Can someone please help me with this question please

Answer:

  y = 1/8x +1/64

Step-by-step explanation:

You want the equation of the line that is tangent to the curve y = x³ -x⁴ in exactly two places.

Since the tangent line is not crossed, the difference between the line and the given curve is a 4th-degree polynomial with two roots, each of multiplicity 2. If those are 'a' and 'b', we can write for line y = mx +p, ...

  mx +p -(x³ -x⁴) = (x -a)²(x -b)² = 0

  x⁴ -x³ +0x² +mx +p = x⁴ -2(a+b)x³ +(a²+4ab+b²)x² -2ab(a+b)x +a²b²

Equating coefficients, we have ...

The coefficient of x³ tells us ...

  a +b = 1/2

The coefficient of x² tells us ...

  0 = (a +b)² +2ab

  0 = (1/2)² +2ab

  ab = -1/8

Using these value, we can find the equation of the line to be ...

  m = -2ab(a+b) = -2(-1/8)(1/2) = 1/8

  p = (ab)² = (-1/8)² = 1/64

The equation of the line is ...

  y = 1/8x +1/64

__

Additional comment

To find the line, we did not need the coordinates of the points of tangency. They are ((1-√3)/4, (3-2√3)/64) and ((1+√3)/4, (3+2√3)/64).

The slope of the line is equal to the slope of the quartic at the point of inflection of its derivative, at x=1/4.

Answer:

$2160

Step-by-step explanation:

Area of a rectangle = Length * Width

A = L * W

Divide both sides by width

W/(A = L * W)/w

[tex]\frac{A}{W} = L[/tex]

Plug in values

[tex]\frac{384}{24} =16[/tex]

Multiply Length and width to find perimeter

2W + 2L = P

plug in values

2(24) + 2(16) =  80

Multiply perimeter by cost per foot

1yd = 3ft

80yd * 3ft = 240ft

240ft * $9 = $2160

In this equation, the regular polygon's area is 72.5.

The area of a regular polygon is determined by multiplying its perimeter by its apex. The following is a common way to write the formula: An apothem's area is equal to 1/2(ap), where a denotes the length and p the circumference. Area of pentagon = 1/2 p an is the fundamental formula for computing the area of a regular pentagon, where p stands for the pentagon's perimeter and a for its apothem.

If a polygon has equal sides and angles, it is considered to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

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Answer:

x=10.

Step-by-step explanation:

4x = 3x + 10

4x - 3x = 10

x = 10

Answer:

To find the final price for the jacket, we need to first calculate the amount of the discount and then add the sales tax.

The amount of the discount is $65.00 * 40% = $26.00. So the price after the discount is $65.00 - $26.00 = $39.00.

The sales tax is $39.00 * 5% = $1.95. So the final price for the jacket is $39.00 + $1.95 = $40.95.

Step-by-step explanation:

Answer:

he final price for the jacket is $40.95.

Step-by-step explanation:

First, let's calculate the discount for the jacket:

Discount = $65.00 * 40% = $26.00

The price of the jacket after the discount is:

$65.00 - $26.00 = $39.00

Next, let's calculate the sales tax:

Sales tax = $39.00 * 5% = $1.95

Finally, let's add the sales tax to the discounted price to find the final price:

Final price = $39.00 + $1.95 = $40.95

So, the final price for the jacket is $40.95.

Answer:

20

Step-by-step explanation:

[tex]\sqrt[3]{64xy^{3}}[/tex] = [tex]\sqrt[3]{64}[/tex] × [tex]\sqrt[3]{x}[/tex] × [tex]\sqrt[3]{y^{3}}[/tex]

a = coefficient

  = [tex]\sqrt[3]{64}[/tex]

∴a = 4

[tex]x^{b}[/tex] = [tex]x^{-2}[/tex]×[tex]\sqrt[3]{x}[/tex]

   = [tex]x^{-2}[/tex]×[tex]x^{\frac{1}{3}}[/tex]

   = [tex]x^{-2+\frac{1}{3}}[/tex]

   = [tex]x^{\frac{-6}{3} + \frac{1}{3}}[/tex]

   = [tex]x^{\frac{-6+1}{3}}[/tex]

[tex]x^{b}[/tex] = [tex]x^{-\frac{5}{3}}[/tex]

∴b = [tex]-\frac{5}{3}[/tex]

[tex]y^{c}[/tex] = [tex]y^{-4}[/tex]×[tex]\sqrt[3]{y^{3}}[/tex]

   = [tex]y^{-4}[/tex]× [tex](y^{3})^{\frac{1}{3}}[/tex]

   = [tex]y^{-4}[/tex] × [tex]y[/tex]

   = [tex]y^{-4 + 1}[/tex]

[tex]y^{c}[/tex] = [tex]y^{-3}[/tex]

∴c = [tex]-3[/tex]

∴Product of a, b and c = [tex](4)[/tex]×[tex](-\frac{5}{3})[/tex]×[tex](-3)[/tex]

                                      = 20

You made a profit of $382.50 from selling the 45 shares of the telecommunications company.

First we need to determine the total cost of purchasing those shares, and then subtract that from the total revenue from selling them.

The total cost of purchasing the 45 shares at a price of $63.00 per share is:

45 shares x $63.00 per share = $2,835.00

The total revenue from selling the 45 shares at a price of $71.50 per share is:

45 shares x $71.50 per share = $3,217.50

To calculate the profit, we subtract the cost from the revenue:

Profit = Revenue - Cost

Profit = $3,217.50 - $2,835.00

Profit = $382.50

Therefore, you made a profit of $382.50 from selling the 45 shares of the telecommunications company.

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The points are scattered in the scatterplot and thus, a line would not be appropriate because the points follow a nonlinear pattern.

Hence, option b is the correct answer.

Numerous different kinds of associations between two variables can be found using a scatterplot.

When there is no pattern visible in the points on a scatterplot, a relationship has no correlation.

When the points on a scatterplot exhibit a pattern rather than a straight line, a relationship is non-linear.

When the points on a scatterplot exhibit a largely straight line pattern, a relationship is linear. We shall look at this relationship in detail.

From the given graph we observe that the points do not follow a linear pattern.

The points are scattered and thus, a line would not be appropriate because the points follow a nonlinear pattern.

Hence, option b is the correct answer.

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The correct question is:

a.) The number of students that are over 145cm = 13

b.) The number of students with the height between 125 cm and 140 cm = 21 students.

C.) The number of students that were in class = 37

A frequency table is defined as a statistical tool that is used to organize the data given so that it makes it more meaningful and easier to understand.

To calculate the number of students that are over 145cm = 8+4+1 = 13 students.

To calculate the number of students that had a height

between 125 cm and 140 cm = 2+5+6+8 = 21 students.

To calculate the number of students that were in class= 3+2+5+6+8+8+4+1 = 37 students.

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Answer:

Percentage of adults = 80%

Number of adults = 2000

Step-by-step explanation:

Percentage of men = 2/5 x 100 = 40%

Percentage of women = 2/5 x 100 = 40%

Percentage of adults = 40+ 40= 80%

If there are 2500 people, then number of adults
= 2500 x 80%

= 2500 x 80/100

= 2000 adults

Answer:

=58%

Step-by-step explanation:

If rate of 5.8% = 1 day

than ? = 10 days

therefore 10/1 × 5.8%

= 10 × 5.8

= 58%

To the nearest whole number

= 58%

The required value of x is equivalent to 30 units.

The state of likeness can be referred to as a similarity. When two elements, things, ideas, or people resemble one another, they are said to be similar. Example: In terms of the number of sides, a square and a rectangle are comparable ( four sides for each). The state of being different can be used to define a difference.

To find the value of x we will use the similarity which corresponding sides of similar triangle are Proportional.

So;

50/x = 75/45

2/x = 3/45

x = 30 units

Thus, required value of x is  30 units.

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A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

First, we need to know the conversion rate between the two units (pounds lb and kilograms kg)

Now, we can convert 90 pounds.

So, 90lb ≈ 41kg

(If you were to round)

The graph of the quadratic function can be seen on the image at the end.

The only way to graph or sketch a function by hand, is by finding some points on the graph and then connecting them.

To find the points we need to evaluate the quadratic equation.

if x = 0

y = 5*0^2 + 2 = 2

So we have the point (0, 2)

if x = 1

y = 5*1^2 + 2 = 7

So we have the point (1, 7)

if x = -1

y = 5*(-1)^2 + 2 = 7

So we have the point (-1, 7)

And so on, once you have enough points, you can graph them on the coordinate axis and then connect them. The graph of the quadratic equation can be seen on the image at the end.

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Answer:

Step-by-step explanation:

To find the angle that Mrs. Becker is looking down at, we can use the tangent function. We know the height of her eyes (6 feet) and the distance from her eyes to the ladybug (100 feet), so we can use the formula:

tan(angle) = height/distance

First, we'll solve for the angle:

angle = tan^-1(height/distance)

angle = tan^-1(6/100)

Using a calculator, we can find that the angle is approximately 0.0349 radians, or approximately 2 degrees.

So, Mrs. Becker is looking down at an angle of approximately 2 degrees.

The variance of the given frequency distribution is 60.92, and the standard deviation is option (b) 7.80.

To calculate the variance of a frequency distribution, we need to first find the mean or average of the data. The formula for calculating the mean is as follows:

mean (μ) = Σfx / Σf

where Σfx represents the sum of the products of each value and its corresponding frequency, and Σf is the sum of all the frequencies.

Using the given data, we can calculate the mean as follows:

μ = (43 + 85 + 119 + 175 + 204 + 243 + 32*1) / (3+5+9+5+4+3+1)

μ = 13.5

Next, we need to calculate the deviation of each data point from the mean. To do this, we subtract the mean from each value and square the result. The formula for this is:

(x - μ)²

Using this formula, we get the following deviations for each data point:

(4 - 13.5)² = 81.00

(8 - 13.5)² = 30.25

(11 - 13.5)² = 6.25

(17 - 13.5)² = 12.25

(20 - 13.5)² = 42.25

(24 - 13.5)² = 110.25

(32 - 13.5)² = 333.22

Next, we need to multiply each deviation by its corresponding frequency, and then sum up the results. The formula for this is:

Σf(x - μ)²

Using the above deviations and frequencies, we can calculate the sum of squares as follows:

Σf(x - μ)² = 381.00 + 530.25 + 96.25 + 512.25 + 442.25 + 3110.25 + 1 x 333.22

Σf(x - μ)² = 1827.48

Finally, we can calculate the variance by dividing the sum of squares by the total number of observations (Σf). The formula for variance is:

σ² = Σf(x - μ)² / Σf

Using the above values, we can calculate the variance as follows:

σ² = 1827.48 / 30

σ² = 60.92

The standard deviation is the square root of the variance. Therefore:

σ = √(60.92)

σ = 7.80

Therefore, the correction option is (b).

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Complete Question:

Find the variance and standard deviation of the following frequency distribution:

x  4    8 11 17 20 24 32

f   3    5  9 5 4 3 1

Answer:

D. Machines, vehicles, furniture, and appliances are not considered liabilities. Liabilities are obligations or debts that a business owes to others. They are usually in the form of loans or accounts payable and represent money that must be paid in the future.

Machines, vehicles, furniture, and appliances are assets, which are resources that a business owns and that have monetary value. Assets can be sold to generate cash or used to produce goods or provide services. While assets can be used to secure loans, they do not represent a debt or obligation that must be paid in the future like a liability

Answer:

D

Step-by-step explanation:

current liability is money owed to suppliers in the form of accounts payable . Current liabilities are typically settled using current assets, which are assets that are used up within one year.

The solution is,

(a) Output = 37

(b) Input = 9

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

Given

y=5x -3

Solving (a): Output, when input = 8

This means that, we solve for y when x = 8

So, we have:

y=5x -3

 =5*8 -3

 =40 - 3

 = 37

Solving (b): Input, when output = 42

This means that, we solve for x when y = 42

So, we have:

y=5x -3

5x = 42+3

    = 45

Collect like terms

Divide both sides by 5

x = 9

Hence, The solution is,

(a) Output = 37

(b) Input = 9

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The formula for compound interest is:

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

where:

A is the total amount of money after t years,

P is the initial principal or deposit amount (in this case $1000),

r is the annual interest rate as a decimal (in this case 1.3% or 0.013),

n is the number of times interest is compounded per year (in this case, let's assume it's compounded annually), and

t is the number of years.

So, the function modeling the total amount of money Brigitte has over time, t, would be:

A = $1000(1 + 0.013)^t

This function shows how the amount of money in the savings account will increase as time goes on due to compound interest.

The two smaller angles are 39 degrees each. The other angle is 106

The measure of the angles would be found using the formula

2*x + 24 = 180

This is because the sum of angles that are in a triangle is = 180

the two equal angles are x + x = 2x

the other angle is 24 greater than 2x

2x + 24 = 180

2x = 180 - 24

2x = 156

x = 78

eaxh of the two equal angles are 78 degrees

while the other angle is 78 + 24 = 106

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Answer:

The total number of boats Paul counted is 24 speed boats + 5 sail boats + 1 rowboat = 30 boats.

So, the experimental probability that the next boat he sees will be a sailboat is 5 sail boats / 30 boats = 1/6.

The experimental probability of an event is defined as the ratio of the number of times the event occurs to the total number of trials or observations.

In this case, Paul observed a total of 24 + 5 + 1 = 30 boats, of which 5 were sailboats.

Therefore, the experimental probability that the next boat Paul sees will be a sailboat is:

Experimental probability = number of sailboats / total number of boats

Experimental probability = 5 / 30

Experimental probability = 1/6

So the experimental probability of seeing a sailboat next is 1/6 or approximately 0.167.

Reason: Split the angle 155 in half to get 155/2 = 77.5

No, [tex]4^{3}[/tex]. 5 is not equal distance away from both [tex]4^{3}[/tex] and [tex]4^{4}[/tex]. However, when x is a perfect square, it is halfway between [tex]x^{3}[/tex] and [tex]x^{4}[/tex]. 5 is halfway between [tex]9^{3}[/tex] and [tex]9^{4}[/tex].

A perfect square is an integer that is the result of multiplying an integer by itself. In other words, it is a number that can be expressed as the product of two equal integers. For example, the number 16 is a perfect square because it can be written as 4 • 4.

Every perfect square has an ending of 1, 4, 5, 6, 9 or 00. (i.e. Even number of zeros). A number that finishes in 2, 3, or 7 is not a perfect square, and so is 8. In essence, a perfect square is the result of multiplying two equal numbers by one another. As a result of multiplying two equal integers (5 and 5) by one another, the number 25 is a perfect square.

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The correct option regarding the domain of the reflected absolute value function is given as follows:

All real numbers.

The domain of a function is the set that contains all possible input values for the function.

The absolute value function is defined for all real numbers, and the reflection does not change the domain, hence the domain is all real numbers.

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In linear equation, $ 618,418.80  will Andrea and Stanley save by choosing Mortgage A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Total Payback = Instalment Amount * No. of Instalments

Mortgage A:

=  $1621.39 * 360

= $ 583,700.40

Mortgage B:

=  $1717.83 * 360

=$ 618,418.80

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The value of expression after change its measurement as;

⇒ 3.4 × 10⁻⁴ kg . m²/ s²

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

The expression is,

⇒ 3.4 × 10⁵ g . cm² / s²

Now, We know that;

⇒ 1 cm = 1/1000 m

⇒ 1 cm = 1/10³ m

⇒ 1 g = 1/1000 kg

⇒ 1 g = 1/10³ kg

Hence, We get;

⇒ 3.4 × 10⁵ g . cm² / s²

⇒ 3.4 × 10⁵ (1/10³) kg . (1/10³)² m²/ s²

⇒ 3.4 × 10⁵ × 10⁻³ × 10⁻⁶ kg . m²/ s²

⇒ 3.4 × 10⁻⁴ kg . m²/ s²

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The velocity of the apple, to the nearest hundredth, when it hit the ground is equal to 13.35 meters per seconds.

In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.

From the information provided about an apple that fell off a branch of the tree, a function that models the velocity of the apple include the following:

Velocity = (19.8d)^{1/2}

Where:

d represents the distance in meters.

Velocity = (19.8 × 9)^{1/2}

Velocity = (178.2)^{1/2}

Velocity = 13.35 meters per seconds.

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Answer:

Step-by-step explanation:

There are several ways to approach this problem, but one common method is to use the complementary counting principle, which states that the number of favorable outcomes can be obtained by subtracting the number of unfavorable outcomes from the total number of outcomes. In this case, the favorable outcome is that the sample contains at least one defective phone, and the unfavorable outcome is that the sample contains no defective phones.

The number of possible samples of 4 phones out of 15 can be calculated as the number of combinations of 4 items from a set of 15, which can be written as:

C(15, 4) = 15! / (4! * (15 - 4)!) = 1365

The number of samples containing no defective phones can be calculated as the number of combinations of 4 phones out of the remaining 12 non-defective phones, which can be written as:

C(12, 4) = 12! / (4! * (12 - 4)!) = 495

So, the number of samples containing at least one defective phone can be calculated as:

1365 - 495 = 870

Therefore, out of the 1365 possible samples of 4 phones, 870 of them contain at least one defective phone.

The perimeter of each shape is obtained adding all of their outer side lengths.

The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.

Hence, for each polygon, you must identify the outer side lengths, and then add them.

The problem is incomplete, hence the standard procedure to find the polygon of a shape was presented.

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