Use the formula n+1/2 to find the median in the list of numbers. ​1, 2,​ 2, 3,​ 3, 3,​ 3, 5,​ 6, 8,​ 9, 10,​ 13, 18,​ 18, 19, 21

Given,

angle I = 54 degrees

angle FBC = 44 degrees

Recall, the sum of the angles in a triangle is 180 degrees. This means that for triangle BIC,

angle B + angle I + angle BCI = 180 degrees

54 + 44 + angle BCI = 180

angle BCI + 98 = 180

angle BCI = 180 - 98 = 82(sum of angles in a triangle)

Since lines AD and EH are parallel,

angle BCI and angle FGI are corresponding angles(They have similar positions and lie on the same side of the transversal, CI)

Thus,

angle FGI = 82(corresponding angles)

angle CGH and angle

angle CGH and angle FGI are vertically opposite angles. Vertically opposite angles are equal. Thus,

angle CGH = 82 degrees

The reason is 'vertically opposite angles'

Answer:

Step-by-step explanation:

distance between the two points:

[tex]\sqrt{ (x_2-x_1)^{2} +(y_2-y_1)^2[/tex]

[tex]\sqrt[/tex](13-6)²+(28-23)²

√(7)²+(5)²

√49+25

√74

distance: 8.6cm

midpoint=

[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]

(6+3/2,23+28/2)

(19/2,51/2)

(9.5,25.5)

We can see from the picture that the function f(x) has roots in x = -5 and x = 5. Using sintetic division with x = 5, we get:

then, we can write the function as:

since we know that another root is x = -5,we can use again the sintetic division on the right factor:

therefore, the function in factored form is:

Given:

A third-degree polynomial function with a negative leading coefficient not appropriate for modeling non-negative real-world phenomena over a long period of time.

Explanation:

Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.

That is, the end behavior of the graph will always be negative on the right.

Final Answer:

Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.

That is, the end behavior of the graph will always be negative on the right.

If you are an apprentice plumber earning an annual salary of $21,060, and you lay claim to 3 allowances, the amount that will be withheld from your weekly pay for federal income tax is: $7.

To obtain the correct amount to be paid, we need to use the table provided by the IRS. First note that there are 52 weeks in a year, so we need to divide your annual earnings by the total number of weeks in a year.

So, 21060/52 = $405

When we look at the table to see the chart for a person who has a weekly wage of 400 - 410, and lays claim to three allowances, we will see that the right amount that such an individual is meant to pay is $7.

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Solution:

Note that Mikayla has three savings accounts that she distributes her money into each paycheck. Now, let us denote by x the money in the accounts, thus if she wishes to put at least $80 into each account this paycheck, this means that the total amount of money must be greater than or equal to 3(80). This is equivalent to say:

this is equivalent to:

so that, we can conclude that the correct answer is:

The graph of the proportional relationship between the two quantities is attached below.

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To determine which option is a representation of the graph we need to make the numer line analysis; to make it we need to notice that the functions has zeros at the points:

once we know this we divide the number line in the following intervals:

now we need check the sign of the function in each interval, to do this we choose a value in them.

For the first interval let's take x=-4, then we have:

From the last expression we notice that the value of the function is positive at this point. Hence the firts interval have positive values for the function.

For the second interval let's take x=-1, then we have:

From the result we conclude that the function is negative in this interval.

For the third interval, let's take x=1, we have:

From the result we conclude that the function is positive in this interval.

For the fourth interval, let's take x=3. then we have:

Then the function is positive in this interval.

Finally, for the fifth interval let's take x=5, then we have:

Then the function is negative in the last interval.

Hence the line analysis is:

The y-intercept of the function happens when x=0, then we have that:

Therefore the y-intercept of the function is 0.

Once we know the information from the line analysis and the y-intercept of the function we conclude that the sketch of the graph is option B.

Two graphs of the function (with different values for the y-axis) are shown below:

This graphs confirm that option B is an approximate sketch of the graph.

Using the sample size relation with the standard normal distribution, the required sample size is 3032 samples.

What is Normal distribution ?

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Using the sample size relation with the standard normal distribution, the required sample size is 673 samples.

n = [(Z* × σ) / ME]²

ME = margin of error

Z* = Z critical at 90% = 1.645

Substituting the values into the equation :

n = [(Z* × σ) / ME]²

n = [(1.645 × 50.2) / 1.5]²

n = (82.6/ 1.5)²

n = 55.06

n ≈ 3032

Therefore, the Number of samples required is 3032 samples.

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Answer::

Explanation:

By the half-angle formula:

Let θ=150°, therefore:

Now, cos 30 = √3/2, thus:

The exact value of cos 75° is:

The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.

The given polynomial expression is 3x² + 3bx - 6x - 6b.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factors of given polynomial can be find using grouping method, that is

(3x² + 3bx) - 6x - 6b

=3x(x+b)-6(x+b)

=(x+b)(3x-6)

=3(x-2)(x+b)

The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.

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to find the x intercept, we need to replace y by 0, so we get

to find the y-intercept we need to replace x by 0

For the given expression √25 = ∛125. As, 5 is equal to 5.

For the given question;

Square root of 25 i.e, √25

To identify the square root of 25, determine the number because when multiplied by itself yields 25. The square root of 25 is thus 5.

To find the cube root of 125, determine the number that when multiplied on its own twice yields 125.

The cube root of 125 is thus 5, because 5×5×5 = 125.

The radical sign with such a small three (named the index) above and on the left is the symbol for cube root.

Thus, both the values are equal.

√25 = ∛125.

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Answer:

7

Step-by-step explanation:

Just add 3.5 twice which is the same as multiplying it by 2

Answer:

7

Step-by-step explanation:

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Among the given options, no one is an equivalent expression.

What is an equivalent expression?

Expressions are said to be equivalent if they do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

In the given options no one satisfies the property of an equivalent expression.

Therefore, among the given options, no one is an equivalent expression.

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Answer:

34%

Explanation:

To write the fraction as a percent we need to divide 34 by 100 and then multiply by 100%, so

34/100 x 100 = 0.34 x 100% = 34%

Therefore, 34/100 as a percent is 34%

Given

gallons which have 20% antifreeze solution = 80

Final concentration = 50% antifreeze solution

Find

Number of galloons with 60% antifreeze solution

Explanation

Let the number of gallons with 60% antifreeze solution = x

According to question

0.6x+0.2(80) = 0.50(x+80)

0.6x+16=0.5x+40

0.1x=24

x=240

Final Answer

Hence 240 gallons of 60% antifreeze solution will be required

The slope of 2 and passes through the point (-8,1)  :  y-1 = 2(x+8)

what is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The standard equation of a line in point slope form is expressed as;

so ,

y-y0 = m(x-x0)

m is the slope

(x0, y0) is the point

Given

Slope m = 5 (assumed value)

Point (-8,1)

Substitute the given data's into the formula

y -1 = 5(x-(-8))

y-1 = 5(x+8)

Hence the required equation is y-1 = 5(x+8)

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we have that

35,867 ------> represents 100%

Applying proportion

Find out how much percentage represents 13,232

100/35,867=x/13,232

solve for x

x=(100/35,867)*13,232

x=36.89% ------> 37%

Answer:

7(1 + 6)

Step-by-step explanation:

Answer:

3.20611579...

Step-by-step explanation:

Kali will have to work a minimum of 10 hours and a maximum of 22 hours to earn between 200 and 400. The inequality representing the solution will be 9 ≤ 15.75x ≤ 22.

In the question, it is stated that Kali earns $15.75 and a flat fee 0f 50. She wants to maintain her earnings between 200 and 400. Potential earning will be 'x'. The equation representing the earnings is 200 ≤ 15.75x + 50 ≤ 400. We will have to solve the inequality and find out the value for x.

=> 200 ≤ 15.75x + 50 ≤ 400

Subtracting 50 from the equation,

=> 150 ≤ 15.75x ≤ 350

Dividing the equation by 15.75

=> 9.52 ≤ x ≤  22.22

So, here x lies between 9.52 and 22.22. After rounding off we get range 10 and 22.

Hence, the solution for the inequality is 9.52 ≤ x ≤  22.22

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Answer: 3 Vans are needed.

Step-by-step explanation:

There are 30 students so already you need 3 vans, if you only have 2 vans, you will be leaving behind 10 students so regardless you need a 3rd van. with 3 vans you can hold 33 people. 30 students+ 3 drivers=33 people.

The inequality that represents the number of vans for the given case is V ≤ 30/11.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

Suppose the number of vans be V.

The number of students for each van is 11.

And, the total number of students is 30.

Now, the inequality for the number of vans can be written as,

11V ≤ 30

⇒ V ≤ 30/11

Hence, the inequality for the number of vans is given as  V ≤ 30/11.

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Answer:20%

Step-by-step explanation:

1500/75=20(%)

Answer:   The average rate of change is −3.

Step-by-step explanation:

The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)

a=−5 , b=5, f(x)=3x2−3x+1.

(f(b)-f(a))/(b-a)= (1-3(5)+3(5)^2-(1-3(-5)+3(-5)^2)) / (5-(-5)) = -3

Answer:

c

Step-by-step explanation:

c

slope = (change in y)/ change in x

Answer:

Step-by-step explanation:

Recall the formula for an arithmetic sequence: [tex]a_{n} =a_{1} +d(n-1)[/tex]

Where d is the common difference and a_1 is the first term of the sequence.

You are given :

a_1=4

a_2=8

a_3=12

Next is to find the common difference d.

To find the common difference, take the next term and subtract it from the current term.

a_2-a_1=8-4=4

Let try the next term start at a_2

a_3-a_2=12-8 =4

Do you see the pattern?

The patter is going up by 4 each time. So the common difference is 4 i.e d=4

Now we just need to plug into the generalize formula above and get

[tex]a_{n}=4+4(n-1)[/tex]

The question asked for the 40th term. Plug 40 into the formula and you will get:

[tex]a_{40}=4+4(40-1)=160[/tex]

I hope this helps!

Given

coordinates (2, 3) and centre points (0,0)

Find

Equation of a circle

Explanation

As we know the standard equation for a circle with centre (h , k ) and r is a radius

since, center is (0 , 0) , the equation becomes

Now, we find the value of radius , it is can find by using the pythagoras theorem,

so,

Final Answer

The equation for a circle passing through (2, 3) is