Answer:
Step-by-step explanation:
The given equations are
x + y = 6- - - - - - - - -1
y + z = 6- - - - - - - -2
x + z = 6- - - - - - - - - 3
From equation 2, y = 6 - z
Substituting y = 6 - z into equation 1, it becomes
x + 6 - z = 6
x - z = 6 - 6
x - z = 0
x = z
Substituting x = z into equation 3, it becomes
z + z = 6
2z = 6
z = 6/2
z = 3
x = 3
Substituting x = 3 into equation 1, it becomes
3 + y = 6
y = 6 - 3
y = 3
ax + by + cz = 0
3a + 3b + 3c = 0
3(a + b + c) = 0
Therefore, it is impossible
= [70 + (-30)] + [2 + (-9)] + [0.3 + (-0.10]
Answer:
33.2
Step-by-step explanation:
70−30+2−9+0.3−0.1
=40+2−9+0.3−0.1
=40+−7+0.3−0.1
=33+0.3−0.1
=33+0.2
=33.2
Answer:
33.2
Step-by-step explanation
If we start from the left and work our way right:
70+(-30) is the same as 70-30 which would give 40
2+(-9) is the same as 2-9 which would give -7
0.3(-0.1) is the same as 0.3-0.1 which would give 0.2
now if you put them together
40-7+.2 gives 33.2
An AP news service story, printed in the Gainesville Sun on May 20, 1979, states the following with regard to debris from Skylab striking someone on the ground: "The odds are 1 in 150 that a piece of Skylab will hit someone. But 4 billion people ... live in the zone in which pieces could fall. So any one person’s chances of being struck are one in 150 times 4 billion—or one in 600 billion." Do you see any inaccuracies in this reasoning?
Answer:
The odds are one in approximately 27 million.Not one in 600 billionStep-by-step explanation:
From the news story, we are told that:
The odds are 1 in 150 that a piece of Skylab will hit someone.
However, 4 billion people live in the zone in which pieces could fall.
Therefore, any one person’s chances of being struck are:
[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]
Therefore, the odds are one in approximately 27 million.
The inaccuracy presented in this reasoning was that the odds are one in 600 billion.
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive positive that is the probability that the bureau finds a match given that the lead at the crime scene and the lead in the possession of the suspect are actually from two differant melts or sources. To estimate the false positive rate the bureau collected 1851 bullets that the agency was confident all came from differant melts. The using its established ctireria the bureau examined every possible pair of bullets and found 658 matches. Use this info to to compute the chance of a false positive.
Answer:
Step-by-step explanation:
Given that, we have 1851 bullets that we KNOW are NOT MATCHES of one another. One by one they examine two bullets at a time.
So, there are 1851 bullets but each time we choose 2.
We have, N choose K = N! / K! (N-k)!
Here, N = 1851 and K = 2
Therefore, 1851 choose 2 = 1851! / 2! (1851-2)!
= 1851! / 2! * 1849!
= 1712175 Possible Combinations
Out of these 653 are false positive.
The chance of getting false positive is = 658 / 1712175
= 0.000384
= 0.0384 %
Therefore, The correct option is
The chance of false positive is 0.0384% Because this probability is sufficiently small (< or = 1%) There is high confidence in the agency's forensic evidence.
What’s the Midpoint of (2,-1) and (1,-2)
Answer:
(3/2,-3/2)
Step-by-step explanation:
The midpoint of (2,-1)(1,-2) is (3/2,-3/2)
Answer:
(1.5,-1.5)
You have to remember the formula to find mid-point and that is:
[tex]midpoint = ( \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} )[/tex]
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
can someone please help meee!???
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where t is the time (in years)
(a) Find the number of feet that the tree will grow in the second year.
(b) Find the number of feet the tree will grow in the third year.
(c) The total number of feet grown during the second year is_____________ ft.
Answer:
a) 0.5367feetb) 0.5223feetc) 0.7292feetStep-by-step explanation:
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown;
[tex]\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C[/tex]
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
[tex]\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet[/tex]
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
[tex]\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet[/tex]
c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown
[tex]\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet[/tex]
The population P of a culture of Pseudomonas aeruginosa bacteria is given by P = −1718t2 + 82,000t + 10,000, where t is the time in hours since the culture was started. Determine the time(s) at which the population was 600,000. Round to the nearest hour.
Answer:
Rounding to the nearest hour, the times at which the population was 600,000 was at 9 hours and at 39 hours.
Step-by-step explanation:
Determine the time(s) at which the population was 600,000.
This is t for which P(t) = 600000. To do this, we solve a quadratic equation.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]P(t) = -1718t^{2} + 82000t + 10000[/tex]
We have to find t for which P(t) = 600000. Then
[tex]600000 = -1718t^{2} + 82000t + 10000[/tex]
[tex]-1718t^{2} + 82000t - 590000 = 0[/tex]
So [tex]a = -1718, b = 82000, c = -590000[/tex]
Then
[tex]\bigtriangleup = 82000^{2} - 4*(-1718)*(-590000) = 2669520000[/tex]
[tex]t_{1} = \frac{-82000 + \sqrt{2669520000}}{2*(-1718)} = 8.8[/tex]
[tex]t_{2} = \frac{-82000 - \sqrt{2669520000}}{2*(-1718)} = 38.9[/tex]
Rounding to the nearest hour, the times at which the population was 600,000 was at 9 hours and at 39 hours.
URGENT!! MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
13. Assume that you have a square. What can you conclude from applying the law of detachment to this conditional?
If you have a square, then you have a rectangle.
A) You have a quadrilateral.
B) All sides are the same length.
C) Squares and rectangles are the same.
D) You have a rectangle.
14. Which two theorems would justify that m∠4 = m∠6, given that m∠5 = m∠6 in the diagram below?
IMAGE BELOW
A) vertical angles theorem, consecutive interior angles theorem
B) vertical angles theorem, alternate interior angles theorem
C) right angles theorem, exterior angles theorem
D) corresponding angles theorem, angle addition theorem
Answer:
d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.
D: i am sure about this.
Step-by-step explanation:
From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.
corresponding angles i believe since they are matching
I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.
4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.
Answer:
13. B
14. D
Step-by-step explanation:
13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.
14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.
2x + 3=-7?what is this even mean
Answer:
2 times some thing and plus 3 equals -7
Step-by-step explanation:
x = -5
Given fix) = 3x- 1 and g(x) = 2x-3, for which value of x does g(x) = f(2)?
X=
2
О
X= 2
NDI
X=
x=4
Answer:
The value of X would be 4.
Answer:
x=4
Step-by-step explanation:
f(2)=3*2-1=5
g(x)=2x-3=5
2x=8
x=4
If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).
Answer:
Step-by-step explanation:
If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).
a)
[tex]L = \lim_{n \to \infty} b_n \\\\\\L= \lim_{n \to \infty} n^{\frac{5.6}{n} }[/tex]
Log on both sides
[tex]In (L) = \lim_{n \to \infty} In (n)^{\frac{5.6}{n} }\\\\= \lim_{n \to \infty} \frac{5.6}{n} In(n)[/tex]
[tex]=5.6 \lim_{n \to \infty} \frac{d}{dn} In(n)/\frac{d}{dn} (n)\\\\=5.6 \lim_{n \to \infty} \frac{1}{n} /1 \\\\=5.6 \lim_{n \to \infty} \frac{1}{n} \\\\=5.6 \times 0\\\\In(L) =0\\\\L=e^0\\\\L=1[/tex]
[tex]\therefore \lim_{n \to \infty} (n)^{\frac{5.6}{n} =1[/tex]
The limit value of given sequece is 1.
To understand more, check below explanation.
Limit of function:The given sequence is,
[tex]b_{n}=n^{5.6/n}[/tex]
We have to find limit of above sequence.
[tex]L=\lim_{n \to \infty} b_n \\\\L=\lim_{n \to \infty}n^{5.6/n} \\\\ln(L)=\lim_{n \to \infty}\frac{5.6}{n}ln(n) \\\\ln(L)=5.6\lim_{n \to \infty}\frac{ln(n)}{n} \\\\ln(L)=5.6\lim_{n \to \infty}\frac{1/n}{1} \\\\ln(L)=5.6*0=0\\\\L=e^{0}=1[/tex]
Therefore, the limit value of given sequece is 1.
Learn more about the limit of function here:
https://brainly.com/question/2166212
B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.
Answer:
19.8 cm
Step-by-step explanation:
Angle B is the complement of angle A, so we have this relation for the angles:
B/A = 3/2 = (90°-A)/A
2(90° -A) = 3A . . . . . cross multiply
180° = 5A . . . . . . . . . eliminate parentheses, add 2A
36° = A . . . . . . . . . . . divide by 5
The relations expressed by the mnemonic SOH CAH TOA remind you that ...
Cos = Adjacent/Hypotenuse
cos(A) = AC/AB
AB = AC/cos(A) = (16 cm)/cos(36°)
AB ≈ 19.8 cm
In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows:
Disk: 269.0, 249.3, 255.2, 252.7, 247.0, 261.6
Oval: 268.8, 260.0, 273.5, 253.9, 278.5, 289.4, 261.6, 280.2 Can you conclude that the mean dissolve times differ between the two shapes? Conduct a hypothesis test at the
α = 5% level.
a. State the appropriate null and alternative hypotheses.
b. Compute the test statistic.
c. Compute the P-value.
d. State the conclusion of the test in the context of this setting.
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.
The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.
We would set up the hypothesis.
a) The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
For disk shaped,
Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8
Standard deviation = √(summation(x - mean)²/n
n1 = 6
Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54
Standard deviation, s1 = √(337.54/6) = 7.5
For oval shaped,
Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375
n2 = 8
Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875
Standard deviation, s2 = √(991.75875/8) = 11.1
b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
Therefore,
t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)
t = - 3
c) The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46
df = 12
We would determine the probability value from the t test calculator. It becomes
p value = 0.011
d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes
According to a survey of business executives, 78% received a pay raise when they asked for one. A random sample of four executives was selected. The probability that all four received a raised when they asked for one is ________. 0.056 0.127 0.237 0.370
Answer:
The probability that all four received a raised when they asked for one is 0.370.
Step-by-step explanation:
Let the random variable X represent the number of business executives who received a pay raise when they asked for one.
The probability that a business executives received a pay raise when they asked for one is, p = 0.78.
A random sample of n = 4 executives was selected.
The events of any executive receiving a pay raise when they asked for one is independent of the others.
The random variable X follows a Binomial distribution with parameters n = 4 and p = 0.78.
The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.78)^{x}\ (1-0.78)^{4-x};\ x=0,1,2,3...[/tex]
Compute the probability that all four received a raised when they asked for one as follows:
[tex]P(X=4)={4\choose 4}\ (0.78)^{4}\ (1-0.78)^{4-4}[/tex]
[tex]=1\times 0.37015056\times 1\\\\=0.37015056\\\\\apporx 0.370[/tex]
Thus, the probability that all four received a raised when they asked for one is 0.370.
Do the points shown represent additive inverses? Explain why or why not
Answer:
Yes additive inverse is two complete opposite numbers if added = 0
Answer:
additive
Step-by-step explanation:
Because the point is not past the postive live or below the negative.
PLEASE HELP
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)^2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer:
Step-by-step explanation:
F(x) results in a parabola with vertex (0,0) wich mean there is only one x-int at that point. g(x) has been shifted the grapgh of f(x) to the right by to units and down by three unites. Now our vertex lies in the point (2,-3) and since the graph was move dow i=of the x-axis we now have two different x-intercepts.
Brian invests £6300 into his bank account.
He receives 4.9% per year compound interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
Amount that Brian has after 2 years = £6932.53
Step-by-step explanation:
To find, the amount that Brian will have after 2 years:
Formula for amount where compound interest is applicable:
[tex]A = P \times (1+\dfrac{R}{100})^t[/tex]
Where A is the amount after t years time
P is the principal.
R is the rate of interest.
In the question, we are given the following details:
Principal amount,P = £6300
Rate of interest,R = 4.9%
Time,t = 2 years
Putting the values in formula:
[tex]A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53[/tex]
Hence, Amount that Brian has after 2 years = £6932.53
Answer:
THE ANSWER IS ABOVE
Step-by-step explanation:
hahahaha
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the favorite sports of respondents are identified as 100 for basketball comma 200 for baseball comma 300 for football comma and 400 for anything else. The average (mean) is calculated for 597 respondents and the result is 256.1 .The data are at the _________________
level of measurement.
Answer:
The data are at the Nominal level of measurement.
The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement.
Step-by-step explanation:
The objective here is to Identify the level of measurement of the data, and explain what is wrong with the given calculation.
a)
The data are at the Nominal level of measurement due to the fact that it portrays the qualitative levels of naming and representing different hierarchies from 100 basketball, 200 basketball, 300 football, 400 anything else
b) We are being informed that, the average (mean) is calculated for 597 respondents and the result is 256.1.
The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement. At nominal level this type of data set do not measure at all , it is not significant to compute their average (mean).
The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts through below.
68.87 78.25 70.44 84.67 79.79 86.33 100.24 98.26
Click the icon to view the table of critical t-values.
a. Determine a point estimate for the population mean travel tax A point estimate for the population mean travel tax is $ 83.36. (Round to two decimal places as needed.)
b. Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.
Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.)
A. The lower bound is $ and the upper bound is $. One can be % confident that all cities have a travel tax between these values.
B. The lower bound is $ and the upper bound is $ The travel tax is between these values for % of all cities.
C. The lower bound is $ and the upper bound is $ There is a % probability that the mean travel tax for all cities is between these values.
D. The lower bound is $ and the upper bound is One can be [95]% confident that the mean travel tax for all cities is between these values.
c. What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?
A. The researcher could decrease the level of confidence.
B. The researcher could decrease the sample standard deviation.
C. The researcher could increase the level of confidence.
D. The researcher could increase the sample mean
Answer:
Step-by-step explanation:
Given that:
68.87, 78.25, 70.44, 84.67, 79.79, 86.33, 100.24, 98.26
we calculate sample mean and standard deviation from given data
Sample Mean
[tex]\bar x = \frac{\sum (x)}{n} =\frac{666.85}{8} \\\\=83.35625[/tex]
Sample Variance
[tex]s^2= \frac{\sum (x- \bar x )^2}{n-1} \\\\=\frac{933.224787}{7} =133.317827[/tex]
sample standard deviation
[tex]s=\sqrt{s^2} \\=\sqrt{133.317827} \\ =11.546334[/tex]
95% CI for [tex]\mu[/tex] using t - dist
Sample mean = 83.35625
Sample standard deviation = 11.546334
Sample size = n = 8
Significance level = α = 1 - 0.95 = 0.05
Degrees of freedom for t - distribution
d-f = n - 1 = 7
Critical value
[tex]t_{\alpha 12, df}= t_{0.025, df=7}=2.365[/tex] ( from t - table , two tails, d.f =7)
Margin of Error
[tex]E = t_{\alpha 12, df}\times \frac{s_x}{\sqrt{n} } \\\\=2.365 \times \frac{11.546334}{\sqrt{8} } \\\\=2.365 \times 4.082246\\\\E=9.654512[/tex]
Limits of 95% Confidence Interval are given by:
Lower limit
[tex]\bar x - E = 83.35625-9.654512\\\\=73.701738\approx 73.702[/tex]
Upper Limit
[tex]= \bar x + E\\=83.35625+ 9.654512\\=93.010762 \approx 93.011[/tex]
95% Confidence interval is
[tex]\bar x \pm E = 83.35625 \pm 9.654512\\\\=(73.701738,93.010762)[/tex]
95% CI using t - dist (73.70 < μ < 93.01)
D. The lower bound is $ and the upper bound is One can be [95]% confident that the mean travel tax for all cities is between these values.
c.What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?
A. The researcher could decrease the level of confidence.
What is 2/3 divided 1/6 ?
Answer: 4
Step-by-step explanation:
in order to divide one fraction by another, you must multiply by the reciprocal(the reverse of a certain fraction). the reciprocal of 1/6 is 6/1. so:
[tex]\frac{2}{3} / \frac{1}{6}[/tex] = multiply by the reciprocal of 1/6
[tex]\frac{2}{3} * \frac{6}{1}[/tex] = cross out
[tex]\frac{2}{1} * \frac{2}{1}[/tex] = multiply
[tex]\frac{4}{1}[/tex] = simplify
4
Answer:
4
Step-by-step explanation:
(2/3)/(1/6)
Eleminate the denominator by multiplying numerator and denominator with whatever is the reciprocal of the denominator. In this case the denominator is 1/6 so the reciprocal is 6/1 or "just" 6.
So, multiply numerator and denominator by 6. The next three (bold) steps, have been written down for explanatory purposes only, and normally are not nessasary.
(2/3)*6 / (1/6)*6
(2/3)*6 / (6/6)
(2/3)*6 / 1
(2/3)*6
12/3
4
2. Calculate the midpoint of the given
segment
|(-2, -3)
(0.1)
(2, 3)
Answer:0,1
Step-by-step explanation:
It’s on edge
Score: 0 of 1 pt
7.4.41
From a standard 52-card deck, how many 5-card hands consist entirely of black cards?
Answer:
so halve the deck is black and halve the deck is red so you have 26 black cards then divide by 5 and you get 5 with 1 card leftover
Solve the following inequality. |-2x + 1| < 13
Please help!!!!
Answer:
x>−6 and x<7
Step-by-step explanation:
Let's solve your inequality step-by-step.
|−2x+1|<13
Solve Absolute Value.
|−2x+1|<13
We know−2x+1<13and−2x+1>−13
−2x+1<13(Condition 1)
−2x+1−1<13−1(Subtract 1 from both sides)
−2x<12
−2x
−2
<
12
−2
(Divide both sides by -2)
x>−6
−2x+1>−13(Condition 2)
−2x+1−1>−13−1(Subtract 1 from both sides)
−2x>−14
−2x
−2
>
−14
−2
(Divide both sides by -2)
x<7
Answer:
x>−6 and x<7
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
P0=6, and the population after 8 weeks is P8=86 Find an explicit formula for the beetle population after n weeks.
After how many weeks will the beetle population reach 236?
Answer:
The number of weeks it will take for the beetle population to reach 236 is 28.75.
Step-by-step explanation:
If a quantity starts at size P₀ and grows by d every time period, then the
quantity after n time periods can be determined using explicit form:
[tex]P_{n} = P_{0} + d \cdot n[/tex]
Here,
d = the common difference, i.e. the amount that the population changes each time n is increased by 1.
In this case it is provided that the original population of beetle was:
P₀ = 6; (week 0)
And the population after 8 weeks was,
P₈ = 86
Compute the value of d as follows:
[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]
Thus, the explicit formula for the beetle population after n weeks is:
[tex]P_{n}=P_{0}+8n[/tex]
Compute the number of weeks it will take for the beetle population to reach 236 as follows:
[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]
Thus, the number of weeks it will take for the beetle population to reach 236 is 28.75.
A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?
Answer:
4 ft
Step-by-step explanation:
288=16 * 18
12+4=16
14+4=18
The dimensions increased by 4 feet.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given;
Dimensions of rectangle = 12 + x and 14 + x
The area of the rectangle= (12 + x) (14 + x) = 288
x² + 26x + 168 = 288
x² + 26x - 120 = 0
(x + 30) (x - 4) = 0
x=-30, x =4
Hence, The dimensions increased by 4 feet.
Learn more about the area;
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Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job collected by AARP (AARP Bulletin, April 2008) Shows that the mean number of weeks a worker aged 55 plus spent to find a job is 22 weeks. The sample standard deviation is 11.89 weeks and sample size is 40.a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job.
b) At 95% confidence, what is the margin of error?
c) What is the 95% confidence interval estimate of the mean?
d) Discuss the degree of skewness found in the sample data. What suggestion would you make for a repeat of this study?
Answer:
Step-by-step explanation:
Hello!
Be the variable of interest:
X: Number of weeks it takes a worker aged 55 plus to find a job
Sample average X[bar]= 22 weeks
Sample standard deviation S= 11.89 weeks
Sample size n= 40
a)
The point estimate of the population mean is the sample mean
X[bar]= 22 weeks
It takes on average 22 weeks for a worker aged 55 plus to find a job.
b)
To estimate the population mean using a confidence interval, assuming the variable has a normal distribution is
X[bar] ± [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]
[tex]t_{n-1; 1-\alpha /2}= t_{39; 0.975}= 2.023[/tex]
The structure of the interval is "point estimate" ± "margin of error"
d= [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]= 2.023*[tex](\frac{11.89}{\sqrt{40} })[/tex]= 3.803
c)
The interval can be calculated as:
[22 ± 3.803]
[18.197; 25.803]
Using s 95% confidence level, you'd expect the population mean of the time it takes a worker 55 plus to find a job will be within the interval [18.197; 25.803] weeks.
d)
Job Search Time (Weeks)
21 , 14, 51, 16, 17, 14, 16, 12, 48, 0, 27, 17, 32, 24, 12, 10, 52, 21, 26, 14, 13, 24, 19 , 28 , 26 , 26, 10, 21, 44, 36, 22, 39, 17, 17, 10, 19, 16, 22, 5, 22
To study the form of the distribution I've used the raw data to create a histogram of the distribution. See attachment.
As you can see in the histogram the distribution grows gradually and then it falls abruptly. The distribution is right skewed.
In the arcade game Skee Ball, players roll a ball up a ramp and receive 10 to 50 points based on where the ball lands. Players will attempt to aim the ball to receive higher scores, which are more difficult to achieve based on size and location. However, if a ball is rolled randomly up the ramp, the probabilities of the ball landing in different scoring areas are not equal. Assume the following probabilities for each possible score:
Score 10 Points 20 Points 30 Points 40 Points 50 Points
Probability 0.50 0.25 0.15 0.07 0.03
Assume that a player rolls three balls at random.
Required:
a. What is the probability of a total score of at least 100 points?
b. If the first ball scores 30 points, what is the probability of a total score of at least 100 points?
c. Are the events "the first ball scores 30" and the "total score is at least 100" independent? Why or why not??
d. What is the expected total score? What is the variance of the score on one roll?
Answer:
Step-by-step explanation:
a) sum of 100 can be achieved from following set of score
10,40,50. This score can be achieved in 3! ways
20,30,50. This score can be achieved in 3! ways
20,40,40. This score can be achieved in 4 ways
30,30,40. This score can be achieved in 4 ways
So,
P(score of 100)=
A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 2010 to 2012. The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q1 + 1.28 Q2 + 0.617 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise Using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 2013?A. The quarterly growth rate in the number of contracts is significantly different from 100% (? = 0.05).
B. The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05).
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
D. The quarterly growth rate in the number of contracts is not significantly different from 100% (? = 0.05).
There is a missing content in the question.
After the statements and before the the options given; there is an omitted content which says:
Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?
Answer:
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
Step-by-step explanation:
From the given question:
The resulting regression equation can be represented as:
[tex]\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3[/tex]
where;
the estimated number of contracts in a quarter X is the coded quarterly value with X = 0
the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise
Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise
Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise
Our null and alternative hypothesis can be stated as;
Null hypothesis :
[tex]H_0 :[/tex] The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)
[tex]H_a:[/tex] The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?
Answer:
Graph C is the answer.
Step-by-step explanation:
Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
If we represent expense in the equation form then it will be
Expense on pencils + expense on erasers = Total expense which is < 3
0.25X + 0.50Y < 3
Now we divide the inequality by 0.25
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)
Now we come to the graphs. Here dotted line graphs are A or C.
We will calculate the slopes of the lines from the graphs A and C to get tha answer.
For Graph A
The end points are (12, 0) and (0, 3)
So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4
For Graph C.
End points the line are (0, 6) and (12, 0)
Slope of the line = (0-6)/(12-0) = -6/12 = -1/2
Therefore Graph C is the answer.
Answer:
Graph C is the answer.
Step-by-step explanation:
Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
If we represent expense in the equation form then it will be
Expense on pencils + expense on erasers = Total expense which is < 3
0.25X + 0.50Y < 3
Now we divide the inequality by 0.25
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)
Now we come to the graphs. Here dotted line graphs are A or C.
We will calculate the slopes of the lines from the graphs A and C to get tha answer.
For Graph A
The end points are (12, 0) and (0, 3)
So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4
For Graph C.
End points the line are (0, 6) and (12, 0)
Slope of the line = (0-6)/(12-0) = -6/12 = -1/2
Therefore Graph C is the answer.
Step-by-step explanation:
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Jenn uses 6 cups of flour to bake 40 muffins. How many muffins can she can bake if she has 15 cups of flour?
Answer:
100 muffins
Step-by-step explanation:
We can use a ratio to solve
6 cups 15 cups
------------- = -----------
40 muffins x muffins
Using cross products
6x = 40*15
Divide each side by 6
6x/6 = 40*15/6
x =100
100 muffins
Answer:
100 muffins
Step-by-step explanation:
If she could bake 40 muffins with 6 cups, then she could bake 80 muffins with 12 cups. Then, we have 3 cups left over, which is half of 6, meaning she can only bake half of her regular amount with 3 cups, which would be 20. 80+20=100
40+40+20=100
