derstand and Determine Simple Probability
In a video game, the player can choose a character from 4 animal characters and 3 human characters. Players can also let the
computer randomly select a character for them.
The player will have the computer randomly select his character.
What is the probability it will pick a human character?
Enter your answer as a fraction in simplest form in the box.
Basic
7
8
9
y
x²
VÕ
L
G

Answer: The range of possible values for the third side of the triangle is: 12.5 < x < 18.9. This is because the length of any side of a triangle must be greater than the difference between the other two sides and less than the sum of the other two sides. Therefore, we have:

Rounding to one decimal place, we get 12.5 < x < 18.9.

Yes, if a, b, and c make up a Pythagorean triple, then ma, mb, and mc will also be Pythagorean triples. This is because the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, applies to all similar triangles.

To illustrate this, let's take the example of the Pythagorean triple (3, 4, 5). We can find its multiples by multiplying each of the sides by a constant factor, let's say 2. So we get (6, 8, 10), which is also a Pythagorean triple. We can verify this by applying the Pythagorean theorem to both triangles:

For the first triangle (3, 4, 5):
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25 (true)

For the second triangle (6, 8, 10):
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100 (true)

As we can see, both triangles satisfy the Pythagorean theorem, and hence are Pythagorean triples.

Therefore, we can conclude that if a, b, and c make up a Pythagorean triple, then ma, mb, and mc will also be Pythagorean triples.

To learn more about  Pythagorean theorem : brainly.com/question/14930619

#SPJ11

The measure of the angle in radians is 11π/12. This was found using the formula for the length of an arc, which involves the radius and angle in radians. Given the radius of 12 and length of the arc 11π, the angle was solved for.

The length of an arc of a circle is given by the formula

length of arc = radius x angle in radians

We are given that the radius of the circle is 12 and the length of the arc is 11π. Let's use the formula above to find the angle in radians

length of arc = radius x angle in radians

11π = 12 x angle in radians

Divide both sides by 12:

11π / 12 = angle in radians

So, the measure of the angle in radians is 11π / 12.

To know more about Circle:

https://brainly.com/question/11833983

#SPJ1

The lateral surface area, of the figure formed by the net = 27 square inches

The correct answer is an option (b)

From the attached figure we can obaerve that the net represents the rectangular pyramid.

Here, the triangular sides of the pyramid represents the lateral surface.

The lateral surface area of the figure is nothing but the total surface area of the triangular faces.

Here, the two triangles have base b₁ = 6 in. and the height h₁ = 4.5 in.

Amd the remaning two triangles have base b₂ = 4 in. and height h₂ = 5 in.

Using the formula for the area of triangle,

A₁ = 2 × (1/2 × base × height)

A₁ = 2 × (1/2 × b₁ × h₁)

A₁ = 2 × (1/2 × 6 × 4.5)

A₁ = 2 × 3 × 4.5

A₁ = 27 sq. in.

And the area of remaining two triangles would be,

A₂ = 2 × (1/2 × base × height)

A₂ = 2 × (1/2 × b₂ × h₂)

A₂ = 2 × (1/2 × 4 × 5)

A₂ = 20 sq. in.

So, the lateral surface area, of the figure formed by the net would be,

A = A₁ + A₂

A = 27 + 20

A = 47 sq. in.

The correct answer is an option (b)

Learn more about the lateral surface area here:

https://brainly.com/question/11385509

#SPJ1

Find the complete question below.

Look at the net. what is the lateral surface area, in square inches, of the figure formed by the net

The researcher would likely use an independent samples t-test.

The researcher would likely use an independent samples t-test to test the hypothesis that men and women differ in the amount of time they spend exercising weekly.

This is because an independent t-test is appropriate when comparing the means of two independent groups, in this case, men and women.

However, before conducting the t-test, the researcher should check if the data meets the assumptions of normality and equal variance. If these assumptions are not met, alternative tests such as the Wilcoxon rank-sum test may be more appropriate.

for such more question on  independent samples

https://brainly.com/question/25223322

#SPJ11

(a) The probability that the steel mill will produce more than 150 metric tons next week is approximately 0.3846 or 38.46%.

(b) The probability that the steel mill will produce between 120 and 160 metric tons next week is approximately 0.6154 or 61.54%.

a. To compute the probability that the steel mill will produce more than 150 metric tons next week, we need to find the area under the probability density function (PDF) of the uniform distribution from 150 to 175.

Since the uniform distribution has a constant PDF, the probability is equal to the ratio of the length of the interval [150, 175] to the length of the entire interval [110, 175]:

P(X > 150) = (175 - 150) / (175 - 110) = 25 / 65 = 0.3846

Therefore, the probability that the steel mill will produce more than 150 metric tons next week is approximately 0.3846 or 38.46%.

b. To determine the probability that the steel mill will produce between 120 and 160 metric tons next week, we need to find the area under the PDF of the uniform distribution from 120 to 160.

Again, since the uniform distribution has a constant PDF, the probability is equal to the ratio of the length of the interval [120, 160] to the length of the entire interval [110, 175]:

P(120 < X < 160) = (160 - 120) / (175 - 110) = 40 / 65 = 0.6154

Therefore, the probability that the steel mill will produce between 120 and 160 metric tons next week is approximately 0.6154 or 61.54%.

Learn more about probability

brainly.com/question/31120123

#SPJ11

The function best models the data in the table is y=2.5x+5.

From the given table, the coordinate points are (-1, 2.5) and (0, 5).

Here, slope (m) = (5-2.5)/(0+1)

m = 2.5

Substitute m=2.5 and (x, y)=(0, 5) in y=mx+c, we get

5=2.5(0)+c

c=5

So, the equation is y=2.5x+5

Therefore, the function best models the data in the table is y=2.5x+5.

To learn more about the equation of a line visit:

https://brainly.com/question/2564656.

#SPJ1

The distance of the mid point of the chord to the center is 8 cm.

Given a circle.

Length of the chord of a circle = 12 cm

Radius of the circle = 10 cm

We have to calculate the distance of the mid point of the chord to the center.

When a line is drawn from the mid point of the chord to the center, there forms a right triangle where hypotenuse is the radius and the legs are the half of the chord and the distance from the mid point to the center.

Using the Pythagoras theorem,

Distance from mid point to the chord = √10² - 6² = √64 = 8 cm

Hence the distance from the center of the chord to the mid point is 8 cm.

Learn more about Chords here :

https://brainly.com/question/1654080

#SPJ4

It is possible that a hybrid battery may need to be replaced after driving 100,000 miles, but it is not necessarily a given. The lifespan of a hybrid battery can vary depending on several factors.

The lifespan of a hybrid battery depends on various factors such as the make and model of the car, the age of the battery, driving habits, and the frequency of use. Some manufacturers claim that their hybrid batteries can last up to 150,000 miles or more. However, if the battery is not properly maintained or if the car is driven aggressively, it may degrade more quickly. Furthermore, extreme temperatures can also affect the lifespan of the battery. For example, very cold temperatures can reduce the battery's capacity, while extremely hot temperatures can cause damage to the cells. Therefore, while it is possible that a hybrid battery may need to be replaced after driving 100,000 miles, it is not necessarily a reasonable claim without considering the specific circumstances of the car and battery. It is best to consult with a certified mechanic to evaluate the condition of the battery and determine if replacement is necessary.

Learn more about battery here

https://brainly.com/question/5059264

#SPJ11

Carmen claims she needs to replace the hybrid battery after driving about 100000 miles. Is this a reasonable claim?

The correct option is c. Analysis of variance.

ANOVA stands for Analysis of Variance, which is a statistical method used to test the equality of three or more population means by analyzing the variance between samples.

In an ANOVA, the variance is partitioned into different components, including the variance between groups and the variance within groups. If the variance between groups is larger than the variance within groups, it suggests that there are significant differences between the means of the groups being compared.

ANOVA is commonly used in experimental research to test the effects of one or more independent variables on a dependent variable. It allows researchers to determine whether the means of different groups are significantly different from one another, and if so, which groups are significantly different.

Overall, ANOVA is a powerful statistical tool that enables researchers to test hypotheses and draw conclusions about the differences between multiple groups or treatments.

Learn more about Analysis of Variance

brainly.com/question/30038124

#SPJ11

To find the width of Todor's area model for the expression 10x² - 5x + 15x, we first factored out the GCF 5x. The factors of the GCF are 5, x, and -1/111, which we wrote in an area model. We then added the absolute values of the coefficients of the factors to get a width of 1 + (1/37).

The expression to factor is 10x² - 5x + 15x

Find the GCF of the terms in the expression

We can factor out 5x from all three terms

10x² - 5x + 15x = 5x(2x - 1 + 3)

The GCF of the expression is 5x.

Write the factors of the GCF with their coefficients in the area model

We can write the area model as in image.

To Find the width of the area model

The width of the area model is the sum of the absolute values of the coefficients of the factors. So, we can add the absolute values of the coefficients in the third row of the area model

|(-5/555)| + |1| + |(-1/111)| = (5/555) + 1 + (1/111) = 1 + (1/37)

Therefore, the width of Todor's area model is 1 + (1/37).

To know more about GCF:

https://brainly.com/question/11444998

#SPJ1

--The given question is incomplete, the complete question is given

"Todor was trying to factor 10x²-5x+1510x

, x, squared, minus, 5, x, plus, 1510x. He found that the greatest common factor of these terms was 555 and made an area model:

What is the width of Todor's area model?"--

The area is 468 inches squared

Calculating the area of the wall art

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

The composite figure

The area of the figure is the sum of the individual areas

So, we have

Area = (15 + 9) x 21 - (21 -19) x 9 - (6 x 3)

= 504 - 18 - 18

= 468 inches squared

Hence, the area is 468 inches squared

Read more about area here:

https://brainly.com/question/25292087

#SPJ1

Answer:

6.2 km x 1000 = 6200 m

Step-by-step explanation:

So, 6.2 kilometers = 6.2 × 1000 = 6200 meters. Conversion of 6.2 kilometers to other length, height & distance units -web

The probability that the average height of the sample men is greater than 69.5 inches is approximately 0.9772 or 97.72%.

To find the probability that the average height of the sample men is greater than 69.5 inches, we will use the Central Limit Theorem and the z-score formula.
Identify the given values:
  - Population mean (μ) = 70 inches
  - Population standard deviation (σ) = 2.5 inches
  - Sample size (n) = 100
  - Sample mean ([tex]\bar{x}[/tex]) = 69.5 inches.

According to the Central Limit Theorem, the distribution of sample means will be approximately normally distributed with mean μ and standard deviation σ/√n.

Calculate the standard deviation of the sample means [tex](\sigma \bar{x} )[/tex]
[tex](\sigma \bar{x} ) = \sigma /\sqrt{n }[/tex]

= 2.5/√100

= 2.5/10

= 0.25
Calculate the z-score using the formula:
[tex]z = ([\bar{x}- \mu )/\sigma\bar{x}[/tex]

= (69.5 - 70)/0.25 = -0.5/0.25

= -2
Use a z-table or calculator to find the probability that a z-score is greater than -2:
  P(z > -2) = 1 - P(z ≤ -2) = 1 - 0.0228 = 0.9772.

For similar question on probability.

https://brainly.com/question/28340049

#SPJ11

The range of the function is {0, 1, 4, 9, 25}.

The given function maps each input value to its corresponding output value:

Domain: The domain of a function refers to the set of all possible input values for which the function is defined. In this case, the given function has input values of 0, 1, 2, 3, and 5. Therefore, the domain of the function is {0, 1, 2, 3, 5}.

Range: The range of a function refers to the set of all possible output values that result from the function. Looking at the given function, the output values correspond to the squares of the input values.

In summary:

Domain: {0, 1, 2, 3, 5}

Range: {0, 1, 4, 9, 25}

Know more about range here:

https://brainly.com/question/28135761

#SPJ11

If the transformation x -> Ax is not one-to-one, it means that there exist two distinct vectors x1 and x2 such that Ax1=Ax2. In other words, there are multiple ways to obtain the same result b using different x vectors.

If the transformation x -> Ax is not one-to-one, it means that there exist two distinct vectors x1 and x2 such that Ax1=Ax2. This implies that the transformation maps different vectors in the domain to the same vector in the range.

In other words, there are multiple ways to obtain the same result b using different x vectors.

This fact has important implications in linear algebra. One consequence is that the matrix A does not have an inverse, since the inverse would have to map the same output b to two different inputs x1 and x2.

Another consequence is that the equation Ax=b has either zero or infinitely many solutions.

Learn more about Injective transformation

brainly.com/question/31383436

#SPJ11

The solution to the equation is x = 4/15

It is important to note that algebraic expressions are described as expressions that are made up of variables, constants, factors and coefficients.

From the information given, we have that;

√4 - 3x/√3x = 2

cross multiply the values, we have;

√4 - 3x = 2√3x

Now, find the square root of both sides, we have;

4 - 3x = 4(3x)

expand the bracket, we have;

4-3x = 12x

collect the like terms

12x + 3x = 4

add the values

15x = 4

Make 'x' subject

x = 4/15

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

The theorem that provides a method for revising probabilities to reflect new information is Bayes' theorem.

Bayes' theorem is a fundamental concept in probability theory and statistics that provides a way to update or revise probability estimates based on new or additional information.

It is named after the English statistician Thomas Bayes, who first formulated the theorem in the 18th century. Bayes' theorem is widely used in various fields such as science, engineering, medicine, finance, and artificial intelligence.

It is an essential tool for solving problems related to decision making, prediction, and classification.

Bayes' theorem is based on conditional probability, which describes the probability of an event given that another event has occurred. The theorem provides a formula for calculating conditional probabilities and allows for the incorporation of new information or evidence into the probability estimate.

To know more about probability refer to-

https://brainly.com/question/30034780

#SPJ11

The quadratic function that satisfies the given conditions is f(x) = (-1/6)(x - 6)(x + 4). Option C is correct.

We can start by using the fact that the roots of the quadratic function are 6 and -4. If a quadratic function has roots of r₁ and r₂, then it can be written in factored form as:

f(x) = a(x - r₁)(x - r₂)

Using this formula, we can write the quadratic function in factored form as:

f(x) = a(x - 6)(x + 4)

Now we can use the given point (2,4) to solve for the value of a. Substituting x = 2 and y = 4 into the equation gives:

4 = a(2 - 6)(2 + 4)

a = -1/6

Therefore, the quadratic function that satisfies the given conditions is:

f(x) = (-1/6)(x - 6)(x + 4). Option C is correct.

Learn more about quadratic function here:

https://brainly.com/question/30929439

#SPJ1

Answer:

34

Step-by-step explanation:

"Seven less than a number"

means that we need to subtract 7 from the

unknown number and the result would be 34.

The cofunction of sin29 = cos61

A cofunction is the complementary function of a trigonometric ratio

To find the cofunction of the given trigonometric ratio, we proceed as follows.

We see that the trigonometric ratio given is a sine function which is sin29 = 14/16.

So, it co function is a cosine.

So, sinx = cos(90 - x) where x = 29

So, sin29 = cos(90 - 29)

= cos61

So, the cofunction of sin29 = cos61

Learn more about cofunction here:

https://brainly.com/question/29896620

#SPJ1

The bearing from the port to the ship can be calculated using trigonometry. The ship’s initial direction of North-25°-West can be represented as an angle of 360° - 25° = 335° measured clockwise from north. After traveling 4 miles in this direction, the ship turns left (90° counterclockwise) and travels 11 miles. This means the ship is now traveling in a direction of 335° - 90° = 245°.

We can represent the ship’s movements as a right triangle with legs of length 4 and 11 miles. The angle between these two legs is 90°, so we can use the Pythagorean theorem to find the distance from the port to the ship: sqrt(4^2 + 11^2) = sqrt(137) ≈ 11.70 miles.

To find the bearing from the port to the ship, we need to find the angle between the north direction and the line connecting the port and the ship. We can use trigonometry to find this angle: tan^-1(11/4) ≈ 69.44°. Since the ship is west of north from the port, this means the bearing from the port to the ship is North-69.44°-West or approximately N69.44°W.

The value of expression in (a/x-h)+k form is,

⇒ - 26 / (x + 7) + 4

We have to given that;

Expression is,

⇒ (4x + 2) / (x + 7)

Now, We can simplify as;

⇒ (4x + 2) / (x + 7)

⇒ 4 - 26 / (x + 7)

⇒ - 26 / (x + 7) + 4

Thus, The value of expression in (a/x-h)+k form is,

⇒ - 26 / (x + 7) + 4

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The equivalent expression that includes a set of parentheses and has a value of 13 is (6 + 8) - (4 × 1) + 3.

To create an equivalent expression with a value of 13 using a set of parentheses, we can combine different mathematical operations. Here's one possible expression:

(6 + 8) - (4 × 1)

In this expression, we have two sets of parentheses. The first set (6 + 8) adds 6 and 8 together, resulting in 14. The second set (4 × 1) multiplies 4 and 1, resulting in 4. Finally, we subtract the value within the second set of parentheses from the value within the first set of parentheses: 14 - 4 = 10.

So, the expression (6 + 8) - (4 × 1) has a value of 10. However, we want to make the value of the expression 13. To do that, we can add 3 to the result:

(6 + 8) - (4 × 1) + 3

Now, when we evaluate this expression, we have 10 + 3 = 13.

Know more about parentheses here;

https://brainly.com/question/28146414

#SPJ11

The divisibility by a prime theorem states that every integer greater than 1 is either itself a prime number or can be expressed as a product of prime numbers.

In other words, every integer greater than 1 can be factored into a unique product of primes. This is a fundamental result in number theory, and is often used to prove other theorems and results.

The proof of this theorem relies on the fact that any integer greater than 1 can be factored into a product of prime factors. We can then use mathematical induction to show that any integer greater than 1 can be expressed as a product of primes.

The base case is that 2 is a prime number, and the induction step relies on the assumption that any integer less than n can be expressed as a product of primes.

This theorem has many important applications, such as in determining the prime factorization of an integer, finding the greatest common divisor of two integers, and solving Diophantine equations. It is also used in cryptography, where it is essential to factor large numbers into their prime factors in order to break certain encryption algorithms.

To know more about integer refer to-

https://brainly.com/question/15276410

#SPJ11

The required expression will be -10 ÷ (-2/5).

Given are the numbers -10, -5/2,-2/5, or 5,

An expression is the numbers, symbols and operators grouped together that show the value of something.

Using the numbers,

-10 ÷ (-2/5).

Hence, -10 ÷ (-2/5) will be the expression.

For more references on expression, click;

brainly.com/question/14083225

#SPJ1

Yes, that is correct. First-order logic includes all of the connectives available in propositional logic, such as "and," "or," "not," "implies," and "if and only if."

However, first-order logic also goes beyond propositional logic by introducing quantifiers and variables to allow for more complex expressions and reasoning.
The relationship between first-order logic, connectives, and propositional logic. First-order logic indeed includes all the connectives available in propositional logic, allowing us to form more complex sentences.
In propositional logic, we use simple statements or propositions that can be true or false. Connectives, such as AND, OR, NOT, and IMPLIES, are used to combine these propositions into more complex expressions.
First-order logic expands upon propositional logic by introducing quantifiers like "for all" (∀) and "there exists" (∃) and predicates, which are relations or properties involving one or more variables. This allows us to represent more complex statements and relationships.
Since first-order logic includes connectives from propositional logic, we can form sentences that combine both quantifiers and connectives, allowing for richer and more expressive representations of information.

Visit here to learn more about  First-order logic:

brainly.com/question/30761328

#SPJ11

The set of all tax returns with either the standard deduction or showing business income, but not filed in 2007, and not selected for audit.

The set (A U B) - C represents the set of all tax returns with either the standard deduction or showing business income, but not filed in 2007.

In other words, it represents the set of all tax returns that have the standard deduction or show business income, but were not filed in 2007, and were not selected for audit.

Learn more about "set"

brainly.com/question/2332158

#SPJ11