find the 7th term of the geometric sequence whose common ratio is 1/3 and whose first term is 6.

Answer:

Step-by-step explanation:

1). If the given triangles are similar their corresponding sides will be proportional.

[tex]\frac{8}{a}= \frac{8}{12}=\frac{5}{b}[/tex]

[tex]\frac{8}{a}= \frac{8}{12}[/tex]

[tex]a=\frac{12\times 8}{8}[/tex]

[tex]a=12[/tex]

[tex]\frac{8}{12}=\frac{5}{b}[/tex]

[tex]b=\frac{5\times 12}{8}[/tex]

[tex]b=7.5[/tex]

2). By using proportional relationship in the similar polygons,

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

[tex]c=\frac{8\times 3}{6}[/tex]

[tex]c=4[/tex]

d = 8

c = e = 4

3). If the pentagons are similar their corresponding sides will be proportional.

[tex]\frac{6}{g}=\frac{8}{18}=\frac{10}{h}= \frac{8}{I}=\frac{6}{f}[/tex]

[tex]\frac{6}{g}=\frac{8}{18}[/tex]

[tex]g=\frac{18\times 6}{8}[/tex]

[tex]g=13.5[/tex]

[tex]\frac{8}{18}=\frac{10}{h}[/tex]

[tex]h=22.5[/tex]

[tex]\frac{8}{18}=\frac{6}{f}[/tex]

[tex]f=13.5[/tex]

[tex]\frac{8}{18}= \frac{8}{I}[/tex]

[tex]I=18[/tex]

Answer:

Orca Correct, Sea Star Wrong. Heart it if it was helpful :D

Step-by-step explanation:

11-4=7. Orca correct.

Sea star...11-4=7

Wrong its 7, not -7

Answer:

The orca is right and the sea star is wrong.

If you were to add 11 to -4, it would no longer be a negative number.

You take four out of 11 which would bring it to a zero. There would be 7 left, therefore the answer being a positive 7.

Answer:

The probability that exactly two have flaws is P (x=2) = 0.2376

Step-by-step explanation:

Here

Success= p= 0.15

Failure = q= 0.85

total number= n= 8

Number chosen = x= 2

Applying the binomial distribution

P (x=x) = nCx p^x(q)^n-x

P (x=2) = 8C2 0.15 ²(0.85)^8

P (x=2) = 0.2376

The success is chosen about which we want to find the probability. Here we want to find the probability that exactly two have flaws so success would be having flaws therefore p = 0.15

Answer:

Joseph must run at least 3 more days to achieve 6 miles per week.

Step-by-step explanation:

Since Joseph runs 2 1/2 miles on Monday, and each day after that, he runs the same 1 1/3 mile route every morning, and his goal is to run at least 6 miles by the end of the week, to determine which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal, the following calculation must be performed:

1/2 = 0.5

2 1/2 = 2.5

1/3 = 0.333

1 1/3 = 1.333

(6 - 2.5) / 1.333 = X

3.5 / 1.333 = X

2.625 = X

Therefore, Joseph must run at least 3 more days to achieve 6 miles per week.

The differential equation

dy/dx = x sin(x ²) / y

is separable as

y dy = x sin(x ²) dx

Integrate both sides:

∫ y dy = ∫ x sin(x ²) dx

∫ y dy = 1/2 ∫ 2x sin(x ²) dx

∫ y dy = 1/2 ∫ sin(x ²) d(x ²)

1/2 y ² = -1/2 cos(x ²) + C

Solve for y implicitly:

y ² = -cos(x ²) + C

Given that y = 1 when x = 0, we get

1² = -cos(0²) + C

1 = -cos(0) + C

1 = -1 + C

C = 2

Then the particular solution to the DE is

y ² = 2 - cos(x ²)

Solving explicitly for y would give two solutions,

y = ± √(2 - cos(x ²))

but only the one with the positive square root satisfies the initial condition:

√(2 - cos(0²)) = √1 = 1

-√(2 - cos(0²)) = -√1 = -1 ≠ 1

So the unique solution to this DE is

y = √(2 - cos(x ²))

Answer:

See Below.

Step-by-step explanation:

Problem A)

We have:

[tex]\displaystyle \csc^2\theta \tan^2\theta -1=\tan^2\theta[/tex]

When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.

So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:

[tex]\displaystyle \left(\frac{1}{\sin^2\theta}\right)\left(\frac{\sin^2\theta}{\cos^2\theta}\right)-1=\tan^2\theta[/tex]

Cancel:

[tex]\displaystyle \frac{1}{\cos^2\theta}-1=\tan^2\theta[/tex]

Let 1/cosθ = secθ:

[tex]\sec^2\theta -1=\tan^2\theta[/tex]

From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:

[tex]\tan^2\theta =\tan^2\theta[/tex]

Problem B)

We have:

[tex]\sin^3x=\sin x-\sin x \cos^2 x[/tex]

Factor out a sine:

[tex]\sin x(\sin^2 x)=\sin x-\sin x\cos^2 x[/tex]

From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:

[tex]\sin x(1-\cos^2 x)=\sin x-\sin x\cos^2x[/tex]

Distribute:

[tex]\sin x- \sin x \cos^2 x=\sin x-\sin x\cos^2 x[/tex]

Problem C)

We have:

[tex]\displaystyle \frac{\cos 2x+1}{\sin 2x}=\cot x[/tex]

Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:

[tex]\displaystyle \frac{\cos^2 x-\sin^2 x+1}{2\sin x\cos x}=\cot x[/tex]

From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:

[tex]\displaystyle \frac{2\cos^2 x}{2\sin x\cos x}=\cot x[/tex]

Cancel:

[tex]\displaystyle \frac{\cos x}{\sin x}=\cot x[/tex]

By definition:

[tex]\cot x = \cot x[/tex]

Answer:

144 meters

Step-by-step explanation:

24 * 6 is 144

Hope this helps:)

Answer:

144 meters

Step-by-step explanation:

24 meters x 6 meters = 144 meters

Equation:

F = (w * da) / dh

F = (400 * 2) / (30)

F = (800) / (30)

F = 26.7 or 27 lb

Answer:

Following are the responses to the given question:

Step-by-step explanation:

In the first example, a team walks into a bar & chooses the random person to speak, in which situation, the woman who walks to the club has made a choice, he has selected a people with and who he wants to speak, it is a subjective preference. A choice cannot be random in statistical since it has a subjective preference. The first interpretation may therefore be randomized in general, but not arbitrary in statistics.

In the second example, i.e., the definition of Building tracks Example, a randomized wood piece is an identical piece or is different in size from other pieces. In this, piece wood has been differentiated by one's looks so, when asked to pick a random piece, we are likely to choose a non-uniform part rather than the uniform one. It is a random racial bias, so again in constructing pursuits the second definition could be random, but not a discrete one in stats.

In the identification numbers of random, we intentionally state that equal probability for each unit in the population of inclusion in the sampling. The definition essentially includes all sorts of predilection, and therefore refers to true allegiance, when we neither make that choice nor want to choose a separate unit.

Answer:

y = 60°

x = 12

Step-by-step explanation:

Because all sets of opposite sides are parallel, opposite angles are equal, and  opposite sides have the same length.

Answer:

2 feet

Step-by-step explanation:

Use the cube volume formula, V = s³, where s is the side length.

Plug in 8 as V, and solve for s:

V = s³

8 = s³

Take the cubed root of each side:

2 = s

So, the length of each side is 2 feet.

Answer:

[tex]2 feet[/tex]

The Solution is:

Use the cube volume formula, V = s³, where s is the side length.

Plug in 8 as V, and solve for s:

V = s³

8 = s³

Take the cubed root of each side:

2 = s

So, the length of each side is 2 feet.

Answer:

3-3x and 3

Step-by-step explanation:

f(x) = 3x-3

g(x) = -x

g(f(x)) in your g(x) substitute x with f(x)

g( f(x) ) = g( 3x-3) = -(3x-3) = -3x+3

is the the second choice from top because -3x+3 is the same with 3 -3x

g(f(x)) =3-3x

g(f(0)) always work from inside first, so first find f(0) than g(f(0))

f(0) = f(x=0) = 3*0-3 = -3

Now we do the g(f(0)) = g( -3) is the same as  

g(x) except that we substitute x for -3, g(x= -3) = -(-3) =3

g(f(0))=3

*an easier way to find the answer for the second problem would have been that we knew that f(g(x) ) = 3-3x so f(g(0)) =3-3*0 = 3

Answer: 32,500

Step-by-step explanation: i don't know

Answer:

32500

Step-by-step explanation:

Without using a calculator

625*52 = (625*4) * (52/4) = 2500 * 13 = 32500

Answer:

The rate of depreciation is 11.87% per year.

Step-by-step explanation:

Given that a brand new car was purchased for $ 28,000 in year 2000, and the car value has dropped to $ 20,000 in year 2003, to determine what could be considered as the rate of depreciation, the following calculation must be performed:

20,000 x (1 + X / 1) ^ 3 = 28,000

20,000 x X ^ 3 = 28,000

20,000X ^ 3 = 28,000

X = 1.1187

Therefore, the rate of depreciation is 11.87% per year.

9514 1404 393

Answer:

  odd

Step-by-step explanation:

If 'a' and 'b' have different parity, the result has odd parity.

__

Assume a=odd, b=even

  (5·odd -3·even) = odd

  (odd^2 +5·even) = odd

  (odd)(odd) +2 = odd

__

Assume a=even, b=odd

  (5·even -3·odd) = odd

  (even^2 +5(odd)) - odd

  (odd)(odd) +2 = odd

_____

The attached verifies this with numbers.

The answer is 2990.8 yd

Formula for SA of cylinder: 2*pi*r*h+2*pi*r^2

Formula for radius: diameter/2

Plug the radius, 17, height, 11, and pi, 3.14, into the formula above.

= 2990.8 yd

Answer:

Step-by-step explanation:

It's 5

Step-by-step explanation:

The 2 lines are parallel to each other which means that angle #5 and 93° are alternate interior angles so by definition, they are equal. Hence angle 5 = 93°

Answer:

2/7 of represents employees who are sick

Step-by-step explanation:

Question:

What fraction represents the employees who are sick

Total People = 7

sick people =2

numerator/denominator

2/7

Answer:

Because if it is zero, then it is multiplied the variable and it will be zero.  For example if I had 0x(squared) + x, it would just be x because zero times any number is zero.  Looking at the problem, I would assume it was quadratic because it had x squared, but it isn't because there are 0 x squared values.

Step-by-step explanation:

Answer: Quadrant 3

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

Explanation:

pi radians = 180 degrees

If angle [tex]\theta[/tex] (greek letter theta) is in quadrant 1, then this places the angle in the northeast quadrant. Adding 180 degrees to theta will move it to the third quadrant, which is in the southwest.

Note: when incrementing through the quadrants (1,2,3,4) we move counterclockwise.

Answer:

26 × 35 = 910=890 I multiply the 26 and 35 together and got 910 and then I round off to nearest 10th and got 900

So the awnser is 890m

Answer:

(x-2)²=9

sqrt both sides

don't forget positive and negative roots

x-2=+/-3

well, she is partially correct

x-2=3 is one answer

she didn't remember the other one the x-2=-3

Step-by-step explanation:

(x-2)²=9

sqrt both sides

don't forget positive and negative roots

x-2=+/-3

well, she is partially correct

x-2=3 is one answer

she didn't remember the other one the x-2=-3

Answer:

B. 9.7

Step-by-step explanation:

√12²-7²=√144-49=√95=9.7

Answer:

-32

Step-by-step explanation:

9(-3) + (-15) ÷ 3 =

-27 + -5 = -32

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:-32

Step-by-step explanation:

Answer:

D,p

Step-by-step explanation:

whattttttt ,why is there no option in D

The Probability that a data value is between 27 and 28 is 9.3%.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 to 1,

Here, mean of the data is 26

P(0 ≤ x - μ ≤ σ/2) = 0.195

P(0 ≤ x - μ ≤ σ/4) = 0.0987

P(σ/4 ≤ x - μ ≤ σ/2) = 0.093

Thus, the Probability that a data value is between 27 and 28 is 9.3%.

Learn more about Probability from:

https://brainly.com/question/11234923

#SPJ2

Answer:

p= 8000n-8000c

Step-by-step explanation:

8000

p= n - c

or

p= 8000n-8000c

Esentially you need to subtract n, the amount they sell each car for by c, the amount it costs to produce a car, (which should be less because the company has to make money) this would give you the total they make a month, P.

Because the amount of cars is constant, 8000, you can always multiply the cost of the car and how much its sold for by 8000. Otherwise, you would have another variable like k, which would be how many cars sold

Answer:

2

Step-by-step explanation:

The solutions are:

(1/2,11/4) and (1,2)

cosine(7 radians ) =

0.75390225434