Thus, the given quadratic equation has two real roots x = 3 and x = -2.
Explain about the solution of quadratic function:A function or mathematical statement of degree two is a quadratic function. This indicates that two is the function's highest power. The roots of all quadratic functions are two.
The quadratic formula is employed to solve a quadratic to discover its roots, which can either be distinct or the same. A quadratic function must first be converted into a quadratic equation by being made equal to zero in order to be solved.Given equation:
x² - x - 6 = 0
Using the quadratic formula:
x = [-b ± √(b² - 4ac) ] / 2a
a = 1 , b = -1 and c = -6
x = [1 ± √((-1)² - 4*1*(-6) ] / 2*1
x = [1 ± √(1 + 24) ] / 2
x = [1 ± 5 ] / 2
Now,
x = (1 + 5)/2 = 3
x = (1 - 5)/ 2 = -2
Thus, the given quadratic equation has two real roots x = 3 and x = -2.
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complete question:
Check whether the given equation has, one solution, two solution ,many solution or no real solution.
x² - x - 6 = 0
thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 137 millimeters, and a variance of 49 . if a random sample of 48 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 3 millimeters? round your answer to four decimal places.
The probability that the sample mean would differ from the population mean by greater than 3 millimetres is 0.0033 + 0.0033 = 0.0066, rounded to four decimal places.
We are given that the population mean diameter of the steel bolts manufactured by Thompson and Thompson is μ = 137 millimeters and the variance is = 49.
We need to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters.
The standard deviation of the sample means is given by the formula:
[tex]\sigma_{\bar{x}} = \frac{\sigma}{{\sqrt{n}}}[/tex]
Substituting the given values, we have:
[tex]\sigma \bar{x}=\frac{\sqrt{49}}{\sqrt{48}}=1.118[/tex]
To find the probability that the sample mean would differ from the population mean by greater than 3 millimeters,
we need to calculate the z-score:
[tex]z=\frac{(\bar{x}-\mu)}{ \sigma _{\bar{x}}}[/tex]
Substituting the given values, we have:
[tex]z=\frac{\bar{x}-137}{1.118}[/tex]
We want to find the probability that |z| > 3/1.118 = 2.683.
Using a standard normal distribution table, we find that the probability of z > 2.683 is 0.0033.
Since this is a two-tailed test, the probability of z < -2.683 is also 0.0033.
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A small tree that is 8 feet tall casts a 4-foot shadow, while a building that is 24 feet tall casts a shadow in the same direction. Determine the length of the building's shadow.
6 feet
12 feet
18 feet
48 feet
Answer:
Using similar triangles, we can set up a proportion:
(tree height)/(tree shadow) = (building height)/(building shadow)
Plugging in the given values, we get:
8/4 = 24/x
Solving for x, we get:
x = (24 x 4)/8 = 12 feet
Therefore, the length of the building's shadow is B. 12 feet.
Please help!! URGENT!! I don’t understand
Answer: 14%
Step-by-step explanation:
Our formula is i=prt but we're trying to find the rate (r) so we'll rearrange it to become r=i/pt.
i = $245
p = $7000
t = 3/12= 0.25 years
[tex]r=\frac{245}{(7000)(0.25)} \\r = 0.14[/tex]
Use the table to answer the question that follows. ROR Portfolio 1 Portfolio 2 Portfolio 3
8. 9% $850 $1,050 $1,175
−5. 1% $2,425 $1,950 $550
12. 4% $280 $1,295 $860
4. 2% $1,400 $745 $550
0. 9% $2,330 $1,050 $2,000
Using technology, calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?
The weighted mean of the RORs for each portfolio, from best to worst, is:
Portfolio 3: 4.36%
Portfolio 2: 3.2%
Portfolio 1: 0.94%
To calculate the weighted mean of the RORs for each portfolio, we need to multiply each rate of return by its corresponding portfolio value, sum the results, and divide by the total value of the portfolios:
Weighted Mean ROR = sum of value / total amount
sum of value = portfolio value x rate of return
For Portfolio 1:
(0.089 x 850) + (-0.051 x 2425) + (0.124 x 280) + (0.042 x 1400) + (0.009 x 2330)
Sum of value = 75.65 - 123.68 + 34.72 + 58.8 + 20.97
= 61.46.
Weighted Mean ROR = 61.46 / (850 + 2425 + 280 + 1400 + 2330)
= 61.46 / 7285
= 0.0094 or 0.94% (third)
For Portfolio 2:
(0.089 x 1050) + (-0.051 x 1950) + (0.124 x 1295) + (0.042 x 745) + (0.009 x 1050)
Sum of value = 93.45 - 99.45 + 160.58 + 31.29 + 9.45
= 195.32.
Weighted Mean ROR = 195.32 / (1050 + 1950 + 1295 + 745 + 1050)
= 195.32 / 6090
= 0.032 or 3.2% (second)
For Portfolio 3:
(0.089 x 1175) + (-0.051 x 550) + (0.124 x 860) + (0.042 x 550) + (0.009 x 2000)
Sum of value = 104.58 - 28.05 + 106.64 + 23.1 + 18
= 224.27.
Weighted Mean ROR = 224.27 / (1175 + 550 + 860 + 550 + 2000)
= 224.27 / 5,135
= 0.0436 or 4.36% (first)
To compare the overall performance of the portfolios, we can rank them based on their weighted mean RORs, from highest to lowest:
Portfolio 3: 4.36%
Portfolio 2: 3.2%
Portfolio 1: 0.94%
Therefore, the overall performance of the portfolios, from best to worst, is Portfolio 3, Portfolio 2, and Portfolio 1.
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Juan can run 38 yards in 5 seconds. If he keeps the same pace, how many yards can he run in 30 seconds? Responses
Answer: 228 yards
Step-by-step explanation:
Answer:
228
Step-by-step explanation:
anova with replication is also known as? repeated measures between-group design mixed design one-way anova
this is "Repeated measures ANOVA, which is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions.
What is a repeated measures ANOVA ?A repeated measures ANOVA is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions. This design is sometimes referred to as a "within-subjects design" because each participant is measured within the same group.
Here are the steps for conducting a repeated measures ANOVA:
State the null and alternative hypotheses.Check the assumptions of the test, which include normality, sphericity, and homogeneity of variance.Calculate the within-subjects sum of squares (SSW), the between-subjects sum of squares (SSB), and the total sum of squares (SST).Calculate the degrees of freedom (df) for each of these sums of squares.Calculate the mean square (MS) for each source of variance by dividing the sum of squares by the degrees of freedom.Calculate the F ratio by dividing the between-subjects MS by the within-subjects MS.Determine the critical value for the F ratio using a table or software.Compare the calculated F ratio to the critical value. If the calculated F ratio is greater than the critical value, reject the null hypothesis and conclude that there is a significant effect of the independent variable on the dependent variable.If the null hypothesis is rejected, follow up with post hoc tests to determine which conditions differ significantly from each other.
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explain why we call the national halothane study an observational study rather than an experiment, even though it compared the results of using different anesthetics in actual surgery.in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.actually, it is an experiment and not an observational study.
We the best reason behind why we call National halothane study is an observational study rather than an experiment is: " In order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned." So, option( b) is right one.
We have data from the National Halothane Study that correlates with important research into the safety of anesthetics used in surgery. The above shows the death rate and aesthetic. There is a relationship between the anesthetic used and the death of the patient. The data was collected after that the anesthesia was administered is started. In the observational study, interesting observer in the subjects & any treatment that the subjects recive are beyond the council of the investigators. Here the motion of anaesthesia is anesthetics used her determined by the doctors and the investigators are simply observing. So, it is an observational study due to because in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. Instead, a patient's anesthetic is selected by his or her doctor(s).
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Complete question:
The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics:27 Anesthetic A Death rate B CD 1.7% 1.7% 3.4% 1.9% There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.
a) in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.
b) in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).
c) there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.
d) actually, it is an experiment and not an observational study.
Find the measures of angle a and B. Round to the nearest degree.
The measure of angle A and angle B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
tan B = 6/11 {opposite/adjacent}
B= tan⁻¹(6/11) {cross multiplication}
B = 28.6105.
tan A = 11/6 {opposite/adjacent}
A= tan⁻¹(11/6) {cross multiplication}
A = 61.3895.
Therefore, the measure of angles A and B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.
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There are 90 pens in a box and 36 of them are red and the rest of them are black What is the ratio of the red pens to black pens
If there are 90 pens in a box and 36 of them are red and the rest of them are black, the ratio of red pens to black pens in the box is 2:3.
The ratio of red pens to black pens in the box can be expressed as a fraction or as a simplified ratio. To do this, we need to determine the number of black pens in the box.
We know that there are 90 pens in total, and 36 of them are red. Therefore, the number of black pens can be found by subtracting the number of red pens from the total:
90 pens - 36 red pens = 54 black pens
Now we know that there are 54 black pens and 36 red pens in the box. To express this as a ratio, we can simplify it by dividing both numbers by their greatest common factor (GCF), which in this case is 18:
36/18 : 54/18
Simplifying further, we get:
2:3
This means that for every 2 red pens, there are 3 black pens in the box.
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In Circle C, the diameter AB bisects the chord EF.
If m
In the circle the mesaure of ∠ACF is 7
What do you mean by Diameter ?The distance from the centre of a circle to any point on the boundary is called the radius. The radius is half of the diameter; 2r=d 2 r = d . The line segment that joins two points on the circle is a chord.
If diameter of a circle bisects a chord ,then it must be perpendicular to the chord.
∴ m∠ACF = 90°
(8x + 34)° = 90°
8x = 90 - 34
x = 56/8
x = 7
Hence,mesaure of ∠ACF = 7
Complete question : In Circle C, the diameter AB bisects the chord EF.
If m∠ACF = (8x+34)°, enter in the correct value of x.
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The diameter of a circle is 10cm find the circumference to the nearest tenth
Answer c= Cm
Answer:
31.4 cm
Step-by-step explanation:
Circumference of circle = D x π
D = 10 cm
π = 3.14
Let's solve
10 x 3.14 = 31.4 cm
So, the circumference of the circle is 31.4 cm
Use the functions f(x) and g(x) to answer the question. F(x)=x²-16; g(x)=x+4
Which answer is equal to (f/g)(x)
A x+4,x=-4
B x+4,x=4
C x-4,x=4
D x-4,x=-4
**All eqaul signs in answers are "do not equal signs"**
Using the functions f(x) and g(x) as F(x)=x²-16; g(x)=x+4, (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4. So, the correct answer is option D.
To find (f/g)(x), we need to divide f(x) by g(x). The notation (f/g)(x) is another way of representing the function f(x)/g(x).
So, we first need to find f(x)/g(x) by dividing f(x) by g(x):
f(x)/g(x) = (x^2 - 16)/(x + 4)
Now, we can plug in the values of x in each option and see which one gives us the correct function.
Option A: (f/g)(-4) = ((-4)^2 - 16)/(-4 + 4) = undefined
Option B: (f/g)(4) = (4^2 - 16)/(4 + 4) = -1
Option C: (f/g)(4 - 4) = (0^2 - 16)/(4 - 4) = undefined
Option D: (f/g)(-4 - 4) = ((-4)^2 - 16)/(-4 - 4) = 0
Therefore, the correct answer is option D: (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4.
Note that options A and C give undefined values because they have x + 4 in the denominator, which makes the function undefined at x = -4 and x = 4, respectively.
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From a piece of cardboard that is 32 inches by 12 inches, you are making a box by cutting equal squares at each corner and folding it up. What size should the squares be for the volume of the box to be maximal? Find x
For the maximum volume of , the value of x must be smaller that is x = 2.90 inch. Size of square = 8.41 sq. in.
Explain about maxima and minima:The issue is an application of maxima and minima, where the unknown quantity is located using the first derivative. Keep in mind that the height of a box is equal to a side of the cut square when the sides are bent upward. Moreover, the box formula's volume is
Volume = length * width * height
Given:
Length of rectangle cardboard l = 32 inchesWidth of rectangle cardboard w = 12 inchesLength of the side of each square - x inxhes.Volume of new box = (32 - 2x)(12 - 2x)x
Rearranging terms:
V = 4x³ - 88x² + 384x
For maximum volume, V' = 0 (first derivative)
V' = 12x² - 167x + 384
V' = 0
12x² - 167x + 384 = 0
Solve using quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
a = 12 , b = - 167 , c = 384
x = [167 ± √(167² - 4*384*12)] / 2*12
x = [167 ± 7√193] / 24
Now,
x = [167 + 7√193] / 24
x = 11.01 inch
and,
x = [167 - 7√193] / 24
x = 2.90 inch
For the maximum volume of , the value of x must be smaller that is x = 2.90 inch.
Size of square = x²
Size of square = 2.90²
Size of square = 8.41 sq. in.
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The function V(t) = 30000(0.85) value V(t) represents the values v(t) of Nancy's car after t years. What is the depreciation rate of Nancy's car?
The depreciation rate of Nancy is 15%.
What is known by depreciation?Depreciation is the reduction in the value of an asset over time due to wear and tear, obsolescence, or other factors. It is a non-cash expense that is recorded on a company's income statement, which reflects the decrease in the asset's value during its useful life. Depreciation is commonly used in accounting to allocate the cost of an asset over its useful life, and it helps businesses to accurately reflect the true value of their assets on their financial statements.
Define function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.
The given function V(t) = [tex](30000*0.85)^{t}[/tex]represents the value of Nancy's car after t years.
Depreciation rate is the rate at which the value of an asset decreases over time. In this case, the depreciation rate of Nancy's car is 1 - 0.85 = 0.15 or 15%.
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Cheyenne has a part-time job at which she gets paid by the hour. The table below shows how much money Cheyenne can earn for working various amounts of hours.
How many hours, h, must Cheyenne work to earn $56.00?
Answer:
Can i see the full answer so I can help you?
Step-by-step explanation:
find the volume of a cylinder with a diameter of 22 yd and a height of 7 yd
V=π(d
2)2h=π·(20.12
2)2·6.4≈2034.42618m
help please its due in a few minuets
Answer:
use desmos graphing calculator it helps alot
Step-by-step explanation:
x^{2}-x-6=0 has two zeros/solutions
x^{2}-x-6=0 has 1 zero/solution
x^{2}-x-6=0 has no zero/solution
what other patterns can you discover in the subway ridership dataset using calculations with multiple operators?
Subway ridership data can reveal useful patterns through calculations with multiple operators, informing decisions about infrastructure and scheduling to better serve riders' needs.
Why Subway ridership data reveal useful patterns through calculations?The subway ridership dataset can reveal a wealth of information through calculations with multiple operators. One such calculation is the average increase or decrease in ridership during specific time intervals. By comparing ridership during peak and off-peak hours or weekdays versus weekends, it is possible to determine when the subway system is busiest and when it is underutilized.
Another useful calculation is the average percentage change in ridership between different stations or subway lines. This can help identify the most popular stations or lines and can inform decisions about where to allocate resources and infrastructure improvements.
Additionally, it is possible to explore the correlation between ridership and other factors such as weather, events, or holidays. By analyzing how ridership fluctuates in response to external factors, transportation planners can adjust schedules and routes to better serve the needs of riders.
Calculations with multiple operators can also reveal patterns in ridership based on time of year or day of the week. By analyzing the average change in ridership on different days or months, transportation planners can make informed decisions about scheduling and staffing.
Finally, regression analysis can be used to identify the overall trend in ridership over time. By examining long-term ridership trends, transportation planners can identify areas for improvement and plan for future infrastructure projects to better meet the needs of subway riders.
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The expression (h) (b, + b₂) gives the area of a trapezoid, with b, and b, representing the two base lengths of a trapezoid and h representing the height. Find the area of a trapezoid with base lengths 4 in. and 6 in. and a height of 8 in. (Lesson 10.2)
Answer:
A = 40 in²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height between the bases b₁ and b₂
here h = 8 , b₁ = 4 , b₂ = 6 , then
A = [tex]\frac{1}{2}[/tex] × 8 × (4 + 6)
= 4 × 10
= 40 in²
Can someone help me fast with this please!?!?!
If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000.
A. 5,220,000 songs were downloaded in the year 2020.
B. There is not enough information to interpret the information.
C. In the year 2020 $5,220,000 was earned from downloaded songs.
D. 2,020 songs were downloaded at a cost of $5,220,000.
the correct answer is A.
5,220,000 songs were downloaded in the year 2020.
If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000?The interpretation of s(2020) = 5,220,000 is "5,220,000 songs were downloaded in the year 2020".
Therefore, the correct answer is A. 5,220,000 songs were downloaded in the year 2020.
Interpretation refers to the process of explaining or giving meaning to information, data, or phenomena. It involves analyzing and making sense of information to draw conclusions or make decisions based on the findings.
Interpretation can involve subjective judgment and may depend on the perspective, assumptions, or biases of the interpreter.
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Help me pls........................
All the possible angle measures are given as follows:
25º and 35º.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.On the first quadrant, we have that:
The cosine is greater than the sine for angles that are less than 45º.The cosine is equals to the sine for an angle of 45º.The cosine is less than the sine for angles that are greater than 45º.More can be learned about trigonometric ratios at brainly.com/question/24349828
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The diagonal of a square is 10
inches long. What is the length, in inches, of each side of the square? Write the answer in simplified radical form.
7.071 is the length, in inches, of each side of the square.
What is meant by "square"?
The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.
Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.
If the side od=f a square is s, the diagonal is s√2
This comes from Pythagoras as diagonal is
√s² + s² = √2s² = s√2
as such s√2 = 10
s = 10/√2
= 10 * √2/√2 * √2
= 5√2
5 * 1.4142 = 7.071
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The life, in years, of a certain type of electrical switch has an exponential distribution with an average life betaequals3. If 300 of these switches are installed in different systems, what is the probability that at most 70 fail during the first year?
The probability that at most 70 switches fail during the first year is low, at around 1.3%.
The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.
The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.
To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.
This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.
Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:
P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)
This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.
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assume the mapping t w p2 ! p2 defined by t a0 c a1t c a2t 2 d 2 a0 c .3 a1 c 4 a2/t c .5 a0 6 a2/t 2 is linear. find the matrix representation of t relative to the basis b d f1; t; t 2 g.
So, the matrix representation of T relative to the basis B = {f1, t, t²} is:
| 2.5 3 0 |
| 0 4 0 |
| 0 0 6 |
To find the matrix representation of the linear transformation T relative to the basis B = {f1, t, t²}, we need to apply T to each element of the basis and then express the result as a linear combination of the basis elements.
Let's apply T to each element of the basis B:
1. T(f1) = T(1) = 2(1) + 0.5(1) = 2.5
2. T(t) = T(c) = 3(c) + 4(c²) = 3f1 + 4t
3. T(t²) = T(c²) = 6(c²) = 6t²
Now, we can express the results as linear combinations of the basis elements:
1. T(f1) = 2.5f1 + 0t + 0t²
2. T(t) = 3f1 + 4t + 0t²
3. T(t²) = 0f1 + 0t + 6t²
Finally, we can form the matrix representation of T relative to the basis B by using the coefficients of the linear combinations as the columns of the matrix:
T matrix = | 2.5 3 0 |
| 0 4 0 |
| 0 0 6 |
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The matrix representation of t with respect to the basis b = [tex]{f1, t, t^2}[/tex] is:
[1/2 -4/3 1 ]
[1 8/3 0 ]
[0 -5/2 3/2 ].
To find the matrix representation of the linear transformation t with respect to the given basis, we need to apply t to each of the basis vectors and represent the result as a linear combination of the basis vectors.
The coefficients of these linear combinations will form the columns of the matrix representation.
First, we apply t to each of the basis vectors:
[tex]t(1) = a0 + a1t + a2t^2 = a0 + a1f1 + a2t - (a1/2)f1 - (3a2/2)t^2[/tex]
[tex]t(t) = a0 + (4/3)a1t + (5/6)a2/t = a0 + (4/3)t + (5/6)t^2 - (4/3)f1 - (5/2)t^2[/tex]
[tex]t(t^2) = a0 + (3/2)a2/t^3 = a0 + (3/2)t^2 - (3/2)f1[/tex]
Next, we represent these results as linear combinations of the basis vectors:
[tex]t(1) = (a0 - a1/2)f1 + (a1 + a2)t - (3a2/2)t^2[/tex]
[tex]= 1f1 + 0t + 0t^2 + (-1/2)f1 + 1t + 0t^2 + 0f1 - (3/2)t^2[/tex]
[tex]= (1/2)f1 + 1t - (3/2)t^2[/tex]
[tex]t(t) = (-4/3)f1 + (a0 + 4/3)t + (5/6)t^2[/tex]
[tex]= 0f1 + 1t + 0t^2 + (-4/3)f1 + (4/3)t + (5/6)t^2 + 0f1 + 0t - (5/2)t^2[/tex]
[tex]= (-4/3)f1 + (8/3)t - (5/2)t^2[/tex]
[tex]t(t^2) = f1 + (a0 - 3/2)t^2[/tex]
[tex]= 0f1 + 0t + 1t^2 + 1f1 + 0t + 0t^2 + 0f1 + (1/2)t^2[/tex]
[tex]= 1f1 + 0t + (3/2)t^2[/tex]
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the major flaw of the linear probability model is that a. the actuals can only be 0 and 1, but the predicted are almost always different from that. b. the regression r2 cannot be used as a measure of fit. c. people do not always make clear-cut decisions. d. the predicted values can lie above 1 and below 0.
The major flaw of the linear probability model is, Option d, which allows predicted values to range from above 1 to below 0
The binary dependent variable, which accepts values of 0 and 1, and the independent variables are assumed to have a linear relationship under the linear probability model.
The anticipated values from the linear probability model, however, can range from 0 to 1, and in some circumstances, they can be either above or below 0. This goes against the dependent variable's probabilistic character and can produce inaccurate forecasts.
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HELP ME PLS
1. If the diameter of a circle is segment AB where Point A is located at (-3, 6), and Point B located at (-8,-1), what is the diameter of the circle?
2√2
√146
√74
74
The diameter of the circle is √74. Answer: C.
What is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.
To find the diameter of the circle, we need to find the distance between points A and B, which will give us the length of the diameter.
Using the distance formula, we have:
d = √[(x2 - x1)² + (y2 - y1)²]
where (x1, y1) = (-3, 6) and (x2, y2) = (-8, -1).
Plugging in the values, we get:
d = √[(-8 - (-3))² + (-1 - 6)²]
= √[(-5)² + (-7)²]
= √[25 + 49]
= √74
Therefore, the diameter of the circle is √74. Answer: C.
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From the top of a 120-foot-high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. How far from the base of the tower is the airplane? Round to the nearest tenth.
1. 126.9 ft
2. 368.6 ft
3. 41.3 ft
4. 348.5 ft
Using a trigonometric relation we can see that the correct option is the last one;
4. 348.5 ft
How to find the distance?We have a right triangle, so we can use trigonometric relations.
The angle at the top of the triangle is a, and it must solve the equation:
a + 19° = 90°
a = 90° - 19° = 71°
Now we can use the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
REplacing what we know:
tan(71) = ?/120 ft
120ft*tan(71) = ? = 348.5ft
That is the distance.
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Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach and
cherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a selling
price of $1. 5 per kg and cherry has a selling price of $4 per kg. The average yield per acre for
lemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre for
lemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cherry
requires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximum
availability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour is
$40 per hour. What is the optimal allocation of acre to the three types of fruit trees?
[1 tonne = 1000kg]
(a) Formulate a linear programming model to maximize the profit.
(b) Find the optimal solution by using simplex algorithm.
(a) The linear programming model to maximize the profit is written as,
Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)
(b) The optimal solution is x1 = 0, x2 = 8/3, x3 = 8, x4 = 0, and the maximum profit is $40.
(a) Linear programming model:
Let x1, x2, and x3 be the number of acres allocated to lemon, peach, and cherry trees, respectively. Then, the objective function we want to maximize is:
Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)
The first term represents the revenue from selling lemons, the second term represents the revenue from selling peaches, the third term represents the revenue from selling cherries, the fourth term represents the cost of fertilizer, and the last term represents the cost of labor.
The constraints are:
x1 + x2 + x3 ≤ 200 (total available land)
10x1 + 12x2 + 10x3 ≤ 20000 (total available labor hours)
x1, x2, x3 ≥ 0 (non-negativity constraints)
(b) Simplex algorithm:
Convert the linear programming model into standard form by introducing slack variables and expressing all variables in terms of these variables.
Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)
Subject to:
x1 + x2 + x3 + x4 = 200
10x1 + 12x2 + 10x3 + x5 = 20000
x1, x2, x3, x4, x5 ≥ 0
In this case, the entering variable is x1, as it has the highest coefficient in the objective function.
Step 5 (continued):
1.6 0.1 0 1 -48 32 <- Z
0.4 0.9 1 1/10 0 40 <- x1
8.4 3.3 0 -1/10 1 1840 <- x5
The entering variable is x3, as it has the highest coefficient in the objective function.
The leaving variable is x1, as it has the smallest ratio of RHS to its coefficient in the x3 column.
x2 x1/12 x3 x5/120 x4 RHS
2.5 1/5 0 -1/60 0 40 <- Z
0.5 -1/5 1 1/60 0 8 <- x3
0.5 2/15 0 1/60 1/10 8/3 <- x2
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Is this true or false, explain how you know.
1/7 • 1/7 • 1/7 = 3/7
Answer: False
Step-by-step explanation:
1/7 x 1/7 = 1/49 x 1/7 = 1/343
Urgent, please help!
It has been proved that the lines MN and PR are parallel because they have the same slope.
How to identify the slope of parallel lines?We are given the coordinates of the points P, Q and R as:
P(-3, -6)
Q(1, 4)
R(5, -2)
Since M is the midpoint of PQ, we have:
M = (-3 + 1)/2, (-6 + 4)/2
M = (-1, -1)
N is the midpoint of QR and so:
N = (1 + 5)/2, (4 - 2)/2
N = (3, 1)
Slope of MN = (1 + 1)/(3 + 1) = 1/2
Slope of PR = (-2 + 6)/(5 + 3)
Slope of QR = 4/8 = 1/2
Both slopes are equal and as such they are parallel lines
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