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.

Answer:

A , E

Step-by-step explanation:

side of the square = 10

there are 4 side in the perimeter

10 · 4 = 40

the radius of the semicircle is the value of the side of the square = 10

there are two equals semicircle, so the total perimeter of these shapes is equal to a complete circle

10 · 2 · π = 20π

total perimeter

40 + 20π

that can be expanded in

10 + 10 + 10π + 10 + 10 + 10π

The value of the fraction 7/15 * (9/-28) is - 3/20.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

On the other hand, a fraction appears in the numerator or the denominator of a complex fraction. The value will be:

= 7/15 * (9/-28)

= -63 / 420

= -3/20

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Answer:

Math Expert Answer

Step-by-step explanation:

So toms equation is y= 4x + 6 and addisons equation is y=10x so they will meet eachother in 1 hour. You can use a desmos calculator to input the equations for the answer

Answer:

1 hour

Step-by-step explanation:

Let's set up an equation for Tom's and Addison's distances: T(x) = 4x + 6, A(x) = 10x, where x is the amount of time since Addison started (in hours).

We solve for A(x) = T(x) and get:

10x = 4x + 6 → subtract 4x from both sides

6x = 6 → divide both sides by 6

x = 1

Therefore, it took Addison 1 hour to catch up with Tom

The probability of a rating that is between 176 and 214 is,

                         [tex]P(176\leq x\leq 214)=0.21994[/tex]

Since the credit ratings are normally distributed.

Now,  apply the formula for normal distribution. Which is shown below,

                   [tex]z=\frac{x-u}{sd}[/tex]

x=credit ratings for applicants.

u=mean.

sd standard deviation.

From the given information,  µ = 210 and   σ = 50

For x = 176,

[tex]z=\frac{176-210}{50} =-0.68[/tex]

In the normal distribution table, the probability corresponding to the -0.68 z-score is 0.25175

For x =214,

[tex]z=\frac{214-210}{50} =0.08[/tex]

In a normal distribution table, the probability corresponding to the z score of 0.08  is 0.03788

Thus,    

[tex]P(176\leq x\leq 214)=0.25175-0.03181=0.21994[/tex]

Hence, The probability of a rating that is between 176 and 214 is,

[tex]P(176\leq x\leq 214)=0.21994[/tex]

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The roots of the quartic polynomial f(x) = x⁴ + 8x³ + 11x² - 9x + 28 are ±1, ±2, ±3, ±4, ±7, ±14, ±28

In the given problem, we have to find the roots of the fourth degree polynomial and factorize the given polynomial equation first in order to obtain three equations which are linear and quadratic equation. We can easily determine the zeros of the  fourth degree polynomial.

Generally, polynomials of fourth degrees are called quartic polynomials.

f(x) = x⁴ + 8x³ + 11x² - 9x + 28

When we factorize this, we wouldn't get a lower value because this quartic polynomial cannot be factorized.

However, we can still find the roots which are the solution to the polynomial and are

x = ±1, ±2, ±3, ±4, ±7, ±14, ±28

These values are the solution to the polynomial.

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complete question : What are the roots of f(x)=x^4+8x^3+11x^2-9x+28

Answer:

Step-by-step explanation:

You want to know the measures of angles ADB and ADC given that inscribed angle BAC is 21° and exterior angle CBE is 58°.

Angle CBE is exterior to triangle CBA with remote interior angles BAC (21°) and ACB. The exterior angle is equal to the sum of the remote interior angles, so ...

  ∠CAB +∠ACB = ∠CBE

  21° +∠ACB = 58°

  ∠ACB = 37° . . . . . . . . subtract 21°

The measure of an inscribed angle is half the measure of the arc it intercepts. This means the measures of all inscribed angles that intercept the same arc are the same.

  ∠ADB = ∠ACB = 37°

  ∠BDC = ∠CAB = 21°

By the Angle Addition theorem, ...

  ∠ADC = ∠ADB +∠BDC = 37° +21°

  ∠ADC = 58°

As we just saw, ...

  ∠ADB = 37°

For angle CAD = 69°, the total of the inscribed angles with vertex A is ...

  ∠CAD +∠CAB = ∠BAD

  69° +21° = 90° = ∠BAD

This means angle BAD intercepts an arc BD of 180°, hence segment BD is a diameter.

__

The attached figure is accurately drawn.

Answer:

A is the only irrational number present.

Step-by-step explanation:

The bottom two numbers can be simplified into 7 and 5. Meanwhile, B is a repeating number. A is a non-repeating and non terminating number.

Answer:

A.

Step-by-step explanation:

An irrational number is any real number that cannot be equally divided by 2 integers. (It's not a perfect square.)

No whole number multiplied by itself equals 27.

Answer:

Step-by-step explanation:

You plug in the number of lawns mowed for "n"

So 1 lawn would be 15(1)  (15 times 1)

15(1)=15

15(2)=30

15(3)=45

15(4)=60

15(5)=75

15(6)=90

15(7)=105

15(8)=120

15(9)=135

15(10)=150

and so on

Answer:

Step-by-step explanation:

The area of the courtyard is given by the expression 24(5x - 1), and the area of the cement walkway is given by the expression 32(5x-1 + 8)- 24(5x-1). To find an equivalent expression for the area of the cement walkway, we can first distribute the 32 and the 24 in the second expression to get:

Area of cement walkway = 32 * (5x-1 + 8) - 24 * (5x-1)

= 32 * 5x-32 - 24 * 5x+24 + 32 * 8 - 24

= 160x-1024 - 120x+576 + 256 - 24

= 40x-448 + 256 - 24

= 40x-192

Therefore, an equivalent expression for the area of the cement walkway is 40x - 192. This expression represents the area of the cement walkway in square yards.

Answer: 79 pages

Step-by-step explanation:

100% - 21% = 79%

So we know that Jay has 79% of the stamps

79% = 0.79

Take 500 times 0.79 = 395 stamps

Then we take 395 divided by 5 = 79 pages

So, 79 pages are filled with stamps

2. The measurement of angle 1 is 113°

3. The measure of ∠1 = 98° and ∠2 = 82°

4. The value of x is 8.

5.  The value of x is 3.

What is the supplementary angle?

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.

2.

Given that, ∠1 and ∠4 are vertical angle.

According to the vertical angle theorem, if two angles are vertical then they are congruent.

Therefore,

∠1 = ∠4

3x + 14 = 5x − 52

Subtract 5x from both sides:

3x - 5x + 14 = -52

-2x + 14 = -52

Subtract 14 from both sides:

-2x = -66

x = -33

Putting x = -33 in ∠1 = 3x + 14

∠1 = 3× 33 + 14 = 113°

3.

Given that, ∠1 = 3x + 8 and ∠2 = 2/3x + 62 are supplementary angles.

Therefore ∠1 + ∠2 = 180°

3x + 8 + 2/3x + 62 = 180°

11/3 x + 70 = 180°

Subtract 70 from both sides:

11/3 x = 110

x = 110 × (3/11)

x = 30

Putting x = 30 in ∠1 = 3x + 8 and ∠2 = 2/3x + 62

∠1 = 3x + 8 = 3×30 + 8 = 98°

∠2 = 2/3x + 62 = (2/3)×30 + 62 = 82°

4.

Given that, Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the measure of angle 3 equals 9x + 59.

Therefore,

∠2  = ∠3

13x + 27 = 9x + 59

Subtract 9x from both sides:

13x - 9x + 27 = 9x -9x +59

4x +27 = 59

Subtract 27 from both sides:

4x = 32

x = 8

5. Given that m∠ABC = 163° and ∠XYZ = 5x + 2 are supplementary angles.

m∠ABC + m∠XYZ =180°

163° + 5x + 2 =180°

165 + 5x = 180

Subtract 165 from both sides:

5x = 15

x = 3

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Answer:

2)  m∠1 = 113°

3)  98° and 82°

4)  x = 8  

    Angles = 131°

5)  x = 3

Step-by-step explanation:

If Angle 1 and Angle 4 are vertical angles, then according the Vertical Angles Theorem they are congruent.

Therefore:

⇒ m∠1 = m∠4

⇒ 3x + 14 = 5x - 52

⇒ -2x + 14 = -52

⇒ -2x = -66

⇒ x = 33

To find the measure of Angle 1, substitute the found value of x into the expression for the angle:

⇒ m∠1 = 3x + 14

⇒ m∠1 = 3(33) + 14

⇒ m∠1 = 99 + 14

⇒ m∠1 = 113°

Given:

If the angles are supplementary, they sum to 180°:

⇒ 3x + 8 + ²/₃x + 62 = 180

⇒ ¹¹/₃x + 70 = 180

⇒ ¹¹/₃x = 110

⇒ 11x = 330

⇒ x = 30

Substitute the found value of x into the expressions for the angles:

⇒ ∠ = 3x + 8

⇒ ∠ = 3(30) + 8

⇒ ∠ = 98°

⇒ ∠ = ²/₃x + 62

⇒ ∠ = ²/₃(30) + 62

⇒ ∠ = 82°

If Angle 2 and Angle 3 are vertical angles, then according the Vertical Angles Theorem they are congruent.

Therefore:

⇒ m∠2 = m∠3

⇒ 13x + 27 = 9x + 59

⇒ 4x + 27 = 59

⇒ 4x = 32

⇒ x = 8

Substitute the found value of x into the expressions for the angles:

⇒ m∠2 = 13x + 27

⇒ m∠2 = 13(8) + 27

⇒ m∠2 = 104 + 27

⇒ m∠2 = 131°

⇒ m∠3 = 9x + 59

⇒ m∠3 = 9(8) + 59

⇒ m∠3 = 72 + 59

⇒ m∠3 = 131°

Given:

If ∠ABC and ∠XYZ are supplementary, they sum to 180°:

⇒ m∠ABC + m∠XYZ = 180°

⇒ 163 + 5x + 2 = 180

⇒ 5x + 165 = 180

⇒ 5x = 15

⇒ x = 3

y=1/2x-8 is the equation of line passing through points  (-2,-9) and (4, -6) is

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The points are (-2,-9) and (4, -6)

Slope=-6+9/4+2

=3/6=1/2

Let us find the y intercept by the point (-2, -9)

-9=1/2(-2)+b

-9=-1+b

-9+1=b

-8=b

Hence, the equation of line passing through points  (-2,-9) and (4, -6) is y=1/2x-8.

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Answer: B

Step-by-step explanation:

1. multiply (-3x+1) by -2 to get -6x+2 -> -6x+2<8

2. then subtract 2 from both sides, -6x+2 -2 < 8 -2 -> -6x<6

3. divide both sides by -6, when dividing an inequality, the inequality symbol switches so you'd have x > -1

so the answer would be B

Answer:

hope u want to know the length of AH.

it is 17 units

Step-by-step explanation:

AGH is 90° (tangent )

AG is 8 units and GH is 15 units (Data)

so using Pythegorus theorem

AG² + GH² = AH²

gives √(8²+15²)

= 17 units

On solving the provided question we can say that - rate is the tip of his shadow moving is [tex]d/dt ( s-x) = ds/dt - dx/dt = 25/3 - 5 = 25/3 - 15/3 = 10/3 ft/s = 10/3 ft/s[/tex]

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is what? A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

triangles and the ratios

15 ft            s

-------- = --------------

6 ft           s-x

Using cross products

[tex]15( s-x) = 6s\\15s -15x = 6s\\15s-6s = 15x\\9s = 15x\\s = 15/9 x\\s = 5/3 x[/tex]

Taking the derivative of each side with respect to time

[tex]ds/dt = 5/3 dx/dt\\We know dx/dt = 5 ft/s\\ds /dt = 5/3 * 5 = 25/3 ft/s\\a) ds/dt = 25/3 ft/s[/tex]

The length of the shadow is ( s-x)

[tex]d/dt ( s-x)\\ds/dt - dx/dt\\25/3 - 5\\25/3 - 15/3\\10/3 ft/s\\b) 10/3 ft/s[/tex]

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The vertex of the function is (-3,3) when the function is y=|2x+6|+3 and the range is -∞<y<∞.

Given that,

The function is y=|2x+6|+3

We have to find the vertex and range.

We know that,

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. This special sort of relationship is what it is called.

So,

|2x+6|=0

2x=-6

x=-6/2

x=-3

Now,

y=|2(-3)+6|+3

y=|-6+6|+3

y=3

The vertex is (-3,3)

Therefore, The vertex of the function is (-3,3) when the function is y=|2x+6|+3 and the range is -∞<y<∞.

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Answer:

x=8

Step-by-step explanation:

|x+5|−6=7

|x+5|−6+6=7+6

|x+5|=13

|x+5|=13

x+5=13

x+5−5=13−5

x=8

Brainliest Please?

Answer:3

Step-by-step explanation: if you fo it wrong so thats the answer

Answer:

third one:

x<-2 or x>2

Step-by-step explanation:

Answer:

third one

Step-by-step explanation:

]

If Frida chose a blue ball, there is a 3/4 probability that she chose a ball from the first box.

The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur.

Probabilistic and odds are two distinct ideas.

Odds are determined by dividing the likelihood of an event by the likelihood that it won't.

So, we have:

Initial box:

3 white balls

2 blue balls.

Next box:

4 white balls.

1 blue ball.

If Frida chose a blue ball, the likelihood that she chose a ball from the first box is:

Probability (P) = (required outcome / Total possible outcomes)

Probability of picking the first box : P(F) = 1/2

Probability of not picking the second box :P(S) 1/2

Probability of picking blue from the first box : P(B | F) = 3/5

Probability of picking blue, but not from the first box : P(Blue not from the second box) P(B|S) = 1/5

If Frida chose a blue ball, there is a chance she chose a ball from the first box:

P(F) * P(B|F) ÷ (P(F) * P(B|F)) + (P(S) * P(B|S))

(1/2 * 3/5) ÷ ((1/2 *3/5) + (1/2 * 1/5)

3/10 ÷ (3/10 + 1/10)

3/10 ÷ 4/10

3/10 * 10/4

= 3/4

Therefore, if Frida chose a blue ball, there is a 3/4 chance that she chose a ball from the first box.

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The linear inequality to represent the number of seashell is w ≥ 14 and the graph is attached below

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

In this problem, Ernest needs at least 14 seashells and he plans to glue 30 seashells on the wall.

An inequality to represent this will be

w ≥ 14

The reason why we are using greater than or equal to sign in this problem is that we need "at least" 14 seashells or more than seashells on the wall.

b)

Kindly find attached below the inequality below.

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Answer: She fills 2 full boxes and has 3 animals left over.

Step-by-step explanation: To find how many full boxes she can fill, we can do 5 x 2, without going over. So, 5 x 2 is 10, so now we subtract 10 from 13 and get 3, so this explains that we that she can fill 2 FULL boxes, yet have 3 animals LEFT OVER. I hoped this helped!

Answer:

2 boxes can be filed completely with 3 stuffed animals left over.

Step-by-step explanation:

Take the number of stuffed animals (13) and dive that by the number that will fit in each box (2).  The remainder is how many extra stuffed animals are left.

13 ÷ 2 = 5 remainder 3

1) To find a standardized score (z-score), take the individual core minus the mean, then divide by the standard deviation: z = (score - mean)/ SD

Shuri's standardized score would be: z = (69.5 - 65)/2.5 = 1.8

2) First, find the z-score for 62 in: z= (62 - 65) / 2.5 = -1.2

Next, look up -1.2 in a z-table. The corresponding number in the table is .1151.

Multiple this number by 100 to get a percentage: .1151 * 100 = 11.51%

Thus 11.51% of people will be less than 62 inches.

3) Outliers are defined differently dependent on who you ask, often values that are 3 standard deviations (or more) above or below the mean are considered an outlier.

Use the same formula for finding a z-score: z= (score - mean)/ SD

For the taller height use 3:

3= (x - 65)/2.5

Do a little algebra and you get: 3(2.5) + 65 = x thus x = 72.5 or taller

For the shorter height, use -3:

-3(2.5) + 65 = x thus x = 57.5 or shorter

If you need to use a different value for an outlier, then use that number in place of +/- 3.

Hence we get the desired answer.

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Your question is incomplete. Please find the missing content below.

A sample of 300 adult women finds that their heights are approximately Normally distributed with an average height of 65 inches and a standard deviation of 2.5 inches.

1) Shuri is 69.5 inches tall. What is her standard score for height?

2) How many women in the sample would you expect to be less than 62 inches tall?

3) How tall or short would a woman have to be to be considered an outlier? Show your work.

Answer:

x = mp - np

Step-by-step explanation:

Make x the subject of m = n + x/p

m = n + x/p

subtract n from both sides:

m - n = n + x/p - n

m - n = x/p

multiply both sides by p:

p(m - n) = p(x/p)

x = p(m - n)

distribute p on right side:

x = mp - np

Linear functions are those whose graph is a straight line and it has the following form. y = f(x) = a + bx.

There are several ways to represent a linear function such ad word form, function notation, tabular form, and graphical form.

The key features of a linear function identified and interpreted from a description as an increasing linear function results in a graph that slants upward from left to right and has a positive slope.

A linear function can be expressed as a point slope or a line with a slope intercept. The ordered pairs will represent points on the line where a table of values representing the function is provided. According to the values in the table, the gradient of the line is a ratio of rise to run. The gradient and initial value of the function are shown in slope intercept form.

A graph with a positive slope and a left-to-right slope is produced by an increasing linear function. A graph with a negative slope and a left-to-right slant is produced by a decreasing linear function. A graph with a constant linear function looks like a horizontal line.

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Answer:

3.5 cm

Step-by-step explanation:

Circumference: C = 2πr

so radius r = C/2π = 22/2π = 3.5 cm

Answer:

the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces is approximately 0.0228

Step-by-step explanation:

To find the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces, we can use the normal distribution.

The standard error of the mean for a sample of size 28 is the standard deviation of the population divided by the square root of the sample size, or 16 / sqrt(28) = 2.8.

This means that the distribution of the sample means is approximately normally distributed with a mean of 344 pieces and a standard error of 2.8 pieces.

To find the probability that the sample mean is more than 350 pieces, we can use the cumulative distribution function of the normal distribution. In this case, we want to find the probability that a normally distributed random variable is greater than 350.

Using a normal distribution calculator or table, we can find that the probability that a normally distributed random variable with a mean of 344 and a standard error of 2.8 is greater than 350 is approximately 0.0228.

Therefore, the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces is approximately 0.0228.

The rate of the plane in still air is 644 kilometers per hour. The rate of the wind is 72 kilometers per hour.

To calculate the rate of the plane in still air and the rate of the wind, we can use the formula Rate = Distance/Time. To calculate the rate of the plane in still air, we can use the distance of 5032 kilometers and the time of 8 hours to get a rate of 644 kilometers per hour. To calculate the rate of the wind, we can subtract the rate of the plane in still air (644 kilometers per hour) from the rate of the plane with the wind (6152 kilometers per hour) to get a rate of 72 kilometers per hour. Therefore, the rate of the plane in still air is 644 kilometers per hour and the rate of the wind is 72 kilometers per hour.

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If meX = mY and mY = meZ, then meX = meZ. This statement demonstrates

According to the transitive property, all the quantities are equal to each other if two quantities are equal to the third quantity.

For the given problem,  if meX = mY and mY = meZ, then meX = meZ

The two properties that are equal is meX and mY

since mY is also equal to meZ then transitive property says that meX and meZ are still equal

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Answer: 8

Step-by-step explanation:

4+4 is the same as 4 times 2

They both equal to 8