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mafiozo [28]
2 years ago
4

The sequence 12, 15, 18, 21, 51, 81, ... consists of all positive multiples of 3 that contain at least one digit that is a 1. Wh

at is the 50th term of the sequence? (2006 National Target #5)
Mathematics
1 answer:
nirvana33 [79]2 years ago
8 0

Answer:

159

Step-by-step explanation:

Using the formula for arithmetic progression,

an = a + (n - 1)d

Where a is the first term

n is the number of terms or nothing term

d is the common difference.

From the question:

a = 12

d = 3

nth = 50

an = 12 + ( 50 - 1) 3

= 12 + (49)3

= 12 + 147

= 159

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Express 5.555... in the form of a geometric series.
Evgesh-ka [11]

5.555 = 5.1 + 0.05 + 0.005

<span>          = 5.5 + 0.05 + 0.05(.1)</span>

<span>            = 5.5 + 0.05/(1-.1)</span>

<span>            =5.5+0.05/.9</span>

<span>            =5.5 + 5/90</span>

<span>            = 5.5+1/18</span>

<span>            =55/10 + 1/18</span>

<span>            = 495/90 + 5/90</span>

<span>            =500/90</span>

<span>            = 50/9</span>

<span>            = 5 5/9</span>


4 0
2 years ago
Four students wrote sequences during math class. Andre mc011-1.jpg Brenda mc011-2.jpg Camille mc011-3.jpg Doug mc011-4.jpg Which
maks197457 [2]
<span>A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

</span>The common ration is obtained by dividing the a term by the preceding term.

Given that f<span>our students wrote sequences during math class with
Andre writing -\frac{3}{4} ,\frac{3}{8} ,-\frac{3}{16} ,-\frac{3}{32} , . . .
Brenda writing </span>\frac{3}{4} ,-\frac{3}{8} ,\frac{3}{16} ,\frac{3}{32} , . . .
Camille writing \frac{3}{4} ,\frac{3}{8} ,-\frac{3}{16} ,-\frac{3}{32} , . . .
Doug writing \frac{3}{4} ,-\frac{3}{8} ,\frac{3}{16} ,-\frac{3}{32} , . . .

Notice that the common ratio for the four students is - \frac{1}{2}.

For Andre, the last term is wrong and hence his sequence is not a geometric sequence.
For Brenda, the last term is wrong and hence her sequence is not a geometric sequence.
For Camille, her sequence is not a geometric sequence.
For Doug, his sequence is a geometric sequence with a common ratio of - \frac{1}{2}.

Therefore, Doug wrote a geometric sequence.
8 0
2 years ago
Read 2 more answers
NEED HELP!
TEA [102]

Answer:

30 minutes

Step-by-step explanation:

20 * 96 / 64 = 30

8 0
2 years ago
Find the equation of the line which passes through (−2, 3) and the point of intersection of the lines x + 2y=0 and 2x − y − 12=0
Alik [6]

Answer: y = 0.794*x + 4.588

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case the points are:

(-2, 3) and the intersection of the lines:

x + 2y = 0

2x - y - 12  = 0

To find the intersection of those lines, we can first isolate one variable in one side of each equality, i will isolate the variable y.

y = -x/2

y = 2x - 12

Now we can write:

-x/2 = 2x - 12

Solving this we can find the value of x at which both lines intersect.

2x + x/2 = 12

(5/2)*x = 12

x = 12*(2/5) = 4.8

Now we evaluate one of the lines in that point and get:

y = -4.8/2 = -2.4

Then these lines intersect at the point (4.8, -2.4)

Now we can find the slope of our equation.

a = (-2.4 - 3)/(4.8 - (-2)) = 0.794

then we have:

y = 0.794*x + b

And we know that when x = -2, y = 3

then:

3 = 0.794*-2 + b

3 + 1.588 = b = 4.588

Then the equation is:

y = 0.794*x + 4.588

3 0
2 years ago
Read 2 more answers
Rachel is bowling with her friends. her bowling ball has a radius of 4 inches. as she bowls she tracks the location of the finge
Goshia [24]

Question Continuation

The finger hole changes by 45 degrees.

Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.

Answer:

f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

Step-by-step explanation:

Given

Let represent radius

r = 4 inches

Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.

Let θ represent the angle

At 12 o'clock mark

θ = 0

When the finger hole changes by 45 degrees

θ = 45°

Convert 45° to radians

θ = 45° * π/180

θ = π/4

So, angle θ is such that θ∈[0, π/4]

This can be represented as

0 ≤ θ ≤ π/4

Calculating the measure of f(θ) in polar coordinates

When θ = 0, f(θ) = r (i.e. the current position of the bowl)

When θ = π/2, f(θ) = rcosθ

This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)

Taking measurement of f(θ) from 0 to π/2

f(θ) = r + rcosθ

f(θ) = r(1 + cos(θ))

So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

7 0
2 years ago
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