Let the random variable x represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of x.

The probability of Ultraviolet performing fourth and Abacus performing last is 1/20.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

In a tour, five bands agree to determine the order of performance on the basis of random selection.

Since, the name of 5 bands are pulled randomly.

The probability of Ultraviolet performing fourth = 1/5

And the probability of Abacus performing last = 1/4, since 1 place is fixed for Ultraviolet.

Probability of Ultraviolet performing fourth and Abacus performing last

= 1/5 x 1/4 = 1/20

The required probability is 1/20.

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The polynomial that represents the area of the booth is 3[tex]t^3[/tex]-12t.

Polynomial is a expression of variable, coefficients, and constants with mathematics operation of subtraction, addition, multiplication, and powers (only positive integers) of variable.

So, basically to calculate polynomials is the same as normal calculations except that the numbers are changed to variables.

Base length = 2[tex]t^2[/tex]-8

Height length = 3t

Calculate the area of triangle. So,

Area of triangle = (1/2) × base × height

= (1/2) × 2[tex]t^2[/tex]-8 × 3t

= (1/2) × 6[tex]t^3[/tex]-24t

= 3[tex]t^3[/tex]-12t

Thus, the area of the booth can be written by this polynomial 3[tex]t^3[/tex]-12t.

Your question is incomplete, but most probably your full question was (image attached).

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Since an adult movie ticket costs $8 and a kid movie ticket costs $6, the equation for the given condition is 8x+6y=40.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The cost of movie ticket for adult= $8

The cost of movie ticket for adult= $6

Total amount to spend= $40

Let x be the number of adult and y be the number of children,

8x+6y=40

The equation for the given condition is 8x+6y=40 as the cost of movie ticket for adult is $8 and for children, it is $6.

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After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.

Given that,

We have to find what is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.

We know that,

1 feet is equal to 12 inches.

So,

We can write as

11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.

11f 7in+ 14f 6in +35.5in+ 30in + 6f 10in

11(12)+7in+14(12)+6+35.5+30+6(12)+10

132+7+168+6+35.5+30+72+10

460.5

Therefore, After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.

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Answer:

4/x

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

Each of the 6 people in Mandy's family orders 2 tacos. Each taco costs $3. What is the total cost of the tacos?

$3 * 2 * 6 = $36

The ordered pair that is on the function y=f(2x+1)+3 is (-3/2, 6)

Here we know that for the function:

y = f(x)

And we know that the point (-2, 3) belongs to the function, this means that:

f(-2)= 3

Now we want to find a point on the function:

f(2x + 1) + 3

If we find x such that:

2x + 1 = -2

2x = -3

x = -3/2

Now we can evaluate the function in that value of x to get:

y = f(2*-3/2 + 1) + 3

y = f(-2) + 3

y = 3 + 3

y = 6

Then we have the point (-3/2, 6) on the function.

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Answer:

6 units away

Step-by-step explanation:

Since they already have the same x-axis I just need to find the difference in the y-axis

Answer:

Step-by-step explanation:

Answer:

  (d)  -(√2)/2

Step-by-step explanation:

You want the exact value of the sine of an angle when its terminal side intersects the unit circle at (√2/2, -√2/2).

The coordinates of the point where the terminal side of angle θ intersects the unit circle are ...

  (cos(θ), sin(θ))

Comparing this to the given point, we find that ...

  sin(θ) = -√2/2

Answer:

180

Step-by-step explanation:

Pentagon has a total interior angle of 540 degrees.

Hexagon has a total interior angle of 720 degrees.

720-540 = 180

Any n-dimensional vector should be able to be represented in space

What is standard form of a polynomial?

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on.

To find the degree of the polynomial, add up the exponents of each term and select the highest sum ( if there are more than 1 variable in single term) or highest power of variable

Any n-dimensional vector should be able to be represented in space.

If it only has terms of degree n, it can only express polynomials of degree n.

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Answer:

altitude=8mm

Step-by-step explanation:

so a^2+b^2=c^2

substitute and you get

a^2+6^2=10^2

a^2+36=100

a^2=100-36=64

a^2=64

a=8

Answer: 8 mm

Step-by-step explanation:

      The altitude of the triangle can also be known as the "height" from the highest point as a straight line perpendicular to the opposite side (the "bottom" which is also known as the "base" of the triangle).

      This altitude makes two right triangles, so we will use the Pythagorean theorem to help us solve.

      a² + b² = c²

      a² + (6)² = (10)²

      a² + 36 = 100

      a² = 64

      a = 8

           The altitude of this triangle is 8 mm.

The coefficient of determination (R² or r-squared) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable.

Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.

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The missing value in the simple interests formula is rate and it is solved to be 4.62%

The formula for simple interest is

= P * T * R / 100

P = principal= $1300

T = time = 18 months = 1.5 years

R = rate = ?

simple interest = $90

substituting the values

90 = 1300 * 1.5 * R / 100

90 * 100 = 1300 * 1.5 * R

9000 = 1950R

R = 9000 / 1950

R = 4.615385

R = 4.62

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The given function f(x) = 2 cos (x) is an even function because the result of the cosine of negative angles are the same with those of positive angles.

To check if a function is odd or even, we have to calculate f(−x).

The function is even if f(-x) = f(x)

The function is odd if f(-x) = -f(x)

We are given the function as; f(x) = 2 cos (x)

f(-x) = 2 cos (-x)

Now, we know that the cosine of a negative angle always gives the same value as the cosine of the positive angle and as such, we can say that;

2 cos (-x) = 2cos (x)

The same result as f(x) which tells us that it is an even function

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Answer:

It will take the plane 11 mph to travel 850 miles

Answer:  x=[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

There are special right triangles in this! First, you need to find out what I am saying.

45-45-90 triangle

The bottom triangle has angles measures of 45, 45, and 90 degrees. There is a theorem that states that the two legs are equal, and the hypotenuse is leg×[tex]\sqrt{2}[/tex].

Plugging it in will give you leg lengths of  [tex]4\sqrt{2}[/tex].

Plug in that number into the side that connects with our next very special triangle:

30-60-90 triangle

Another theorem states that the hypotenuse is shorter leg times 2, the longer leg is shorter leg times [tex]\sqrt{3}[/tex].

Great! We have the shorter leg. Now we need to find the hypotenuse. Multiply [tex]4\sqrt{2}[/tex] by 2, and you get [tex]8\sqrt{2}[/tex]. That is x!

The final answer to this problem is: x=[tex]8\sqrt{2}[/tex]

Hope this helped a lot!

Pattern Recognition is defined as the pattern is a number, shape, or something repeated in a particular way. Analysis of patterns should consider on different basis. The correct option is option (d).

The main basis of Pattern Recognition are the following:

1. Color change

2. Shape change

3. Rotation change

4. Size change

we have given three shapes pattern and we have to find out the perfect shape for forth place and the required shape follow the order like others.

After examine the pattern, we can see that the first figure is a filled triangle and the second figure is a hollow circle. This pattern is maintained alternately. The last figure(3rd place) is an open circle, so the next figure is a filled triangle.

So, the correct option is d.

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The value of x in the first circle is 2, and in the second circle is 4 after applying the intersecting secants theorem.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

Applying intersecting secants theorem:

4(4 + x) = 3(3 + 5)

16 + 4x = 24

4x = 8

x = 2

In the second circle:

9(4x) = 8(4x+2)

After solving we get:

x = 4

Thus, the value of x in the first circle is 2, and in the second circle is 4 after applying the intersecting secants theorem.

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The scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.

What is sampling bias?

Sampling bias occurs when some members of a population are systematically more likely than others to be chosen for a sample. In the medical world, this is known as ascertainment bias. Because it threatens external validity, specifically population validity, sampling bias reduces the generalizability of findings.

Sampling bias occurs when some people in a community being surveyed are purposefully placed to be chosen or not chosen over others. If a sample process consistently favors some results over others, it is said to be biased. Ascertainment bias particularly in biological areas)/ and systematic bias are other terms for sampling bias. Bias can be intentional, but it is frequently unintentional.

Hence, the scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.

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Answer:

C. x = -5/3 and x = 2

Step-by-step explanation:

Bring the 10 over to the other side of the equation.

3x² - x - 10 = 0

Factorise.

(3x + 5)(x - 2) = 0

3x + 5 = 0 or x - 2 = 0

3x = -5 or x = 2

x = -5/3 or x = 2

The probability that fewer than 22 customers in the sample buy coffee during their visit is 0.7764.

What is a normal approximation to the binomial?

When we utilize a continuous distribution (the normal distribution) to approximate a discrete distribution, we use the normal approximation to the binomial (the binomial distribution). The Central Limit Theorem states that if the sample size is high enough, the sampling distribution of the sample means approximates normality.

In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Given, 55% of the customers buy coffee, p = 0.55

Sample of 35 customers, n = 35

mean  [tex]\mu[/tex] = np = 35*0.55 = 19.25

standard deviation, [tex]\sigma = \sqrt{np(1-p)}[/tex] = [tex]\sqrt{35*0.55*0.45}[/tex] = 2.94

So,  the probability that fewer than 23 customers in the sample buy coffee is

P(X < 22 - 0.5) = P(X < 21.5)

= [tex]P(\frac{X-\mu}{\sigma} < \frac{21.5-19.25}{2.94})[/tex]

= P(Z<0.765) = 0.7764

Hence, the probability that fewer than 22 customers in the sample buy coffee during their visit is 0.7764.

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The traditional division of a day into 24 hours of 60 minutes each, with each minute made up of 60 seconds.

A tool used to measure and indicate time is a clock, often known as a timepiece.

One of the earliest human creations, the clock satisfies the requirement to measure time intervals less than those found in natural units like the day, lunar month, and year.

Over the centuries, various physical mechanisms have been utilized to power devices.

A few clocks that predate the contemporary model and are based on natural movement include:

A sundial displays the location of a shadow on a flat surface to indicate the time. There are various duration timers; the hourglass is one well-known type. The two time-telling devices that may be the oldest are water clocks and sundials.

The development of led to a significant advancement.

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Answer:

The answer is 1/2

Step-by-step explanation:

x1 y1. x2. y2

(5, 8) (2, 2)

So you suppose to subtract xl by x2 then subtract y1 by y2

5-2.

------=

8-2.

which equal 3/6. Which 3/6 is equal to 1/2

If a set of exam scores forms a normal, symmetrical distribution with all measures of central tendency in the center of the distribution we can say about student's score that, about an equal number of students had relatively high and relatively low score.

A symmetrical distribution entails that the scores have the same number at a given distance above or below the average. Therefore an equal number of people had relatively high and relatively low scores. This contradicts most having relatively high or low scores, or not drawing any conclusions about scores.

Symmetrical distribution is evident when values of variables occur at a regular interval. In addition, the mean, median and mode occur at the same point.

Three of the many ways to measure central tendency are the mean, median and mode.

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The mean and the variance of the areas produced by these explosive devices is 314

Variance:

In statistics, variance refers a measure of dispersion that takes into account the spread of all data points in a data set.

Given,

Here explosive devices used in mining operations produce nearly circular craters when detonated. the radii of these craters are exponentially distributed with mean 10 feet.

Now, we need to find the mean and variance of the areas produced by these explosive devices.

In order to find the means and variance we have to use the formula ,

A = πr²

Here the value of r is 10,

Then the value of A is calculated as,

=> A =  π(10)²

=> A =  π x 100

We know that the value of  π = 3.14, then the value of A is,

=> A = 3.14 x 100

=> A = 314.

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The probability that there will be at least 12 successes in the total 18 trials with 60% rate of success is ¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰

Binomial Probability distribution, In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments.

We have given that :

Rate of sucess (p) = 60% = 0.6

Rate of failure (q) = 1 - 0.6 = 0.4

Number of trials (n) = 18

We want to find P(there will be at least 12 sucess)

Use binomial distribution to find given mentioned probability.

X ~ Bin( 18, 0.6)

P (X= x ) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Let, X= Number of success among 18

So that it suitable for binomial distribution with parameters are n and p.

P(there will be atleast 12 success)

= P(X>= 12)

18

= ∑ ⁿCₓ (p)ˣ(q)⁽ⁿ⁻ˣ⁾ =

x = 12

¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰

= say x

Hence, the required probability is x

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The derivative of the given function using product rule is 6x+1 .

What is Product Rule?

This rule is used when we want to differentiate a function that may be regarded as the product of one or more functions.

Let u(x) and v(x) be differentiable functions.Then the product of the functions u(x)v(x) is also differentiable and: (uv)′=u′v+uv′

Main Body:

We add the derivative of the first times the second to the first times the

derivative of the second.

Power Rule:

If f(x)=xn

where n is any real number, then:

(xⁿ)′=nxⁿ⁻¹

. We have,

f(x) = (x-1) (3x+4)

Differentiate with respect to z by using product rule

(uv)′=u′v+uv′

h' (x) = (x-1)' (3x+4) +(x-1)(3x+4)'

h'(X) = 1(3x+4) + (x-1) (3)

On simplifying:

h'(x) = 3x+4 +3x-3

h'(x) = 6x +1

Hence the derivative of function is 6x+1.

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There are 123 different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

Probability: The branch of mathematics known as probability deals with numerical expressions of the probability that an event will occur, or the probability that a statement will be true.

The probability of an event is a number between 0 and 1, with approximately 0 meaning improbability and 1 meaning certainty.

The probability of an event occurring increases with its probability. A simple example is tossing a fair (fair) coin.

Both outcomes (heads and tails) have equal probability, the coin is fair, heads are more likely than tails, there are no other possible outcomes, and either outcome has half the probability.

According to our question:

Let n be the maximum number of subsets of 5 elements that can be chosen from the first 14 natural numbers,

where at least 2 of the 5 digits are consecutive.

We created a block of two consecutive numbers ((1,2), (2,3), (13,14), etc.).

Now you can select this block in 13 different ways. You have to choose 3 numbers from the remaining 12 numbers.

So, from the multiplication principle, we know that we have 13 × (123).

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