of the cost to the cost.
20% of $2.50 is $0.50.
So, the selling price per pound is $2.50 + $0.50 = $3.00.
Hope this helps, and have a great day!
What is the meaning of "concatenation"?
Answers
Answer:
Concatenation means joining number characters from string end to string end.
Step-by-step explanation:
Example:
concatenation of "water" and "bottle" is "waterbottle"
In math 1, 234, 5678 is 12345678
In your word problem the concatenation of "x" and "f" is X=F
Hopefully, this was helpful!! :)
Construct the confidence interval for the population variance for the given values. Round your answers to one decimal place.
n=9
, s2=17.3
, and c=0.98
Answers
With 98% confidence, we can say that the population variance is between 7.36 and 71.09.
What is probability?
Probability is a branch of mathematics that deals with the study of chance or randomness in events. It is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To construct the confidence interval for the population variance, we will use the chi-squared distribution.
First, we need to calculate the chi-squared values for the lower and upper bounds of the confidence interval using the following formulas:
χ²_L = (n - 1) * s² / χ²(α/2, n-1)
χ²_U = (n - 1) * s² / χ²(1-α/2, n-1)
where n is the sample size, s² is the sample variance, α is the level of significance, and χ²(α/2, n-1) and χ²(1-α/2, n-1) are the chi-squared values with α/2 and 1-α/2 degrees of freedom, respectively.
Substituting the given values, we get:
χ²_L = (9 - 1) * 17.3 / χ²(0.01, 8) ≈ 3.355
χ²_U = (9 - 1) * 17.3 / χ²(0.99, 8) ≈ 29.587
Next, we can use these chi-squared values to construct the confidence interval for the population variance:
(V_L, V_U) = [(n - 1) * s² / χ²_U, (n - 1) * s² / χ²_L]
Substituting the given values, we get:
(V_L, V_U) = [(9 - 1) * 17.3 / 29.587, (9 - 1) * 17.3 / 3.355]
Simplifying, we get:
(V_L, V_U) ≈ [7.36, 71.09]
Therefore, with 98% confidence, we can say that the population variance is between 7.36 and 71.09.
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Find the Perimeter of the given figure. Remember that this is a composite figure. Be sure to show your work or explain how you found your answer in question
Answers
Answer:
Start off with the 20ft sides
20x2 =40ft
40ft + 8ft = 48ft
Now we need to find the perimeter of the half circle.
Since we know the diameter of the half circle is 8ft, we can use the following formula: Diameter x Pi = Circumference
Plug in:
8ft x 3.14159 = 25.132ft
25.132 /2 gives us the perimeter of the half circle
25.132 / 2 = 12.566
Rounded = 12.57 ft
48 ft + 12.57 ft = 60.57 feet perimeter.
The perimeter of the given solution is 76.56 feet.
We need to find the perimeter of the figure by splitting the figure into a rectangle and a semi-circle. The radius for the semi-circle is found by dividing the diameter by 2, Radius = 8 ÷ 2 = 4.
Therefore, the formula for finding the Perimeter of the given rectangle is
P = 2( l+b )
P = 2( 20 + 8)
P = 56 feet.
now, the formula for the circumference of a semi-circle is
C = [tex]\pi[/tex]r + 2r
C = 3.14( 4) + 2 (4)
C = 20.56 feet.
Therefore, the perimeter of the given figure is
The perimeter of the rectangle + circumference of the Semi-circle
= 56 + 20.56
= 76.56 feet
Therefore, the perimeter of the given solution is 76.56 feet.
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Help with this problem guys
no trolling please i really need it
Answers
Answer:
[tex]\textsf{1.}\quad \sf \overline{AZ} = 28 \; meters[/tex]
[tex]\textsf{2.}\quad \sf \overline{AM} = 28 \; meters[/tex]
[tex]\textsf{3.}\quad b = \sf 4[/tex]
[tex]\textsf{4.}\quad \sf Perimeter = 112\; meters[/tex]
[tex]\textsf{5.}\quad \sf \overline{MX} = 22\; meters[/tex]
[tex]\textsf{6.}\quad \sf \overline{AX} = 10\sqrt{3}\; meters[/tex]
[tex]\textsf{7.}\quad \sf \overline{EX} = 10\sqrt{3}\; meters[/tex]
[tex]\textsf{8.}\quad \sf \overline{AE} = 20\sqrt{3}\; meters[/tex]
Step-by-step explanation:
Side lengths and value of bAll sides of a rhombus are the same length. Therefore, for rhombus MAZE:
[tex]\sf \overline{AZ} = \overline{AM} = \overline{ZE} = \overline{EM}[/tex]
Given:
[tex]\overline{\sf AZ} =8b-4[/tex][tex]\overline{\sf AM} =5b+8[/tex]As the sides of a rhombus are the same length, we can equate the expressions for sides AZ and AM, and solve for b:
[tex]\begin{aligned}\overline{\sf AZ}&=\overline{\sf AM}\\8b-4&=5b+8\\8b-4-5b&=5b+8-5b\\3b-4&=8\\3b-4+4&=8+4\\3b&=12\\3b \div 3&=12 \div 3\\b&=4\end{aligned}[/tex]
Therefore, the value of b is 4.
To find the length of AZ and AM, substitute the found value of b into one of the expressions:
[tex]\begin{aligned}\overline{\sf AZ}&=8b-4\\&=8(4)-4\\&=32-4\\&=28\end{aligned}[/tex]
Therefore, as AZ = AM, then AZ = 28 and AM = 28.
[tex]\hrulefill[/tex]
PerimeterAs the sides of a rhombus are equal in length, each side length is 28 meters (as found previously).
The perimeter of rhombus MAZE is the sum of its side lengths. Therefore:
[tex]\begin{aligned}\sf Perimeter\;MAZE&=\sf \overline{AZ} +\overline{AM} +\overline{ZE}+ \overline{EM}\\&=28+28+28+28\\&=112\; \sf meters\end{aligned}[/tex]
Therefore, the perimeter of rhombus MAZE is 112 meters.
[tex]\hrulefill[/tex]
DiagonalsThe point of intersection of the diagonals of rhombus MAZE is point X.
As the diagonals of a rhombus are perpendicular bisectors of each other, then:
[tex]\sf \overline{AX}=\overline{EX}\quad and \quad \overline{AX}+\overline{EX}=\overline{AE}[/tex]
[tex]\sf\overline{MX}=\overline{ZX}\quad and \quad\overline{MX}+\overline{ZX}=\overline{MZ}[/tex]
Given MZ = 44 meters, and MX is half of MZ, then:
[tex]\sf \overline{MX}=\overline{ZX}=22\;meters[/tex]
As the diagonals bisect each other at 90°, m∠MXA= 90°. Therefore, ΔMXA is a right triangle with hypotenuse AM = 28 and leg MX = 22.
As we know the lengths hypotenuse AM and leg MX, we can use Pythagoras Theorem to calculate the length of the other leg, AX:
[tex]\begin{aligned}\sf \overline{AX}^2+\overline{MX}^2&=\sf \overline{AM}^2\\\sf \overline{AX}^2+22^2&=\sf 28^2\\\sf \overline{AX}^2&=\sf 28^2-22^2\\\sf \overline{AX}&=\sqrt{\sf 28^2-22^2}\\\sf \overline{AX}&=\sf 10\sqrt{3}\; meters\end{aligned}[/tex]
As the diagonals bisect each other, AX = EX. Therefore:
[tex]\sf \overline{EX}=\sf 10\sqrt{3}\; meters[/tex]
The length of diagonal AE is the sum of segments AX and EX. Therefore:
[tex]\begin{aligned}\sf \overline{AE}&=\sf \overline{AX}+\overline{EX}\\&=\sf 10\sqrt{3}+10\sqrt{3}\\&=\sf 20\sqrt{3}\; meters\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Note: The attached diagram is drawn to scale.
Write a real-world problem that could be represented by 5x+ 30 ≥ 90.
Answers
Answer: If Jamie is selling bags of carrots for $5 each and already has $30 what would he use to calculate how much money he made.
6. Atwo-story building measures 21 feet from the ground. A scale model shows the building to be 3 inches tall. How many inches would an 84-foot building be in the model?
Answers
Answer:
84 feet is equal to 1008 inches. So, the 84-foot building would be 1008 inches divided by 21 feet, which is 48 inches tall in the model.
The average salary for a Queens College full professor is $85,900. If the average salaries is normally distributed with
standard deviation of $11,000, find the percentage of professors that make more than $75,000.
Answers
According to the question approximately 83.89% of professors make more than $75,000 calculated by forming the equation.
Explain equation?When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.
This issue can be resolved using the conventional normal distribution. First, we need to standardize the value of $75,000 using the formula:
z = (x - μ) / σ
where x is indeed the value we wish to standardise, is indeed the mean, and is the deviation.
z = (75,000 - 85,900) / 11,000
z = -0.99
Next, we look up the area to the right of z = -0.99 in the standard normal distribution table or by using a calculator. The area to the left of z = -0.99 is 0.1611, so the area to the right of z = -0.99 is:
1 - 0.1611 = 0.8389
Therefore, approximately 83.89% of professors make more than $75,000.
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Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 28 inches long. What is the side length of each piece?
A.14in
B. 14 √2in
C. 14 √3in
D.28 √2in
Answers
After cutting the squares, the length of each shorter side (and the side length of each triangular quilt piece) is approximately 14√2 inches i.e. B.
What are squares?
A square is a two-dimensional shape with four straight sides that are of equal length and four right angles (90-degree angles) at the corners. It is a special case of a rectangle, where all four sides are the same length. A square can also be thought of as a special type of rhombus, where the angles are all right angles.
Now,
Since the hypotenuse of each triangle is 28 inches long, we know that this is also the longest side of the right triangle formed by the two shorter sides of the triangle. Let's call one of the shorter sides x.
Using the Pythagorean Theorem, we can find the length of the other shorter side:
c²= a² + b²
28² = x² + x²
784 = 2x²
x² = 392
x = √(392)
x=14√2 in
Therefore, the length of each shorter side (and the side length of each triangular quilt piece) is approximately 14√2 inches (rounded to two decimal places).
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It takes 3 friends, who all paint at the same rate, 9 hours to paint a room together. How many would it take for only 1 of the friends to paint the room?
a. 3
b. 6
c. 9
d. 27
Answers
ANSWER: 27 because the less people there is the more longer it takes
A dilation centered at the origin maps the point (4,6) to the point (5/2,15/4). What is the scale factor of the dilation
Answers
We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).
The dilation is given as (4,6) to (5/2,15/4). That is to say:
[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]
We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
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ABCD is a trapezium. P is a point along AC such that AP=4PC. DC=1/4AB.
a) express PB in terms of a and b in its simplest form
b) express DP in terms of a and b in its simplest form
c) does DPB form a straight line?
Answers
Answer:
a) We can use similar triangles to find PB in terms of a and b. Let x be the length of AD. Then, using the fact that AP = 4PC, we have:
PC = CP = x - b
AP = 4(x - b)
Also, using the fact that DC = (1/4)AB, we have:
AD = x
AB = 4DC = x/4
BC = AB - AD = x/4 - x = -3x/4
Now, consider the similar triangles PBC and ABD:
PB/AB = BC/AD
PB/(x/4) = (-3x/4)/x
PB = -3/4(x/4) = -3x/16
Finally, substituting x = a + b, we have:
PB = -3(a + b)/16
b) Using the same similar triangles as in part (a), we have:
DP/DC = PB/BC
DP/(1/4)AB = PB/(-3x/4)
DP = -3/4(PB)(DC/BC)AB
DP = -3/4(PB)(1/4)/(AB - AD)AB
Substituting the expressions for PB, AB, and AD from part (a), we get:
DP = -3(a + b)/16 * 1/4 / (-3(a + b)/4) * (a + b)/4
DP = -3/16 * 1/4 * 4/(3(a + b)) * (a + b)
DP = -3/16
So, DP = -3/16(a + b)
c) To check if DPB forms a straight line, we need to verify if the slopes of DP and PB are equal. Using the expressions we found in parts (a) and (b), we have:
Slope of PB = Δy/Δx = (-3/16(a+b) - 0)/(0 - (-3(a+b)/16)) = 3/16
Slope of DP = Δy/Δx = (-3(a+b)/16 - (-3/16(a+b)))/(1/4 - 0) = -3(a+b)/4
Since the slopes are not equal, DPB does not form a straight line.