Answer:
423.8
Step-by-step explanation:
you have to add the taxes and insurance together then subtract it by the gross salary and then you get your answer brainly please
a rectangular poster is to contain 392 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?
The dimensions of the poster be so that the least amount of poster is used are A = 6L + 4W + 412.
Let the length and width of the printable area of the poster be L and W, respectively. Then, the total dimensions of the poster can be expressed as L + 2(2) and W + 2(1), since there are 2-inch margins at the top and bottom, and 1-inch margins on the left and right.
We know that the area of the printable area of the poster is 392 square inches. Therefore, we can write the equation: LW = 392
We want to minimize the total area of the poster, which is given by:
A = (L + 2(2))(W + 2(1)) = (L + 4)(W + 2)
Expanding this expression, we get:
A = LW + 2L + 4W + 8
Substituting the equation for LW, we get:
A = 392 + 2L + 4W + 8
Simplifying, we get:
A = 2L + 4W + 400
To minimize this expression, we can take the partial derivatives with respect to L and W and set them equal to zero:
[tex]∂A/∂L = 2 = 0 => L = 0[/tex]
[tex]
∂A/∂W = 4 = 0 => W = -100[/tex]
These values do not make sense in the context of the problem. Therefore, we can conclude that the dimensions of the poster that minimize the amount of poster used cannot be found using this method.
Instead, we can use the fact that the printable area of the poster has a fixed area of 392 square inches, and that the margins have fixed dimensions. We can express the area of the poster as:
A = (L + 4)(W + 2) = LW + 4L + 2W + 8
Substituting the equation for LW, we get:
A = 392 + 4L + 2W + 8
Simplifying, we get:
A = 4L + 2W + 400
To minimize this expression, we can again take the partial derivatives with respect to L and W and set them equal to zero:
[tex]∂A/∂L = 4 = 0 => L = 0[/tex]
[tex]∂A/∂W = 2 = 0 => W = -200[/tex]
These values do not make sense in the context of the problem. Therefore, we can conclude that the dimensions of the poster that minimize the amount of poster used cannot be found using this method either.
We can try a different approach. We can use the fact that the printable area of the poster has a fixed area of 392 square inches, and that the total area of the poster is given by:
A = (L + 4)(W + 2) + 2(L + 4) + 2(W + 2)
Expanding this expression, we get:
A = LW + 6L + 4W + 20
Substituting the equation for LW, we get:
A = 392 + 6L + 4W + 20
Simplifying, we get: A = 6L + 4W + 412
To minimize this expression, we can take the partial derivatives with respect to L and W and set them equal to zero:
[tex]∂A/∂L = 6 = 0 => L = -2/3[/tex]
[tex]∂A/∂W = 4 = 0 => W = -3/2[/tex]
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A survey of 7th and 8th grade student who were asked whether or not they were in favor of or against school uniforms. This two-way table shows the results. How many 7th grade students are against school uniforms?
Julian goes to a store an buys an item that costs � x dollars. He has a coupon for 20% off, and then a 4% tax is added to the discounted price. Write an expression in terms of � x that represents the total amount that Julian paid at the register.
The expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.
What is Percentage?
Percentage is a way of expressing a proportion or fraction as a quantity out of 100. The word "percent" means "per hundred," so percentages are often denoted by the symbol %, which represents one part in a hundred.
The first step is to find the discounted price after the 20% discount. This can be found by multiplying the original price by (1 - 0.2), which represents a 20% reduction.
Discounted price = x - 0.2x = 0.8x
Next, a 4% tax is added to the discounted price. This can be found by multiplying the discounted price by (1 + 0.04), which represents a 4% increase.
Total amount paid = (0.8x) * (1 + 0.04) = 0.84x
Therefore, the expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.
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true or false: at the initial examination in the framingham study, coronary heart disease was found in 5 per 1000 men ages 30-44, and in 5 per 1000 women ages 30-44. the inference that in this age group men and women have an equal risk of getting coronary heart disease is incorrect because the data are prevalence data and not incidence data. group of answer choices true false
The inference is that, Incorrect because of a failure to distinguish between incidence and prevalence.
What is inference drawn from statistics?
Utilising data analysis to determine characteristics of a probability distribution at play, statistical inference is the process. Through the use of estimation and hypothesis testing, inferential statistical analysis infers characteristics of a population. It is presumed that a bigger population than the observed data set was sampled for this data collection.
What distinguishes random assignment from random sampling inferences?
As a method of choosing participants for your study's sample, random selection or random sampling can be used. The sample can be divided into control and experimental groups using random assignment, however.
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The complete question is -
At the initial examination in the Framingham study, coronary heart disease was found in 5 per 1,000 men aged 30yrs to 44yrs and in 5 per 1,000 women aged 30yrs to 44yrs. The inference that in this age group men and women have an equal risk of developing coronary heart disease is Selected Answer: A. Correct Answers: A. Correct B. Incorrect because of a failure to distinguish between incidence and prevalence C. Incorrect because a proportionate ratio is used when a rate is required to support the inference D. Incorrect because of failure to recognize a possible cohort phenomenon E. Incorrect because there is no control or comparison group.
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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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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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:
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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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.
Please help offering 15 points!!
Answer: C 70%
Step-by-step explanation:
First you need to add up how many students are participating in the study. 4+6+12+8+4=34. There are 24 people who own more than 5 video games. This means that it is 24/34. This equals about 70%
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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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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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
Twins Isaac and Isaiah were just born. Isaac weighs
6
66 pounds
2
22 ounces and Isaiah weighs
5
55 pounds
4
44 ounces.
How many ounces do Isaac and Isaiah weigh together?
ounces
Therefore , the solution of the given problem of unitary method comes out to be Isaac and Isaiah are 182 ounces in total.
Definition of a unitary method.Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.
Here,
We must first change the weights of Isaac and Isaiah from pounds and ounces to ounces before adding them to determine their combined weight.
Weight of Isaac: six pounds 2 ounces = 6 * 16 + 2
= 96 + 2
= 98 ounces
Isaiah is 5 pounds in weight.
= 5 * 16 + 4
= 80 + 4
= 84 ounces
Together, Isaac and Isaiah weighed
98 ounces + 84 ounces = 182 ounces
As a result, Isaac and Isaiah are 182 ounces in total.
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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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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
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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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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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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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.
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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!!!!!!I NEED THIS ASAP!!!!!
Find x,y, and z
Applying the right triangle altitude theorem and the leg rule, we have:
5. x = 6; y ≈ 6.7; z ≈ 13.4 6. x = 32; y ≈ 35.8; z ≈ 17.9
What is the Right Triangle Altitude of a Theorem?The right triangle altitude theorem states that the altitude drawn on the hypotenuse of a right triangle is equal to the geometric mean of the two line segments into which the altitude divides the hypotenuse.
5. To find x, apply the right triangle altitude theorem, which is:
x = √(3*12)
x = √36
x = 6
Using the leg rule, we can find y and z. It is expressed as:
hypotenuse/leg = leg/part
Therefore, substitute and find y:
(3 + 12) / y = y / 3
Cross multiply:
y² = 15 * 3
y = √45
y ≈ 6.7
Find z using the leg rule:
15/z = z/12
z² = 180
z = √180
z ≈ 13.4
6. Use the same theorem and leg rule as done in question 5:
Find x:
16 = √(8 * x)
16² = 8x
256 = 8x
x = 256/8
x = 32
Find y using the leg rule:
(8 + 32) / y = y/32
y² = 40 * 32
y = √1,280
y ≈ 35.8
Find z:
40/z = z/8
z² = 40 * 8
z = √320
z ≈ 17.9
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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]
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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A football team consists of:
• 10 sixth graders
• 14 seventh graders
• 16 eighth graders
A student on the team will be randomly chosen to participate in the coin toss each of the 40
games of the season.
What is a reasonable prediction for the number of times a sixth or seventh grader will be
chosen?
A reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24 out of the 40 games.
What is reasonable prediction?
A reasonable prediction is a prediction made with a reasonable degree of accuracy or likelihood, based on available information and knowledge. It is based on facts, past events, and logical assumptions, and is not based on conjecture or guesswork. Reasonable predictions can be made about future events, trends, and outcomes, and can be used to inform decisions, plans, and strategies.
The total number of sixth and seventh graders on the team is:
10 sixth graders + 14 seventh graders = 24 students
The total number of students on the team is:
10 sixth graders + 14 seventh graders + 16 eighth graders = 40 students
To find the expected number of times a sixth or seventh grader will be chosen in the coin toss, we can use the proportion of sixth and seventh graders to the total number of students:
(expected number of times) = (proportion of sixth and seventh graders) * (total number of coin tosses)
(expected number of times) = (24/40) * 40
(expected number of times) = 24
Therefore, a reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24.
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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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Solve the Simple Interest
Ruby contributes 12% of the total cost of her individual health care. This is a $57.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year? Find its employer share.
Using simple interest we know the Total value of annual health coverage is $9000.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan.
Compound interest is excluded from the calculation and just the original principal is used.
Simple interest applies to all loans, not just specific ones.
Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
So, complete yearly health coverage calculation
Let x be the total annual healthcare budget.
Ruth contributes 18% of the entire cost of healthcare, or $67.50 for two weeks. (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
The total amount paid for the entire year is 135 x 12 = 1620.
She foots 18% of the overall annual health care costs, as was already established.
Then,
18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= $9000
Therefore, using simple interest we know the Total value of annual health coverage is $9000.
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Correct question:
Ruth contributes 18% of the total cost of her individual health care. This is a $67.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?
please help with these assap will give brainlest!!
Answer:
below
Step-by-step explanation:
58.
(72 + 75 + 68 + 70 + 73 + 72 + 76 + 72 + 69 + 72 ) divided by 10 = 71.9
59.
order- 68, 69, 70, 72 , 72, 72, 72, 73, 75, 76
median = (72 + 72) divided by 2 = 72
61.
I dont know what MAD means
this is all I could do rn