The arc length apothem shown below is 15 feet. Part 1) State the equation that relates arc length to central angle. Part 2) Find the angle apothem in radians. Part 3) Convert your answer from Part 2 to degrees and write it to the nearest hundredth of a degree

Answer:

The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.

Step-by-step explanation:

We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.

Let X = binomial random variable

So, X ~ Binom(n = 50, p = 0.2)

Now, the mean of the binomial distribution is given by;

         Mean of X, E(X) = n [tex]\times[/tex] p

                                    = 50 [tex]\times[/tex] 0.2 = 10

Now, the variance of the binomial distribution is given by;

        Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)

                                         = 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)

                                         = 10 [tex]\times[/tex] 0.8 = 8

Also, the standard deviation of the binomial distribution is given by;

        Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]

                                                              = [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]

                                                              = [tex]\sqrt{8}[/tex] = 2.83

Answer:

The equation is always false

Step-by-step explanation:

arctan1/4+arctan2/7=1/2arccos3/5

0.24497866+0.27829965=1/2(0.92729521)

0.52327832                 =0.46364760

not equivalent and will never be.

Answer:

9

Step-by-step explanation:

What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.

We can now use a proportion to find the value of w.

[tex]\frac{4}{3} = \frac{12}{x}[/tex]

Cross multiply:

[tex]12\cdot36 = 36\\\\36\div4=9[/tex]

Hope this helped!

Answer: 9

Step-by-step explanation:

Answer:

[tex]y = 4x + 14[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation we must first find the slope of the line

Slope of the line using points (−2, 6) and (2, 14) is

[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]

Now we use the slope and any of the points to find the equation of the line.

Equation of the line using point ( - 2, 6) and slope 4 is

[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]

We have the final answer as

[tex]y = 4x + 14[/tex]

Hope this helps you

The number two is a function

First rule of function: for each element of A there is one and only one element of B

For example, in the first one -5 is "collegated" to -2 and 3. So this isn't a function.

Naturally,  every element of B can have more element of A

Answer:  [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Step-by-step explanation:

[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

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          Hi my lil bunny!

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When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A. remainder

B. dividend

C. quotient

D. divisor

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

a. remainder

Step-by-step explanation:

took the test

dont leave your house without a vest

or you will get hit in the vital organs in your chest

Answer:

50hours

Step-by-step explanation:

Given that there are 400 pages in Sheila's favorite book.

The average number of words per page in the book is 300

She types an average rate of 40words per minute.

So to type 400pages of the book

Total number of words in the pages = 400×300 = 120000 words

Typing rate : 40words ------- 1minute

120000 words ----------- x minutes

Hence we have 40 × X mins = 120000 × 1min

Make X the subject

40X = 120000minutes

X = 120000/40

X = 3000minutes

Since 60minutes = 1hour

3000minutes = 3000minutes/60

= 50hours

Hence it took her 50hours to type 400pages

Solution:

The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.

Answer:

[tex]\dfrac{-14}{9}[/tex].

Step-by-step explanation:

The given number is [tex]-1.\overline{5}[/tex].

We need to find a rational number in fraction form that is equivalent to given number.

Let [tex]x=-1.\overline{5}[/tex]

[tex]x=-1.555...[/tex]     ...(1)

Multiply both sides by 10.

[tex]10x=-15.555...[/tex]  ...(2)

Subtracting (1) from (2), we get

[tex]10x-x=-15.555...-(-1.555...)[/tex]

[tex]9x=-14[/tex]

Divide both sides by 9.

[tex]x=\dfrac{-14}{9}[/tex]

Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].

Answer:

The legs are 12 cm each, so the hypotenuse is

√(144+144)=12√2

Step-by-step explanation:

Applying the Pythagorean Theorem, the length of the hypotenuse is:  12√2 cm.

Given the two legs of the right triangle to be 12 cm

c² = 12² + 12².

c² = 288

c = √288

c = 12√2 cm

Therefore, applying the Pythagorean Theorem, the length of the hypotenuse is:  12√2 cm.

Learn more about, the Pythagorean Theorem on:

https://brainly.com/question/654982

Answer:

1.16

Step-by-step explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0)  =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) =  0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the  left until the first column is reached, we see that the value was 1.1.  similarly, we did the same in the  upward direction until the top row is reached, the value was 0.06.  The intersection of the row and column values gives the area to the two tail of z.   (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877

Answer:

±7 sqrt(2) = x

Step-by-step explanation:

98 - x^2 = 0

Add x^2 to each side

98 =x^2

Take the square root of each side

±sqrt(98) = sqrt(x^2)

±sqrt(49*2) = x

±7 sqrt(2) = x

Answer:

[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]

Step-by-step explanation:

[tex]98-x^2 =0[/tex]

[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]

[tex]98=x^2[/tex]

[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]

[tex]\pm \sqrt{98} =x[/tex]

[tex]\sf Simplify \ radical.[/tex]

[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]

[tex]\pm 7\sqrt{2} =x[/tex]

[tex]\sf Switch \ sides.[/tex]

[tex]x= \pm 7\sqrt{2}[/tex]

Answer:

x = -264/35

y = -36/5

Step-by-step explanation:

-6y + 11y = -36

-4y + 7x = -24

Solve for y in the first equation.

-6y + 11y = -36

Combine like terms.

5y = -36

Divide both sides by 5.

y = -36/5

Plug y as -36/5 in the second equation and solve for x.

-4(-36/5) + 7x = -24

Expand brackets.

144/5 + 7x = -24

Subtract 144/5 from both sides.

7x = -264/5

Divide both sides by 7.

x = -264/35

Answer: -264/35

Step-by-step explanation:

i did my work on a calculator

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]

   =>  [tex]\alpha = 5\%[/tex]

  =>    [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

Stratified Random sampling.

Step-by-step explanation:

As per the scenario, It is stratified random sampling as it divides students into strata which represent Sophomores, Juniors, and Seniors.

Simple random samples of the given sizes of the proportional to the size of the stratum which is to be taken from every stratum that is to be about 10 percent of students from every class that is selected here.

Hence, according to the given situation, the correct answer is a random stratified sampling.

Answer:

  53

Step-by-step explanation:

Let's start with the given relation:

  2x -7 = (x+4) +5

  x = 16 . . . . . . . . . add 7-x

  3x +5 = 3(16) +5 = 53 . . . . . multiply by 3 and add 5

The value of 3x+5 is 53.

julissa gave equal oranges in 6 apartments

she gave each apartment 5 oranges

so total no. of oranges are = 6×5 = 30

Answer:

D. 30

Step-by-step explanation:

Answer:

y = $1.542 per lb

Step-by-step explanation:

given data

mixed-nut blend store cost  2005 = $1.35 per lb

blend cost in 2010 = $1.83 per lb

solution

we consider here y = cost of a pound

and x year = after 2005

we will use here linear equation model

so

[tex]\frac{y - 1.35}{1.83-1.35} = \frac{x-10}{5 - 0}[/tex]    .........................1

solve it we get

5y - 6.75 = .48 x

so

at 2007 year here x wil be 2

so

[tex]y = \frac{0.48 \times 2 + 6.75}{5}[/tex]  

solve it we get

y = $1.542 per lb

Answer:

Desmos could come in handy

Answer:

Step-by-step explanation:

x² - 5x - 36

To factor the expression rewrite -5x as a difference

That's

x² + 4x - 9x - 36

Factor out x from the expression

x( x + 4) - 9x - 36

Factor out -9 from the expression

x( x + 4) - 9( x+ 4)

Factor out x + 4 from the expression

The final answer is

Hope this helps you

Answer:

[tex] \boxed{(x - 9) \: (x + 4) }[/tex]

Option A is the correct option.-

Step-by-step explanation:

( See the attached picture )

Hope I helped!

Best regards!

Answer:

Step-by-step explanation:

Given that v(x) = g(x)×(3/2*x^4+4x-1)

Let's find V'(2)

V(x) is a product of two functions

● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)

We are interested in V'(2) so we will replace x by 2 in the expression above.

g'(2) can be deduced from the graph.

● g'(2) is equal to the slope of the tangent line in 2.

● let m be that slope .

● g'(2) = m =>g'(2) = rise /run

● g'(2) = 2/1 =2

We've run 1 square to the right and rised 2 squares up to reach g(2)

g(2) is -1 as shown in the graph.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's derivate the second function.

Let h(x) be that function

● h(x) = 3/2*x^4 +4x-1

● h'(x) = 3/2*4*x^3 + 4

● h'(x) = 6x^3 +4

Let's calculate h'(2)

● h'(2) = 6 × 2^3 + 4

● h'(2) = 52

Let's calculate h(2)

●h(2) = 3/2*2^4 + 4×2 -1

●h(2)= 31

■■■■■■■■■■■■■■■■■■■■■■■■■■

Replace now everything with its value to find V'(2)

● V'(2) = g'(2)×h(2) + g(2)× h'(2)

● V'(2)= 2×31 + (-1)×52

●V'(2) = 61 -52

●V'(2)= 9

let each box length be 1

for white triangle

area = ½bh

=½(4)(2)

=4

for orange triangle

area=½(2)(3)

=3

for blue marked boxes

each of the box

area=l²

=(1)²

=1

there are 16 boxes

so the total area will be 16

total area of the hexagon = 4+3+16

=23 square units

[tex]A_1=\dfrac{1}{2}(3+5)\cdot 3=12\\A_2=1\cdot5=5\\A_3=\dfrac{1}{2}(5+1)\cdot 2=6[/tex]

So the area of the whole shape is [tex]12+5+6=23[/tex]

Answer:

b

Step-by-step explanation:

Answer:

5 5/12

Step-by-step explanation:

31/6 feet + 1/4 foot

= 31/6 + 1/4

= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]

=  [ 124/24 ] + [ 6/24 ]

= (124 + 6) / 24

= 130 / 24

= 5 10/24

= 5 5/12

Hope this helps!  Tell me if I'm wrong!

━━━━━━━☆☆━━━━━━━

▹ Answer

1/2k - 3/5

▹ Step-by-Step Explanation

2/5k - 3/5 + 1/10k

Collect like terms:

2/5k + 1/10k = 1/2

Final Answer:

1/2k - 3/5

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1/2k - 3/5

Step-by-step explanation:

Hey there!

Well the only fraction needed to combine are,

2/5 and 1/10.

To add them we need to make 2/5 have a denominator of 10.

To do that we multiply 5 by 2.

5*2 = 10

What happens to the denominator happens to the denominator.

2*2 = 4

Fraction - 4/10

4/10 + 1/10 = 5/10

5/10

simplified

1/2

1/2k - 3/5

Hope this helps :)

Answer:

1 hour

Step-by-step explanation:

Hello, let's say that her departure trip takes t in minutes, as her return speed is 3 times her departure speed, she took t/3 for the return and we know that this 40 minutes less, so we can write.

t/3=t-40

We can multiply by 3

t = 3t -40*3 = 3t - 120

This is equivalent to

3t -120 = t

We subtract t

2t-120 = 0

2t = 120

We divide by 2

t = 120/2 = 60

So this is 60 minutes = 1 hour.

Thank you.

Answer:

Increasing

0°≤x≤180°

Decreasing

180°≤x≤360°

Answer:

[tex]\Large \boxed{\sf True}[/tex]

Step-by-step explanation:

[tex]\sf A \ diameter \ that \ is \ perpendicular \ to \ a \ chord \ bisects \ the \ chord.[/tex]

Answer:

True!!

I just did the assignment and got it right

Answer:

40.5

Step-by-step explanation:

diameter^2 = (3 +6)^2 + (5+4)^2

or, d^2 = 9^2 + 9^2

or, d^2 = 81 +81

or,d^2 =162

or d=√ 162

• d= 81

then radius = d/2

r = 81/2

•r= 40.5 ans