i need help on number 7. Please use 4 points

Firstly, let us define natural numbers.

Natural numbers are simply positive intergers, that is integers that are greater than zero e.g 1,2,3,4...

Secondly, when is a set said to be closed under a particular operation?

A set is said to be closed under an operation if and only if the operation on any two elements of the set produces another element of the same set. for example when you perform an operation (like addition) on a set of number (like natural numbers) it must give you a number from that same set.

E.g

let's check whether natural numbers are closed under the operation of adddition.

taking two numbers 3 and 5.

since the operation gives us 8, which is a natural number, it means natural numbers are closed under the operation of addition.

Back to the main question, which is to check whether natural numbers are closed under the operation of subtraction.

taking two cases.

case 1; taking numbers 3 and 5

case 2: taking numbers 7 and 2

From the two cases, case 2 gave us a natural number while case 1 does not give us a natural number.

This means that Natural numbers are not Closed under subtraction.

Because subtraction operation on natural numbers does not necessarily produce another natural number.

On a general note;

Natural numbers are closed under Addition and Multiplication operations

while They are not closed under subtraction and division operation

Answer:

The sale price is $46.86

Explanation:

Given an original price of $71, and a markdown of 34%

The sale price is:

$71 - (34% of $71)

= $71 - (0.34 * $71)

= $71 - $24.14

= $46.86

Answer:

The sale price is $46.86

Explanation:

Given an original price of $71, and a markdown of 34%

The sale price is:

$71 - (34% of $71)

= $71 - (0.34 * $71)

= $71 - $24.14

= $46.86

By using the linear equation y=3x we draw the graph for proportional relationship.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same

the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0).

By the definition of proportional relationship of graph, we can reduce relationship between the values on the x-coordinate and y-coordinate of the given graph

As they are  proportional and represented by euation

y = 3x

Where, x represent the time and y represent the number of sit-ups.

Hence by using the linear equation y=3x we draw the graph for proportional relationship.

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A strict inequality is one which involves the use of

A non-strict inequality is one which involves the use of

A strict inequality is used in a case when the two values being compared or related to one another cannot be equal to one another. That is, they are different.

A non-strict inequality is used in case when there is a possibility that the two values being compared can be equal to one another.

The length of 5 rolls of toilet papers is 99 4/3

So, the length of one roll will be = 99 4/3 ÷ 5 = 20 1/15 inches

The line segment BD has a length of 18 units

The possible figure is added as an attachment

From the question, we have the following parameters:

The lengths BE and ED implies that the point E is between the endpoints B and D

Since the shape is a parallelogram, then the point E is halfway between the endpoints B and D

So, we have

BE = ED

Substitute the known values in the above equation

6x + 44 = -6x - 16

Evaluate the like terms

So, we have

12x = -60

Divide both sides by 12

x = -5

Substitute x = -5 in BE = 6x + 44

So, we have

BE = 6 x -5  + 44

Evaluate

BE = 14

The length is then calculated as

BD = 2 x BE

So, we have

BD = 2 x 14

Evaluate

BD = 18 units

Hence, the length of BD is 18 units

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Given the sentence, the sum of 5 times a number and 4 is 3.

The information would translate to;

ANSWER:

Looking at the 4th net, we see it has what seems to be 4 squares in a line. And two of them are each one united into another square.

Then, when we join the left side of the left square and the right side of the right square, we obtain a 3D object with 4 square faces, and 2 empty faces also in the form of a square.

After that, we can fold down the upper square face, and fold up the other one.

We will get the following 3D object, that is a cube:

Therefore, the 4th net makes a cube.

Let p be the number of pavilion seats and l be the number of lawn seats. Since there were sold 1400 tickets, we can write

and since the total money was $32000, we can write

Then,we have the following system of equations

Solving by elimination method.

By multiplying the first equation by -30, we have an equivalent system of equation

By adding these equations, we get

then, l is given by

Now, we can substitute this result into the equation p+l=1400 and obtain

which gives

Then, How many tickets of each type were sold? 400 for pavilion seats and 1000 for lawn seats

How many pavilion seats were sold? 400 tickets

SOLUTION

Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.

Step 2: From the two quantities expressed as decimals, we can see that :

CONCLUSION :

SOLUTION:

Case: Z-scores and probabilities

Given: z-score of standard normal distribution, z= 1.65

Required: To get the percentage of observation

Method: We will be reading it off the z-score table

Step 1: First we see what the table looks like

Step 2: From the table, we trace 1.65 by looking at 1.6 on the column title and 0.05 on the row title

Step 3: We observe the value is 0.4505

This translates to 45.05%.

However, we are interested in the values above the 45.05%. So everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score

To get the z-score above this, we do:

1 - 0.9505

P(> z) = 0.0495 or 4.95%

Final answer:

A) The answer is 4.95%

The sum of 3 and r can be represented by "3 + r"

If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:

From the graph, we are to determine the following:

(a) We are to find the option that costs less if Abdul drives 300 miles of the rental car and also how much less is it from the other option.

Option A: when x = 300, y = 140

Option B: when x = 300, y = 120

So the difference is:

140 - 120 = 20

So the option that costs less is B

And it costs $20 lesser than option A

(b) For what number of miles does the option costs the same and if Abdul drives less than that amount, what option cost more.

Option A: when x = 100, y = 60

Option B: when x = 100, y = 60

Therefore, the number of miles where the options cost the same is 100 miles.

If Abdul drives less than the amount:

That is x < 100, the B > A,

Which means, if Abdul drives less than 100 miles, Option B, costs more.

We have a mean of 63.6 inches and a standard deviation of 2.53 inches. We want to find the probability for our random sample to have a greater mean than 64 inches. We can do that by finding the probability of getting women higher than 64 inches in the original group. To do that, we're going to use a z-table.

First, let's convert 64 inches to a z-score:

Using a right z-table, we have

This z-table gives us the area between the middle of the bell curve and our desired value.

This means, the probability of getting a sample higher than our value, will be 0.5 minus the probability given by the z-table.

Then, we have our result.

Answer:

45.1

Step-by-step explanation:

96 x .47  = 45.12

Rounded to the nearest tenth is 45.1

Percent means per hundred [tex]\frac{47}{100}[/tex]  to divide by 100 you move the decimal place to places to the left.

Answer

The common ratio and the ratio of the perimeters of the two triangles are exactly the same (2/3).

Explanation

The common ratio is obtained by expressing corresponding sides as a fraction of each other.

The common ratio for this triangles = (8/12) = (6/9) = (12/18) = (2/3)

Perimeter is expressed as the sum of all the exterior dimensions of a figure.

For the first figure, Perimeter = 8 + 6 + 12 = 26 inches

For the second figure, Perimeter = 12 + 9 + 18 = 39 inches

Ratio of perimeters = (26/39) = (2/3)

Hope this Helps!!!

The hole appears in the rational function when the numerator and the denominator have the same zeroes

Since the rational function is

Factorize the denominator

The rational function h(x) is

Since (x + 7) is in both numerator and denominator

Then there is a hole at x + 7 = 0

Let us find the value of x

The whole is at x = -7

Then simplify the fraction to find the value of y at x = -7

Cancel the bracket (x+7) up by the same bracket down

Substitute x by -7

The hole is at (-7, -1/14)

We have

Multiples of 4: 4, 8, 12, 16, 20

Multiples of 6: 6, 12, 18, 24, 30,

the least common multiple is the first number share between these numbers as we can see the first number share is 12

We have to write the standard form, Ax+By=C, of the line that has a slope m = -6 and y-intercept b = 10.

To do that we use that information to write the slope-intercept form of the equation and then rearrange it into standard form.

The slope-intercept for the line is:

We can then rearrange it as:

Answer: 6x + y = 10

Answer:

Parallelograms, Squares, Rectangles, and Rhombuses

Step-by-step explanation:

The equation of the line which is parallel to the line y = x + 6, and which passes through the point (8, 7) is; y = x - 1

Parallel lines are lines do not intersect and which while on the same plane, have the same slope.

The given line to which the required line is parallel to is y = x + 6

The point through which the required line passes = (8, 7)

The slope of the given line, y = x + 6, is 1,

The slope of parallel lines are equal, which gives;

The slope of the required line is 1

The equation of the required line in point and slope form is therefore;

y - 7 = 1×(x - 8) = x - 8

y = x - 8 + 7 = x - 1

The equation of the required line in slope–intercept form is; y = x - 1

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an = ar^ (n- 1)

for n = 3 (3rd term)

r = common ratio = 4/ 2 = 2

a3 = 2 (2) ^ (3-1)

a3 = 2 (2)^2

a3 = 2 (4)

a3 = 8

n= 4 (4th term)

a4 = 2 (2)^(4-1)

a4 = 2 (2)^3

a4 = 2 (8)

a4 = 16

2, 4 , 8 , 16

Solution:

In the figure;

Thus;

Thus;

In any triangle, the sum of the internal angle is always up to 180º.

Then, for triangle ABC:

Use it to solve x:

In the triangle ACD:

Use it to solve y:

In order to convert from fluid ounce to pint, we need to know that 16 fluid ounces is equivalent to 1 pint.

Then, to find how many pints is 24 fluid ounces, we can use a rule of three:

So 24 fluid ounces is equivalent to 1 1/2 pints, therefore the correct answer is C.

Explanation:

The test contains 10 questions, each one can be answered either with 'true' or with 'false' which means that for each question there are only 2 options.

We need to find the number of ways in which the test can be completed.

To answer the question we use the fundamental counting principle:

In this case, there are 2 ways to complete each question, therefore, we multiply that by the 10 questions that we have:

This can be simplified to

which is equal to:

Answer:

1024

The row echelon form of the matrix is presented as follows;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

[tex]\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

The conditions of a matrix in the row echelon form are as follows;

Dividing Row 1 by -3 gives:

[tex]\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Subtracting Row 1 from Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}[/tex]

Adding Row 2 to Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}[/tex]

Dividing Row 2 by -2, and Row 3 by 18 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The above matrix is in the row echelon form

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The mass of the wood in pounds is 1.826 pounds.

From the information, the wood cutter measures a piece of wood to be 830 grams and there are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pound.

Therefore,the mass will be represented as x

This will be:

830 grams = 0.83 kilograms

0.83/1 = x/2.2

Cross multiply

x = 2.2 × 0.83

x = 1.826 pounds.

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SOLUTION

Let the electric bill for September be x.

October's bill is $2.65 less than the September bill

This means that October's bill = x - 2.65

September + october bill = $174.65

That means that x + x - 2.65 = 174.65

Now let's find x which is september's bill

So September's bill is $88.65, now each student pays

So each student owe $29.55 for the month of September

We use the formula for the area "A" of a square with equal sides of length "l":

Since we know the value of the area is:

We substitute that value into the formula for the area:

Next, we take the square root of both sides of the equation:

On the right side, the exponent and the square root will cancel, and we will get "l", and on the left side, we calculate the square root:

Which can be rounded to the closest value, that is 15 ft.

Answer: 15 feet