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Real roots and distinct roots are the two types of roots of quadratic function.

Given,

Real roots;-

We are aware that anytime we resolve a linear or quadratic equation, we obtain the equation's value variable, or in other words, we identify the equation's solution. We refer to this "solution" as the real roots. For instance, when we solve the equation x27x+12=0, the real roots come out to be 3 and 4.

Distinct roots;-

Whenever the answers to a quadratic equation have two distinct values that may be represented by real numbers on a number line. It is known as distinct roots.

Here,

How do you tell which roots are distinct and real?

The discriminant is the expression b² - 4ac for the quadratic equation ax² + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b² - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b² - 4ac = 0.

That is,

The quadratic function has real roots and distinct roots.

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Total number of permutations of abcde in which the first character is a, b, or c and the last character is c, d, or e is 48 permutations.

Case 1 : First letter is "a", last letter is any of {c, d, e}. Hence there are 3!  ways of arranging the remaining three letters

3! * 3 = 18 combinations.

Case 2 : First letter is "b", last letter is any of {c, d, e}. Hence there are 3!  ways of arranging the remaining three letters

3! * 3 = 18 combinations.

Case 3 : First letter is "c", last letter is any of {d, e}. Hence there are 3! ways of arranging the remaining two letters

3! * 2 = 12 combinations.

Hence, total number of combinations = 18 +18 + 12 = 48 permutations.

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Mean from a frequency table is when we find the mean average from a data set which has been organised into a frequency table.

To calculate the mean we find the total of the values and divide the total by the number of values. The number of values is the total frequency.  This can be abbreviated to nn.

[tex]Mean = \frac{total}{number of values} =\frac{total}{n}[/tex]

We can use an extra column to help.

Mean is a measure of central tendency, it is a value that can be used to represent a set of data.  

E.g. The frequency table shows the number of people living in 1616 flats.

There are 55 flats with 11 person living there, so we work out 1\times5=51×5=5

There are 66 flats with 22 people living there, so we work out 2\times6=122×6=12

There are 33 flats with 33 people living there, so we work out 3\times3=93×3=9

There are 22 flats with 44 people living there, so we work out 2\times4=82×4=8

The number of values (n)(n) is the total frequency, here n=16n=16

mean = total/n

         =34/16

         = 2.125

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The smallest sample size that will satisfy the conditions for the use of a normal model to represent the sampling distribution is 30, as stated in option (a).

The smallest sample size that will satisfy the conditions for the use of a normal model to represent the sampling distribution is determined by the Central Limit Theorem, which states that if the sample size is greater than or equal to 30, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

According to this theorem, if the sample size is greater than or equal to 30, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. Therefore, the smallest sample size that will satisfy the conditions for the use of a normal model is 30. The answer is therefore option (a).

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The ratio that describes the number of baskets the player made to the number of baskets the player attempted is 9:15. This can be simplified to 3:5.

The ratio of the number of baskets made by the player to the number of baskets attempted is 9/15. This ratio can be simplified to 3/5, which means that for every 5 baskets attempted, the player made 3 baskets. This ratio can also be expressed as a percentage by dividing the number of baskets made by the number of baskets attempted and multiplying the result by 100%. In this case, the percentage of baskets made by the player is 60% (9 baskets made / 15 baskets attempted * 100% = 60%). This means that out of every 100 baskets attempted by the player, he made 60 baskets.

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The probability of an individual scoring above 500 on the GMAT is 0.5984.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the centre of the range.

Given:

[tex]\mu[/tex] = 527

[tex]\sigma[/tex] = 112

Now, z= (500-527)/112

z= -27/112

z= -0.2410

and, P( X>500)= P(z> -0.2401)

                        = 1- 0.4052

                        = 0.5984

Hence, the probability of an individual scoring above 500 on the GMAT is 0.5984.

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The given data (2, 2, 3, 3, 4, 4, 5, 5, 6, 6) has no mode.

A mode is defined as the value that has the highest frequency in a given set of values. It is the value that appears the most number of times.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.

The mode is the value that occurs the most often in a given set of data.

Given data:  2, 2, 3, 3, 4, 4, 5, 5, 6, 6.

In the given observations, data is repeated an equal number of times.  

So, the given data has no mode.

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Conscientiously cleaning your devices is crucial, as any residue that remains on your device may impact the accuracy of your measurements. The material your device is made of plays a significant role in the cleaning method you should use.

A tool used to measure a physical amount is called a measuring instrument. Measurement is the process of gathering and comparing physical quantities of actual things and events in the physical sciences, quality control, and engineering.

The process of measuring yields a number associating the subject under study and the referenced unit of measurement, and established standard objects and occurrences are employed as units. These numerical relations are acquired using measuring devices and rigorous test procedures that specify the instrument's use.

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Answer:

a. 1350

b. 6500

Step-by-step explanation:

1.5%×4500=5850

1350+4500=5850

Step-by-step explanation:

Bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Now, According to the question:

The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Standard Equation

The standard form to find the value of X in multiplication operation is

Multiplicand × Multiplier = Product

Let us take Multiplier as x,

Multiplicand × x = Product

Then the formula to find the value of x is

X = product / Multiplicand

Example of how to find the value of x.

Find the value of x for the given expression: 10x = 50

Given: 10x = 50

X = 50/10

X = 5

Therefore, the value of x is 5.

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In this given equation, any value of x and y will work, which will cause it to have infinite number solutions

What is an equation?

An equation is a mathematical statement showing that two or more values or mathematical expressions are equal or equivalent.

We represent an equation with the equation symbol (=).

Given the equation:

3x + 2y = 5

The lineear equation has infinitely many solutions

We know the standard form of a linear equation is:

ax + by = C

In this given equation, any value of x and y will work, which will cause it to have infinite number solutions

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The standard form of the polynomial function with zeroes 1, 2, -2, and -3 is

[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The zeroes of a polynomial:

x = 1, 2, -2, and -3.

This can be written as,

(x - 1)(x - 2)(x + 2)(x + 3) = 0

Simplify to get the equation.

(x² - 2x - x + 2)(x² + 3x + 2x + 6) = 0

(x² - 3x + 2)(x² + 5x + 6) = 0

[tex]x^4[/tex] + 5x³ + 6x² - 3x³ - 15x² - 18x + 2x² + 10x + 12 = 0

[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0

Thus,

The equation of the polynomial is [tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.

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Answer:

the answer is 20

Step-by-step explanation:

20+0=20

Mean and Median are not the same.

Mean is the average value of a given dataset. Mean is calculated by adding all the values in the dataset and divided by the number of values.

Median is defined as the number in the middle of the dataset. Median is calculated by arranging the values in ascending order and finding out the middle most term. If there are two middle terms, then we calculate the average of both.

Mean is the arithmetic average, while median is the positional average. There may be various external factors that contribute in defining the mean. So for uneven data, median is the more robust value. Mean defines the central value of data, but median defines the midpoint of data and classify the data points to two sets, higher value or lower value.

So mean is the average of the given dataset and Median is the mid value of the dataset when arranged in ascending order.

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Answer:

Division

Step-by-step explanation:

Simple, the fraction bar basically represents the operation of division in math!

Answer:

13

Step-by-step explanation:

39/3

Answer:

The solution to the system of equations is x = 9/12 and y = 27/60.

Step-by-step explanation:

To solve a system of equations, we can use elimination or substitution. In this case, we can use elimination by adding the equations together. When we add the two equations, the y-terms will cancel out, leaving us with an equation in terms of x only.

First, let's add the equations:

-5y + 3x = 3

-8y + 9x = -12

-----------

-13y + 12x = -9

Then, we can divide both sides of the equation by -13 to get the value of x:

(-13y + 12x) / -13 = (-9) / -13

12x = 9

x = 9/12

Since we know the value of x, we can substitute it back into either of the original equations to find the value of y:

-5y + 3(9/12) = 3

-5y + 27/12 = 3

-5y = -27/12

y = 27/60

Therefore, the solution to the system of equations is x = 9/12 and y = 27/60.

According to the SSS disbursement account, it takes 2 business days for approval.

The term disbursement refers to the payment of federal student aid funds to the student by the school.

Here we have to find the number of days taken for SSS disbursement account approval.

In order to find the solution, we must know the process of SSS disbursement policy, that takes the payment data and transforms it into a disbursement instrument.

Here we have given that, as per the SSS disbursement policy, it takes member-borrower shall receive the full short-term loan proceeds in their account within two banking days from the loan date provided the payment instruction of SSS was sent before the cut-off time.

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Answer:

l = 2w   (length is twice the width)

P = 2l + 2w

54 = 2l + 2w  (but we know l equals 2w so we can replace l with 2w)

54 =2(2w) + 2w

54 = 6w

w = 9

l =2(9)   (l = 2w

l=18

A = lw

g(x)=-x^2 is the reflection of your function f(x) over the x-axis.

What is function?

The function f(x)=x2 is a parabola facing upward with its vertex at (0,0), and including the points (1,1), (2,4), (-1,1), and (-2,4).

A function that is a reflection across the x-axis compared to f(x) would be the mirror image of f(x). It would have the opposite y-values for each x-value. It would also have its vertex at the same place as f(x).

Therefore, it would be a parabola pointing downward, with the points (1, -1), (2,-4), (-1,-1), and (-2,-4).

To get the opposite values for y, you simply need to place a negative in front of the x2. So the function would be g(x) = - x2.

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Answer:

total number of votes = 5696

Step-by-step explanation:

the 5 part of the ratio relates to 3560 no votes , then

3560 ÷ 5 = 712 ← value of 1 part of the ratio , then

3 × 712 = 2136 ← number of yes votes

total number of votes = yes + no = 2136 + 3560 = 5696

Yes, you can use the Side-Side-Angle (SSA) Congruence Theorem to prove that two triangles are congruent.

The SSA Congruence Theorem states that if two sides of one triangle have the same length as two sides of another triangle, and the included angle in the first triangle is congruent to the included angle in the second triangle, then the two triangles are congruent.

Here is an example of how you can use the SSA Congruence Theorem to prove that two triangles are congruent:

Let's say you have two triangles, triangle ABC and triangle DEF. You are given that the length of side AB is equal to the length of side DE, the length of side AC is equal to the length of side DF, and angle A is congruent to angle D.

To prove that triangle ABC is congruent to triangle DEF, you would need to show that all of the corresponding parts of the triangles are congruent. Since the lengths of two sides (AB and DE) and the included angle (angle A and angle D) are congruent, you can use the SSA Congruence Theorem to conclude that triangle ABC is congruent to triangle DEF.

It's worth noting that the SSA Congruence Theorem is not always sufficient to prove that two triangles are congruent. If the conditions of the theorem are not met, you may need to use other methods, such as the ASA Congruence Theorem or the HL Congruence Theorem, to prove congruence.

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Without using a calculator, the square root of an integer is

1. Use multiplication to calculate the ideal square root.

2. Use division to calculate the ideal square root.

3. Use nearest perfect square number to find the square root of non-perfect squared numbers.

Given that,

We need to figure out how to calculate a number's square root without a calculator.

We know that,

There are some ways to find

First

Use multiplication to calculate the ideal square root.

A number that, when multiplied by itself, equals the first number is the number's square root.

3 is therefore the square root of 9.

Because 3 multiply by 3 is 9

That is 3×3=9

√9=3

Second

To calculate the square root, we use division.

A whole number can also be divided by a number until you get an answer that is the same as the number you used to divide the whole number in order to determine its square root.

For instance: Four is the square root of sixteen.

Because 16 divided by 4 is 4

That is 16÷4=4

√16=4

Third

We must compare the number with a nearly perfect squared number in order to determine the square root of non-perfect squared numbers.

For example: the square root of 63 is not a perfect square.

So,

The closest perfect square integer right now is 64, and its square root value is 8.

So, we can say the square root of 63 as 7.98.

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The height of the yield sign is 15.5 inches.

The total amount of space allotted to a triangle's three sides in a two-dimensional plane is known as the area of a triangle. The fundamental formula for a triangle's area is A = [tex]\frac{1}{2}*b*h[/tex], which states that the area of a triangle is equal to half the product of its base and height.

To find the height of the yield sign, we need to use the following formula, which is:

area= length*height

The result of substituting in the data we are aware of is:

558=36*h

h= [tex]\frac{558}{36}[/tex]

h= 15.5

Therefore the height of a standard yield sign when the area is 558 square inches and each side is 36 inches is 15.5 inches.

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A binomial expression is of the form (x + y)ⁿ. The given binomial expression (2x + 3)⁵ has 6 terms in it.

Binomial is said to be the algebraic expression containing exactly two terms.

Examples of binomials are 4x² + 5y², xy² + xy, x + y, x² + 3, etc.

The number of terms in the binomial expression (x + y)ⁿ is given as,

Number of terms = n + 1

where, n is the power of ( x + y )

In the above given binomial expression, (2x + 3)⁵, n = 5.

N = n + 1 = 5 + 1 = 6

Thus, there are a total of 6 terms in the above expansion.

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Answer:

14: 15 or 2: 15 pm

Step-by-step explanation:

1/2 times 60 = 30 minutes

2 1/2 hours = 2 hours and 30 minutes

Take

11:45

+ 2:30

13:75

1 hour only has 60 minutes, so 13:75 = 14:15 or 2:15 pm

So, his appointment was at 2:15 pm

The steps of the  step method are:

Problem solving is an essential skill in life. It helps us to find solutions to difficult situations and can be applied to almost any area of life. One effective way to approach problem solving is to use the 4-step method. This method is designed to help you analyze a situation, plan an action, execute the plan, and evaluate the results. In this essay, we will discuss the benefits of using the 4-step method to solve problems.

The first step of the 4-step method is to analyze the situation. This involves identifying the problem and its causes. Taking the time to understand the problem before attempting to solve it can help ensure that the solution is effective. By analyzing the situation, you can determine the most effective solution and avoid wasting time and resources on ineffective solutions.

The second step of the 4-step method is to plan an action. This involves developing a plan of action to address the problem. Taking the time to plan ahead can help ensure that the solution is tailored to the specific situation. It can also help to minimize the risk of unexpected problems or delays during the execution of the plan.

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Answer:

i believe it is G

[tex] \frac{7}{3} [/tex]

The statement is "a car wash operator wants to see if offering a discount to local residents would create a greater income." This is an observational study.

A method of study in which participants are observed or certain outcomes are measured. There is no attempt made to change the outcome (for example, no treatment is given).

Experimental investigations include introducing an intervention and observing its results. Experimental investigations are frequently randomized, which means that the individuals are assigned to groups at random. People who qualify are randomly allocated to one of two or more groups in a randomized controlled experiment (RCT).

Cohort studies, case-control studies, and cross-sectional studies are the three different kinds of observational research.

In an observational study, the researchers just observe the participants without interfering with them or attempting to sway the results. In other words, neither the researchers nor the individuals are placed in experimental groups or in charge of the therapies.

Thus, the above mentioned statement is an observational study.

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As the standard deviation 35 is high so the values are far from the mean.

In the statistics, standard deviation is an estimation that implies how far each available data apart from mean value. In a word, it is a measure of variances of data in relation to the mean. A low standard deviation indicates that values are closer to mean value and high standard deviation indicates the values are distributed widely.

Standard deviation of a given data set 35 means that all data set are 35 unit far from the mean value. As the value is high so all the values are dispersed widely relative to the mean value.

In the other hand, this high standard deviation implies there are enough variances in the given data in relation to the mean.

Standard deviation is one of the measures of risk assessment. Imagine an organization published a number of statistical observation data. If we find a high standard deviation, then it will be high risk of collapse of the business.

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