Question: How to do this?
When factoring a trinomial in the form ax^2+bx+c factors of the product of a and should be used to split the bx term. (Check the picture for more info)

As a result, according to the findings of the experiment, the odds of both rolled a six-sided dice and getting an even amount and using a coin flip and getting tails are 1/2.

Probability and probability, as well as its cognates in various modern languages, come from the educated Latin of the Middle Ages called probabilism, which Cicero used to refer to a viewpoint as being plausible or generally accepted.

Based on the outcomes of the experiment, we must calculate the likelihood of each occurrence to determine which one is most likely to occur.

Since there are third even number out of a possible six, the chance of hitting an even value on a six-sided dice is 3/6 or 1/2. Peyton deduced from the experimental findings that the probability of rolling a more even number was 12/24 or 1/2.

Due to the significance of the two possible scenarios (heads or tails) each of which has an equal chance of happening, the probability for a coin being flipped and getting tails is 1/2. Peyton deduced from the experiment's findings that tails was flipped 25/50 or 1/2 of the time.

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The event of flipping a coin and landing on tails is more likely to occur based on the given experiments.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you toss a fair coin, the probability of getting heads is 1/2, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

To compare the likelihood of the two events, we need to calculate their respective probabilities.

The probability of rolling an even number on a six-sided die is 3/6 or 1/2, since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

The probability of flipping a coin and getting tails is also 1/2, since there are two possible outcomes (heads or tails) and each is equally likely.

Using these probabilities, we can calculate the expected number of times each event would occur in a given number of trials:

Rolling an even number: expected number of even rolls = (1/2) x 24 = 12

Flipping tails: expected number of tails = (1/2) x 50 = 25

Comparing the expected numbers, we can see that flipping tails is more likely to occur than rolling an even number. Therefore, the event of flipping a coin and landing on tails is more likely to occur based on the given experiments.

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The probability that the first person picked will be female is 2/5.

Two quantities are compared to form a ratio. Discover how to calculate the ratio of two items, such as apples to oranges.

Total audience = 120

Ratio of males to females; 3:2

Total males : 3*120/ 5 = 72

Total females: 2*120/5 = 48

Probability that the first person picked will be female = total females / total audience

Probability = 48 / 120

Probability = 2/5

Thus, the probability that the first person picked will be female is 2/5.

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The answer would be 9°

Answer:

90 degree as
4 x 180 / 8 =90

Step-by-step explanation:

Therefore , the solution of the given problem of variable comes out to be because a function's domain is all possible input values, not possible outcome values, b is not true.

A trait that can be measured and have different values is called a variable. A few instances of variables include height, age, salary, birthplace province,equation , academic standing, and type of residence.

Here,

A. Although all relations are functions, not all functions are relations.

c. Each input value will only have one output value if a connection is a function.

d. At least one input will have more than one exit value if a relation is not a function.

e. The input and result of a function are independent and dependent variables, respectively.

Because a function's domain is all possible input values, not possible outcome values, b is not true.

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Answer:

64/3.25 = 19.7 mi/inch.

Step-by-step explanation:

Therefore, the sine of angle R in triangle PQR is 5/13.

A triangle is a polygon with three sides and three angles. It is one of the most basic shapes in geometry and is found in many different areas of mathematics and science, including physics, engineering, and architecture. Triangles can be classified based on the lengths of their sides and the measures of their angles.

There are several types of triangles, including:

Equilateral triangle: A triangle with three equal sides and three equal angles of 60 degrees each.

Isosceles triangle: A triangle with two equal sides and two equal angles opposite those sides.

Scalene triangle: A triangle with no equal sides and no equal angles.

Right triangle: A triangle with one angle measuring 90 degrees, which is also the angle between the two shorter sides, called the legs. The longest side is called the hypotenuse.

Acute triangle: A triangle where all three angles are acute, or less than 90 degrees.

Obtuse triangle: A triangle with one obtuse angle, or greater than 90 degrees.

Here,

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, to find sin R, we need to first identify which side of the triangle is opposite angle R and which side is the hypotenuse.

From the given information, we know that PR is the hypotenuse, since it is opposite the right angle at vertex Q. Therefore, the side opposite angle R is PQ, which has a length of 5 cm.

Using the Pythagorean theorem, we can find the length of the remaining side QR:

QR² = PR² - PQ²

QR² = 13² - 5²

QR² = 144

QR = 12 cm

Now we have all three sides of the triangle, so we can use the definition of sine to find sin R:

sin R = opposite/hypotenuse = PQ/PR = 5/13

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Answer:

A

Step-by-step explanation:

two numbers that times to make -12 but add to make +4

+6×-2=-12

+6+-2=4

Answer:

Step-by-step explanation:

Take the numbers as x and x +4. So the numbers are 8 and 12.

The distribution shape (skewed left, skewed right, or symmetric) is most likely to result in the mean being substantially smaller than the median - C. A distribution that is skewed left will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the left. Therefore the correct option is option C.

Distribution shape refers to the pattern or form of a set of data as plotted on a graph. It explains how the numbers are distributed or clustered together and might be symmetric, skewed left, or skewed right. A symmetric distribution has data that is spread evenly around the mean, but a skewed distribution has a longer tail on one side than the other. Skewed left indicates that the tail extends to the left, whereas skewed right indicates that the tail extends to the right.

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The correct piecewise definition for the function y = |x + 5| - 2 is,

y = x + 3, for x ≥ -5 and y = - x - 7, for x < - 5.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

Given, y = | x + 5 | - 2.

Now, y = (x + 5) - 2, for x + 5 ≥ 0 and y = - (x + 5) - 2, for x + 5 < 0.

y = x + 3, for x ≥ -5 and y = - x - 7, for x < - 5.

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In the case of a Pitot-static (or Prandtl) probe, it measures the pressure and velocity at two different points and, using the Bernoulli equation, the pressure difference between the two points is then used to calculate the velocity of the flow.

The Pitot-static (or Prandtl) probe is able to measure the velocity in a sheared region of a steady incompressible flow because of the Bernoulli equation. The Bernoulli equation states that the sum of the pressure, velocity and potential energies per unit mass is constant. This means that if the pressure, velocity and potential energy of the flow is known at one point, then it can be calculated at any other point. In the case of a Pitot-static (or Prandtl) probe, it measures the pressure and velocity at two different points and, using the Bernoulli equation, the pressure difference between the two points is then used to calculate the velocity of the flow.

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The intersection point of the system of equation are known as solution of system of equation.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Here is a graph of a system of equations shown in figure.

Now, We know that;

For a system of equation, when the lines are cut into a point then the point is known as the solution of the system of equations.

Here, The graph of system of equations are cut into a point (5, 1).

Hence, The solution of system of equation is the point where the graph of equation are intersect each other.

Thus, The intersection point of the system of equation are known as solution of system of equation.

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Answer:

q = -2

q = -7

Step-by-step explanation:

Simple: Graph the equation.

The linear equations are:

G = 75 + 16t

Y = 95 + 12t

And both of them will have the same amount of money after 5 weeks.

Here we will use the variable t to define the number of weeks after the beginning of the year.

Then we can write the two linear equations:

G = 75 + 16t

Y = 95 + 12t

Both of them will have the same amount when:

75 + 16t =  95 + 12t

Solving for t we will get:

16t - 12t = 95 - 75

4t = 20

t = 20/4 = 5

They will have the same amount after 5 weeks.

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Answer:

4 1/2in. by 4in.

The tables that reprsesent a linear function is (d)

From the question, we have the following parameters that can be used in our computation:

The table of values

A table of value that is a linear function is a table that has a constant rate

i.e. as x changes, y changes constantly

Using the above as a guide, we have the following:

In table (d) x changes constantly by 1 and y constantly changes by 5

Hence, the table is table (d)

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The first answer is 17, the second answer is -1, and the third answer is 55. To estimate these numbers, round each number to the nearest integer, which would be 15, 0, and 80 respectively.

When estimating a number, the best approach is to round the number to the nearest integer. This means that any number with a decimal point should be rounded either up or down depending on the number after the decimal point. For example, 15.23 should be rounded up to 16, while 15.835 should be rounded down to 15. To estimate the numbers given, 15.23 should be rounded to 15, 6.88 should be rounded to 7, and -8.1 should be rounded to 0. Finally, 80.38 should be rounded to 80. Therefore the estimated answers would be 15, -1, and 80, respectively. This method of rounding is useful when an exact answer is not required, and can help to quickly estimate a number without needing to work out the exact answer.

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The prime factorization of 735000 is 2² × 3³ × [tex]5^4[/tex]. We can determine that 735000 has 144 divisors using the formula for the number of divisors.

The multiplicative principle can be used to calculate the number of 735000's divisors. The prime factorization of 735000 is given by the basic theorem of mathematics as follows:

735000 = 2³ × 3²× 5³ × 7²

We must take into account all feasible permutations of the prime factors of 735000 in order to determine the number of its divisors. Typically, if a composite number can be divided into prime factors:

n = p1a1 × p2a2 × ... × pkak

where a1, a2,..., pk are positive integers and p1, p2,..., pk are separate prime numbers, then n has the following number of divisors:

(a1 + 1) × (a2 + 1) × ... × (ak + 1)

As we can select any exponent between 0 and ai for each prime factor pi, there are (ai + 1) possibilities for each prime factor, and the sum of all the choices for all prime aspects is the total number of alternatives.

In the case of 735000, we have:

a1 = 3, a2 = 2, a3 = 3, a4 = 2

So the number of divisors of 735000 is:

(3 + 1) × (2 + 1) × (3 + 1) × (2 + 1) = 4 × 3 × 4 × 3 = 144

Therefore, 735000 has 144 divisors.

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The probability of hitting a yellow balloon on the first try is 10/25 or 2/5. After hitting the first yellow balloon, there are now 24 balloons left on the board, with 9 of them being yellow. The probability of hitting a yellow balloon on the second try is 9/24 or 3/8. To find the probability of both events happening, we multiply the probabilities together:

P(first yellow) * P(second yellow) = (2/5) * (3/8) = 6/40 = 3/20

Therefore, the probability that the next balloon hit is also yellow given that the first balloon hit is yellow is 3/20.

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The value of partial derivative at (u, v) = (1, pi/4), by using chain rule is ∂(f ∘ r)/∂u = 0.586 and ∂(f ∘ r)/∂v = 1.414.

To compute ∂(f ∘ r)/∂u and ∂(f ∘ r)/∂v using the chain rule, we need to first calculate the partial derivatives of f with respect to its three variables: x, y, and z.

∂f/∂x = 2xy + z^2

∂f/∂y = x^2 + 2yz

∂f/∂z = y^2 + 2xz

Next, we need to find the partial derivatives of r with respect to u and v:

∂r/∂u = ⟨cos(u), sin(u), 0⟩

∂r/∂v = ⟨0, 1, 1⟩

Using these partial derivatives, we can now apply the chain rule:

∂(f ∘ r)/∂u = (∂f/∂x)(∂x/∂u) + (∂f/∂y)(∂y/∂u) + (∂f/∂z)(∂z/∂u)

= (2xy + z^2)(-sin(u)) + (x^2 + 2yz)(cos(u)) + (y^2 + 2xz)(0)

= -2√2 + 2

= 0.586

∂(f ∘ r)/∂v = (∂f/∂x)(∂x/∂v) + (∂f/∂y)(∂y/∂v) + (∂f/∂z)(∂z/∂v)

= (2xy + z^2)(0) + (x^2 + 2yz)(0) + (y^2 + 2xz)(1)

= 2√2

= 1.414

Therefore, at (u, v) = (1, pi/4), ∂(f ∘ r)/∂u = 0.586 and ∂(f ∘ r)/∂v = 1.414.

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The pattern using the rule n x 4, starting at 9 is 9, 36, 72, 108, 144, 180, 216, 252, 288, 324

To create this pattern, we start with the number 9 and then apply the rule n x 4 to each subsequent number. This means that we multiply each number by 4 to get the next number in the pattern. So:

9 x 4 = 36

36 x 4 = 72

72 x 4 = 108

108 x 4 = 144

144 x 4 = 180

180 x 4 = 216

216 x 4 = 252

252 x 4 = 288

288 x 4 = 324

And so on, if we wanted to continue the pattern.

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The product of (14x⁵ + 6x) and (9x⁵ + 5x) is 126x¹⁰ + 124x⁶ + 30x².

A mathematical arithmetic operation is multiplication.

Moreover, it is the practice of repeatedly adding the same expression kinds.

Example: 2 x 3 means that 2 is multiplied by 3 or that 3 is multiplied by 2 times.

To multiply the two expressions (14x⁵ + 6x) and (9x⁵ + 5x),

we can use the distributive property and multiply each term in the first expression by each term in the second expression.

First, we can use FOIL (First, Outer, Inner, Last) method to multiply the two binomials.

FOIL:

(14x⁵)(9x⁵) + (14x⁵)(5x) + (6x)(9x⁵) + (6x)(5x)

Simplifying each term gives:

126x¹⁰ + 70x⁶ + 54x⁶ + 30x²

Combining like terms, we get:

126x¹⁰ + 124x⁶ + 30x².

Therefore, the product is  126x¹⁰ + 124x⁶ + 30x².

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Answer:

36cm^2

Step-by-step explanation:

8×9=72

72÷2=36

36cm^2

i.e. a² + b² = c²

A sampling is a subset of an unit that is tested or examined in to make inferences about the larger population, whereas a census refers to the entire population, things, or information we're interested in analyzing.

Population pyramids that are expansive, constrictive, or stationary can be created using age-sex distributions.

The term "population" in the context of statistics means the whole set of individuals, objects, or metrics we're interested in investigating.

A sample, on the other hand, is a portion of a population that is actually measured or observed in order to draw conclusions about the full population.

Before we can determine the sample and population of a math issue, we must first select the topic we're interested in finding out.

For instance, if we were to look at worldwide average heights, the population would be made up of everyone alive today.

Choosing whether to investigate the whole population or simply a subset of it is the next stage.

If we are studying the overall community, no sample is necessary.

Hence, even if we are only looking at a small section of the population, we must collect a sample.

For instance, if we were to study the heights the people there, the population would be the whole of the United States.

We might measure the elevations of 1000 people randomly selected from the population, drawn from different regions of the United States, if we wished to sample this population.

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i have attached an image of the bearing of 075°

Festival dances can be a fun and enjoyable way to enhance fitness. Dancing is a physical activity that can help improve cardiovascular health, increase endurance, improve flexibility, and build strength.

Festival dances often involve a combination of movements that are both aerobic and anaerobic, which can provide a full-body workout. The fast-paced, high-energy movements can help increase heart rate, boost metabolism, and burn calories.

In addition, festival dances require coordination, balance, and agility, which can help improve motor skills and increase overall physical performance. The repetition of dance movements can also help improve muscle memory and develop muscle strength and tone.

Participating in festival dances can also have mental health benefits. Dancing can help reduce stress, improve mood, and boost self-confidence.

Overall, festival dances can be a great way to enhance fitness while having fun and experiencing different cultures.

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Yes, if a ≡ b (mod m) and c ≡ d (mod m), then a − c ≡b − d (mod m).

To prove this, let a, b, c, d, and m be integers with m ≥ 2. Since a ≡ b (mod m), there exists an integer k such that a - b = km. Similarly, since c ≡ d (mod m), there exists an integer l such that c - d = lm.

Therefore, a - c = (a - b) + (c - d) = km + lm = (k + l)m.

So, a - c ≡ b - d (mod m) because a - c - (b - d) is divisible by m.

This proves that if a ≡ b (mod m) and c ≡ d (mod m), then a − c ≡b − d (mod m).

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y=2*(1/2)ˣ----y intercept at(0,2),graph apprοaches 0 as x increases.

y=3ˣ ----y intercept at(0,1),graph apprοaches pοsitive infinity as x increases.

y=(1/4)ˣ----y intercept at(0,1),graph apprοaches 0 as x increases.

The pοint where the line οr curve crοsses the axis οf the graph. If a pοint crοsses the x axis then its called x- intercept, If a pοint crοsses the y axis then its called y-intercept.

1) y=2*(1/2)ˣ

when x=0

y=2*(1/2)⁰

=2*1

y=2

x ,y=(0,2)

2) y=3ˣ

when x=0

y=3⁰

y=1

x ,y=(0,1)

3) y=(1/4)ˣ

when x=0

y=(1/4)⁰

y=1

x ,y=(0,1)

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Answer:

Lauren will have 13 pieces of wire, each 2/3 ft. long, and 1/3 ft. of wire left over.