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.

Answers

Answer 1

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.


Related Questions

Score: 0 of 1 pt
7.4.41
From a standard 52-card deck, how many 5-card hands consist entirely of black cards?

Answers

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

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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

Answers

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.

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?

Answers

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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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

Answers

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.

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?

Answers

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.

What is the value of (Negative one-half)–4?
A) -16
B) Negative StartFraction 1 Over 16 EndFraction
C) StartFraction 1 Over 16 EndFraction
D) 16

Answers

Answer:

It would be 16!!!

The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.

What is the value of the expression?

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (-1/2)⁻⁴

Simplify the equation, then we have

⇒ (-1/2)⁻⁴

⇒ (-2)⁴

⇒ -2⁴

⇒ 16

The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.

More about the value of the expression link is given below.

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what is the solution set for the equation (x+3)(x-8)=0

Answers

Answer:

x= -3    x=8

Step-by-step explanation:

(x+3)(x-8)=0

We can use the zero product property to solve

x+3 =0   x-8 =0

x= -3    x=8

Answer:

x=8

Step-by-step explanation:

A fair die is rolled twice, with outcomes X for the first roll and Y for the second roll. Find the moment generating function MX`Y ptq of X ` Y . Note that your answer should be a function of t and can contain unsimplified finite sums.

Answers

Answer:

[tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]

Step-by-step explanation:

The objective is to find the moment generating  function of  [tex]M_{X+Y}(t) \ of \ X+Y[/tex].

We are being informed that the fair die is rolled twice;

So; X to be the value for the  first roll

Y to be the value of the second roll

The outcomes  of X are:  X = {1,2,3,4,5,6}

Where ;

[tex]P (X=x) = \dfrac{1}{6}[/tex]

The outcomes  of Y are:  y = {1,2,3,4,5,6}

Where ;

[tex]P (Y=y) = \dfrac{1}{6}[/tex]

The outcome of Z = X+Y

[tex]= \left[\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\ (2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\ (3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6) \\ (4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6) \\ (5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6) \\ (6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6) \end{array}\right][/tex]

= [2,3,4,5,6,7,8,9,10,11,12]

Here;

[tex]P (Z=z) = \dfrac{1}{36}[/tex]

∴ the moment generating function [tex]M_{X+Y}(t) \ of \ X+Y[/tex]is as follows:

[tex]M_{X+Y}(t) \ of \ X+Y[/tex] = [tex]E(e^{t(X+Y)}) = E(e^{tz})[/tex]

⇒ [tex]\sum \limits^{12}_ {z=2 } et ^z \ P(Z=z)[/tex]

= [tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]

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.

Answers

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

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 25 years?

Answers

Answer:

Step-by-step explanation:

[tex]100 (0.96)^{25} =[/tex] around 36.04

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).

Answers

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.

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.

Answers

Answer:

a) 0.5367feetb) 0.5223feetc) 0.7292feet

Step-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]

f(x)=x^3-3x^2-9x+4 find the intervals on which f is increasing or decreasing b. find the local maximum and minimum values of f. c. find the intervals of concavity and inflection points

Answers

Answer:

Please read the complete answer below!

Step-by-step explanation:

You have the following function:

[tex]f(x)=x^3-3x^2-9x+4[/tex]   (1)

a) To find the interval on which f is increasing or decreasing, you first calculate the critical points of f(x).

You calculate the derivative f(x) respect to x:

[tex]\frac{df}{dx}=3x^2-6x-9[/tex]    (2)

Next, you equal the derivative to zero, and then you find the roots of the polynomial by using the quadratic formula:

[tex]3x^2-6x-9=0\\\\x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(-9)}}{2(3)}\\\\x_{1,2}=\frac{6\pm12}{6}\\\\x_1=-1\\\\x_2=3[/tex]

Then, the critical points are x=-1 and x=3

Next, you calculate df/dx for a values of x to the left and to the right of the critical points x1 and x2. If df/dx < 0 the function is decreasing, if df/dx > 0 the function is increasing.

for x = -1.01

[tex]\frac{df(-1.01)}{dx}=3(-1.01)^2-6(-1.01)-9=0.12[/tex]

Then, in the interval (-∞,-1), the function is increasing

for x = -0.99

[tex]\frac{df(-0.99)}{dx}=3(-0.99)^2-6(-0.99)-9=-0.11[/tex]

In the interval (-1,3) the function is decreasing

for x = 3.01

[tex]\frac{df(3.01)}{dx}=3(3.01)^2-6(3.01)-9=0.12[/tex]

In the interval (3,+∞) the function is increasing

b) To find the local minimum and maximum you use the second derivative of the function:

[tex]\frac{d^2f}{dx^2}=6x-6[/tex]     (3)

you evaluate the second derivative for the critical points x1 and x2, if the second derivative is positive, you have a local minimum. If the second derivative is negative, you have a local maximum:

for x1 = -1

[tex]6(-1)-6=-12<0[/tex]

x=-1 is a local maximum

for x2 = 3

[tex]6(3)-6=12>0[/tex]

x=3 is a local minimum

c) upward concavity: (-1,3)

downward concavity: (-∞,-1)U(3,+∞)

The inflection points are calculated with the second derivative equal to zero:

[tex]6x-6=0\\\\x=1[/tex]

For x = 1 you have an inflection point

Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 18 specimens of a particular species, 5 resprouted after fire. Estimate with 99.5% confidence the proportion of all shrubs of this species that will resprout after fire.

Answers

Answer:

The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]

99.5% confidence level

So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]

We cannot have a negative proportion, so we use 0.

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]

The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).

Jenn uses 6 cups of flour to bake 40 muffins. How many muffins can she can bake if she has 15 cups of flour?

Answers

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

Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
y = -2
y = x + 2
y = x + 3
y=x-5

Answers

Answer:

y = x - 2

Step-by-step explanation:

y = x + b

3 = 5 + b

y = x - 2

We can use the slope intercept form of a line.

y = mx+b where m is the slope and b is the y intercept

y = 1x +b

Substitute the point into the equation

3 = 1*5+b

3 = 5+b

Subtract 5 from each side

3-5 = 5+b-5

-2 =b

y = x-2

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?

Answers

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.

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).

Answers

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)

One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?

Answers

Answer:

a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.

= [70 + (-30)] + [2 + (-9)] + [0.3 + (-0.10]

Answers

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

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).

Answers

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

PLEASE HELP. if f(x)=x and g(x)=2, what is (f*g)(x)

Answers

Answer:

Step-by-step explanation:

hey

(f*g)(x) = f(g(x)) = f(2) = 2

second answer is correct

thanks

2x + 3=-7?what is this even mean

Answers

Answer:

2 times some thing and plus 3 equals -7

Step-by-step explanation:

x = -5

can someone please help meee!???

Answers

the answer is the first one <3

A bottle maker believes that 14% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 622 bottles would be less than 11%

Answers

Answer:

[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]

And we can use the normal standard distribution table and we got:

[tex] P(Z<-2.156) =0.0155[/tex]

Step-by-step explanation:

For this case we know the following info given:

[tex] p =0.14[/tex] represent the population proportion

[tex] n = 622[/tex] represent the sample size selected

We want to find the following proportion:

[tex] P(\hat p <0.11)[/tex]

For this case we can use the normal approximation since we have the following conditions:

i) np = 622*0.14 = 87.08>10

ii) n(1-p) = 622*(1-0.14) =534.92>10

The distribution for the sample proportion would be given by:

[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}}) [/tex]

The mean is given by:

[tex] \mu_{\hat p}= 0.14[/tex]

And the deviation:

[tex]\sigma_{\hat p}= \sqrt{\frac{0.14*(1-0.14)}{622}}= 0.0139[/tex]

We can use the z score formula given by:

[tex] z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]

And replacing we got:

[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]

And we can use the normal standard distribution table and we got:

[tex] P(Z<-2.156) =0.0155[/tex]

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.

Answers

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

The probability that a freshman at a certain college takes an introductory statistics class is 0.21. What is the probability that a randomly selected freshman from this college does not take an introductory statistics class

Answers

Answer:

[tex] P(A) = 0.21[/tex]

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

[tex] P(A')=1-0.21= 0.79[/tex]

Step-by-step explanation:

For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:

[tex] P(A) = 0.21[/tex]

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

[tex] P(A')=1-0.21= 0.79[/tex]

Classify the following triangle .check all that apply

Answers

Answer:

Its right and scalene.

It has a right angle and all the sides are diferent.

SOMEONE PLEASE HELP ME ASAP PLEASE!!!​

Answers

Answer:

7.1

Step-by-step explanation:

d = sqrt(7^2 + -1^2)= sqrt(50)=7.1

Answer:

by using distance formula

putting values

d=√(-1-6)²+(-4--5)²

d=√(-7)²+(1)²

d=√49+1

d=√50

d=5√2=7.1

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

Answers

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

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