How can I draw a frequency table to represent the information given? how can I calculate the realtive frequency of a size 6 shoe? How can I calculate the probability that if a pupil is chosen at random, that he/she wears a size 7 shoe?

Her monthly income for last month was $1,093.56

Here, we want to calculate the monthly income for Dee Saint

Mathematically, from the information given in the question, we can have this as;

Maximum number of identical boxes with no. of supply items in each box will be:

a. 78 boxes with 1 pencil and 1 eraser in each box.

b. 195 boxes with 1 notebook and 1 folder in each box.

c. 65 boxes with 1 eraser, 1 marker and 2 folders in each box.

First Lana will make 78 boxes with 1 pencil and 1 eraser in each box. After that she'll be left with

143 - 78 = 65 erasers.

Secondly she will make 195 boxes with 1 notebook and 1 folder in each box. After that she'll be left with

330 - 195 = 135 folders.

Next she will make 65 boxes with 1 eraser, 1 maker and 2 folders in each box.

By doing this she will be able to make maximum number of identical boxes.

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Given

To find the missi

Notice that in the fraction

Can be interpreted as "36 out of every 100"

As a percentage, this means 36%

First, we need to develop each case or take care of the following:

One number is greater than another if it is more at the right of the Real Line.

A negative number is lower than a positive number.

Between two negative numbers, the greater is the one near to zero.

Let develop the numbers:

A. 50 - 16pi is approximately -0.265472

B. 16 - sqrt(410) approximately equals to -4.24845

C. -sqrt(20) + 1/2 is approximately equals to -3.97213

D. 7/3 - (7*pi)/3 is approximately equaled to -4.99705

So taking into account the previous reasons at the beginning, we have that the number near to zero is -0.265472, which is the first option. Option A.

A game center has a $5 admission fee (this is the y-intercept of the equation)

It charges $0.50 for each game played (this is the slope of the equation)

The equation can be written as

Where y is the cost and x is the number of games played.

To plot the graph, you can either find some (x, y) coordinates using the above equation.

Or you can plot it using the concept of slope and y-intercept.

Start at the point of y-intercept (0, 5)

The slope is 0.50 = 1/2

Then go 1 unit up and two units to the right that is your next point.

Repeat the same, 1 unit up and two units to the right that is your next point and so on...

Let us plot the graph

Scale: one small box = 1 unit

x-axis = number of games

y-axis = Cost ($)

The given angle and angle 3 are corresponding angles, that is, angles that are on the same corner at each intersection. Graphically,

Corresponding angles are congruent, so

On the other hand, angle 3 and angle 4 are supplementary angles, that is, add up to 180°. Graphically,

So, you have

Therefore, the measures of the numbered angles are

Given the parallelogram ABCD:

The sum of every two adjacent angles = 180

so,

m∠B + m∠C = 180

m∠C = 180 - m∠B = 180 - 114 = 66

So, the answer will be m∠C = 66

The pattern is:

3

3x3

3x3x3

and so on

So it's 3^6 = 729

Answer: the second option

Answer:

2:5

Step-by-step explanation:

8:20

= 4:10 (simplifying)

= 2:5

Answer:

2:5

Step-by-step explanation:

8=2*2*2,    20=2*2*5

cancel out the numbers they have in common

8=2*2*2,  20=2*2*5

=2,5

as a ratio

2:5

Since (-5)2 using the exponential symbol can be written as (-5)^2

This means -5 in 2 places

(-5)X, using the exponential symbol, can be written as (-5)^X

X(-5), using the exponential symbol can be written as X^(-5)

Therefore:

(-5)X - X(-5) = 17, in exponential form, can be written as:

(-5)^X - X^(-5) = 17

We are asked to determine the value of "x" and "y".

To determine the value of "y" we will use the facto that since WP is a median this means that:

Substituting the values in terms of "y" we get:

Now, we solve for "y". To do that we will first subtract "7y" from both sides:

Now, we subtract 11 from both sides:

Now, we divide both sides by -4:

therefore, the value of "y" is 4.

Now, to determine the value of "x" we will use the fact that since WP is an angle bisector we have that:

We also have the:

Therefore, we have:

Now, we substitute the values:

Now, we divide both sides by 2:

Now, we subtract 2x from both sides:

Now, we subtract 12 from both sides:

This means that the value of "x" is 20.

To determine if WP is an altitude we need to determine if the angle APW is 90 degrees. To do that we use the fact that the sum of the interior angles of a triangle always adds up to 180, therefore:

We substitute the values in terms of "x":

Now, we substitute the value of "x":

Solving the operations:

now, we subtract 90 from both sides:

Since WPA is 90 degrees and WP is a median and bisector this means that WP is an altitude.

To solve number 14, we will make use of the Law of Cosines, which states that:

As in our problem b = 15, c = 13 and A = 95°,we can replace these values in the formula and solve for a:

In our case, a is the segment BC.

Answer: 20.7

First, let's sketch the problem:

To find the horizontal distance d, we can use the cosine relation of the angle 74.5°.

The cosine is equal to the length of the adjacent leg to the angle over the length of the hypotenuse.

So we have:

SOLUTION

From the question we want to know how many cubic-feet of a warehouse can contain 430 boxes, whereby "each one" of these 430 boxes measures 12 inches by 8 inches by 9 inches

Firstly we have to change these inches of the sides of ecah of these boxes to feet.

12 inches make a foot.

Hence each box in feet will measure

So each boxes in feet will measure half cubic foot.

The warehouse that will contain 430 of these boxes should measure

Hence, the answer is 215 cubic-feet

As given by the question

There are given that in the right triangle DEF, angle D is 90 degrees and angle f is 12 degrees less than angle E.

Now,

The sum of the three measures of a triangle is always 180 degree

So,

Where angle D is 90 degree

Then,

Also we are given that

Therefore, substituting for F back into E+F=90

Then,

So, angle E is 34 degrees, which is the answer.

We are given the following inequality:

To solve this inequality we will subtract 1 to both sides:

And thus we get the solution.

Answer:

$18,000

Explanation:

Let us represent the tax by y and the property value by x. If the tax is proportional to the property value, then the relationship between y and x is the following.

where k is the constant of propotionality.

Now, to paraphrase, we are told that when y = $9,000, then x = $500,000. This means

and we need to solve for k.

Dividing both sides by 9000 gives

which simplifies to give

With the value of k in hand, our formula now becomes

We can now find the tax when x = 1,000,000.

Putting in x = 1,000,000 into the above formula gives

which simplifies to give

This means, the tax on a property assessed at $1,000,000 is $18,000.

We have a initial deposit of $10,000 (PV=10,000).

The investment last 6 years (t=6).

The annual interest rate is 3.2% (r=0.032) and is compounded continously.

The equation to calculate the future value FV of the inverstment for this conditions is:

The value of her investment will be $12,116.71.

EXPLANATION:

Given;

We are given the quadratic equation as shown below;

Required;

We are required to solve for x by completing the square method.

Step-by-step solution;

We start with the constant 13.

Subtract 13 from both sides of the equation;

Next we take the coefficient of x (that is -8). We half it, and then square the result. After that we add it to both sides of the equation;

We now have;

We can now simplify this;

We now factorize the left side of the equation;

we can now refine our equation to become;

We can now solve for x as follows;

Take the square root of both sides;

Therefore;

ANSWER:

Let's analyze all the statements and see why they are false or true.

A. FALSE

The tallest plant in variety B is just 18 tall, while the variety A we have 21.

B. FALSE

We do have plants in A that have the same height as B.

C. FALSE

The standard deviation measure how far it's from the mean, the variety B has a 2.4 standard deviation, which means that the height can be more distant from the mean than in variety A.

D. True

Justified by C. Variety A has a 1.2 standard deviation, which means it's more likely to be closer to the mean

Answer:

240 m³

Explanation:

The volume of a pyramid is equal to:

Where B is the area of the base and H is the height of the pyramid.

Then, the base of the pyramid is a triangle, so the area of a triangle is equal to:

Where b is the base of the triangle and h is the height of the triangle. So, replacing b by 16 m and h by 9 m, we get:

Finally, replacing B by 72 m² and H by 10 m, we get that the volume of the pyramid is equal to:

Therefore, the volume is 240 m³

Given:

There are given that the triangle, ABC.

Where:

Explanation:

According to the question, we need to prove that the isosceles triangle:

So,

From the concept of the isosceles triangle:

The isosceles triangle is defined when two sides of the length of any triangle are equal.

Then,

First, we need to find the length of the sides by using the distance formula:

So,

Then,

And,

Final answer:

Hence, the step and values of the sides are shown below;

And,

The side CA and AB is congruence by the definition of h

And,

Triangle ABC is an isosceles triangle by the the defination of b.

Assuming the dashed lines are parallel and perpendicular to the base, we can start by draw a third parallel line that passes through C and naming some distances:

Now, we can see that the given angles are alternate interior angles with respect to the angles formed by the new perpendicular line and the lines AC and BC:

Now, we can see that b and the base a + 24 are related with the tangent of 48°:

Also, b and a are related with the tangent of 17°:

We can solve both for b and equalize them:

Now, we can relate a and x with the sine of 17°:

And x is the distance between A and C, the storm. Thus the answer is approximately 31.2 miles, fourth alternative.

We are asked to find the sum of the following expressions

First of all, expand the parenthesis

Now, collect the like terms together and add/subtract

Therefore, the sum of the given expressions in the simplest form is

Okay, here we have this:

Considering the provided information, we are going to calculate the requested rate of change, so we obtain the following:

We will replace in the rate of change formula with the following points: (1990, 1.2) and (1994, 1.6), then we have:

Rate of change=(f(b)-f(a))/(b-a)

Rate of change=(1.6-1.2)/(1994-1990)

Rate of change=0.4/4

Rate of change=0.1 Billion

Finally we obtain that the average rate of change in the number of public library visits from 1990 to 1994 is 0.1 billion.

We are given that the length a rectangular-shaped figure is 2 feet longer than its width. This can be written mathematically as:

Where "l" is the length and "w" is the width. WE are also told that the area is 13 square feet. Since the area is the product of the length and the width this means the following:

From the previous equation we solve for the length by dividing both sides by its width:

Now we replace this in the first equation:

Now we multiply both sides by the width:

Subtracting 13 to both sides:

We get a quadratic equation. To solve this equation we will factor the equation by completing the square:

Factoring the parenthesis:

Now we add 14 to both sides:

Taking square root to both sides:

Subtracting 1 to both sides:

We take the positive value for the width, that is:

Now we replace this value of the width in the first equation:

Therefore, the dimensions are:

The original width of the rectangular piece of metal is 21 inches.

let us take into consideration the width of the rectangle be x,

Length is given to be 5 inches more than the width

∴ length = x+5

Now squares of side 1 inch is cut from all the corners of the rectangle to form a box in the form of a cuboid.

New length of the base of the box = (x+5) - 2 = x+3 inches

new width of the box = x -2 inches

Height of the box = 1 inch

Volume of the box that is formed

= (x+3 ) · (x -2) × 1

= x² - x - 6

The given volume of the box is 414 cubic inches

Therefore:

x² - x - 6 = 414

or, x² - x -420 = 0

Solving the quadratic equation by middle term factorization we get :

or, ( x - 21 ) ( x + 20 ) = 0

Now either x=-20( not possible)

or , x =21 inches.

Therefore the original width of the rectangle is 21 inches.

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Given the following numbers

To find the greatest common factor, G.C.F.

The factor that can divide through two or more numbers evenly is the G.C.F

The factors of 20 and 32 are as follows

The common factors between 20 and 32 is

Hence, the GCF of 20 and 32 is 4

Alternatively

Finding the G.C.F using table to find the G.C.F of 20 and 32

Therefore, the G.C.F is

Hence, the G.C.F of 20 and 32 is 4

Explanation

We are given the following functions:

We are required to determine the following:

This is achieved thus:

Hence, the answer is: