For the polynomial –2m2n3 2m?n3 7n2 – 6m4 to be a binomial with a degree of 4 after it has been fully simplified, which must be the missing exponent on the m in the second term?

In conclusion Since the coefficient a can be any nonzero constant, there are infinitely many possible graphs of f(x) that satisfy the given conditions.

How to find?

Since the zeros of the polynomial function are 3 - i/4 and 3 + i/4, we know that the function can be factored as:

f(x) = a(x - 3 + i/4)(x - 3 - i/4)

where a is a constant.

To simplify the expression, we can multiply the two factors in the parentheses:

f(x) = a[(x - 3)²2 - (i/4)²2]

Now, we can use the fact that i²2 = -1 to simplify further:

f(x) = a[(x - 3)²2 + 1/16]

This is the vertex form of a quadratic function with vertex (3, 1/16) and minimum value 1/16. Since the coefficient a can be any nonzero constant, there are infinitely many possible graphs of f(x) that satisfy the given conditions.

To know more about graph related question visit:

https://brainly.com/question/17267403

#SPJ1

The interest that is charged on the past six months of the investment period could be obtained by the use of the interest formula.

The term interest refers to the money that accrues on an investment or the money that is charged on top of a loan. The interest could be simple (charged only on the principal) or compound (charged on both the principal and the interest).

Thus, the interest that is charged on the past six months of the investment period could be obtained by the use of the interest formula.

Learn more about interest:https://brainly.com/question/13324776

#SPJ4

The difference between the compound interest and simple interest for 7 years is $3,944.72 or approximately $3,944.73.

We have to calculate the difference between the compound interest and simple interest for 7 years. The principal amount is $3,000, and the interest rate is 9%. The formula for simple interest can be represented as,

I = Prt

where I is the simple interest, P is the principal amount, r is the rate of interest, and t is the time taken.

The interest for one year using simple interest will be,

I = Prt = $3,000 × 0.09 × 1 = $270

So, the interest for 7 years using simple interest will be $270 × 7 = $1,890.

The formula for compound interest can be represented as,

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

where A is the amount, P is the principal amount, r is the rate of interest, t is the time taken, and n is the number of compounding periods.

The interest for 7 years using compound interest will be,

A = $3,000(1 + 0.09/1)^(1 × 7) = $5,834.72

The interest Lori will receive in the 7th year with compound interest can be calculated as follows:

Amount for 6 years = $3,000(1 + 0.09/1)^(1 × 6) = $5,178.38

Amount for 7 years = $3,000(1 + 0.09/1)^(1 × 7) = $5,834.72

Interest for 7th year with compound interest = $5,834.72 - $5,178.38 = $656.34

The interest for 7 years using simple interest is $1,890.

The interest for 7 years using compound interest is $656.34 + interest for the first 6 years.

Interest for 6 years using compound interest,

A = $3,000(1 + 0.09/1)^(1 × 6) = $5,178.38

The total interest for 7 years using compound interest is $5,178.38 + $656.34 = $5,834.72.

The difference between the compound interest and simple interest for 7 years is $5,834.72 - $1,890 = $3,944.72, which is the answer.

However, it is not one of the options. So, we need to round it off to the nearest cent.

The difference rounded to the nearest cent is $3,944.73 - $3,944.72 = $0.01

Hence, the difference between the compound interest and simple interest for 7 years is $3,944.72 or approximately $3,944.73.

Learn more about simple interest visit:

brainly.com/question/30964674

#SPJ11

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer:

6

Step-by-step explanation:

24 x 1/4

=24/4

=6

its 6

The gamma distribution with parameters $\alpha$ and $\beta$ is a probability distribution that can be derived using the transformation $x = \beta y$.

The probability density function of the gamma distribution is:

f(x; α, β) = \frac{(\beta x)^{\alpha - 1} e^{-\beta x}}{\Gamma(\alpha)}

where $\alpha$ is the shape parameter and $\beta$ is the rate parameter.

The derivation is as follows:

* The gamma function is defined as:

Γ(α) = \int_0^{\infty} x^{\alpha - 1} e^{-x} dx

* Using the transformation $x = \beta y$, we get:

Γ(α) = \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* We can then write the probability density function of the gamma distribution as:

f(x; α, β) = \frac{1}{\Gamma(\alpha)} \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* This is the same as the probability density function of the gamma distribution with parameters $\alpha$ and $\beta$.

The mean and variance of the gamma distribution can be found using the following formulas:

E(X) = \alpha \beta

Var(X) = \alpha \beta^2

to learn more about probability click here:

brainly.com/question/29221515

#SPJ11

Answer:

8- pound box

Step-by-step explanation:

We can use unit rates to solve this problem.

8 lbs : $7.40 = 1 lbs : $0.925

4 lbs : $5.38 = 1 lbs : $1.345

Answer:

Mr. Reed still needs to run 7 5/12 miles to reach his Step-by-step explanation:

2 3/4 and 2 1/3 need to be converted to a common denominator of 12:

2 9/12 and 2 4/12

Then we need to convert the original 12 1/2:

12 6/12

Add the miles he's already run:

2 9/12 + 2 4/12 = 5 1/12

Subtract the total amount run from the total goal:

12 6/12 - 5 1/12 = 7 5/12

Therefore, he still needs to run 7 5/12 miles to meet his total 12 1/2 (or 12 6/12) miles goal.

Answer: z should equal 17 or 2

Step-by-step explanation: assuming this is related to angles, and they are supplementary, you need to do 6z+1+77=180 the answer would be 17, if the angles are complimentary you need to do 6z+1+77=90 and the answer is 2

Answer:

60.3504

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

well, one quarter of a year is 3 months, so at the end of third quarter, 9 months have passed, and since a year has 12 months, 9 months are simply 9/12 of a year.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$960\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases}\)

\(A=960\left(1+\frac{0.07}{4}\right)^{4\cdot \frac{3}{4}}\implies A=960(1.0175)^3\implies A\approx 1011.29\)

Answer:

V = 96.16

Step-by-step explanation:

Formula:

V = πr²h

r = d/2 = 1.75

V = 3.14(1.75)²10

V = 96.16

Answer:

$13,766.70

Step-by-step explanation:

Since he paid 56% with the scholarship, that means $6,057.35 is 44% of the total tuition

To find the total cost of tuition, divide 6,057.35 by 0.44

6,057.35/0.44

= 13766.70

So, the cost of Parker's tuition was $13766.70

At D-Luxe Detailing, teams of employees, the expression, f(5) < 5 told us that employees service five cars in less than five hours . So, option(b) is right answer.

A function is defined as a kind of rule that gives us one output for an input . If we put something for x, we get one output valur for f(x) . We would say that f(x) is a function of x since x is the input value.

We have , At D-Luxe Detailing has a team of employees who carefully wash and detail customers' cars. The function , f(x) represents the total hours which employees spend to wash x cars i.e. f(x) denotes time in hours. Now, the expression is f(5) < 5, here x= 5 that is number of car washed by employees is equals to five. but f(5) < 5 that value of f(x) is less than 5 when we input x = 5 . So, this expression told us that five cars are washed by employees in less than 5 hours.

To learn more about function, refer:

https://brainly.com/question/11624077

#SPJ4

Complete question:

At D-Luxe Detailing, teams of employees carefully wash and detail customers' cars. The

function f(x) gives the total number of hours they spend servicing x cars.

What does f(5) < 5 tell you?

a)In 5 hours, the employees service less than 5 cars.

b) The employees service 5 cars in fewer than five hours.

c)The employees service 5 cars in under 5 hours.

Answer:

The correct answer would be B! -7

Answer: 2.95x+39.95(12)

Step-by-step explanation:

Hi, to answer this question we have t write an expression with the information given:

The yearly cost for x movie rentals is equal to : the product of the cost of each movie (2.95) and the number of movies (x) ;plus the product of the monthly fee (39.95) and the number of months in a year (12)

Mathematically speaking:

2.95x+39.95(12)

Answer:

D-295x+39.95(12)​

Step-by-step explanation:

EDG2021

Answer:

7

Step-by-step explanation:

5x4=20

20/2=10

17-10=7

Answer:

your answer is 7

Step-by-step explanation:

17-5×4÷2

P- parenthesis

E- Exponents

M- Multiplication

D- Divide

A- Add

S- Subtract

Answer:

In explanation

Step-by-step explanation

Ok for me to tell you I'm going to give an example.

Data set=

40,50,60,30,105,19,40

For this data set our mode would be 40 because mode is the number that appears most in a data set and as you can see 40 appears twice while every other number only appears once.

For median=would also be 40.

Because median is the number that is in the middle when you sort them least to greatest so 40 is in the middle when you put them in least to greatest.

The maximum is 105

Because the maximum is the highest number in the data set so 105 is the biggest number.

Range is 86.

For range is the highest number subtracting the lowest number and highest number is 105 and lowest number is 19 so 105 - 19=86

Hope this helps have a great day:)

Using the master theorem, the time complexity of the given recurrence relation T(N) - 9T(N/9)+N(IgN) has been found. The answer is T(n) = Θ(nlogb(a)) = Θ(n * log n), which implies that the time complexity is of O(nlog n).

For the given recurrence relation, T(n) - 9T(n/9)+N(IgN), we have to find the time complexity using the master theorem, which is given below:

Master Theorem:

Consider a recurrence relation T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1 and f(n) is an asymptotically positive function. Then, we have the following cases:

Case 1: If f(n) = O(nᵏ) for some constant k < logb(a), then T(n) = Θ(nlogb(a)).

Case 2: If f(n) = Θ(nᵏlogm(n)) for some constant k = logb(a), then T(n) = Θ(nᵏlog(m+1)n).

Case 3: If f(n) = Ω(nᵏ) for some constant k > logb(a), and if a.f(n/b) ≤ cf(n) for some constant c < 1 and sufficiently large n, then T(n) = Θ(f(n)).

In the given recurrence relation, we have a = 9, b = 9 and f(n) = n * log n.

Comparing a with bᵏ, we get a = bᵏ.

∴ k = 1

Taking log with base 9 on both sides, we get:

log₉T(n) = log₉(9T(n/9) + n * log n)log₉T(n) = log₉9 + log₉T(n/9) + log₉n * log₉log(n)log₉

T(n) = 1 + log₉T(n/9) + log₉n * log₉log(n)For f(n) = n * log(n), nᵏ = n¹, so k = 1 > 0.

Therefore, according to master's theorem, T(n) = Θ(n * log n).

Using the master theorem, the time complexity of the given recurrence relation T(N) - 9T(N/9)+N(IgN) has been found. The answer is T(n) = Θ(nlogb(a)) = Θ(n * log n), which implies that the time complexity is of O(nlog n).

To know more about recurrence relation visit:

brainly.com/question/32732518

#SPJ11

The private spilled 0.35 litres of fuel

The first step is to convert 6.5 hectolitres to litres

= 6.5 × 100

= 650 litres

Next is to convert millilitres to litres

= 350/1000

= 0.35 litres

Hence the number of litres spilled is 0.35 litres

Read more here

https://brainly.com/question/18239674?referrer=searchResults

#SPJ1

To evaluate each integral in terms of areas, we need to understand that the integral represents the area under the curve of a function, f(x), between two points on the x-axis.

Let's discuss each integral:

(a) ∫₀⁸ f(x) dx: This represents the area under the curve of f(x) from x = 0 to x = 8. The integral calculates the accumulated area along this interval.

(b) ∫₀²⁰ f(x) dx: Similarly, this represents the area under the curve of f(x) from x = 0 to x = 20. It's a broader interval than (a), so it covers more area under the curve.

(c) ∫²⁰²⁸ f(x) dx: This integral represents the area under the curve of f(x) between x = 20 and x = 28. It's important to note that the interval is now shifted to the right compared to (a) and (b).

(d) ∫¹²²⁸ f(x) dx: This integral calculates the area under the curve of f(x) from x = 12 to x = 28. The interval here is larger than in (c), covering more area under the curve.

(e) ∫¹²²⁸ |f(x)| dx: This integral evaluates the area under the absolute value of f(x) from x = 12 to x = 28. The absolute value ensures that negative function values contribute positively to the area calculation, preventing any cancelation of areas.

(f) ∫₀⁸ f(x) dx: This integral is the same as (a), representing the area under the curve of f(x) from x = 0 to x = 8.

Each integral evaluates the area under the curve of f(x) for different intervals on the x-axis, providing insights into the total accumulated area in those intervals.

To learn more about function  click here

brainly.com/question/12431044

#SPJ11

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

To learn more about angles click here:

brainly.com/question/22891563

#SPJ11

Answer:

the answer to this question is 11

The cash back you would receive on your purchases of $2,738.21 using this credit card is $33.92.

To calculate the cash back you would receive using the given credit card, we need to multiply the total amount spent in each category by the corresponding cash back percentage, and then add up those amounts.

For gas purchases, you spent $134.92, so the cash back earned on that amount would be:

$134.92 x 3% = $4.05

For grocery store purchases, you spent $384.23, so the cash back earned on that amount would be:

$384.23 x 2% = $7.68

For all other purchases, you spent a total of:

$2,738.21 - $134.92 - $384.23 = $2,219.06

So the cash back earned on that amount would be:

$2,219.06 x 1% = $22.19

Adding up the cash back earned in each category, we get:

$4.05 + $7.68 + $22.19 = $33.92

∴ Cashback = $33.92

To learn more about amount click here

brainly.com/question/26082270

#SPJ1

Answer:

$75

Step-by-step explanation:

If their bill is $55 and they leave a $20 tip that's pretty much adding 20 +55

so $20 + $55 dollars is $75.

I hope that helped.

Answer: $75

Step-by-step explanation:

Add the tip to the bill to get the total.

$55 + 20 = $75

Answer:

x = -∛115

Step-by-step explanation:

x^3 - (-115) = 0

= x^3 + 115

Factoring

(a+b) • (a^2-ab+b^2) =

   a^3-a^2b+ab^2+ba^2-b^2a+b^3 =

   a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=

   a^3+0+0+b^3=

   a^3+b^3

(115 isn't a cube.)

Polynomial roots

P: -1, -5, -23, -115, 1, 5, 23, 115

Q: 1

P/Q: -1, -5, -23, -115, 1, 5, 23, 115

Divisor(s): None

In these sets of data, there are no rational roots shown.

Step-by-step explanation(part 2):

x^3 + 115 = 0

x^3 = -115

x  =  ∛-115

Negative numbers will always have real cube roots.

∛ -115 = ∛ -1 × 115  = ∛ -1 × ∛ 115 = (-1) × ∛ 115

Therefore,

x = -∛115

4 hours is the time the drama club spend doing dress rehearsals.

Fraction is represented as the part of the whole.

Fractions are used to depict that the components of a whole or group of items. Two components make up one fraction. The numerator is the number that appears at the top of the represented  line. It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the given line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed.

We need to find 10% of 40 hours:

10%*40

Convert 10% to a fraction, as I find it makes the math simpler. To do this, we can simplify put 10 over 100 as any percentage is that number over 100:

\(\frac{10}{100}\) × 40

Simplify the fraction:

\(\frac{1}{10}\) × 40 = \(\frac{40}{10}\) = 4

They spent 4 hours doing dress rehearsals.

To learn more about fraction, visit:

https://brainly.com/question/10354322

#SPJ1

The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

To know more about corresponding  visit:

brainly.com/question/31493107

#SPJ11