a) Alex is closer to the state record.
b) The 8th grade should be awarded the 100 points.
How to obtain the amounts?The amounts are obtained applying the proportion for the unit conversion between feet and inches, as follows:
12 inches = 1 feet.
Alex jumped 38 feet 11 2/3 inches, hence the distance that Alex jumped, in feet, is given as follows:
38 + (11.67/12) = 38.98 feet.
(also conversion of mixed number to decimal, 11 and 2/3 = 11 + 2/3 = 11.67).
Alex' difference to the record of eight graders is given as follows:
40.17 - 38.98 = 1.19 feet.
Eric's difference to the record of seventh graders is given as follows:
38 + (1.6/12) - 36.89 = 1.24 feet.
1.19 feet is a smaller difference than 1.24 feet, hence Alex is closer to the state record.
As Alex was closer, and he is an eight grader, this means that the 8th grade should be awarded the 100 points.
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bob had 612 qt of paint. he used 323 qt to paint a room how much paint does bob have left? hint: you might have to re-group! enter your answer in the box as a mixed number in simplest form. qt
The quantity of paint left with Bob after painting a room from the quantity of 6 1/2 is equal to 2 5/6 qt.
As given in the question,
Quantity of paint Bob had is equal to 6 1 / 2 qt
Quantity of paint used by Bob to paint a room is equal to 3 2 / 3 qt
Quantity of paint left with Bob after painting is equal to :
= Total quantity - Used quantity
= ( 6 1 / 2 ) - ( 3 2 / 3 )
= ( 13 / 2 ) - ( 11 / 3 )
= ( 39 - 22 ) / 6
= 17 / 6
= 2 5/6 qt
Therefore, the quantity of paint left with Bob from 6 1/2 qt after painting the room is equal to 2 5/6 qt.
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we want to set up a christmas tree and put some lights on it. let's design and implement the light switches. we want to control the lights by two switches. one of the switches is in the living room and one at the entrance hallway. you should design the associated circuit, so that the lights are on if the switches mismatch.
By using logic gate, it can be concluded-
XOR table is used in this case?
What is logic gate?
Logic gate is a device which is used to build digital circuit.
Logic gate can make passage for a system to pass through when some logical conditions are fulfilled.
Different types of logic gates are-
AND gate, OR gate, NAND gate, XOR gate, NOR gate etc.
Here one switch is in the entrance hallway and other is in the living room.
The lights are on if the switches mismatch.
For this case, XOR table is used
A B Result
0 1 1
1 0 1
0 0 0
1 1 0
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¿Do you think that Mexico is transitioning to a green economy? why?
Answer:
Step-by-step explanation:
yes probaly
im doing this for point
Personally, he considered that Mexico is indeed transitioning to a green economy, because the economy is adjusting towards the sustainable and adequate use of resources.
¿What is the green economy?It is a type of economy that is based on developing sustainable and sustainable processes in all its processes and activities, this in favor of caring for the planet and its natural elements.
¿Does Mexico seek to have a green economy?It can be said that Mexico is transitioning to a green economy, this can be observed, for example:
In the implementation of sustainable and sustainable strategies of companies.In the appropriate and increasingly efficient use of many natural resources.¡Hope this helped!
Find the degree measure of each angle in the triangle.
Answer:
∠N° = 19°
∠M° = 35°
∠L° = 126°
Step-by-step explanation:
Total angle in a triangle: 180°
∠N° = x°
∠M° = ( 2x - 3 )°
∠L° = ( 7x - 7 )°
180 = N + M + L
180 = x + 2x - 3 + 7x - 7
180 = 10x - 10
10x = 180 + 10
10x = 190
Divide both side by 10
x = 19
∠N° = x° = 19°
∠M° = ( 2x - 3 )° = ( 2(19) - 3 )° = 35°
∠L° = ( 7x - 7 )° = ( 7(19) - 7 )° = 126°
Is the exponential representation below increasing or decreasing?
y=200(0.75)x
The exponential representation is a decreasing function
How to determine if the exponential representation is increasing or decreasing?From the question, we have the following parameters that can be used in our computation:
y = 200(0.75)x
Rewrite properly
So, we have the following representation
y = 200(0.75)ˣ
An exponential function is represented as
y = abˣ
Where
b = rate
This means that
b = 0.75
Since b is less than 1, then the function is a decreasing function
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Nicole has saved $120 toward the purchase of a new bike. She gets a job that pays $12 an hour. She saves 25% of her hourly wage to purchase the new bike. She uses the equation y=(0.25)(12)x+ 120 to determine how much money she has saved toward the purchase of the new bike. What is the slope of the line represented by Nicole's equation?
A. 120
B. 0.25
C. 12
D. 3
Answer: The correct answer is B.
Step-by-step explanation:
The slope of a line in the form of y = mx + b is represented by the coefficient m. In this case, the slope of the line represented by Nicole's equation is:
y = (0.25)(12)x + 120
The coefficient m is 0.25.
Empirical Rule 06
IQ scores can be described using a Normal distribution with a mean of 100 and a standard deviation of 15.
Using the Empirical '68-95-99.7' Rule, what percent of IQ scores are above 130?
Answer:
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data lies within one standard deviation of the mean, 95% lies within two standard deviations, and 99.7% lies within three standard deviations.
In this case, the mean is 100 and the standard deviation is 15, so approximately 95% of the data lies within two standard deviations of the mean. Since two standard deviations of 100 is 30 (15 * 2), this means that approximately 95% of the data lies within the range of 70 to 130. Therefore, approximately 5% of the data lies outside of this range, with 2.5% lying below 70 and 2.5% lying above 130.
Therefore, the percent of IQ scores that are above 130 is approximately 2.5%.
an ice cream company is going to open new stores in los angeles, chicago, and new orleans. the monthly cost for a square foot .find the total monthyl rent for all three stores.find the total monthyl rent for of rental space in each city was follows. los angeles $5.25, chicago $6.95 and new orleans $4.25. the store in los angels will be 560 square , chicago will be 330 square feet and new orleans will be 495 square feet.
The total monthly rent for these three stores is $8,786.25.
What is total ?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.
The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.
The monthly cost for a square foot of rental space in each city is as follows:
Place Monthly Cost for a Square Foot
Los Angeles $5.75
San Francisco $6.95
Seattle $4.25
It is also provided that the store in Los Angeles will be 580 square feet, the store in San Francisco will be 500 square feet, and the store in Seattle will be 465 square feet.
Compute the total monthly rent for these three stores as follows:
Total Monthly Rent = Monthly Cost for a Square Foot × Area
= (5.75 * 580) +(6.95 * 500) +(4.25 * 465)
= 3335 + 3475 + 1976.25
= 8786.25
Thus, the total monthly rent for these three stores is $8,786.25.
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Question 14 of 50
In a transformation, the preimage is the original figure and the image is the figure in the new location.
False
True
Answer:
True
Step-by-step explanation:
Graph the following inequality. 8x+y>-4
Answer:
8x + y > 4
y > -8x + 4
Calculate the difference and enter below. -9-(-10)
Answer: 1
Step-by-step explanation: So, since this is a subtraction problem of negative numbers, we will make this an inverse operation, and make this an addition problem (It's easier to solve) So, now it will be written as -9 + 10. This is the same as 10-9, which would give us our answer; 1. I hoped this helped.
one period of a sine function or cosine function is called one amplitude incorrect: your answer is incorrect. of the sine curve or cosine curve.
The correct answer is cycle. A sine or a cosine function represent periodic functions where the value of the function is repeats after a definite interval.
What do you mean by periodic function?
A periodic function can be defined as:
A function returning to the same value at regular intervals. Though periodic motion and oscillatory motion sound the same, not all periodic motions will be oscillatory motion.
Image result for periodic function
If a function has a repeating pattern like sine or cosine, it is called a periodic function. The period is the length of the smallest interval that contains exactly one copy of the repeating pattern.
A motion that repeats itself at regular intervals is termed periodic motion. 1. A motion that does not repeat itself at regular intervals is termed non-periodic motion. 2. After a certain period of time, an object exhibiting periodic motion returns to its original position.
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The SAT and ACT are the two major standardized tests that colleges use to evaluate applicants. Most students take just one of these tests. However, some students take both. This Excel file gives the scores of 60 students who took both tests. Can we relate the two tests? Plot the data with SAT on the x axis and ACT on the y axis and answer the questions below.
Student SAT ACT
1 1000 24
2 870 21
3 1090 25
4 800 21
5 1010 24
6 880 21
7 860 19
8 1040 24
9 920 17
10 850 22
11 740 16
12 840 17
13 840 19
14 780 22
15 500 10
16 1060 25
17 830 19
18 830 20
19 780 12
20 870 21
21 1440 32
22 1190 30
23 1120 27
24 1120 25
25 490 7
26 800 16
27 590 12
28 800 18
29 1050 23
30 830 16
31 990 24
32 960 27
33 870 18
34 890 23
35 700 16
36 880 21
37 970 21
38 880 24
39 930 22
40 1020 24
41 920 22
42 980 27
43 860 23
44 790 14
45 810 19
46 1030 23
47 420 21
48 620 18
49 1080 23
50 1220 30
51 800 20
52 1150 28
52 1000 19
54 1080 22
55 1140 24
56 970 20
57 1030 25
58 970 20
59 920 21
60 1060 24
Question 1. Find the slope and intercept of the least squares regression line (draw the least squares line on your plot).
intercept (use 4 decimal places)
1.6263
slope (use 4 decimal places)
.0214
Question 2. Give the value of the test statistic for a test of H0: ß1 = 0.
(use 4 decimal places)
Question 3. If the alternative hypothesis is Ha: ß1 ? 0, what is the rejection region if the significance level of the test is a = .05? Use this t-table to determine your answer.
t =
t =
Question 4. What is the correct conclusion for this hypothesis test?
Do not reject the null hypothesis H0; the SAT score is not useful for predicting the ACT score.
Reject the null hypothesis H0 and conclude that in a linear model SAT score is useful for predicting the ACT score.
Question 5. Determine a 95% confidence interval for the slope ß1 of the least squares line (use 3 decimal places in your answers; use this t-table to determine the correct t-value).
lower endpoint of confidence interval
upper endpoint of confidence interval
the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted
Given that many high school students take either the SAT or the ACT.
However, some students take both.
Data were collected from 60 students who took both college entrance exams.
SAT score ACT score with a of 180.
Average 912 21
standard deviation 180 5
Correlation between the two variables r = 0.817
WE have for two variables if we have correlation coefficient then the square of correlation coefficient gives the fraction of variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores
So we find square of r
i.e. r by the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted
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Answer:
j
Step-by-step explanation:
can someone help me figure out how to solve this problem
Answer:
In an arithmetic sequence, each term is obtained by adding the common difference to the previous term. In this case, the common difference is 3, so the formula for the nth term of the sequence can be written as:
a^n = a^1 + (n-1) * d
where a^1 is the first term of the sequence, and d is the common difference.
Since the first term of the sequence is -25 and the common difference is 3, we can plug these values into the formula to find the 30th term of the sequence:
a^30 = (-25) + (30-1) * 3
= (-25) + 29 * 3
= (-25) + 87
= 62
Therefore, the 30th term of the sequence is 62.
Step-by-step explanation:
what is the value of the estimated standard error for the following set of d (differneces) scroes 4, 8, 4 ,4
The value of the estimated standard error is 1.
The set of d (differneces) scroes: 4, 8, 4 ,4
Consider,
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Mean of the D-score is [tex]$$\begin{aligned}\bar{d} & =\frac{1}{n} \sum d_i \end$[/tex]
[tex]=\frac{1}{4}[/tex](4+8+4+4)
=5
Standard deviation of D-score is given by [tex]$$\begin{aligned}\hat{\sigma} & =\sqrt{\frac{1}{n-1} \sum_{i=1}^n\left(d_i-\bar{d}\right)^2} \\& =\sqrt{\frac{1}{4-1}\left\{(4-5)^2+(8-5)^2+(4-5)^2+(4-5)^2\right\}} \end[/tex]
The value of the estimated standard error for the following set D scores is
[tex]$$\begin{aligned}\widehat{\mathrm{SE}(d)} & =\frac{\hat{\sigma}}{\sqrt{n}} \\& =\frac{2}{\sqrt{4}}\end{aligned}$$[/tex]
[tex]=\frac{2}{2}=1[/tex]
Therefore, the value of the estimated standard error for the following set of d scroes is 1.
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Right Answers Only! thank you
Answer:
D
Step-by-step explanation:
The equation is like this :
Popcorn + 5(Price of each juice bottle) = total cost
1.59 + 5j = 13.34
Subtract both sides with 1.59
5j = 11.75
A and C are obviously wrong
B is wrong because there is only one of the juice bottle in the diagram
The answer is D
2. A local manufacturing firm produces four different metal products, each of which must be machined, polished and assembled. the specific times requirements ( in hours) for each products are as follows
Machining hours Polishing hours Assembling hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Pruduct IV 4 3 1
Step-by-step explanation:
To find the total time required to produce each product, we can add up the machining, polishing, and assembling hours for each product. For example, for Product I, the total time required would be:
Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours
We can do this for each product to find the total time required for all four products:
Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours
Total time for Product II = 2 hours + 1 hour + 1 hour = 4 hours
Total time for Product III = 2 hours + 2 hours + 2 hours = 6 hours
Total time for Product IV = 4 hours + 3 hours + 1 hour = 8 hours
So, the total time required to produce all four products is 6 hours + 4 hours + 6 hours + 8 hours = 24 hours.
Emilio buys liter bottles of shampoo when the store has the promotion shown. Write an expression in two different ways to represent the total cost 0f 3 liters of shampoo. Let L be the regular price of a liter bottle.
The expressions for the total costs are 2L + 0.7L and 2.7L
How to determine the expression for the total cost?From the question, we have the following parameters that can be used in our computation:
Number of litres = 3
Regular price = L
Discount = 30%
This means that there is a discount on the third item
So, we have the following expression
Total amount = 2 * L + L * (1 - discount)
Substitute the known values in the above equation, so, we have the following representation
Total amount = 2 * L + L * (1 - 30%)
Total amount = 2 * L + L * 0.7
This gives
Total amount = 2L + 0.7L
Evaluate the sum
Total amount = 2.7L
Hence, the expression is 2.7L
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The expression for the total cost of 3 liters of shampoo is written as
2.7 L2L + 7L/10How to write the expressionLet L be the regular price of a liter bottle
The expression is written in decimal and in fraction
For the promotion buy 2 liters get 30% of 3rd liter
30% off = 0.3 off
= (1 - 0.3)
= 0.7
The total cost will be
= 2 * L + 0.7 * L
= 2L + 0.7L
= 2.7 L
The cost of three bottles of shampoo is 2.7L
In another way
= 2L + (1 - 0.3)L
= 2L + 0.7L
using fractions
= 2L + 7L/10
= 27L/10
the other way is writing in fraction
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a movie production company is releasing a movie with the hopes that many viewers will return to see the movie in the theater for a second time. their target is to have 40 million viewers, and they want more than 40% of the viewers to want to see the movie again. they show the movie to a test audience of 140 people, and after the movie they asked them if they would see the movie in theaters again. of the test audience, 66 people said they would see the movie again.
Answer: the test is 47 percent
Step-by-step explanation: 66 out of 140 is 47 percent so it would work
an article in neurology (1998, vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. the investigators measured an intelligence score of 10 pairs of twins, and the data follow: pair birth order: 1 (first) birth order: 2 (second) 1 6.08 5.73 2 6.22 5.80 3 7.99 8.42 4 7.44 6.84 5 6.48 6.43 6 7.99 8.76 7 6.32 6.32 8 7.60 7.62 9 6.03 6.59 10 7.52 7.67 (a) State the appropriate hypotheses. (b) Create a Paired- T test at α=0.05 in Minitab and find the P-value. Do you reject the null?
The p - value of the given hypothesis is P(2<x<6.75) is 0.49974
How to calculate p - value?
In statistics, p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve.
Here we have given that an article in neurology (1998, vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. the investigators measured an intelligence score of 10 pairs of twins, and the data.
And we need to find the value of p from it.
Here we have the following sample data,
=>2,5.73,5.80,6.08,6.22,7.99,7.44,6.48,7.99,6.32,7.60,6.03,7.52,8.42,6.84,6.43,8.76,6.32,7.62,6.59,7.67
Through the sample data we ahve identified the following values,
Standard Deviation, σ: 1.3737491940207
Count, N: 21
Sum, Σx: 141.85
Mean, μ: 6.7547619047619
Variance, σ2: 1.8871868480726
in order to find the p-value, we have to calculate the z score for the given data,
Z score = (x - μ)/σ
=> (2 - 6.75)/ 1.37
=> -3.46715
P-value from Z-Table:
=> P(x<2) = 0.000263
=> P(x>2) = 1 - P(x<2) = 0.99974
=> P(2<x<6.75) = 0.5 - P(x<2) = 0.49974
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christopher is working two summer jobs, making $7 per hour babysitting and making $10 per hour washing cars. in a given week, he can work no more than 16 total hours and must earn a minimum of $130. if xx represents the number of hours babysitting and yy represents the number of hours washing cars, write and solve a system of inequalities graphically and determine one possible solution.
Christopher can work average 9 hours babysitting and 7 hours washing cars in a given week to meet the minimum wage requirement and not exceed the maximum hours he can work.
Christopher is working two summer jobs and has a maximum of 16 hours to work in a given week. He is making $7 per hour babysitting and $10 per hour washing cars. To meet the minimum wage requirement of $130, he needs to make a total of $130 in a week. We can represent this using a system of inequalities. The first inequality is 7xx + 10yy ≥ 130, which means that the total wages (7 times the hours babysitting plus 10 times the hours washing cars) must be greater than or equal to $130. The second inequality is xx + yy ≤ 16, which means that the total hours (babysitting plus washing cars) must be less than or equal to 16. Graphically, we can solve this system of inequalities to find the possible solutions. One possible solution is x = 9 and y = 7, meaning Christopher can work 9 hours babysitting and 7 hours washing cars in a given week to meet the minimum wage requirement and not exceed the maximum hours he can work.
Graphically:
7xx + 10yy ≥ 130
xx + yy ≤ 16
7xx + 10yy = 130
xx + yy = 16
Therefore, the solution is x = 9 and y = 7.
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Please help will mark Brainly
Answer:
C.
Step-by-step explanation:
Since Y is confirmed to cost 18
It will cancel out Answer "A" and "D"
It says River Z costs 2 dollars per hours plus a 10 dollar deposit
So that would cancel Answer "B" because you're not removing 10 dollars from the 2 dollars per hour.
So it would be...
Y= c = 18
X= c = 2n + 10
[tex]3-2\sqrt3\\[/tex]
Answer:
=3−√3 (Decimal: 1.267949)
Step-by-step explanation:
3−√3
=3−√3 (Decimal: 1.267949)
This is the best I could do! hope it helps!!
Suppose you are designing and conducting a poll to see which of the Congressional candidates are popular in your area. Use the terminology and concepts that we are learning in Lesson 1 - population, sample, sampling methods, representative sample, and presentation of data....
1. Discuss the following in your own words :
the population that you are trying to predict,
where and how are you selecting your sample,
what sampling method would you use,
how would you assure that you are selecting a representative sample, and
show an example of how you would present your data.
The population we're trying to predict is the population that is going to be Voters in our area, the where should probably be well as above our area, and the how now, generally speaking, we want to do a simple, random, or a random sample of some sort, random sample.
For instance, what you could do would be something like choose: random addresses in the area and send a survey, but sending a survey could introduce self-selection bias. So it would be ideal to visit in person basically and ask a few questions making sure the representative sample or how to ensure that we're getting a representative sample would be to, for instance, filter the random results and make sure that we have an even distance.
Ensure that there's an equal number within each quadrant of the town, basically split up the town. Split towns into regions of populations or population densities and make sure we get the same proportion from each region. However, we end up splitting the town into different regions. We show the proportion or show who is the most popular candidate in each 1 of the regions, so it could be something like this. That was supposed to be an alternative to a bar graph. The number of results for each different candidate depends on whether or not there's a sort of well-defined districts or areas in the town, but most sorts of relatively large cities have things like that. So the idea would be to represent not just the location, but also the information that you gain separately.
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Split up the town so that there are an equal amount in each of its four quadrants. Make sure we receive the same proportion from each region by dividing towns into population or population density regions. But ultimately, we divide the town into many parts. It might look something like this since we display the percentage or the candidate who is most supported in each location. That was meant to be a bar graph substitute. Whether or not a town has clearly defined districts or areas affects the amount of results for each candidate, although this is true of most types of moderately large cities.
find $m\angle1$ .two triangles a b c and q r s are drawn. angles b and q are labeled with a single arc. angles a and s are marked with a double arc. angles a and b are labeled 45 degrees and 80 degrees respectively. angle r is labeled 1.
The measure of angle 1, m∠1, found using the congruency of the angles and the angle sum property of a triangle is 55°
What is the angle sum property of a triangle?The angle sum property of a triangle specifies that the sum of the interior angles of a triangle is 180°
Please find attached the presentation of the details of the question as a drawing of the triangles created with MS Word
The parameters of the question are;
The number of arcs on angles b and q = Single arcs
Therefore, based on the arc markings indicating congruency of the angles, we get;
Angle b is congruent to angle q ∠b ≅ ∠q
Therefore, ∠b = ∠q, by the definition of congruency
The number of arcs on angle a and angle s = Double arcs
Therefore, angle a is congruent to angle s based on the arc markings, which indicates;
∠a ≅ ∠s
∠a = ∠s by the definition of congruency
The label on angle ∠a = 45°
The label on angle ∠b = 80°
∠a = ∠s, therefore, ∠s = 45°, by substitution property
∠b = ∠q, therefore, ∠q = 80° by substitution
∠s + ∠q + ∠1 = 180° Angle sum property of a triangle
45° + 80° + m∠1 = 180°
m∠1 = 180° - (45° + 80°) = 55°
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the sampling distribution of the sample mean is close to normal distribution a. only if the parent population is unimodal, not badly skewed, and does not have outliers.
C) The Central Limit Theorem states that the sample mean's sampling distribution is very similar to a normal distribution.
The central limit theorem is founded on what?The idea of a sampling distribution, which is the probability distribution of a statistic for a large number of samples taken from a population, is the foundation of the central limit theorem.
What are the central limit theorem's two main tenets?To summarize, the following two distributions are linked by the central limit theorem: The population's distribution of the variable. The testing dissemination of the mean.
What is As far as possible Hypothesis?The CLT is a statistical theory that holds that the mean of all samples taken from a population with a finite level of variance will roughly match the population mean if a sufficient number of samples are taken from that population.
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Full Question = The sampling distribution of the sample mean is close to the normal distribution
A. only if the parent population is unimodal, not badly skewed, and does not have outliers.
B. no matter what the distribution of the parent population of what the value of n.
C. if n is large, no matter what the distribution of the parent population.
D. if the standard deviation of the parent population is known.
E. only if both n is large and parent population has a normal distribution.
A contractor is building a new house and wants to determine the size of its foundation. The length of the
foundation is 6 feet more than 2 times its width. The value of the area of the foundation (in square feet)
is 1046 more than the value of the perimeter of the foundation (in feet). Which of the following values
are correct? Show work.
A. Area: 1196 sq ft
B. Worth: 23 ft
C. Perimeter: 150 ft
D. Length 29 ft
Answer:
A, B, C
Step-by-step explanation:
You want to find the dimensions, perimeter, and area of a foundation such that the length is 6 feet more than twice the width, and the area is 1046 more that the value of the perimeter.
SetupWe can let x and y represent the length and width, respectively. Then the given relations translate to the equation ...
A = LW . . . . . . . area formula
P = 2(L +W) . . . . perimeter formula
y = 2x +6 . . . . . relation between dimensions
xy = 2(x +y) +1046 . . . . . relation between perimeter and area
SolutionUsing the first equation to substitute for y, we have ...
x(2x +6) = 2(x +(2x +6)) +1046
2x² +6x = 6x +1058 . . . . . . . . . . . . eliminate parentheses
x² = 529 . . . . . . . . . . . . . subtract 6x and divide by 2
x = √529 = 23 . . . . . . . . . width; matches B
y = 2(23) +6 = 52 . . . . length
area = (23)(52) = 1196 . . . area; matches A
perimeter = 2(23 +52) = 2(75) = 150 . . . . matches C
The area is 1196 square feet. (A)
The width is 23 feet. (B)
The perimeter is 150 feet. (C)
1/a+1/b=1/c, what is the average (arithmetic mean) of a and b?
The arithmetic mean of a and b in the expression 1/a + 1/b = 1/c is 2c.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
Given, An expression of the form 1/a + 1/b = 1/c.
We know average of two numbers is sum of those numbers divided by 2.
So, {(1/a) + (a/b)}/2 = 1/c.
Now to keep the equality we also have to divide the RHS by 2.
Therefore, {(1/a) + (a/b)}/2 = (1/c)/2.
{(1/a) + (a/b)}/2 = (1/c)×((1/2).
{(1/a) + (a/b)}/2 = 1/2c.
So, The arithmetic mean of 1/a + 1/b is 1/2c.
Now taking the reciprocal of 1/a and 1/b which is a and b the arithmetic mean is
2c.
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Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) ∫(e^x+ 1/8x) dx
The general indefinite integral of ([tex]e^{x}[/tex]+ 1/8x) is ∫([tex]e^{x}[/tex]+ 1/8x) dx
= [tex]e^{x}[/tex]+ 1/4x + C
General indefinite integral
An integral is considered to be indefinite if it has no upper or lower bounds.
The most generic anti-derivative of f(x) is known as an indefinite integral and denoted, in mathematics, by F(x), which is any anti-derivative of f(x).
f(x) dx = F(x) + C
The integral of [tex]e^{x}[/tex] = [tex]e^{x}[/tex]
so ∫[tex]e^{x}[/tex] dx = [tex]e^{x}[/tex] + C
The integral of 1/8x = 1/4x,
so ∫1/8x dx = 1/4x + C
To find the integral of ([tex]e^{x}[/tex] + 1/8x), add the integrals of each term:
∫([tex]e^{x}[/tex]+ 1/8x) dx = [tex]e^{x}[/tex] + 1/4x + C
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Chee is ordering a taxi from an online taxi service. She has to pay a flat charge just to
order the taxi, and then has to pay per mile, depending on how far she travels. She
wrote an equation to represent her total cost, y = 1.3x + 5, where y represents the
total cost in dollars and cents, and a represents the number of miles she travels.
What is the meaning of the y-value when x = 1?
A) The flat charge to order the taxi.
B) How far Chee can ride for $1.
C) The total charge for 1 mile.
D) The change in the total cost for every one additional mile traveled.
Answer: c?
Step-by-step explanation:
this is a guess :)