The volume of the box shown in the diagram is 40π3 cubic units. Find the length of ‘x’.
Answer:
4: 4[tex]\pi^2[/tex]
Step-by-step explanation:
2[tex]\pi[/tex] x 5 x [tex]x[/tex] = 10[tex]\pi x[/tex]
10[tex]\pi x[/tex] = 40[tex]\pi ^3}[/tex]
x = 4[tex]\pi^2[/tex]
Answer:
4π units
Step-by-step explanation:
v=lwh
40π^3=2π×5×h
40π^3=10π^2×h
h=40π^3/10π^2
h=4π units
mark brianliest if my answer suit your question please.
An analysis of 8 used trucks listed for sale in the 48076 zip code finds that the power model ln(\hat{price})=3.748-0.1395ln(miles)ln(price^)=3.748−0.1395ln(miles), for price (in thousands of dollars) and miles driven (in thousands), is an appropriate model of the relationship. If a used truck has been driven for 47,000 miles, which of the following is closest to the predicted price for the truck?(A) $9.46(B) $24.80(C) $3,210.00(D) $9,460.00(E) $24,800.00
Answer:
(E) $24,800.00
Step-by-step explanation:
[tex]ln(\hat{price})=3.748-0.1395ln(miles)[/tex]
If a used truck has been driven for 47,000 miles
Miles=47 (in thousands)
We therefore have:
[tex]ln(\hat{price})=3.748-0.1395ln(47)\\ln(\hat{price})=3.2109\\$Take the exponential of both sides\\e^{ln(\hat{price})}=e^{3.2109}\\Price=e^{3.2109}\\$Price=24.80 \\Since the price is in thousands of dollars\\Price=24.80 X \$1000\\Predicted Price=\$24800.00[/tex]
The correct option is E.
Determine the next term in the sequence.
14,33,55,83,114....
Answer:
You can't find the next solution without more information.
Step-by-step explanation:
Suppose a simple random sample of size 50 is selected from a population with σ=10σ=10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
a. The population size is infinite.
b. The population size is N=50,000.N=50,000.
c. The population size is N=5000.N=5000.
d. The population size is N=500.N=500.
Answer:
a) [tex]\sigma_{\bar x} = 1.414[/tex]
b) [tex]\sigma_{\bar x} = 1.414[/tex]
c) [tex]\sigma_{\bar x} = 1.414[/tex]
d) [tex]\sigma _{\bar x} = 1.343[/tex]
Step-by-step explanation:
Given that:
The random sample is of size 50 i.e the population standard deviation =10
Size of the sample n = 50
a) The population size is infinite;
The standard error is determined as:
[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]
[tex]\sigma_{\bar x} = 1.414[/tex]
b) When the population size N= 50000
n/N = 50/50000 = 0.001 < 0.05
Thus ; the finite population of the standard error is not applicable in this scenario;
Therefore;
The standard error is determined as:
[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]
[tex]\sigma_{\bar x} = 1.414[/tex]
c) When the population size N= 5000
n/N = 50/5000 = 0.01 < 0.05
Thus ; the finite population of the standard error is not applicable in this scenario;
Therefore;
The standard error is determined as:
[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]
[tex]\sigma_{\bar x} = 1.414[/tex]
d) When the population size N= 500
n/N = 50/500 = 0.1 > 0.05
So; the finite population of the standard error is applicable in this scenario;
Therefore;
The standard error is determined as:
[tex]\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }[/tex]
[tex]\sigma _{\bar x} = \sqrt{\dfrac{500-50}{500-1} }\dfrac{10}{\sqrt{50} } }[/tex]
[tex]\sigma _{\bar x} = 1.343[/tex]
A Biology test contains 10 multiple choice questions each with 5 choices and one correct answer. If a law school student just randomly guesses on each of the 10 questions, i.e., the probability of getting a correct answer on any given question is 0.2. Assume that all questions are answered independently. (a) What is the probability that the student answers at least 9 questions correctly
Answer:
0.0004% probability that the student answers at least 9 questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. All questions are answered independently. This means that we use the binomial distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question, we have that:
[tex]n = 10, p = 0.2[/tex]
What is the probability that the student answers at least 9 questions correctly
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0.000004[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0 [/tex]
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.000004 + 0 = 0.000004[/tex]
0.0004% probability that the student answers at least 9 questions correctly
What is the first step of the following division problem? (8x3 – x2 + 6x + 7) ÷ (2x – 1)
Answer:
The first step is to determine how many times 2x goes into 8x^3
Step-by-step explanation:
The first step is to determine how many times 2x goes into 8x^3
4x^2
--------------------------
2x-1 | (8x3 – x2 + 6x + 7
8x^3 -4x^2
Answer:
A
Step-by-step explanation:
i just took the test
A large western state consist of 4341 million acres of land. Approximately 83% of this land is federally owned. Find the number of acres that are not federally owned
Answer:
737.97 acres
Step-by-step explanation:
Given
Approximately 83% of a large western state land is federally owned.
Total land in percentage will be 100%
% of land not federally owned = Total land in percentage - % of land federally owned = 100% - 83% = 17%
Thus, percentage of land not federally owned = 17% of total land
Also given "A large western state consist of 4341 million acres of land"
Therefore,
number of acres that are not federally owned = 17% of total western state land
number of acres that are not federally owned = 17/100 * 4341 = 737.97
Thus, 737.97 acres of western state land are not federally owned.
which law would you use to simply the expression 3^10/3^4 quotient power power of a quotient product of powers power of a product
2.24 Exit poll: Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walker. They found that 57% of the respondents voted in favor of Scott Walker. Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree, while 45% of those who voted against Scott Walker had a college degree. Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. What is the probability that he voted in favor of Scott Walker? (please round to 4 decimal places)
Answer:
0.4929 = 49.29% probability that he voted in favor of Scott Walker
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Having a college degree.
Event B: Voting for Scott Walker.
They found that 57% of the respondents voted in favor of Scott Walker.
This means that [tex]P(B) = 0.57[/tex]
Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree
This means that [tex]P(A|B) = 0.33[/tex]
Probability of having a college degree.
33% of those who voted for Scott Walker(57%).
45% of those who voted against Scott Walker(100 - 57 = 43%). So
[tex]P(A) = 0.33*0.57 + 0.45*0.43 = 0.3816[/tex]
What is the probability that he voted in favor of Scott Walker?
[tex]P(B|A) = \frac{0.57*0.33}{0.3816} = 0.4929[/tex]
0.4929 = 49.29% probability that he voted in favor of Scott Walker
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
78.5 cm^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
A = pi (5)^2
A = 25pi
Letting pi = 3.14
A = 25(3.14)
A =78.5 cm^2
Letting pi be the pi button
A =78.53981634
Rounding to the nearest tenth
78.5
Answer:
78.5 cm²
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr²
We know the radius of the circle is 5 centimeters.
r=5
Substitute 5 in for r.
a=π(5²)
Evaluate the exponent. 5² is equal to 5*5, which equals 25.
a=π(25)
Multiply 25 and pi
a=78.5398163397
Round to the nearest tenth. The 3 in the hundredth place tells use to leave the 5 in the tenths place as is.
a≈78.5
Add appropriate units. Area always uses units², and the units in this case are centimeters.
a≈78.5 centimeters²
The area of the circle is about 78.5 square centimeters.
Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications. A sample of one day's output of kortholts from the Melodic Kortholt Company showed the following frequencies: Plant A Plant B Row Total Specification Met 85 35 120 Specification Not Met 15 25 40 Column Total 100 60 160 Find the chi-square test statistic for a hypothesis of independence. Multiple Choice 7.22 14.22 -0.18 14.70
Answer:
The value of Chi-square test statistic for a hypothesis test of independence is 14.22.
Step-by-step explanation:
The data provided is for one day's output of Kortholt's from the Melodic Kortholt Company.
The formula to compute the chi-square test statistic for a hypothesis of independence is:
[tex]\chi^{2}=\sum {\frac{(O-E)^{2}}{E}}[/tex]
The formula to compute the expected frequencies (E) is:
[tex]E=\frac{\text{Row Total}\times \text{Column Total}}{N}[/tex]
Consider the Excel output attached.
Compute the value of Chi-square test statistic as follows:
[tex]\chi^{2}=\sum {\frac{(O-E)^{2}}{E}}[/tex]
[tex]=1.333+2.222+4.000+6.667\\=14.222\\\approx 14.22[/tex]
Thus, the value of Chi-square test statistic for a hypothesis test of independence is 14.22.
four apples and one banana cost £1.40 seven apples and one banana cost £2.00 work out the cost of an apple and the cost of a banana .
Answer:
apple: £0.20banana: £0.60Step-by-step explanation:
Let "a" and "b" represent the costs of one apple and one banana, respectively. Then the purchases can be written ...
4a +b = 1.40
7a +b = 2.00
Subtracting the first equation from the second gives ...
(7a +b) -(4a +b) = (2.00) -(1.40)
3a = 0.60 . . . . simplify
a = 0.20 . . . . . .divide by 3
Using this in the first equation, we have ...
4(0.20) +b = 1.40
b = 0.60 . . . . . subtract 0.80
The cost of an apple is £0.20; the cost of a banana is £0.60.
What value of x makes 3(x + 4) = 3x + 4 true?
Well lets see.
[tex]3(x+4)=3x+4\implies 12 = 4\implies x\notin\mathbb{C}[/tex].
There are no such x-es that satisfy the equation.
Oliver had $43 on the day before his birthday. After he received some money for his birthday, he had $68. Write an equation to find how much money Oliver received for his birthday.
Answer:
$25
Step-by-step explanation
If oliver had $43 before his birthday he was given (+) an amount of money, in order to find out how much money was given you need to reverse the equation (-) $68-$43= $25
The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the standard deviation is 50. A subject earns a score of 155. How many standard deviations from the mean is the value 155
Answer:
The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].
Step-by-step explanation:
The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score: an observation from the normally distributed data that we want standardize using [1].[tex] \\ \mu[/tex] is the population mean.[tex] \\ \sigma[/tex] is the population standard deviation.Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.
For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.
These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.
A subject earns a score of 155. How many standard deviations from the mean is the value 155?
From the question, we know that:
x = 155.[tex] \\ \mu = 155[/tex].[tex] \\ \sigma = 50[/tex].Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{155 - 155}{50}[/tex]
[tex] \\ z = \frac{0}{50}[/tex]
[tex] \\ z = 0[/tex]
As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:
[tex] \\ x = \mu[/tex]
Therefore
[tex] \\ z = 0[/tex]
So, the value 155 is zero standard deviations from the [population] mean.
Which is enough information to prove that line s is parallel to line t
Answer:
line s and t would not meet even if you extend them and also they have the same slope and gradient
Simplify -|-5 + 2|. this is all of the question
Answer:
-3
Step-by-step explanation:
-(absolute value of -3)
-(3)
-3
Over which interval is the graph of fx =-x2 + 3x + 8 increasing
Answer:
Step-by-step explanation:
it is increasing in [tex]]-\infty;3/2][/tex]
because this is like
[tex]f(x)=ax^2+bx+c[/tex]
where a > 0
and -b/a=3/2
Section 1: Write the following times in 24-hour clock time:
a) 7:15 a.m -
b) 1:05 am
c) 2:01 p.m
d) 9:22 p.m
e) 12:25 am
Section 2: Write the following times in 12-hour clock time.
a) 1155 hours
b) 1005 hours
c) 1714 hours
d) 0756 hours
e) 1345 hours
Answer:
Section 1:
a) 7:15 a.m - 19:15
b) 1:05 am - 01:05
c) 2:01 p.m - 14:01
d) 9:22 p.m - 21:22
e) 12:25 am- 24:25
Section 2:
a) 1155 hours - 11:55am
b) 1005 hours -10:05am
c) 1714 hours - 5:14pm
d) 0756 hours - 7:56am
e) 1345 hours- 1:45pm
Answer:
12:25 am= 00:25
Step-by-step explanation:
As part of an insurance company’s training program, participants learn how to conduct an analysis of clients’ insurability. The goal is to have participants achieve a time in the range of 30 to 47 minutes. Test results for three participants were: Armand, a mean of 37.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 38.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 38.5 minutes and a standard deviation of 2.9 minutes.
a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Participants :
Armand: Cpk _____ Cp Capable ? No/Yes
Jerry: Cpk _____ Capable ? Yes/No
Melissa Cp ________ No/Yes
b.Can the value of the Cpk exceed the value of Cp for a given participant?
yes or no
Answer:
1) cpk < 1.33, therefore it is not capable
b) cpk = 1.33, therefore it is capable
c) cpk < 1.33, therefore it is not capable
2) Cpk can never be greater than the Cp, but can be equal to it
Step-by-step explanation:
Upper limit (USL) = 47 minutes and Lower limit (LSL) = 30 minutes
1)
a) mean (μ) = 37 minutes, standard deviation (σ) = 3 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-37}{3*3},\frac{37-30}{3*3} )=min(1.11,0.78)=0.78[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*3}=0.94[/tex]
cpk < 1.33, therefore it is not capable
b) mean (μ) = 38 minutes, standard deviation (σ) = 2 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38}{3*2},\frac{38-30}{3*2} )=min(1.5,1.33)=1.33[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2}=1.42[/tex]
cpk = 1.33, therefore it is capable
c) a) mean (μ) = 38.5 minutes, standard deviation (σ) = 2.9 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38.5}{3*2.9},\frac{38.5-30}{3*2.9} )=min(0.98,0.98)=0.98[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2.9}=0.98[/tex]
cpk < 1.33, therefore it is not capable
2) Cpk can never be greater than the Cp, but can be equal to it
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $26,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $292,000 in revenues, how many sections of each course should it offer?
Finite Math section(s)
Applied Calculus section(s)
Computer Methods section(s)
Answer:
meh
Step-by-step explanation:
A woman forgot her bank ATM PIN but she was able to recall some of the pin.
1)the 1st digit is half of the 2nd pin
2)the sum of 2nd and 3rd is equal to 10
3)the 4th is equal to the 2nd plus 1
4)the sum of all digits is 23
show workings please
what is the ATM digit?
The PIN is 4829
Step-by-step explanation:
let s take 4 numbers a b c and d
the PIN is abcd
we know that
(1) a = b/2
(2) b+c=10
(3) d=b+1
(4) a+b+c+d=23
from (2) c = 10 - b
from (3) d = b + 1
so (4) gives
b/2 + b + 10 - b + b +1 = 23
so
3/2 b = 23 -11 = 12
b = 12*2/3 = 8
so d = 9
c = 10-8=2
and a = 4
so the PIN is 4829
thank you
1. Two people have $10 to divide between themselves. Each person names a number (nonnegative integer) no more than 10. If the sum of the two numbers is at most 10, each person gets the named amount of dollars, and the rest of the money is destroyed. If the sum exceeds 10, and the numbers are different, the person who has named the smaller number, receives the corresponding number of dollars, and the second person receives the rest. If the sum exceeds 10, and the numbers are equal, each person receives $5. Determine the be
Answer:
Step-by-step explanation:
Determine the best response of each player to each of the other player’s actions; plot them in a diagram and thus find the Nash equilibria of the game.
The best response for player 2 can be stated as:
(where X1 equals the dollar that a person names and Y2(X1) being the amount the person receives)
X1 Y2(X1)
0 10
1 9,10
2 8,9,10
3 7,8,9,10
4 6,7,8,9,10
5 5,6,7,8,9,10
6 5,6
7 6
8 7
9 8
10 9
Th best responses for player 1 would be the same.
Nash equilibria is the set of strategies that every person forms given no person has any incentive to change. Hence, we can say that there are 4 Nash equilibria: (5,5) , (5,6) , (6,5) , (6,6)
Please help. I’ll mark you as brainliest if correct!!!!!
[tex]x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9[/tex]
Answer:
x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9
Step-by-step explanation:
A fair 6-sided die is colored in the following way: The faces of 1 - 3 are colored red. The faces of 4 and 5 are colored blue. The face of 6 is colored green. What is the probability that the face comes up red OR a prime number
Answer:
There are 6 total possibilities, 3 red faces and 3 prime numbers however, 2 and 3 are prime numbers and they are red as well so total successful outcomes = 3 + 3 - 2 = 4. This means that the answer is 4 / 6 or 2 / 3.
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]1 \: 2\:3[/tex] are red
[tex]5[/tex] is prime.
Total of [tex]4[/tex] possibilities out of [tex]6[/tex]
[tex]\frac{4}{6}[/tex]
A square of area 36cm2 is cut to make two rectangles, A and B The ratio of Area A to Area B is 2 : 1 Work out the dimensions of rectangle A and B
(Need help with this question)
Answer:
Given..hope it helps
Step-by-step explanation:
Area of square= 36cm2 = total area
Side of square= √36= 6cm
Ratio a:b = 2:1
so let's take total area as 3x
while a is 2x and b is 1x
3x= 36 (given)
x= 36/3 = 12
so area of each rectangle--
area A= 2x= 24cm2
area B= x= 12cm2
While finding the dimensions, they both have a common length since they are from the same square which will be 6cm (side)
So,
Dimensions of rectangle A= 6cm * 4cm
Dimensions of rectangle B= 6cm * 2cm
An equilateral triangle have always _________ vertex and _______ lines of symmetry.
a) (3 , 1)
b) ( 4, 0)
c) (3 , 3 )
d) (3, 2 )
Answer:
hey mate,
here is your answer. Hope it helps you.
C-(3,3)
Step-by-step explanation:
An equilateral triangle, which has three equal sides, has three lines of symmetry. This is because you can fold an equilateral triangle in three halves and the are equal. Hence an equilataral triangle has three vertices and 3 lines of symmetry.
An organization will give a prize to a local artist will be randomly chosen from among 6 painters,2 sculptors, and 9 photographers. What is the probability that the artist chosen will be a painter or a sculptor?
Answer: [tex]\bold{\dfrac{8}{17}=47.1\%}[/tex]
Step-by-step explanation:
[tex]\dfrac{\text{painter or sculptor}}{\text{total artists}}=\dfrac{6+2}{6+2+9}=\dfrac{8}{17}[/tex]
a line has a slope of -3/4 and passes through the point (-5, 4). what is the equation of the line?
Answer:
y = -3/4x-1/4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = -3/4x +b
We have a point (-5,4)
4 = -3/4 (-5) +b
Changing to a common denominator
16/4 = 15/4 +b
subtracting 15/4 from each side
16/4-15/4 = -15/4 +15/4 +b
1/4 = b
y = -3/4x-1/4
Answer:
book
Step-by-step explanation:
kmgktn
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
HELP PLEASE
Answer:
All real numbers greater than or equal to -3
Step-by-step explanation:
First look at graph where the line points to which direction of the graph
And look for any closed or open circles in the graph
Since in the graph has a close circle at (-3,-2) meaning it includes that x-value for its domain.
With the graph going to positive infinity it states that the domain is all real numbers.
So in conclusion it has a domain of all real numbers greater than or equal to -3