world problem in length (trigonometry) geometry not chemistry

Answer:

  46

Step-by-step explanation:

The geometry can be modeled by a right triangle. The diagonal measure is the hypotenuse, and the height is one leg. The width is the other leg, and can be found using the Pythagorean theorem.

__

The relation between the leg lengths (a, b) and the hypotenuse (c) is ...

  c² = a² +b²

Solving for b gives ...

  b = √(c² -a²)

In this problem, we have c=55 and a=30. Then the width of the TV is ...

  b = √(55² -30²) = √(3025 -900) = √2125

  b ≈ 46.098

The width of the TV is about 46.

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]\boxed{\sf x = \dfrac{1}{21}}[/tex]

Explanation:

[tex]\rightarrow \sf 3x+7-6= \dfrac{8}{7} - 0[/tex]

simplify the following

[tex]\rightarrow \sf 3x+1= \dfrac{8}{7}[/tex]

subtract 1 from both sides

[tex]\rightarrow \sf 3x+ 1 -1= \dfrac{8}{7} - 1[/tex]

simplify the following

[tex]\rightarrow \sf 3x= \dfrac{1}{7}[/tex]

multiply both sides by 1/3

[tex]\rightarrow \sf 3x \cdot \dfrac{1}{3}= \dfrac{1}{7}\cdot \dfrac{1}{3}[/tex]

simplify the following

[tex]\rightarrow \sf x = \dfrac{1}{21}[/tex]

[tex]3x + 7 - 6 = \frac{8}{7} - 0 \\ \\ 3x + 1 = \frac{8}{7} \\ \\ 3x = \frac{8}{7} - 1 \\ \\ 3x = \frac{ 8 - 7}{7} \\ \\ 3x = \frac{1}{7} \\ \\ x = \frac{1}{7 \times 3} \\ \\ x = \frac{1}{21} .[/tex]

The product of variables in inverse proportion is constant, so the equation is [tex]\boxed{xy=-3}[/tex]

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:

[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.

Answer:

  $188.06

Step-by-step explanation:

The total cost for the film will be the sum of film cost, applicable sales tax, and applicable shipping charges. The film cost will be the product of the number of rolls and the cost per roll.

__

  film cost = (18 rolls) × ($9.95 /roll) = $179.10

  sales tax = 0.05 × $179.10 = $8.96

There is no shipping charge associated with the camera shop purchase, so the total cost is ...

  camera shop cost = film cost + sales tax = $179.10 +8.96 = $188.06

__

  film cost = (18 rolls) × ($9.76 /roll) = $175.50

  shipping charge = $15.00

There is no sales tax associated with the mail order, so the total cost is ...

  mail order cost = film cost + shipping charge = $175.50 +$15.00 = $190.50

__

The price from the camera shop is the better of the two prices. The purchase there would cost you $188.06 for 18 rolls of film.

_____

Additional comment

The after-tax charge per roll of film at the camera shop is 9.95×1.05 = 10.4475. This is $0.6975 more than the basic charge per roll from the mail order company. In order to get the shipping charge of $15 to be less than $0.6975 per roll, the number of rolls ordered must be more than 15/0.6975 = 21.5.

An order of 22 rolls of film from the mail order company would cost less than from the camera shop. ($229.50 vs. $229.85)

Answer:

A. 5 feet

Step-by-step explanation:

Answer: 1

Step-by-step explanation:

[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]

Answer:

-3/2, -1

Step-by-step explanation:

Each coordinate contains one [tex]x[/tex] value and one [tex]y[/tex] value, [tex](x,y)[/tex].

If we work out the midpoint of each of these individually, it makes it much easier to find the midpoint of the line.

Let's take the [tex]x[/tex] values first. Our first  [tex]x[/tex] value is -4 and our second [tex]x[/tex] value is 1. Imagine the integers between -4 and 1 laid out in a sequence:

[tex]-4, -3, -2, -1, 0, 1[/tex]

If you take the middle value of this sequence, you get the midpoint of the [tex]x[/tex] values.

In this case, the middle is between values -2 and -1, leaving us with a midpoint of -1.5. This as a fraction is [tex]-\frac{3}{2}[/tex].

Now let's look at the [tex]y[/tex] values. Our first [tex]y[/tex] value is 2 and our second [tex]y[/tex] value is -4. Again, let's imagine those numbers laid out in a sequence:

[tex]2, 1, 0, -1, -2, -3, -4[/tex]

Here, the middle of these values is -1, and this is the midpoint of the [tex]y[/tex] values.

So if we put these two values in a coordinate, we get the midpoint of the line.

In this case, we get [tex](-\frac{3}{2} ,-1)[/tex].

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

Answer:

D.

Step-by-step explanation:

EDG 2022

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:

[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:

[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:

how many times does 4.2 go into 14.7

1. 4.2

2. 8.4

3. 12.6

14.7-12.6=2.1 or one half of 4.2

3.5

Hope This Helps!!!

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

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                              

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

[tex]\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455[/tex]

a)

[tex]\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%[/tex]

b)

[tex]\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%[/tex]

c)

[tex]\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%[/tex]

d)

[tex]A[/tex] - at least one is spoilt

[tex]A'[/tex] - none is spoilt

[tex]P(A)=1-P(A')[/tex]

We calculated [tex]P(A')[/tex] in a).

Therefore

[tex]P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%[/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.

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

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.

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

Answer:

Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45

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:

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:

B=CD-A