Represent the following situations in the form of quadratic equations:

(i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. What is the speed of the train?

I need help (⁠☆⁠▽⁠☆⁠) ​

1. the equation of the quadratic function is: y = (8/65)(x + 5)(x - 13)

2. The axis of symmetry is the line x = 0 (the y-axis).

What is quadratic function?

The quadratic equation with roots -5 and 13 can be written as:

y = a(x + 5)(x - 13)

where a is a constant that depends on the coefficient of the quadratic term.

To find the value of a, we can use the fact that the coefficient of the quadratic term is the sum of the roots, multiplied by -1:

a = -(sum of roots) / (product of roots)

a = -(-5 + 13) / (-5 * 13)

a = 8 / 65

Therefore, the equation of the quadratic function is:

y = (8/65)(x + 5)(x - 13)

What is symmetry?

2. The axis of symmetry is the line x = 0 (the y-axis).

To find the axis of symmetry, we can use the formula:

x = -(b / 2a)

where a and b are the coefficients of the quadratic function. In this case, a = 8/65 and b = 0, since there is no linear term.

Substituting these values, we get:

x = -(0 / (2 * (8/65)))

x = -0

Therefore, the axis of symmetry is the line x = 0 (the y-axis).

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Therefore there is graph below and whole process of graph

g(x) = -1/x (x).

g(x) = 1/(-x + 5).

Describe equation?

A mathematical equation is a formula that uses the equals symbol (=) to denote the equality of two expressions.

A formula would be 3x - 5 = 16,

for instance. We may determine the value of the variable x by solving this equation: x = 73.

We can apply a number of transformations on f to convert f(x) to g(x) (x).

A . Starting with the graph of f(x) = 1/x for function a, we can perform a vertical reflection to obtain the graph of g(x) = -1/x (x).

B . Starting with the graph of f(x) = 1/x, we can apply a horizontal shift to the function b's graph, g(x) = 3/(x + 2).

We can apply a number of transformations on f to convert f(x) to g(x) (x).

For instance, we can use the following transformations to change f(x) = x2 into g(x) = (x - 3)2 + 2:

- Replace x with to move the graph 3 units to the right (x - 3)

- Apply a horizontal shift to the left of two units and a vertical stretch of three factors to f f(x) = 1/x.

Starting with the graph of f(x) = 1/x, we may apply a horizontal shift to the right by 5 units and a vertical reflection to obtain the graph of function c, g(x) = 1/(-x + 5).

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Therefore , the solution of the given problem of equation comes out to be y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.

What is correlation?

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect

What is an equation?

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.

Here,

The least squares technique can be used to determine the equation of the line, presuming that the line of best fit is a linear regression line.

The findings that we get using a calculator or statistical software are as follows:

=> y = -0.9x + 5.5 is the equation of the line of best fit.

=> R = -0.83 is the correlation coefficient (r).

We can infer that there is a negative link between the two variables because the correlation coefficient (r) is negative.

This implies that the value of y tends to decline as the value of x rises.

As a result, y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.

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The angle m∠A + m∠C = 180° in the inscribed quadrilateral ABCD.

To prove that m∠A + m∠C = 180° in an inscribed quadrilateral ABCD with circle O, follow these steps:
1. Statement: Quadrilateral ABCD is inscribed in circle O.
  Reason: Given.
2. Statement: m∠BCD = 2(m∠A) and m∠DAB = 2(m∠C).
  Reason: Inscribed Angle Theorem
3. Statement: m∠BCD + m∠DAB = 360°.
  Reason: The sum of the measures of the angles in a circle is 360°.
4. Statement: 2(m∠A) + 2(m∠C) = 360°.
  Reason: Substitution Property (from steps 2 and 3).
5. Statement: m∠A + m∠C = 180°.
  Reason: Division Property of Equality (divide both sides of the equation in step 4 by 2).

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Answer:

a. The middle 99.7% of students between 0.04 and 0.10.
b. The range for the 16% of lowest BACs is 0.06 or below.

c. 2.28% of students have a BAC above 0.09.

To find the range, use the properties of the normal distribution and the given mean (0.07) and standard deviation (0.01).

The middle 99.7% of students between 0.04 and 0.10.

To find the range use the z-score corresponding to the 16th percentile (z ≈ -1).

The range for the 16% of lowest BACs is 0.06 or below.

To find the percentage, find the z-score for 0.09 first.

Approximately 2.28% of students have a BAC above 0.09.

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The lateral surface area of the triangular prism container is 270 cm².

We will begin with the calculation of perimeter of equilateral triangle.

Perimeter = 3 × sides

Perimeter = 3 × 6

Perimeter = 18 cm

Now calculating the lateral surface = perimeter of base × height

Keep the values in formula

Lateral surface of equilateral triangle prism = 18 × 15

Performing multiplication again

Lateral surface area = 270 cm²

Thus, the lateral surface area of the container is 270 cm².

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The picture is added of equilateral triangle with dimensions.

when y = 5 in the equation y = -3x + 5, the value of variable x is 0.

An equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.

the steps to find out what x is in the equation y = -3x + 5 for y = 5:

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The complete question is:

I need a step by step process for to find out what, "x" is in this problem. y = -3x +5 for y=5

We can't make any inferece of any definitive conclusions about the entire populations of students in the two classes.

What is population in Mathematics?

In mathematics, population refers to a group of individuals, objects, or events that share a common characteristic or feature. This group is the target of a study, and the goal is to make generalizations about the entire population based on a sample from that population.

For example, in a study on the average height of adult males in a particular country, the population would be all adult males in that country. However, it is not practical to measure the height of every single adult male in the country, so a sample is taken instead. The sample is a subset of the population and should be chosen in such a way that it is representative of the entire population.

To make an inference about the quiz scores of all the students in class A compared to all the students in class B, we can compare the medians of the two classes. The median is the middle score when the scores are arranged in order.

The scores of the 20 students in class A are

85, 86, 88, 89, 90, 90, 91, 92, 93, 94, 94, 94, 95, 96, 97, 98, 99, 99, 100, 100

And the scores of the 20 students in class B are

75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94

To find the median score for each class, we need to find the middle score. For class A, the middle score is 94 (since there are an even number of scores, we take the average of the middle two). For class B, the middle score is also 87.

Comparing the medians of the two classes, we see that the median score for class A (94) is higher than the median score for class B (87). This suggests that the quiz scores for class A may be higher overall than the quiz scores for class B. However, it's important to note that this is only based on a sample of 20 students from each class, so we can't make any definitive conclusions about the entire populations of students in the two classes.

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Correct question is "Two math classes took the same quiz. The scores of 20 randomly selected students from each class are listed below. Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in class a compared to all the students in class b?

Here the scores of the 20 students in class A are 85, 86, 88, 89, 90, 90, 91, 92, 93, 94, 94, 94, 95, 96, 97, 98, 99, 99, 100, 100

And the scores of the 20 students in class B are

75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94"

Answer:

If y=0, then 4y^2•2y^4 = 4(0)^2•2(0)^4 = 0.

Therefore, any of the options that involve y, such as A) 6y^6 or C) 8y^6, would also be equal to 0.

The only option that is still a valid answer is B) 6^8, which is simply 6 to the 8th power, or 1679616.

Hope This Helps!

A rough graph of T as a function of time t for hot water running from a tap would likely show an exponential decay curve.

Initially, the temperature of the water will be close to the temperature of the hot water supply in the house. However, as the water continues to flow, the temperature will gradually decrease due to heat loss through the pipes and the ambient temperature of the surrounding air. This decay will likely be exponential, with a relatively steep initial drop in temperature followed by a more gradual decrease over time. The graph would show an asymptotic approach towards room temperature as the water continues to flow. The exact shape of the curve will depend on a variety of factors, such as the length and material of the pipes, the ambient temperature, and the temperature of the hot water supply.

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To find the amount of interest you will owe, we need to calculate the interest using the formula:

Interest = Principal * Rate * Time

Where:

- Principal = $777 (the amount you owe)

- Rate = 18% per year (expressed as a decimal, or 0.18)

- Time = 1 year (since you have been making payments for a year)

Plugging in these values, we get:

Interest = $777 * 0.18 * 1

Interest = $139.86

So, the amount of interest you will owe is approximately $139.86.

The probability calculation resulted in (a) 2.28% (b) zero.

a) To find the proportion of components that exceed 10,200 kilograms per square centimeter in tensile strength, we need to find the area to the right of 10,200 under the normal distribution curve. Using the z-score formula, we have:

z = (x - mu) / σ

z = (10,200 - 10,000) / 100

z = 2

Looking up the area to the right of z = 2 in a standard normal distribution table or using a calculator, we find this to be approximately 0.0228. Therefore, about 2.28% of the components exceed 10,200 kilograms per square centimeter in tensile strength.

b) To find the probability that a randomly chosen metal component has a tensile strength of fewer than 9,500 kilograms per square centimeter, we need to find the area to the left of 9,500 under the normal distribution curve. Using the z-score formula, we have:

z = (x - mu) / σ

z = (9,500 - 10,000) / 100

z = -5

Looking up the area to the left of z = -5 in a standard normal distribution table or using a calculator, we find this to be approximately 0.

Therefore, the probability that a randomly chosen metal component has a tensile strength of fewer than 9,500 kilograms per square centimeter is essentially 0.

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The range interval of the given data is {73,80]

and range for term 2 is [74,80]

You may have studied the techniques for determining a representative value for the provided data in statistics, or the measure of central tendency. Remember that there are three ways to measure central tendency: mean, median, and mode.

Spatial Statistics

Due to the fact that the measurements of central tendency do not provide sufficient detail about a given set of data. Another factor that must be investigated in statistics is variability. We require a single number to characterize variability, much like measures of central tendency. This one number has demonstrated a certain amount of dispersion. You will discover more about range, one of the dispersion measures, in this post.

According to the given problem

the range of any date is equal to the interval of lower and upper limits,

So

Form term 1

Our data start from 73, 74,,75,76,78,79,80

So according to the given data 73 is the lower limit and 80 is the upper limit

The range interval of the given data is {73,80]

and range for 2

in  term 2 the lower limit is 74 so our range  is [74,80]

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We can therefore find the other angle of right angle triangle by

Pythagoras , then x = 142 - y   and    y = 142 - x

A fundamental theorem in geometry that deals with the sides of a right triangle is known as the Pythagorean theorem. In it, it is said:

a+ b² = c²

where the lengths of the right triangle's legs are a, b, and c, and the length of the hypotenuse (the side across from the right angle) is c

Nevertheless, if we know the other two, we can use the fact that the total of the angles in a triangle is always 180 degrees to determine one of the angles. We are aware that angle C in this situation is 38 degrees.

We thus have:

x + y + 38 = 180

Calculating x and y results in:

x = 142 - y

y = 142 - x

We can therefore find the other angle if we know the value of one. To determine the real figures, we still want further details.

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The number of committees with 4 members can be formed from a group of 10 people are 210 different committees

To find the number of different committees with 4 members that can be formed from a group of 10 people we can use the combination formula which is,

nCr = n!/r!(n-r)!

where:

nCr = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

from the given data:

n = 10

r = 4

From the above formula, we can write the equation as:

= 10C4

=C(10,4)

= 10! / (4! * 6!)

= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)

= 210

Therefore, 210 different committees with 4 members can be formed from a group of 10 people.

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An independent samples t-test would be appropriate to analyze the difference in running speed between rats that received a steroid drug supplement and those that did not.

The appropriate statistical test to analyze the difference in running speed between two groups of rats (one receiving a steroid drug supplement and one not receiving it) would be a t-test. Specifically, an independent samples t-test would be suitable for this type of comparison, assuming that the data meets the assumptions for parametric testing.

This test would compare the means of the two groups and assess the probability that the observed difference is due to chance alone. A significant result would indicate that the difference in running speed is unlikely to be due to chance and is instead likely to be a true effect of the steroid drug supplement

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Answer:

(a) = 0.92
(b) = 0.7613

Step-by-step explanation:

Here are some information to help us answer these problems:

Given That:

P(A) = 0.69
P(B) = 0.23

Then,

Problem (a): P(A ∪ B) when, A ∩ B = ∅:

P(A ∪ B) = 0.69 + 0.23 - 0 = 0.92



Problem (b): P(A ∪ B) when, A ∩ B ≠ ∅:

P(A ∪ B) = 0.69 + 0.23 - (0.69 × 0.23) = 0.7613




I hope you find this easy to understand....

Have any questions? Write in the comments.

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According to Benford's law, 5 will be the first digit of a random number set is d. less often than 4.

According to Benford's law, which is an empirical law about the frequency distribution of leading digits in many real-life collections of numerical data, the digit 5 is actually the second least frequent leading digit after 1 and is less common than 4 as a first digit. In actuality,

Benford's rule states that the likelihood of a number having four as its first digit is nearly thirty percent, whereas the likelihood of a number having 5 as its first digit is approximately 25%. This is due to the fact that numbers with smaller starting digits are more common than those with bigger leading digits in many naturally occurring datasets.

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(12, 23)  are the coordinates of the center of the rectangle with coordinates (6, 38) and (18, 8).

To find the coordinates of the center of the rectangle in the standard (x, y) coordinate plane, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are:

((x₁ + x₂) / 2, (y₁ + y₂) / 2)

In this case, the opposite vertices of the rectangle have coordinates (6, 38) and (18, 8). We can use these coordinates to find the midpoint of the rectangle as follows:

The x-coordinate of the midpoint is (6 + 18) / 2 = 12.

The y-coordinate of the midpoint is (38 + 8) / 2 = 23.

Therefore, the coordinates of the center of the rectangle are (12, 23)

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The  expression that makes the equation true is A)40 ÷ (5 x 2) x 17.55.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here first solve given expression then,

=> 13.5 x (1.2 + 4) = 13.5×1.2+13.5×4 = 70.2

Now solving option expressions then,

A) 40 ÷ (5 x 2) x 17.55 = 40÷10×17.55 = 4×17.55 = 70.2

B) 36 ÷ (4.8 − 2.6) x 3 = 36÷2.4×3 = 45

C) 22 x (3.6 − 1.2) + 4 = 22×(2.4)+4 = 56.8

D) 18 ÷ (3 x 3) x 35.2 = 18÷ 9×35.2 = 2×35.2 = 70.4

Hence the  expression that makes the equation true is A)40 ÷ (5 x 2) x 17.55.

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Answer: To solve this problem, we can use trigonometry and the relationship between angle, distance, and altitude in a right triangle.

Let's denote the angle the pilot was flying at takeoff as θ. We can then use the tangent function to find θ, since:

tan(θ) = opposite/adjacent

In this case, the opposite side is the altitude the pilot reached (1500 feet), and the adjacent side is the distance the pilot traveled before reaching that altitude (2 miles = 10560 feet). So we can plug in these values and solve for θ:

tan(θ) = 1500/10560

θ = tan⁻¹(1500/10560)

θ ≈ 7.67 degrees

So the pilot was flying at an angle of approximately 7.67 degrees at takeoff from the runway.

Step-by-step explanation:

There are various techniques to simplify algebraic expressions, including:

1. Combining like terms: In an algebraic expression, like terms are terms that have the same variable raised to the same power. To simplify the expression, we can combine these like terms. For example, in the expression 3x + 2y + 5x - 4y, we can combine the x terms and the y terms to get 8x - 2y.

2. Distributing: When a number or variable is outside a set of parentheses and is being multiplied by a sum or difference inside the parentheses, the number or variable can be distributed to each term inside the parentheses. For example, in the expression 3(x + 2), the 3 can be distributed to both x and 2, resulting in the simplified expression 3x + 6.

3. Simplifying exponents: When an expression contains exponents, rules of exponentiation can be used to simplify the expression. For example, in the expression x^2 * x^3, the exponents can be added to give x^(2+3) = x^5.

4. Factoring: When an expression contains common factors, those factors can be factored out. For example, in the expression 2x^2 + 4x, both terms have a factor of 2 and a factor of x, so these factors can be factored out to give 2x(x + 2).

The area of the base (B) to be 15.588 cm², the height of the prism (h) to be 22 cm, and the volume (V) of the prism to be 343.996 cm³.

Area is a measure of the size of a two-dimensional surface or shape. It is measured in square units such as square meters (m2), square centimeters (cm2), square kilometers (km2), and square miles (mi2). Area can also be calculated for three-dimensional shapes, such as cubes and spheres, by multiplying length, width, and height. For example, the area of a cube with sides of length 10 cm would be 1000 cm2. Area is an important concept in mathematics and has many practical uses in real life.


Base Area (B):
To calculate the area of the base, we use the formula for the area of an equilateral triangle: B = (√3/4) × a², where a is the side length.

In this case, a = 6 cm. Therefore, B = (√3/4) × 6² = 15.588 cm².

Height (h):
The height of the prism is the height of the triangle (12 cm) plus the height of the floor (10 cm). Therefore, h = 12 cm + 10 cm = 22 cm.

Volume (V):
The volume of the prism is equal to the area of the base times the height of the prism. Therefore, V = B × h = 15.588 cm² × 22 cm = 343.996 cm³.

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First thing you need to do is raise the decimal. Once you've raised the decimal then you should continue through the problem as if it were a standard long division question.

Start with the first number which is 6.

6 divided by 3 is 2. That means you can subtract 6 from the first number.

Then, you bring down 3 and do the same thing.

3 divided by 3 is 1. Subtract 3 from 3 and then bring down the next number.

Finally, 3 divided by 9 is three.

By following this process, you should get 2.13 as your final answer.

Look at the image below for more reference.

Answer:

x=56

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

x = 56

Step-by-step explanation:

Given that-

x/7 - 4 = 4

x/7 - 4 + 4 = 4 + 4                 >> Add 4 to both sides

x/7 = 8                

7x/7 = 8 × 7                             >> Multiply both sides by 7

x = 56

Check Answer-

Substitute x in the equation the check.

56/7 - 4 = 4              >> 56/7 = 8

8 - 4 = 4                  >> 8 - 4 = 4

4 = 4                        >> Correct

RevyBreeze

The probability that the mean yield of the 80 one acre plots chosen will be within 2 bushels of the population mean is 0.9332. The assumptions made to answer part (a) are that the population standard deviation is known, the sample is randomly selected, and the sample size is large (n>=30)

a) We can use the central limit theorem to approximate the distribution of the sample mean. The distribution of the sample mean can be approximated as a normal distribution with a mean of 107 bushels and a standard deviation of 12/√80=1.34 bushels. Therefore, we can find the probability that the sample mean falls within 2 bushels of the population mean using the standard normal distribution.

P(105 ≤ X ≤ 109) = P(Z ≤ (109-107)/1.34) - P(Z ≤ (105-107)/1.34)

= P(Z ≤ 1.49) - P(Z ≤ -1.49)

= 0.9319 - 0.0681

= 0.8638

Therefore, there is an 86.38% probability that the mean yield of the 80 one acre plots will be within 2 bushels of the population mean.

b) Assumptions made:

The sample of 80 one acre plots is selected at random.

The one acre plots are independent of each other.

The population standard deviation is known and remains constant.

The distribution of the yield of corn per acre is approximately normal.

The sample size is large enough (n≥30) to apply the central limit theorem.

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Answer:

Step-by-step explanation:

Using the distributive property, we can simplify the expression as follows:

3(r+2) + 5(r+t-2)

= 3r + 3(2) + 5r + 5t - 5(2)

= 3r + 6 + 5r + 5t - 10

= 8r + 5t - 4

Therefore, the simplified expression is:

8r + 5t - 4