-8, {0, -3, 1, -1}, {-1, 1, -2}, {3, -5, 4, -1}, {4, -2, 2}

We have a class of a total of 267 students.

The professor has a sample of 59 students, where 22 of them did not complete their essays.

This equals a proportion of:

If this sample is representative of the class, we can use this proportion to estimate how many students did not complete the essay.

To do that we multiply the total number of students by the proportion we have just calculated:

Answer: it can be estimated that approximately 100 students did not finish their essay.

Answer:

Explanation:

Here, we want to write the given number in standard notation

The form we have given, is the scientific notation

To write in the standard form, we consider the scientific notation as they are the same

We have the standard notation as:

Answer:

63 square meter

Explanation:

Area of the parallelogram = Base * Height

From the given diagram;

Base = 9m

Height = 7m

Area of the parallelogram = 9m * 7m

Area of the parallelogram = 63 square meter

Part A.

The composition of f ang g is given by

where we have inserted 3x-7 in the place of x in function f. Then, we have

Therefore, the answer is

Part B

Similarly to the previous case, we have

which gives

then, the answer is

Part C.

In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.

Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).

To solve this system of linear equations using the elimination method, first, add both equations:

Now solve for y dividing by 7 on both sides of the equation:

Finally, replace the value of y in any of the initial equations, for example in equation 1

Therefore, the solution of the system of equations is

1.

The shelves can be assumed to be straight lines, and as straight lines have a 180° angle, then:

We know the value of m∠2. Thus, we can replace it and solve for m∠1:

2.

If we can suppose that the top and middle shelves are cut by a transversal, then ∠1 and ∠5 are corresponding angles.

3.

When two parallel lines are cut by a transversal, they form corresponding angles, and these are equal in measure. Therefore, as:

Then we can say that the top and middle shelves are parallel.

4.

As m∠11 = m∠2, we can say that they are alternate exterior angles, which are formed when parallel lines are cut by a transversal. Therefore, the bottom shelf is parallel to the top shelf.

5.

Finally, we can see that as m∠11 = 120°, we are in the same situation as in question 1, for which we conclude that m∠9 = 60°. Now, we have the same situation as in question 2, in which m∠5 and m∠9 are corresponding. Thus the bottom shelf is parallel to the middle shelf.

We are given the following fraction

We are asked to write it in the simplest form.

Notice that the number 14 is a multiple of number 7.

That is 7 times 2 is equal to 14.

Which means that 7 divided by 14 must be equal to 2

So the fraction becomes

Therefore, the simplest form of the given fraction is 1/2

Please note that the simplest form means that it cannot be further simplified.

1.- Determine the vertex...

2.- The axis of symmetry...

3.- The y-intercept...

4.- Plot a point...

5.- Plot another point...

The above is the correct order of the cards, now the reason for that first you have to find the vertex. Now, the axis of symmetry is a straight line that passes through the vertex. Later you have to find another 2 points reflected by the symmetry axis and finally construct the graph.

First let's remember what a Rational number is. A Rational number is that one that can be written in this form (as a fraction):

Where "a" is the numerator and "b" is the denominator.

Integers include negative numbers and, positive numbers and zero. For example, these are Integers:

An Integer is always a Rational number, because it can be written as a fraction with denominator 1:

Then:

A Rational number that is not an Integer is different from a Rational number that is an Integer, because the first one must be written with a denominator. For example:

but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):

Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.

We have a system of equation problem

x= cost of almonds per pound

y= cost of the jelly beans per pound

For the first equation, we have

3 pounds of almonds

8 pounds of jelly beans

total $34

so the equation is

3x+8y=34

For the second equation we have

5 pounds of almonds

2 pounds of jelly beans

total $17

so the equation is

5x+2y=17

so our system of equation is

In order to solve the system we will multiply the second equation by -4

then we sum the equation above with the first equation

then we sum similar terms and isolate the x to find the value of x

then we substitute the value of x=2 in the first equation and we find the value of y

The solution is

x= $ 2 cost of each pound of almond

y= $3.50 cost of each pound of jelly beans

Notice that the line passes through the point (0,1) and the point (3,-1). Then, we have the following:

now we can find the equation of the line using the slope and the y-intercept:

therefore, the equation of the line is y=-1/3x+1

In order to determine the number of thermos, divide by 3 by 2/3, as follow:

the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.

Given

Total number of members = 22

Find

Possible ways of selection of president, a secretary and a treasurer

Explanation

As we know , the number of possible ways of selection is given by

there are three members required so , r = 3

now , substitute the values in above equation

Final Answer

Possible ways of selection of president, a secretary and a treasurer = 9240

The pie chart provides the following information;

The sum of angles in a circle is 360 degrees.

Thus, we have;

Then;

(a)

(b)

To first answer this question, we need to find the slope of the linear equation. We have the following information:

x1 = 1960, y1 = 3.91

x2 = 1980, y2 = 3.81

Then

Then, we have that the linear model will be:

Or

This is the linear model.

Then, to use the model to estimate the record time in 2000 and in 2020, we have:

And

Therefore, the linear model is y = -0.005x + 13.71.

The estimation for the record time in 2000 is 3.71 minutes.

The estimation for the record time in 2020 is 3.61 minutes.

This is a linear model.

Given:

To divide the decimals, we must take care of the decimal points

So, we will divide it as follows:

So, the answer will be 0.27 ÷ 0.9 = 0.3

Given;

Then, we can find the point estimation as;

Thus, the margin of error E is;

A 95% confidence interval for population proportion p is;

The lower bound is;

The upper bound is;

you must first get the variables on the same side of the equal sign. It yields,

if we also pass the constant 8 to the right hand side, we have

Hence, the left and right hand sides are equal to

hence, we have

since minus times minus is plus, we obtain

and it can be reduced to

Finally, the answer is

Answer:

y= 1/3

Step-by-step explanation:

SOLUTION

The correct option is A

Points with coordinates (x,y) on a graph can also be expressed thus:

So with the above explanation, we can answer the question.

The point (-3,-5) on the graph means that x=-3 and y=-5

So it can be expressed as a function in the form:

The correct option is A

Solution

Therefore the correct answer is

The polar form of a complex number

The rectangular form of a complex number

The vertices B, C and D form a right triangle.

Knowing 2 sides of the tright triangle, like BD and BC, we can find the length ofthe third side, DC, using the Pythagorean theorem: the sum of the squares of the length of the legs, DC and BC, is equal to the square of the length of the hypotenuse BD.

Replacing with the values, we can calculate DC:

Answer:

The correct options are

A: 80

B: Pythagorean theorem

Answer:

3 1/24

Step-by-step explanation:

So,

We could draw the situation of the problem as follows:

We want to find the horizontal distance, which we will call "x".

To find it, we could use the trigonometric ratio: tan(a).

This ratio relations the opposite side of the angle given (a) and its adjacent side. So, we could write:

Now, if we solve for x:

This is, x = 2232.49 ft

In order to get the required expression you take into account that when you eliminate a prenthesis preceded by a minus sign, terms inside the parenthesis change their sign.

Then, for the following expression, you have:

- k - (-6.2m + 1)

- k + 6.2m - 1 that is, signs inside the parenthesis have changed

SOLUTION:

Step 1:

An adult's ticket costs $11

A child's ticket costs $6

The number of Adult's tickets sold is x

The number of Children's tickets sold is y

The total number of tickets sold is 60

The total amount of sales made is $460

Step 2:

We need to form two equations based on the information given in the question;

Explanation:

We can do a diagram of triangle CDE:

The sum of the measures of the interior angles of any triangle is 180º. We can write an equation:

Solve for x:

And with x = 15, replace into the expression for the measure of angle C to find it:

Answer:

m

From the Venn diagram shown above we notice that the conclusion is false. This comes from the fact that even if all queens are women not all women are quenss.

Solving Angle Problems.

It follows therefore that

The correct answer is the measure of angle P is 32 degrees