Line u passes through points (7, 2) and (10, 10). Line v passes through points (10, 8) and
(2, 11). Are line u and line v parallel or perpendicular?

Answers

Answer 1

Line u and line v are perpendicular lines by the relation of their slopes.

What is Slope?

Slope of a line is the ratio of the difference of the y coordinates of two points to the x coordinates of those points. Slope is commonly denoted by the letter 'm'.

If a line passes through the points (x₁, y₁) and (x₂, y₂), then slope of the line,

m = (y₂ - y₁) / (x₂ - x₁)

Slopes of two lines, m₁ and m₂, are equal if they are parallel ⇒ m₁ = m₂.

Slopes of two lines, if the lines are perpendicular have the relation,

m₁ × m₂ = -1.

First let's find the slopes of the given lines.

Let m₁ be the slope of line u and m₂ be the slope of line v.

Line u passes through (7, 2) and (10, 10).

m₁ = (10 - 2) / (10 - 7) = 8/3

Line v passes through (10, 8) and (2, 11).

m₂ = (11 - 8) / (2 - 10) = 3/(-8)

Slopes are not equal, so they are not parallel.

m₁ × m₂ = [tex]\frac{8}{3}[/tex] × [tex]\frac{3}{-8}[/tex] = -1.

So the lines are perpendicular.

Hence the given lines u and v are perpendicular.

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Related Questions

f(x) =2/x^2 and g(x) = 4x^3 find fg(1)​

Answers

Answer:

Functions

Step-by-step explanation:

ok so you gotta substitute x into the original then expand simplify collect like terms then your done

A ring-shaped region is shown below. Its inner radius is 15 yd. The width of the ring is 3 yd. Find the area of the shaded region. Use 3.14 for π. Do not round your answer.

Answers

Answer:

612.3 in.²

Step-by-step explanation:

Inner circle diameter = 34 in.

Inner circle radius = r = 17 in.

Outer circle diameter = 34 in. + 5 in. + 5 in. = 44 in.

Outer circle radius = R = 22 in.

The are of the ring is the area of the outer circle minus the area of the inner circle.

A = πR² - πr²

A = π(R² - r²)

A = 3.14[(22 in.)² - (17 in.)²]

A = 612.3 in.²

Yaqub ha a bag of green and yellow pin. 3/7 of the pin are green
He pick out a green pin from hi bag and give it to hi iter
2/5 of the remaining pin in hi bag are green
how many of the remaining pin in hi bag are green and how many are yellow?

Answers

The number of remaining green and yellow pins is 14 pins and 21 pins.

A proportion is a mathematical calculation that compares two numbers. According to proportion, two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.

The fraction of green pins present in the bag is 3/7. Then, the fraction of yellow pins present in the bag is 4/7.

When Yaqub picks up the green pin and gives it to his sister, the new fraction of green and yellow pins are 2/5 and 3/5.

Let x be the number of pins remaining in the bag after 1 pin less. This is written as,

[tex]\begin{aligned}\frac{3}{7}x-1 &= \frac{2}{5}x\\\frac{3}{7}x-\frac{2}{5}x&=1\\x&=35\end{aligned}[/tex]

There are about 35 pins remaining in the bag.

Then, the number of green pins remaining is (2/5) × 35 = 14 pins.

The number of yellow pins remaining is (3/5) × 35 = 21 pins.

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at a 95% level of confidence we want to estimate the population mean for a quantitative varible that is normally distributed in the population there a 10 individuals in the random sample what is the value of

Answers

As per the given confidence interval, the value of the mean is 1.96

The term confidence interval means a range of numbers constructed around a point estimate such as a sample mean or sample proportion.

Here we need to find at a 95% level of confidence we want to estimate the population mean for a quantitative variable that is normally distributed in the population there a 10 individuals in the random sample what is the value of mean.

While In the large-sample case, a 95% confidence interval estimate for the population mean is given by

=> x ± 1.96σ/√n.

Where the population standard deviation is denoted as σ, is unknown, And the the sample standard deviation is used to estimate σ in the confidence interval formula.

Here by the quantity 1.96σ/√n is often called the margin of error for the estimate.

Then the quantity σ/√n is the standard error, and 1.96 is the number of standard errors from the mean necessary to include 95% of the values in a normal distribution.

Therefore, the interpretation of a 95% confidence interval is that 95% of the intervals constructed in this manner will contain the population mean.

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2(x+1.25) =3.5 without distributive property

Answers

Answer:

x = 0.5

Step-by-step explanation:

2 (x+1.25) = 3.5

Divide by 2 on both sides.

x + 1.25 = 1.75

Subtract 1.25 on both sides.

x = 0.5

Answer:

x = 0.5

Step-by-step explanation:

2(x+1.25) =3.5

Divide both sides by 2.

x+1.25 = 3.5/2

x + 1.25 = 1.75

Subtract 1.25 from both sides.

x = 0.5

5350 divided by Equals 5.35

Answers

Answer:

1000

Step-by-step explanation:

you could write this as 5350 divided by x = 5.35

multiply both sides by x you get 5.35x = 5350

divide both by 5.35

x =1000

or you could just do 5350/5.35 which is 1000

therefore 5350 divided by 1000 would be 5.35

g if we randomly selected 3 people born in 1988, what's the probability that they all have different birthdays

Answers

The probability that they all have different birthdays is 0.903 or 90.3%.

1. Calculate the number of days in a year.

There are 365 days in a year.

2. Calculate the number of possible combinations for 3 people.

There are 365 x 365 x 365 = 4,738,625 possible combinations for 3 people.

3. Calculate the number of combinations where all 3 people have different birthdays.

There are 365 x 364 x 363 = 4,324,320 combinations where all 3 people have different birthdays.

4. Calculate the probability.

The probability that they all have different birthdays is 4,324,320 / 4,738,625 = 0.903 or 90.3%.

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Question 7
GEOMETRY The perimeter of a square is four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the
square is 4 centimeters. Write an equation in point-slope form to find the perimeter y of a square with side length x.

Answers

Answer:

y= 4x + 0

Step-by-step explanation:

The perimeter y of a square with side length x can be described by the equation y = 4x + 0.

The perimeter of a square is equal to four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. We can use this information to write an equation in point-slope form to describe the relationship between the side length of a square and its perimeter.

Point-slope form is a way of writing the equation of a line when we know the slope of the line and the coordinates of a point on the line. In this case, the slope of the line is 4, since the perimeter of a square is four times the length of one side. The coordinates of a point on the line are (1, 4), since the side length of a square is 1 centimeter and the perimeter of the square is 4 centimeters.

We can use this information to write the equation of the line in point-slope form. The equation of a line in point-slope form is given by the following equation:

y - y1 = m(x - x1)

where y is the y-coordinate of a point on the line, y1 is the y-coordinate of a known point on the line, m is the slope of the line, and x is the x-coordinate of a point on the line.

In this case, we can substitute the values we know into the equation above to get:

y - 4 = 4(x - 1)

This simplifies to:

y = 4x + 0

Therefore, the equation in point-slope form that describes the relationship between the side length x of a square and its perimeter y is y = 4x + 0.

This equation tells us that for any square, the perimeter is four times the side length plus zero. For example, if the side length of a square is 5 centimeters, then the perimeter is 4 x 5 + 0 = 20 centimeters. If the side length of a square is 10 centimeters, then the perimeter is 4 x 10 + 0 = 40 centimeters.

In summary, the perimeter y of a square with side length x can be described by the equation y = 4x + 0.

You have a meeting with a potential client for your printing business. To demonstrate your
professionalism, you should arrive for the appointment:

A) Right on time.

B) A few minutes early to ensure that you can find the office and be well prepared for the
meeting.

C) An hour early so that the potential client will know you are eager to get their business.

D) Within a few minutes before or after the arranged time.

Answers

The correct option for given situation is,

⇒ To demonstrate your professionalism, you should arrive for the appointment ''Right on time''.

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;

You have a meeting with a potential client for your printing business.

And, To demonstrate your professionalism, you should arrive for the appointment.

Now, We know that;

The rule of business is,

To demonstrate your professionalism, you should arrive for the appointment on the right time.

Therefore, The correct option for given situation is,

⇒ Right on time

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Please answer this Geometry - Conditional Forms question.

The statement “If I do not get a uniform, then I do not make the team” is the contrapositive of which of the following conditional statements?
A) If I do not get a uniform, then I do not make the team.
B) If I do not make the team, then I do not get a uniform.
C) If I get a uniform, then I make the team.
D) If I make the team, then I get a uniform.

Answers

Answer:

B) If I do not make the team, then I do not get a uniform.

Step-by-step explanation:

The contrapositive of a conditional statement is formed by negating both the antecedent and the consequent of the statement and then swapping their order. In the case of the statement "If I do not get a uniform, then I do not make the team," the contrapositive is "If I do not make the team, then I do not get a uniform."

There were 794 fih at 9:00 A. M. The dolphin were fed at 5:00 P. M. There were 209 fih left etimate how many fih the dolphin ate

Answers

the number of fih at 9:00 A.M. (794), which yields 209 fih, the number of fih left at 5:00 P.M. is 585 fih

Subtract the number of fih at 9:00 A.M. (794) from the number of fih left at 5:00 P.M. (209).

794 - 209 = 585

Therefore, the dolphin ate 585 fih.

To estimate how many fih the dolphin ate, we must first subtract the number of fih at 9:00 A.M. (794) from the number of fih left at 5:00 P.M. (209). This gives us 585 fih, which is the estimated number of fih that the dolphin ate. This calculation can be verified by subtracting the number of fih the dolphin ate (585) from the number of fih at 9:00 A.M. (794), which yields 209 fih, the number of fih left at 5:00 P.M.

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a researcher wishes to test whether the mean of a normally distributed population is greater than 1.06 at the 5% significance level. based upon 22 independent observations, she observes a sample mean of 1.77 and a sample standard deviation of 0.84 . determine the observed value of student's t statistic rounded to the nearest hundredth. (rounding counts!)

Answers

The observed value of student's t statistic rounded to the nearest hundredth is 1.72.

Explain the term significance level?The likelihood that an event (like a statistical test) may have happened by chance is the significance level of the occurrence. When the level, or the possibility of the occurrence occurring by chance, is quite low, the event is considered noteworthy.

The stated data is-

Sample size n = 22Significance level = 5%

Thus,

Degree of freedom = n -1

Df = 22-1

Df = 21

As, the significance level is 5% then test is right tailed.

So,

Alpha value = 0.05

Now,

For alpha value = 0.05 and degree of freedom = 21.

t- critical value = 1.721 (from the t-statiscts table).

Thus, the observed value of student's t statistic rounded to the nearest hundredth is 1.72.

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Please Help!! I'm super confused!

(2x ⋅ -3/y)^-3 ⋅ (-5x/y)^2

Answers

Answer: -25y/216x

Step-by-step explanation: - 25y / 216x

Answer:

(-30x^2/y^2)^5

Step-by-step explanation:

First, we can simplify the exponent in the first term by using the property that (a^m)^n = a^(m⋅n). This property tells us that we can calculate the exponent of the first term by multiplying the exponent of the base by the exponent of the power, which gives us (-3)⋅(-3) = 9. This means that the first term can be rewritten as (2x ⋅ -3/y)^9.

Next, we can simplify the second term by calculating its exponent in the same way, which gives us (-2)⋅(2) = -4. This means that the second term can be rewritten as (-5x/y)^-4.

We can then combine the two terms by using the property that (a^m)⋅(b^n) = (a⋅b)^(m+n). This property tells us that we can calculate the exponent of the combined terms by adding the exponents of the individual terms, which gives us 9 + (-4) = 5. This means that the entire expression can be rewritten as (2x ⋅ -3/y)^9 ⋅ (-5x/y)^-4 = (2x⋅-3/y⋅-5x/y)^5.

Finally, we can simplify the base of the combined terms by multiplying the factors together, which gives us (2x⋅-3/y⋅-5x/y) = -30x^2/y^2. This means that the entire expression can be rewritten as (-30x^2/y^2)^5.

an equation for a tangent to the graph of y=arcsin(x/2) at the origin is

Answers

y=x/2 is equation for a tangent to the graph of y=arcsin(x/2) at the origin.

In order to fing the equation of tangent of any graph we need 2 things

 i . A point on the graph

 ii . Slope a line on that point

Given y=[tex]sin^-^1(\frac{x}{2} )[/tex]

put x=0

y = [tex]sin^-^1[/tex] (0)

=> y =0

so the graph passes through point (0,0)

now we have to find slope of the graph

slope = [tex]y^'[/tex] = [tex]\frac{d(y)}{dx}[/tex]

=> [tex]\frac{1}{\sqrt{4-x^2} }[/tex]

slope of line at point (0,0) is 1/2

so equation of line is y-0=1/2(x-0)

so the equation of tangent to the given graph is y=x/2

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the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model. t or f

Answers

True. the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

what is slope in statistics?

The slope and intercept of a line reveal the steepness of the line and the location in which it intersects an axis. The slope and intercept of the logistic relationship of the two variables can be utilized to get the average change rate. The ratio of a change in the variable y to the rise in the x component is known as the the line's slope.

Briefing:

Y = a + bX, where X seems to be the mediating variable and Y is the response variable, is the equation of a linear regression line. A is the intersection (the result of y for x = 0), and b is the line's slope.

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Establish the identity.
(csc 0+1)(csc 0-1) = cot 0

a. Multiply and write the left side expression as the difference of two squares: ?

b. The expression from the previous step is equivalent to cot 0 using what?
OA. Cancellation Property
OB. Quotient Identity
OC. Pythagorean Identity
OD. Reciprocal Identity
OE. Even-Odd Identity

pls help asap i can’t pass this class without passing this test

Answers

To establish the given identity, we need to first multiply the left side of the equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+1)(csc0-1)

We can then apply the difference of squares formula to this expression to get:

(csc0+1)(csc0-1) = (csc0+1)(csc0-1)

Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.

Therefore, the given identity is established using the Pythagorean Identity. This means that the correct answer is C. Pythagorean Identity.

What is G2? answer quick peasee

Answers

G(2)=4. Hope this helps

List all of the integer values that could take that would satisfy the inequality shown on the number line below. ​

Answers

List all of the integer values that could take that would satisfy the inequality shown on the number line below. ​

(-2 , 1.5)

Algebra 2 Questions that i need help with

Answers

The graph has a horizontal intercept at (1, 0)

The line x = 0 (the y-axis) is a vertical asymptote; as x→0+,y→∞

The graph is decreasing if 0 < b < 1.

The domain of the function is x > 0, or (0, ∞)

The range of the function is all real numbers, or (−∞,∞)

What is function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The set of all positive real numbers serves as the function's domain. Assume that base 10 is written when no base is specified for the log. The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally. The graph would be moved upward if k>0.

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Shade 2 circles. Shade 7/4 more

Answers

Answer:

The answer is 3 3/4

Step-by-step explanation:

2 7/4 = 15/4 = 3 3/4

Jason was riding his bicycle, making deliveries on his newspaper route. He had no less than 12 newspapers left to deliver.

Which number line represents this scenario?

number line with closed circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the right
number line with closed circle at point 12, shaded to the right

Answers

The number line to represent the given scenario is number line with close circle at point 12 and shaded to the right. The correct option is (D).

What is a number line?

A number line is the pictorial representation of numbers on a graph. The reference point on the number line is known as origin and all the numbers right to the origin are taken as positive and those left to it are negative numbers.

The number of newspapers to be delivered is not less than 20.

Suppose the number of newspaper left at any time be x.

Then, the inequality for the given situation can be written as,

x ≥ 12

This implies all the whole numbers greater than and including 12 on the number line.

Hence, the solution can be represented as all numbers greater than and equal to 12.

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given that a = b/(1+b) , express b in terms of a.
[tex]a = \frac{b}{1 + b} [/tex]

Answers

Answer:

b = - [tex]\frac{a}{a-1}[/tex]

Step-by-step explanation:

a = [tex]\frac{b}{1+b}[/tex] ( multiply both sides by 1 + b to clear the fraction )

a(1 + b) = b ← distribute parenthesis on left side

a + ab = b ( subtract b from both sides )

a + ab - b = 0 ( subtract a from both sides )

ab - b = - a ← factor out b from each term on left side

b(a - 1) = - a ( divide both sides by a - 1 )

b = - [tex]\frac{a}{a-1}[/tex]

Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches. If 500 men want to enlist in the U.S. Marine Corps, how many would you not expect to meet the height requirements?

Answers

Answer:

19

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Mean μ = 69.0 inchesStandard deviation σ = 2.8 inches

Therefore, if the heights of men are normally distributed:

[tex]\boxed{X \sim\text{N} \left(69.0, 2.8^2 \right)}[/tex]

where X is height in inches.

Given:

The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches.

Find the probability that the heights of men is between 64 and 78 inches by calculating P(64 ≤ X ≤ 78).

Calculator input for "normal cumulative distribution function (cdf)":

Lower bound: x = 64Upper bound: x = 78μ = 69.0σ = 2.8

⇒ P(64 ≤ X ≤ 78) = 0.9622733869...

To calculate how many men who want to enlist in the U.S. Marine Corps would not expect to meet the height requirements from a group of 500, multiply 500 by 1 less than the probability found above:

⇒ 500 × [1 - P(64 ≤ X ≤ 78)]

⇒ 500 × [1 - 0.9622733869...]

⇒ 500 × 0.03772661307...

⇒ 18.86330654...

Therefore, we would expect for 19 men to not meet the height requirements.

Water is dripping from an inverted cone with a diameter of 12 cm 12cm and a height of 12 cm 12cm at a rate of 1 cm 3 / sec 1cm3/sec. At what rate is the water level decreasing when the radius of the water's surface is r

Answers

The rate is the water level decreasing when the radius of the water's surface is r = 2cm is 0.08 cm/sec or dh/dt = - 0.08 cm/sec.

We have given that,

Water is dripping from an inverted cone.

height , h = 12 cm

diameter , d = 12 cm

so, radius, r = 6 cm

rate , dV/dt = - 1 cm³/sec

At any point, the portion of the cone that is filled will have the ratio of radius/height = 6/12 = 1/2. Put another way, h = 2r.

we have to calculate the rate is the water level decreasing , dh/dt when radius of the water's surface is r = 2 cm .

Volume of cone , V = 1/3 π (r)²h = 1/3π (h/2)²h

plugging all known values,

V = 1/3 ( h³/4)π

differentiating with respect to h we get,

dV/dh = 1/3(3h²)π/4 , h = 12

= 1/12(3× 4r²)π ( from r = 2 cm)

= 4π cm²

but we have required, dh/dt = dV/dt × dh/dV

= - 1 cm³/sec × 1/4π cm²

= - 1/4π cm/sec

= - 0.0792 ~ 0.08 cm/sec

Hence, the required value is - 0.08 cm/sec.

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Complete question:

Water is dripping from an inverted cone with a diameter of 12 cm and a height of 12 cm at a rate of 1 cm3 /sec. At what rate is the water level decreasing when the radius of the water's surface is r = 2 cm?"

Find the sales tax
Selling Price 70.00
Rate of Sales Tax 7%
Sales tax ?
The sales tax is [aswer]

Answers

The sales tax is $4.90

the edwards's theater chain has studied its movie customers to determine how much money they spend on concessions. the study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. what spending amount corresponds to the top 87th percentile?

Answers

The study revealed that 87% of movie customers spend an average of $6.39 or less on concessions.

To calculate the spending amount that corresponds to the top 87th percentile, we must first calculate the z-score. To do this, subtract the mean of $4.11 from the desired percentile of $6.39, resulting in a difference of $2.28. Next, divide the difference of $2.28 by the standard deviation of $1.37, resulting in a z-score of 1.67. Finally, use a z-score table to find the corresponding percentile of 87%. This means that 87% of movie customers spend an average of $6.39 or less on concessions.

z-score = (6.39 - 4.11) / 1.37 = 1.67

percentile = 87%

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Which choice is equivalent to the product below?

sqrt45 ×sqrt10

Answers

Answer:

Below

Step-by-step explanation:

= sqt (45*10) = sqrt (450) = 15 sqrt 2

The expression √45 × √10 is simplified using the property of square roots to give an equivalent choice of 15√2

How to simplify the expression with square roots

The product √45 × √10 can be simplified by using the property of square roots that states √(a × b) = √a × √b.

By application of this property, we have that:

√45 × √10 = √(45 × 10).

To simplify further, we find that 45 and 10 have a common factor of 5, and thus,

45 × 10 = 5 × (9 × 10)

45 × 10 = 5 × 90.

Now, we can rewrite √(45 × 10) as √(5 × 90).

Using the same property again, we obtain √5 × √90. Finally, we recognize that 90 can be factored into 9 × 10.

Thus;

√45 × √10 = √(2 × 9 × 25)

√45 × √10 = √2 × √225

√45 × √10 = √2 × 15

√45 × √10 = 15√2

Therefore, the expression√45 × √10 have an equivalent of 15√2

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Solve for the value of x

A. 20
B. 10
C. 45
D. 3

Answers

Answer:

10

Step-by-step explanation:

[tex]x + 5 = 15 \\ x + 5 - 5 = 15 - 5 \\ x = 10 [/tex]

Precalc wohoo help would rlly appreciate it

Answers

Refer to the photo taken. Let me know if you understand it. If you don’t, I can try and fix it.

Answer:

1. Apply a Pythagorean Identitie

2. Seperate the quotient into two terms.

3. Divide the common factor

4. Apply a reprical identity.

Step-by-step explanation:

The steps below in the image I just wrote.

I am not sure if your teacher would let you have a cheat sheet on the test or quiz. Remember your reciprocal identities and Pythagorean identities.

Could someone help me with this it would be appreciated

Answers

Answer:

0.65

Step-by-step explanation:

The probability that we would get tails is 0.35

so the probability we will get heads is

1 0.35 = 0.65

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How would you limit the domain to make this function one to one f(x)=3-x^2 PLEASE PLEASE PLEASE HELP Pls helpppppppppppppppppppppp Yall click on the photo to see it! 100 points! Please don't answer nonsense that is a waste of my points! Please and thank you in the circuit shown in the figure (figure 1), find the magnitude of current in the upper branch. The vapor pressure of liquid ethyl amine, C2H5NH2, is 40.0 mm Hg at 233 K.A sample of C2H5NH2 is placed in a closed, evacuated container of constant volume at a temperature of 349 K. It is found that all of the C2H5NH2 is in the vapor phase and that the pressure is 63.0 mm Hg. If the temperature in the container is reduced to 233 K, which of the following statements are correct?Choose all that apply.Liquid ethyl amine will be present.No condensation will occur.Only ethyl amine vapor will be present.The pressure in the container will be 42.1 mm Hg.Some of the vapor initially present will condense. Choose the best answer. adnde vamos para estudiar? vamos a la universidad. vamos a la juguetera. vamos a la fbrica. vamos a la farmacia. assuming that net credit sales for year 2 totaled $270,000, what is the company's most recent accounts receivable turnover? True or False: chinese, japanese, and thai have features that make them more difficult candidates for natural language processing. Let P(n) be the statement that 13 +23 ++n3 = (n(n+1)/2)2 for the positive integer n.a) What is the statement P(1)?b) Show that P(1) is true, completing the basis step of the proof.c) What is the inductive hypothesis?d) What do you need to prove in the inductive step?e) Complete the inductive step, identifying where you use the inductive hypothesis.f) Explain why these steps show that this formula is true whenever n is a positive integer. if a company wants to sell 100 shares to raise $1,000 with earnings per share of $2, what would the share price need to be? when using eui-64, what is the correct result of inverting the seventh bit of the interface id with an interface id of b2c3:7aa0:8801? Anyone know the answer?0.08m^3 to kg marta is a pregnant woman suffering from severe iodine deficiency. as a result of the deficiency, she has a high risk of giving birth to a child with Describe the Earth-sun-moon system including the cyclic patterns of lunar phases, eclipses of the sun and moon, and seasons. Juan claims that y=4x^3+1 is a function, but not a linear function. Select the statement that supports Juan's claim.A. The function does not contain the point (0,0)B. The coefficient of x^3 is not 1C. The graph of the function does not form a straight lineD. The function increases choose a sentence with correct use of hyphens Shawna wants to ensure that she has a good income throughout her retirement. Which method could she employ?. Suppose Yakov runs a small business that manufactures shirts. Assume that Yakov is a price taker, and the market price is $20 per shirt. The following table represents Yakov's cost structure per hour: If Yakov produces and selis three shirts, his total revenue (TR) would be and his profit would be . Yakov's marginal revenue (MR) from third shirt he sells is , and his marginal cost (MC) of producing a third shirt is The following graph shows Yakov's total cost curve (based on the previous table). Use the blue points (circle symbols) to plot total revenue and the green points (triangle symbols) to plot profit for the first seven shirts that Yakov produces, including zero shirts. Hint: You will have to plot eight points for each line. Plot your points in the order in which you would like them connected, Line segments will conne the points automatically. COST, REVENUE, AND PROFIT (Dollars per hour) Calculate Yakov's marginal revenue and marginal cost for the first seven shirts he produces and plot them on (circle symbol) to plot marginal revenue and the orange points (square symbol) to plot marginal cost. shirts per hour. When he does this, the marginal cost of the last shir As the graphs indicate, Yakov's profit is maximized when he produces he produces is additional shirt (that is, one more shich is than would maximize his profit) is , which is than the price Yakov receives each shirt he selis. Therefore, Yakov's profit-maximizing quantity corresponds to the intersection of the curves. Because Yakov is a price taker, this last condition can aiso be written as based on demographic data, there is a good chance you will find yourself speaking before what kinds of audiences?