A red die is tossed and then a green dieis tossed. What is the probability thatthe red die shows a six or the green dieshows a six?Hint: The two events are not mutually exclusive. So to the find theprobability of the union, use:P(A or B) = P(A) + P(B) - P(A and B)[?]

Since we have a right triangle, we can relate the angle 28 with x and side 34 by meand of the sine function, that is,

where x is the hypotenuse. By moving x to the left hand side, we have

and by moving sin28 to the right hand side, we get

since sin28=0.4694, we have

then, x is given by

by rounding down, the answer is option D: x=72.4

According to the problem, there are 600 seats in the auditorium.

112 less than the number of seats in the gymnasium.

So, to find the number of seats in the gymnasium, we just have to add 122 and 600 because the auditorium has 112 seats less.

So,

We could write the following equation, where "x" is the number of miles travelled.

If we solve this equation, the first thing we're going to do is to let all "x terms" in a side of the equation and all the numbers in the other side. If "25" is summing in a side, it will change its sign when we pass it to the other side. Like this:

Now, we substract the numbers above and get:

Now, if 0.35 is multiplying "x", we are going to pass this number to divide the amount in the other side:

Therefore, Ken travelled 77 miles.

Given,

The coordinates of the points are (2,6) and (7, 2).

Required:

The distance between the points and the midpoint of the points.

The distance between two points is calculated as,

Hence, the distance between the points is 6.4

The midpoint is calculated as,

Hence, the midpoint is (4.5,4).

ANSWER:

C. $1,538.46

STEP-BY-STEP EXPLANATION:

To understand the question we must take into account that it is the gross payment, which is the payment received by the employee agreed with the company, without taking into account deductions or bonuses.

Therefore, we calculate it with the total payment divided by the amount of payments, like this:

So the correct answer is C. $1,538.46

Answer:

Step-by-step explanation:

18098

Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91

organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98

(a) Complete the grouped frequency distribution for the data.

79 to 83 -> 3

84 to 88 -> 4

89 to 93 -> 6

94 to 98 -> 2

(b) Construct a histogram for the data.

the histogram can be constructed using the information obtained in point (a)

Answer:

The y-intercept b for the derived equation is;

Explanation:

Given that the line passes through the point (4,-9) and has a slope of -1/2;

Applying the point-slope form of linear equation;

substituting the slope and the given point;

Comparing it to the slope intercept form of linear equation;

where;

m = slope

and b = y-intercept

Therefore, the y-intercept b for the derived equation is;

The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.

Answer: Options B and D.

The formula for Final Amount, A after compounding for n period of times is given by

Where A = amount

p= principal

r = rate (in %)

n = number of compounding periods

From the question.

A=21,000, p = ?, r=6, n = 3 x 2 = 6

The amount that must be deposited at the beginning is 14,804.17

In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then

if the first member is a girl and the other three needs to be boys, the number of possibilities are

then, divide in order to find the probability

In the form of the equation

S = m D + b

S represented on the y-axis

D represented on the x-axis

The independent is x

The dependent is y

Then D is the independent

S is the dependent

let us find the correct answer

Remember that the sum of the interior angles is 180. Then, we have the following equation:

This is equivalent to:

solve for M-angle:

Then, te correct answer is :

ANSWER

y = -3x + 3

EXPLANATION

We want to write the equation in slope-intercept form, which is the form:

y = mx + c

where m = slope; c = intercept

To do that, we have to use the point-slope method:

y - y1 = m(x - x1)

where (x1, y1) = point the line goes through

From the question:

m = -3

(x1, y1) = (0, 3)

So, we have that:

y - 3 = -3(x - 0)

y - 3 = -3x

=> y = -3x + 3

That is the equation of the line in slope-intercept form.

given the inequality :

- 7(x + 4) + 3x < 8x - 2(2x - 2)

so,

-7x - 28 + 3x < 8x - 4x + 4

combine like terms:

-7x + 3x - 8x + 4x < 28 + 4

-8x < 32

Divide both sides by -8

Do not forget to flip the inequality sign

so,

x > -4

so, The solution is the interval ( -4 , ∞ )

On the number line the solution will be :

The smallest possible interger of x = -3

​

Average is computed as follows:

Factoring

Factor the expression:

Divide the expression into two halves:

Factor b^2 from the first group and xb from the second group:

Now find the greatest common multiple of 72 and 96:

72= 2*2*2*3*3

96=2*2*2*2*2*2*3

Now we take the common factors with their least number of repetitions:

GCF=2*2*2*3=24

Now we find the GCF of 90 and 120:

90=2*3*3*5

120=2*2*2*3*5

GCF=2*3*5=30

Taking the GCF of each group:

Now we finally take out 3z+4h from both groups:

This last expression can be further factored by taking out 6b from both terms:

This is the final expression factored as much as possible

The Jensen's Alpha of the mutual fund is given as follows:

α = 3.

The Jensen's Alpha of a mutual fund is calculated according to the rule presented as follows:

α = [Rp - (Rf + Bp x (Rm - Rf))]

The parameters of the problem are defined as follows:

Hence, in the context of this problem, the values of the parameters are given as follows:

Rp = 14, Rf = 5, Bp = 1.2, Rm = 10.

Hence the Jensen's Alpha of the mutual fund is given as follows:

α = [Rp - (Rf + Bp x (Rm - Rf))]

α = [14 - (5 + 1.2 x (10 - 5))]

α = 3.

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Area of rectangle is given by:-

So the correct answer is

In the linear equations shown on the coordinate grid, the values of x that satisfies both equations is 2 (option b).

The graph of both equations intersect at the point where x equals 2.

6. Measure of angle 1 is 60 degrees because it congruent to angle 4 because they are opposed by the vertex

7. Measure of angle 3 is equal to 180 - angle 1 - angle 2 = 180 - 60 - 40 = 80 because these three angles sum 180 degrees

8. Measure of angle 5 is 40 degrees because it congruent to angle 2 because they are opposed by the vertex

9. Measure of angle 6 is equal to angle 3, because they are congruent, so it measures 80 degrees

10. Mesure of angle 7 is equal to the sum of angles 1 and 2 because they are congruent, so measure of angle 7 is 100

11. 80

12. 60

13. 120

14. 60

15. 120

Given:

The function g(x) is one-one.

Required:

We need to find the values of the inverse image of the function g(x).

Explanation:

Recall that the image of distinct elements of the function is distinct.

There exist an inverse of g(x) since g(x) is one to one.

The inverse image of the given can be written as follows.

Consider the equation

Final answer:

Since we are told there are 4 parts of sand for every 9 of gravel, the ratio of sand to gravel is 4/9.

Answer:

x=-6. y=6. xy=-36

x=-2. y=-3. xy=6

x=1. y=2. xy=2

The perimeter is the sum of the side lengths of a polygon. Now, let it be:

• l,: the length of the rectangle

• w,: the width of the rectangle

Considering the information given and the previous definition, we can write and solve the following system of equations.

We can use the substitution method to solve the system of equations.

Step 1: We combine like terms in Equation 2.

Step 2: We substitute the value of l from Equation 1 into Equation 2.

Step 3: We solve for w the resulting equation.

Step 4: We replace the value of w in Equation 1.

Thus, the solution of the system of equations is:

The length of the rectangle is 13 inches, and the width of the rectangle is 4 inches.

The net price and trade discount for the good is.539.4 and 359.6 respectively.

From the information given, tuw.Sony Hd flat-screen list price is 899 and has a discount: 5/4 net price:

The net price will be:

= List price × (1 - Discount rate)

= 899 × (1 - 40%)

= 899 × 60%

= 899 × 0.6

= 539.4

The trade discount will be:

= List price - Net price

= 899 - 539.4

= 359.6

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Complete question:

Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price and discount 40%

The restricted values of x for the following rational expression.

x = 0

x = -3/4

Restricted values are those values in a rational expression that bring the denominator to zero. When referring to "Market Value," the term "restricted value" denotes the property's value under the assumption that it is subject to a temporary governmental or private limit on rentals and tenant income levels. The denominator's real numbers that have a value of 0 are not included in the domain. The word "restrictions" refers to these values. Similar to how fractions are simplified, rational expressions can be too. Cancel the common factors after factoring the numerator and denominator. Place a zero as the denominator. Put the equation to rest. The restricted values are the answer or answers.

Rational expressions should first be multiplied, and then the numerator and denominator should be factored. Next, common factors should be cancelled. Notify yourself of the domain's limitations.

−5x– 8/x² + 4 = 0

- 5x - 8/[tex]x^{2}[/tex] = -4

x = 0

x = -3/4

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We can use the definition:

Looking at the figure we can see the values:

But we don't have the hypotenuse value, we must use the Pythagorean theorem to find it

Now we have the hypotenuse we can find all values

Answer;

Medain for morning is 25

Median for evening is 21.5

Explanation;

Here, we want to create frequency tables for each of the given groups

We start with the morning group

The frequency table for it is as follows;

Now, we proceed to the afternoon group

We have this as follows;

Lastly, we will want to get the median value of both groups

To do this, we need to re-arrange the values in the data set in ascending or descending order

For the purpose of this solution, we shall be using the ascending order mode. Then from here, we pick out the middle value

For the morning group, we have;

12, 19,21, 23,25,27,31,36,39

Since the numbers are 9, the middle number will be the 5th number since it leaves equal spread of values on the left and right

Thus, we have the median value as 25

The afternoon set, we have it as;

8,8,11,15,16,27,34,39,43,51

We proceed to choose the mid 5th values comig from both ends

We have this as;

We have these values as; 16 and 27

We add these and divide by 2

We have this as;