What is the equation of a cubic function whose roots are 4,3 and -3 and goes through the point (2,20)
Write answer in the form
Y=a(x-x1)(x-x2)(x-x3)

His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

Two or more expressions with an Equal sign is called as Equation.

Sheldon wants to buy two shirts at the store.

They were each originally $14.99, but one of the shirts is on sale this week for 10% off.

A 6% sales tax is applied to the total cost of the shirts.

0.90 • 14.99 + 14.99 • 1.06 = n

The first term in the equation, 0.90 • 14.99, represents the cost of the shirt that is on sale.

The 10% discount is applied to the original price of $14.99, which is why we multiply by 0.90.

This term calculates the discounted price of the first shirt.

The second term in the equation, 14.99 • 1.06, represents the cost of the second shirt, plus the 6% sales tax that is applied to both shirts.

This term calculates the total cost of the second shirt with sales tax.

Hence, His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

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Using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

The entire amount or sum of the two whole numbers is obtained by adding them.

The process of addition involves combining two or more numbers to determine their sum.

Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.

For instance, 7 + 7 equals 14.

So, we can get the total time using addition as follows:

= 0.6 + 2.4 + 5.2 + 1.4 + 1.8

= 11.4 hours

Therefore, using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

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Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).

As h gets smaller, the distance between the two points gets smaller.

The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = sin(x) using first principles, substitute f(x + h) = sin(x + h) and f(x) = sin(x) into the formula:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x+h)-\sin(x)}{(x+h)-x}\right][/tex]

Use the sin addition formula to expand sin(x + h).

[tex]\boxed{\sin(A + B) = \sin A \cos B + \cos A \sin B}[/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)+\cos(x)\sin(h)-\sin(x)}{(x+h)-x}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)-\sin(x)+\cos(x)\sin(h)}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)+\cos(x)\sin(h)}{h}\right][/tex]

Separate the sin(x) and cos(x) terms into two fractions:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)}{h}+\dfrac{\cos(x)\sin(h)}{h}\right][/tex]

When h gets really small, we can use the small angle approximation to rewrite cos(h).

[tex]\boxed{\cos (h) \approx 1-\dfrac{1}{2}h^2}[/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(1-\dfrac{1}{2}h^2-1\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(-\dfrac{1}{2}h^2\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]

Cancel the common factor, h:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[-\dfrac{1}{2}h\sin(x)+\cos(x)\right][/tex]

As h → 0, the first term → 0:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]

Answer:

range = 33

Step-by-step explanation:

the range of a data set is the difference between the largest and smallest values in the set.

largest value = 163 and smallest value = 130 ( from diagram ), then

range = 163 - 130 = 33

f is increasing on (-infty, -4) and (2,infty) since that's where you'd be walking uphill.

f is never decreasing.

f is constant on (-4,2), since that's where it's completely flat.

The company’s revenue (R) from a particular distributor that buys x units is R(x) = 8999.93x

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Given:

original price = $9000 per unit.

let the number units bought be x

then amount= 9000x.

If the price reduces the list price by seven cents times the number of units bought .

7cents= 0.07 dollar

Then,

R(x) = 9000x - 0.07x

R(x) = 8999.93x

Hence, R(x) = 8999.93x.

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The mean, variance, and standard deviation of this sample is 377.5, 7007.5 meters^2 and 83.7 metres respectively. The 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters. we find that the p-value for a t-statistic of -3.61 is less than 0.01.

To calculate the mean, variance, and standard deviation of this sample, we can use the following formulas:

Using the formulas, we get:

Mean = (365 + 350 + 380 + 400 + 395 + 375 + 385 + 380 + 390 + 370 + 360 + 370 + 380 + 370 + 400 + 385 + 375 + 385 + 380 + 375) / 20

= 377.5 meters

Variance = [(365-377.5)^2 + (350-377.5)^2 + (380-377.5)^2 + ... + (380-377.5)^2 + (375-377.5)^2] / (20-1)

= 7007.5 meters^2

Standard deviation = square root of variance = sqrt(7007.5) = 83.7 meters

Therefore, the mean skidding distance is 377.5 meters, the variance is 7007.5 meters^2, and the standard deviation is 83.7 meters.

To estimate the true mean skidding distance of the road with a 95% confidence interval, we can use the following formula:

Confidence interval = sample mean ± (t-value * (standard deviation / sqrt(sample size)))

Here, the sample mean is 377.5 meters, the standard deviation is 83.7 meters, and the sample size is 20. To find the t-value, we need to look it up in a t-distribution table with 19 degrees of freedom. From the table, we find that the t-value for a 95% confidence interval is 2.093.

substituting the values, we get:

Confidence interval = 377.5 ± (2.093 * (83.7 / sqrt(20)))

= 377.5 ± 37.0

Therefore, the 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters.

The assumptions needed for this inference to be valid are:

The sample is a random sample from the population of skidding distances along the road.

The skidding distances follow a normal distribution in the population.

The sample size is large enough (at least 30) or the population standard deviation is known.

To check these assumptions, we can use a normal probability plot to check for normality and calculate the sample size to see if it is large enough. We can also use previous studies or expert knowledge to check if the assumption of normality is reasonable.

To test the logger's claim that the mean skidding distance is at least 425 meters, we can perform a one-sample t-test. The null hypothesis is that the mean skidding distance is 425 meters, and the alternative hypothesis is that it is less than 425 meters.

Using the formula for the t-statistic, we get:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

= (377.5 - 425) / (83.7 / sqrt(20))

= -3.61

From a t-distribution table with 19 degrees of freedom, we find that the p-value for a t-statistic of -3.61 is less than 0.01. Therefore, we reject the null hypothesis and can conclude that there is not enough evidence to support the logger's claim. Therefore, we do not agree with the logger's claim.

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Using commutative and associative properties of addition, the solution for given expression is -5.

What is commutative and associative property?

The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.

These properties tell that one can add in any order, the result will always be the same.

We are given an expression as 8+(-8-5).

So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.

Hence, the solution for given expression is -5.

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Answer:

Step-by-step explanation:

(1/3) x 81=27 people

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the solution:

Calculate the government deposit: For every $1.00 you deposit, the government deposits $2.00. So if you deposit the maximum of $100.00 each month, the government deposit would be $100.00 * $2.00 = $200.00.

Calculate the total deposit each month: The total deposit each month is the sum of your deposit and the government deposit, so it would be $100.00 + $200.00 = $300.00.

Calculate the number of months: You started with $100.00 and made the maximum deposit of $100.00 each month for 5 years. Five years is 5 * 12 = 60 months.

Calculate the total deposit over 5 years: Over 5 years, you made 60 deposits of $300.00 each, so the total deposit over 5 years would be 60 * $300.00 = $18,000.00.

Calculate the final balance: Adding the initial deposit of $100.00 to the total deposit over 5 years, the final balance in your account after 5 years would be $18,000.00 + $100.00 = $18,100.00.

So, at the end of 5 years, if you deposited the maximum of $100.00 each month into the College Savings fund, you would have $18,100.00 in your account.

The length of the caple is √3125 cm. (option C)

The caple and the tower would form a right triangle. The caple would be the hypotenuse. The tower would be the length and the distance from the base of the tower would be the base.

In order to determine the length of the caple, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where:

c² = 25²  + 50 ²

c² = 625 + 2500

c² = 3125

c= √3125 cm

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A.) f(x-2)+f(2x)

To find this expression, we can substitute the definition of f(x) into the expression and simplify:

f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]

= 10x - 20 - 4 + 20x - 4

= 30x - 28

Therefore, f(x-2)+f(2x) = 30x - 28.

Given f(x) = 10x - 4, we need to find f(2a) - f(a).

f(2a) = 10(2a) - 4 = 20a - 4

f(a) = 10a - 4

Therefore,

f(2a) - f(a) = (20a - 4) - (10a - 4)

= 10a

Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.

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Answer:

Step-by-step explanation:

To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.

This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:

OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2

Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.

If a poll is to be conducted in an elementary school by interviewing 50 students, the following samples have been described as either representative or not representative as follows:

a. The first 50 students leaving the cafeteria. Not representative

b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. Representative

c. Ten students randomly chosen from each of the 5 areas of campus. Representative

d. Five students from 10 teachers' classes. Representative

A representative sample is a small collection from a larger group from which any information obtained will be as good as the larger group. While choosing a representative sample, the researcher should take care not to zone the participants from a given section of the population. This will cause the information to be skewed and not objective.

Selecting 50 students leaving a cafeteria will not be representative because this might only represent a section of the school that will be giving their response based on a certain mood.

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The solution is:  (A) y+4=-3(x+6), is the equation of the line in point-slope form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:

y-y1 = m (x-x1)

Given the point:

(x1,y1) = (-6, -4)

Slope, m= -3

x1 = -6,

y1 =-4

Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:

we get,

y+4=-3(x+6)

The correct option is A.

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complete question:

The graph of a line has a slope of -3 and passes through the point (-6,-4).

What is the equation of the line in point-slope form?

Oy + 4 = -3(x + 6)

y + 6 = -3(x + 4)

y-4 = -3(x-6)

y-6 = -3(x – 4)

Answer:

The correct answer is D. 7 pounds.

Step-by-step explanation:

The weight of the baby when its born is 7 pounds.

The positive angle which is less than 360 degrees and is co-terminal with -305 as required is; 55°.

It follows from the task content that the position angle which is co-terminal with -305° as required is to be determined.

Let the positive angle in discuss be; x.

Therefore, the angle x = 360 + (-305)

Consequently, it can be calculated as follows;

x = 360 - 305.

x = 55°

Hence, the required value of the positive co-terminal angle is; 55°.

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The quotient and remainder, written as partial fractions, of 15x²+52x+43/3x²+5x-8 would be  A/(3x + 8) + B/(x - 1) where A is -8/3 and B is 1.

What in mathematics is a partial fraction?

The fractions that are utilized to break down a rational expression are called partial fractions.

                     Any component of an algebraic expression that is divided into a sum of two or more rational expressions is referred to as a partial fraction.

15x²+ 52x + 43/3x²+5x-8

15x²+52x +43/3x² + ( 8 -3)x - 8

15x²+52x +43/3x² + 8x -3x - 8

15x²+52x +43/3x(x - 1) +8(x - 1 )

15x²+52x +43/(3x + 8)(x -1 )

A/(3x + 8) + B/(x - 1)

To find the value of A;

3x + 8 = 0

x = -8/3

To find the value of B;

x - 1 = 0

x = 1

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No, the marked price of $73.25 is not correct.

To calculate the sale price, we start by multiplying the original price by the discount percentage:

$95.00 * 0.25 = $23.75

This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:

$95.00 - $23.75 = $71.25

Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.

Given the information that the average of the ages of 5 women is 47 years and that their ages are 48, y, 52, 50, and (2y-5), we can set up the following equation:

(48 + y + 52 + 50 + 2y - 5) / 5 = 47

Expanding the equation and simplifying, we get:

5y = 244

y = 48.8

So the age of the woman whose age is represented by the variable y is 48.8 years.

The oldest woman is represented by the age of 52 years, which is the largest of all the ages.

Therefore, the age of the oldest woman is 52 years.

The numbers can be arranged as follows

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

Applying the sequence the to make the expression 1 2 3 4 5 6 7 8 9 equal to 30 using addition and subtraction signs:

(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30

You can use parentheses to group the numbers and then add or subtract the groups to get the desired result.

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The exact measure of an angle whose measure is 18° in radians is; pi over 10.

Recall, it follows from angle measurements that;

π radians ==== 180°

Hence, it follows from proportion that the measure of 18° in radians, x can be determined as follows;

x = 18 π radians / 180

x = π / 10 radians.

Ultimately, the required measure of 18° in radians as required is; π / 10.

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Step-by-step explanation:

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Answer:

C = 60t + 100

Step-by-step explanation:

our flat fee is 100 dollars, meaning you're charged straight up $100, and then for each hour the electrician works, you're charged another $60

this means that 100 stays constant, while the amount of times you multiply 60 changes based on the amount of hours the electrician works

therefore, our equation will be C = 60t + 100, where C represents the total cost while t represents the hours the electrician works

for our table, we can use the equation we just found to make one

the easiest and most reasonable numbers will be 1, 2, 3, 4, and 5, because it's unreasonable to charge a proportional amount for something such as 1.2948 hours

using the equation, we plug 1, 2, 3, 4, and 5 into C = 60t+100 to find C for t

C = 160, 220, 280, 340, 400

T = 1, 2, 3, 4, 5

Answer:a rectangular prism has  height  4m, length 6m & width 5m

thus the surface consist of two  4*6 vertical surfaces

                                          two 4*5 vertical surfaces

                                        & two 6*5 top & bottom surfaces

that is

            2(4*6) =  48

            2(4*5) =  40

            2(6*5) =  60

total surface area =  48+40+60 = 148m²

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) We can find the position vectors of the points L, M, and N by taking the average of the position vectors of the points they lie between.

The midpoint of AB is given by:

N = (A + B)/2 = (41 + (41 + 21))/2 = (41 + 62)/2 = 51.5i

The midpoint of AD is given by:

L = (A + D)/2 = (41 + 6k)/2 = 23i + 3k

The midpoint of BD is given by:

M = (B + D)/2 = (41 + 21 + 6k)/2 = 31i + 3.5k

Now, we can find the vector MN by subtracting the position vectors of M and N:

MN = M - N = (31i + 3.5k) - (51.5i) = -20.5i + 3.5k

The angle between the directions of MN and OB can be found using the dot product:

cos(θ) = (MN . OB) / (|MN| * |OB|)

where θ is the angle between the two vectors. We can find the dot product and the magnitudes of the vectors as follows:

MN . OB = -20.5i + 3.5k . 41i + 21j = -20.5 * 41 + 3.5 * 21 = -847.5

|MN| = √((-20.5)^2 + (3.5)^2) = 21

|OB| = √(41^2 + 21^2) = √(1764) = 42

Substituting these values into the formula for cos(θ), we get:

cos(θ) = (-847.5) / (21 * 42) = -0.5

The angle θ can be found from the cosine inverse:

θ = cos^-1(-0.5) = 120 degrees

So, the angle between the directions of MN and OB is 120 degrees.

(b) To find the value of p, we can use the intersection of the lines through P and B and the lines through C and L. Let's call the intersection point R.

The line through P and B can be represented as P + t(B - P) = R

where t is a scalar and R is the position vector of the intersection point. Similarly, the line through C and L can be represented as:

C + s(L - C) = R

where s is a scalar. Setting these two expressions equal to each other, we get:

P + t(B - P) = C + s(L - C)

Expanding and simplifying, we get:

P + t(41i + 21j + 6k) = 21i + 6s(23i + 3k)

Comparing the i, j, and k components, we get:

P + 41t = 21 + 6s * 23

t = (21 - P)/41

6s = (P - 21)/23

s = (P - 21)/138

Substituting s back into the equation for C + s(L - C), we get:

C + (P - 21)/138 * (L - C) = R

21i + 6k + (P - 21)/138 * (23i + 3k - 6k) = R

Expanding, we get:

21i + 6k + (23/138) * Pi + (3/138) * k = R

Comparing the i and k components, we get:

21 + (23/138) * P = Ri

6 + (3/138) * P = Rk

Solving for P, we get:

P = 138 * (Ri - 21)/23 = 138 * (Rk - 6)/3

So the value of p for which the line through P and B intersects the line through C and L is given by the above formula.

Answer: god

Step-by-step explanation: god god god god god god god god

Option A:  Both functions are positive and decreasing on the interval.

The table shows that f(x) decreases when x increases in the interval (0,7) and (0, 3)

All the values of f(x) are positive in the interval (0,3).

For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.

Also all the values of f(x) are positive in the interval.

Then, both functions are positive and decreasing in the interval.

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Answer:

You will pay 81.25

Step-by-step explanation:

If the cost is 35% off, you will need to pay 100% - 35% = 65%

125 * 65 %

125 *.65

81.25

You will pay 81.25