(i) Write 3^-2 as a fraction
(ii) Find the value of 3X^0 when X=5

Answer:

Step-by-step explanation:

In ratio and proportion , when we compare two ratios or we can say two fractions then they are said to be equivalent when both of them are same.

Answer:

2 is the highest degree because it's the only exponent

The required two numbers are 9 and 41.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let x be the lesser number, and y be the greater number.

From the question, we know that:

x + y = 50 (Equation 1: The sum of the two numbers is 50)

y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)

The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.

Then, two numbers are x = 9 and y = 41.

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Answer:

The price of a table is rs1720

Step-by-step explanation:

Let C and T be the individual prices of the tables and chairs.

We know that 3C + 4T = rs7540

We are then told that C = rs220, so we can enter that into the equation to find T:

3C + 4T = rs7540  

3(220) + 4T = rs7540  [for C = rs220]

660 + 4T = 7540

4T = rs6880

T = rs1720

Check:

Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?

Chairs:   rs660

Tables:  rs6880

Total = rs7540  YES

The fraction of the voters who voted in favor of the measure will be 1/5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it.

The fraction of the voters who voted in favor of the measure will be given as,

⇒ 20%

⇒ 20 / 100

⇒ 1 / 5

The fraction of the voters who voted in favor of the measure will be 1/5.

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Answer:

-15

Step-by-step explanation:

That's the answer because

-15+4=-11

-15+4=-11-11<-7

Answer: 1271

Step-by-step explanation:

620 + (105% × 620) =

620 + 105% × 620 =

(1 + 105%) × 620 =

(100% + 105%) × 620 =

205% × 620 =

205 ÷ 100 × 620 =

205 × 620 ÷ 100 =

127,100 ÷ 100 =

1,271

Answer:128 cm^2

Step-by-step explanation:

The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.

avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.

a)

Hence average value of f(x) on 0≤x≤2

= 1/2 ∫f(x)  with 0 and 2 as intervals

Since integration is basically the area under the curve we get

avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]

Since from 0 to 1, the figure is a triangle and beyond that a straight line we get

1/2[1/2 X 1 X 1 + 0]

= 1/4 sq units

b)

Similarly, the average value of g(x) on 0 ≤ x ≤ 2

1/2[area from 0 to 1 + area from 1 to 2]

= 1/2[0 + 1/2]

= 1/4 sq units

c) here we need to find the average of f(x) . g(x)

Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1

Hence we see that on multiplying the functions, the resultant has to be a 0 function.

Hence its average value will be 0.

d)

Average(f) . Average(g) = 1/4 X 1/4

= 1/16

Average of (f.g) = 0

Hence the statement is false

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Complete Question

The figure attached to the left is a graph of f(x), and below to the right is g(x).

The figure below to the left is a graph of f(x), a

(a) What is the average value of f(x) on 0≤x≤2? avg value = __________

(b) What is the average value of g(x) on 0≤x≤2? avg value = __________

(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________

(d) Is the following statement true?

Average(f) . Average(g)=Average(f.g)

A. Yes

B. No

Answer:

Below

Step-by-step explanation:

Slope - intercept form is    y = mx + b    you just need to manipulate the given equation to this form

-x +3y = 6         add 'x' to both sides of the equation

3y = x + 6         divide by 3

y = 1/3 x + 2      Done !

The park should be expanded based on the information as the majority want the expansion.

From the information, on the small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded.

Also, the results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.

Based on the above the number of people that wants the expansion will be:

= (150 + 40) / 250 × 100

= 190 / 250 × 100

= 76%

It should be expanded.

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The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).

In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.

In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(2(9) + 3(-1))/(2 + 3)],  [(2(6) + 3(-4))/(2 + 3)]

P(x, y) = [(18 - 3)/(5)],  [(12 - 12)/5]

P(x, y) = [15/5],  [0/5]

P(x, y) = [3, 0]

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Complete Question:

Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?

The trigonometric ratios for the triangle in this problem are given as follows:

The three trigonometric ratios are defined as follows:

The sides are connect by the right angle, of 90 degrees, while the hypotenuse is the straight line segment that connects the endpoints of each of the sides.

Then the trigonometric ratios presented on the bullet points are used for angles A and B in this problem.

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The Triangle Similar to ΔABC is ΔDEF in which m <E = 80 and m <F = 35.

The Correct option is (A).

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Given:

In  ABC, m<A= 65 and m<B= 80

Now, using Angle sum Property

m<A + m <B + m <C = 180

65+ 80 + m<C= 180

m <C = 180 - 145

m <C = 35

So, the similar Triangle will be  DEF in which m <E = 80 and m <F = 35.

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The probability of getting 2 blue is 1/9.

You are choosing replacement marbles. The trials (marble selections) are independent from one another and follow the binomial distribution.

1/3 of the time, a blue marble will be the first one chosen.

(This is due to the fact that 4 out of 12 marbles are blue, therefore 4/12 equals 1/3.

A blue marble is 1/3 more likely to be chosen the second time.

The two probabilities can be multiplied to obtain the following results because the marble selections are independent:

The likelihood of receiving two blues is (1/3)2 =1/9.

Therefore, there is a 1/9 chance of obtaining two blues.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

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The volume of the triangular prism is 120 cm cube.

A triangular prism  is a three-sided prism.  The volume of a triangular prism can be represented as follows:

volume of a triangular prism = 1 / 2 bhl

where

Therefore,

b = 10 cm

h = 12 cm

l = 6 cm

Therefore,

volume of a triangular prism = 1 / 2 × 10 × 12 × 6

volume of a triangular prism = 1 / 2 × 120 × 6

volume of a triangular prism = 60 × 6

volume of a triangular prism = 120 cm³

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An expression that describes the team’s total points will be 2w + t.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator

In this case, the soccer team earns 2 points for a win and 1 point for a tie.

Let w represent the number of wins and t represent the number of ties.

The expression that describes the team’s total points will be:

= 2(w) + t

= 2w + t

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The first left turn, the value of d will be -1i, indicating that the robot is now facing north.

Value is the worth of something, which can be measured in terms of money, time or importance. It is something that is sought after and desired. Value can also be seen in terms of a person's character, morals, beliefs, and principles. It is an intangible concept that is difficult to quantify, but it is often sought after and is an important aspect of life. Value is what makes something worthwhile and irreplaceable.

The robot will need to be able to detect walls. As it moves through the maze, it will need to be able to detect when it is about to hit a wall. This can be done using sensors. The sensors should be able to detect the wall and the distance from the wall. This will allow the robot to turn in the correct direction and avoid hitting the wall.

The robot will also need to be able to detect when it has reached the end of the maze. This can be done by programming the robot to recognize when it has come to a dead end, or when it has reached a certain point in the maze. Once the robot has reached the end, it can then turn around and exit the maze.

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The probability that the sample mean is between 1300 and 1400 is approximately 1.34%.

We can use the Central Limit Theorem and the standard normal distribution to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the distribution of the population.

Since we have a sample of 80 observations, we can assume that the sample mean follows a normal distribution with a mean of 1460 (the population mean) and a standard deviation of:

Standard deviation of the sample mean

= population standard deviation ÷ [tex]\sqrt {sample size[/tex]

[tex]= 270 \div \sqrt{80} = 27[/tex]

So the standard deviation of the sample mean is 27.

We can now standardize the interval between 1300 and 1400 by subtracting the mean and dividing it by the standard deviation of the sample mean.

[tex]Z_1[/tex] = (1300 - 1460) / 27 = -2.59

[tex]Z_2[/tex] = (1400 - 1460) / 27 = -2.22

We need to find the area under the standard normal distribution curve between Z1 and Z2.

Using a standard normal table or a calculator with the standard normal distribution function, we can find the probability that a random variable from the standard normal distribution is between -2.59 and -2.22. This probability is approximately 0.0134 or 1.34%.

Therefore, the probability that the sample mean is between 1300 and 1400 is approximately 1.34%.

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The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).

The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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a. E(B) = 9.5

b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

c. Standard variable shows how much deviation from mean variable.

In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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Answer:

The answer to the proportion is 45:25.

Step-by-step explanation:

To solve this proportion, we can use cross multiplication. That is, we can multiply the numerator of the first ratio (45) by the denominator of the second ratio (10) and the numerator of the second ratio (50) by the denominator of the first ratio (?). This will give us

45 x 10 = 500 and 50 x ? = 500.

If we divide both sides of the equation by 50, we get

? = 25.

Therefore, the answer to the proportion is 45:25.

The values for figure is  x = 2, y = 9,

GH = 8, GJ = 7,

FE = 3, GE = 7​.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.

Given figure shows

GH parallel to EG

GH = EG

GH = 3y - 19

EG = 8

3y - 19 = 8

3y = 27

y = 9

GH = 3y - 19 = 3(9) - 19 = 8

and GJ parallel  to JE

GJ = JE

GJ = 3x + 1

JE = 5x - 3

3x + 1 = 5x - 3

5x - 3x = 1 + 3

2x = 4

x = 2

values are,

GJ = 3x + 1 = 3(2) + 1 = 7

JE = 5x - 3 = 5(2) - 3 = 7

FE = 6x - y

substitute values,

x = 2, y = 9

FE = 6x - y = 6(2) - 9 = 12 - 9 = 3

Hence x = 2, y = 9

GH = 8, GJ = 7,

FE = 3, GE = 7​.

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Therefore , the solution of the given problem of probability comes out to be  thus brand A is more prefer by the person as probability of B IS 0.43.

A probability is a number that represents the likelihood that a certain event will occur. Probabilities may be expressed as percentages

range from 0% to 100% or from 0 to 1.

Here,

Given :

Which brand of pasta do Texas and California prefer

Because brand B is preferred by 45 persons in Texas, the answer would be A.

There are 105 persons that favor brand B overall.

=> 45/105

=> 15/ 35

=> 0.42857...

So ,

rounded it would be 0.43,

thus brand A is more prefer by the person

Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.

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As per the given conditions in the question, the amount of money that the second son was left with by the man is 2,40,000.

To add two fractions with different denominators, you must first find a common denominator. A common denominator is a number that is divisible by both denominators of the fractions. Once you have a common denominator, you can add the numerators of the fractions together and place the sum over the common denominator. Then simplify the fraction if possible.

The reciprocal of a fraction is another fraction whose numerator and denominator are flipped. For example, the reciprocal of the fraction 2/3 is 3/2. The product of a fraction and its reciprocal is always equal to 1. To find the reciprocal of a fraction, simply swap the numerator and denominator.

Considering the conditions given in the question,let us suppose that the third son was left with x part of the money,

so we can use the equation,

part of money left for fist son + part of money left for second son + part of money left for third son = total part of money

or, 1/2 + 3/8 + x = 1

therefore, x = 1/8

Also we know that the third son was left 80,000 ,

so 1/8 of total money = 80,000

therefore, total money = 80000 * 8 =6,40,000

Now the amount left for the second son is , 3/8 of total money

which is equal to , 3/8 of 6,40,000 = 2,40,000

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a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram

b) For this one the class width is given to be the following: class with = 10 .  See the attachment for table

c)  See the attachment for the graph

What is histogram ?

A histogram is a collection of rectangles with bases and the gaps between class boundaries. All of the rectangles are contiguous, and each rectangle bar represents some kind of data. Rectangles have heights that are proportionate to the corresponding frequencies for both related and dissimilar classes.

a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram

b) For this one the class width is given to be the following: class with = 10 .  See the attachment for table

c)  See the attachment for the graph

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On solving the provided question, we can say that the values of the equation here will be y +1 = 8X 8y = 16 => y = 9.455

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y+1= -4(x - 2) 2x8y = 16​

x = 0

y +1 = 8X 8y = 16

y = 9.455

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When selecting four coins from a jar containing quarters, loonies, and toonies, there are a total of 27 unique combinations.

This can be calculated by using the formula for combination, which is nCr.

In this case,

n is the total number of coins in the jar (3) and

r is the number of coins selected (4).

Therefore, 3/(4(3-4)) = 3/0 = 3/1 = 3,

which is the number of possible combinations in the jar for the quarters, loonies, and toonies. When you multiply 3 by 3, you get 9, and when you multiply 9 by 3 again, you get 27.

Therefore, there are 27 unique coin combinations when selecting four coins from the jar.

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Identification if a polynomial is a sum or difference of two cubes can be done by factorizing the provided polynomial.

A polynomial is a mathematical expression that is a sum of one or more terms. Each term is a constant or a variable raised to a non-negative integer power and multiplied by a coefficient. The degree of a polynomial is the highest degree of the terms in the expression. A polynomial with one variable is called a univariate polynomial, and a polynomial with more than one variable is called a multivariate polynomial. Polynomials are used in various areas of mathematics, physics, engineering, computer science, and other fields. They can be used to model a wide range of phenomena and to solve problems that involve polynomial equations or inequalities.

Factorization, also known as factoring, is the process of breaking down a mathematical expression into a product of simpler factors. The goal is to express a given expression as a product of simpler expressions, which can be useful in solving equations and understanding the structure of the expression.

Factor the polynomial completely into its irreducible factors.

Look for terms that are of the form (x - a)^3 or (x + a)^3, where a is a constant. These are the cubes that you are looking for.

If there are two such terms, check if they can be combined into a single term by adding or subtracting them. If they can, then the polynomial is a sum or difference of two cubes.

If there are more than two such terms, check if any two of them can be combined in the same way. If they can, then the polynomial is a sum or difference of two cubes.

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The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms only x is the variable.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms.

if we solve the above equation, we get

2x + 3 = 7

or, 2x = 7 - 3

or, 2x = 4

or, x = 2

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