the quotient of a number and -7 and decreased by 2 is 10 find the number

Answer:

1137

Step-by-step explanation:

5675+453

6128

Now

7265-6128

1137

Answer:

A.   4.5 ft

B.    4 ft

C.    1 ft

Step-by-step explanation:

If you pretend that h is replacing y and d is replacing x and you would graph the equation, then you would get a parabola that opens down.

You would need to find the vertex of the parabola.  The ordered pairs would be (d, h) instead  of the normal (x, y).  

A.  The maximum height will be the h value of the vertex

B.   Let h = 0 and solve the equation for d.  That will give you distance from the stump that the frog landed.

C.  The distance from the log at the maximum height is the d value of the vertex

So, that is what is needed to be done.

Without me going thru all the work, the vertex is (1, 4.5) and the solutions to the equation when h = 0 are 4, -2  (discard -2 since a distance cannot be negative)

So the answer to A is 4.5 ft.

The answer to B is 4ft.

The answer to C is 1 ft.

Now, can you find the vertex on your own and can you solve the equation when h = 0?  I hope so.  OK?

A function assigns the values. The maximum height will be when the horizontal distance is 1feet from the log.

A function assigns the value of each element of one set to the other specific element of another set.

A.) The maximum height of the frog,

h = -0.5d²+d+4

dh/dd = -0.5(2d)+1

dh/dd = -d+1

0=-d+1

d = 1

The maximum height will be when the horizontal distance is 1feet from the log.

h = -0.5(1)² + 1 + 4

h = -0.5 + 1 + 4

h = 4.5

Hence, the maximum height of the frog will be 4.5 feet.

B.) The Distance between the frog and the stump when the frog land can be found,by putting h=0.

0 = -0.5(d)²+ d + 4

d²-2d-8=0

d²-4d+2d-8=0

d(d-4)+2(d-4)=0

d = 4, -2

Since the distance can not be negative, the frog is 4 feet away from the stump when the frog land.

C.) The maximum height will be when the horizontal distance is 1feet from the log.

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When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Variables with values that are determined by chance are called random variables (option a).

Random variables are variables whose values are determined by chance or randomness. They are often used in probability theory and statistics to model uncertain or unpredictable phenomena. The values of random variables can come from various sources, such as the outcome of a random experiment, the result of a random process, or the measurement of a random quantity.

Random variables can take on different types of values, including numerical values (such as integers or real numbers) or categorical values (such as "heads" or "tails" in a coin toss). The possible values that a random variable can take are known as its sample space.

Random variables are commonly denoted by capital letters, such as X, Y, or Z. Each value in the sample space of a random variable is associated with a probability or likelihood of occurring, which can be described using a probability distribution. The probability distribution provides information about the likelihood of different outcomes or values of the random variable.

Random variables are fundamental in many areas of mathematics, statistics, and science. They play a crucial role in understanding and modeling uncertainty, making predictions, analyzing data, and making informed decisions in various fields, including finance, engineering, biology, and social sciences.

The complete question is:

Variables with values that are determined by chance are called _______.

a) random variables.

b) erratic variables.

c) specialized.

d) inconsistent variables.

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Answer:

Step-by-step explanation:

Negative Exponent Rule:

, this says that negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents.

In a genogram, various symbols and lines represent different aspects of a person's familial relationships and attributes. Here's a breakdown of the symbols you mentioned:

1. Square: A square in a genogram indicates a male individual. It represents the person's gender and is used to distinguish between male and female family members.

2. Circle: A circle in a genogram indicates a female individual. It represents the person's gender and is used to distinguish between male and female family members.

3. Solid horizontal line: A solid horizontal line in a genogram represents a marital relationship between two individuals. The line connects a square (male) and a circle (female) to show that they are married or in a committed partnership.

4. Broken line: A broken line in a genogram represents a non-blood relationship, such as an adoptive parent-child relationship or a step-sibling connection. It is used to show relationships that are not based on biological ties.

5. X through a square/circle: An X through a square or a circle indicates that the individual is deceased. This symbol is used to show that the person has passed away and is no longer living.

6. Solid vertical line: A solid vertical line in a genogram represents a parent-child relationship. It connects an individual (either a square or circle) to their parent(s), showing the biological connection between the family members.

These symbols and lines help provide a visual representation of a person's family history and relationships, making it easier to analyze and understand the various connections within a family tree.

Overall, a genogram is a visual representation of a family tree that includes important information about relationships, health issues, and other relevant details. By understanding the various symbols and indicators used in a genogram, it is possible to gain a deeper understanding of family dynamics and relationships, as well as potential risk factors for various health conditions. As such, genograms are an important tool for healthcare providers, therapists, and other professionals working with individuals and families.

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The results are: P(1,1) = 1/36, P(both odd) = 1/4, P(even, odd) = 1/2, P(2 anywhere) = 1/18, P(sum of 8) = 5/36, P(sum of 1) = 0

Probability is measure for an event occurring. It is a number between 0 and 1, where 0 represents an event that is impossible and 1 represents an event that is certain.

Here are the probabilities for each event:

P(1,1) = 1/36

Both dice need to show a 1, which can only happen in one way out of the 36 possible outcomes.

P(both odd) = 1/4

Both dice need to show an odd number, which can happen in 9 out of the 36 possible outcomes: 1-1, 1-3, 1-5, 3-1, 3-3, 3-5, 5-1, 5-3, 5-5. So the probability is 9/36, which simplifies to 1/4.

P(even, odd) = 1/2

The first die needs to show an even number (2, 4, or 6), and the second die needs to show an odd number (1, 3, or 5). This can happen in 18 out of the 36 possible outcomes: 2-1, 2-3, 2-5, 4-1, 4-3, 4-5, 6-1, 6-3, 6-5. So the probability is 18/36, which simplifies to 1/2.

P(2 anywhere) = 1/18

The number 2 can appear in two ways: either the first die shows a 2 and the second die can be any number (1, 2, 3, 4, 5, or 6), or the second die shows a 2 and the first die can be any number (1, 2, 3, 4, 5, or 6). So there are two ways out of the 36 possible outcomes for the number 2 to appear. Thus the probability is 2/36, which simplifies to 1/18.

P(sum of 8) = 5/36

There are five ways to get a sum of 8: 2-6, 3-5, 4-4, 5-3, and 6-2. So the probability is 5/36.

P(sum of 1) = 0

It is not possible to get a sum of 1 when rolling two dice, so the probability is 0.

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Answer: they should be 2cm apart

Step-by-step explanation: This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km). We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.

Answer:

3.5

Step-by-step explanation:

I think it's mid point is 3.5

Answer:

  all real numbers

Step-by-step explanation:

There is nothing on the graph to indicate the function is undefined for any values of x. The domain is all real numbers.

Answer:

Domain is all real numbers.

Step-by-step explanation:

The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x.

Answer:

17/12

Step-by-step explanation:

3/4 = x - 4/6

Add 4/6 to both sides.

3/4 + 4/6 = x - 4/6 + 4/6

simplify:

17/12 = x

Therefore, x = 17/12

Answer:

Katie,

Once the skydiver reaches terminal velocity, then he will be falling with constant speed. The distance he falls in time t will then be d = (160 ft/s)·t. And his altitude above the ground (height h) will be his altitude when the parachute opened minus the distance he has fallen so we can write:

h = (3200 ft) - (160 ft/s)·t

As a point of interest, the time it will take him to fall all the way to the ground is t = (3200 ft)/(160 ft/s) = 20 s

Answer:

h(t) = -16t^2 + 200

Step-by-step explanation:

With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17\(\frac{1}{3}\)

With one third of a serving remaining, there are 17 servings total.

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Answer:

Picture 1:

Step 1- Given

Step 2- Addition Property of Equality

Step 3- Division Property of Equality

Picture 2:

Step 1- Given

Step 2- Combine Like Terms

Step 3- Subtraction Property of Equality

Picture 3:

Step 1- Given

Step 2- Distributive Property

Step 3- Combine Like Terms

Step 4- Division Property of Equality

Picture 4:

Step 1- Given

Step 2- Distributive Property

Step 3- Combine Like Terms

Step 4- Addition Property of Order

Step 5- Division Property of Order

Picture 5:

Step 1- Given

Step 2- Distributive Property

Step 3- Subtraction Property of Order

Step 4- Addition Property of Order

Step 5- Combine Like Terms

Step 6- Division Property of Order

Hope this helps :)

Step-by-step explanation:

Answer: x=32, y=45, z=45

Step-by-step explanation:

Now, x is cut in half on a flat plane which is a supplementary angle (2 angles that add up to 180 degrees) so just subtract 148 from 180 and you get 32.

Since a line cuts y and z equally in half and the line it is connected to is perpendicular (right angle), we can safely say both angles are equal to 45 degrees.

Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

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Answer:

56

Step-by-step explanation:

because it is a right angle so 90 _ 34 = 56

Answer:

the answer should be 56 as 90-34=56

The value of the length of the hypotenuse is,

⇒ c = √85

Since, Three vertices and three angles totaling 180 degrees make up a triangle, a three-sided polygon with three sides.

And, Two rays (half-lines) that share a terminal make up an angle. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

We have to given that;

In triangle ,

Perpendicular side = 9 mm

Base = 2 mm

Since, We know that;

The Pythagorean theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of its two opposite sides.

Hence, By Pythagoras theorem we get;

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ c² = 9² + 2²

⇒ c² = 81 + 4

⇒ c = √85

Thus, The length of the hypotenuse is,

⇒ c = √85

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Answer:

answer is option A PQ AND JN

PQ and JN are a pair of lines that are non-intersecting, non-parallel, and non-coplanar, so they are skew lines.

Skew lines are a pair of lines that are non-intersecting, non-parallel, and non-coplanar. This implies that skew lines can never intersect and are not parallel to each other. For lines to exist in two dimensions or in the same plane, they can either be intersecting or parallel.

In the cuboid,

1) PQ and JN

Here, PQ and JN are a pair of lines that are non-intersecting, non-parallel, and non-coplanar, so PQ and JN are skew lines.

2) MQ and KO

Here, MQ and KO are parallel lines.

3) ON and NQ

Here, ON and NQ are intersecting lines

D) OP and JM

Here, MQ and KO are parallel lines.

Therefore, option 1 is the correct answer.

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Answer:

It is A.

Step-by-step explanation:

Easiest way is to break down each days into hours and minutes thenn go from there

Answer:

Step-by-step explanation:

Initial value of house is $478000

Change in value is 8% greater:

We need 8% of Value

\(\\ \sf\longmapsto 8\%\:of\;478000\)

\(\\ \sf\longmapsto 0.08(478000)\)

\(\\ \sf\longmapsto 38240\$\)

Current value:-

\(\\ \sf\longmapsto 478000+38240=516240\)

Answer:

65

Step-by-step explanation:

Answer:

108 degrees

Step-by-step explanation:

In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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If on a turn, the player moves forward the number of spaces equal to the first number rolled and then moves backward the number of spaces equal to the second number rolled. Then the probability that a player ends up 2 spaces ahead of where he started on a turn is 11%.

To end up 2 spaces ahead of where the player started, the number of spaces forward should be more than the number of spaces backward by 2.

⇒ First number - Second number = 2

All satisfied outcomes = (3,1), (4,2), (5,3) and (6,4).

Total possible outcomes = 36(6 outcomes for the first roll multiplied by 6 outcomes for the second roll)

\(Probability = \frac{All \ satisfied \ outcomes}{Total \ possible \ outcomes} = \frac{4}{36} = \frac{1}{9}\)

Converting this to percentage,

\(\frac{1}{9}\) x 100 = 11.11 ≈ 11%

Therefore, the probability that a player ends up 2 spaces ahead of where he started on a turn is 11%.

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Answer:

\(x+5\)

Step-by-step explanation:

\(\left(4x-5\right)-\left(3x-10\right)\)

\(\mathrm{Apply\:rule}:\quad \left(a\right)=a\)

\(\left(4x-5\right)=4x-5\)

\(=4x-5-\left(3x-10\right)\)

\(\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a-b\right)=-a+b\)

\(-\left(3x-10\right)=-3x+10\)

\(=4x-5-3x+10\)

\(\mathrm{Group\:like\:terms}\)

\(=4x-3x-5+10\)

\(\mathrm{Add\:the\:numbers:}\:-5+10=5\)

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

\(\mathrm{Add\:similar\:elements:}\:4x-3x=x\)

\(=x+5\)

Answer:

6/8

Step-by-step explanation:

3?4=.75

6/8=.75

Answer:

6

Step-by-step explanation:

The ratio of 3 to ? must be equivalent to the ratio of 4 to 8. Since 4 to 8 is a multiple of 2, 3 to ? must also be a multiple of 2. Here it is broken down:

\(4*2=8\)

\(3*2=6\), therefore ?=6.

Answer:

$113.08

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r/m)^mn

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

m = number of compounding

14,000(1.12)^2 =  17,561.60

14,000 ( 1 + 0.12/2)^(2x2) = 17674.68

Difference :  17674.68 -   17,561.60 = $113.08