A junk drawer at home contains eight pens four of which work what is the probability that a randomly grab three pens from the drawer and don’t end up with a pen that works express your answer as a fraction in lowest terms or decimal rounded to the nearest million

We have that 1 cubic meter is equivalent to 1.308 cubic yards. Then, we can use a rule of three to find the value in yards of 1.37 cubic meters:

therefore, 1.37m³ is equivalent to 1.792yd³

The simplified value of the given expression in the form of a fraction is  [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .

The given expression is:  [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

we will use the properties of exponents to simplify the expression.

Taking the powers of the like terms and combining we get :

[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]

[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]

Therefore we get the simplified equation for the expression.

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.

A variable is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.

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Coordinate of the Hospital = (-6, -4)

Coordinate of City Hall = (0,0)

We have a segment AB of which we know the coordinates of A(3,6) and the midpoint M(5,1).

We have to find the coordinates of B.

We know that the coordinates of the midpoint M are the average of the coordinates of the endpoints A and B, so we can write:

Now we have the x-coordinate of B in function of the x-coordinates of A and M.

The same can be calculated for the y-coordinate:

Then, we can replace and calculate:

Then, the coordinates of B are (7,-4).

Answer: B = (7,-4)

The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. The

water output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a

total water output of 1025 L. How long was each sprinkler used?

Let

x ------> the number of hours of Hill family's sprinkler

y ------> the number of hours of Stewart family sprinkler

so

we have that

x+y=55 -------> x=55-y ------> equation 1

15x+25y=1025 ------> equation 2

Solve the system

Substitute equation 1 in equation 2

15(55-y)+25y=1025

solve for y

825-15y+25y=1025

10y=1025-825

10y=200

y=20

Find the value of x

x=55-20) -----> x=35

therefore

She bought the bike by 3,000 six years ago, we are assuming the value of her mountain bike depreciated 20% each year

1 year

3,000*20% = 600

2year

3,000-600 = 2,400*20% = 480

3year

2,400-480 = 1920*20% = 384

4 year

1920-384= 1,536*20% = 307.2

5 year

1,536-307.2= 1,228.8*20% = 245.76

6year

1,228.8 - 245.76 = 1,043.04*20% = 208.608

1,043.04 - 208.608 =834.432

Rounded to the nearest dollar

= 834

Answer:

Recursive formula:

a_n = a_n-1 + 14,

a_1 = 16.5

Explicit formula: a_n = 14(n - 1) + 16.5

Each movie costs the same amount.

Explanation:

Looking at the numbers we see that each next term a_n is 14 added to the previous term, a_n-1 and the first term a_1 is 16.5; therefore, we can say

Step 1

Given;

Step 2

The probability of an event is given as;

Thus,

Answer;

Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].

What is the rectangle?

A rectangle is a two-dimensional flat shape. In an [tex]XY[/tex]  plane, we can easily represent a rectangle, where the arms of x-axis and y-axis show the length and width of the rectangle, respectively.

Area of rectangle = Length × Width

Here given that,

[tex]L=\frac{7}{8}m[/tex]

[tex]W=\frac{3}{4}m[/tex]

So,

Area of rectangle = [tex](\frac{7}{8}m)*(\frac{3}{4}m)\\[/tex]

[tex]=\frac{21}{32}m^2[/tex]

Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].

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Let the number of door wreath sold is x.

Let the number of candy bar sold is y.

The inequality can be represented as,

Thus, the above inequation gives the required inequality.

The given expression is,

So, expanding we have,

Given:

The bins can hold no more than w(b) < 200 pounds.

The crate can hold no more than w(c) < 50 pounds.

The number of bins is n(b) = 3.

The number of crates is n(c) = 2.

The objective is to find the correct number line for the graph.

Explanation:

The maximum quantity of bins can be calculated as,

The maximum store capacity can be calculated as,

Solution

For this case we can do the following:

m < PQR = 7x -19

m < OPQ= 2x-3

m < QOP= x+16

We need to satisfy that:

(180- m Replacing we got:

(180- 7x +19) + 2x -3 + x+16= 180

-7x +2x +x = -19+3 -16

-4x = -32

x= 8

Then m

Let's remember that the equation of a line always has the form:

where "m" and "b" are constant numbers that we must find. Now, let's find "m" first. "m" is called the slope of the line, and it represents the relationship between the changes in y (second component) and the changes in x (first component). So it isn't surprising that we can compute it by:

Having calculated "m", we know that, (for the point (42.3,82) must lie in the line)

Then,

This implies that the equation of our line is

Here is a graph of the line:

Comment: Our line is represented with a red color.

The distributive property states:

so:

The general equation of circle with centre (h.k) and radius r is,

Simplify the equation to obtain the centre and radius of circle.

So center of circle is (-1,5) and radius 4.

Check below, please.

1) In this question, we're going to remember two concepts: The perimeter is the sum of the lengths of each segment of each letter.

2) So let's start counting each tiny square so that we can get to know the length.

The letter "L" is actually, with this typography, two rectangles:

So, the perimeter (2P) is equal to:

2P =15 +15 +7+3+3+10+3

2P= 56 units

As for the area:

Using the Rectangle formula, then we can write down the area as:

Area:

3) In this letter "O" we can divide it into two trapezoids, and two parallel rectangles:

Note that we need to find the length of those corners shaped like triangles, we can use the Pythagorean Theorem, considering the "rise over run" and write:

So the Perimeter can be written:

And for the area, we can find the area of those two trapezoids and two rectangles writing this:

4) And now, finally the letter "u":

For the corners let's assume they are triangles, and then we can write the following since those corners are like hypotenuses:

And for the inclined lower part of the letter "u", we can write:

Therefore, we can write the Perimeter as:

And for the area, we can see from bottom to top: One trapezoid, a par of parallelograms, and two rectangles. Hence, we can write:

5) So, each letter by area and perimeter:

To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.

Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.

Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.

To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.

hello

between 5/3 and 9/16, 5/3 is greater than 9/16

ANSWER:

5 x j = 80

STEP-BY-STEP EXPLANATION:

The sentence as an equation would be the multiplication of j and 5 equal to 80, just like this:

ok

Total money = $300

money spend = $15

300 ---------------------- 100

15 ---------------------- x

x = (15 x 100)/300

x = 1500/300

x = 5

Jennie spent 5% of her money

To solve it, use a rule of three. $300 is 100%, so we need to calculate which percent is $15 of the total amount.

In a rule of three, it's necessary to use cross multiplication and then division.

That's why I multiplied 15 by 100 and then I divided by 300.

15 is 5% of $300

Answer:

Explanation:

Here, we want to get the gradient of the line L3

The equation of a straight line can be expressed as:

where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)

Now,let us write the equation of the first line in the slope-intercept form

Mathematically, we have this as:

The gradient of the first line is 3

Now,let us get the gradient of the second line L3

Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1

Thus, we have it that:

A rectangular box has six faces. The surface area is given by the sum of the area of those faces. Parallel faces have the same area, therefore, we just need to calculate the area of three of them and multiply by 2. The surface area of our gift box is:

The surface area of the box is 5400 cm².

An equation is a mathematical expression that contains an equal sign. The objective of an equation is usually to determine the value of an unkown variable, commonly referred to x or y. In order to do that, however, we need to isolate the variable on the left side and this has to be done in a way that mantains the balance in the equation. This means that whatever operation we do on one side we have to perform the same exact operation on the other side. Let's take a look at an example.

For this equation we have the unknown variable x, which is the value we want to find. Our goal is to isolate the variable on the left side, however we can see that there is one x on the right side, the first step will be to move this to the left side, this is what means to move the lowest variablem term first, because if we were to move "3x", which is the highest variable term, we would have to perform more steps to solve the equation.

To move the term "x" from the right to the left we need to subtract both sides by "x", this is because when we subtract "x-x" on the right side, the result will be 0 and we will be left with unkown variables only on the left. Let's check this out:

As we can see by doing so we eliminated the variable on the right side. Now we want to remove the 9 from the left side, we will have to perform a similar operation by subtracting 9 from both sides.

Now we have only a variable term on the left side, but it still being multiplied by 2 and we don't want that, so we have to divide both sides by 2.

With this we achieved the goal of the equation, which was to find the value of x. In short we always want to isolate the variable on the left side and to do that we will have to perform the inverse operation of the other terms in both sides of the equation, if a term is adding we need to subtract on both sides, if it is multiplying we need to divide on both sides and so on. We have to do that first with the term that contains the letter of lowest value, like we did with this one.

Answer:

$2875

Explanation

Given

Principal P = $2,500

Rate R = 15%

Time T = 1year

Get the interest on $2500

Simple Interest = PRT/100

Simple Interest = 2500 * 15 * 1/100

Simple Interest = 25*15

Simple Interest = $375

Amount owed altogether = Pricipal + Interest

Amount owed altogether = $2500 + $375

Amount owed altogether = $2875

The equation to solve is:

We use distributive property [a(b+c)=ab+ac], simplify and solve for b:

From here, we can't solve.

It is the same equation.

No Solution.

Solution

The image below contain the solution

1) To find how many miles per gallon that freight train makes is to find a rate. We can find it in two ways, either by setting a proportion or by finding the slope.

2) Note that this direct variation depicted by the graph is proportional. Therefore, let's find the slope by picking two points:

3) Thus, the answers are:

Let's begin by listing out the information given to us:

The road rises by 7 feet every 100 horizontal feet

The equation becomes:

Slope (m) = Δy/Δx = 7/100 = 0.07

Slope (m) = 0.07

1) Notice that:

Therefore the recursive formula for the first sequence is:

2) Notice that:

Therefore the recursive formula for the second sequence is:

Answer:

Left sequence:

Right sequence: