The variables x and y vary directly. Write an equation that relates the variable. Then find x when y=16.

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

The window has a length of 21 inches

From the question, we have the following parameters

Area of the window = 336 square inches

Width of the window = 16 inches

The area of the window is the product of its dimensions

So, we have

Area = Width of the window x Length of the window

Substitute the known values in the above equation

So, we have the following equation

336 = 16 * Length

Divide both sides by 16

Length = 21

Hence, the length is 21 inches

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Part A

The variable are;

Plywood, wood planks, quarts of paint

Part B

Let p represent Plywood

Let w represent Plank of wood

Part c

Let p represent Plywood

Let w represent Plank of wood

Let q represent quarts of paint

We are asked to find the final expression in exponent for, of the product of two radical expressions as shown below:

We will be addressing each factor at a time, first in the cubic root, and second in the square root.

Cubic root:

notice that the pure number (64) can be written as the perfect cube of the number 4 since 4^3 = 64. That means that a factor 4 will come out of the cubic root, and no factor 4 will be left in the root.

Now we are going to address the variables g and y which are inside the root, and try to find if they contain any perfect cube expression (perfect cubes will cancel out of the cubic root simplifying then the notation).

We notic that g^4 can be written as g^3 times g, so g^3 will come out of the cubic root as "g", and a factor "g" would be left inside the cubic root. Similarly, the factor y^2 cannot get out of the cubic root because it doesn't have a perfect cube in it.

We are then left with the following expression:

Now, we recall the property of fractional exponents associated with roots of a factor:

Using this, the cubic root can be expressed as fractional exponents, as we show below:

Now we proceed to simplify the expression with the square root. This is much simpler, since all factor inside can be written as perfect squares:

64 = 8^2

g^4 = (g^2)^2 (the double square of g)

y^2 is already a perfect square.

Therefore, the square root is simplified entirely and we are left with the following factors:

8 g^2 y

Now we combine via the multiplication what we found for the cubic root and what we found for the square root:

Therefore the power (r) of the factor g is the fraction: 10/3

The power (s) of the factor y is the fraction 5/3

and the constant number "k" is 32.

To answer this question we will use the following formula for the z-score:

Substituting = 2000h, = 40h and x=2100h we get:

Simplifying the above result we get:

Using tables we get:

Then:

The above result as a percentage is:

Answer:

At least 26 bags of cat chow is required for a period of one year to fulfil the demand at the wildlife shelter in North Carolina

Quantity of cat chow sold in each bag = 20 lb

Consumption in lb of cat chow per week in the wildlife shelter = 10 lb

Number of weeks in a year = 52 weeks

The total quantity of cat chow required for 52 weeks = Weekly consumption of cat chow*Number of weeks

= 10*52

= 520 lb

Number of bags required = Toal quantity of cat chow required for 52 weeks/ Quantity of cat chow sold in each bag

= 520/20

= 26 bags

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We need to find the magnitude and direction from vector A of the resultanr vector.

How many miles of gas does my car travel if it used 2 gallons of gas with a speed of 4 mi/h?

We know that the angle 2 and the anlge 4 are equal because of oposite angles so:

and we can solve for x so:

So:

Now we also know that angle 1 and 3 are equal and the sum of the internal angles must be:

So angle 1 is equal to 132º

The true statement based on the information is that D. There were fewer attendees than purchased tickets.

A box and whisker plot is a graphical representation of variance in a set of data. A histogram analysis is sufficient in most circumstances, but a box and whisker plot can provide more detail while allowing different sets of data to be displayed in the same graph.

The box and whisker figure highlights data on the number of Broadway tickets sold and actual attendance at the performances. In this case, the graph shows that the number of tickets are more.

Therefore, the correct option is D.

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Answer:

See below and attached Venn Diagram3

Step-by-step explanation:

No need to change Venn diagrams It is perfectly clear

The completed Venn Diagram is attached for your convenience

Answer:

Explanation:

A bag contains 11 red marbles and 4 blue marbles.

• The total number of marbles = 11+4=15

1 marble of any color is chosen random from the bag with a probability of 1/15.

A situation that can be modeled using such a situation must be one that also has a probability of 1/15.

In Option D,

As the image attached shows, the horizontal distance reached by the ball is 40 feet.

Notice that the horizontal movement goes from 0 to 40, this means the domain is

Since x-values are domain values.

Answer: f(4) = -18

Step-by-step explanation:

f(4) = -3(4 + 2)

= -3(6)

= -18

Wednesday's game generated $2020

Let the amount generated by Wednesday's game be x

Let the amount generated by Saturday's game be y

The two games together earn $4920 for the team. That is,

x + y = 4920....................(1)

Wednesday's game generates $880 less than Saturday's game

x = y - 880.................(2)

Make y the subject of the formula in equation (2)

y = x + 880..................(3)

Substitute equation (3) into equation (2)

x + x + 880 = 4920

x + x = 4920 - 880

2x = 4040

Divide both sides by 2

2x/2 = 4040/2

x = 2020

Wednesday's game generated $2020

Solution

A coin has two possible outcome

We have 5 marbles

The final answer

Answer:

5(km)/1(hr)

Step-by-step explanation:

You multiply the 30 minutes to make one hour, and with that, you also multiply the 2.5 kilometers to get 5. You multiply the 2.5 because we multiply both sides of an equation.

Uniform line movement.

We have that the data is:

Time (t) = 30 m = 0.5 h

Distance (d)= 2.5 km

Speed (v) = ?

Since it asks us for the speed in Km/h, we make a time conversion, from minutes to hours. Knowing that 1 hr = 60 minutes, then

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{30 \not{m}*\left(\frac{1 \ h}{60 \not{m})\right)=0.5 \ h } } \end{gathered}$}}[/tex]

To calculate the speed, divide the distance by the time. We apply the following formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{Speed=\frac{Distance}{Time} } \end{gathered}$}}[/tex]

We substitute our data in the formula and solve:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{d}{t} } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{2.5 \ km}{0.5 \ h} } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=5 \ km/h} \end{gathered}$} }}[/tex]

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

A data set is a group of figures or values related to a specific topic. a list of words, numbers, or symbols, the values of which are frequently the outcomes of an investigation or observation. There are typically multiple variables in data sets.

A dataset is an organized group of data typically connected to a certain body of work. An organized collection of data kept as several datasets is called a database.

In an ordered data set, the median is the value in the middle. The mean is calculated by dividing the sum of all values by the total number of values. The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

Therefore, the correct answer is option c) The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.

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Given:

Required:

We need to find the number of thousands.

Explanation:

Multiply 10 and 3.

The number of thousands is 30.

Final answer:

There are 30 thousands.

Given the following trigonometric expression:

We will simplify the expression as follows:

First, taking sin (x) as a common

Second, we will use the following trigonometric identity:

Finally, substitute the trigonometric identity number (1) into the given expression

So, the answer will be sin (x)

We will have the following:

*First: We would determine the piecewise function that describes the graph.

Since we can see that the function increases by a factor of 2 and decreases by the same factor we would have:

This is:

*Second: We calculate the inverse of the piecewise function:

That is:

From this we can see that the inverse of that graph would in fact represent a function, a non-continuous function. [It will represent a function as long as it follows the parameters stablished in the first point]

Solution

The Amount after t years is given by

The Percentage annual increase is

Hence, the account increase 75% annually

From the question, we can deduce the following:

Length = 5.6 meters

Width = 7.3 meters

Height = 4.5 meters

Where:

1 ft = 0.3048 m

1 cubic foot = 7.48 gallons

Let's find the amount of gallons of water in the tank if the tank is filled to 1 foot below the top of the tank.

Let's first sketch the tank.

We have:

Now, let's find the volume of the tank(total amount of water it can carry).

Apply the formula:

Thus, we have:

Now, to find the amount of water presently in the tank since it is filled 1 ft below the top of the tank, we have:

Therefore, the volume of the water in the tank is 171.5 cubic meters.

Now, let'c convert from cubic meters to gallons.

Where:

1 foot = 0.3048 m

Thus, we have:

Now, to convert from cubic feet to gallons, where:

1 cubci foot = 7.48 gallon

We have:

Therefore, there are 45273.86 gallons of water filled in the tank.

In this problem, we have the transformation

A(-3,4) -------> A'(-15,20)

so

The rule is

(x,y) -----> (5x,5y)

the answer is option b

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

Given the expression

To find the value of the expression you have to follow the order of operations:

- Parentheses

- Exponents

- Multiplication/Division

- Addition/ Subtraction

• First, you have to solve the operations inside the parentheses term:

Solve the division first and then the sum:

• Write the result on the original expression:

• The next step is to solve the multiplication and finally solve the difference

The value of the expression is 7

The given set in roster method is written as {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.

Given that, M={x : x is an integer and 2 ≤ x ≤20.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Now, the given set in roster method can be written as follows:

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Therefore, the given set in roster method is written as {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.

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"Your question is incomplete, probably the complete question/missing part is:"

Write the given set in roster method: M={x : x is an integer and 2 ≤ x ≤20

The algebraic expression which correctly represents the word phrase and it's solution are respectively; 29 equals 11.5 plus m over 2.5; m = 43.75.

It follows from the task content that the algebraic expression of which represents the word phrase is to be determined.

First, the quotient of a number, m and 2.5 can be represented algebraically as; m/2.5.

Therefore, since; Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5, we have;

29 = 11.5 + (m/2.5)

The solution is therefore as follows;

29 -11.5 = (m/2.5)

17.5 = (m/2.5)

m = 2.5 × 17.5

m = 43.75.

Therefore, the correct answer choice is; 29 equals 11.5 plus m over 2.5; m = 43.75.

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The associated matrix associated to the linear transformation is A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex].

Linear transformations are applications between two vector spaces that preserves the properties of vector addition and the product of a vector and a scalar. In this problem, we find the following linear transformation between the two bases:

W → V

(w₁, w₂, w₃, w₄) → v₁

Then, there is the following relationship:

V = A · W

Where A is the associated matrix. The matrix V has four rows and one column and the matrix W has two rows and one column. Then, by property of multiplication of matrices, the associated matrix has four rows and two columns. Then, the associated matrix is:

A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex]

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