A box has three balls, one white and two red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:

a. Let F= the event of getting the white ball twice.
b. Let G= the event of getting two balls of different colors.
c. Let H= the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?

Answer:

C. she is not beautiful and not clever.

Step-by-step explanation:

A. she is beautiful but not clever. B. she is beautiful and clever

C. she is not beautiful and not clever.

D. she is beautiful or not clever.

p: she is beautiful

q :she is clever

~p^ (~q) in verbal form

~p = she is not beautiful

~q = she is not clever

~p^ (~q) = she is not beautiful and not clever.

C. she is not beautiful and not clever.

Answer:

-10, 12, -9 and 13

Step-by-step explanation:

Given the recursive sequence

a1 = -10

an = n - an-1

a2  = 2 - a1

a2 = 2  - (-10)

a2 = 2+10

a2 = 12

a3 = 3 - a2

a3 = 3  - (12)

a3 = -9

a4  = 4 - a3

a4 = 4  - (-9)

a4 = 4+9

a4 = 13

Hence the first 4 terms are -10, 12, -9 and 13

Answer:

4.91e-2 in decimal form is 0.0491

Answer:

153.3852

Step-by-step explanation:

After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2

Answer:

153.385

Step-by-step explanation:

153.38519

153.38519

The digit to the right of the thousandth (the the one, which is bolded) is less than or equal to 4, which means we round down.

153.38519 ≈ 153.385

Hope this helps.

Answer:

See image below for answer:)

Step-by-step explanation:

Answer:

1. k = 15

2. d = 20

3. n = 3

Answer:

jjanation:jdgjdjgdjgjkdkidjgjghdjjghhkd

Step-by-step explanation:

If you use synthetic division, you get,

[tex]2x {}^{3} + 2x + 4 + \frac{0}{x + 2} [/tex]

Which is,

[tex]2x {}^{3} + 2x + 4[/tex]

Answered by GAUTHMATH

Answer:

The correct answer is:

2x^3+2x+4

Step-by-step explanation:

I got it right on the Plato test.

9514 1404 393

Answer:

  B.  ∠A ≅ ∠E

Step-by-step explanation:

The similarity statement tells you the corresponding angles are ...

  ΔCAB ~ ΔCED

  ∠C ≅ ∠C . . . . listed first in the similarity statement

  ∠A ≅ ∠E . . . . listed second in the similarity statement

  ∠B ≅ ∠D . . . . listed third in the similarity statement

The relationship between angles A and E is properly shown in answer choice B.

do u mean rectangle is longer or rectangles lenght is longer

Answer:

b=4/ 5

Step-by-step explanation:

Answer:

Equation = (x - 6 )² + ( y + 3 )² = 9

Step-by-step explanation:

The circle passes through ( 6, 0) and  ( 6 , -6)

They are the coordinates of the diameter.

Using this we can find the centre of the circle.

Find the centre of the circle.

Centre of the circle is the mid- point of (6, 0) and ( 6, -6)

      [tex]Centre = (\frac{x_1+x_2}{2} , \frac{y_1 + y_2}{2})[/tex]

                 [tex]=(\frac{6 + 6}{2}, \frac{0 + (-6)}{2})\\\\=(6, -3)[/tex]

Find the radius of the circle.

[tex]Radius = \frac{Diameter }{2}[/tex]

Diameter is the distance between the points (6 , 0) and ( 6, - 6)

[tex]Diameter = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2\\}[/tex]

               [tex]=\sqrt{(6-6)^2 + (-6 -0)^2}\\\\=\sqrt{0 + 36} \\\\= 6[/tex]

Therefore,

    [tex]Radius ,r = \frac{6}{2} = 3[/tex]

Standard equation of a circle:

[tex](x - a)^2 + (y - b)^2 = r^2 \ where \ (a , b) \ is \ the\ centre \ coordinates.[/tex]

Therefore , equation of the circle ;

                    [tex](x - 6)^2 + (y + 3)^2 = 3^2\\\\(x -6)^2 + (y + 3)^2 = 9[/tex]

Answer: Choice D

9, 30, 93, 282, 849

============================================================

Explanation:

The notation [tex]a_1 = 9[/tex] tells us that the first term is 9

The notation [tex]a_n = 3*(a_{n-1})+3[/tex] says that we multiply the (n-1)st term by 3, then add on 3 to get the nth term [tex]a_n[/tex]

So if we wanted the second term for instance, then we'd say

[tex]a_n = 3*(a_{n-1})+3\\\\a_2 = 3*(a_{2-1})+3\\\\a_2 = 3*(a_{1})+3\\\\a_2 = 3*(9)+3\\\\a_2 = 27+3\\\\a_2 = 30\\\\[/tex]

If we want the third term, then,

[tex]a_n = 3*(a_{n-1})+3\\\\a_3 = 3*(a_{3-1})+3\\\\a_3 = 3*(a_{2})+3\\\\a_3 = 3*(30)+3\\\\a_3 = 90+3\\\\a_3 = 93\\\\[/tex]

and so on.

The terms so far are: 9, 30, 93

You should find the fourth and fifth terms are 282 and 849 respectively if you keep this pattern going.

Therefore, the answer is choice D

Answer:

g(-1 )=-1 and g(2)+g(1)=7

Step-by-step explanation:

If g(x) = x^3+x^2-x-2 find g(-1)

if we find g(-1)

we substitute all the x's in the function with -1

-1^3+-1^2-(-1)-2

-1^3 = -1

-1^2 = 1

-1+1+1-2

(two minuses make a plus)

-1+1 = 0

0+1 = 1

1-2 = -1

if x=-1, g(-1) is -1

g(2)+g(1)

substitute the x's in the function with 2 and 1 and add your results

2^3+2^2-2-2

2^3 = 8, 2^2 = 4

8+4-2-2

8+4= 12, 12-2 = 10, 10-2 = 8

g(2)=8

g(1) now

1^3 + 1^2-1-2

1^3=1, 1^2 = 1

1+1-1-2

1+1 = 2, 2-1 = 1, 1-2 = -1

g(3) = -1

g(2) (which equals 8) + g(3) (which equals -1) =

8+(-1) = 7

g(2)+g(3)=7

Answer:

Franco comió 8/3 de pizza.

Fabián comió 5/6 de pizza.

Queremos saber quien comió más.

Entonces básicamente queremos ver cuál número es más grande, 8/3 o 5/6,

Podemos reescribir el primero como:

8/3 = (2 + 3 + 3)/3 = 2/3 + 3/3 + 3/3 = 2/3 + 1 + 1

      = 2 + 2/3

En cambio, para el número 5/6, el numerador es menor que el denominador, entonces sabemos que:

5/6  < 1

Claramente podemos ver que 8/3 > 5/6

Entonces podemos concluir que Franco comió más.

tiệm cận ngang của đồ thị 3/x+3

Answer:

X = 32

Step-by-step explanation:

Angle BEC = 43 degrees

You find X by setting up the equation 137 = 3x+41

Solve for x

You find angle BEC by subtracting 137 from 180, finding the acute angle that brings the obtuse angle up to 180 degrees (a flat line)

Answer:

x = 32 degree and angle BEC = 43 degree

Step-by-step explanation:

3x + 41 = 137 degree (being vertically opposite angles)

3x = 137 - 41

x = 96/3

x = 32

angle BEC be y

137 + y =180 degree (being linear pair)

y = 180 - 137

y = 43 degree

therefore angle BEC = 43 degree

Answer:

A circle to start off, encompassing almost the entire figure, then a triangle, with D, A and C as its vertices, then a fan (a sector of a circle), with C, E and B as its vertices. Next, a chord (DA) which serves as a line segment at the same time, and finally three rays, starting from C and ending in A, B and E respectively. In total, six geometric figures.

Step-by-step explanation:

Hope this helped!

9514 1404 393

Answer:

  y = 21/x

Step-by-step explanation:

The inverse variation relation means ...

  y = k/x

For the given values, we can determine the constant k:

  3 = k/7

  3×7 = k = 21

Then the function is ...

  y = 21/x

Answer:

A is your answer, my guy

Step-by-step explanation:

4x1=4

3x-1=-3

5x1=5

4+(-3)+5=6

6x1=6

8x-1=-8

6x1=6

6+(-8)+6=4

4x1=4

2x-1=-2

6x1=6

4+(-2)+6=8

Answer:

Option E. None of the above.

Step-by-step explanation:

From the question given above, the following data were obtained:

f(x) = (x – 5)/(2x + 3)

Inverse of f(x) => f¯¹(x) =?

Recall:

When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e

f(x) × f¯¹(x) = 1

With the above information, we can determine the inverse of function given above as follow:

f(x) = (x – 5)/(2x + 3)

Inverse of f(x) => f¯¹(x) =?

f(x) × f¯¹(x) = 1

(x – 5)/(2x + 3) × f¯¹(x) = 1

f¯¹(x)(x – 5) / (2x + 3) = 1

Cross multiply

f¯¹(x)(x – 5) = (2x + 3)

Divide both side by (x – 5)

f¯¹(x) = (2x + 3) / (x – 5)

Thus, the inverse of the function is (2x + 3) / (x – 5).

Option E gives the correct answer to the question.

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

[tex]f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5[/tex]

Simplifying:

[tex]f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}[/tex]

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

[tex]P(A) = \int_{5}^{15} = \frac{375}{t^4}[/tex]

Integral of [tex]\frac{1}{t^4} = t^{-4}[/tex] is [tex]\frac{t^{-3}}{-3} = -\frac{1}{3t^3}[/tex]

Then

[tex]\int \frac{375}{t^4} dt = -\frac{125}{t^3}[/tex]

Applying the limits, by the Fundamental Theorem of Calculus:

At [tex]t = 15[/tex], [tex]f(15) = -\frac{125}{15^3} = -\frac{1}{27}[/tex]

At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]

Then

[tex]P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}[/tex]

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

[tex]P(B) = \int_{5}^{10} = \frac{375}{t^4}[/tex]

We already have the integral, so just apply the limits:

At [tex]t = 10[/tex], [tex]f(10) = -\frac{125}{10^3} = -\frac{1}{8}[/tex]

At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]

Then

[tex]P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}[/tex]

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087[/tex]

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

Answer:

10 quarts

Step-by-step explanation:

.1(8) + 1(x) = .6(x + 8)

.8 + x = .6x + 4.8

.4x = 4

x = 10

10 quarts

Answer: 4)

Step-by-step explanation: angles 2 and 3 equal 7 because they are both missing angle 4 to make it either 180 degrees or 360 degrees respectively.

Answer:

Surface Area = 54 in^2

Step-by-step explanation:

SA = [tex]6a^{2}[/tex]

SA = [tex]6(3)^2[/tex]      Solve for the exponents first

SA = 6(9)       Then multiply

SA = 54 square inches

Answer:

B. Same shape

C. Similar

Step-by-step explanation:

The three angles in ∆XYZ are congruent to the corresponding three angles in ∆UVW.

Also, the ratio of the corresponding side lengths of ∆XYZ to ∆UVW are the same. i.e. WU/XY = VW/XZ = UW/XZ = 2

Therefore, we can conclude that they are similar because they have the same shape even though their sizes are different.

Answer:

c. one-tailed test, with rejection region in the upper tail.

Step-by-step explanation:

One tailed test is statistical test in which critical area of distribution is one sided and greater or less than certain value. One tailed test can be left or right sided depending on the population distribution. Rejection region of the one tailed test will determine whether to accept or reject the null hypothesis.

Answer:

The answer is A

Step-by-step explanation:

just took it on egde