Lesson 14
Reflecting points page 134
How do I upload a picture to get help with this?

Step-by-step explanation:

Given:

A+B+C= π

<=> 3A+3B+3C = 3π

<=> cos(3A+3B) = - cos3C

<=> cos3A.cos3B-sin3A.sin3B = - cos3C

<=> cos3A.cos3B = sin3A.sin3B  - cos3C (1)

similarly  apply for the other two angles, we have:

Grouping three equations, (1) + (2) + (3), we have:

<=> cos3A.cos3B+cos3B.cos3C+cos3C.cos3A = sin3A.sin3B + sin3B.sin3C + sin3C.sin3A - ( cos3A  + cos3B + cos3C )

= 1  

Hope it can find you well.

Using the sum of angles in a triangle and cosine identities, we proved that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) equals 1.

Given that A + B + C = π, we will use trigonometric identities and properties to prove the required equation.

Hence, we have proven that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) = 1 for angles A, B, and C summing up to \pi.

Answer:

The right answer is:

(i) The student who weighed the rock 20 times.

Step-by-step explanation:

Both students are taking a sample from the population. In this case, the population is all the possible weight that can be measured by the scale they are using.

Independently of the sample size, the sampling distribution mean will be centered in the population mean, so they are estimating the true weight of the rock unbiased.

But the spread of the sampling distribution, measaured by the standard deviation, depends on the sample size.

The bigger the sample, the narrower the sampling distribution is expected o be. So it is more likely to be closer to the true mean with a bigger sample.

The right answer is:

(i) The student who weighed the rock 20 times.

Answer:

P(1) = 0.2857

P(2) = 0.1428

P(3) = 0.1428

P(4) = 0.1428

P(5) = 0.1428

P(6) = 0.1428

Step-by-step explanation:

From the question, we know that Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers, so we can write the following equation:

P(1) = 2X        

Where X is the probability of rolling each of the other five numbers or:

P(2) = P(3) = P(4) = P(5) = P(6) = X  

Additionally, the sum of all the probabilities is 1, so:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

Now, we can replace P(1) by 2X and P(2), P(3), P(4), P(5) and P(6) by X, as:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

2X  +   X   +    X   +   X  +   X   +   X  = 1

Finally, solving for X, we get:

7X = 1

X = 1/7

X = 0.1428

So, the probability of rolling a 1 is equal to:

P(1) = 2X  = 2*(0.1428) = 0.2857

And the probability of rolling each of the other five numbers is:

P(2) = P(3) = P(4) = P(5) = P(6) = X  

P(2) = P(3) = P(4) = P(5) = P(6) = 0.1428

Answer:

It's D.

Step-by-step explanation:

Answer:

3(x - 2)(x - 5)

Step-by-step explanation:

Factor 3 from all terms within the trinomial:

(3x² - 21x + 30)/3 = x² - 7x + 10

3(x² - 7x + 10)

Simplify.

(x² - 7x + 10)

x               -5

x               -2

3(x - 2)(x - 5)* is your answer.

* remember to bring the 3 that you factored out in the beginning and stick it to the front.

~

Answer:

see below

Step-by-step explanation:

x and 80 are adjacent, supplementary angles

Supplementary angles add to 180

x+80 =180 degrees

Subtract 80 from each side

x+80-80=180-80

x=100

Answer:

[tex] 12 +18 + x+y + z +w[/tex]

In this special case we know that [tex] x+y =12[/tex] and [tex] z+w =18[/tex]  and for this case we can add all the values 12+18 +12+18=60 and that represent the perimeter  

Step-by-step explanation:

For this case we know that the perimeter is given by:

[tex] 12 +18 + x+y + z +w[/tex]

In this special case we know that [tex] x+y =12[/tex] and [tex] z+w =18[/tex]  and for this case we can add all the values 12+18 +12+18=60 and that represent the perimeter  

Answer:

See explaination

Step-by-step explanation:

Stoke theorem proposes that the surface integral of the curl of a function over any surface bounded by a closed path is equal to the line integral of a particular vector function round that path.

The Stoke Theorem can be used if you see a two dimensional region bounded by a closed curve, or if you see a single integral ie a line integral.

See attached file for further solution.

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

the 2 given angles are vertical angles, meaning they are equal.

38x-1 = 75

solve the above equation, and x = 2

Answer:

2

Step-by-step explanation:

Those two angles are equal:

75 = 38x - 1

so, add 1 to both

76 = 38x

divide by 38

2 = x

Answer: -1.17

Step-by-step explanation:

I guessed and got it right

Final answer:

The z-score of a baseball pitch thrown at 86.2 mph is -1.17, calculated using the z-score formula with a mean pitch speed of 89 mph and a standard deviation of 2.4 mph. Thus, option A is correct.

Explanation:

The question asks for the z-score of a baseball pitch thrown at a speed of 86.2 mph, given that the mean speed of pitches is 89 mph with a standard deviation of 2.4 mph. To find the z-score, we use the formula:

Z = (X - μ) / σ

Where Z is the z-score, X is the value in question (86.2 mph), μ is the mean (89 mph), and σ is the standard deviation (2.4 mph).

Plugging in the values, we get:

Z = (86.2 - 89) / 2.4

Z = -2.8 / 2.4

Z = -1.17

Thus, the z-score of the pitch thrown at 86.2 mph is -1.17, rounded to two decimal places.

Answer:

THIS IS A RIDDLE

Step-by-step explanation:

GO TO THE RIDDLE SECTION

Answer:

Use order of operation

Step-by-step explanation:

Answer:

2(x+8)(x-7)

Step-by-step explanation:

If the question is asking 2x^2+2x-112, then the answer is 2(x+8)(x-7).

First, you factor out the two: 2(x^2+x-56)

Next, you find something that adds to x and multiplies to -56: 8 and -7

After, you get 2(x+8)(x-7)

Answer:

m = all real numbers

Step-by-step explanation:

Using this equation, you end up with 0 = 0. This means that m is all real numbers.

Answer:

173

Step-by-step explanation:

Same thing as last time, just instead of 90, it's 180.

Answer:

The largest value is -2 from -16/ 8

The largest absolute value is -108  from -16*8

Step-by-step explanation:

Are you asking for the greatest value?

The largest number?

-16 * 8 =   - 108

-16 / 8 = -2

-16 + 8 = -8

-16 - 8 = -24

The largest value is -2 from -16/ 8

The largest absolute value is -108  from -16*8

Answer:

The answer is A. True

Step-by-step explanation:

The range of Fx) = 7*4^x is all positive real numbers.

hope this helps : )

Answer:

Formula could be :: (N)4 with n being the number

Step-by-step explanation:

Answer:

It's B) 0.25 * 4^n-1 and third one is B

Step-by-step explanation:

Answer: 24 in.2

30 in.2

20.8 in.2

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

We notice this is an arithmetic sequence.

14, 9,  4.

common difference = d = 14 - 9 = 5

first term a_1 = 14

Find 6th term a_6

a_n = (n -1)*d + a_1

a_6 = (6 -1)*5 + 14

a_6 = 5*5 + 14 = 25 + 14 = 39

Answer:

Length of x ~ 10.5; Option B

Step-by-step explanation:

1. There are three radii present in this problem. Of that the diamter is supposedly 42.2 units. Given that the radii should be ⇒ 42.2 / 2 ⇒ 21.2 units

2. With that being said the 3rd radii contains parts x and 10.6. By radii congruency, the length of all radii should be the same, so this 3rd radii should = 21.2 units as well. If so, by the Partition Postulate 21.2 = x + 10.6

3. Through algebra let us solve for x:

21.2 = x + 10.6,

x = 21.2 - 10.6,

Answer ~ Length of x: 10.5

Answer:

Step-by-step explanation:

The volume of a cube is the cube of the edge dimension. Here, that dimension is 5/8 in, so the volume is ...

  V = s³ = (5/8 in)³ = 125/512 in³ . . . volume of the cube

The volume of a cube 1/8 inch on a side is ...

  V = (1/8 in)³ = 1/512 in³

Clearly, a volume that is 125/512 in³ will require 125 of the cubes of size 1/512 in³ to fill it.

  125 of the smaller cubes will fit inside.

_____

Alternate solution

You can also determine the number of smaller cubes by considering it takes 5 of them in each direction to make 5/8 inch. Then the volume is 5³ = 125 of the smaller cubes.

Answer:

99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Step-by-step explanation:

We are given that a survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know."

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                                 P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of people who disagree with the statement = [tex]\frac{1812}{2625}[/tex] = 0.69

           n = sample of respondents = 2625

           p = population proportion of people who disagree with statement

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                   of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

= [ [tex]0.69-2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] , [tex]0.69+2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] ]

 = [0.667 , 0.713]

Therefore, 99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Answer:

100(2m)

(1+0.4)

Nathan=0.4 is the percent added =the 40 percent added to the 10 amoebas

Jennifer=the first equation is how many total amoebas Jennifer has in total

Answer:

Hope this helps!

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below for the full explanation to the above question.

The final expression for the triple integral in spherical coordinates is:

[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ

To evaluate the given integral efficiently in spherical coordinates, we'll set up the triple integral over the unit ball centered at the origin. The integral represents the volume element for a sphere, which we can express in spherical coordinates as follows:

∭D (x² + y² + z²)^(3/2) dV

In spherical coordinates, the volume element dV is given by:

dV = ρ² sin(φ) dρ dφ dθ

Here, ρ represents the radial distance from the origin, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).

The limits of integration for the triple integral in spherical coordinates can be set as follows:

ρ: 0 to 1 (since D is the unit ball, ρ ranges from 0 to the radius of the sphere, which is 1)

φ: 0 to π/2 (since we only need to consider the upper half of the sphere)

θ: 0 to 2π (covering a full revolution around the z-axis)

Now, we can express the integral using these limits and the volume element:

∭D (x² + y² + z²)[tex]^{(3/2)[/tex] dV

= ∫[0 to 2π] ∫[0 to π/2] ∫[0 to 1] (ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) dρ dφ dθ

Simplifying the integrand:

(ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) = ρ³ ρ sin(φ) = ρ⁴ sin(φ)

Therefore, the final expression for the triple integral in spherical coordinates is:

[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ

Learn more about triple integral click;

https://brainly.com/question/30404807

#SPJ6

Answer:

[tex]P(x\geq 17)=0.00128[/tex]

Step-by-step explanation:

The probability that the man gets x out of 20 correct follows a Binomial distribution, so the probability is calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Where n is the number of identical experiments and p is the probability of success. In this case n is 20.

Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.

Then, the probability that he gets x out of 20 correct is equal to:

[tex]P(x)=\frac{20!}{x!(20-x)!}*0.5^{x}*(1-0.5)^{20-x}[/tex]

Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:

[tex]P(x\geq 17)=P(17)+P(18)+P(19)+P(20)\\[/tex]

Where:

[tex]P(17)=\frac{20!}{17!(20-17)!}*0.5^{17}*(1-0.5)^{20-17}=0.00108719\\P(18)=\frac{20!}{18!(20-18)!}*0.5^{18}*(1-0.5)^{20-18}=0.00018119\\P(19)=\frac{20!}{19!(20-19)!}*0.5^{19}*(1-0.5)^{20-19}=0.00001907\\P(20)=\frac{20!}{20!(20-20)!}*0.5^{20}*(1-0.5)^{20-20}=0.00000095[/tex]

So, [tex]P(x\geq 17)[/tex] is equal to:

[tex]P(x\geq 17)=0.00108719+0.00018119+0.00001907+0.00000095\\P(x\geq 17)=0.00128[/tex]

The probability that he would have done at least 17 out of 20 if he had no ESP is 0.00128 and this can be determined by using the binomial distribution formula.

Given :

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict the outcome in advance. He gets 17 out of 20 correct.

The formula of the binomial distribution is given by:

[tex]\rm P(x)=\dfrac{n!}{x!(n-x)!}\times p^x \times (1-p)^{n-x}[/tex]

Now, put all the known terms in the above formula.

[tex]\rm P(x)=\dfrac{20!}{x!(20-x)!}\times 0.5^x \times (1-05)^{20-x}[/tex]

Now, the probability that he would have done at least 17 out of 20 if he had no ESP:

[tex]\rm P(x\geq 17) = P(17)+P(18)+P(19)+P(20)[/tex]

where:

[tex]\rm P(17)=\dfrac{20!}{(20-17!)}\times 0.5^{17}\times 0.5^{20-17}=0.00108719[/tex]

[tex]\rm P(18)=\dfrac{20!}{(20-18!)}\times 0.5^{18}\times 0.5^{20-18}=0.00018119[/tex]

[tex]\rm P(19)=\dfrac{20!}{(20-19!)}\times 0.5^{19}\times 0.5^{20-19}=0.00001907[/tex]

[tex]\rm P(20)=\dfrac{20!}{(20-20!)}\times 0.5^{20}\times 0.5^{20-20}=0.00000095[/tex]

So, the value of P(x [tex]\geq[/tex] 17) is:

[tex]\rm P(x\geq 17)= 0.00108719+0.00018119+0.00001907+0.00000095[/tex]

[tex]\rm P(x\geq 17)= 0.00128[/tex]

For more information, refer to the link given below:

https://brainly.com/question/2561151

Answer:

it is b

Step-by-step explanation:6 square

Answer:

b

Step-by-step explanation: