3.
Which of the following equations does not have a real solution?
(A) x + x = 1
(B) x + x=0
(C) x*x=0
(D) x*x=-1

The probability that both Nic and Tim win = \(\frac{x}{y}\) = \(\frac{C^{2} _{2} }{C^{2}_{10} }\) = \(\frac{2}{90}\)

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

Nic and Tim each purchased one raffle ticket.

Nic and Tim a total of raffle tickets are sold = 10

Then the winners will be selected = 2

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

Let us assume,

The winners will be selected = x

Nic and Tim a total of raffle tickets are sold= y

So,

We can write,

y = \(C^{2} _{10}\)

x = \(C^{2} _{2}\)

Then,

We divide the winners will be selected to Nic and Tim a total of raffle tickets are sold,

So,

\(\frac{x}{y}\) = \(\frac{C^{2} _{2} }{C^{2}_{10} }\)

\(\frac{x}{y}\) = \(\frac{C^{2} _{2} }{C^{2}_{10} }\) = \(\frac{1*2}{10*9}\)

\(\frac{x}{y}\) = \(\frac{C^{2} _{2} }{C^{2}_{10} }\) = \(\frac{2}{90}\)

Therefore,

The probability that both Nic and Tim win = \(\frac{x}{y}\) = \(\frac{C^{2} _{2} }{C^{2}_{10} }\) = \(\frac{2}{90}\)

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Answer:

obtuse acute straight obtuse

Step-by-step explanation:

Answer:

1. a   2. b   3. c  4. d

Step-by-step explanation:

you have to simplify but 2/2 to make the denominator 13 on number 3 and 4

The area enclosed by the ellipse \(\frac{x^2}{4}+\frac{y^2}{81}=1\) is 60 square units.

The general form of the equation of ellipse is  \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Given the equation of ellipse is,  \(\frac{x^2}{4}+\frac{y^2}{81}=1\)

⇒ \(\frac{x^2}{2^2}+\frac{y^2}{9^2}=1\)

That is, a = 2 and b = 9

Now,  \(\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}\)

⇒ \(y=\frac{9}{2} \sqrt{4-x^2}\)

Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant

Therefore, Area of ellipse in the first quadrant, A = \(\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx\)

Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0

A = \(\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx\)

  = \(\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx\)

  = \(\int\limits^2_0{9 sin^2\theta} \, dx\)

 = \(\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta\)

  = \(\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta\)

  = \(\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta\)

  = \(\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta\)

  = 27/2 x (-cosθ) - 9/6 x (-cos3θ) |  θ = 0 to  θ =  π/2

  = 15 square units.

Therefore, the area enclosed by ellipse  \(\frac{x^2}{4}+\frac{y^2}{81}=1\) = 4 x A = 4 x 15 = 60 square units.

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The probability that the mean of the sample would differ from the population mean by less than 36 points is 0.0316

To calculate the probability that the mean of the sample would differ from the population mean by less than 36 points, we need to use the Central Limit Theorem.

The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

Given:

Standard deviation (σ) = 421 points

Mean (μ) = 1728 points

Sample size (n) = 309 tests

To calculate the probability, we need to find the z-score associated with a difference of 36 points and then find the corresponding probability using the standard normal distribution table or a statistical calculator.

The formula for the z-score is:

z = (x - μ) / (σ / √n)

Plugging in the values:

z = (36 - 0) / (421 / √309)

Calculating the z-score:

z = 36 / (421 / √309)

z ≈ 2.1604

Now, we need to find the probability associated with this z-score. Looking up the z-score of 2.1604 in the standard normal distribution table, we find that the probability is approximately 0.9842.

However, we need to consider both tails of the distribution because we're looking for a difference in either direction (less than 36 points or greater than -36 points). Therefore, we need to find the area in both tails.

Since the standard normal distribution is symmetric, we can calculate the area in one tail and multiply it by 2 to get the total probability.

Area in one tail = 1 - 0.9842

Area in one tail ≈ 0.0158

Total probability = 2 * 0.0158

Total probability ≈ 0.0316

Rounding the answer to four decimal places, the probability that the mean of the sample would differ from the population mean by less than 36 points is approximately 0.0316.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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It is proved that f(g(x)) = g(f(x)) =  x , So f(x) and g(x) are inverses of one other

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We are given the function as;

f(x) = 5x + 2

g(x) = (x -2)/ 5

If two functions f(x)  and g(x) are inverses of each other, their compositions will equal

f(g(x)) = 5[ (x -2)/ 5] + 2

f(g(x)) = x - 2 + 2

f(g(x)) = x

Now,

g(f(x)) =  ((5x + 2) -2)/ 5

g(f(x)) =  (5x + 2 -2)/ 5

g(f(x)) =  x

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Answer:

95x + 65 = c      

Step-by-step explanation:

Answer:

3) a. f(-4) = 2

   b. f(0) = 0

   c. f(3) = -1.5

   d. f(-5) = 0

   e. x = -4

    f. x= 0

4) a. f(-1) = 1

   b. f(3) = -1

   c. 1

   d. -5

5) f(6) = 2

   f(2) = 4

   f(0) = 7

   f(5) = 1.5

    x=4

Answer:

see below

answers as required.

3)

a. \(f\)(-4) = 2

b. \(f\)(0) = 0

c. \(f\)(3) = -1.5

d. \(f\)(-5) = 0

e. x = -4

f. x= 0

4)

a. \(f\)(-1) = 1

b. \(f\)(3) = -1

c. 1

d. -5

5)

\(f\)(6) = 2

\(f\)f(2) = 4

\(f\)(0) = 7

(5) = 1.5

x=4

Answer:

they played 20 games together

Step-by-step explanation:

use percentages

Let x be the number of total games.

If 60% is won games then 40% is lost games.

(8/x)*100 = 40

8/x = 4/10

80 = 4x

X = 80/4

Therefore the number of games is 20

The exponential function is y = 1200(1.04)^t and the investment amount after 16 years is $2247.58.

What is exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Jayden invests $1,200 in a savings account. Each year, the value increases by 4%.

Let t = time in years

Let y = amount of money invested in savings account

Start with $1200 and each year add 4% interest to the amount in the bank.

1st year: Interest = 1200 × (0.04) = $48

This is added to the previous amount -

= $1200 + $1200 × (0.04)

= $1200 (1+0.04)

= $1200 (1.04)

= $1248

2nd year: Previous amount + interest on the previous amount

= $1248 (1+0.06)

= $1248 (1.06)

= $1297.92

So, the exponential formula becomes -

y = 1200(1.04)^t

Now, to find the value of investment after 16 years, substitute t = 16.

y = 1200(1.04)^t

y = 1200(1.04)^16

y = 1200(1.87298125)

y =$2247.58

Therefore, the value of investment after 16 years is $2247.58.

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The value of x from given quadrilateral ABCD is 27°.

In the given quadrilateral ABCD, ∠A=3x+5, ∠B=2x+15, ∠C=4x and ∠D=4x-10.

We know that, the sum of interior angles of quadrilateral is 360°.

Here, ∠A+∠B+∠C+∠D=360°

3x+5+2x+15+4x+4x-10=360°

13x+10=360°

13x=350°

x=350/13

x=26.9

x≈27°

Therefore, the value of x from given quadrilateral ABCD is 27°.

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Yes, if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

What is AAS congruence rule?

AAS congruence rule or theorem states that if two angles of a triangle with a non-included side are equal to the corresponding angles and non-included side of the other triangle, they are considered to be congruent.

Let us see the proof of the theorem:

Given: AB = DE, ∠B=∠E, and ∠C =∠F. To prove: ∆ABC ≅ ∆DEF

If both the triangles are superimposed on each other, we see that ∠B =∠E and ∠C =∠F. And the non-included sides AB and DE are equal in length. Therefore, we can say that ∆ABC ≅ ∆DEF.

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Answer:

211,200 unidades de productos que debes obtener en el año 2018 si quieres incrementar la productividad de la fuerza laboral en un 10% utilizando 24,000 horas laborales.

Step-by-step explanation:

Datos de 2017

Unidades = 200.000

Horas laborales = 25,000

Unidades por hora laboral = 200.000 / 25.000 = 8

2018

Horas de mano de obra = 24.000

Unidades por hora laboral = 8

Unidades totales = 24,000 * 8 = 192,000

Queremos aumentar la productividad en un 10%

10% de 8 = 0,8 Se deben producir 0,8 adicionales cada hora para obtener un 10% más de productividad.

El nuevo número de unidades producidas después de una mayor productividad será

8+ 0.8 = 8.8 unidades por hora

Unidades totales = 24,000 * 8.8 = 211,200 unidades serán producidas.

211,200 unidades de productos que debes obtener en el año 2018 si quieres incrementar la productividad de la fuerza laboral en un 10% utilizando 24,000 horas laborales.

2017 data

Units = 200,000

Labor Hours = 25,000

Units per labor hour = 200,000/25,000= 8

2018

Labor Hours = 24,000

Units per labor hour = 8

Total Units = 24,000*8 =192,000

We want to increase the productivity by 10 % so

10 % of 8 = 0.8   An additional 0.8 must be produced each hour to get 10 % more productivity.

The new number of units produced after increased productivity will be

8+ 0.8 = 8.8 units per hour

Total units = 24,000* 8.8=   211,200 units will be produced.

211,200 units of products you must obtain in the year 2018 if you want to increase the productivity of the labor force by 10% using 24,000 labor hours.

Answer:

A. y = 9√3

Step-by-step explanation:

The relationship of the sides of the triangles are as follows:

First leg = x

Second leg = x√3

Hypotenuse = 2x

Since we know the first leg is 9, multiply that by √3.

Therefore, y = 9√3.

The probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 11/12

To calculate the probability of rolling two fair six-sided dice and getting a sum of 4 or higher, we first need to calculate the total number of possible outcomes.

The number of possible outcomes when rolling two dice is 6 × 6 = 36, since each die has 6 possible outcomes.

Now, let's find the number of outcomes that result in a sum of 4 or higher. We can do this by listing all the possible outcomes:

Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes

Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes

Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes

Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes

Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes

Sum of 10: (4, 6), (5, 5), (6, 4) = 3 outcomes

Sum of 11: (5, 6), (6, 5) = 2 outcomes

Sum of 12: (6, 6) = 1 outcome

Therefore, the number of outcomes that result in a sum of 4 or higher is 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.

Therefore, the probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 33/36 = 11/12.

To find the probability of getting a sum of 44 or higher, we need to subtract the probability of getting a sum of 43 or lower from 1:

Sum of 2: (1, 1) = 1 outcome

Sum of 3: (1, 2), (2, 1) = 2 outcomes

Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes

Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes

Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes

Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes

Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes

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Answer:

It would take 17 hours to get to the cabin.

Explanation:

1054 / 62 = 17

Answer:

C. -1/3= 1/-3

Step-by-step explanation:

The answer is -1/3= 1/-3 because if you divide them to check, they will be the same.

Use calculator to check.

-1/3=-0.3

1/-3=-0.3

Hope this helps!

Answer:

D. 578pi

Step-by-step explanation:

Sorry if that's wrong

Answer:

Sheldon has to sell at least 143 cups of coffee to purchase the kayak.

Step-by-step explanation:

First write an expression:

15 + 0.25x ≥ 50.75

Next use inverse operations:

15 + 0.25x - 15 ≥ 50.75 - 15

0.25x ≥ 35.75

0.25x ÷ 0.25 ≥ 35.75 ÷ 0.25

x ≥ 143

Sheldon has to sell at least 143 cups of coffee to purchase the kayak.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

143 cups

Step-by-step explanation:

Sheldon gets a flat $15, as well as 25 cents for each cup of coffee made.

He needs $50.75 to buy a Kayak.

Set the equation. Let the amount of cups of coffee = c.

0.25c + 15 = 50.75

Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and equals:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 15 from both sides of the equation:

0.25c + 15 = 50.75

0.25c + 15 (-15) = 50.75 (-15)

0.25c = 50.75 - 15

0.25c = 35.75

Next, divide 0.25 from both sides of the equation:

(0.25c)/0.25 = (35.75)/0.25

c = 35.75/0.25

c = 143

Sheldon will need to sell 143 cups of coffee.

~

If the spinner is fair and has an equal chance of landing on each color, then the best prediction possible for the number of times it will land on blue when spun 11 times is 2.

If the spinner is fair, then the probability of it landing on each color is equal. Since the spinner has four colors, the probability of it landing on blue is 1/4 or 0.25.

To determine the best prediction possible for the number of times it will land on blue, we can multiply the probability of it landing on blue (0.25) by the total number of spins (11):

0.25 x 11 = 2.75

However, since we cannot have a fractional number of spins, we must round to the nearest whole number. Since 2.75 is closer to 3 than to 2, we might initially think that the best prediction for the number of times it will land on blue is 3. However, since we are looking for the best prediction possible, we need to consider the probabilities of landing on other colors as well. If we predict that the spinner will land on blue 3 times, then we are predicting that it will land on each of the other colors 2 times. This means that our total prediction is:

Blue: 3

Red: 2

Green: 2

Yellow: 2

              Blue: 2

              Red: 3

              Green: 3

              Yellow: 3

This prediction is the best possible because it gets as close as possible to landing on each color 2 times while still being a whole number. Therefore, the best prediction possible for the number of times the spinner will land on blue when spun 11 times is 2.

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The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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Answer:

y=12

Step-by-step explanation:

Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Answer:

  47.5 cm

Step-by-step explanation:

You want the height of a trapezoid with bases of lengths 135 cm and 105 cm, and an area of 5700 cm².

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  5700 = 1/2(135 +105)h

  5700 = 120h

  h = 5700/120 = 47.5

The height of the tabletop is 47.5 cm.

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Answer: y=2x+6

Step-by-step explanation:

8x-4y=-24

-8x-4y=-8x

-4y=-8x-24

-4          -4

y=8/4x+24/4

Answer is y=2x+6

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