An ordinary (Pair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of andereCompute the probability of each of the following svents.Event A: The sum is greater than 7.Event B: The sum is divisible by 3 or 6 (or both).Write your answers as fractions

The area of the shaded part is:

The area of the shaded part is the subtraction of the area of the unshaded part from the area of the whole circle.

Area of the ushaded part is:

Area of the circle is:

Area of the shaded part is:

The sum of a rational number and a rational number is rational. ALWAYS

The sum of a rational number and an irrational number is irrational.

The product of an irrational number and an irrational number is irrational. SOMETIMES

For example, the product of multiplicative inverses like √2 and 1/√2 will be 1

The product of a nonzero rational number and an irrational number is irrational.​

ANSWER:

1st option: 1 is a constant

4th option: 9x + 4y + 1 written as a sum of three terms

STEP-BY-STEP EXPLANATION:

We have the following equation:

From the following equation we can say the following:

• The only constant term is 1

• None of the terms are similar

• There are a total of 3 terms

• The coefficients are 9 and 4

• The factors are 9, 4, 1, x and y

From the above we can affirm that the true statements are:

• 1 is a constant

• 9x + 4y + 1 written as a sum of three terms

Given:

cos(2t) = 0.8

Take the cos⁻' of both-side of the equation.

cos⁻' cos(2t) = cos⁻'(0.8)

2t = cos⁻'(0.8)

Calculate the value of the right- hand side with your calculator in radians.

2t =0.6435

Divide both-side of the equation by 2

t ≈ 0.32

Currently

Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.

In 5 years

Amy's age will be (x + 5) years.

Dianne's age will be:

The sum of their ages in 5 years is 91. Therefore, we have:

Solving, we have:

Amy is 29 years old. Therefore, Dianne will be:

ANSWER:

Amy is 29 years old, and Dianne is 52 years old.

Problem:

How much money would you have if you deposited $100.00 in an account that earned 8% interest after 20 years?.

Solution:

Step 1: Calculate 8% of the given amount ($100.00):

Step 2: Add the above value to the money deposited:

$100.0 + $8 = $108.0

Thus, we can conclude that the money in this account after 20 years is $108.0

The weight of the granite pyramid in tons is 1350 tons.

A pyramid is a three-dimensional shape.

The granite pyramid is 50 feet high and has a square base of 30 feet on a side.

Granit weighs 180 pounds per cubic foot.

Therefore, the weight in tons of the pyramid can be calculated as follows;

Hence,

volume of the granite pyramid = 1 / 3 b² h

Therefore,

volume of the granite pyramid = 1 / 3 × 30² × 50

volume of the granite pyramid = 45000 / 3

volume of the granite pyramid = 15000 ft³

Hence,

1 ft³ = 180 pounds

15000 ft³ = ?

weight = 2700000 pounds

1 pounds = 0.0005 tons

2700000 pounds = ?

Therefore,

weight of the pyramid granite in tons = 1350 tons

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The maximum number of turning points based on the degree of the polynomial is 2.

Turning point = n-1, where n is the degree of the polynomial.

Therefore, the maximum number of turning points based on the degree of the polynomial is 2.

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Answer:

Answer is 20 degrees
:)

Answer:

30 curtains

Step-by-step explanation:

You have 6 times as many seamstresses so you will get 6 times as many curtains

6 * 5 = 30 curtains

(-6,4)

Multiply each coordinate by 1/2

( -6 * 1/2 , 4 * 1/2) = (-3,2)

True

P(B) = 2/3

P(An B) = 1/6

What will P(A) have to be for A and B to be independent?

Remember that

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true

substitute given values

1/6=P(A)*(2/3)

solve for P(A)

Answer:

(B)a=18

Explanation:

The difference of a and 7 translated as an expression is:

Thus, the equation is:

To solve for a, add 7 to both sides of the equation:

The correct choice is B.

Answer: [tex]x > 4[/tex]

Step-by-step explanation:

[tex]8x-2x+7 > 21+10\\\\6x+7 > 31\\\\6x > 24\\\\x > 4[/tex]

Answer:

The design fee is $40.

Step-by-step explanation:

The y intercept means the cost when the number of shirts ordered is 0. This means that in the context of this problem the y intercept is the design fee.

Given

-1 = 8x + 2

Answer

-1 = 8x + 2

-1 -2 =8x

-3 = 8x

x = -3/8

The equation to represent the profit earned y, for selling x, number of shirts is y = 5x.

Given that:-

Selling Price of T-shirt = $ 15

Profit earned per T-shirt = $ 5

We have to form an equation to represent the profit earned y, for selling x, number of shirts.

We know that,

Profit earned by selling 1 T-shirt = $ 5

Hence, profit earned by selling x T-shirts = 5*x

We know that,

Profit earned by selling x T-shirts = y

Hence, we can write,

y = 5x

Hence, the equation that represents the profit earned y, for selling x, number of shirts is y = 5x.

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The given information is:

The starting population of bacteria is 390.

The population quadruples every 20 minutes.

To find the equation of the population in terms of minutes, we can apply the following formula:

Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.

If we replace the known values, we obtain:

To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:

Thus, after 1 hour there are 24960 bacterias.

Answer:

B, C, D and E.

Explanation:

The proof and reasons for each step is given below:

Step 1:

Statement: RSTU is a parallelogram.

Reason: Given

Step 2:

Statement: RS is parallel to TU and RU is parallel to TS

Reason: (B)Definition of a parallelogram

Step 3:

Statement: ∠RSU≅∠TUS and ∠RUS≅∠TSU.

Reason: (C)Alternate Interior angles are congruent

Step 4:

Statement: SU≅US.

Reason: (E)corresponding parts of congruent triangles are congruent.

Step 5:

Statement: Triangle RSU≅Triangle TUS.

Reason: AAS Congruence Theorem

Step 6:

Statement: RS≅TU and RU≅TS

Reason: (D)Opposite sides of a parallelogram are congruent.

The reasons that support the proof are B, C, D and E.

open up or down, vertex:(0,-4), passes through: (-3,5)​

In this problem we have a vertical parabola open upward

the equation in vertex form is equal to

y=a(x-h)^2+k

where (h,k) is the vertex

we have

(h,k)=(0,-4)

substitute

y=a(x)^2-4

Find the value of a

with the point (-3,5)

substitute in the equation

5=a(-3)^2-4

5=9a-4

9a=5+4

9a=9

a=1

therefore

the equation is

y=x^2-4

answer is

Let the age of the youngest child (Ben) be x years.

Since the ages are consecutive integers, the ages of the other 2 are (x + 1) and (x + 2).

It was given that the age of the youngest child is four more than eight times the age of the oldest child. This means that:

We can rearrange the equation above and solve for x as a quadratic equation:

Using the factorization method, we have:

Since the age cannot be negative, the age of the youngest child is 10.

Therefore, the ages are:

Given:

The area of the rectangle, A=65ft^2.

Let l be the length of the rectangle and w be the width of the rectangle.

It is given that the length of the rectangle is two feet less than 3 times the width.

Hence, the expression for the length of the rectangle is,

Now, the expression for the area of the rectangle can be written as,

Since A=65ft^2, we get

Equation (1) is similar to a quadratic equation given by,

Comparing equations (1) and (2), we get a=3, b=-2 and c=-65.

Using discriminant method, the solution of equation (1) is,

Since w cannot be negative, we consider only the positive value for w. Hence,

Now, put w=5 in equation (A) to obtain the value of l.

Therefore, the length of the rectangle is l=13 ft and the width is w=5 ft.

In direct variation function, variables x and y are related by the next formula:

y = kx

where k is the constant of variation.

Isolating k for the above formula, we get:

k = y/x

Computing y divided by x with the values of the table:

Given that all the quotients are different, then the linear function is not a direct variation

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following fraction

Now to reduce to its simplest form, we must simplify

GIVEN

The inequality:

SOLUTION

The inequality is to be solved.

Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:

ANSWER

We want to write

as decimal, doing it on a calculator we have

But we only need three decimal places, then the result is

The axis of symmetry for each function are x = -4 and x =1

The functions are given as

f(x) and h(x)

As a general rule of functions;

The axis of symmetry for a function is the x-coordinate of the vertex of the function

In f(x), we have

f(x)=3(x+4)² + 1​

The vertex of this function is

(x, y) = (-4, 1)

So, the axis is x = -4

For function h(x), we have

The vertex of this function is

(x, y) = (1, -3)

So, the axis is x = 1

Hence, the axis of symmetry are x = -4 and x =1

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The amount of freight transported by rail was 580 billion ton-miles in 1960.

The amount increased at a rate of 2.32% per year.

a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is

Where

y represents the final number after "x" periods of time

a represents the initial number at x=0

r represents the growth rate, expressed as a decimal value

x represents the number of time intervals that have passed

For this example, the initial amount is a=580 billion

The growth rate is r=2.32/100=0.0232

You can determine the equation as follows:

b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞

To graph it, you have to determine at least two points of the graph, I will determine 3

For x=-100

For x=0

For x=10

The points are

(-100,58.53)

(0,580)

(10,729.51)

Plot the points and then draw an increasing line from -∞ to +∞

c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000

This value is approximate x=23.57

This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.

Add the number of years to the initial year to determine the date:

By 1983 the number of ton-miles transported will exceed the trillion.

Answer:

I think its done this way. But I don't know if the answer is correct.

We are given the equation 7x+8=4x-10 and we want to find the value of x, such that the equality holds. To do so, we will start with the equation and the solve it for x. That is, we will apply mathematical operations on both sides of the equation, so we end up "ilosating" the x on one side of the equality sign. We start by

First, we subtract 4x on both sides, so we get

Now, we subtract 8 on both sides, so we get

Finally, we divide both sides by 3, so we get

so x=-6.