a system of equations is graphed on the set of axes below

The standard deviation of the groups of data is 3.3 .

The standard deviation is calculated using the formula [tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]

Where σ is the standard deviation.

x denotes the data of the population.

N is the size of the population.

μ is the mean of the population.

The given population is 7,9,11,14,15,16

Here N= 6

Mean (μ) = (7+9+11+14+15+16)÷6 = 72/6=12

Now we will put the values in the above equation to calculate the sd.

[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{6}}\sum _{i=1}^{6}\left(x_{i}-{12 }\right)^{2}}}}[/tex]

Simplifying we get:

σ = √(64/6)

σ = 3.2659..

σ = 3.3

The standard deviation is a statistic that indicates the degree of volatility or dispersion in a set of numerical values.

A low standard deviation shows that possibly the values tend toward being close to the mean, sometimes referred to as the expected value of the set, whereas a large standard deviation suggests that the values are distributed over a wider range.

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3/4 yards of a lace for each bow

for 12 yards of lace:?

Simply divide the 12 yards of lace by the lace required by each bow (3/4)

12 / (3/4) = 16 bows

Given

The graph

Two boundary points

(0,7) (2,0)

We need to solve the inequality:

Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:

The solution set is:

This means that x is less than 3/7, or

x is less than 0.4286

On the number line it looks:

ANSWER

True

EXPLANATION

To solve the inequality given:

-7x < 24

we have to divide both sides of the inequality by -7.

Dividing both sides of an inequality causes the sign to change direction (or be reversed) and so we will have:

x > -24 / 7

Therefore, it is true that the sign will be reversed.

1. Expressing 60km per 28 minutes in its simplest form requires us to get it per 1 minute. This, we can easily obtain by:

2.143 km per minute

2. The ratio is a rate. A rate is a measure of a quantity with respect to another, especially with respect to time.

As can be seen, this ratio is speed. Speed is a measure of distance covered per time.

A bag of numbered lottery balls contains he numbers 1 through 50.

One ball is selected at random.

From 50 balls, one ball can be selected in 50 different ways.

So, the total number of points in sample space is 50.

Let us consider the event that the number is a multiple of 8 be A.

There are six numbers between 1 o 50 which are multiple of 8.

Therefore, one ball can be selected from 6 balls in 6 different ways.

So, the number of points in sample space in favour of the event A is 6.

Therefore, by the classical definition of probability,

Then, the probability that the selected number is not a multiple of 8 is

So, the required probability is 22/25.

We can solve these systems of equations as follows:

We have:

And we can solve this system by substitution as follows:

Now, we can substitute the corresponding value of y into the second equation as follows:

Now, we can substitute the value x = -21 into either of the original equations to find the value of y. We will use the first equation:

Therefore, the solution to this first system is (-21, 36).

We can check this result if we substitute both values into the original equations:

Therefore, the solution to the first system of equations is (-21, 36).

Second Case

We can rewrite the system as follows:

And we can solve this system by the elimination method: We have to multiply one of the equations by -1 and then add them algebraically as follows:

If we add both equations, then we have:

And now we can substitute this value in either equation to find y:

And we got y = 3.

Therefore, the solution to this system is equal to (-2, 3), and we can also check the solutions using the original equations:

In summary, we have that:

The solution to the first system ---> (-21, 36).

The solution to the second system ---> (-2, 3).

When translating into mathematical equations, "is" uses the equal sign and "difference" means that the operation to be used is subtraction.

So, "43 is the difference of Chrissy's age and 14" is written as:

43 = C - 14

The resulting polynomial consists of four terms , it is called a quadrinomial.

The base of the ladder is 4 ft away from the buliding

Here, we want to calculate the distance from the building to the base of the ladder

To properly answer this, an image of the question is needed

We have this as follows;

From the diagram, what we want to calculate is the distance d

To calculate this, we need the appropriate trigonometric identity

Firstly, we need to identify the parts of the triangle present

As we can see, we have the hypotenuse which is the side that faces the right angle and also is the longest side

The side we want to get is the adjacent

Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine

Thus, we have it that;

To multiply polynomials, we use the distributive law

The last part follows by the laws of exponentials, finally we combine like terms

If he earned $40 in total and it took 4 hours to finish everything, he earns in an hour:

Answer: Samuel earns $10.00. Letter C.

Answer:

He got paid 10$ an hour. It does not say he gets paid for cleaning his room. Step-by-step explanation:10 x 4 = 40$

Step-by-step explanation:

The magnitude of a number is the absoulute value of the number. Recall, the absolute value of a number is always positive. The absolute value of a is written as IaI

Hence,

magnitude of - 7.5 is 7.5

The correct option is D

We are asked to determine the density of the cork. To do that we will use the following formula:

Where:

The volume of the cork is the same as the volume that it displaced of water, therefore, we have:

Now, we substitute the values and we get:

Solving the operations:

Therefore, the density of the cork is 0.24 g/ml.

ANSWER:

Angle x is 103 degrees

EXPLANATION

The sum of all the angles in a triangle is 180 degrees

Hence, Let angle A = 27 degrees

Angle B = 50 degrees

Angle C = x degrees

Triangle sum theorem state that

50 + 27 + x = 180

77 + x = 180

x = 180 - 77

x = 103 degrees

Two ratios are equivalent if the division between them is equal to one. We need to look at the options to check for which these are true.

For A:

Since the answer is different than one, this is not the correct option.

For B:

Since the result of the division is one for both ratios, the correct option is "B".

Given the first four terms of this sequence:

We can see a pattern. To analize this pattern, let's first check the difference between those terms.

From those differences, we can verify the following equations:

From this, we can write the general rule for this sequence:

This sequence gives us:

Then, we have the following 3 terms. (20, 5, 1.25)

The pythagorean theorem is :

where c is the hypotenuse

a and b are the legs of the triangle.

From the problem, a = x, b = 19.1 and c = 30.5

Using the formula :

The answer rounded to the nearest tenth is x = 23.8

The mean is the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are

the numbers given in the question are

there are 7 numbers in total.

Therefore, the mean will be

Hence,

the mean of the above set of values to the nearest tenth is = 7.1

We need to do something to both equations so we can eliminate one variable

We can multiply the first equation by 3 and the second equation by 4

3( 4x-2y = 7) yields 12x -6y = 21

4( 3x-3y = 15) yields 12x -12y = 60

Now when we subtract

12x -6y = 21

-(12x -12y = 60)

---------------------------

12x -6y = 21

-12x +12y = -60

------------------------

6y = 39

The x terms are eliminated

Choice D multiply the top equation by 3 and the bottom equation by 4

Answer:

The products MN and LN are not possible.

Explanation:

Matrix multiplication is only possible when the column number of the first matrix equals the row number of the second matrix.

Now, matrix L is a 2 x 2 matrix and N is a 5 x 2 matrix. Now L has 2 columns and N has 5 rows. Meaning, that columns of L are not equal to the rows of N. Therefore, matrix multiplication is not possible.

Matrix M is 2 x 4 and matrix N is 2 x 2. Since columns of matrix M equal the rows of matrix N, matrix multiplication is possible.

Therefore,

WE have the following:

When t = 4

Answer:

Explanation:

Given that the line

is changed to

The coterminal angle is 943° .

Coterminal angles are angles with the starting side on the positive x-axis and a shared terminal side. They are in standard position. Examples include the coterminal nature of the angles 30, -330, and 390. The phrase "coterminal angle" refers to angles with the same starting side and terminal side. If the specified angle is given in radians or degrees, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. It is possible to find all possible coterminal angles. The coterminal angle is described in mathematics as the angle formed by two angles drawn side by side in the same plane. Furthermore, both of them share the same location for their terminal sides. As an illustration, 405 and -315 are the coterminal angles of 45.

1294° = 360° + 934°

So the coterminal angle for 1294° is 934° .

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Answer:

A sophomore is less likely than a Junior to have a job.

Explanation:

Given the table in the attached image.

The total number of sophomores is

The number of sophomores with a job is;

The probability that a sophomore had a job is;

The total number of Juniors is

The number of Juniors with a job is;

The probability that a Junior had a job is;

From the derived Probability, we can observe that the probability that a Junior had a job is greater than the probability that a Sophomore had a job.

Therefore, A sophomore is less likely than a Junior to have a job.

To find the angle A we need to find first the value of x. To do this we need to use the fact the the addition of the interior angles of any triangle is 180°.

The right side angle is equatl to 4x+4 since its vertically opposite to the one shown in the picture. The upper angle is 100° since it has to be supplementary to the angle of 80° shown in the picture.

With this in mind we have the equation:

Solving for x we have:

Once we know the value of x we plug it in the expression for the angle A:

Therefore the angle A is 40°.

Explanation:

A rotation 270 degrees counterclockwise happens when the y and x axis value are interchanged and the interchanged y value becomes negative.

When we look at the options given, we look for the image whose rotation is in the positive x axis and negative y axis.

Also the movement will be thrice while moving anticlockwise.

From the options, the one which fits into the description above is B.

There is a movement of counterclockwise

Given:

The function is given as

Required:

We want to find the value of

Explanation:

Final answer:

19

Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.

Answer: 8 and 12, 1, and 15 are like terms.