Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
I need help with the k+1 part of the proof

Answer:

Where is the equation?

Step-by-step explanation:

Answer:

I don't understand

Step-by-step explanation:

Are you Issac?

What is the question?

Answer:

This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].

For the proof, make use of the fact that:

[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and

[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].

Step-by-step explanation:

Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.

Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:

[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].

Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:

[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].

Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].

Answer:

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have that:

The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].

Sample of n games:

This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Answer:

x=9

Step-by-step explanation:

Answer:

the answer is 10

Step-by-step explanation:

Answer:

(a) The mean is 0

(b) The median is -30

(c) The mode is unimodal

Step-by-step explanation:

Given

[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]

Solving (a): The mean.

This is calculated using:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]

[tex]\bar x =\frac{0}{8}[/tex]

[tex]\bar x =0[/tex]

Solving (b): The median

First, arrange the data

[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]

There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.

[tex]Median = \frac{-4-2}{2}[/tex]

[tex]Median = \frac{-6}{2}[/tex]

[tex]Median = -3[/tex]

Solving (c): The mode

The item that has occurs most is -10.

Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).

Answer:

300 miles

Step-by-step explanation:

425 / 17 = 25

25×12=300

Answer:

1,736 chocolate cover peanuts

Step-by-step explanation:

do 28×62 hope this helps

Answer:

1736 chocolate-covered peanuts

Step-by-step explanation:

[tex]\frac{1}{62} :\frac{28}{y}[/tex]

1 · y = 62 · 28

y = 1736

Answer:

4.5 hours

Step-by-step explanation:

8t + 10(7-t) = 61

8t +70-10t=61

-2t = 61-70

-2t= -9

t = -9/-2

t = 4.5

Answer:

to put the equation into standard for we must multiply the terms on the right side of the equation. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Step-by-step explanation:

y

=

(

x

−

13

)

(

x

−

12

)

becomes:

y

=

(

x

×

x

)

−

(

x

×

12

)

−

(

13

×

x

)

+

(

13

×

12

)

y

=

x

2

−

12

x

−

13

x

+

156

We can now combine like terms:

y

=

x

2

+

(

−

12

−

13

)

x

+

156

y

=

x

2

+

(

−

25

)

x

+

156

y

=

x

2

−

25

x

+

156

Answer:

94

Step-by-step explanation:

We know that a straight line adds up to 180 degrees, and angle QPS, summed up by angles QPR and RPS, equals that.

Therefore,

angle QPS = QPR + RPS

180 = QPR + RPS

180 = 7x-4+9x-40

180 = 16x-44

224= 16x

x = 222/16 = 14

QPR  = 7x-4 = 94

Answer:

x=3

Step-by-step explanation:

Answer:

The answer is 0.5

Answer:

rhe answer is r= .50

Step-by-step explanation:

125-75=50

Answer:

[tex]x\approx 5.48[/tex]

Step-by-step explanation:

Draw a line from the center of the circle O to the end of either side of the line marked as 4. This line represents two things:

In this case, both are important. Since [tex]x[/tex] is also a radius of the circle, the line must be equal to [tex]x[/tex], since all radii of a circle are equal. To find the length of this line, use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

Since we're solving for the hypotenuse and the two legs are 5.1 and 2, we have:

[tex]5.1^2+2^2=c^2,\\26.01+4=c^2,\\c^2=30.01,\\c=5.47813836992\approx \boxed{5.48}[/tex] (round as necessary).

Answer:

[tex]y=2[/tex]

Step-by-step explanation:

In [tex]y=a\cos(bx-c)+d[/tex], [tex]d[/tex] represents the vertical shift. The midline of the function is given by [tex]y=d[/tex], because the parent function [tex]y=\cos x[/tex] has a midline at [tex]y=0[/tex]. Therefore, the midline of the function [tex]y=\cos (\frac{2\pi}{3}x)+2[/tex] is [tex]\boxed{y=2}[/tex]

Answer:- Hey Buddy! Hope this helps:-

12.5%= 125/10 and when simplified becomes 25/2

pls mark brainliest

9514 1404 393

Answer:

  (a) On a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1

Step-by-step explanation:

A log function does not have a graph that is a line, parabola, or hyperbola. Its graph has a vertical asymptote at x=0, and a x-intercept at x=1. It has positive slope everywhere.

Answer:

A. Acute

B. 80 degrees

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

3    :    4

^          ^

II          II

red    blue

Answer:

Hence when the radius is halved the area is divided by 4

2.5 inches^2

Step-by-step explanation:

Given data

Area= 10inches^2

We know that the expression for the area of  a circle is given as

Area= πr^2

10= 3.142*r^2

10/3.142= r^2

r^2= 3.18

Square both sides

r= √3.18

r= 1.78 inches

Now let us half the radius and find the area of the new circle

r/2= 1.78/2

r= 0.89

Area of the new circle is

Area= 3.142*0.89^2

Area= 3.142*0.7921

Area= 2.5 inches^2

Answer:

The distance between A(-8, 4) and B(4, -1) is 13 units.

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula given by:

[tex]\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

We have the two points A(-8, 4) and B(4, -1). Let A(-8, 4) be (x₁, y₁) and let B(4, -1) be (x₂, y₂). Substitute:

[tex]d=\sqrt{(4-(-8))^2+(-1-4)^2}[/tex]

Evaluate:

[tex]d=\sqrt{(12)^2+(-5)^2}[/tex]

So:

[tex]d=\sqrt{144+25}=\sqrt{169}=13\text{ units}[/tex]

The distance between A(-8, 4) and B(4, -1) is 13 units.

___________________________________

[tex]\quad\quad\quad\quad\tt{A.) x\tiny{1}\small{=-8}, y\tiny{1}\small{=4}}[/tex]

[tex]\quad\quad\quad\quad\tt{B.) x\tiny{2}\small{=4}, y\tiny{2}\small{=-1}}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{(x \tiny{2} \small{ - x \tiny{1} \small {)}^{2} + (y \tiny{2} \small{ - y \tiny{1} \small{)}^{2} } }}} [/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{(4 - \small{ (- 8}{))}^{2} + ( \small{- 1)}\small{ - {4)}}^{2} }}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{ ( {12)}^{2} + {( -5)}^{2} }}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{ {144} + {25}}}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{ 169}}[/tex]

[tex]\quad\quad\quad\quad\tt{d = 13}[/tex]

[tex]\quad\quad\quad\quad\boxed{\boxed{\tt{\color{magenta}d = 13}}}[/tex]

___________________________________

#CarryOnLearning

✍︎ C.Rose❀

Answer:

84

Step-by-step explanation:

god bless stay safe po

Answer: wheres the photo ?

Step-by-step explanation:

Answer:

-3-4=-7

-3+(-4)

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

[tex]\displaystyle -x^3+10x^2-48x+64[/tex]

Step-by-step explanation:

We want to find the minimum-degree polynomial with real coefficients and zeros at:

[tex]x= 4+4i\text{ and } x = 2[/tex]

As well as a y-intercept of 64.

By the Complex Root Theorem, if a + bi is a root, then a - bi is also a root.

So, a third root will be 4 - 4i.

The factored form of a polynomial is given by:

[tex]P(x)=a(x-p)(x-q)...[/tex]

Where a is the leading coefficient and p and q are the zeros. More factors can be added if necessary.

Substitute:

[tex]P(x)=a(x-(2))(x-(4+4i))(x-(4-4i))[/tex]

Since we want the minimum degree, we won't need to add any exponents.

Expand the second and third factors:

[tex]\displaystyle \begin{aligned} (x-(4+4i))(x-(4-4i))&=(x-4-4i)(x-4+4i) \\ &= x(x-4-4i)-4(x-4-4i)+4i(x-4-4i)\\ &=x^2-4x-4ix-4x+16+16i+4ix-16i-16i^2\\ &= x^2-8x+32\end{aligned}[/tex]

Hence:

[tex]P(x)=a(x-2)(x^2-8x+32)[/tex]

Lastly, we need to determine a. Since the y-intercept is y = 64, this means that when x = 0, y = 64. Thus:

[tex]64=a(0-2)(0^2-8(0)+32)[/tex]

Solve for a:

[tex]-64a=64\Rightarrow a=-1[/tex]

Our factored polynomial is:

[tex]P(x)=-(x-2)(x^2-8x+32)[/tex]

Finally, expand:

[tex]\displaystyle \begin{aligned} P(x) &=-(x^2(x-2)-8x(x-2)+32(x-2)) \\&=-(x^3-2x^2-8x^2+16x+32x-64)\\&=-(x^3-10x^2+48x-64)\\&= -x^3+10x^2-48x+64\end{aligned}[/tex]

9514 1404 393

Answer:

  x = 25

Step-by-step explanation:

The parallel lines divide the triangle sides proportionally.

  x/40 = 15/24

  x = 40(15/24) . . . . multiply by 40

  x = 25

Answer:

Step-by-step explanation:

Answer:

The amount of interest he paid at the end of the loan is $ 311.85.

Step-by-step explanation:

Given that Juan borrowed $ 1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%, to determine what is the amount of interest he paid at the end of the loan, the following calculation must be performed:

(1500 x 0.0297) x 7 = X

44.55 x 7 = X

311.85 = X

Therefore, the amount of interest he paid at the end of the loan is $ 311.85.

Answer:

158

Step-by-step explanation:

The cost of the minimum spanning tree to connect all four landmarks will be $158.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The cost to make a path connecting all four landmarks is based on the proposal shown.

The cost of path A is $29.

The cost of path B is $59.

The cost of path C is $32.

The cost of path D is $38.

Then the cost of the minimum spanning tree to connect all four landmarks will be

Total cost = cost of path A + cost of path B + cost of path C + cost of path D

Total cost = $29 + $59 + $32 + $38

Simplify the expression, then we have

Total cost = $29 + $59 + $32 + $38

Total cost = $158

More about the Algebra link is given below.

https://brainly.com/question/953809

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