Quadrilateral A' B'C'D' is the image of quadrilateral ABC D under a translation.

a. The value of r = 3, -1/2.

b. The 4th term of each progression;

As, per the given question;

Let the first three terms of GP be a, ar, and ar².

The 1st, 2nd and 3rd terms of a GP equals 1st, 9th and 21st terms of an AP respectively.

where, 'r' is the common ratio in GP and 'd' is the common difference in AP.

Part 1: Multiply equation 1 by 5 and 2 by 2 and subtract 1 from 2.

2ar² - 5ar - 3a = 0

Put a = 8 and solving.

16r² - 40r - 24 = 0.

Factorising the above equation;

(r - 3)(2r + 1) = 0

Thus, r  = 3 and r = -1/2

Part 2:

Case 1: For r = 3; a =8;

ar = a + 8d

d = 2.

Thus, 4th term = a + 3d

                        = 8 + 3×2

4th term = 14.

For GP;

4th term = ar³

              = 8(3)³

4th term = 216.

Case 2: For r = -1/2; a =8;

ar = a + 8d

d = -3/2

Thus, 4th term = a + 3d

                        = 8 + 3×(-3/2)

4th term = 7/2

For GP;

4th term = ar³

              = 8(-1/2)³

4th term = -1.

Therefore, the values for the r and 4th term is estimated.

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Answer:

D. 22.5

Step-by-step explanation:

120 divided by 8

plus 60 divided by 8

= 22.5

Given :

Data interpretation refers to the process of using diverse analytical methods to review data and arrive at relevant conclusions. The interpretation of data helps researchers to categorize, manipulate, and summarize the information in order to answer critical questions.

The importance of data interpretation is evident and this is why it needs to be done properly. Data is very likely to arrive from multiple sources and has a tendency to enter the analysis process with haphazard ordering. Data analysis tends to be extremely subjective. That is to say, the nature and goal of interpretation will vary from business to business, likely correlating to the type of data being analyzed. While there are several different types of processes that are implemented based on individual data nature, the two broadest and most common categories are “quantitative analysis” and “qualitative analysis”

.

U.S. population in 2018 was estimated to be 327,200,000

people who were 18-29 years old = 30,357,000

people who were 65 years=  52,431,000

85% of the 30,357,000 people who are 18-29 years old have tried vaping or

electronic cigarettes = 30,357,000 x85/100

people ages 18-29 said they have tried vaping or e-cigarettes

=2,580,345

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The integers from 6 to 10 (inclusive).will be D. {6, 7, 8, 9, 10}.

It should be noted that the integers given are from 6 to 10 (inclusive).

In this case, this simply means the numbers from 6 to 10.

Therefore, the appropriate number will be: D.

{6, 7, 8, 9, 10}

In conclusion, the correct option is D.

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Answer:

[tex]\sf (A' \cap B) \cup (A' \cap C') =\{1,6,7\}[/tex]

Step-by-step explanation:

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

Therefore, the complement sets are:

[tex]\begin{aligned}\sf A' & = \text{U}-\sf A\\& = \{1,2,3,4,5,6,7,8 \}- \{2,4,5,8 \}\\& = \{1,3,6,7 \}\end{aligned}[/tex]

[tex]\begin{aligned}\sf B' & = \text{U}-\sf B\\& = \{1,2,3,4,5,6,7,8 \}- \{1,4,6 \}\\& = \{2,3,5,7,8 \}\end{aligned}[/tex]

[tex]\begin{aligned}\sf C' & = \text{U}-\sf C\\& = \{1,2,3,4,5,6,7,8 \}- \{1,2,3,4,5 \}\\& = \{6,7,8 \}\end{aligned}[/tex]

Solution

[tex]\begin{aligned}\sf (A' \cap B) \cup (A' \cap C') & = \sf \left(\{1,3,6,7 \} \cap \{1,4,6\} \right) \cup \left(\{1,3,6,7 \} \cap \{6, 7, 8 \} \right)\\\\& = \sf \{1,6\} \cup \{6,7 \} \\\\& = \sf \{1,6,7\} \end{aligned}[/tex]

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Answer:

[0, 8)

Step-by-step explanation:

To find the range, compute the values of the function at the edges of the interval.

The interval edges are -1 and 3

f(x = -1)  = (-1)² - 1 = 1 - 1 = 0.

f(x = 3) = 3² - 1 = 9 - 1 = 8   but does not include 3 so

so range of f(x) : 0  ≤ f(x) < 8

Note that we cannot have f(x) ≤ 8 only < 8 since the interval does not include x = 3

Range in interval notation is [0, 8)

The use of the square brackets on the left means the number is included in the interval; so 0 is included ( ≥ ).

The round brackets on the right mean that the number is not include (< 8 )

Answer:

x> 1/2 y+5/2

i hope this helps you <33

Las soluciones para los dos primeros ejercicios son:

Vamos a ver la primer operacion, está es:

10² + 6³ - [4*(5 - 2)]²

Primero se resuelve lo que esta adentro del parentesis, en este caso:

5 - 2 = 3

Reemplazamos eso:

10² + 6³ - [4*(3)]²

Luego se resuelve lo que está dentro de los corchets:

4*3 = 12

Reempazamos eso para obtener:

10² + 6³ - [12]²

Ahora podemos resolver los exponentes, recordar que el exponente nos dice cuantas veces debemos multiplicar un número por si mismo, entonces:

10² = 10*10 = 100

6³ = 6*6*6 = 216

[12]² = 12*12 = 144

Reemplazando eso obtenemos:

100 + 216 - 144 = 316 - 144 = 172

Veamos tambien el siguiente problema:

-3² + (-2)⁴ + - 4³ + (-2)⁴

Apliquemos los exponentes, primero tenemos:

-3²

Notar que el exponente se le aplica solamente al 3, no al signo, entonces:

-3² = -(3)² = -3*3 = -9

En cambio, en:

(-2)⁴

El exponente si se le aplica al signo, entonces:

(-2)⁴ = (-2)*(-2)*(-2)*(-2) = 4*4 = 16

Los otros dos terminos dan:

- 4³ = -4*4*4 = -64

(-2)⁴ = 16

Reemplazando eso en la expresión:

-3² + (-2)⁴ + - 4³ + (-2)⁴ = -9 + 16 - 64 + 16 = -41

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Answer:

11. 6

13. 73

15. 588

17. 139

19. 18

21. 18

23. 8

Step-by-step explanation:

To solve these equations, you simplify each expression. You also use the order of operations.

Answer:

1propotion 2fraction is how it goes

Answer:

  (a) $191,005.52

  (b) $180,309.67

  (c) lose $10,695.85

Step-by-step explanation:

You want the future values of an ordinary annuity of $12,000 over 12 years at interest rates of 5% and 4%. You also want the difference between the values.

The future value of an ordinary annuity with n annual deposits of P, at interest rate r compounded annually is given by ...

  FV = P((1+r)^n -1)/r

The value of $12,000 deposited for 12 years at 5% is ...

  FV = $12,000((1.05^12 -1)/0.05 = $191,005.52

At the end of 12 years, she will have $192,005.52 in her account.

The value of $12,000 deposited for 12 years at 4% is ...

  FV = $12,000((1.04^12 -1)/0.04 = $180,309.67

At the end of 12 years, she will have $180,309.67 in her account.

The amount at 5% is greater, so by investing in her sister's firm, the woman would lose ...

  $192,005.52 -180,309.67 = $10,695.85 . . . . amount lost

Answer:

  a. (-12, 14), (6, 2), (-3, 8)

  b. yes; R(-12, 14)

Step-by-step explanation:

Points P(-6, 10), Q(0, -6), and R lie on a line, with one of them being the midpoint of the other two. You want to know the possible locations of R, and its location if RQ=√208.

Point M is the midpoint of AB when ...

  M = (A +B)/2

If M and A are given, then B is ...

  2M -A = B . . . . . . above equation solved for B

There are three choices for the location of R.

P is the midpoint

  R = 2P -Q = 2(-6, 10) -(0, 6) = (-12, 20-6)

  R = (-12, 14)

Q is the midpoint

  R = 2Q -P = 2(0, 6) -(-6, 10) = (6, 12 -10)

  R = (6, 2)

R is the midpoint

  R = (P +Q)/2 = ((-6, 10) +(0, 6))/2 = (-6, 16)/2

  R = (-3, 8)

The possible coordinates of R are (-12, 14), (6, 2), (-3, 8).

The length of the given segment PQ is ...

  d = √((x2 -x1)² +(y2 -y1)²) . . . . . distance formula

  d = √((0 -(-6))² +(6 -10)²) = √(6² +(-4)²) = √(36 +16) = √52

This is half the length of RQ, so we must have P as the midpoint of RQ.

This distance information chooses one of the three points found in part (a), R(-12, 14).

Using their concepts, we have that the measures are given as follows:

a) Mean of 1.0126.

b) Average deviation of 0.01632.

c) Percent deviation of 1.6%.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For this problem, the 5 observations are given as follows:

1.040, 0.989, 1.009, 1.026, 0.999.

Hence the mean is given by:

M = (1.040 + 0.989 + 1.009 + 1.026 + 0.999)/5 = 1.0126.

The average deviation of a data-set is given by the sum of the absolute values of the difference between each value and the mean, divided by the number of observations.

Hence:

Ad = (|1.040-1.0126| + |0.989-1.0126| + |1.009-1.0126| + |1.026-1.0126| + |0.999-1.0126|)/5 = 0.01632.

The percent deviation of a data-set is given by the absolute deviation divided by the mean and multiplied by 100%.

Hence:

0.01632/1.0126 x 100% = 1.6%.

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Trevor spent $23.31

Peaches are sold at $2.56 per pound

Watermelons are sold at $3.25 per pound

Mangos are sold at $2.75 per pound

Trevor bought 1 pound of peaches

3 pounds of watermelon= 3 × 3.25

= 9.75

4 pounds of mangos= 4 × 2.75

= 11

The total amount spent is

= 11 + 9.75 + 2.56

= 23.31

Hence Trevor spent $23.31

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$0.29 you save if you buy the big bag instead of 2 small bags .

The unitary method is a strategy that determines the value of many units based on the value of a single unit in addition to calculating the value of a single unit using the values of multiple units.

We must divide the value of one thing by the number of other items we wish to calculate the value of before multiplying that result by one.

From the question,

A huge bag of flour weighing 10 lbs costs $3.69 in total.

Currently, one 5-lb small bag costs $1.55.

Consequently, two 5-lb little bags cost $3.10 each.

Cost difference equals big bag cost minus two small bag expenses.

The price difference is equal to $3.69 minus $3.10.

$0.29 is the cost difference.

By purchasing two small bags of floor instead of one large bag, you will save $0.29.

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Rene's limeade has a weaker flavor as calculated by division of fractions.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

Concentration of Jaylan's limeade [tex]=\frac{3}{4} \div\frac{1}{5} = \frac{15}{4} =3.75[/tex]

Therefore as calculated by division of fractions, concentration of Jaylan's limeade is 3.75 cups of water for 1 cup of lime juice.

Concentration of Rene's Limeade[tex]=\frac{2}{3} \div\frac{1}{6} = \frac{12}{3} =4[/tex]

Therefore as calculated by division of fractions, concentration of Rene's limeade is 4 cups of water for 1 cup of lime juice.

Hence Rene's limeade has a weaker flavor as calculated by division of fractions.

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Considering the volume of the hemisphere, it is found that she can make 48 cookies.

The volume of an hemisphere of radius r is given as follows:

[tex]V = \frac{2\pi r^3}{3}[/tex]

The radius is half the diameter, hence, for this problem:

r = 11.5/2 = 5.75.

Hence the volume of the bowl in cubic inches is given as follows:

V = 2π(5.75)³/3 = 398.16 cubic inches.

Consider the volume of a single cookie, the number of cookies that she can make is given by:

398.16/8.295 = 48 cookies.

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Answer:

3452

Step-by-step explanation:

Simplify the expression, and add/muiltiply where necessary.

The expression  can be simplified to:

x + y/100

Where x is the month and y the day. This is why it always works.

Let's define the two variables x and y as the month of your birth and the day of your birth respectively.

Now let's write the expression by following the steps, you should get:

((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100

Now let's simplify the expression we will get:

((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100

(((91x - 13 + y + 3)*11 - x - y)/10 + 11)/100

(((91x - 10 + y)*11 - x - y)/10 + 11)/100

((1001x - 110 + 11y - x - y)/10 + 11)/100

(( 1000x - 110 + 10y)/10 + 11)/100

You already can see what will happen here:

(( 1000x - 110 + 10y)/10 + 11)/100

(100x - 11 + y + 11)/100

(100x + y)/100 = x + y/100

So the expression will do the exact same thing for every values of x and y that you decide to use, it does not depend on your exact date of birthday.

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hi  

2* 5/8  =   10/8  =  5*2 /4*2 = 5/4

and  2*1/4 =  1/2

so :   2*5/8   /  2/4   =    5/4   / 1/2  =  5/4 * 2/1  =   5*2 / 2*2*1 =  5/2

Answer:

[tex]=1\frac{1}{6}[/tex] or 7/6

Step-by-step explanation:

[tex]=\frac{21}{8}\div \frac{9}{4}[/tex] <- Convert to improper fraction
[tex]=\frac{21}{8}\times \frac{4}{9}[/tex] <- Fraction Rule
[tex]=\frac{84}{72}[/tex]
[tex]=\frac{7}{6}[/tex]
[tex]=1\frac{1}{6}[/tex]

Answer:5.1,5.2,5.3,5.4,5.6,5.7,5.8,5.9,

Step-by-step explanation:

The width of each column is 3.375.

According to the statement

We have to find that the width of the each column.

So, For this purpose, we know that the

Width is the the horizontal measurement taken at right angles to the length.

In other words, It is the distance from one side to the other side which measures across a particular shape or object whose lengths are forming right angles with the sides as in the case of a rectangle.

From the given information:

A production assistant must divide a page of text into two columns. If the page is 6 3/4 inches wide.

Then

width of the page = 27/4 inches

And the number column is divided into page = 2

Then

The width of column = width of the page/ column in a page

The width of column = 27/4/ 2

The width of column = 6.75/ 2

The width of column = 3.375.

So, The width of each column is 3.375.

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The required inequality solution is x ≤ 8.

What is inequality?

x represents the number(no.) of people who can go to the amusement park.

They have no more than $125(one hundred twenty-five) to spend

Parking 15.00(fifteen), Tickets 12.50(12.five zero) per person

$15 + $12.50x ≤ $125

x = 110/12.5 ≤ 8.8

x ≤ 8

Therefore, the required inequality solution is x ≤ 8.

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Answer:

Inequality: 20p+9 ≤ 125

Answer: p ≤ 5.8

Step-by-step explanation:

Solve:

20p+9≤125

subtract -9 from both sides

20p≤116

20p/20 ≤ 116/20 Divide both sides by 20

p ≤ 5.8