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erma4kov [3.2K]
3 years ago
5

The cycles for two different events are shown in the table. Each of these events happened in the year 2000. What is the next yea

r in which both will happen if the summer Olympics cycle is 4 and the U.S census cycle is 10?
Mathematics
2 answers:
Umnica [9.8K]3 years ago
7 0
The answer is 2020 (the LCF for 10 and 4 is 20)
krok68 [10]3 years ago
7 0

Answer with explanation:

Cycle for Summer Olympics =14

Cycle for Census =10

We have to find the year in which both will fall together.

Among H C F and L C M, Lowest common multiple gives the greatest number which is divisible by both the numbers that is 14 and 10.

14= 2 × 7

10 = 2×5

L C M of 14 and 10 = 2 × 5×7= 70

So, in 2070 ,the two summer Olympics as well as US census cycle will fall.

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eimsori [14]
I would go with D) incenter but im not too sure. 
x
7 0
3 years ago
Read 2 more answers
Point N is on line segment MO. Given NO = 2x– 3, MO = 3x + 5, and
spin [16.1K]

Answer:

The numerical length of MO is 20 units

Step-by-step explanation:

Let us solve the question

∵ Point N is on line segment MO

→ That means point N divides segment MO into two parts MN and NO

∴ MO = MN + NO

∵ MO = 2x + 5

∵ MN = 2x + 3

∵ NO = 2x - 3

→ Substitute them in the equation above

∴ 3x + 5 = (2x + 3) + (2x - 3)

→ Add the like terms in the right side

∵ 3x + 5 = (2x + 2x) + (3 - 3)

∴ 3x + 5 = 4x + 0

∴ 3x + 5 = 4x

→ Subtract 3x from both sides

∵ 3x - 3x + 5 = 4x - 3x

∴ 5 = x

∴ The value of x is 5

→ To find MO substitute x by 5 in its expression

∵ MO = 3x + 5

∴ MO = 3(5) + 5

∴ MO = 15 + 5

∴ MO = 20 units

The numerical length of MO is 20 units

5 0
3 years ago
Color blindness is an inherited characteristic that is more common in males than females. Let F represent female, and C represen
malfutka [58]

Answer:

0.513 = 51.3% probability of being a female.

Step-by-step explanation:

We are given the following formula:

P(F \cup C) = P(F) + P(C) - P(F \cap C)

In which:

Event F: Female

Event C: Red-green color blindness.

Probability of a Female

We have to find P(F), which is given by:

P(F) = P(F \cup C) + P(F \cap C) - P(C)

We are given by:

P(C) = 0.039, P(F \cap C) = 0.004, P(F \cup C) = 0.548

So

P(F) = P(F \cup C) + P(F \cap C) - P(C) = 0.548 + 0.004 - 0.039 = 0.513

0.513 = 51.3% probability of being a female.

5 0
3 years ago
4x what = 364<br><br> please put the calculation
NNADVOKAT [17]

Answer:

91

Step-by-step explanation:

<em>4 x 91 = 364</em>

To work this out, we must do the inverse operation. The inverse (opposite) of x (times or multiply) is ÷ (divide).

So, we do 364 ÷ 4 = 91

Hope this helps!

- profparis

7 0
2 years ago
What is the period and midline?
OverLord2011 [107]
\bf \qquad \qquad \qquad \qquad \textit{function transformations}&#10;\\ \quad \\&#10;% function transformations for trigonometric functions&#10;\begin{array}{rllll}&#10;% left side templates&#10;f(x)=&{{  A}}cos({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;&#10;\end{array}\qquad

\bf \begin{array}{llll}&#10;% right side info&#10;\bullet \textit{ stretches or shrinks}\\&#10;\quad \textit{horizontally by amplitude } |{{  A}}|\\&#10;\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\&#10;\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\&#10;\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\&#10;\bullet \textit{vertical shift by }{{  D}}\\&#10;\qquad if\ {{  D}}\textit{ is negative, downwards}\\&#10;\qquad if\ {{  D}}\textit{ is positive, upwards}\\&#10;&#10;&#10;\end{array}

\bf \begin{array}{llll}&#10;\bullet \textit{function period}\\&#10;\qquad \frac{2\pi }{{{  B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\&#10;\qquad \frac{\pi }{{{  B}}}\ for\ tan(\theta),\ cot(\theta)&#10;\end{array}&#10;

so if you notice yours \bf \begin{array}{llll}&#10;3.2cos&\left( \frac{5}{3}\theta \right)+&6.1\\&#10;&\ \uparrow&\uparrow \\&#10;&B&D &#10;\end{array}

now.. normally the function \bf 3.2cos&\left( \frac{5}{3}\theta \right)
 has a D value of 0, or no vertical shift, and the amplitude and the period simply make the wave taller and thinner, but the midline is still the x-axis

now, with D = 6.1, that moves the midline  up vertically that much

now.. the period, well, B = 5/3, normal period of cosine is 2\pi
so, the new period will be \bf \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{5}{3}}\implies \cfrac{6\pi }{5}

notice the picture below
the vertical shift by the D component, or 6.1, moved the midline to y = 6.1 :)

6 0
3 years ago
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