Answer:
A)5 pi
Step-by-step explanation:
To get the increase, we must find the area of the circle when the radius was 2 inches and subtract it from the area of the circle when the radius increases to 3 inches. The difference is the increase in the area of the circle.
A circle of radius r has an area A given as
A = Pi r²
Hence when the radius was 2 inches, the area A
= Pi × 2²
= 4 Pi square inches
when the radius increases to 3 inches, the area
= Pi × 3²
= 9 Pi square Inches
The increase in area
= 9 Pi - 4 Pi
= 5 Pi
Suppose we take repeated random samples of 50 college students from the same population and determine a 95% confidence interval for the mean GPA from each sample. Which of the following statements is true regarding the confidence intervals?
A. The intervals are centered around the population mean GPA.
B. The intervals are centered around the sample mean GPA.
C. 95% of the intervals will contain the sample mean in the long run.
D. 95% of the intervals will contain the population mean in the long run.
Answer:
B. The intervals are centered around the sample mean GPA.
D. 95% of the intervals will contain the population mean in the long run.
Step-by-step explanation:
Confidence interval:
Depends on two things: The sample mean and the margin of error.
Lower end: Sample mean - margin of error
Upper end: Sample mean + margin of error
This means that the intervals are centered around the sample mean.
x% level:
x% of the intervals will contain the population mean in the long run.
So the true statements are:
B. The intervals are centered around the sample mean GPA.
D. 95% of the intervals will contain the population mean in the long run.
Please answer this correctly
Answer:
The range would decrease by 2
Step-by-step explanation:
The range is the difference between the highest number and the lowest number.
8 is the highest number and 1 is the lowest number here, so to find the range we would subtract 1 from 8. 8-1=7
But since 8 is being replaced by 6, we would subtract 1 from that instead.
6-1=5
The range decreased from 7 to 5, so it decreased by 2.
Hope that helps :)
how to solve the birth rate in a certain country in 1994 was 14.6 births per thousand population. in 2004 the birth rate was 14.32 births per thousand. let x represent years after 1994 and y represent the birth rate. assume the relationship is linear
Answer:
[tex]y(x)=-0.028x+14.6[/tex]
Step-by-step explanation:
We are to write a linear equation that relates y in terms of x
The Birth Rate in 1994 = 14.6 births per thousand population.
The Birth Rate in 2004 = 14.32 births per thousand population.
A linear equation is of the form y=mx+b, where:
x=Number of Years after 1994y=the birth ratem=Birth rate per yearStep 1: Determine the birth rate per year
In 1994, x=0, y=14.6 thousands
In 2004, x=10, y=14.32 thousands
[tex]m=\dfrac{14.32-14.6}{10-0}\\=\dfrac{-0.28}{10}\\m=-0.028[/tex]
Substituting m into our linear equation, we have:
[tex]y(x)=-0.028x+b[/tex]
When x=10, y=14.32
[tex]14.32=-0.028(10)+b\\b=14.32+0.28\\b=14.6[/tex]
Therefore, a linear equation that relates y in terms of x is:
[tex]y(x)=-0.028x+14.6[/tex]
Un importante grupo de inversionistas, asociado a una línea de buses interurbanos, está considerando instalar un centro logístico de mantención, a usted le ha encargado la evaluación de este proyecto, considerando un horizonte de 5 años. el estudio técnico del proyecto indica que se requiere disponer de un galpón 1000 m2 dentro de las instalaciones que la empresa ya cuenta, además de un acceso pavimentado con cimientos especiales de 6000 m2. el costo de construcción del galpón es de $ 42 por m2, y el costo de construcción del acceso pavimentado es de $ 32 por cada m2. adicionalmente, se requiere adquirir servidores de punta para realizar el check de los buses antes de comenzar sus recorridos, su costo se estima en $ 630.000, además se necesitan equipos especiales para la revisión de los neumáticos, con un costo de $ 400.000. finalmente, se deberá conseguir un terreno al interior del terminal de buses, con una superficie de 1 m2, con un costo de $50 por m2.
Answer:
Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = $ 1,264,000
Total start-up amount required, according to the details provided in the question = $1,264,000
Step-by-step explanation:
- Hay 1000 m² de espacio de almacén para construir a $ 42 por m². Dinero total requerido = 1000 × 42 = $ 42,000.
- Hay 6000 m² de espacio de acceso pavimentado para construir a $ 32 por m². Dinero total requerido = 6000 × 32 = $ 192,000.
- Compra de servidores de última generación para revisar los autobuses antes de comenzar sus recorridos. Costo total = $ 630,000.
- Se necesita comprar equipo especial para revisar los neumáticos. Costo = $ 400,000.
Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = 42000 + 192000 + 630000 + 400000 = $ 1,264,000
¡¡¡Espero que esto ayude!!!
English Translation
- There is 1000 m² of warehouse space to construct at $42 per m². Total required money = 1000 × 42 = $42,000
- There is 6000 m² of paved access space to construct at $32 per m². Total money required = 6000 × 32 = $192,000
- Purchase of state-of-the-art servers to check the buses before starting their tours. Total Cost = $630,000
- Purchase of special equipment is needed to check the tires. Cost = $400,000
Total start-up amount required, according to the details provided in the question = 42000 + 192000 + 630000 + 400000 = $1,264,000
Hope this Helps!!!
Data on the number of work days missed and the annual salary increase for a company’s employees show that, in general, employees who missed more days of work during the year received smaller raises than those who missed fewer days. A detailed analysis shows that the number of days missed explains 60% of the variation in salary increases. What is the correlation between the number of days missed and salary increase?
Answer:
Step-by-step explanation:
Correlation describes how strongly pairs of given variablé are related. In this case, a detailed analysis that was carried out shows that the number of days missed by employees explains 60% of the variation in salary increases and also impressed upon this fact that employees who missed more days of work during the year received smaller raises than those who missed fewer days.
From the analysis, we can draw a conclusion that there is a correction between days missed and variation in salary increase and that this type of correction is a negative correlation where an increase in the number of days missed will lead to a decrease in the raises awarded to each employee.
What type of error is present in the underlined
sentence?
Which is the best revision to fix the error?
Answer:
Type of error: Run-on(comma splice).
Best revision to fix it: Adding a semicolon after beginners .
Explanation:
A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.
In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:
'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'
Answer:
Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.
What type of error is present in the underlined sentence?
✔ run-on
Which is the best revision to fix the error?
✔ adding a semicolon after instrument
Step-by-step explanation:
if 3x+2y=72 and y=3x, then x whoever solve I give them all my points
Answer:
[tex]x=8[/tex]
[tex]y=24[/tex]
Step-by-step explanation:
3x+2y=72
If y=3x, we plug it into our equation and get:
3x+2×3x=72
3x+6x=72
9x=72
Divide both sides by 9
x=8
Answer:
x = 8
Step-by-step explanation:
3x + 2y = 72
Put y as (3x), and solve for x.
3x + 2(3x) = 72
Multiply 2(3x).
3x + 6x = 72
Add like terms 3x and 6x.
9x = 72
Divide 9 into both sides and isolate x.
x = 72/9
x = 8
The value of x is 8.
Five pulse rates are randomly selected from a set of measurements. The five pulse rates have a mean of 65.4 beats per minute. Four of the pulse rates are 57, 55, 62, and 83. a. Find the missing value. b. Suppose that you need to create a list of n values that have a specific known mean. Some of the n values can be freely selected. How many of the n values can be freely assigned before the remaining values are determined? (The result is referred to as the number of degrees of freedom.)
Answer:
a) 70b) n-1Step-by-step explanation:
Mean is defined as the sum total of data divided by the total number of data.
[tex]\overline x = \frac{\sum Xi}{N}[/tex]
Xi are individual data
N is the total number of data = 5
Given the mean of the pulse rate = 65.4
a) Let the 5pulse rates be our data as shown: 57, 55, 62, 83 and y where y is the missing value. According to the formula:
[tex]65.4 = \frac{57+55+62+83+y}{5}[/tex]
[tex]65.4 = \frac{257+y}{5}\\ 257+y = 65.4*5\\257+y = 327\\y = 327-257\\y = 70[/tex]
The missing value is 70
b) Since the total list of numbers is n values with a specific known mean, if some of this values can be freely selected, the number of n values that can be freely assigned before the remaining values are determined is any values less than n i.e n-1 values.
From the formula for calculating mean:
[tex]\overline x = \frac{\sum Xi}{N}\\{\sum Xi} = N\overline x[/tex]
This shows that the sum of all the values is equal to the product of the total values and the mean value. Since we can freely choose n-1 values, then sum of the set of data can be written as [tex]\sum \sumx^{n-1} _i__=_1 Xi[/tex]
[tex]\sum \sumx^{n-1} _i__=_1 Xi \ =\ N \overline x[/tex]
The number of n values which is referred to the degree of freedom is n-1
What is the area of the triangle below?
18
Answer:
D. 32 sq. unit s
Step-by-step explanation:
4×18/2=32
Explain why it isn’t always best to solve a system of equations by graphing. Give an example in which this is the case.
Answer:
the graph may be difficult to drawthe answer may be difficult to read from the graphStep-by-step explanation:
We assume the concern is with systems of linear equations. Systems of non-linear equations will have some of the same issues.
A system of equations is nicely solved by graphing if the graph(s) can be made easily and if the solutions can be easily read from the graph. If those conditions are not met, then solving a system graphically may not be feasible.
The attached graph shows a system of equations that would be difficult to solve graphically by hand. (A graphing calculator helps immensely.)
The system in our example is ...
x - 3y = 38x -31y = -43We have chosen the second equation to have a slope similar to that of the first equation, so that the lines gradually come together. That makes it difficult to read the point of intersection from the graph. The second equation also has no obvious integer solutions, so graphing it in the first place can be difficult. If the solutions have a fractional part, the exact value of the fraction may be impossible to determine from the graph.
In short, ...
creating the graph(s) may be difficultreading the graph with sufficient precision may be difficultA bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected. Identify each of the following, rounding your answers to the nearest cent when appropriate:
1. $mu=?
2. $sigma=?
3. $=n=$
4. $mu_{overlinex}=$x=?
5. $sigma_{overlinex}=$x=?
Answer:
1. [tex]$ \mu = \$306,500 $[/tex]
2. [tex]\sigma = \$24,500[/tex]
3. [tex]n = 150[/tex]
4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]
5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]
Step-by-step explanation:
The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500.
From the above information, we know that,
The population mean is
[tex]$ \mu = \$306,500 $[/tex]
The population standard deviation is
[tex]\sigma = \$24,500[/tex]
Suppose a random sample of 150 Americans is selected
[tex]n = 150[/tex]
Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.
The sample mean would be the same as the population mean that is
[tex]$ \mu_{x}= \mu = \$306,500 $[/tex]
The sample standard deviation is given by
[tex]\sigma_x = \frac{\sigma}{\sqrt{n} }[/tex]
Where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.
[tex]\sigma_x = \frac{24,500}{\sqrt{150} } \\\\\sigma_x = \$ 2,000 \\\\[/tex]
Therefore, the required parameters are:
1. [tex]$ \mu = \$306,500 $[/tex]
2. [tex]\sigma = \$24,500[/tex]
3. [tex]n = 150[/tex]
4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]
5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]
Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
What is the approximate measure of angle K? Use the law of sines to find the answer.
20°
34°
41°
53°
Answer:
The approximate measure of angle K is 34°
Step-by-step explanation:
In ΔJKL
∠L = 105°
JK = 4.7
JL = 2.7
Sine Rule:
[tex]\frac{SinA}{a} = \frac{SinB}{b}= \frac{SinC}{c}[/tex]
So,[tex]\frac{SinL}{JK} = \frac{SinK}{JL}\\\frac{SinL}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105 \times 2.7}{4.7} = SinK\\\frac{(0.9659 \times 2.7)}{4.7} = Sin K\\\frac{2.60793}{4.7} = Sin K\\0.5549 = Sin K\\Sin^{-1}(0.5549)= K\\K = 33.70[/tex]
K ≈ 34°
So, Option B is true
Hence The approximate measure of angle K is 34°
Answer:
B) 34
Step-by-step explanation:
Adult male heights are a normal random variable with mean 69 inches and a standard deviation of 3 inches. Find the height, to the nearest inch, for which only 8 percent of adult males are taller (i. find the 92nd percentile)
Answer:
The height (corresponding to the [tex] \\ 92^{nd}[/tex] percentile) is (to the nearest inch) 73 inches (and, approximately, only 8% of adult males are taller than this height.)
Step-by-step explanation:
Roughly speaking, the [tex] \\ 92^{nd}[/tex] percentile is the x value (in the distribution) for which 92% of the observations in the [normal] distribution are below this x value, and 8% of the observations are above this x value.
To answer this question, we already know that:
Heights are a normal random variable, i.e, it follows a normal distribution.The mean for this distribution is [tex] \\ \mu = 69[/tex] inches.The standard deviation is [tex] \\ \sigma = 3[/tex] inches.Strategy for solving the question
For solving this, we have to use here the following key concepts: z-scores, the cumulative standard normal distribution, and the cumulative standard normal table.
Z-scores
To find the [tex] \\ 92^{nd}[/tex] percentile, we can use z-scores or standardized values. A z-score is a value that tells us the distance in standard deviations units from the mean. When the z-score is positive, it means that the value is above the mean. A negative indicates that the z-score is below the mean. The formula to obtain a z-score is as follows:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score.[tex] \\ \mu[/tex] is the mean.[tex] \\ \sigma[/tex] is the standard deviation.Cumulative standard normal distribution and corresponding table
We still need to know the corresponding z-score, z, for the cumulative probability of 92%. For this, we have to consult the standard normal table, available on the Internet or in any Statistics books.
In this case, we look in the different columns of the standard normal table a probability value (exact or approximate) to 0.92 and then find the value for z that corresponds to this probability. The value for z is between 1.40 (0.91924) and 1.41 (0.92073).
Using z = 1.40 in [1], we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ 1.40 = \frac{x - 69}{3}[/tex]
Then, solving for x:
Multiplying by 3 at each side of the equation:
[tex] \\ 1.40 * 3 = x - 69[/tex]
Adding 69 at both sides of the equation:
[tex] \\ (1.40 * 3) + 69 = x[/tex]
[tex] \\ x = (1.40 * 3) + 69[/tex]
[tex] \\ x = 4.20 + 69[/tex]
[tex] \\ x = 73.20[/tex]
That is, the [tex] \\ 92^{nd}[/tex] percentile is 73.20 inches, and to the nearest inch, this percentile is 73 inches.
This result indicates that, approximately, 92% of the heights are below 73 inches, and only 8% of heights are taller than this height.
The shaded area in the graph below shows an area of 0.08076 (8.076%) for 73.20 inches.
Solve the equation? Help Please !!!?!?! 3-x/2>12
Answer:x<-18
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
-1/2x+3>12
Step 2: Subtract 3 from both sides.
-1/2x+3-3>12-3
-1/2x>9
Step 3: Multiply both sides by 2/(-1).
(2/-1)*(-1/2x)>(2/-1x)*(-1/2x)
X<-18
:D
AC =
Round your answer to the nearest hundredth.
A
5
35
B
C
Answer:
2.87 = AC
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 35 = AC /5
5 sin 35 = AC
2.867882182= AC
To the nearest hundredth
2.87 = AC
Tyler drew a figure that has two pairs of equal sides, four angles formed by perpendicular lines, and two pairs of parallel sides. What geometric term best describes the figure Tyler drew? What geometric term best describes the figure Tyler drew?
Answer:
A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.
The manager of a warehouse would like to know how many errors are made when a product’s serial number is read by a bar-code reader. Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.
Just to be sure, the manager has six more samples taken:
33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each
How do the mean and standard deviation change, based on all 12 samples?
Answer:
The mean and standard deviation changed to 23.5 and 14.62 respectively, based on all 12 samples.
Step-by-step explanation:
We are given that the Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.
Representing the data in tabular form;
X [tex]X - \bar X[/tex] [tex](X - \bar X)^{2}[/tex]
36 36 - 20.5 = 15.5 240.25
14 14 - 20.5 = -6.5 42.25
21 21 - 20.5 = 0.5 0.25
39 39 - 20.5 = 18.5 342.25
11 11 - 20.5 = -9.5 90.25
2 2 - 20.5 = -18.5 342.25
Total 1057.5
Now, the mean of these value is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{36+14+21+39+11+2}{6}[/tex]
= [tex]\frac{123}{6}[/tex] = 20.5
Standard deviation formula for discrete distribution is given by;
Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{1057.5 }{6-1} }[/tex] = 14.54
Now, the manager has six more samples taken:
33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each
So, the modified table would be;
X [tex]X - \bar X[/tex] [tex](X - \bar X)^{2}[/tex]
36 36 - 23.5 = 12.5 156.25
14 14 - 23.5 = -9.5 90.25
21 21 - 23.5 = -2.5 6.25
39 39 - 23.5 = 15.5 240.25
11 11 - 23.5 = -12.5 156.25
2 2 - 23.5 = -21.5 462.25
33 33 - 23.5 = 9.5 90.25
45 45 - 23.5 = 21.5 462.25
34 34 - 23.5 = 10.5 110.25
17 17 - 23.5 = -6.5 42.25
1 1 - 23.5 = -22.5 506.25
29 29 - 23.5 = 5.5 30.25
Total 2353
Now, the mean of these value is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{36+14+21+39+11+2+33+45+34+17+1+29}{12}[/tex]
= [tex]\frac{282}{12}[/tex] = 23.5
Standard deviation formula for discrete distribution is given by;
Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{2353 }{12-1} }[/tex] = 14.62
Gail baked some muffins. She sold 2/7 of the muffins on Monday. She sold 1/3 more of the muffins on Tuesdays than on Monday. What fraction of the muffins did Gail sell on the two days?
Which statements are true of the function f(x) = 3(2.5)x? Check all that apply
Answer:
The function is exponential.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers
The true statements are:
[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential functionThe function represents an exponential growthThe domain of the function is the set of all real numbersThe function is given as:
[tex]\mathbf{y = 3(2.5)^x}[/tex]
An exponential function is represented as:
[tex]\mathbf{y = ab^x}[/tex]
Where: a represents the initial value, and b represents the rate
This means that:
[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential function
By comparison:
[tex]\mathbf{b = 2.5}[/tex]
When b > 0, then the function represents an exponential growth
2.5 is greater than 0.
So, the function represents an exponential growth
Lastly, there is no restriction to the values of x.
So, the domain of the function is the set of all real numbers
Read more about exponential functions at:
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Suppose that there are six universities and each will produce five mathematics Ph.D.s this year, and there are five colleges that will be hiring seven, seven, six, six, five math Ph.D.s, respectively. No college will hire more than one Ph.D. from any given university. Will all the Ph.D.s get a job? Explain.
Answer:
No. If a collegue hire 7 math Ph.D.s, at least 2 will be from the same university.
The only way to have a job for all of them is that all colleges hire 6 math Ph.D.s, one from each university.
Step-by-step explanation:
If the condition is that no college will hire more than one Ph.D. from any given university, no college can hire more than 6 math Ph.D.s, as there are only 6 universities to choose from. If they hire seven, they have to repeat some university, violating the condition.
Then, the only way to have a job for all of them is that all colleges hire 6 math Ph.D.s, one from each university.
For every 1% increase in
unemployment, there is a 2%
decrease in potential GDP. This
creates a GDP gap. What is the GDP
gap when there is 4.5%
unemployment?
Answer:
The GDP gap is 9 % when there is 4.5 % unemployment.
Step-by-step explanation:
The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:
[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]
The GDP gap at a given increase in unemployment can be estimated by the following expression:
[tex]\frac{g}{u} = r[/tex]
[tex]g = r\cdot u[/tex]
Where:
[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.
[tex]u[/tex] - Increase in unemployment rate, measured in percentage.
[tex]g[/tex] - GDP gap, measured in percentage.
If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:
[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]
[tex]g = 9\,\%\,GDP[/tex]
The GDP gap is 9 % when there is 4.5 % unemployment.
Edwin has 3 1 2 gallons of green paint. He uses 2 3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage. How much paint does Edwin use for the mural?
Answer:
1 1/6
Step-by-step explanation:
Edwin used a quantity of 2.833 gallons of paint for the mural which is the difference between the quantity of paint at the beginning and the used for the bedroom.
We have been given that Edwin has 3 1/2 gallons of green paint. He uses 2/3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
To determine the quantity of paint Edwin used for the mural.
The quantity of paint Edwin used for the mural is the difference between the quantity of paint at the beginning and the used for the bedroom.
The quantity of paint used for the mural = 3 1/2 gallons - 2/3 gallons
The quantity of paint used for the mural = 3.5 - 0.66
The quantity of paint used for the mural = 2.833
Thus, Edwin used a quantity of 2.833 gallons of paint for the mural.
Learn more about the fractions here:
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find the equation of the line passing through the points (2,4) and (3,2). find both green and grey box
Answer:
y = -2x +8
Step-by-step explanation:
The 2-point form of the equation of a line is useful when two points are given.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (2 -4)/(3 -2)(x -2) +4
y = -2(x -2) +4
y = -2x +8
Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer:
Answer:
N(L) = 20
The expected number of left handed people is 20.
Step-by-step explanation:
Given;
Percentage of left handed people P(L) = 10%
Total number of selected people N(T) = 200
The Expected number of left handed people N(L) is;
N(L) = Total number of selected people × Percentage of left handed people/100%
N(L) = N(T) × P(L)/100%
Substituting the given values;
N(L) = 200 × 10%/100%
N(L) = 200 × 0.1
N(L) = 20
The expected number of left handed people is 20.
A cooler has a temperature of 32 degrees Fahrenheit. A bottled drink is placed in the cooler with an initial temperature of
70 degrees Fahrenheit. The function
[tex]f(t) = {ce}^{ (- kt)} + 32[/tex]
,represents the situation, where t is time in minutes, C is a
constant, and k is a constant.
After 3 minutes the bottle has a temperature of 42 degrees. What is the approximate value of k?
Answer:
[tex]k \approx 0.44[/tex]
Step-by-step explanation:
Given function:
[tex]f(t) = (ce)^{-kt}+32[/tex]
As per question statement:
Initial temperature of bottle is 70 [tex]^\circ F[/tex].
i.e. when time = 0 minutes, f(t) = 70 [tex]^\circ F[/tex]
[tex]70 = ce^{-k\times 0}+32\\\Rightarrow 38 = ce^{0}\\\Rightarrow c = 38[/tex]
After t = 3, f(t) = 42[tex]^\circ F[/tex]
[tex]42 = 38 \times e^{-k\times 3}+32\\\Rightarrow 42-32 = 38 \times e^{-3k} \\\Rightarrow 10 = 38 \times e^{-3k} \\\Rightarrow e^{3k} = \dfrac{38}{10}\\\Rightarrow e^{3k} = 3.8\\\\\text{Taking } log_e \text{both the sides:}\\\\\Rightarrow log_e {e^3k} = log_e {3.8}\\\Rightarrow 3k \times log_ee=log_e {3.8} (\because log_pq^r=r \times log_pq)\\\Rightarrow 3k \times 1=log_e {3.8}\\\Rightarrow 3k = 1.34\\\Rightarrow k = \dfrac{1.34}{3}\\\Rightarrow k \approx 0.44[/tex]
Hence, the value is:
[tex]k \approx 0.44[/tex]
How many pairs are shown ?????????
Answer:8 i ithink
Step-by-step explanation:
Answer:
12, go for 24.
Step-by-step explanation:
There are 6 sides of a cube.
There are 2 pairs of parallel line segments for each side.
6 x 2 = 12
Although that answer is not there, you should go for 24. Since there are 2 variables for each line segment, 12 x 2 = 24. Not sure, hope this helps.
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A group of campers is going to occupy 4 campsites at a campground. There are 14 campsites from which to choose. In how many ways can the campsites be chosen?
There are
possible ways to choose the campsites.
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Answer:
24024 are the total number of ways of choosing 4 campsites out of 14.
Step-by-step explanation:
We are given that there are a total of 14 campsite out of which 4 campsites are to be chosen.
It is a simple example of selection problem.
Number of ways to choose the first campsite = 14
Now, one campsite is chosen, 13 campsites are left.
Therefore,
Number of ways to choose the second campsite = 13
Now, one more campsite is chosen, 12 campsites are left.
Therefore,
Number of ways to choose the third campsite = 12
Now, one more campsite is chosen, 11 campsites are left.
Therefore,
Number of ways to choose the fourth campsite = 11
So, total number of ways for choosing 4 campsites out of 14:
14 [tex]\times[/tex] 13 [tex]\times[/tex] 12 [tex]\times[/tex] 11 = 24024
Hence, answer is 24024.
Consider the differential equation4y'' − 4y' + y = 0; ex/2, xex/2.Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]).The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) =
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
Answer:
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Step-by-step explanation:
Suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward along the z-axis a distance of 9 units. What are the coordinates of your position
Answer:
The coordinates of the new position are
(x, y, z) = (7, 0, -9)
Step-by-step explanation:
So assuming a 3D plane x, y, z
The starting point is the origin that is
(x, y, z) = (0, 0, 0)
Move a distance of 7 units along the positive x-axis
(x, y, z) = (7, 0, 0)
Then move a distance of 9 units downwards along the z-axis
downward = negative and upward = positive
(x, y, z) = (7, 0, -9)
Therefore, the coordinates of the new position are
(x, y, z) = (7, 0, -9)
Refer to the attached plot where the above coordinates are plotted on a 3D surface using an online 3D plotter.
Each small box corresponds to 1 unit.
The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.
Answer:
Step-by-step explanation:
Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation
V ' ( t ) = − 26400 e^− 0.49 t .
t = time (in days)
.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:
V'(6) = − 26400 e− 0.49 (6)
V'(6) = -26400e-2.94
V'(6) = -26400×-0.2217
V'(6) = $5852.88
V'(6) = $5,853 to nearest dollars
V'(6) = 585300cents to nearest cent
To get v(6), we need to get v(t) first by integrating the given function as shown:
V(t) = ∫−26400 e− 0.49 t dt
V(t) = -26,400e-0.49t/-0.49
V(t) = 53,877.55e-0.49t + C.
When t = 0, V(t) = $170,000
170,000 = 53,877.55e-0 +C
170000 = 53,877.55(2.7183)+C
170,000 = 146,454.37+C
C = 170,000-146,454.37
C = 23545.64
V(6) = 53,877.55e-0.49(6)+ 23545.64
V(6) = -11,945.63+23545.64
V(6) = $11,600 (to the nearest dollars)
Since $1 = 100cents
$11,600 = 1,160,000cents