Find the mean for the given set of data.
-4,-3,-1,-1, 0, 1
-1 1/3
-1
-3/4

Answer:

[tex]\sf t_{20}= 0[/tex]

Step-by-step explanation:

      [tex]\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }[/tex]

6th term is 14 ⇒ [tex]\sf t_6 = 14[/tex]

                a + (6 - 1)d = 14

                    a  +  5d = 14  --------------(I)

14th term is 6 ⇒[tex]\sf t_{14} = 6[/tex]

             a + (14-1)d = 6

                  a + 13d = 6 ----------------(II)

Subtract equation (II) from equation(I)

        (I)          a + 5d = 14

        (II)         a + 13d = 6

                    -    -          -

                            -8d = 8

                               d  = 8 ÷(-8)      

                              [tex]\sf \boxed{\bf d= (-1)}[/tex]

Plugin d = -1 in equation (I)

a + 5(-1) = 14

      a -5  = 14

             a = 14 + 5

             [tex]\sf \boxed{\bf a = 19}[/tex]  

20th term:

 [tex]\sf t_{20}= 19 + 19*(-1)[/tex]

       = 19 - 19

   [tex]\sf \boxed{\bf t_{20} = 0}[/tex]

Answer:

0

Step-by-step explanation:

The number of terms of an Arithmetic progressions has the formular.

Tn = a + ( n - 1 ) d

From the question,

6th term = 14

14th term = 6

Therefore,

a + 5d = 14 -----------(1)

a + 13d = 6 ----------(2)

subtracting

-8d = 8

dividing bothsides by -8

[tex] \frac{ - 8d}{ - 8} = \frac{8}{ - 8} \\ d = - 1[/tex]

Therefore,

common difference= -1

substituting the value of d into equation (1)

a + 5 ( -1) = 14

a - 5 = 14

a = 14 + 5 = 19

First term = 19

For the 20th term

T 20 = a + 19d

19 + 19 ( -1 )

19-19 = 0

Therefore,

20th term = 0

Answer:

(2, 60°)

Step-by-step explanation:

A point in polar form (a,b) is represented by a radius and an angle (r, ϴ). To convert, use the formula r² = a² + b² to get r, and  [tex]tan^{-1}[/tex](b/a) = ϴ

[tex]r = \sqrt{1^{2} + \sqrt{3} ^{2} }[/tex]

[tex]r = \sqrt{1+3}[/tex]

[tex]r = \sqrt{4}[/tex]

= 2

[tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]/1) = ϴ

= 60°

tan45° = cot45° = 1

---> If tanA + cotA = 2, then A is 45°.

---> tan²A + cot²A = 1² + 1² = 2

The correct answer is 2

Answer:

3

Step-by-step explanation:

height = constant * width

let's rearrange this equation

constant = height/width

let's pick several  points as a proof

15/5 =3

6/2 =3

1.5/0.5 = 3

hope this helps you!!

Answer:

(0, -5)      (10/3, 0)

Step-by-step explanation:

First, convert the given equation into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = 10

2y = 3x - 10

y = 3/2x - 5

The y-intercept is -5.

Next, to find the x-intercept, let y = 0 and solve for x. X-intercept is the point where the graph intersects the x-axis, so the y-coordinate of x-intercepts are always 0.

3x - 2*0 = 10

3x - 0 = 10

3x = 10

x = 10/3

X-INTERCEPT

Plug y=0 into the equation and solve the resulting equation 3x=10 for x.

The x-intercept:

[tex]\left(\frac{10}{3},0\right)\approx \left(3.33333333333333,0\right)[/tex]

Y-INTERCEPT

Plug x=0 into the equation and solve the resulting equation −2y=10 for y.

The y-intercept:

[tex]\left(0, -5\right)[/tex]

It takes 4 weeks at minimum for each pair to hug at least once if they sit in random order.

Analyzing the Given Information

As per the given information,

Number of people = 8

It is given that they sit in random order every week.

W e assume that the order is not repeated.

There are 4 pairs and since a person hugs both the persons on his immediate left and right.

Determining the Number of Weeks

Total number of people to be hugged by each person = 7

Number of people hugged by a person in one week = 2

So, number of weeks taken by each to huge every other person = 7/2

⇒ It will take (3 +1) for every pair to hug.

It takes 4 weeks at a minimum for every pair to hug if we assume that  their order is not repeated.

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Answer:

Step-by-step explanation:

All pyramids have a volume as one-third of a prism with the same base area and the same height.

This will make the formula for the volume [tex]\frac{1}{3}(base*height)[/tex]. We already know the height of the pyramid is 10, but the area of the base for this rectangle would be its length and its width. Let's calculate this:

[tex]7*2.3=16.1\hspace{0.1cm}in^2[/tex]

Let's put these values back into the formula:

[tex]V=\frac{1}{3}(16.1*10)\\ V=\frac{1}{3}(161)\\ V= 53.7\hspace{0.1cm}in^3[/tex]

The total surface area of the composite figure is calculated as 444 m².

Total surface area = surface area of the bottom rectangular prism + surface area of the top triangular prism - area of the shared surface.

Surface area of the triangular prism = (S1 + S2+ S3)L + bh = (16 + 10 + 10)5 + (6)(16) = 276 m²

Rectangular prism surface area = 2(wl + hl + hw) = 2(5×16 + 4×16 + 4×5) = 328 m²

Area of shared surface = 2(16)(5) = 160 m²

Total surface area = 328 + 276 - 160 = 444 m².

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Answer:

False

Step-by-step explanation:

Prisms can have more than one base.

Answer:

Step-by-step explanation:

We are given two sides and one angle opposite to one of the known sides.

In order to find the missing side we need to use the law of sines.

Find the angle opposite to the second known side, let it be x.

Find the missing third angle y, using angle sum theorem:

Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.

Note. At this point you can use the law of cosines as we have found the angle between the known sides.

So the required distance is 7.7 km

The isosceles triangle is proved below.

The complete information wasn't found. The proofing of the triangle will be illustrated. It should be noted that the angles opposite to the equal sides of an isosceles triangle are also equal.

Proof: Consider an isosceles triangle ABC where AC = BC.

We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

We first draw a bisector of ∠ACB and name it as CD.

Now in ∆ACD and ∆BCD we have,

AC = BC                                                                (Given)

∠ACD = ∠BCD                                                    (By construction)

CD = CD                                                               (Common to both)

Thus,  ∆ACD ≅∆BCD                                        (By SAS congruence criterion)

So, ∠CAB = ∠CBA                                              (By CPCT)

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Answer:

Yes,

Common ratio = 5.

Step-by-step explanation:

If its geometric it will have a common ratio.

5/1 = 5

25/5 = 5

125/25 = 5

So its geometric with commo ratio 5.

The slope intercept equation can be represented as follows:

y = 9 / 7 x + 1

y = 11 / 4 x - 8

y = 11 / 8 x + 6

The slope intercept equation can be represented as follows:

y = mx + b

where

Therefore,

The slope intercept equation can be represented as follows:

9x - 7y = - 7

7y = 9x + 7

y = 9 / 7 x + 1

11x - 4y = 32

4y = 11x - 32

y = 11 / 4 x - 8

11x - 8y = -48

8y = 11x + 48

y = 11 / 8 x + 6

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If the mean is 382 and standard deviation is 97 then according to empirical rule 50% students scored  between 285 and 479 on the exam.

Given mean of 382 and standard deviation of 97.

We have to calculate the percentage of students scored between 285 and 479 on the exam.

Percentage is a number or ratio that is expressed in terms of 100.

We have to use z statistic in this question.

z=X-μ/σ

where μ is mean and

σ is standard deviation

from 285 to 382

z=285-383/97

=-1

p value =0.1587.

From 382 to 479

z=479-382/97

=97/97

=1

p value =0.3413

Total probability from 285  to 382 is 0.3413+0.1587=0.5

Percentage=5/10*100

=50%

Hence the percentage of students scored between 285 and 479 is 50%.

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The inflation rate between 2017 and 2018 is 2.86%.

Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.

The inflation rate = (2018 CPI / 2017 CPI) - 1

(180 / 175) - 1 = 0.0286 = 2.86%

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The quadrants of the points that needs to be graphed  are:

Since the points that was given are:

A(2, 4)        B(0, -3)  

C(1, -1)       E(-4,1)    

G(-3,-2)      I(0, 2)

D(3, 3)        F(2,0)  

H(-2, 3)     J(-1,-4)

Then, we plot all the coordinate above on a graph (see image attached)

Hence, from the image attached graph, the categories that can be seen are:

Quadrant 1 is  Points A and D

Quadrant 2 is  Points E and H

Quadrant 3 is Points G and J

Quadrant 4 is Points C

x-axis-  Point F

y-axis- Point B and I

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Answer:

x = 90°

Step-by-step explanation:

Hello!

The sum of angles on a straight line is 180°.

To find the value of angle x°, we can subtract all the given angles form 180°.

The value of x is 90°.

Step-by-step explanation:

Chapter 3 of Wheels of Change .

But the bicycle craze had a more lasting impact on women’s clothing than just the use of bloomers. Thanks in large part to cycling, the innovation of rational dress reformers were starting to take effect by the end of the 1890s. Corsets were on their way out, dresses were getting shorter, and women no longer wore the heavy, bulky undergarments that gave them round, unnatural shapes. These changes went a long way toward unburdening women and setting the stage for them to be healthier and more active in the coming century.

Based on the excerpt, women in the 1890s became more independent and their lives improved as a result of

a rise in the popularity of bicycles.

a rise in the popularity of corsets.

cycling becoming less socially acceptable.

clothing becoming more restrictive.

Answer:

to promote safer, more comfortable styles of dress for women

Step-by-step explanation:

to promote safer, more comfortable styles of dress for women

Answer:

Exact Form: x = -5/2

Decimal Form: x = -2.5

Mixed Form: x = 2 1/2

Answer:

Step-by-step explanation:

5(x+2)=3x+5

5x+10=3x+5

5x=3x-5

2x=-5

x=-0.4

Answer:

just divide 3125 by 5 and your answer is 625

Step-by-step explanation:

Using division, 3125 by 5 and get answer 625.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

If 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  a / b = a divided in b equal parts.

We have been given 5x = 3125

Divide by 5 each sides;

x = 3125/5

x = 645

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The following integer values of x satisfy the given inequality,

4, 5, 6, 7, 8

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made using inequality.

Solving the Inequality

The given inequality is,

5x + 4 > 19

5x > 19 - 4

5x > 15

x > 15/5

x > 3

So, the required values of x must be greater than 3 in the given interval, [2,8]

Thus, the integer values of x in the the interval [2,8] that satisfy the given inequality are 4, 5, 6, 7 and 8 (∵ Square brackets of an interval denote inclusion of the terminal values).

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Answer: 480

Step-by-step explanation:

20(12)(2) = 480

Answer:

See below

Step-by-step explanation:

Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear

Shipping points are independent organizational entities within which processing and monitoring of the deliveries, as well as goods issue, is carried out. A delivery is processed by one shipping point only.

"FOB shipping point" or "FOB origin" means the buyer is at risk once the seller ships the product. The purchaser pays the shipping cost from the factory and is responsible if the goods are damaged while in transit. "FOB destination" means the seller retains the risk of loss until the goods reach the buyer.

Please check the attached file for a complete answer.

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[tex]x = y + 5 \\ y = x - 5[/tex]

[tex]x = \frac{3}{8} y \\ y = \frac{8}{3}x [/tex]

[tex]x = - y - 2 \\ y = - 2 - x[/tex]

[tex]x = 6y + 1 \\ 6y = x - 1 \\ y = \frac{x - 1}{6} [/tex]

[tex]x = y - 11 \\ y = x + 11[/tex]

[tex]x = 8y \\ y = \frac{x}{8} [/tex]

[tex]x = \frac{ - 1}{3} y \\ y = - 3x[/tex]

[tex]basically \: flip \: x \: and \: y \: then \: solve \: for \: y[/tex]

Answer:

Step-by-step explanation:

The key word "product" tells us to multiply.

And, you probably know, but "integer" just means "number".

The question is, essentially:
A × B = 162 where A is half of B.

As someone who was never gifted in math, my best suggestion for something like this is to grab a calculator and start dividing 162 by all the numbers below 10. You will know you've got your answer when the calculator gives you a number that is twice the number you divided by.

In this case, I divided 162 by 9 and got 18. Since 9 is half of 18, and multiplied they make 162, we know this is the correct answer.

Hope this helps

Answer:

B

Step-by-step explanation:

Drop an altitude. Either of the two resulting right triangles with legs of length 5 and x and a hypotenuse of 10.

By the Pythagorean theorem, it follows that the answer is B.

The table that represents a function is:

A function is an expression that represents the relationship between two variables. The variables in this case are the dependent and independent variables.

To identify a function, you need to note that no variable of x should be equal to y.

The formular is represented this way: y = f(x). The table that satisfies this condition is the Y table.

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The expression that represents well the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64. (Correct choice: B)

Geometric sequences are exponential expressions with discrete domain, whose form is presented and explained below:

[tex]f(n) = a \cdot r^{n-1}[/tex], where a, r are real numbers and n is a natural number.     (1)

Where:

According to the statement, we know that the first term of the geometric sequence is 8 and between any two consecutive terms there is a common ratio of 2. If we know that a = 8, r = 2 and n = 4, then the fourth term of the series by means of (1) is:

[tex]f(4) = 8 \cdot 2^{4-1}[/tex]

f(4) = 8 · 8

f(4) = 64

The expression that represents the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64.

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