The slope of line 2 is -2/9, The lines have the same slope & the two lines are parallel.
To find out whether the lines through the given points are parallel, perpendicular, or neither:
The slope of a line is calculated as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of line 1 is:
[tex]m_1 = \frac{9-5}{-8-10} \\\\m_1 = \frac{4}{-18} \\\\m_1 = -\frac{2}{9}[/tex]
Hence, the slope of line 1 is -2/9.
The slope of line 2 is:
[tex]m_1 = \frac{-6--4}{11-2} \\\\m_1 = \frac{-2}{9} \\\\m_1 = -\frac{2}{9}[/tex]
Hence, the slope of line 2 is -2/9.
Hence the answer is, the slope of line 2 is -2/9, The lines have the same slope & the two lines are parallel.
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A spinner with 7 equal parts labeled g, a, b, c, d, e, f. a point is chosen in the circle at random. determine which of the statements are true. check all that apply. it is unlikely the point is in region a. it is likely the point is in region c. it is likely the point is in region g. it is impossible for the point to be in region h. it is certain that the point will land in a lettered region.
Answer:
Step-by-step explanation:
interior point methods the affine scaling algorithm convergence of affine scaling the potential reduction algorithm the primal path following algorithm the primal-dual path following algorithm an overview exercises notes and sources
It identifies possible future routes for advancement using interior-point approaches for linear programming.
The majority of interior-point techniques fall into one of three groups: affine-scaling techniques, potential reduction techniques, or central path techniques. Along with impractical interior approaches and homogeneous self-dual methods for linear programming, these techniques are examined. Some theoretical problems with interior-point techniques are also covered, such as the dependence of complexity bounds on non-standard metrics other than the problem's input length L. Finally, the study finishes with comments on how interior-point methods and the simplex approach compare in terms of how well they perform when tested against the NITLIB suite, a common set of test problems.
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A jacket normally costs £79.50.
In a sale there is 30% off the normal price.
What is the sale price of the jacket?
Answer:
The sale price of the jacket is £55.65
Step-by-step explanation:
Because when you need to know how much is the discount so we take:
£79.50 x ( 30 ÷ 100 ) = £23.85 ( We take 30 ÷ 100 because it is 30% which means [tex]\frac{30}{100}[/tex] )
Then you need to minus the 30% to find the sale price when it's discount:
£79.50 - £23.85 = £55.65
So the Answer is: £55.65
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A cell phone company offers two texting plans. People who use plan a pay 10 cents for each text sent or received. People who use plan b pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received.
0.10x < 12 + 0.02x and x < 150 are the answers.
What is an inequalioty?
A relationship between two expressions or values that are not equal to each other is called ‘inequality’ .
Plan A: 0.10x
Plan B: 12 + 0.02x
It depends on how many texts they receive each month. If they send or receive only 50 text messages a month, plan A will be the plan to go with. They will pay $5.00 for plan A and they would pay $13 for plan B. If they send or receive 1000 text messages a month, plan B will be the plan to go with. They will pay $100.00 for plan A and they would pay $32 for plan B.
0.10x = 12 + 0.02x
-11.90x = 0.02x
x = 150
For you to want plan A, the inequality would be x < 150 and for you to want plan B, the inequality would be x > 150. In other words, you must send or receive less than 150 text messages to want plan A and you must send or receive over 150 text messages for you to want plan B.
For sending x texts, the cost of Plan A in dollars is
0.10x
For sending x texts, the cost of Plan B in dollars is
12 + 0.02x where 12 is the monthly charge regardless of texts sent
We want the Plan A charge to be less than the Plan B charge, so the inequality is ...
0.10x < 12 + 0.02x
b. Subtract 0.02x both sides ,we obtain:
0.08x < 12
Divide by 0.08 both sides,we get
x < 12/0.08
x < 150 the solution to the inequality
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A cell phone company offers two texting plans. 0.10x < 12 + 0.02x and x < 150 are the answers.
What is an inequality?A relationship between two expressions or values that are not equal to each other is called ‘inequality’ .
Plan A: 0.10x
Plan B: 12 + 0.02x
It depends on how many texts they receive each month. If they send or receive only 50 text messages a month, plan A will be the plan to go with. They will pay $5.00 for plan A and they would pay $13 for plan B. If they send or receive 1000 text messages a month, plan B will be the plan to go with. They will pay $100.00 for plan A and they would pay $32 for plan B.
0.10x = 12 + 0.02x
-11.90x = 0.02x
x = 150
For you to want plan A, the inequality would be x < 150 and for you to want plan B, the inequality would be x > 150. In other words, you must send or receive less than 150 text messages to want plan A and you must send or receive over 150 text messages for you to want plan B.
For sending x texts, the cost of Plan A in dollars is 0.10x
For sending x texts, the cost of Plan B in dollars is 12 + 0.02x
where 12 is the monthly charge regardless of texts sent
We want the Plan A charge to be less than the Plan B charge, so the inequality is ...
0.10x < 12 + 0.02x
b. Subtract 0.02x both sides ,we obtain:
0.08x < 12
Divide by 0.08 both sides, we get
x < 12/0.08
x < 150 the solution to the inequality
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Eight measurements were made on y = glucose concentration and x = fermentation of brand of malt liquor. Minitab was used to analyze the data. A scatter plot of y is given below and a Scatterplot of y: vs » 75 70 65 60 55 50 1 2 4 6 7 8 We fit two models the first is a linear regression model of y on r and the second is a quadratic regression model of y on r below and . Partial output from Minitab is given LINEAR MODEL Analysis of Variance Adj SS Adj MS F-Value Source DF P-Value Regression 1 0.054 0.0536 0.00 0.982 586.821 97.8036 Error 6 Total 7 586.875 Coefficients Term Coef SE Coef T-Value P-Value VIF 7.71 Constant 57.96 7.52 0.000 0.04 1.53 0.02 0.982 1.00 X: QUADRATIC MODEL Analysis of Variance Source DF Adj SS Adj MS 525.11 F-Value P-Value 262.55 21.25 Regression 2 0.004 Error 5 61.77 12.35 Total 7 586.88 Coefficients Term Coef SE Coef T-Value P-Value VIF 84.48 4.90 Constant 17.23 0.000 15.87 2.50 -6.35 0.001 21.25 X: 6.52 1.768 0.271 0.001 21.25 X:*x (a) Choose the model you feel is appropriate for the data. Justify (b) Using your chosen model, what is the change in y for one unit change in x? (c) What is the proportion of variation explained by the model?
The quadratic model is appropriate, because it based on the scatter plot and p-value of the regression, the change in y for one unit change in x is 70.378 and Proportion of variation explain by the model is 0.8947.
In the given question we have given a scatter plot of y is given below and a Scatter plot of y, linear model and quadratice model.
(a) We have to choose the model that we feel is appropriate for the data.
The quadratic model is appropriate, because it based on the scatter plot and p-value of the regression that is less than quadratic model in the analysis of variance.
(b) Using our chosen model, we have to find the change in y for one unit change in x.
As there is change in one unit in x.
The change in y
y=84.48 -15.87*1+1.768*1*1
y=70.378
(c) We have to find the proportion of variation explained by the model.
Proportion of variation explain by the model=(Regression SS)/(Total SS)
Proportion of variation explain by the model=525.11/586.88
Proportion of variation explain by the model=0.8947
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The write question is given below:
The data for the number of hand-held gaming devices sold for the past 5 weeks are 15 units, 20 units, 25 units, 30 units, and 17 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 3 the three-period moving average forecast for week 6 is ________.a. 24 unitsb. 17 unitsc. 20 unitsd. 30 units
Setting k = 3, the three-period moving average forecast for week 6 is 24 (option A)
A moving average method is a time series average that moves through the series by replacing the last term of the previous averaged group and adding the next term in each consecutive average.
A moving average of an order n, k = n, is calculated as:
(x₁ + x₂ + ... + xₙ) / n
The given data is:
Week Number of units sold
1 15
2 20
3 25
4 30
5 17
Using k = 3 means the order of the moving average is 3, hence
forecast for week 6 = (25 + 30 + 17) / 3 = 24 (option A)
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What are the 7 types of numbers?.
The 7 types of numbers are:-
1) Natural Numbers.
2) Whole Numbers.
3) Integers.
4) Rational Numbers.
5) Irrational Numbers.
6) Real numbers.
7) Complex numbers.
What is a number?A mathematical value used to indicate the amount is called a number. A number is a mathematical notion that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers.
Explain the different types of numbers.1) Natural Numbers: Positive integers from 1 to infinity are known as natural numbers, often referred to as counting numbers. The collection of natural numbers is referred to as "N," and its members are N = 1, 2, 3, 4, 5,.
2) Whole Numbers: Whole numbers do not include any fractional or decimal portions and are known as non-negative integers. It is represented by the symbol "W," and the set of whole numbers contains W = 0–1, 2–3, 4–5,..........
3) Integers: An integer is any whole number, but it also contains a collection of negative natural numbers. The set of numbers represented by "Z" is Z = -3, -2, -1, 0, 1, 2, 3
4) Real Numbers: Real numbers are all positive and negative integers, fractional, and decimal values that do not contain imaginary numbers. The letter "R" stands for it.
Any number that can be expressed as a ratio of one number to another is referred to be a rational number. This implies that every integer that may be expressed as p/q. The rational number is represented by the letter "Q."
5) Irrational Numbers: The sign "P" stands for an irrational number, which is a number that cannot be described as a ratio of one over another.
6) Complex Numbers (C): A complex number is one that can be expressed as a+bi, where a and b are real numbers and I is an imaginary number.
7) Imaginary Numbers: The complex numbers that may be expressed as the product of a real number and a fictitious unit are known as imaginary numbers.
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a $4\times 4\times 4$ open cubical box contains $64$ identical small cubes that exactly fill the box. how many of these small cubes touch the bottom or one of the four lateral sides of the box?
Total number of identical cubes that touch he bottom or one of the four lateral sides of the box is 52
4 x 4 x 4 open cubical box contains 64 identical small cubes that exactly fill the box
The 2 ends = 16 each small identical cubes touch the end sides
2*16 = 32
The 2 sides=8 each small identical cubes touch the lateral sides
2*8=16
On The bottom there are four small identical cubes
Total number of identical cubes that touch he bottom or one of the four lateral sides of the box will be
32 + 16 + 4 = 52
Thwerefore, Total number of identical cubes that touch he bottom or one of the four lateral sides of the box is 52
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a quarter-circle with radius 4 centered at o is drawn, as shown. in addition, semi-circles centered at the midpoints of oa and ob are drawn. find the area of the shaded region.
If the area of quarter-circle is 4pi and semi-circles is 2pi then the area of the given shaded region is 0.
What is the area formula to a circle?A = π r²
A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.
What is a semi-circle?A semicircle is a half circle created by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends. The diameter of the circle is the name given to this line.
if we have quarter-circle of
R=4 then;
Area= 4^2*pi/4
A = 4pi
so, for semi-circles having center at midpoints of oa and ob;
Area= 2^2*pi/2
= 2pi
The shaded region is the quarter-circle of radius 4 at o and subtracts the two semi-circles which are centered at the midpoints of oa and ob. So the required area of given shaded regions;
A=4pi - 2pi - 2pi
= 0
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a wire is cut into two pieces, one of length and the other of length . the piece of length is bent to form an equilateral triangle, and the piece of length is bent to form a regular hexagon. the triangle and the hexagon have equal area. what is ?
The value of a/b is [tex]\sqrt{6}[/tex] / 2
What is called mensuration?The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.
What is mensuration in real life?Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.
According to the question:-
Side of an equilateral triangle equals a/3.
Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].
Hexagonal side equals b / 6.
The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2
= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]
So
sqrt (3) / 36 a2 = sqrt (3) / 24 b2
So
A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]
a^2 / b^2 = [ 36 / 24 ]
a^2/ b^2 = 3/2
A/ B = Sqrt(3) / Sqrt(2)
=Sqrt(6) / 2
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Which lines are parallel to 8x 2y = 7? select all that apply.
The slope of the parallel line is the same slope as this line the slope is 4.
Coplanar lines that do not intersect are said to be parallel. Parallel lines have the same slope in two dimensions.
The formula to determine whether any two lines with the equations y=m1x+c1 and y=m2x+c2 are parallel is m1=m2, where m1 and m2 are the slopes of the two lines.
The slope in the following form is the coefficient of the x when the y value is a unit value.
y = mx + c where m is the slope and c is the crossing on the y-axis.
From
8x - 2y = 5
8x = 5 + 2y = 8x
2y = 8x - 5
y = 4x - 2.5
So the slope is 4. It is irrelevant that it is parallel as only the c value will be different in a parallel line.
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question 1 an online gardening magazine wants to understand why its subscriber numbers have been increasing. what kind of reports can a data analyst provide to help answer that question? select all that apply.
Reports that describe how many customers shared positive comments about the gardening magazine on social media in the past year.
Reports that compare past weather patterns to the number of people asking gardening questions to their social media. Reports that examine how a recent 50%-off sale affected the number of subscription purchases. Reports that predict the success of sales leads to secure future subscribers.
What is data analyst?
In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data. A data analyst examines data to find significant consumer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information. Although it is recommended that data analysts have a basic understanding of statistics and mathematics, many of their tasks may be completed without it. However, data analysts often need to be familiar with statistics, linear algebra, and calculus.
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what does a researcher do with the mixed significance results he or she may have found in a multiple regression analysis?
The researcher will Eliminate the nonsignificant independence variable and rerun the regression.
Meaning of multiple regression analysis: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables. The objective of multiple regression analysis is to use the independent variables whose values are known to predict the value of the single dependent value.
When modeling the relationship between a single response variable and multiple regressor variables, multiple regression analysis is used.
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$0–$10,275
10%
$10,276–$41,175
12%
$41,176–$89,075
22%
$89,076–$170,050
24%
$170,051–$215,950
32%
$215,951–$539,900
35%
> $539,901
37%
Determine the effective tax rate for a taxable income of $23,470. Round the final answer to the nearest hundredth.
11.12%
12.00%
13.49%
15.63%
The effective tax rate for a taxable income of $23,470 is given by:
12%.
How to obtain the tax rate?The tax rates are given from the table, depending on the taxable incomes, which are the inputs of the table.
The rates for each taxable income range are given as follows:
Between $0 and $10,275: Tax rate of 10%.Between $10,276 and $41,175: Tax rate of 12%.Between $41,176 and $89,075: Tax rate of 22%.Between $89,076 and $170,050: Tax rate of 24%.Between $170,051 and $215,950: Tax rate of 32%.Between $215,951 and $539,900: Tax rate of 35%.Above $539,901: Tax rate of 37%.A taxable income of $23,470 is on the second range, hence the tax rate is of 12% and the second option is correct.
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Answer:
11.12%
Step-by-step explanation:
10275 × 10% = 1027.5
23470 - 10276 = 13194
13194 × 12% = 1583.28
Then we add it all up
1027.5 + 1583.28 = 2610.78
Then we would determine the effective tax rate for a taxable income of 23470.
[tex]\frac{2610.78}{23470}[/tex] × 100 = 11.12%
Therefore, the effective tax rate for the income of 23470 is 11.12%.
The heights of tomato plants are normally distributed with a mean of 3. 56 feet and a standard deviation of 0. 25 foot. About what percent of tomato plants have a height greater than or equal to 3. 22 feet? use the z-table to answer the question. About % of tomato plants have a height greater than or equal to 3. 22 feet. Round the percent to two decimal places, if necessary.
The required percent of tomato plants have a height greater than or equal to 3. 22 feet is 91.31%
What is Z score ?Z-score shows how much a given worth contrasts from the standard deviation. The Z-score, or standard score, is the quantity of standard deviations a given information point lies above or underneath mean. Standard deviation is basically an impression of how muchchangeability inside a given informational collection.
According to question:mean(ù) = 3.56, standard deviation(S) = 0.25
We know that
Z = x-û/s
P(X>3.22) = P(z ≥ 3.22-3.56/0.25)
P(z≥-1.36) from the Z-table
1-P(z≥-1.36)
1 - 0.0869
0.9131
In percent, 91.31%
Thus, percent of tomato plants have a height greater than or equal to 3. 22 feet is 91.31%
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The total cheese production in 2006 is 7.7 billion pounds and the total cheese production in 2014 is 9.7 billion pounds
The total cheese production in 2006From the question, we have the following function that can be used in our computation:
y = 7(1.03)ˣ
Such that
x = Number of years after 2003
In the year 2006, the value of x is calculated as
x = Current year - 2003
So, we have
x = 2006 - 2003
Evaluate
x = 3
Substitute x = 3 in the equation y = 7(1.03)ˣ
y = 7(1.03)³
Evaluate
y = 7.7
The total cheese production in 2014In the year 2014, the value of x is calculated as
x = Current year - 2003
So, we have
x = 2014 - 2003
Evaluate
x = 11
Substitute x = 11 in the equation y = 7(1.03)ˣ
y = 7(1.03)¹¹
Evaluate
y = 9.7
Hence, the amount of cheese is 9.7 billion pounds
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Given â–³abc ~ â–³xyz, what is the value of cos(z)? five-thirteenths five-twelfths twelve-thirteenths twelve-fifths
Using trigonometric functions, the value of cos(z) in the given triangle is (C) 12/13.
What are trigonometric functions?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Sine, Cosine, and Tangent are the three fundamental trigonometrical operations.
So, the value of cos(z) is:
The matching angles are congruent since the triangles are comparable. As a result, cos C = cos Z and m C = m∠Z.
Cosine has an adjacent/hypotenuse ratio.
Since the side with the number 12 is next to angle C and 13 is the hypotenuse of this triangle, cos C = 12/13.
Since C and Z will have the same angles and cosines, cos Z will also equal 12/13.
Therefore, the value of cos(z) in the given triangle is (C) 12/13.
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Correct question:
Given â–³abc ~ â–³xyz, what is the value of cos(z)?
a. five-thirteenths
b. five-twelfths
c. twelve-thirteenths
d. twelve-fifths
The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that
the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses
are
a. H0: u < 40.1 Ha: u >= 40.1
b. H0: u => 40.1 Ha: u < 40.1
c. H0: u > 40.1 Ha: u <= 40.1
d. H0: u = 40.1 Ha: u =/= 40.1
b. H0: u => 40.1 Ha: u < 40.1
The null and alternative hypothesis are:
H₀ : µ = 40.1
Hₐ : µ < 40.1
If we want to test the claim that there is a reduction in the average work week, the null hypothesis should state:
- The alternative hypothesis should state the claim: there is a reduction in the average work week. This can be written as the true mean is less than 40.1
- The null hypothesis should state the oposite of the alternative hypothesis: that there is no significant reduction in the average work week. This can be written as the true mean is equal to 40.1.
Then, the null and alternative hypothesis are:
H₀ : µ = 40.1
Hₐ : µ < 40.1
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A bag contains 7 coins, of which 6 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, what is the probability of each of the following outcomes? (Enter your probabilities as fractions.)
(a) Heads will occur exactly twice.
(b) Heads will occur at least twice.
(a) Heads will occur exactly twice.
a) The probability Heads will occur exactly twice is 1/2.
b) The probability Heads will occur at least twice is 5/8.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Total coins = 7
Fair coins =6
One coin had head on both side.
Outcome of tossing a coin three times
{ HHH, TTT, HTT, THT, TTH, THH, HTH, HHT}
a) The probability Heads will occur exactly twice
= 4/8
= 1/2
b) The probability Heads will occur at least twice
= 5/8
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Jutine tarted her own landcaping buine. She charge $6 an hour for mowing lawn and $11 for pulling weed. In September he mowed lawn for 13 hour and pulled weed for 5 hour. How much money did he earn in September?
The money earned by Jutine in the month of September is $133.
According to the question,
We have the following information:
Jutine charges $6 an hour for mowing lawn and $11 for pulling weed. In September he mowed lawn for 13 hour and pulled weed for 5 hour.
Now, the amount earned by mowing the lawn can be found using multiplication:
6*13 = $78
Now, we have the amount earned by pulling weeds by using the same concept:
11*5 = $55
Now, the total money earned in September:
$(78+55)
$133
Hence, the money earned by Jutine in the month of September is $133.
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Raymond work in an electronic tore and get a 12 percent employee dicount. The original cot of a video game ytem i $175. What i the dicounted price of the game ytem?
If the original cost of a video game item is $175 with a 12% discount then the discounted price of the game item would be $154.
What is a discount?
A fixed amount off a price means subtracting the fixed amount from the original price. For example, if a service normally costs $95, and you have a $20 off coupon, you would deduct $20 from $95 to get the final price: $95 - $20 = $75.
The price of the video game item is $175.
The applied discount = 12%
Then the total saving = 175*12%
= 175 * 0.12
= 21
Discounted price = total price - total saving
= 175 - 21
= $154.
Hence, if the original cost of a video game item is $175 with a 12% discount then the discounted price of the game item would be $154.
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Apply the Gram-Schmidt orthonormalization process to transform the given basis for Rn into an orthonormal basis. Use the Euclidean inner product for Rn and use the vectors in the order in which they are given. B = {(0, 0, 7), (0, 1, 1), (1, 1, 1)}
To apply the Gram-Schmidt orthonormalization process, we first need to calculate the projection of the first vector onto the other two vectors.
What are vectors?Mathematics' version of a vector is an entity with both magnitude and direction. On a graph, they can be seen as arrows, with the length of the arrow denoting magnitude and the direction denoting direction. The movement or velocity of an item, as well as its acceleration or force, are frequently described by vectors in physics. They may also be used in geometry to represent how far an item has moved from one point to another. Vectors can be added and subtracted, as well as their magnitude multiplied or divided by a scalar. They are a crucial resource for comprehending and examining the motion of things in space.
How to solve?
p = (u * v) / (v * v) * v
For the first vector (0, 0, 7)
p1 = (0, 0, 7) * (0, 1, 1) / (0, 1, 1) * (0, 1, 1) * (0, 1, 1) = 0 * (0, 1, 1) = (0, 0, 0)
p2 = (0, 0, 7) * (1, 1, 1) / (1, 1, 1) * (1, 1, 1) * (1, 1, 1) = 0 * (1, 1, 1) = (0, 0, 0)
Therefore, the orthogonal component of the first vector is (0, 0, 7) - (0, 0, 0) - (0, 0, 0) = (0, 0, 7).
Next, p = (u * v) / (v * v) * v
For the second vector (0, 1, 1), we have:
p = (0, 1, 1) * (1, 1, 1) / (1, 1, 1) * (1, 1, 1) * (1, 1, 1) = 1 * (1, 1, 1) = (1, 1, 1)
Therefore, the orthogonal component of the second vector is (0, 1, 1) - (1, 1, 1) = (-1, 0, 0).
Finally, |u| = sqrt(u * u)
For the first vector (0, 0, 7), we have:
|(0, 0, 7)| = sqrt((0, 0, 7) * (0, 0, 7)) = sqrt(0 + 0 + 49) = 7
Therefore, the normalized vector is (0, 0, 1).
For the second vector (-1, 0, 0), we have:
|(-1, 0, 0)| = sqrt((-1, 0, 0) * (-1, 0, 0)) = sqrt(1 + 0 + 0) = 1
Therefore, the normalized vector is (-1, 0, 0).
Therefore, the orthonormal basis for R3 is {(0, 0, 1), (-1, 0, 0), (1, 1, 1)}.
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What is a counterexample for the conjecture? if the perimeter of a rectangle is 40 units, the area must be at least 1 square unit.
The counterexample is a rectangle with length 19.99 and width 0.01, in which case the area is 0.1999 and the perimeter is still 40.
Given ,
The perimeter of the rectangle is 40 units.
According to the statement, if the area is at least one unit and the perimeter is 40.
A counterexample to disprove this statement is the rectangle with dimensions of 19.99 units in length and 0.1 units in width, which has an area of 0.1999 square units and a perimeter of 40 units.
As a result, it is shown by a counterexample that an area does not necessarily need to be at least one unit when the perimeter is 40 units.
Any departure from a generalization constitutes a counterexample. A counterexample refutes the generalization in logic, and it does so persuasively in the disciplines of math and philosophy.
By using counterexamples to show that specific conjectures are false, mathematicians can avoid going down dead ends. They can then learn to modify hypotheses in order to arrive at testable theorems. It has been stated that the development of mathematics is greatly influenced by the discovery of theorems and counterexamples.
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If the margin of error decreases and the sample size remains the same, the level of confidence.
Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down
What is level of confidence?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.
We are given asked when the sample size is kept the same,
What will happen to the level of confidence if the margin of error decreases?we know that the margin of error is nothing but a statistic which tells us how many percentage points our results will differ from the real population value.we know that when a greater error is allowed, the more will be the confidence(fundamental concept of confidence intervals)
Let Margin of Error be represented by E and the confidence level by C hence the relationship goes like this,
E↑⇔C↑and E↓⇔C↓
Here we are asked when the sample size is kept the same, what will happen to the level of confidence if the margin of error decreases .
The answer is that Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down.
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If cos(x) = negative one-fourth and tan(x) < 0, what is sin(2x) ?
The trigonometric function sin2x = -0.49
Given that,
cos(x) = -1/4 tan(x) < 0
x = cos⁻¹(-1/4)
x = 104.47
We will solve the trigonometric function as;
To find sin2x,
Let,
sin2x = sin 2 * 104.47
= sin208.95
= -0.484
≅ -0.49
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Answer:
B. -√15 / 4
Step-by-step explanation:
I can feel it in my nuggets
what is the probability p that a 3 will occur any given time the die is rolled? (enter your probability as a fraction.)
Let x be a random variable with probability density function what is the value of c.
The value of c is 1/2, where x is a random variable with a probability density function.
A number or item that depends on random occurrences is formalized mathematically as a random variable, also known as a random quantity, aleatory variable, or stochastic variable. It is a function or mapping from potential outcomes, such as the potential upper sides of a coin flip, such as heads (H) and tails (T), in a sample space to a measured space, frequently the real numbers.
Statistics has historically only used the phrase "random variable" in the context of real-valued cases. In this situation, it is easy to describe things like a random variable's expected value and variance, its cumulative distribution function, and the moments of its distribution thanks to the structure of the real numbers.
A probability density function, also known as the density of a continuous random variable, is a function used in probability theory whose value at any given sample in the sample space can be interpreted as giving a relative likelihood that the random variable's value would be close to that sample.
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the dow jones industrial average is: an equally weighted index of all stocks traded on the new york stock exchange. an index of the 500 largest corporate stocks in america. an index of 30 major stocks. the most representative of the stock market indexes.
The dow jones industrial average is c) the index of 30 major stocks. the most representative of the stock market indexes.
The Dow Jones Industrial Average, in short DJIA, moreover known as the Dow 30, maybe a stock market index that tracks 30 huge, publicly-owned blue-chip companies exchanging on the New York Stock Exchange and Nasdaq. The Dow Jones is named after Charles Dow, who made the record in 1896 beside his trade accomplice Edward Jones. The DJIA was outlined to serve as an intermediary for the well-being of the broader U.S. economy. Often referred to basically as the Dow, the DJIA is one of the most-watched stock market lists in the world. Whereas the Dow incorporates a run of companies, all can be depicted as blue-chip companies with reliably steady profits.
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The dow jones industrial average is:
a) an equally weighted index of all stocks traded on the new york stock exchange.
b )an index of the 500 largest corporate stocks in america.
c) an index of 30 major stocks. the most representative of the stock market indexes.
1. what is the equation of the ellipse whose center is at the origin, foci at (2,0) and (-2,0), and the length of the major axis is 10 units?
x²/21 + y²/25 = 1 is the equation of the ellipse
How to find the equation of an ellipse?
Given: the length of the major axis = 10 and foci = (0, ± 2)
Since the foci are on the y-axis, the major axis will be along the y-axis. Thus, the equation of the ellipse is:
x²/b² + y²/a² = 1
Since the length of the major axis = 2a. Thus:
2a = 10
a = 10/2 = 5
a² = 5² = 25
c = 2
c² = a² - b²
2² = 5² - b²
4 = 25 - b²
b² = 25 - 4 = 21
Substitute a² = 25 and b² = 21 into the equation:
x²/b² + y²/a² = 1
x²/21 + y²/25 = 1
Therefore, the equation of the ellipse is x²/21 + y²/25 = 1
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How do you prove SSS similarity theorem?.
According to the SSS test for triangle similarity, two triangles are considered similar if their third sides are proportionate to one another.
According to the statement, we have stated:
If two triangles ABC and DEF have the relationship
BC/EF = AC/DF = AB/DE, then
Triangle ABC therefore resembles triangle DEF.
This suggests that Angle A, Angle B, and Angle C are all equal to Angle D, Angle E, and Angle F.
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