Suppose ø is an angle in the standard position whose terminal side is in Quadrant I and tan ø = 60/11

Answer:

a) 11.03% probability that exactly two are red.

b) 98.64% probability that at most 2 are red.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the skittles are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

12 + 10 + 8 + 9 + 22 = 61 skittles.

A). exactly 2 are red

Desired outcomes:

2 red, from a set of 8.

3 non-red, from a set of 61 - 8 = 53.

So

[tex]D = C_{8,2}*C_{53,3} = \frac{8!}{2!(8-2)!}*\frac{53!}{3!(53-3)!} = 655928[/tex]

Total outcomes:

Five skittles from a set of 61. So

[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{655928}{5949147} = 0.1103[/tex]

11.03% probability that exactly two are red.

B). At most 2 are red

Desired outcomes:

None red(5 from a set of 53)...

One red(from a set of 8), and four non-read(4 from a set of 53).

Two red(655928), as found in a.

So

[tex]D = C_{53,5} + C_{8,1}*C_{53,4} + 655928 = \frac{53!}{5!48!} + \frac{8!}{1!7!}*\frac{53!}{4!49!} + 655928 = 5868213[/tex]

Total outcomes:

Five skittles from a set of 61. So

[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{5868213}{5949147} = 0.9864[/tex]

98.64% probability that at most 2 are red.

Answer:

t = 6.3

Step-by-step explanation:

N=Noe^(-kt)

No = 14 grams

k = .1092

We want to find t when N = 7 or 1/2 of 14

N=Noe^(-kt)

7 = 14 e ^ (-.1092t)

Divide each side by 14

1/2 = e ^ (-.1092t)

take the natural log of each side

ln (1/2) = ln e ^ (-.1092t)

ln (1/2) = -.1092t

Divide each side by -.1092

ln (1/2)/ -.1092 = t

t≈6.3475

Rounding to the nearest tenth

t = 6.3

Answer: 6.3

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

40 / 100= .4

.4 x 45 = 18

18/18= 1

1x 100= 100

Answer:

100

Step-by-step explanation:

:D

Answer:

43°

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

–2(3x – 1) = –6x – 1

       -6x + 2 = -6x - 1 (IMPOSSIBLE, ZERO)

2(3x – 1) = 6x – 2

      6x - 2 = 6x - 2 (INFINITE)

2(3x – 1) = –6x – 2

      6x - 2 = -6x - 2 (ONE, x can be the number 0)

Answer:

The set of all output values of a function. Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then the range is {1,4,9,...}

Answer:

[tex]2\dfrac{11}{12}[/tex]

Step-by-step explanation:

The first step is to ensure that all of the fractions have a common denominator.

[tex]3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}[/tex]

Hope this helps!

Answer:

The probability that next year Greenville will receive the following amount of rainfall A) At most 55 inches of rain is 0.7734, B) at least 62 inches of rain is 0.0516, C) Between 46 and 55 inches of rain is 0.0387

D Having rainfall of above 65 inches would be considered as an extremely wet year

Step-by-step explanation:

A. To find the probability that next year Greenville will receive at most 55 inches of rain we would have to make the following calculation:

P(X<55)

=P((X-mean)/s<(55-49)/8)

=P(Z<0.75)

=0.7734

The probability that next year Greenville will receive at most 55 inches of rain is 0.7734

B. To find the probability that next year Greenville will receive at most 62 inches of rain we would have to make the following calculation:

P(X>62)

=P(Z>(62-49)/8)

=P(Z>1.63)

=0.0516

The probability that next year Greenville will receive at most 62 inches of rain is 0.0516

C. To find the probability that next year Greenville will receive at Between 46 and 55 inches of rain we would have to make the following calculation:

P(46<X<54)

=P((46-49)/8 <Z<(54-49)/8)

=P(-0.38 <Z< 0.63)

=0.3837

The probability that next year Greenville will receive Between 46 and 55 inches of rain is 0.3837

D. Here consider a value that is more two standard deviations above the mean as an unusual vale. That is:

X=2σ+μ

=2(8)+49

=65

Therefore, having rainfall of above 65 inches would be considered as an extremely wet year.

Answer:

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

Step-by-step explanation:

[tex]3(x+4)^2-81=0 \\\\3(x^2+8x+16)-81=0 \\\\3x^2+24x+48-81=0 \\\\3x^2+24x-33=0 \\\\x=\dfrac{-24\pm\sqrt{24^2+4(3)(33)}}{2(3)}= \\\\\dfrac{-24\pm\sqrt{972}}{6}= \\\\\dfrac{-24\pm 18\sqrt{3}}{6}= \\\\-4\pm 3\sqrt{3}[/tex]

Hope this helps!

Answer:

14.50 cm  

Step-by-step explanation:

The Midsegment Theorem states that the midsegment connecting the two sides of a triangle is parallel to the third side, and its length is half that of the third side.  

Thus, ∆XYZ  is similar to ∆QRS with a scale factor of 2.

Also, the perimeter of ∆XYZ  is twice that of ∆QRS.

For ∆QRS, P = 2.93 cm + 2.04 cm + 2.28 cm = 7.25 cm

∴ The perimeter of ∆XYZ = 2 × 7.25 cm =14.50 cm

The Perimeter of triangle WXY is 14.5cm

The formula for calculating the perimeter of the triangle WXY is given as:

Perimeter of triangle WXY = XY + YZ + XY

From the given triangle;

Also,

Perimeter of triangle WXY = 2QR + 2QS + 2RS

Perimeter of triangle WXY = 2(2.93) + 2(2.28) + 2(2.04)

Perimeter of triangle WXY = 5.86 + 4.56 + 4.08

Perimeter of triangle WXY = 14.5cm

Hence the Perimeter of triangle WXY is 14.5cm

Learn more on perimeter of triangles here:  https://brainly.com/question/24382052

Answer:

I). X= 1,0. II) 1.72

Step-by-step explanation:

Using quadratic formula

Answer:

12.5 hours

Step-by-step explanation:

The data which represents the battery life, in hours, experienced by six users is given below:

10 14 14 16 13 8

To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.

[tex]Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5[/tex]

The point estimate for the web browsing battery life of the iPad is: 12.5 hours

Answer:

Step-by-step explanation:

To check which option is correct we will first make transition matrix.

Let the state 1 and state 2 represent the automobile and light rail

So, the transition is given by

[tex]P=\left[\begin{array}{ccc}0.80+0.05&0.15\\0.5+0.15&0.80\end{array}\right][/tex]

[tex]P=\left[\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right][/tex]

Since P as no any entry zero so, P as not absorbing stochastic matrix

Also,

[tex]|P| = \left|\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right| \\\\=0.85\times0.8-0.15\times0.2\\\\=0.65\neq0[/tex]

since |P| ≠ 0

Answer:

47.85

Step-by-step explanation:

33% of 145

of means multiply

Changing to decimal form

.33* 145

47.85

Step-by-step explanation:

cross multiply, set up ur equation like so

33. x

100 = 145

100x=4785

100

x=47.85

Answer:

  81

Step-by-step explanation:

2-digit squares are 16, 25, 36, 49, 64, 81.

Their sums of digits, are ...

  7, 7, 9, 13, 10, 9

The square 81 has a sum of digits equal to its square root.

Answer:

24 g

Step-by-step explanation:

We first find the mass of 24 % alcohol in 400 g of hand sanitizer. Let x be the mass of alcohol. So, x/400 × 100 % = 24 %

x/400 = 0.24

x = 0.24 × 400

  = 96 g

The mass of the other chemicals is thus 400 g - 96 g = 304 g

We now find the mass of 30 % alcohol in 400 g of hand sanitizer. Let y be the mass of alcohol. So, y/400 × 100 % = 30 %

y/400 = 0.30

y = 0.30 × 400

  = 120 g

The mass of the other chemicals is thus 400 g - 120 g = 280 g

The mass of other chemicals that needs to be evaporated is thus 304 g - 280 g = 24 g

Answer:

14.69% of men are SHORTER than 67 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches.

This means that [tex]\mu = 69.8, \sigma = 2.67[/tex]

What percentage of men are SHORTER than 67 inches

This is the pvalue of Z when X = 67. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{67 - 69.8}{2.67}[/tex]

[tex]Z = -1.05[/tex]

[tex]Z = -1.05[/tex] has a pvalue of 0.1469

14.69% of men are SHORTER than 67 inches

Answer:

Step-by-step explanation:

hello

from 4x-y=8 we can say that y = 4x-8

we substitute in the first equation to get

5x + 4 (4x-8) = 10

then

5x + 16 x -32 = 10

<=> 21x = 32+10=42

<=> x = 42/21 = 2

and then y = 8-8=0

don t hesitate if you need any further explanation

thanks

Answer: x = 2, y = 0 or (2 , 0)

Step-by-step explanation:

Solving using substitution is where you solve for a variable in one of the two equations in the system then plug it into the other.

For an easier plug in we can take the second equation. 4x-y = 8.

From here we need to isolate the y variable which is easier to isolate than x, in my opinion.

Subtract the 4x over.

-y = 8-4x

Now divide by a -1 so y is positive.

y= -8 + 4x

Now plug this in for y in the other equation.

5x + 4(-8 + 4x) = 10

Distribute the 4.

5x - 32 + 16x = 10

Combine like terms

21x - 32 = 10

Add the 32.

21x = 42

Divide by 21.

x = 2

Now that we have solved for one variable we can plug this into either equation and solve for the other.

I will plug it into the second equation.

4(2) - y = 8

Simplify.

8 - y = 8

Subtract 8.

-y = 0

Divide by -1.

y = 0

So the x and y values are.

x = 2

y = 0

Answer:

a) Residents of San Antonia, Texas

b) Response variable

c) Explanatory variable

d) Observational study

e) Response bias

f) The appropriate scope of interest is the " relationship between age and the weekly average usage of local parks in San Antonia"

Step-by-step explanation:

a) In this study, the objects or entities on which observation is done are the residents of San Antonia, hence they are the observational units.

b) In this observation, the number of visits per week is the response variable because it is the outcome of the observation. It is a dependent variable that varies due to variation in the ages.

c) Age is the variable that helps to predict the average number of visits to the park, it can then be called the predictor variable. It is independent of any external variable.

d) This is an observational study because it is meant to observe the relationship between the ages and the average number of visits to the park per week. The variables are not randomly assigned.

e ) The type of bias that is most concerning in this study is response bias. This is because it is a paper survey and their can be invalid responses either due to unfaithfulness or ignorance of the respondents.

f) The appropriate scope of the inference in this study is the relationship between the ages and the weekly average usage of local parks in San Antonia.

Answer:

h=7.65

Step-by-step explanation:

H is directly proportional to the square root of p;

Let k be the constant of proportionality;

Means h=k√p

This means for corresponding points of h and p such that (h1,p1) and (h2,p2) we have;

h1/√p1=h2/√p2

Let h= 5.4 when p = 1.44 and h when p =2.89 be respectively (h1,p1) and (h2,p2)

So that

5.4/√1.44=h/√2.89

5.4/√1.44 ×√2.89 = h

7.65= h

h=7.65

Answer:

Step-by-step explanation:

We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]

Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In our case, a = 1, b = -4 and c =2. Then the solutions are

[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]

[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]

We have that x = u-1. So the original solutions are

[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]

[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]

Answer: x+4

Step-by-step explanation: part one- x+4

Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4

Answer: student tickets = 208

Adult tickets = 97

Step-by-step explanation:

x + y = 305

x = 305 - y

5x + y = 693

Substituting

5 (305 - y) + y = 693

1525 - 5y + y = 693

-4y = -832

y = 832 / 4 = 208

5

Step-by-step explanation:

5 goes into 10 but 2 does not go into 5

Answer:

3 x^2 y^2

Step-by-step explanation:

Simplify the following:

3 x y x y

3 x y x y = 3 x^2 y^2:

Answer: 3 x^2 y^2

Answer:

D. 6x-4 9/10<= 18 1/8

Step-by-step explanation:

Sorry I'm a little late :(

Answer:

y=3

Step-by-step explanation:

If we use LCM and take 3 plus y it equals x so if x equals x it is then y

Answer:

D

Step-by-step explanation:

I took the Plato Course

Answer:

The answer depends on the shape of the trapezoid...

Step-by-step explanation:

A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)

Area = (a+b/2) * h

IF the sides are a = 3 ,b = 3 and height  = 4

THEREFORE:

(3+3/2) * 4

6/2 * 4

3 * 4

12

Hope it helped.... Please mark as brainliest..thanks!!!

Answer: C

Step-by-step explanation:

Since the sides are marked with the little lines, you know they are congruent with each other. Since the sides are congruent, you know the hypotenuse will be congruent.

You can argue that these triangles are similar, but the difference is that similar triangles are the same shape, but not the same size. These triangles are congruent because they are the same size and shape. Therefore, the hypotenuse is congruent.

Answer:

It would be 131.95 if they want the answer in pi it would be 42 pi

Step-by-step explanation:

Answer:

i

Step-by-step explanation:

It's imaginary, or it can also be referred to as i.