What are the 3 types of multiplication?.

The side length of the square is 18.5 m

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

a = Radical s

where s is the area of the square.

Rewrite the above equation

So, we have the following representation

a √s

Given that the area of a square is 343m

We have

a =√343

Evaluate the root

a =18.5

Hence, the side length is 18.5 meters

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Factorization by remarkable identities use the following identities, a²  + 2ab + b² , a²  - 2ab + b² , a²  - b² , and x²  + x (a + b) + ab.

An algebraic expression is factorized when it is written as the product of its factors. These variables, factors, or algebraic expressions might be present.

Use of Identities in Factorization utilizing identities is substantially simpler when employing some of the identities that exist.

Several expressions that need to be factored have the following forms or may be transformed into them: a²  + 2ab + b²,  a²  - 2ab + b² , a²  - b² , and x² + x (a + b) + ab. Using Identities, I, II, III, and IV, it is simple to factorize these expressions.

Using each identity individually, we will study factorization in this part.

(a + b)²  = a²  + 2ab + b²

(a - b)²  = a²  - 2ab + b²

a²  – b²  = (a + b) (a – b)

(x + a) (x + b) = x²  + x (a + b) x + ab

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Complete question:

How to do factorisation by remarkable identities?

The Factor analysis is a statistical method for analyzing the intercorrelations among various measures or test scores.

Factor analysis is a technique used to reduce a large number of variables to a smaller number of factors. This technique extracts the maximum common variance from all variables and puts them into the common score. This score can be used for further analysis as an index for all variables. A "factor" is a set of observed variables with similar response patterns. These are associated with hidden variables that are not directly measured (called noise variables). Factors are listed by their factor loadings, or the amount of variation in the data they can explain. There are two types: exploratory and confirmatory.

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The system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions when the coefficients of x and y are the same ratio on both equations,

2x + 3y = 4

6x + 27y = 12

For the system of equations to have infinite solutions, the ratio of the coefficients of x and y must be the same. In this case, the ratio of the coefficients of x is 2/6 = 1/3 and the ratio of the coefficients of y is 3/27 = 1/9. Since the ratio of the coefficients is not the same, the system of equations does not have infinite solutions.

Hence, the value of k for which the system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions is not exist.

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Four ways of solving an equation are Graphical, Elimination, Substitution, and Cross multiplication.

Graphical method: To solve linear equations graphically, first draw the graph for both equations in the same coordinate graph and locate the intersection point on the graph.

Elimination method: In this method, any of the coefficients is first eliminated by equating. After eliminating the coefficient, the equations are resolved to get the other equation. For example:

3x + 2y = 9 ———–(i)

x – y = 6 ———–(ii)

Here, if equation (ii) is multiplied by 3, the coefficient of “x” will become equal and can be eliminated.

So, multiply equation (ii) × 3 and then subtract equation (i)

3x + 2y - 9 - 3x-3y-18 = 0

y = -9/5

Now, put the value of y = 1.8 in equation (ii).

So, x – 1.8 = 6

x = 4.2

Substitution method: To solve a linear equation using this method, first, take the value of one variable separately from any of the equations. Then, substitute the value of this variable in the second equation and solve it.

Cross multiplication method: Linear equations can be easily solved using this method. This technique is used to simplify the solution. The following formula is used for solving 2 variable equation:

x /(b₁ c₂ − b₂ c₁) = y / (c₁ a₂ − c₁ a₁) = 1 /(b₂ a₁− b₁a₂)

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Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true. Hence, statement 1 is true.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

From the given spinner we can observe that:

P (Purple) = 2 / 8

P (Yellow) = 2/8

P (Blue) = 3/8

P (Orange) = 1/8

Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true.

Hence, statement 1 is true.

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After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

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The complete question is given in the image.

92 inches² paper would be needed to wrap the prism completely.

What is the Surface Area of a Rectangular Prism?

The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.

Given here, The dimensions of the rectangular prism are 8,3,2 in inches.

Total surface area of a rectangular prism

= 2(lb + bh + lh)

Thus TSA

= 2(24+16+6)

= 92 inches²

Hence, 92 inches² paper would be needed to wrap the prism completely.

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Answer:

42 feet

Step-by-step explanation:

Since they are similar, that means the rectangles are reduced copies of each other. So, to find the length, you have to do 60/(40/28), to get the length of the pool. 40/28 is the ratio. 60/(40/28) = 42, so the answer is 42 feet.

Answer: 42 feet

Step-by-step explanation:

Width of pool to patio = 28 : 40

28 : 40 = 7 : 10

Multiply both sides by 6:

42 : 60, so the length of the pool is 42 feet

The zeros of a polynomial are the values of x that make the polynomial equal to 0.

To find the zeros, you need to set the equation equal to 0 and solve for x. The multiplicity of a zero is the number of times that the factor (x – zero) is a factor of the polynomial. To find the multiplicity of a zero, you need to find the highest power that x appears in the equation. For example, if the equation is (x-2)2•(x+1)3, then the zero is 2, and the multiplicity is 2.

The zeros of a polynomial are the values of x that make the equation equal to zero. The multiplicity of a zero is the number of times the factor (x - zero) occurs in the equation. To find the zeros and multiplicity of a polynomial, the polynomial needs to be factored into linear factors. The zeros are the x-intercepts of the equation (where the graph crosses the x-axis). The multiplicity is the power of the factor (x - zero). For example, if the equation is (x-2)^2(x-5), the zeros are x=2 and x=5 and the multiplicity of the zeros is 2 for x=2 and 1 for x=5.

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Answer:

x = 17, y = 8

Step-by-step explanation:

Answer:

y-8

X-17

Step-by-step explanation:

Look at the ratio. If BC is 2x of ZY, then multiply the sides of XZ and YX by 2

The modal  number of the pairs of shoes owned by the children is 3 pairs of shoes.

In mathematics, the modal number or mode, is the number that appears on the data set the most times out of all the numbers that appear on a set of numbers or data.

In the case of this line graph on the number of pairs of shoes that children own, the modal number would be 3 pairs of shoes as this is the highest number according to the fact that 5 students own 3 pairs of shows.

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The question is:

What is the modal number of pairs of shoes owned by the children?

Answer::

Solution:



Altitude =

5

2

−4

2

​

=3

Area =

2

1

​

(base)(height)

=

2

1

​

×8×3=12cm

2

.

solutio

The answers to the two blank portions are, √64 = 8 and ∛1000 = 10.

We are aware that there are two different sorts of radicals. Surds are created when a number is raised to a power that makes it greater than zero but less than one. Indices are created when a number is raised to a power that makes it bigger than one.

We know 10×10 = 100.

10¹×10¹ = 100.

10² = 100.

√100 = 10.

Similarly ∛1000 = 10.

As ∛1000 = ∛(10×10×10) = ∛10³ = 10.

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Solutions of given inequality expression are d = 7 and d = 9  

Mathematical expressions with inequalities are those in which the two sides are not equal to each other but less or greater than the other.

In other words, it is defined as a non-equal comparison between two expressions. Just like equations, these expressions are also made up of variable and constant terms.  

The signs that we used in Inequatility expressions are

≠ for not equal

< for less than  

> for greater than  

Here we have

d > 5 is an Inequality, which means d is greater than 5  

Then the given expression will be satisfied for all the values which are greater than 5

Therefore,

Solutions of given inequality expression are d = 7 and d = 9

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The slope and y-intercept represent, time worked, x Wages earned,

y($) is 9.25.

In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.

From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.

The point-slope form of a linear equation is y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

We can use the data from the table to find the slope of the line.

m = (y2 - y1) / (x2 - x1)

We can use the first two data points (x1 = 1, y1 = 9.25) and (x2 = 3, y2 = 27.75) to find the slope:

m = (27.75 - 9.25) / (3 - 1) = 18.5/2 = 9.25

Now we have the slope, we can use the point (x1 = 1, y1 = 9.25) to find the y-intercept, b

9.25 = 9.25 * 1 + b

we can find b is 0

So, the equation of the line in slope-intercept form is y = 9.25x + 0

The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.

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The slope and y-intercept represent, time worked, x Wages earned, y($) is 9.25.

In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.

From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.

The point-slope form of a linear equation is y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is a point on the line.

We can use the data from the table to find the slope of the line.

m = (y₂ - y₁) / (x₂ - x₁)

We can use the first two data points (x₁ = 1, y₁ = 9.25) and (x₂ = 3, y₂ = 27.75) to find the slope:

m = (27.75 - 9.25) / (3 - 1)

= 18.5/2

= 9.25

Now we have the slope, we can use the point (x₁ = 1, y₁ = 9.25) to find the y-intercept, b

9.25 = 9.25 * 1 + b

We can find b is 0

So, the equation of the line in slope-intercept form is y = 9.25x + 0

The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.

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The time to complete one swing or period is 16.4 seconds and the length is 3.3 meters

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

L = 67 meters and g = 9.81 m/s²

The time, t, in seconds, that it takes for one swing or period of the pendulum can be modeled by the equation:

t = 2π(√(L/g))

Substitute the known values in the above equation, so, we have the following representation

t = 2π(√(67/9.81))

Evaluate

t = 16.4 seconds (approx)

Here, we use the same equation and solve for L

In this case, t = 9.6

t = 2π(√(L/g))

substitute the known values in the above equation, so, we have the following representation

9.6 = 2π(√(L/9.81))

So, we have

L = (9.6/(2π))² * 9.81

Evaluate

L = 3.3 meters (approx)

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Answer:

28.8 days

Step-by-step explanation:

If. 15 scout = 24 days

than. 18 scout = ?

= 18/15 × 24 days

= 432/15

= 28.8 days.

If 15 scout can sell all their troops cookie's in 24 days than 18 scout too will sell cookies in 28.8 days.

The distance, to the nearest foot, the plane has flown is 3926.887 feet.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians

The horizontal runway, the distance plane flied and the height gained forms a right angled triangle.

Let x be the distance plane flied.

Height gained = 950 feet

Angle that plane makes with the horizontal runway = 14°

Sin 14 = Opposite side / Hypotenuse

Sin 14 = 950 / x

x = 950 / sin 14

x = 3926.887 feet

Hence the distance plane flied is 3926.887 feet.

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Perimeter is directly proportional to number of squares, x and is 4x where x is the number of squares.

What is perimeter ?

Perimeter is the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of a shape. It is commonly used to measure the size of a closed shape such as a square, rectangle, or circle. The formula for perimeter depends on the shape in question.

The statements that are true about the relation between the number of squares and the perimeter of the rectangles they form are:

As the number of squares increases, the perimeter of the rectangle also increases.

The perimeter of the rectangle is 4 times the number of squares.

The perimeter increases by 4 for every increase in 1 square.

The perimeter is calculated by multiplying the number of squares by 4.

The perimeter is directly proportional to the number of squares.

Perimeter is directly proportional to number of squares, x and is 4x where x is the number of squares.

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Answer:  x = 13, and the angle measures are 131, 49, 131, 49.

Step-by-step explanation:

7x + 40 = 10x + 1

40 = 3x + 1

39 = 3x

x = 13

The obtuse angle is 131, and the acute one is 49.

The 5 steps in solving equations by substitution are

If we take an example ,

Substituting y = 3+x in equation 1 we get,

3x + 2(3 + x) = 11

3x + 6 + 2x = 11

5x = 5

x = 1

Put the value of x = 1 in the equation -x + y = 3

we get -1 + y = 3

so y = 4

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The inverse of an inverse function is the original function.

For example, if a function f(x) has an inverse function g(x) such that f(g(x)) = x and g(f(x)) = x for all x in their respective domains, then the inverse of g(x) is f(x).

This is because when you apply the inverse function twice, it cancels out the effect of the inverse, and leaves you with the original function.

In mathematical notation, if f^-1(x) is the inverse of f(x), then (f^-1)^-1(x) = f(x)

So the inverse of an inverse is the original function, which means that (f^-1)^-1 = f

It's also worth noting that any function and its inverse are always one-to-one function, meaning that each element of the domain of the function corresponds to exactly one element of the range and vice-versa, which makes it possible to define an inverse function.

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Answer: answer is 5/6, check my photo to understand

Answer: 5/6

Step-by-step explanation:

The probability that a randomly chosen unsatisfactory screen came from Philips is approximately 0.4444.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Let's call the probability that a screen came from Philips "P".

know that 55% of the screens came from Corning Inc. and the rest came from Philips, so:

P = 1 - 0.55 = 0.45

We also know that the probability of getting an unsatisfactory screen from Corning Inc. is 1%, while the probability of getting an unsatisfactory screen from Philips is 4%:

P(unsatisfactory | Corning Inc.) = 0.01

P(unsatisfactory | Philips) = 0.04

Using Bayes' theorem, the probability that a randomly chosen unsatisfactory screen came from Philips can be calculated as:

P(Philips | unsatisfactory) = P(unsatisfactory | Philips) * P(Philips) / [P(unsatisfactory | Philips) * P(Philips) + P(unsatisfactory | Corning Inc.) * P(Corning Inc.)]

Substituting the values we have:

P(Philips | unsatisfactory) = 0.04 * 0.45 / [0.04 * 0.45 + 0.01 * 0.55] = 0.444444... or approximately 0.4444

Therefore, the probability that a randomly chosen unsatisfactory screen came from Philips is approximately 0.4444.

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The probability that a randomly chosen unsatisfactory screen came from Philips is 46.48%.

Let's call P(Philips) the probability that a randomly chosen screen came from Philips, and P(Unsatisfactory | Philips) the probability that a screen is unsatisfactory given that it came from Philips. Then we can use Bayes' theorem to find P(Philips | Unsatisfactory), the probability that a screen came from Philips given that it is unsatisfactory.

Bayes' theorem states:

P(A | B) = P(B | A) * P(A) / P(B)

where A and B are events, P(A | B) is the conditional probability of A given B, P(B | A) is the conditional probability of B given A, P(A) is the probability of A, and P(B) is the probability of B.

In this case,

A = "the screen came from Philips"

B = "the screen is unsatisfactory"

So:

P(Philips | Unsatisfactory) = P(Unsatisfactory | Philips) * P(Philips) / P(Unsatisfactory)

We are given:

P(Unsatisfactory | Philips) = 4% = 0.04

P(Philips) = 45% = 0.45 (since 55% came from Corning Inc.)

P(Unsatisfactory) = P(Unsatisfactory | Corning Inc.) * P(Corning Inc.) + P(Unsatisfactory | Philips) * P(Philips)

= 1% * 55% + 4% * 45% = 0.55% + 1.8% = 2.35%

So:

P(Philips | Unsatisfactory) = 0.04 * 0.45 / 0.0235 = 46.48%

So the probability that a randomly chosen unsatisfactory screen came from Philips is 46.48%.

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The equivalent expression of the given value is sqrt 9x/5. Option D

We have to note that when we are dealing with this expression, we have to bear in mind one of the rules of surd that states that; √P/√Q = √P/Q. This is the rule of surd that would guide our operation here.

We have that;

√9x^2/√5x

This would be the same as;

√9x^2/5x

According to the rule above, we now have;

√9x/5

Thus, by the use of the laws of surd we would have the expression √9x/5 as shown in the solution above.

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The cost of 250 bricks, delivered to a worksite, is $170. The cost of 400 bricks delivered is $245 and the cost to have 320 bricks will delivered $217.6 .

The cost of 250 bricks, delivered to a worksite, is $170.

So , we can calculate the single brick cost need to divide 170/250=0.68

Single brick cost is 0.68

The cost of 400 bricks delivered is $245.  In this case a single brick cost is 0.6125

The answers is different from the first answer we can calculate  320  brick cost 320×0.68=217.6

The following equation is used to calculate the Cost Per Brick. To calculate the cost per brick, divide the total cost of the bricks by the number of bricks. Bricks in 1 cubic Feet (cft) = Volume of brickwork/ Volume of one brick with mortar. Thus, thumb rule formula: No. of bricks in wall per Cubic Feet= (Area in Cft × 14).

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The average temperature during the winter in the Arctic tundra i -34C which is also 93.2 degrees Fahrenheit

The difference between the freezing point of water and its boiling point at normal atmospheric pressure is divided into exactly 100 equal parts to determine the temperature in degrees Celsius (degrees). Water has a freezing point set at 0° and a boiling point set at 100°.

Therefore, a 100°C difference is precisely equivalent to a 180°F difference. As a result, each degree in Celsius is equivalent to 1.8 degrees Fahrenheit.

The 34 Celsius to Fahrenheit formula is a linear function:

[°F] = ([34] x 9 ⁄ 5) + 32.

Therefore, we get:

34 C to F = 93.2 °F

34 °C in °F = 93.2 Fahrenheit

34 C in F = 93.2 degrees Fahrenheit

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