write an equation to represent the following statement 29 is 6 more than K solve for K

K =

Answer:

8.4ft

Step-by-step explanation:

Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]

[tex]\theta[/tex] is the central angle = π/3 rad

r is the radius of the circle = 8ft

Substituting the values into the formula above we have;

[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]

[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]

Hence, the length of the arc s is approximately 8.4 ft.

Answer:

Part A- 6

Part B- 3

Part C- 3/22100

Step-by-step explanation:

Part A-

Use the permutation formula and plug in 3 for n and 2 for k.

nPr=n!/(n-k)!

3P2=3!/(3-2)!

Simplify.

3P2=3!/1!

3P2=6

Part B-

Use the combination formula and plug in 3 for n and 2 for k.

nCk=n!/k!(n-k)!

3C2=3!/2!(3-2)!

Simplify.

3C2=3!/2!(1!)

3C2=3

Part C-

It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.

I believe the answer is 3/22100

I honestly suck at probability but I tried my best.

Answer:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

[tex]y=a\cos(b(x-c))+d[/tex]

Where:

[tex]|a|[/tex] is the amplitude

[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

[tex]c[/tex] is the horizontal displacement

[tex]d[/tex] is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:

[tex]\frac{2\pi}{b}=2[/tex]

[tex]2\pi=2b[/tex]

[tex]\pi=b[/tex]

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

[tex]\frac{\max-\min}{2}[/tex]

[tex]\frac{54-4}{2}[/tex]

[tex]\frac{50}{2}=25=a[/tex]

Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]

Because cosine starts at the minimum, [tex]c=0[/tex].

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Answer:

retype that im not understanding .

Step-by-step explanation:

Answer:

The correct answer for the best line of fit is C: y = 1/3x+12

Step-by-step explanation:

So our goal here is to find the best equation that matches the line of fit.

So right away we can already eliminate two of the options because in the scatter point it shows that the starting y-intercept is 12 and two of the options have a y-intercept of 15. So we are able to tell that Option B and Option D isn't the equation for the lien of fit.

Now we are left with Option A and Option C, which both have a y-intercept of 12. To find the right equation that best matches the line of fit we look at the slope. Option A has a slope of 3x while Option C has a slope of 1/3x, to tell what slope the line of has we applied both option's slope and see which one matches it.

When we match Option A's slope which is 3x it doesn't match because a slope of 3x is going first going up the y-axis 3 times then moving through the x-axis 1 time. Which would had made the line of fit more steep.

Next we match Option C's slope which is 1/3x this slope matches the line of fit because in the scatter plot it clearly shows  it going up 1 time on the y=axis and 3 times through the x-axis. Which made the line of fit not that steep.

So the correct answer to this question is C:  y = 1/3x+12.

Here a picture of the line of fit if it has a slope of 3x.

Answer:

correct answer  C: y = 1/3x+12

Step-by-step explanation:

i just did the problem

Answer:

  16x^3 +64x^2 -40x

Step-by-step explanation:

Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:

  8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)

  = 16x^3 +64x^2 -40x

Answer:

LL

Step-by-step explanation:

We have two right triangles

The two legs are congruent

We can use the LL congruence theorem

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

A

Step-by-step explanation:

When subtracting 7 on the left of the equation, he also needs to subtract 7 from the right of the equation.

Step 2 should be:

⅓X +7 -7= 15 -7

What he is trying to do here by subtracting 7 is to move all the constants, that is numbers without any variables such as x, to one side of the equation.

⅓X= 8

X= 8 ×3

X= 24

Answer:

Volume: 112 m³.

Surface area: 172 m².

Step-by-step explanation:

The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.

The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.

2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².

Hope this helps!

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Step-by-step explanation:

Formula for compound interest is given by

[tex]A = P(1 + R) ^{n} [/tex]

Where

A is the amount at the end of the period

P is the principal

R is the rate

n is the period

The interest = A - P

From the question

P = $ 3200

n = 3 years

R = 40%

So we have

[tex]A = 3200 \times 2.744[/tex]

A = $ 8780.80

The interest is

$ 8780.80 - $3200

Hope this helps you

Answer:

8.1% decrease

Step by step

To find precentage decrease we use formula:

Percent decrease= original amount-new amount/original amount(100%)

percent decrease= 7,400-6,800/7,400(100%)=300/37=8.1%

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )

AB × cos54° = 39 ( divide both sides by cos54° )

AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B

Explanation:

1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given

2. ∆CRH ~ ∆HSC — AA similarity theorem

3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent

4. CH ≅ HC — reflexive property of congruence

5. ∆CRH ≅ ∆HSC — SAS congruence theorem

6. CR ≅ HS — CPCTC

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer:

x= 1 + or - sr37/4 got it from a sitr

Here you go.

I really hope I helped. Good luck.

Answer:

x = 10

Step-by-step explanation:

We know x = 6

asked: x + 4

Plus it in =>

6 + 4

=> 10

Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

15.9degrees

Step-by-step explanation:

in photo above

Answer:

[tex]\boxed{15.95\°}[/tex]

Step-by-step explanation:

The angle can be found by using trigonometric functions.

tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]

tan (θ) = [tex]\frac{4}{14}[/tex]

θ = [tex]tan^{-1} \frac{4}{14}[/tex]

θ = 15.9453959

θ ≈ 15.95

Answer:

Step-by-step explanation:

Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;

a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))

Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }

since i² = -1

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }

From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and  sin(A+B) = sinAcosB + cosAsinB

The equation becomes

= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }

= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }

= 18{cos((41π)/30) + isin(41π)/30)) }

b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))

c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))

let A = pi/5 and B = 7pi/6

z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))

On rationalizing we will have;

= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))

= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}

= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}

From trigonometry identity; cos²B+sin²B = 1

= 16{cos(A+ B)-i(sin(A+B)}/64

=  16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64

= 16{ (cos 41π/30)-isin(41π/30)}/64

Z1/Z2 = (cos 41π/30)-isin(41π/30)/4

Answer:

13. 16(cos(41 π/30)+ isin(41 π/30))

14. Mine asked for z2 magnitude so I got 8 (magnitude is the same as modulus which is r)

15. 1/8 (cos(29 π/30)+ isin(29 π/30))

Step-by-step explanation:

13. Since we’re multiplying z1, and z2, use De Moivre’s theorem by multiplying the r values (2 and 8) and adding the theta values (π/5 and 7π/6). Adding the angle values should lead you to have 41 π/30, and the rest is self-explanatory.

14. Explanation is in the answer, just take the r value from z2 for magnitude (at least that’s what’s on my practice assignment)

15. Use De Moivre’s theorem again, this time with division, so you will divide the r values (2 divided by 8) and subtract the theta values (π/5 minus 7π/6). 2/8 simplifies to 1/8 and when subtracting with 6π/30 - 35π/30 (finding common denominators) you should get 29π/30.

Answer:

N(n+1) = N(n)^2 - 1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2 - 1, n>0, N(0) = 2

Step-by-step explanation:

Year 0 = 2 trees

year 1 = 2^2-1 = 3

year 2 = 3^2-1 =8

year 2 = 8^2-1 =63

...

Recursive formula

Let

n = integer year number

N(n) = number of trees to plant in year n

N(n+1) = N(n)^2-1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2, n>0, N(0) = 2

Whats the options???

Answer:

11 + Mai's Score = 59

Step-by-step explanation:

You need to add 11 and Mai's score together to get 59, so with the values given we can make the equation 11 + Mai's Score = 59.

*depending on the question, Mai's score may need to be said as a letter variable, so:

If m = mai's score,

11 + m = 59

I hope this helped! :)

Answer:

Arrow from 0 to 4.7 and from 4.7 to 2.4

Step-by-step explanation:

4.7 is also 0+4.7

arrow from 0 to 4.7.

-2.3 from 4.7 is 4.7-2.3=2.4

arrow from 4.7 to 2.4.

Answer:

Use the interactive number line to find the difference.

4.7 - 2.3 = 4.7 + (-2.3) =

✔ 2.4

Step-by-step explanation:

Answer:

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

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

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]

P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]

P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

Answer:

It does not have an answer as 3x != 3x + 13 or not equalivalent

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

3x+8=9+3x-14

Combine like terms

3x+8 = 3x -5

Subtract 3x from each side

8 = -5

This is never true so there is no solution

Answer:

  19.9 days

Step-by-step explanation:

The amount remaining after d days is ...

  a = (1/2)^(d/7)

We want to find d when a = 0.14

  log(a) = (d/7)log(1/2)

  d = 7·log(0.14)/log(1/2) ≈ 19.855 ≈ 19.9

The farmers need to wait about 19.9 days for it to be safe.

Answer:

the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)