Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]​

Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes, the values are mathematically given as

Generally, the equation for Material-handling cost for one lens mathematically given as

MH1=Total projected costs for material handling /{Total number of direct labor hours x Direct labor hours per unit)

MH1={$50,000/10.000)x 200

MH1=$1,000

2)

Material-handling cost for one mirror

MH2=Total budgeted material handling cost/ Total number of direct labor hours x direct labor hours per unit

MH2={$50,000/10.000)x 200

MH2=$1,000

3) Material-handling cost per lens

[tex]MH3=\frac{Total projected costs for material handling}{\frac{Number of material moves per lens + Number of material moves per mirror}{(Total number of lenses)}}* Material moves per lens[/tex]

[tex]MH3=\frac{50,000}{\frac{5+15}{25}}*5[/tex]

MH3=$1500

4)

[tex]MH4=\frac{Total projected costs for material handling}{\frac{Number of material moves per mirror + Number of material moves per lens}{(Total number of mirror)}}* Material moves per mirror[/tex]

[tex]MH4=\frac{50,000}{\frac{5+15}{25}}*5[/tex]

MH4=$1500

Read more about lens

https://brainly.com/question/20598911

#SPJ1

Answer:

[tex]\boxed {\frac{343}{360}}[/tex]

Step-by-step explanation:

Probability Rule :

[tex]\boxed {P(A\cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B \cap C)}[/tex]

Solving :

⇒ 3/5 = 3/8 + 5/15 + 4/9 - P (A ∩ B ∩ C)

⇒ P (A ∩ B ∩ C) = 3/8 + 1/3 + 4/9 - 1/5

⇒ P (A ∩ B ∩ C) = 135/360 + 120/360 + 160/360 - 72/360

⇒ P (A ∩ B ∩ C) = (135 + 120 + 160 - 72) / 360

⇒ P (A ∩ B ∩ C) = 343/360

Answer:

[tex]g(x) = x^3+1\\f(x) = x^2[/tex]

Step-by-step explanation:

Answer:

f(x)=x^2 and g(x)=x^3+1

Step-by-step explanation:

to find y=f(g(x))

substitute g(x) into f(x)

y= (x^3+1)^2.

The cash flow in year 1 is $15.

A growing perpetuity increases continuously and indefinitely.

Cash flow = present value x (rate of return - growth rate)

214 x (10% - 3%)

214 x 0.07 = $15

To learn more about present value, please check: https://brainly.com/question/17322936

#SPJ1

Answer:

[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]

Step-by-step explanation:

(3a³-6b³) (4a² + 5b²) -> Simplify not Multiply

Expand (3a³-6b³) (4a² + 5b²) using the FOIL Method.

Apply the distributive property.

[tex]3a^3(4a^2+5b^2)-6b^3(4a^2+5b^2)[/tex]

[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2+5b^2)[/tex]

[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]

Simplify each term.

Rewrite using the commutative property of multiplication.

[tex]3*4a^3a^2+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]

↓

[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]

Equation Simplified.

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

Hope this helped!

Answer:

A

Step-by-step explanation:

[tex]s=\frac{a+b+c}{2}[/tex]

multiply both sides by 2

[tex]2s = a + b +c[/tex]

substract b and c from both sides to get a by itself

[tex]a = 2s - (b + c)\\a = 2s - b - c[/tex]

so the answer is A.

Answer:

25

Step-by-step explanation:

bc i guess

Answer:

Using the formula of geometric progression, we get 5.3333333. After rounding off to the nearest hundredth or to the two digit place after the decimal, we get 5.33.

Step-by-step explanation:

Concept: Given expression means that [tex]4(\frac{1}{4} )^{n-1}[/tex] is a series that starts from n = 1 and ends at n = 10. Or we can say that the given expression is a summation from n = 1 to n = 10. This will make a geometric progression. Use the formula of geometric progression to find the answer.

[tex]4(\frac{1}{4})^{0} + 4(\frac{1}{4})^{1} + 4(\frac{1}{4})^{2} +...+ 4(\frac{1}{4})^{10}\\4\frac{-(\frac{1}{4} )^{11} +1}{-\frac{1}{4} +1} \\4\frac{1}{\frac{3}{4} } \\\frac{16}{3} \\5.33333333\\[/tex]

Now, we want the answer to the nearest hundredth. This means that the answer should have two digits after the point.

The answer, to the nearest hundredth is 5.3333333

For more explanation, refer the following link

https://brainly.com/question/27959890

#SPJ10

For different function different results are shown below.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

We have been given a graph of piecewise function. Using that we have to select the function from given choices which is represented by graph.

g(x) = −2x, −2 < x < 0

Answer:

NO. Because g(x) = −2x has negative slope so that means it goes downward also there is no y-intercept in g(x) = −2x but the only graph that has y-intercept in given graph goes upward so that can't be answer.

g(x) = −2, x < −2

Answer:

YES. Because g(x) = −2 is a horizontal line which is only on the left side of x=-2. Graph of this part is present in given graph. So yes it is answer.

g(x) = x − 2, −2 < x < 1

Answer:

NO. Because g(x) = x−2 has y-intercept at y=-2 and slope 1 so that means graph of g(x)= x-2 must be going upward and crossing at y=-2 but there is no such graph. Hence this can't be answer.

g(x) = −2x + 6, x ≥ 1

Answer:

YES. Because g(x) = −2x+6 satisfies the graph which is going downward.

g(x) = x/2+ 1, –2 ≤ x < 1

Answer:

YES. Because g(x) = x/2+ 1 satisfies the graph which is going downward.

Learn more about function from:

https://brainly.com/question/12431044

#SPJ1

Answer: i think this is the answer sorry if i am wrong.

g(x) = −2, x < −2,

g(x) = −2x + 6, x ≥ 1,

g(x) = x/2  + 1, –2 ≤ x < 1

Step-by-step explanation:

Here is the graph

Answer:

pi [π] is the ratio of a circle's circumference to its diameter, and it is constant [meaning it is always the case] for all circles.

{this is a long number, 3.141592653589793238... is not even the full length, but 3.14 [or 3.14159] is typically used for estimation}

The significance of pi is typically centered in math--it can be used to find values that we don't know of circles. There are other areas of math that have been related back to the value of pi--which is incredible, and genuinely relevant.

We can find pi in the shape of rivers, physics--including waves--DNA

[+ anywhere there is a circle]

hope this helps!! :)

Answer:

ratio of circle's circumference to diameter

it is constant

Answer:

h(x) = -2|x+2| + 2

Step-by-step explanation:

let me know if you want an explanation :))

Answer:Yes, the point lies on the line.

Step-by-step explanation:

Given coordinate of the locus = (1,2)

 Equation of the line  2x+4y = 10

Unknown:

Does the given coordinate lie on the line?

Solution:

The equation given is that of a straight line. To solve this problem, we simply plug the coordinates of the point back into the equation and check if solves it.

  x  = 1 and y = 2;

  2x+4y = 10

So;

   2(1) + 4(2) gives 2 + 8 = 10

Yes, the point lies on the line.

The best buy is a 9 oz box of rice $1.25. (option d)

In order to determine the best buy, the unit cost of each option has to be determined. The best buy is the option with the lowest unit cost. The unit cost can be determined by dividing the total cost by the total quantity.

Unit cost = total cost / total oz

$0.90 / 6 = $0.15

$1.93 / 12 = $0.16

$2.42 / 16 = 0.151

$1.25 / 9 = 0.14

To learn more about division, please check: https://brainly.com/question/13281206

#SPJ1

The probability that a random alcoholic can kick the habit without professional help is 0.273 .

Probability is the study of likeliness of an event to happen.

It has a range of 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.

It is given that

The alcoholics that need professional help to stop drinking is 72.7 %

Therefore the probability of this is 72.7 /100 = 0.727

The probability that they will not need professional help is given by

q = 1 - p

q = 1 -0.727

q = 0.273

Therefore the probability that a random alcoholic can kick the habit without professional help is 0.273 .

To know more about Probability

https://brainly.com/question/11234923

#SPJ1

The correct answer is option b which is the break-even quantity will be 20217 units.

The point at which the company will not have any profit and loss on the products they manufactured they only get the amount they invested in manufacturing the product is called the break-even point.

Given that:-

If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400.

The formula for calculating break-even quantity will be given as:-

[tex]BEQ = \dfrac{FC}{SP-VC}[/tex]

Here,

FC = Fixed cost = $281000

SP = Selling price = $33

VC = Variable cost = $21

The fixed cost is reduced by $38400 so the fixed cost now:-

FC = $281000 - $38400

FC = $242600

[tex]BEQ = \dfrac{242600}{33-21}[/tex]

BEQ = 20217 units

Therefore the correct answer is option b which is the break-even quantity will be 20217 units.

To know more about break-even quantity follow

https://brainly.com/question/21137380

#SPJ1

Answer:

the answer is a.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: The best estimate of the number of miles that Alexia run is 4 miles.

Step-by-step explanation:

Since we have given that

Length of lap is given by

Number of laps around her neighborhood = 3

So, Total number of miles that Alexia ran is given by

Hence, the best estimate of the number of miles that Alexia run is 4 miles

Answer:

Step-by-step explanation:

Comment

The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.

Givens

Arc 1 = 94

Arc2 = d

interior angle = 75

Formula

(d + 94)/2 = interior angle/1

Solution

(d + 94)/2 = interior angle/1               Cross Multiply

1*(d + 94) = 75 *2                           Combine

d + 94 = 150                                        Subtract 94 from both sides

d + 94 - 94 = 150 - 94                         Combine

d = 56

Answer: d = 56

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

En este problema tenemos un sistema formado por dos triángulos similares, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo pequeño) y AP'' (triángulo grande), así como de los lados AM y AB, así como los lados AN y AC, así como los mismos ángulos en la misma distribución. (Semejanza Lado - Ángulo - Lado)

En consecuencia, obtenemos las siguientes proporciones:

AP'/AP'' = MN/BC = 1/2     (1)

Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:

[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }[/tex]

[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}[/tex]

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

Para aprender sobre triángulos semejantes: https://brainly.com/question/21730013

#SPJ1

The correct answer to this question is Option (4).

Answer:

D.

Step-by-step explanation:

EDG 2022

Step-by-step explanation:

3x - 2 is formatted in the formula y = mx + c

To substitute for 3x - 2

y = 3x -2

The Maximax decision is that Susan should build a very large gas station due to the largest value of row maximums.

A decision table can be defined as a type of table that is used for the graphical representation of the actions to perform, especially based on given conditions and business level rules.

The decision table for Susan’s problem is shown below:

Size            Good market   Fair market   Poor market    Row maximum

Small              50,000           20,000            -10,000           50,000

Medium          80,000           30,000            -20,000          80,000

Large              100,000          30,000            -40,000          100,000

Very large      300,000         25,000            -160,000         300,000

Thus, the Maximax decision is for Susan to build a very large gas station due to the largest value of row maximums.

For the Maximin decision, we have:

Size            Good market   Fair market   Poor market    Row minimum

Small              50,000           20,000            -10,000           -10,000

Medium          80,000           30,000            -20,000          -20,000

Large              100,000          30,000            -40,000          -40,000

Very large      300,000         25,000            -160,000         -160,000

Therefore, the Maximin decision is that Susan should build a small gas station due to the largest value of row minimums.

For the equally likely decision, we would find the row average:

Row 1 = (50,000 + 20,000 - 10,000)/3 = 20,000.

Row 2 = (80,000 + 30,000 - 20,000)/3 = 30,000.

Row 3 = (100,000 + 30,000 - 40,000)/3 = 30,000.

Row 4 = (300,000 + 25,000 - 160,000)/3 = 55,000.

Hence, the equally likely decision is that Susan should build a very large gas station due to the largest value of row average.

Read more on decision making here: https://brainly.com/question/13171394

#SPJ1

Complete Question:

Even though independent gasoline stations have been having a difficult time, Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline.  After a careful analysis, Susan developed the following table:

a. Develop a decision table for this problem

b. What is the maximax decision?

c. What is the maximin decision?

d. What is the equally likely decision?

Answer:

Step-by-step explanation:

Comment

I'm going to assume that this is not a closed figure. The top is open like a water trough for horses.

There are 2 semicircular ends which add up to 1 whole circle.

There is 1 base area. The base area has a width of one of the semicircles. It has a length of 15 cm.

Solution

2 semi circles

r = d / 2

r = 20/2

r = 10

Area = pi r^2    This area is for 2 semicircles which = 1 circle.

Area = 3.14 * 10^2

Area = 3.14 * 100

Area =                                                  314

Trough

r = d / 2  

d= 20

r = 20/2

r= 10

w = 2*pi*r / 2

w = 2*3.14 *10/2

w = 31.4 cm

L = 15 cm

Area = 15 * 31.4

Area =                                                   471

Total Area =                                         785                              

There is no solution for b.

The rule for operations done in exponents are

(a) [tex]a^m*a^n=a^{m+n}[/tex]

(b) [tex]a^m/a^n=a^{m-n}[/tex]

(c)[tex](1/a)^m=a^{-m}[/tex]

Given the expression (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b+2 baseline = 12

the expression (one-twelfth) superscript negative 2 b simplifies that [tex](1/12)^{-2b}[/tex]

12 superscript negative 2b+ 2 simplifies that [tex]12^{-2b+2}[/tex]

so the final expression (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b+2 baseline = 12 will be

[tex](1/12)^{-2b}[/tex] * [tex]12^{-2b+2}[/tex] =12

⇒[tex]12^{-(-2b)}\\[/tex] * [tex]12^{-2b+2}[/tex] =12

⇒[tex]12^{2b[/tex] * [tex]12^{-2b+2}[/tex] =12

⇒[tex]12^{2b-2b+2}[/tex]=12¹

equating the exponts of the both sides

⇒2b-2b+2=1

⇒2=1 (not accepted because un-logic condition)

Therefore there is no solution.

Learn more about exponent

here: https://brainly.com/question/11975096

#SPJ10