А
What is the measure of ZDAB?
&
B
Enter your answer in the box.
D
96°
C
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Answer:

It would be 16!!!

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

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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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

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

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.

Answer:

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

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]

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

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).

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]

Answer:

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]

Answer:

D = 0 , Dx = 4 , Dy = -6 , Dz = 2

Step-by-step explanation:

As per cramer's rule,

D = |   7    6    4  |  = 0

      |   3    3    3  |

      |   4    4    4  |

Dx =  |  10    6    4  | = 4

        |   1    3    3    |

        |   2    4    4   |

Dy = |   7    10    4  | = -6

       |   3    1     3   |

       |   4    2    4   |

Dz =  |  7    6    10 | = 2

        |   3    3    1   |

        |   4    4    2  |

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.

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:

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Answer:

Step-by-step explanation:

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

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.

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

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:

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)

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

Answer:

Step-by-step explanation:

hey

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

second answer is correct

thanks

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.

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

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]

Answer:

Its right and scalene.

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

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.

Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

The dimensions increased by 4 feet.

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.

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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

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

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

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.