I found this proof by induction that all people in canada are the same height, i was wondering what is the incorrect step?

Step 1: In any group that consists of just one person, everybody in the group has the same age, because after all there is only one person!
Step 2: Therefore, statement S(1) is true.
Step 3: The next stage in the induction argument is to prove that, whenever S(n) is true for one number (say n=k), it is also true for the next number (that is, n = k+1).
Step 4: We can do this by (1) assuming that, in every group of k people, everyone has the same age; then (2) deducing from it that, in every group of k+1 people, everyone has the same age.
Step 5: Let G be an arbitrary group of k+1 people; we just need to show that every member of G has the same age.
Step 6: To do this, we just need to show that, if P and Q are any members of G, then they have the same age.
Step 7: Consider everybody in G except P. These people form a group of k people, so they must all have the same age (since we are assuming that, in any group of k people, everyone has the same age).
Step 8: Consider everybody in G except Q. Again, they form a group of k people, so they must all have the same age.
Step 9: Let R be someone else in G other than P or Q.
Step 10: Since Q and R each belong to the group considered in step 7, they are the same age.
Step 11: Since P and R each belong to the group considered in step 8, they are the same age.
Step 12: Since Q and R are the same age, and P and R are the same age, it follows that P and Q are the same age.
Step 13: We have now seen that, if we consider any two people P and Q in G, they have the same age. It follows that everyone in G has the same age.
Step 14: The proof is now complete: we have shown that the statement is true for n=1, and we have shown that whenever it is true for n=k it is also true for n=k+1, so by induction it is true for all n.

The amount to be invested​ now, or the present value​ needed, is $22873.75

We solve the problem using the compound interest formula for amount

A = P(1 + r)ⁿ where

Making P subject of the formula, we have

P = A/(1 + r)ⁿ

Given that

Substituting the values of the variables into the equation, we have

P = A/(1 + r)ⁿ

P = 50000/(1 + 0.07)¹⁴

P = 50000/(1.07)¹⁴

P = 50000/1.7317

P = 22873.75

So, the amount to be invested​ now, or the present value​ needed, is $22873.75

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The value of the missing length in the image shown using the Pythagoras theorem is x = 65

An equation is an expression that shows the relationship between two or more variables and numbers.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.

Let h represent the missing red line. Using Pythagoras:

x² = h² + 25²

h² = x² - 25²

Also:

r² = h² + 144²

r² = x² - 25² + 144²

And:

(144 + 25)² = r² + x²

(144 + 25)² = (x² - 25² + 144²) + x²

x = 65

The value of the missing length in the image shown using the Pythagoras theorem is x = 65

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The probability that the squad will have exactly two male members is; 0.0816

We are given;

Total number of people in cheerleading squad = 13

Number of Men = 8

Number of Women = 5

We are told that a 6 member squad is selected and now we want to find the probability that the squad will have exactly two male members.

Thus;

P(exactly 2 male members) = (8C2 * 5C4)/(13C6)

P(exactly 2 male members) = 140/1716

P(exactly 2 male members) = 0.0816

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I've done it on the attached pages.

I hope this helps you...

Answer:

[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]

Step-by-step explanation:

Greetings !

a. (fog)(x)= f[g(x)] = 7(x+1)

b. (gof)(x) = g[f(x)] =7x+1

c. (fog)(4)=7(4)+7=28+7=35

d. (gof)(4)= 7(4)+1=28+1=29

(fog)(x)

(gof)(x)

(fog)(4)

(gof)(4)

The number of people that have watched the video is 858 people

A function is a mathematic rule. We know that a function shows the rule that is to  be carried out and is often written in the form of an equation.

Now we have the function shown as; f(x) = 33(1.3)x. Since we know that the term x is referred as the number of days the video has been online.

Thus,  f(x) = 33(1.3)(20) thus we can now say that the number of people who have vied the video in twenty days is 858 people.

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Answer: the answer is B or 858

Step-by-step explanation: The answer is B or 858

The function that represents the difference between the moving companies' rates is:

h(x) = -2x + 200.

The difference of two functions is found subtracting the like terms from the functions.

In this problem, the functions for the rates are given as follows:

Hence the difference is given by:

h(x) = 3x + 400 - (5x + 200) = 3x - 5x + 400 - 200 = -2x + 200.

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Answer:0.333

Step-by-step explanation:4+8=12 so there is only 4 chances it can be male so 4/12=0.333

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

probability (P) is calculated as

P = (desired result ) ÷ ( number of possible results )

here desired result is choosing a male from 4 males

number of possible results = 4 + 8 = 12 , then

P( male) = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

Step-by-step explanation:

The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.

The explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...

  [tex]a_n=a_1+d(n-1)[/tex]

For first term a₁ = 10010 and common difference d = -250, the explicit rule is ...

  [tex]a_n=10010-250(n-1)[/tex]

On day 14, n=14, and the number of words written is ...

  [tex]a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760[/tex]

The writer would write 6760 words on the 14th day.

Answer:

now we know that

book is 120page

__6785

There are some ways by which move the steps from sequence and series method like

Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.

According to the statement

we have to explain the moving steps to change the position of the given three disk from one peg to another.

So, for the solution of this problem

Firstly we know that the sequence and series

An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements.

we have to use the sequence and series method.

So, according to this method

Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.

So, there are some ways by which move the steps from sequence and series method like

Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.

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If adding only twelve, you must leave out three of the fifteen, and the number of ways is = 15! / (3! * 12!).

1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12∗13∗14∗15 over

(1∗2∗3)∗(1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12) =

13∗14∗15 over

(1∗2∗3)

27306 = 455

Answer: If all toppings are distinct, then you have C 4 15 combinations. If there are three distinct toppings, you have 3 ⋅ C 3 15 combinations (because we have C 3 15 choices for toppings and then 3 choices for which of those three toppings is doubled).

Step-by-step explanation:

The simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x  - 4x³√10x

The complete question is added as an attachment

From the attached figure, the product expression is:

2√8x³(3√10x⁴ - x√5x²)

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) =  2 *2x√2x(3x²√10 - x²√5)

Evaluate the products

2√8x³(3√10x⁴ - x√5x²) =  4x√2x(3x²√10 - x²√5)

Open the bracket

2√8x³(3√10x⁴ - x√5x²) =  12x³√20x  - 4x³√10x

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) = 24x³√5x  - 4x³√10x

Hence, the simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x  - 4x³√10x

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Answer:

Second option

Step-by-step explanation:

edge

Answer:

1. e

Step-by-step explanation:

18/3 +2(12-5)

=6+2(7)

=6+14

=20

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]

Divide 18 by 3 to get 6.

Therefore, the correct option is "E".

================================================================

[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]

It seems that none of the options is correct.

[tex]\textit{sum of all interior angles in a polygon}\\\\ S =180(n-2) \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ S =1620 \end{cases}\implies 1620=180(n-2) \\\\\\ \cfrac{1620}{180}=n-2\implies 9=n-2\implies \underline{11=n} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{sum of all exterior angles in a regular polygon}\\\\ n\theta = 360 \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{angle~in}{degrees}\\[-0.5em] \hrulefill\\ \underline{n=11} \end{cases}\implies 11\theta =360\implies \theta =\cfrac{360}{11}\implies \theta \approx 32.7^o[/tex]

A regular polygon is a figure in which all the sides have the same length that is, they are equal and all the interior angles are of the same measure.

This regular polygon is a hendecagon.

A hendecagon is a polygon that has 9 equal sides.

( n - 2 ) 180° = 1620

As a second step, we divide by 180:

We divide

We change the direction, as the sign is negative, in the change of direction it starts to add.

We add both numbers.

Answer: the measure of the exterior angle of the regular polygon (hendecagon) is 11. ✅

Examples of population parameter are mentioned below .

According to the question

Population parameter :

A population parameter is a numerical descriptive measure of a population or a number that describes something about an entire group or population.  

The examples of population parameter is

1. The average weight of all middle-aged female Americans. The population consists of all middle-aged female Americans, and the parameter is µ.

2. The average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

3. The average height of a class X. This is a parameter because it is states something about the entire population of class X.  

Hence, examples of population parameter will depend on the population .

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The equations to represent the relationship are ƒx3/5=4 4/5 and 4 4/5 divided 3/5 =f

Fractions are written as a ratio of two integers. For instance a/b is a fraction.

If Anastacio distributed 4 4/5 kg of seed among several bird feeders and put 3/5 kg of seed in each feeder, the expression that represents the number of bird feeders that Anastacio filled is given as;

Number of bird feeder = 4 4/5 ÷ 3/5

f = 4 4/5 ÷ 3/5

Multiply both sides by

f * 3/5 = 4 4/5   ÷ 3/5 * 3/5

f * 3/5 = 4 4/5

Hence the equations to represent the relationship are ƒx3/5=4 4/5 and 4 4/5 divided 3/5 =f

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The linear equations that corresponds to the table is y = 4x + 3

The missing table of values in the complete question is given as:

x y

0 3

3 15

7 31

10 43

Start by calculating the slope of the equation using

m = (y2 - y1)(x2 - x1)

Substitute the values on the table in the above equation

m = (15 - 3)/(3 - 0)

Evaluate the difference

m = 12/3

Evaluate the quotient

m = 4

The linear equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 4(x - 0) + 3

Evaluate the expression

y = 4x + 3

Hence, the linear equations that corresponds to the table is y = 4x + 3

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Answer:

x = 7

Step-by-step explanation:

since the points all lie on the same line then the slopes of adjacent points will have the same slope.

calculate the slope using R and S then equate to slope using R and T or S and T

calculate slope using slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = S (- 1, - 1 )

[tex]m_{RS}[/tex] = [tex]\frac{-1-(-3)}{-1-(-5)}[/tex] = [tex]\frac{-1+3}{-1+5}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = T (x, 3 )

[tex]m_{RT}[/tex] = [tex]\frac{3-(-3)}{x-(-5)}[/tex] = [tex]\frac{3+3}{x+5}[/tex] = [tex]\frac{6}{x+5 }[/tex]

equating [tex]m_{RS}[/tex] and [tex]m_{RT}[/tex]

[tex]\frac{6}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

x + 5 = 12 ( subtract 5 from both sides )

x = 7

Answer:  $200  (choice B)

Explanation:

Notice that 100/4 = 25 which matches with the fact the cost is $25 per hour.

Therefore, 8 hours will yield a total cost of 8*25 = 200 dollars

The cost for Susan to rent a truck for her entire 8-hour work day is $200. Therefore, option B is the correct answer.

Given that, if it costs Susan $25 to rent a truck for 1 hour and $100 to rent a truck for 4 hours.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Cost of rent of truck for 8 hours = 1 hour rent × Number of hours

= 25 × 8

= $200

The cost for Susan to rent a truck for her entire 8-hour work day is $200. Therefore, option B is the correct answer.

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Answer:

-3

Step-by-step explanation:

(-3, -1), (-5, 5)

Each point is (x, y).

slope = (difference in y)/(difference in x)

slope = (-1 - 5)/(-3 - (-5)) = -6/(-3 + 5) = -6/2 = -3

The slope is -3

The right option is (c).

As a result of the plane intersecting the cone here at an angle of 50° being less than the angle between the generator and central axis at an angle of 50°, a conic section is created.

A smooth curve in a plane known as a hyperbola is one whose geometric characteristics or equations for which it is the solution set characterize it. Two parts of a hyperbola, known as connected components or branches, are mirror reflections of one another and resemble two infinite bows.

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I understand that the question you are looking for is:

"The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?"

(a)circle

(b)ellipse

(c)hyperbola

(d)parabola

Answer:

   [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

mean: (22+12+14+14+13+9)=14

|22-14| + |12-14| + ... + |9-14| =16

MAD = 16/6 = [tex]\frac{8}{3}[/tex]

In triangle XYZ, angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c. Then, the side XZ which is the perpendicular, is opposite to ∠Y. Side XZ is adjacent to the ∠Y, and side ZY, which is the base, is also adjacent to ∠Y. We can say that ∠Y has been formed by the sides XZ and ZY.

It is given that,

In triangle X Y Z, angle X Z Y is a right angle or 90°.

The length of the hypotenuse XY is c.

⇒ The side with length c is adjacent to ∠Y.

The sides XZ and ZY form the right angle, thus one is base and the other is perpendicular.

Now, in relation to ∠Y, side ZY of length a is the base (adjacent to angle Y)

Similarly, side XZ of length b forms the perpendicular and is opposite to ∠Y.

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The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°

In triangle ∆MDK, we have;

m = 16.4

d = 22

k = 19

Using cosine rule, we get;

d² = m² + k² - 2•m•k•cos(D)

Therefore;

2•m•k•cos(D) = m² + k² - d²

[tex]D = arccos \left( \frac{ {m}^{2} + {k}^{2} - {d}^{2} }{2 \cdot m \cdot k} \right)[/tex]

Which gives;

[tex]D = arccos \left( \frac{ {16.4}^{2} + {19}^{2} - {22}^{2} }{2 \times 16.4 \times 19} \right) \approx {76}^{ \circ} [/tex]

The correct option is therefore;

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Answer:

76

Step-by-step explanation:

Use the Law of Cosines to find m∠D

.The figure shows the same triangle as in the beginning of the task. Angle M D K is highlighted in red.

Set up the equation for the Law of Cosines.

d2=k2+m2−2kmcosD

Substitute the given values and solve for m∠D

.222=192+16.42−2(19)(16.4)cosD

Simplify.

484=629.96−623.2cosD

Subtract 629.96

.−145.96=−623.2cosD

Divide by −623.2

0.234=cosD

Use the inverse cosine function to find m∠D

and round to the nearest degree.

The figure shows a screen of a graphical calculator. The inverse cosine of 0 point 2 3 4 is calculated. The result is 76 point 4 6 7 3 1 6 4 6.

m∠D=cos−1(0.234)≈76∘

Therefore, m∠D≈76∘

hope it helps you!

.

Answer:

86

Step-by-step explanation:

t = ten's digit    u= one's digit

t + u = 14            t = 2u - 4

In the first equation substitute for t 2u - 4 that we find in the second equation above.

t + u = 14

2u - 4 + u = 14  Combine the u's

3u - 4 = 14  Now add 14 to both sides

3u = 18  Divide both sides by 3

u = 6.  We found the unit's digit, now we will find the ten's unit by plugging in 6 for u in the first equation above.

t + u = 14

t + 6 = 14  Subtract 6 from both sides

t = 8

So, your answer is 86.

The scale factor is 2.875 miles per inch. Then the actual distance from the library to the park will be 2.875 miles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Micah drew a map of his neighborhood. The actual distance from his house to the school is 5.75 miles. Then the scale factor is given as,

Scale factor = 5.75 / 2

Scale factor = 2.875 miles per inch

Then the actual distance from the library to the park is given as,

D = 1 x 2.875

D = 2.875 miles

The scale factor is 2.875 miles per inch. Then the actual distance from the library to the park will be 2.875 miles.

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The missing diagram is given below.

Answer:

2.875 miles per inch

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12

7x3=21

[tex]\frac{12}{21} = \frac{4}{7}[/tex]

Charles' weight = Edith's weight + 20% of Edith's weight

We'll use a variable to represent Edith's weight, x.

The decimal form of 20% is 0.2.

60 = x + 0.2x

60 = 1.2x

x = 50

Edith's weight is 50kg.

Hope this helps!