Write an expression to represent "triple the
quotient of a number and three."

The possible outcomes of an event is the sample space

The product of the sample spaces of the single events determines the total number of possible outcomes of a compound event

Assume that the number of outcomes of n single events are:

\(n_1\), \(n_2\), \(n_3\),........ \(n_n\)

When these single events are combined, they form a compound event.

The number of outcomes of the compound event is the product of the number of outcomes of the single events.

i.e.

\(Outcomes = n_1 * n_2 * ......... n_n\)

Hence, the product of the sample spaces of the single events determines the total number of possible outcomes of a compound event

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Answer:

( B ) lng = 5

Step-by-step explanation:

The function f(x) = (1/3)x³ - (1/2)x² - (199/6)x + (211/6).

To find f(x) based on the given information, we can use integration.

Given that f′′(x) = 2x² - x, integrating once gives:

f′(x) = (2/3)x³ - (1/2)x² + C₁

where C₁ is a constant of integration.

Using the given information that f′(2) = 163, we have:

f′(2) = (2/3)2³ - (1/2)2² + C₁ = 8/3 - 2 + C₁ = 163

Solving for C₁, we get:

C₁ = 163 + 2 - 8/3 = 521/3

Substituting this value of C₁, we get:

f′(x) = (2/3)x³ - (1/2)x²+ 521/3

Integrating f′(x) once more, we get:

f(x) = (1/2)x⁴ - (1/6)x³ + (521/3)x + C₂

where C₂ is a constant of integration.

Using the given information that f(1) = 3, we have:

f(1) = (1/2)1⁴ - (1/6)1³ + (521/3)1 + C₂ = 3

Solving for C₂, we get:

C₂ = 3 - (1/2) + (1/6) - (521/3) = -169/3

Substituting this value of C₂, we get the final expression for f(x):

f(x) = (1/2)x⁴ - (1/6)x³ + (521/3)x - 169/3

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To calculate the volume of the cylindrical container in cubic centimeters, we need to determine the dimensions of the container. The volume of the cylindrical container is 216π cubic centimeters.

Since each ball has a diameter of 6 cm, their radius will be half of that, which is 3 cm. When three balls are packed inside the container, they form a triangular arrangement where the centers of the balls touch each other.

In this arrangement, the distance between the centers of two adjacent balls will be equal to the diameter of a single ball, which is 6 cm. Therefore, the height of the cylindrical container will be equal to the diameter of a ball, which is 6 cm. The radius of the container will be the distance from the center of the container to the center of one of the balls, which is equal to the sum of the radius of a ball (3 cm) and the radius of another ball (3 cm), resulting in a total radius of 6 cm.

Using the formula for the volume of a cylinder (V = πr²h), where r is the radius and h is the height, we can calculate the volume of the container. Substituting the values, the volume of the container is V = π(6 cm)²(6 cm) = 216π cm³.

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5.25 or 5 1/4

I worked it out I hope this helps :)

Answer:

D. x + y = 125

   y = 1/2x + 11

Step-by-step explanation:

Rosa = y

Yareli = x

The given expression is cos(tan⁻¹ 5). Let y = tan⁻¹ 5. Then, tan y = 5. Therefore, we have a right triangle where opposite side = 5 and adjacent side = 1. Then, hypotenuse = √(5² + 1²) = √26

3. a. cos (tan-¹5)

The given expression is cos(tan⁻¹ 5). Let y = tan⁻¹ 5. Then, tan y = 5

Therefore, we have a right triangle where opposite side = 5 and adjacent side = 1.

Then, hypotenuse = √(5² + 1²) = √26

Then, cos y = adjacent/hypotenuse= 1/√26

Therefore, cos (tan⁻¹ 5) = cos y = 1/√26b. cot(sin-¹-)

The given expression is cot(sin⁻¹ x).

Let y = sin⁻¹ x

Then, sin y = x

Therefore, we have a right triangle where opposite side = x and hypotenuse = 1. Then, adjacent side = √(1 - x²)

Then, cot y = adjacent/opposite = √(1 - x²)/x

Therefore, cot(sin⁻¹ x) = cot y = √(1 - x²)/x4.

a. π+3cos¹¹(x + 1) = 0

Let cos⁻¹(x + 1) = y

Then, cos y = x + 1

Therefore, we have cos⁻¹(x + 1) = y = π - 3y/3So, y = π/4

Then, cos y = x + 1 = √2/2 + 1 = (2 + √2)/2π + 3(π/4) = (7π/4) ≠ 0

There is no solution to the given equation.

b. 2tan⁻¹(2) = cos⁻¹x

Let y = tan⁻¹(2)

Then, tan y = 2

Therefore, we have a right triangle where opposite side = 2 and adjacent side = 1. Then, hypotenuse = √(1² + 2²) = √5

Therefore, sin y = 2/√5 and cos y = 1/√5

Hence, cos⁻¹x = 2tan⁻¹(2) = 2y

So, x = cos(2y) = cos[2tan⁻¹(2)] = 3/5

c. sin⁻¹ x = cos⁻¹(2x)

Let sin⁻¹ x = y

Then, sin y = x

Therefore, we have a right triangle where opposite side = x and hypotenuse = 1.

Then, adjacent side = √(1 - x²)

Then, cos⁻¹(2x) = z

So, cos z = 2x

Therefore, we have a right triangle where adjacent side = 2x and hypotenuse = 1.

Then, opposite side = √(1 - 4x²)

Then, tan y = x/√(1 - x²) and tan z = √(1 - 4x²)/2x

Hence, x/√(1 - x²) = √(1 - 4x²)/2x

Solving this, we get x = ±√2/2

Therefore, sin⁻¹ x = π/4 and cos⁻¹(2x) = π/4

Therefore, the given equation is true for x = √2/2.5.

Proof Given: tan x + cos x = sin x (sec x + cot x)

We know that sec x = 1/cos x and cot x = cos x/sin x

Therefore, the given equation can be written as tan x + cos x = sin x (1/cos x + cos x/sin x)

Multiplying both sides by sin x cos x, we get sin x cos x tan x + cos² x = sin² x + cos² x

Multiplying both sides by 1/sin x cos x, we get tan x + sec² x = 1

This is true. Hence, proved.

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Answer:

in order from top row to bottom row

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total no. of children = 366

let the number of boys be x

and the no. of girls be x + 28

According to the question,

x + x + 28 = 366

2x + 28 = 366

2x = 366 - 28

2x = 338

x = 338 / 2

x = 169

So the no. of boys = x = 169

and the no. of girls = x + 28 = 169 + 28 = 197

( you can also recheck it by adding the no. of boys and the no. of girls

that is, 169 + 197 = 366 which equal to the total no. of children )

Hope this helps

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The peach grower can maximize their harvest by planting 55 trees per acre.

A peach grower finds that if he plants 80 trees per acre, each tree will yield 60 bushels of peaches.

He wants to maximize his harvest. Given that if he plants 80 trees per acre, each tree will yield 60 bushels of peaches; therefore, the yield per acre will be

,60 × 80 = 4800 bushels of peaches.

Now, let's find out how many trees should he plant per acre to maximize his harvest. Let's assume he plants x trees per acre.

Thus, the yield of each tree will decrease by (x - 80) × 2 bushels of peaches.

Therefore, the yield of each tree will be,(60 - (x - 80) × 2) bushels of peaches.And the yield per acre will be,

The yield per acre = x × (60 - (x - 80) × 2) bushels of peaches.

Now, we need to maximize the yield per acre, we can differentiate the yield per acre with respect to x and equate it to 0.

Then solve for x to find the value of x which will give maximum yield.The yield per acre

= x(60 - 2(x - 80))

= x(220 - 2x)

Differentiate the above expression with respect to x and equate it to 0,dy/dx

= 220 - 4x = 0 ⇒

4x = 220 ⇒x = 55

Hence, he should plant 55 trees per acre to maximize his harvest.

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There are infinitely many ways to represent a fraction using different whole numbers as numerator and denominator.

Andrew and Molly can both be correct by choosing different whole numbers to represent the same fraction, 5/3, in different ways.

Andrew might have drawn a picture of 5/3 using a whole number multiple of 3 as the denominator, such as 9, and then dividing the shape into 5 equal parts. So, each part represents 1/3 of the shape, and there are 5 such parts. In this case, the numerator of the fraction is 5, and the denominator is 9. Hence, Andrew's drawing represents the fraction 5/9.

On the other hand, Molly might have drawn a picture of 5/3 using a whole number multiple of 6 as the denominator, such as 6, and then dividing the shape into 5 equal parts. So, each part represents 1/6 of the shape, and there are 5 such parts. In this case, the numerator of the fraction is 5, and the denominator is 6. Hence, Molly's drawing represents the fraction 5/6.

Therefore, Andrew and Molly can both be correct by choosing different whole numbers to represent the same fraction, 5/3, in different ways. It is important to note that there are infinitely many ways to represent a fraction using different whole numbers as numerator and denominator.

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Answer:

y = -1/2

Step-by-step explanation:

−7⋅

Answer:

Step-by-step explanation:

y/-7=1/14

use cross multiplication

Hope it helps

The statistics are as follows:

a) The standard deviation for the sampling distribution of the sample mean can be calculated using the formula: standard deviation of the sampling distribution = standard deviation of the population / square root of the sample size. In this case, the standard deviation of the population is 1.85 grams and the sample size is 24. Therefore, the standard deviation for the sampling distribution of the sample mean is 1.85 / √24 ≈ 0.377 grams.

b) To calculate the probability of finding a random slice of pizza with a mass of less than 65.5 grams, we need to use the standard normal distribution. We can convert the value of 65.5 grams to a z-score using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (65.5 - 66.4) / 1.85 ≈ -0.49.

We can then use a standard normal distribution table or a calculator to find the probability corresponding to this z-score. The probability of finding a random slice of pizza with a mass of less than 65.5 grams is approximately 0.3133.

c) To calculate the probability of choosing a random sample of 24 slices of pizza having a mean mass of less than 65.5 grams, we need to use the sampling distribution of the sample mean. Since the population mean is 66.4 grams and the standard deviation of the sampling distribution of the sample mean is 0.377 grams (as calculated in part a), we can calculate the z-score using the formula: z = (X- μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation of the sampling distribution, and n is the sample size. Plugging in the values, we get z = (65.5 - 66.4) / (0.377 / √24) ≈ -2.96.

Again, we can use a standard normal distribution table or a calculator to find the probability corresponding to this z-score. The probability of choosing a random sample of 24 slices of pizza having a mean mass of less than 65.5 grams is approximately 0.0086.

d) To find the sample mean that represents the bottom 15% (the 15th percentile), we need to find the z-score corresponding to this percentile. Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a cumulative probability of 0.15. The z-score is approximately -1.04.

We can then use the formula: z = (X- μ) / (σ / √n) to solve for the sample mean. Rearranging the formula, we have X= μ + z * (σ / √n). Plugging in the values, we get X= 66.4 + (-1.04) * (1.85 / √24) ≈ 65.77 grams.

So, the sample mean that represents the bottom 15% (the 15th percentile) is approximately 65.77 grams.

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Answer:

180

Step-by-step explanation:

❄ Hi there,

let us combine the like terms and create an equivalent expression –

\(\large\begin{gathered} \sf{9+a-5b-2} \\\sf{9-2+a-5b}\\\sf{7+a-5b} \end{gathered}\)

That's as far as we can go.

❄

The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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Answer: 20

Step-by-step explanation:

According to the given triangle the value of sin A = 4/5

In a right-angled triangle, the sin of an angle is equal to the ratio of the opposing side to the hypotenuse according to the sin theta formula.

Sin A = Opposite angle / hypotenuse= 4/5

There are about six trigonometric ratios—sine, cosine, tangent, cosecant, secant, and cotangent—which describe the many configurations that can be made in a right-angled triangle.

Trigonometry can only be used to solve a side of a right-angled triangle when the lengths of the other two sides and the angle of a side are already known. Before utilizing algebra to determine the value for the unknown side, one must first select a ratio that includes both the unknown and the given sides.

We are aware that the angle-length relationship in right-angled triangles will be covered in trigonometry.

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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of SinA=3/5.

Given that,

In the picture there is a triangle with ABC angles.

Sides AB=5, BC=3, CA=4

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

According to the sin theta formula, the sin of an angle in a right-angled triangle is equal to the ratio of the opposite side to the hypotenuse.

Sin A = Opposite side / hypotenuse

SinA=3/5

Therefore, SinA=3/5.

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Answer:

There are 24 students in the class.

Step-by-step explanation:

If four students are 1/6 of the class, you need to multiply 4 times 6 to get 24.

Answer:

About 33 years.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Simple Interest Rate Formula: \(\displaystyle A = P(1 + r)^t\)

Logarithm Property 1: \(\displaystyle log(a^x) = xloga\)

Step-by-step explanation:

Step 1: Define

Identify

P = 5000

r = 5% = 0.05

A = 25000

t = unknown

Step 2: Solve for t

a. 80% of 90 is the same as of 90 - False

b. 45% of 60 is 27 - True

c. 20% of 90 is the same as as of 90- True

d. 25 is 35% of 80 -False

a. 80% of 90 is not the same as 90. To find 80% of 90, we multiply 90 by 0.8, which gives us 72. Therefore, the statement is false.

b. To find 45% of 60, we multiply 60 by 0.45, which gives us 27. Therefore, the statement is true.

c. 20% of 90 is the same as of 90. To find 20% of 90, we multiply 90 by 0.2, which gives us 18. Therefore, the statement is true.

Lastly, for question d. 25 is not 35% of 80. To find 35% of 80, we multiply 80 by 0.35, which gives us 28. Therefore, the statement is false.

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Answer:

D: {-4, 0, 1, 2}

R: {-4, -3, 1}

Step-by-step explanation:

Answer:

369,000

Step-by-step explanation:

$6000x5.5x12

Answer:

hbjjkhjbhkbhj

Step-by-step explanation:

Answer:

- 1/80

Step-by-step explanation:

Answer:

D

Step-by-step explanation

When rounding, you want the number to change as little as possible. It is easier for the number to be 250 instead of 200 because 229 is closer to 250. in the same way, 3.22 is closer to 3 than 4. Now to check this, if you do 229 x 3.22, you get 737.38. Now looking at the answer choices, this is most definitely closest to 750. Given all this, I think it is safe to say D is the answer.

Hope this helps!

Answer:

Step-by-step explanation:

mathmatically the answer would be 10 but realistically since we have tax it would be 9. but go with 10

Solution :

Given initial velocity, v= 48 ft/s

Acceleration due to gravity, g = \($12\ ft/s^2$\)

a). Therefore the maximum height he can jump on Mars is

     \($H_{max}=\frac{v^2}{2g}$\)

     \($H_{max} = \frac{(48)^2}{2 \times 12}$\)

               = 96 ft

b). Time he can stay in the air before hitting the ground is

   \($T=\frac{2v}{g}$\)

  \($T=\frac{2 \times 48}{12}$\)

     = 8 seconds

c).  Considering upward motion as positive direction.

     v = u + at

We find the time taken to reach the maximum height by taking v = 0.

     v = u + at

     0 = 16 + (12) t

     \($t=\frac{16}{12}$\)

        \($=\frac{4}{3} \ s$\)

We know that, \($S=ut + \frac{1}{2}at^2$\)

Taking t =  \($=\frac{4}{3} \ s$\)  , we get

\($S=16 \times\frac{4}{3} + \frac{1}{2}\times(-12) \times \left(\frac{4}{3}\right)^2$\)

\($S=\frac{32}{3}$\)  feet

Thus he can't reach to 100 ft as it is shown in the movie.

d). For any jump whose final landing position will be same of the take off level, the final velocity will be the initial velocity.

Therefore final velocity is = -16 ft/s