What is the simplified form of this expression? (4x2-3x+8)-(2x² + 2x - 5) 4x²-5x + 13 2x²5x+3 2x²-x+3 2x²-5x + 13

Answer: 325

Step-by-step explanation:

723 -73 =650 divided by 2

Hope this helps

The correct options are

B.) GJ / MP = GH / MN

C.) ∠H≅∠N

By using the property of similarity of triangles, We get

The corresponding sides of the similar triangles are proportional to each other and the corresponding angles are congruent to each other.

So, given △GHJ∼△MNP  

⇒ GH/MN = HJ/NP = GJ/MP , and

∠G ≅ ∠M , ∠H ≅ ∠N , ∠J ≅ ∠P........(1)

The given options are :

A.) m∠J=m∠P

B.) GJ / MP = GH / MN

C.) ∠H≅∠N

D.) HJ ≅ NP

E.) GH=MN

Now, from equation (1)

The correct options are

B.) GJ / MP = GH / MN

C.) ∠H≅∠N

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The probability of getting a queen if a card is drawn out from a pack of 52 cards is 1/13

Probability is the chance of an event to occur with respect to the given conditions.

Probability of an event P(E) = number of favorable outcomes (n)/total number of outcomes(N)

P(E) = n/N

Total cards in a pack (N) = 52

Number of queens (n) = 4

P(getting a queen from pack of cards) = Number of queens/Total cards in a pack

P(E) = n/N

P(E) = 4/52

P(E) = 1/13

Hence, the probability of the given event is 1/13.

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Answer:

9

Step-by-step explanation:

8x - 4x = 36

4x = 36

x = 36/4 = 9

Answer:

9

Step-by-step explanation:

8n-4n=36

n=9

8(9)-4(9)=36

The best count on the tuition axis will be $5,000.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The senior counselor is making a histogram of the yearly cost of tuition of 20 colleges.

And, Tuition ranges from $5,000 to $51,000 a year.

Now,

Since, Tuition ranges from $5,000 to $51,000 a year.

And, There are 20 colleges.

Hence, We get;

The best count on the tuition axis will be $5,000.

Thus, he best count on the tuition axis will be $5,000.

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The difference between the total amount of bags of box tops collected by 4th grade to 5th grade is 2 (1/16). Option D

The given parameters that will help us to get the difference are

The fractions,  

We shall be solving the fractions in pars then later we find the difference.

[4 3/12 +5 5/16 +3 3/8} -  {3 1/4 +4 1/2 + 3 1/8}  

Simplify by find the  LCM of each side

[12{12+15+18}/48 ] - {10 (2+4+1)/8

Simplify to get

12 (45/48)   - 10[7/8]

subtracting the fractions to have

2 [45 - 42]/48

Making it more simpler to get

2 1/16

Therefore the difference between the two fractions is 2 1/16

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If a function is defined as z = f(x), then the inverse of the function f is x = f-1 (x) i.e. f-1 defined from z to x.

In mathematics, function is an expression that explains the relationship between the variable and other variable. In this expression, one variable is independent and the other is dependent. unction and into function.

There are four types of functions. There is one to one function, many to one function, onto function, one to one and onto function.

Inverse function refers to the expression where the original output becomes the opposite.

These are the expressions used in mathematics to solve the problems and equations. In other fields of science, inverse function is also used.

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Answer:

-33/35

Step-by-step explanation:

turn mixed fraction into an improper fraction

-2 1/5 = -11/5

times both fractions

(a) The point estimate of the population variance is 400

(b) According to the 90% confidence interval, the population variance is 152 ≤ σ² ≤ 800

(c) According to the 90% confidence interval, the population standard deviation is 23.8 ≤ σ ≤  41.1

Standard deviation

in probability, standard deviation refers the measure of how dispersed the data is in relation to the mean.

Given,

Here we know that because of staffing decisions, managers of the a certain hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 25 days of operation shows a sample mean of 300 rooms occupied per day and a sample standard deviation of 20 rooms.

Here we need to find the following.

a)  Here the point estimate of the population variance is calculated as,

=> Square of S = S²

The value of S is 20

=> 20² = 400

b) As per the confidence interval, the population variance is calculated as,

n = 20

S² = 400

Then the variance is

=> (n-1)s²/0.05  ≤ σ² ≤  (n-1)s²/0.95

When we apply the values on the equation, then we get

=>  (20-1) x 400/0.05  ≤ σ² ≤  (20 - 1) x 400/0.95

Variation 152 ≤ σ² ≤ 800

c) Finally, the Standard Deviation is calculated as,

=> 23.8 ≤ σ ≤  41.1

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Answer:

The answer is option (C). Four Rivers Bank

Explanation:

a). The total amount Jane will receive after 5 years after investing $40,000 in the Mystic Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

A = the future value of the initial investment

P = initial investment amount/principal amount

r = the annual interest rate

n = the number of times that interest is compounded per unit t

t = the time the money is invested for

In our case;

P=$40,000

r=12/100=0.12

n=interest is compounded quarterly which is four times a year=4

t=5 years

Replacing values in the formula;

A=40,000(1+0.12/4)^(4×5)

A=40,000(1+0.03)^20

A=40,000×1.806

A=72,244.45

The total amount Jane will receive after 5 years if she chooses to invest with the Mystic Bank is $72,244.45

b). The total amount Jane will receive after 5 years after investing $40,000 in the Four Rivers Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

P=$40,000

r=14/100=0.14

n=interest is compounded semiannually which is two times a year=2

t=5 years

Replacing values in the formula;

A=40,000(1+0.14/2)^(2×5)

A=40,000(1+0.07)^10

A=40,000×1.967

A=78,686.05

The total amount Jane will receive after 5 years if she chooses to invest with the Four Rivers Bank is $78,686.05

c). The best deal would be to invest with Four Rivers Bank for 5 years since the total amount Jane will receive after 5 years will be $78,686.05 which is greater than $72,244.45, which is the total amount she will receive if she chooses to invest with Mystic Bank

The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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Answer:

12d+12m+3a+6c

Step-by-step explanation:

distribute 3 by multiplying

The translation rule that maps A(-4, -2), B(-2, 6) and C (4, 4) to A' (-2, -2) B' (0, -10) and C' (6, -8) is

(x + 2, y + 4)

The transformation rule is solved by comparing the both preimage and image transformations as follows

preimage  image

A(-4, -2)   A' (-2, -2)

B(-2, 6)     B' (0, -10)

C (4, 4)     C' (6, -8)

x direction

-4 + x = -2, x = -2 + 4 = 2

-2 + x = 0, x = 0 + 2 = 2

4 + x = 6, x = 6 - 4 = 2

y direction reflection on the x axis leads to change of sign

preimage  image

A(-4, -2)   A' (-2, 2)

B(-2, 6)     B' (0, 10)

C (4, 4)     C' (6, 8)

-2 + y = 2, y = 2 + 2 = 4

6 + y = 10, y = 10 - 6 = 4

4 + y = 8, y = 8 - 4 = 4

The transformation rule is (x + 2, y + 4)

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Single transformation maps ABC onto A'B'C' is reflection.

Given :

Reflection the single  transformation maps ABC onto A'B'C' is reflection .

The rigid transformations can map triangle Δ ABC onto triangle Δ FED is reflection then translation .

The rigid transformations that will map Δ ABC to Δ DEF is rotation then translation .

pair of triangles can be proven congruent by the HL theorem is rotation then translation .

rigid transformation S can map Triangle abc onto Triangle dec is reflection then rotation .

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Only twice or less, according to 40% of respondents. Suppose the researchers are curious about the percentage of the population that would respond that it was two or less times, in which case the test statistic would be -0.208 and the standard deviation would be 0.048.

H0: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is equal to or greater than 0.5.

Ha: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than 0.5.

Set the alpha level

α = 0.05

Calculate the test statistic

n = 618 (women only)

p = 0.4 (from Table 3)

Standard Deviation = sqrt[p*(1-p)/n]

Standard Deviation = sqrt[0.4*(1-0.4)/618]

Standard Deviation = 0.048

Test Statistic = (0.4 - 0.5) / 0.048

Test Statistic = -0.208

Step 4: Make a decision

Since the test statistic (-0.208) is less than the alpha level (0.05), we reject the null hypothesis and conclude that the population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than

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An odd degree polynomial with a negative leading coefficient would have endpoint behavior of "as x approaches -∞, y approaches ∞ and as x approaches ∞, y approaches -∞.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² - 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The leading coefficient and the degree of the monomial n have an impact on the final behavior.

The function behaves the same at both "ends" when n is even. They both either approach + ∞ or they both approach depending on the sign of the leading coefficient.

The behaviour of the function at both "endpoints" is the reverse when n is odd. Which one is +∞and which one is depends on the sign of the leading coefficient.

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Answer:

A ≈ 154 units²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius)

to calculate the area we require to know r

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

given

x² + y² + 4x - 8y - 29 = 0

collect x and y terms together and add 29 to both sides )

x² + 4x + y² - 8y = 29

obtain standard form for circle using the method of completing the square

add ( half the coefficient of the x/ y terms)² to both sides

x² + 2(2)x + 4 + y² + 2(- 4)y + 16 = 29 + 4 + 16

(x + 2)² + (y - 4)² = 49 = r² ← in standard form

Then

A = πr² = π × 49 ≈ 154 units² ( to the nearest whole unit )

It's True because zero cannot divided by any number it is undefined.

In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0, where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by 0, gives a (assuming a ≠ 0); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst

It's True because zero cannot divided by any number it is undefined.

let us consider

x = 3

and y =0

x/y = 3/0 = undefined

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The length of each Plan A workout will be 1.25 hours and the length of each Plan B workout will be 1.25 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let 'x' be the number of hours of plan A and 'y' be the number of hours of plan B. Then the equations are given as,

2x + 6y = 10

x + 3y = 5            ...1

5x + 3y = 10        ...2

Subtract equation 1 from equation 2, then we have

5x - x = 10 - 5

4x = 5

x = 1.25 hours

Then the value of 'y' is calculated as,

1.25 + 3y = 5

3y = 3.75

y = 1.25

The length of each Plan An exercise will be 1.25 hours and the length of each Plan B exercise will be 1.25 hours.

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No, we do not have enough information to find out the percentage of Americans who either do not follow football or do not follow basketball. We would need to know the percentage of Americans who do follow both sports.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.

The percent sign (%), which denotes a division by 100, is used. Therefore, 25% translates to 25/100, or 1/4. Dividing by 100 will change a percentage to a decimal. Therefore, 25% is equal to 25/100, or 0.25. A decimal can be multiplied by 100 to become a percentage (just move the decimal point 2 places to the right)

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Heteroscedastic residuals will have roughly the same variance for any value of X. Hence:

The correct option is C.

Hetero means that they are different/vary. Homoscedastic would mean that they do not change as the value of x changes.

When the variance of the residuals is uneven throughout a range of measured values, this is referred to as heteroskedasticity. The analysis results may be flawed if heteroskedasticity is present and the population employed in the regression has unequal variance.

One presumption regarding the residuals/errors in OLS regression is that they have the same, but unmeasured, variance. The term "constant variance" or "homoscedasticity" refers to this. Heteroscedasticity is the issue when this presumption is broken.

Hence we get the required answer.

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The time is taken by the substance to decay, if A radioactive substance decays according to [tex]A = A_o \times e^{-0.0037t}[/tex] Where A₀ is the initial amount and t is the time in years. If A0=740 grams is  185.18 years.

Atoms in radioactive materials naturally decay. They are capable of emitting gamma radiation, beta radiation, and alpha radiation. They cannot be turned off, so controlling them is more challenging than controlling X-ray sources.

Given:

The initial amount, A₀ = 740 g,

The final amount, A = 373 g,

Calculate the time by using the formula given below,

[tex]A = A_o \times e^{-0.0037t}[/tex]

373 = 740 [tex]\times e^{-0.0037t}[/tex]

[tex]e^{-0.0037t}[/tex] = 373 / 740

[tex]e^{-0.0037t}[/tex] = 0.504

Taking log on both sides,

㏑ 0.504 - ㏑ 0.0037 = t

t = 185.18

Therefore, the time taken by the substance to decay if A radioactive substance decays according to A=A0e−0.0037t, where A0 is the initial amount and t is the time in years. If A0=740 grams is 185.18 years.

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The product of first ten prime number is 6.67*10^9 and the number of zeros are nine.

A zero is formed by the product of 2 and 5. Thus, to find the number of zeroes, we have to find the number of 2s and 5s in 10! We see that there are 8 twos and 2 fives. Since forming a 0 requires a 2 and a 5, only 2 zeroes will be there at the end of 10!

The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29

The multiplication of these number is 2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9

The number of zeros are nine.

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Equations have two complex solutions if their discriminant is negative. So, option A is the correct answer.

In algebra, the discriminant of any equation is a quantity that is used to find out about the nature of the roots using the formula = b²-4ac. It tells us if there are no solutions, one solution, or two.

Here, we have been told that the discriminant is negative.

From the formula, we can say that = D = b²-4ac < 0.

Here, if D<0, then x becomes an imaginary value. This means that the roots are going to be imaginary i.e., complex. Thus, the two roots that we get as a result of the formula are both going to be complex.

So, option A is the answer.

The complete that you might be looking for is given below.

If the discriminant of an equation is negative, which of the following is true of the equation

A. it has two complex solutions

B. it has one real solution

C. it had two real solutions

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Answer:

a.two complex solutions

Step-by-step explanation:

The value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]

What is Combination of Function ?

The domain of an arithmetic combination of functions f and g consists of all real numbers that are common to the domains of f and g.

Given expression,

f(x) = 4x + 1

g(x) = √x

Now, find (f · g)(x)

(f · g)(x) = f( g(x) )

Next, insert the value of g(x) in f(x) value by replacing x value in f(x)

(f · g)(x) = 4 ( √x ) + 1

            = 4√x + 1

Next, find (g · f)(x)

(g · f)(x) = g( f(x) )

Now, insert the value of f(x) in g(x) value by replacing x value in g(x)

(g · f)(x) = √4x + 1

            = [tex]\sqrt{4x+1}[/tex]

Hence, the value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]

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6/11 is the probability that a randomly selected student speaks French, given that the student is male

It is a branch of mathematics that deals with the occurrence of a random event.

There are 11 members who speak french and 5 are females in 11 members

5/11

p(a given b) = p(a and b) / p(b).

6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40

probability that a person speaks french is 11/40

p(a given b)=6/40/11/40

=6/40×40/11=6/11

Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.

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Proving  that the maximum spanning tree of g contains the widest paths between every pair of vertices .

Suppose now we were to add an edge from the widest path into the spanning tree in a place that it won't cause a cycle.

so every path between our two nodes must contain some edge between two previously unconnected nodes.

The weight of the edge we removed was equal to the width of the original path, and because the path was that every edge in the new path must have had more weight than that edge.

This means that our new spanning tree must have strictly more total weight than the original, which contradicts the definition of the original 'maximum' spanning tree.

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m= 9.

[tex]0.4(20 - 10m) = 2.5 - 2m - 12.5[/tex]

[tex](0.4)(20)-(0.4)(10m)= 2.5 - 2m - 12.5\\ \\(8)-(4m)= 2.5 - 2m - 12.5\\ \\8-4m= 2.5 - 2m - 12.5[/tex]

[tex]8-4m-8= 2.5 - 2m - 12.5-8\\ \\-4m=2.5-2m-20.5\\ \\-4m=-2m-18[/tex]

[tex]-4m+2m=-2m-18+2m\\ \\-2m=-18[/tex]

[tex]\frac{-2m}{-2} =\frac{-18}{-2} \\ \\m=9[/tex]

[tex]0.4(20 - 10(9)) = 2.5 - 2(9) - 12.5\\\\0.4(20 - (90)) = 2.5 - (18) - 12.5\\ \\0.4(-70) = -28\\ \\-28=-28[/tex]

That's correct. Therefore, m= 9 is the correct answer!

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

The solution for the inequality -5n < -15 is n < 3.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

-5n < -15

Divide both sides by -5.

n < -15/-5

n < 3

This means,

n is greater than 3.

We can represent this on a number line.

<-------__-1__0__1__2__3__4__5__6__7------>

                                          o------------------->

Thus,

The solution for the inequality -5n < -15 is n < 3.

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