compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (4 points)compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (4 points)

The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

What is the probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

An order does not matter so it is a Combination.

There are 16 men and we are going to choose 12 --> ₁₆C₁₂

There are 30 people and we are going to choose 12  --> ₃₀C₁₂

₁₆C₁₂ / ₃₀C₁₂

\(= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}\)  

= 0.00002104211

= 2.1 × 10⁻⁵

Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

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a)  [a] = LT⁻⁴, [b] = LT⁻³, and [c] = L T⁻².

b) The acceleration of the body is 12at² + 6bt

c) The time-dependent force acting on the body is 12ma.

Given equation:

x(t)=at⁴+bt³+ct

where a, b, and c are constants.

(a) Dimensions of the constants in the position equation.The dimensions of the constants in the position equation are

[a] = LT⁻⁴, [b] = LT⁻³, and [c] = L T⁻².

(b) Acceleration of the body

The velocity of the body v(t) is given by taking the derivative of position equation with

respect to time t.

v(t) = x'(t) = 4at³ + 3bt²

The acceleration of the body is given by taking the derivative of velocity equation with respect to time t.

a(t) = v'(t)

= 12at² + 6bt

(c) Time-dependent force acting on the body.

The time-dependent force acting on the body is given by taking the derivative of acceleration equation with respect to time t.

F(t) = m a'(t)

= m (12a)

where m is the mass of the body.

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The distinct prime factors of 9999 are 3, 11, and 101. So the sum of each distinct prime factor of 9999 is 115.

To find the sum of the distinct prime factors of 9999, we first need to factorize 9999 into its prime factors.

9999 can be factorized as follows:

9999 = 3 * 3333

= 3 * 3 * 1111

= 3 * 3 * 11 * 101

So, the distinct prime factors of 9999 are 3, 11, and 101.

The sum of these distinct prime factors is:

3 + 11 + 101 = 115

Therefore, the sum of each distinct prime factor of 9999 is 115.

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Answer:

E. 54

Step-by-step explanation:

To find the area just multiply the base times the height. In this problem it would just be 6x9= 54.

Answer:54 cm ^2

Step-by-step explanation:

9 times 6 is 54

Answer:

4r-7

Step-by-step explanation:

-14+7-9r+13r

combine like terms

4r-14+7

combine like terms

4r-7

hope this helped :)

Answer:

-7 + 4r

Step-by-step explanation:

You need to combine like terms for this problem. All the basic numbers(without the r) are added together. -14 + 7 = -7. Then the numbers with the r's are added together. -9r + 13r = 4r. This comes out to -7 + 4r

1. No environmentally produced diseases are inherited afflictions. Some psychological disorders are not inherited afflictions. Therefore, some psychological disorders are environmentally produced diseases. This statement invalid.

2. All watercolors are paintings. Some watercolors are masterpieces. Therefore, some paintings are masterpieces. This statement is invalid.

3. No illegal aliens are persons who have a right to welfare payments, and some migrant workers are illegal aliens. Thus, some persons who have a right to welfare payments are migrant workers. This statement is valid.

4. No insects that eat mosquitoes are insects that should be killed. All dragonflies are insects that eat mosquitoes. Therefore, no dragonflies are insects that should be killed. This statement is invalid.

5. All corporations that overcharge their customers are unethical businesses. Some unethical businesses are investor-owned utilities. Therefore, some investor-owned utilities are corporations that overcharge their customers. This statement is valid.

A Venn diagram uses overlapping circles and other shapes to show logical relationships between two or more groups of elements. It often helps to organize things graphically by highlighting similarities and differences between elements.

Venn diagrams, also known as set diagrams or logic diagrams, are widely used in mathematics, statistics, logic, education, linguistics, computer science, and economics. Venn diagrams became part of his "new mathematics" curriculum in the 1960s, so many people encounter them for the first time when learning mathematics or logic in school. These can be simple diagrams spanning 2 or 3 sets of a few items, or can be very sophisticated including 3D presentations as you progress to 6 or 7 sets or more. There is also They are used to reason about and represent how objects are related to each other within a particular "universe" or segment. Venn diagrams are widely used in presentations and reports as they allow users to visualize data in a clear and powerful way. These are closely related to Euler diagrams, differing in that the set is omitted if it has no elements. Venn diagrams show relationships even when the set is empty.

Suppose our universe is made up of pets and we want to compare the types of pets that families agree on.

Set A contains my favorites: dogs, birds, hamsters.

Set B contains Family B's preferences: dog, cat, fish.

Set C contains family C's favorites: dog, cat, turtle, and snake.

Overlapping or intersecting 3 sets contains only Dog. it's like having a dog

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The solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.

What is inequality?

In mathematics, the term 'inequality' is defined as a statement or equation with an ordered relationship like greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

-5 < 9- 6x

Adding 5 both the side we get,

5 - 5 < 9 - 6x + 5

⇒ 0 < 14 - 6x

⇒ 14 - 6x > 0

Dividing both the side by 6 we get,

⇒ 14 < 6x

⇒ x > 14/6 = 7/3

or, x ≤ 7/3

this is the required solution of the given inequality.

Thus, the solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.

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Answer:

a= 1 , b= 3 , c= –3

\(x = \frac{ - b \frac{ + }{} \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{ - 3 \frac{ + }{} {} \sqrt{ {3}^{2} - 4(1)( - 3)} }{2(1)} \\ = \frac{ - 3 \frac{ + }{} \sqrt{9 + 12} }{2} = \frac{ - 3 \frac{ + }{} \sqrt{21} }{2} \\ \\ x = \frac{ - 3 \frac{ + }{} \sqrt{21} }{2} \\ \\ x = 0.79 \\ x = - 3.79\)

I hope I helped you^_^

If there were 132 crayons in John's backpack, the number of blue crayons is equal to blue crayons.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

3 crayons = 8 blue crayons

132 crayons = X blue crayons

By cross-multiplying, we have the following:

3x = 132 × 8

3x = 1,056

x = 1,056/3

x = 352 blue crayons.

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Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Answer:

2 14/15

Step-by-step explanation:

2 1/3 + 3/5

~Turn into improper fractions

7/3 + 3/5

~Find common denominators

35/15 + 9/15

~Add

44/15 or 2 14/15

Best of Luck!

The student can improve the investigation by using balls that are the same mass. This is because the investigation aims to study the effect of gravity on objects on Earth, and the gravitational force acting on an object is directly proportional to its mass. Therefore, in order to compare the effect of gravity on different objects, they should all have the same mass.

Using balls of different masses will make it difficult to draw any valid conclusion about how the gravitational force operates on different materials. For measuring the circumference of the balls, we would not be able to draw any conclusive results on the effect of gravity. The other option of dropping the balls from the same height is already part of the criteria mentioned and is used to ensure a consistent experimental setup.

we can say that years of experience explain 95.4% of the variation in the number of units sold per day by the digital music retailer. years of experience explain approximately 95.4% of the variation in the number of units sold by the digital music retailer.

In the given problem, we need to find out how much variation in the number of units sold does years of experience explain. The given problem can be solved with the help of regression analysis.Regression Analysis:Regression analysis is the method used to understand how one variable is affected by another variable. It shows the relationship between two variables with the help of a line of best fit. The line of best fit can be represented with the help of the following equation:y = a + bxwhere,y = dependent variablea = interceptb = slope of the line of best fitx = independent variableLet's represent the given data with the help of the table below:Given DataTable:We know that, y = a + bxWe also know the following terms:    * y-intercept (a) = 21.01    * Slope of the line of best fit (b) = 3.2Hence, we can write the following equation:y = 21.01 + 3.2xWe can interpret the above equation as follows:For each additional year of experience in the market, the digital music retailer sells an additional 3.2 units per day.The coefficient of determination (R²) is a statistical measure that shows how much of the variance in the dependent variable is explained by the independent variable(s). In the given regression analysis table, the value of R² is 0.954.

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Answer:

a) 79.6

b) 437.8

Step-by-step explanation:

First, you have to do 318.4/4 to find the rate she goes in the duration of an hour. The rate is 79.6, which means she travels at a rate of 79.6 kilometers per hour.

Then, you have to find the distance she takes to travel in 5.5 hours, so you have to do 5.5*79.6 which is 437.8.

So, Hannah travels 437.8 kilometers in 5.5 hours.

Answer:

I believe the answer is A.

Answer:

The data in the table represent an exponential function.

\(y = 2( {3}^{x} )\)

Answer:

x ≤ 9

Step-by-step explanation:

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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Answer: i) 512,000 cm³      ii) 512,000 cc        iii) 512 litres

Step-by-step explanation:

Volume (V) of a cube is side (s) cubed:    V = s³

Given: s = 80 cm

i) V = (80 cm)³

      = 512,000 cm³

ii) 512,000 cm³ = 512,000 cc

iii) 512,000 cm³ × 1 liter/1000 cm³ = 512 liters

Answer:

(-3/4, -7/2)

Step-by-step explanation:

y= −2x − 5

y= 2x − 2

2y = -7

y = -7/2

y= 2x − 2

-7/2 = 2x - 2

2x = -3/2

x = -3/4

(x,y) = (-3/4, -7/2)

Answer:

-3/4 or -7/2

Step-by-step explanation:

C(g) = 25g

C(15) = 25*15

C(15) = 375

The production cost of making g = 15 calculators is $375 since C(g) is the general cost for g calculators.

Answer:

The probability of landing on 8 twice is 1/64

Step-by-step explanation:

If you spin the spinner once, there are 8 possibilities each time (1-8). The possibility of landing on the number 8 is 1 of these 8 possibilities. Its probability is therefore 1/8

Each spin is independent. In other words, the spins do not affect each other. The number you land on during the first spin does not impact the second spin's number. The probability of landing on 8 the second time is the same as the first time: 1/8

Because the two events are independent, we find the probability of them both occurring by multiplying them together.

1/8 times 1/8= 1/64

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Answer: 25 km

Step-by-step explanation:

The car moves with a speed of 40 km/h for 15 minutes, which is 0.25 hours, so the distance covered in this time is:

distance = speed × time = 40 × 0.25 = 10 km

Then, the car moves with a speed of 60 km/h for the next 15 minutes, which is another 0.25 hours. The distance covered in this time is:

distance = speed × time = 60 × 0.25 = 15 km

Therefore, the total distance covered by the car is the sum of the distances covered during the two intervals:

total distance = 10 + 15 = 25 km.

A composition that is symmetrical can help to create balance and harmony, making it pleasing to the eye. It is a useful concept in many areas of art, design, and architecture.

If a line is drawn down the center of a composition and each side corresponds to the other, then the composition has symmetry. Symmetry is a property that occurs when a shape or object is identical or nearly identical when divided by a line or plane. It is a fundamental concept in mathematics and art, particularly in geometry, algebra, and design.

A composition is said to be symmetrical if there is an axis of symmetry. An axis of symmetry is a line that divides a shape into two identical halves. When a composition has an axis of symmetry, it can be mirrored or reflected over that line to create a balanced and harmonious design.

Therefore, a composition that is symmetrical can help to create balance and harmony, making it pleasing to the eye. It is a useful concept in many areas of art, design, and architecture.

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Answer:

Triangle A - Equilateral

Triangle B - Scalene

Triangle C - Scalene

Step-by-step explanation:

Equilateral triangles are where all the sides are equal, because triangle A has 3 equal lengths of 16, we know it is an equilateral.

Scalene triangles are where no sides match, and because triangle B and C have all different lengths, we know these are scalene.

None of the triangles in these examples are isosceles because isosceles triangles have 2 of the same lengths, and one different.

Before doing the answer , we should know some properties of triangles ;

Now , Checking for Triangle A :-

As , it's all sides are of equal length 16 , So option 3) Equilateral ✓

Now , Checking for Triangle B :-

As , it's all sides are of different length , So option 1) Scalene ✓

Now , Checking for Triangle C :-

As , it's all sides are of different length , So option 1) Scalene ✓

The Taylor series for a function f about x=1 is an infinite sum that represents the function using its derivatives at x=1. It starts with the value of the function at x=1 and includes terms involving higher derivatives multiplied by powers of (x-1) divided by factorials. It allows us to approximate the function near x=1 using a polynomial.

1. The first term, f(1), represents the value of the function at x=1.
2. The subsequent terms involve the derivatives of the function at x=1. The second term, f'(1)(x-1), is the first derivative of f at x=1 multiplied by (x-1).
3. Each subsequent term involves higher derivatives of f at x=1, with each derivative being multiplied by (x-1) raised to a power and divided by the corresponding factorial.

The Taylor series is a way to represent a function as an infinite sum of terms derived from its derivatives at a specific point. In this case, the Taylor series for function f about x=1 is given by f(x) = f(1) + f'(1)(x-1) + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

Each term involves a derivative of f evaluated at x=1, multiplied by (x-1) raised to a power and divided by the corresponding factorial. By including more terms in the series, we can approximate the function better near x=1 using a polynomial.

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Answer:

x=2/3

Step-by-step explanation:

25-(3x+5)=2(x+8)+x

25-3x-5=2x+16+x

20-3x=3x+16

20-3x-3x=16

20-6x=16

6x=20-16

6x=4x=4/6

simplify

x=2/3

Answer:

x=2/3

Step-by-step explanation:

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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Answer: Josh is incorrect because nickels are worth 5 cents each and 33 can not be divided by 5 exactly.