A box contains 4 white ribbons and 8 pink ribbons. Determine whether the events of picking a white ribbon and then another white ribbon without replacement are independent or dependent. Then identify the indicated probability.
a. independent; 1/11
b. dependent; 1/12
c. dependent; 1/11
d. independent; 1/12

Answer:

c) 100

Step-by-step explanation:

This is the best choice because the number is not too low or too high. He will get an accurate probability.

Answer: 6 animals should go in each pen.

Step-by-step explanation:

Total sheep = 54

Total cows = 24

Total pigs = 30

Highest number of animals are possible in each pen such that animals are distributed in pens with the same number = Greatest common divisior (54,24, 30)

54= 6 x 9

24= 6 x 4

30 = 6 x 5

So, Greatest common divisior (54,24, 30) = 6

Hence, 6 animals should go in each pen.

Answer:

Step-by-step explanation:

Using the double angle formulas,

cos(2x) = cos^2(x) - sin^2(x) ............(1)

1            = cos^2(x) + sin^2(x)............(2)

add (1) and (2)

1 + cos(2x) = 2 cos^2(x)

=> cos^2(x) = (1/2) (1+cos(2x))  ..............(3)

f(x) =  7 cos^2 (x)  

substituting (3)

f(x) = (7/2) (1+cos(2x))

Answer:

Number of blue markers  = 9

Step-by-step explanation:

Given that there are 24 red markers.

Probability of randomly choosing a red marker is 1 in 3.

Probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

That means the ratio of red markers to total markers is 1:3.

Here number of favorable cases are 24 i.e. the number of red markers

and Total number of cases are equal to total number of markers.

Let T be the total number of markers.

As per definition of probability:

[tex]\dfrac{1}{3}=\dfrac{24}{T}\\\Rightarrow \bold{T = 72}[/tex]

Also, given that the probability of choosing a blue marker is 1 in 8.

Let the number of blue markers be B.

As per definition of probability:

[tex]\dfrac{1}{8}=\dfrac{B}{72}\\\Rightarrow \bold{B = 9}[/tex]

Hence, the answer is:

Number of blue markers  = 9

Answer:

0.012 millimeters

Step-by-step explanation:

First, we solve for  0.000004 m to mm = 0.004 mm x 3 = 0.012 millimeters

Answer:

The correct answer is A because subtract 28.50 from 45.50 and you get the answer of 17$ for the belt

Answer: 24

Expenation:  

Left handed females = x

right handed females = 348 - x

right handed males = y

left handed males = 204 - y

204 - y = 4x

348 - x = 3y

4x + y = 204  . . . . . . . (1)

x + 3y = 348  . . . . . . . (2)

From (2),  x = 348 - 3y

subsituting for x in (1), we have

4(348 - 3y) + y = 204

1392 - 12y + y = 204

12y - y = 1392 - 204

11y = 1188

y = 1188/11 = 108

x = 348 - 3y = 348 - 3(108) = 348 - 324 = 24

Answer:

24

Step-by-step explanation:

i got it right

Answer:

Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Step-by-step explanation:

The formula for average rate of change of f(x) over [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given function is

[tex]r(x)=x^2+2x-5[/tex]

[tex]r(0)=(0)^2+2(0)-5=-5[/tex]

[tex]r(3)=(3)^2+2(3)-5=10[/tex]

Now,

[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]

[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]

From the graph it is clear that q(0)=-4 and q(3)=5.

[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]

[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]

It is given that  function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.

[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]

[tex]m_3=\dfrac{0-6}{3}=-2[/tex]

From the given table it is clear that s(0)=-13 and s(3)=5.

[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]

[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]

Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Answer:

0.8413 or 84.13%

Step-by-step explanation:

The difference from 4320 grams from the mean is:

[tex]d=4320-3958=362\ grams[/tex]

This is exactly 1 standard deviation.

According to the empirical rule, 68.26% of all data is within 1 standard deviation of the mean, which means that 34.13% of all data is within the mean and 1 standard deviation over the mean. We also know that the mean is at the 50th percent of the normal distribution.

Therefore, the probability that the weight will be less than 4320 grams is:

[tex]P(X\leq 4320) = 0.50+0.3413=0.8413 = 84.13\%[/tex]

The probability is 0.8413 or 84.13%

Answer:

B. x^3 + 3x^2

Step-by-step explanation:

Volume of a rectangular prism=width * length * height

V=w*l*h

h=3 greater than the length of the base

h=x+3

Length of the base=x

Width=x

Substituting values into the formula

V=w*l*h

=(x)*(x)*(x+3)

Multiplying

=(x^2)(x+3)

=x^3 + 3x^2

Option B is the correct answer

The expression [tex]x^3 + 3x^2[/tex]  represents the volume of the prism, in cubic units.

We have given that the,

The height of a right rectangular prism is 3 units greater than the length of the base.

The edge length of the square base is x units.

[tex]Volume of a rectangular prism=width * length * height[/tex]

[tex]V=w*l*h[/tex] ......(1)

We have given that the

h=3 greater than the length of the base

and length of the base is x

Hence, [tex]h=x+3[/tex]

[tex]Length of the base=x[/tex]

[tex]Width=x[/tex]

Substituting values l h and w into the formula (1) we get,

[tex]V=w*l*h[/tex]

[tex]=(x)*(x)*(x+3)[/tex]

[tex]=(x^2)(x+3)[/tex]

[tex]=x^3 + 3x^2[/tex]

Therefore the expression  

[tex]x^3 + 3x^2[/tex]  

represents the volume of the prism, in cubic units.

To learn more about the volume of the prism visit:

https://brainly.com/question/23963432

Answer:

The number of boys, x = 12

Step-by-step explanation:

Given that the sum of the ages of the boys in a class = 84 years

The number of boys = x

A new boy aged 8 years 1 month is added and the average age increases by 1 month

We have

Average age = 84/x = y

Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]

New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;

84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]

[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]

(x + 1008)×(12·x + 12) = 1105× 12·x

12·x² -1152·x + 12096 = 0

x² -96·x + 1008 = 0

(x - 84)×(x - 12) = 0

Therefore, x = 12 or 84,

The number of boys are 12 or 84

For there to bee 84 boys, their average age would be one year each

Given that they are boys not babies, then there are only 12 boys.

Answer:

Option (D)

Step-by-step explanation:

Given quadrilateral in the circle is a cyclic quadrilateral.

By using the property of cyclic quadrilateral,

"Sum of each pair of opposite angles is 180°".

In the given cyclic quadrilateral,

d + 57° = 180°

d = 180 - 57

d = 123°

Similarly, c + 31° = 180°

c = 180° - 31°

c = 149°

Therefore, Option (D) will be the answer.

Answer:

678 ft²

Step-by-step explanation:

The opposite sides of the cuboid are congruent, thus surface area is

2(11 × 9) ← front and back + 2(11 × 12) ← top and base + 2(12 × 9) ← sides

= 2(99) + 2(132) + 2(108)

= 198 + 264 + 216

= 678 ft²

Answer:

x=-5

Step-by-step explanation:

The answer is x = -5. The explanation and answer is in the image below.

Answer:

B. (4.75,-22)

Step-by-step explanation:

Step: Solve 3.2x+0.5y=4.2for x:

3.2x+0.5y=4.2

3.2x+0.5y+−0.5y=4.2+−0.5y(Add -0.5y to both sides)

3.2x=−0.5y+4.2

3.2x

3.2

=

−0.5y+4.2

3.2

(Divide both sides by 3.2)

x=−0.15625y+1.3125

Step: Substitute−0.15625y+1.3125 for x in−1.6x−0.5y=3.4:

−1.6x−0.5y=3.4

−1.6(−0.15625y+1.3125)−0.5y=3.4

−0.25y−2.1=3.4(Simplify both sides of the equation)

−0.25y−2.1+2.1=3.4+2.1(Add 2.1 to both sides)

−0.25y=5.5

−0.25y

−0.25

=

5.5

−0.25

(Divide both sides by -0.25)

y=−22

Step: Substitute−22 for y in x=−0.15625y+1.3125:

x=−0.15625y+1.3125

x=(−0.15625)(−22)+1.3125

x=4.75(Simplify both sides of the equation)

Answer:I think it’s 7x^3

Step-by-step explanation:

Answer:

R = 21.8° to the nearest tenth

Step-by-step explanation:

To find Angle R we use tan

tan ∅ = opposite / adjacent

From the question

The opposite is 2

The adjacent is 5

So we have

tan R = 2/5

R = tan-¹ 2/5

Hope this helps you

Answer:

1:3

Step-by-step explanation:

9/3 = 3

3 is the scale factor

Answer:

a) [tex]D = 600 -4.9t^2[/tex]

b) 11.06 seconds

c) 108.39 m/s

d) 10.37 m/s

Step-by-step explanation:

Given:

Distance, s = 600 m

Acceleration, a = g = 9.8 [tex]m/s^2[/tex]

a) Distance of stone above ground level at time 't'.

First of all, we need to find the distance traveled in time 't' and then we will subtract it from 600 to find the answer.

The formula is given as:

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

where u is the initial velocity which is 0 in this case.

[tex]s=0\times t+\dfrac{1}{2}\times 9.8 \times t^2\\s =4.9t^2[/tex]

Distance of stone above ground level at time 't',

[tex]D = 600 -4.9t^2[/tex]

b) Time taken by stone to reach the ground. i.e. D = 0

Using above equation, putting D = 0

[tex]0 = 600 -4.9t^2\\\Righttarow 4.9t^2 = 600\\\Rightarrow t = \sqrt{\dfrac{6000}{49}} = 11.06\ sec[/tex]

c) Velocity with which it strikes the ground i.e. [tex]v=?[/tex]

Using the formula:

[tex]v=u+at[/tex]

[tex]v = 0 +9.8 \times 11.06\\v = 108.39\ m/s[/tex]

d) If initial velocity, u = 7 m/s, time taken to reach the ground = ?

In this case total distance traveled = 600 m

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

[tex]600=7 t+\dfrac{1}{2}\times 9.8t^2\\\Rightarrow 600=7 t+4.9t^2\\\Rightarrow 4.9t^2+7 t-600=0\\\Rightarrow 49t^2+70 t-6000=0[/tex]

Solving the above equation:

t = 10.37 seconds

The answers are:

a) [tex]D = 600 -4.9t^2[/tex]

b) 11.06 seconds

c) 108.39 m/s

d) 10.37 m/s

A) The distance (in meters) of the stone above ground level at time t is; d(t) = 600 - 4.9t²

B) The time it takes the stone to reach the ground is; t = 11.07 seconds

C) The velocity at which the stone strikes the ground is; v = -108.486 m/s

D) The time it takes to reach the ground when thrown downwards with a speed of 7 m/s is; t = 10.37 s

A) Using Newton's 2nd equation of motion, we have;

d(t) = d_o + ut - ½gt²

Plugging in the relevant values, we have;

d(t) = 600 + 0(t) - 0.5(9.8)t²

d(t) = 600 - 4.9t²

B) The time it takes for the stone to reach the ground is when d(t) = 0. Thus;

0 = 600 - 4.9t²

4.9t² = 600

t² = 600/4.9

t = √(600/4.9)

t = 11.07 seconds

C) Velocity at which is strikes the ground will be gotten from Newton's first equation of motion;

v = u - gt

v = 0 - (9.8 × 11.07)

v = -108.486 m/s

D) The stone is thrown downwards with a speed of 7 m/s.

Thus;

600 - 7t - 0.5(9.8t²) = 0

-4.9t² - 7t + 600 = 0

Using online quadratic equation solver gives;

t = 10.37 s

Read more at; https://brainly.com/question/17188989

Answer:

4 Pi

Explanation:

72/360 = 1/5 so the length of the arc is (1/5) the circumference or

(1/5) ( 2 Pi * 10)  => C = 2 Pi r

(20/5) Pi =

4 Pi

Answer: A) 18(1.15)x

Step-by-step explanation:

18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.

Answer:

A) y = 18(1.15)x

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

x − 3y

Let x =3 and y = -2

3 -3(-2)

3 + 6

9

Answer: D

Step-by-step explanation:

If we substitute -12 into this equation we get:

[tex]-3[-12-8]+1.5[/tex]

[tex]-3[-20]+1.5[/tex]

Because -20 is in absolute value, we simply just use 20.

Thus,

[tex]-3(20)+1.5\\= -60+1.5\\= -58.5[/tex]

Answer:

D

Step-by-step explanation:

Answer:

60 + 0.05d

Step-by-step explanation:

Answer:

Answer D I believe :)

Step-by-step explanation:

x^4-33x^2-108

rewrite as a difference

x^4+3x^2-36x^2-108

factor out x^2

x^2(x^2+3)-36x^2-108

factor out -36

x^2(x^2+3)-36(x^2+3)

factor out x^2+3

(x^2+3)(x^2-36)

factor x^2-36

(x^2+3)(x-6)(x+6)

set x^2+3 equal to 0

x^2+3=0

solve for x

x=+/-[tex]\sqrt{3}[/tex]i

set at factors

(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)

I hope this helps.

Step-by-step explanation:

in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .

then again find the slope for each equation by the formula

slope= -coefficient of x / coefficient of y

for example,

X+y is greater or equals to 5

or, X+y= 5

or, X=5-y

or, when y is equals to zero

X= 5

and when X is equals to zero

y= 5

then plot the above point in the graph with respect to its slope and the shaded part is the solution

A=24in² this th ans because the side of cube is 24 cm

Answer: The volume is 33 cubic centimeters.

Step-by-step explanation:

First find the volume of the square pyramid on top of the cube. To find the volume of the square pyramid you use the volume  a^2*h/3 a is the side length of the base of the square pyramid and h is the height all divide by 3.

So we can say that the side length of the base of the square pyramid is 3 because it has the same side length base as the cube.

V= 3^2 * 2 /3

V= 9 * 2 /3

V= 18/3

v= 6  

So the volume of the square pyramid is 6 so now we need to find the volume of the cube and add them together.

Volume of the a cube uses the formula s^3 where s is the side length.

V= 3^3

v= 3*3*3

v= 27  

The volume of the cube is 27.

Add 6 and 27 to find the total volume.

6 +27 = 33

Answer:

{1,2,3}

Step-by-step explanation:

The others will not show all the numbers from the set to make the inequality true

Answer:

1,2,3

Step-by-step explanation: