Jury Duty Three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
a. Define the experiment.
b. List the simple events in S.
c. If each person is just as likely to be a man as a woman, what probability do you assign to each simple event?
d. What is the probability that only one of the three is a man?
e. What is the probability that all three are women?

Answer:

2/3

Step-by-step explanation:

Your −3x + 3 −1 is not an equation and thus has no solution.

If, on the other hand, you meant

−3x + 3 = 1

then -3x = -2, and  x = 2/3

Answer:

24 units²

Step-by-step explanation:

A rhombus is divided into 4 right triangles when it's two diagonals intersect at right angles. All the sides are of equal lengths.

Therefore, a simple method to use to find the area of the given rhombus is to calculate the area of one of the right triangles, and multiply by 4.

Area of right triangle = ½*base*height

Height = 3

Base = [tex]\sqrt{5^2 - 3^2} = \sqrt{16} = 4[/tex] (Pythagorean theorem)

Area of right triangle = ½*4*3 = 2*3 = 6 units²

Area of rhombus = 4(6 units²) = 24 units²

Answer:

(1, -9)  yes

(7,3)  no

(-9,4)  no

(0, -9) yes

Step-by-step explanation:

The y value must be -9

The x value can be any value to satisfy   the equation y = -9

Question: Perform the following computation with radicals. Simplify the answer.  √6 • √8

Answer:

[tex] 4\sqrt{3} [/tex]

Step-by-step explanation:

Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.

Thus,

[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]

[tex] = \sqrt{48} [/tex]

[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]

[tex] = 4\sqrt{3} [/tex]

Answer:

[tex]\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p<0}\\\boxed{n\geq\dfrac{2-2c}{p}\ \text{for}\ p>0}[/tex]

Step-by-step explanation:

[tex]-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq\dfrac{2-2c}{p}}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}[/tex]

Answer:

A=108 cm²

Step-by-step explanation:

length (l)=3w

perimeter=2l+2w

P=2(3w)+2w

48=6w+2w

width=48/8

w=6

l=3w=3(6)=18

Area=l*w

A=18*6

A=108 cm²

Answer:

n + 1

Step-by-step explanation:

Starting with the integer 'n,' we represent the "next integer" by n + 1.

Answer: c = 4.97 and c = -1.97

Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex]

So, for the function f(x) = [tex]2x^{3}-9x^{2}-60x+1[/tex] on interval [-4,9]

[tex]f'(x) = 6x^{2}-18x-60[/tex]

f(-4) = [tex]2.(-4)^{3}-9.(-4)^{2}-60.(-4)+1[/tex]

f(-4) = 113

f(9) = [tex]2.(9)^{3}-9.(9)^{2}-60.(9)+1[/tex]

f(9) = 100

Calculating average:

[tex]6c^{2}-18c-60 = \frac{100-113}{9-(-4)}[/tex]

[tex]6c^{2}-18c-60 = -1[/tex]

[tex]6c^{2}-18c-59 = 0[/tex]

Resolving through Bhaskara:

c = [tex]\frac{18+\sqrt{1740} }{12}[/tex]

c = [tex]\frac{18+41.71 }{12}[/tex] = 4.97

c = [tex]\frac{18-41.71 }{12}[/tex] = -1.97

Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97

Answer:

Step-by-step explanation:

(f/g) = (3 - 2x ) / (1/x + 5) You could go to the trouble to simplify all of this, but the easiest way is to just put in the 8 where you see an x

(f/g)8 = (3 - 2*8) / (1/8 + 5)

(f/g)/8 = (3 - 16 / (5 1/8)          1/8 = 0.125

(f/g) 8 = - 13 / ( 5.125)

(f/g)8 = - 2.54

Answer:

C

Step-by-step explanation:

In order to solve these you have to use pemdas, which is the order for which you solve these equations from left to right.

Its, parenthesis, exponents, multiplication, division, addition, subtraction.

when using this strategy it will show that

a=48

b=76

c=91

d=63

Answer:

540

Step-by-step explanation:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99

Answer:

540

Step-by-step explanation:

Hey there!

Well we need to first find all the palindromic numbers,

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99

Add

= 540

Hope this helps :)

Answer:

The straight time pay for $ 7.60 per hour and 40 work hours per week is $ 304.

Step-by-step explanation:

Let suppose that worker is suppose to work 8 hours per day, so that he must work 5 days weekly. The straight time is the suppose work time in a week, the pay is obtained after multiplying the hourly rate by the amount of hours per week. That is:

[tex]C = \left(\$\,7,60/hour\right)\cdot (40\,hours)[/tex]

[tex]C = \$\,304[/tex]

The straight time pay for $ 7.60 per hour and 40 work hours per week is $ 304.

Answer:

Step-by-step explanation:

This is best read on the number line.

Look at the picture.

[tex]-\dfrac{17}{2}=-8\dfrac{1}{2}=-8.5[/tex]

Answer:

[tex]\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }[/tex]

Step-by-step explanation:

Hello, first of all, we will check if we can factorise the polynomials.

[tex]\boxed{x^2+6x+8}\\\\\text{The sum of the zeroes is -6=(-4)+(-2) and the product 8=(-4)*(-2), so}\\\\x^2+6x+8=x^2+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)[/tex]

[tex]\boxed{x^2+3x-10}\\\\\text{The sum of the zeroes is -3=(-5)+(+2) and the product -10=(-5)*(+2), so}\\\\x^2+3x-10=x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)[/tex]

[tex]\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)[/tex]

[tex]\boxed{x^2+3x-4}\\\\\text{The sum of the zeroes is -3=(-4)+(+1) and the product -4=(-4)*(+1), so}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=(x+4)(x-1)[/tex]

Now, let's compute the product.

[tex]\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}[/tex]

So the correct answer is the first one.

Thank you.

Answer:

place value of 3 in 783.97 is 3

Step-by-step explanation:

Answer:

Units

Step-by-step explanation:

The units start counting from 3 because after the point that is the 9 start counting tenth

Answer:

1) a) 0.8

b) 0.6

2) a) 0.08

b) 0.14

Step-by-step explanation:

1) Given

[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]

Let us learn about a formula:

[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]

(a) If A and B are mutually exclusive i.e. no common thing in the two events.

In other words:

[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0

Using above formula:

[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]

(b)  P(A and B) = 0.2

Using above formula:

[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]

*************************************

1) Given

[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]

Let us learn about a formula:

[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex]  for dependent events

[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.

(a) If A and B are independent events :

Using the above formula for independent events:

[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]

(b)  [tex]P(A / B) = 0.7[/tex]

Using above formula:

[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]

Answer:

The greater than symbols looks like this    >    , and the less than symbol looks like? <

Answer:

Greater than symbol: >

Less than symbol: <

Greater than or equal to symbol: ≥

Less than or equal to symbol: ≤

Equal symbol: =

In this case, you are answering with the greater than symbol as well as the less than symbol.

The greater than symbols looks like this > , and the less than symbol looks like < .

Answer:

-13

-10

Step-by-step explanation:

A x = B

To find X

A ^ -1 A  x = A ^ -1 B

x = A^ -1 B

x = -3/2  -5/2      2

     -1       -2         4

Across times down

-3/2 * 2 + -5/2 *4 = -13

-1 *2 -2 * 4 = -10

The matrix is

-13

-10

Answer:

[tex]\Large \boxed{\bold{D.} \ \left[\begin{array}{ccc}-13\\ -10\end{array}\right]}[/tex]

Step-by-step explanation:

[tex]AX=B[/tex]

To find [tex]X[/tex]

[tex]X=A^{-1} \cdot B[/tex]

[tex]\displaystyle \left[\begin{array}{ccc}-\frac{3}{2} \cdot 2 + - \frac{5}{2} \cdot 4\\ -1 \cdot 2 + -2 \cdot 4\end{array}\right][/tex]

[tex]\displaystyle \left[\begin{array}{ccc}-3 + - 10\\ -2 + -8\end{array}\right][/tex]

[tex]\displaystyle \left[\begin{array}{ccc}-13\\ -10\end{array}\right][/tex]

Answer:

Matched or paired data

Step-by-step explanation:

In statistics the different types of study included experimental and observational with the matched or paired data.

The observational study is one in which there is no alteration in the obseravtions or any change. It is purely based on observations.

The experimental study is one in which some experiment or change is brought about to see the effects of the experiment and the results are recorded as before and after treatment etc.

The matched or paired study is one in which two or more groups are simultaneously observed , recorded to find the difference between them or other parameters which maybe useful for the differences or similarities.

Answer:

$12,78

Step-by-step explanation:

$142 × 0,15 = $21,3

$21,3 × 0,6 = $12,78

Answer:

reject null hypothesis if calculated t value > 2.624

Step-by-step explanation:

n = 15

To calculate degree of freedom, n -1 = 14

The claim says ud>0

The decision rule would be to reject this null hypothesis if the test statistics turns out to be greater than the critical value.

With df =14

Confidence level = 0.01

Critical value = 2.624 (for a one tailed test)

If the t value calculated is > 2.624, we reject null hypothesis.

Using the t-distribution and it's critical values, the decision rule is:

At the null hypothesis, we test if the mean is not greater than 0, that is:

[tex]H_0: \mu \leq 0[/tex]

At the alternative hypothesis, we test if the mean is greater than 0, that is:

[tex]H_1: \mu > 0[/tex].

We then have to find the critical value for a right-tailed test(test if the mean is more than a value), with 15 - 1 = 14 df and a significance level of 0.01. Using a t-distribution calculator, it is [tex]t^{\ast} = 2.624[/tex].

Hence, the decision rule is, according to the test statistic t:

A similar problem is given at https://brainly.com/question/13949450

Answer:

C) f(x) increases by 900%

Step-by-step explanation:

The rate of change is

f(4) - f(3)

---------------

4-3

f(4) = 9*4 = 36

f(3) = 9*3 = 27

36 -27

---------------

4-3

9

-----

1

The rate of change is 9

To change to a percent, multiply by 100%

9*100% = 900%

Answer:

Increases by 900%

Step-by-step explanation:

● f(x) = 9x

The rate of change is:

● r = (36-27)/(4-3) = 9

So the function increses nine times wich is equivalent to 900%

Answer:

Option (D)

Step-by-step explanation:

Formula to get the area of a regular polygon in a circle will be,

Area = [tex]n[\frac{1}{2}\times (\text{Base})\times (\text{Height})][/tex]

        = [tex]n[\frac{1}{2}\times (\text{s})\times (\text{h})][/tex]

Here 'n' is the number of sides.

If n increases, h approaches r so that 'rh' approaches r².

In other words, if the number of sides of the polygon gets increased, area of the polygon approaches the area of the circle.

Therefore, Option (4) will be the answer.

In this exercise it is necessary to have knowledge about polygons, so we have to:

Letter D

Then using the formula for the area of ​​a regular polygon we find that:

[tex]A=n(1/2*B*H)\\=n(1/2*S*H)[/tex]

So from this way we were not able to identify the option that best corresponds to this alternative.

See more about polygons at  brainly.com/question/17756657

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

tanθ = [tex]\frac{y}{x}[/tex]

Given : Polar equation as 'θ' = [tex]-\frac{5\pi }{6}[/tex]

Therefore, [tex]\text{tan}(-\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex]

[tex]-\text{tan}(\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex]   [Since tan(-θ) = -tanθ]

[tex]\text{tan}(\pi -\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex] [Since -tanθ = tan(π - θ)]

[tex]\text{tan}\frac{\pi }{6}[/tex] = [tex]\frac{y}{x}[/tex]

[tex]\frac{y}{x}=\frac{\sqrt{3}}{3}[/tex]

y = [tex]\frac{\sqrt{3} }{3}x[/tex]

Therefore, y = [tex]\frac{\sqrt{3} }{3}x[/tex] will be the rectangular form of the polar equation.

Option (1) will be the correct option.

Answer:

Graph 2

Step-by-step explanation:

As you can see the first equation is present with a negative slope, and none of the graphs have a line plotted with a negative slope, besides the second graph. That is your solution.

Answer:

The answer is "253"

Step-by-step explanation:

In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:

Given:

[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]

[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]

integrate the above value:

[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]

When the value of n=1 then t=0

[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]

so the value of  n is:

[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]

when we put the value t= 15 then,

[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]

Answer:

M= 521.1 g

Step-by-step explanation:

1st.  Find the volume of the cube:   V=3³=27 cm³

As the weight of V= 1 cm³ cube  is 19.3 g the weight of the cube=27 cm³ is

M=27*19.3= 521.1 g

Answer:

204/1015 (irreducible) = 20.1%

1/8120 (irreducible) = 0.01232%

1/5832 (irreducible) = 0.01715%

1/6 (irreducible) = 16.67%

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf A) \ 12}[/tex]

Step-by-step explanation:

Frequency of a specific data value at an interval is the number of times the data value repeats in that interval.

Cumulative frequency is found by adding each frequency to the frequency that came before it.

cStep-by-step explanation:

Answer:

Washer $735

Dryer $245

Step-by-step explanation:

If x is the cost of the washer, and y is the cost of the dryer, then:

x + y = 980

x = 3y

Solve with substitution.

3y + y = 980

4y = 980

y = 245

x = 735