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Troyanec [42]
2 years ago
10

75 = 4(2)^x

Mathematics
1 answer:
Valentin [98]2 years ago
3 0

Answer:

4.229

Step-by-step explanation:

75 = 4(2)^x

75/4 = 2^x

Apply ln both sides

ln(75/4) = ln(2^x)

ln(75/4) = x ln(2)

x = ln(75/4) ÷ ln(2)

x = 4.22881869

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Prove that there is only one circle determined by three noncollinear points
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Answer:

O lies on the perpendicular bisector of AB. ... Then, O' will lie on the perpendicular bisector PQ and RS. We know that, two lines cannot intersect at more than one point, So O' must coincide with O. Hence, there is one and only one circle passing through three non collinear points

Step-by-step explanation:

6 0
2 years ago
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Last year, Nicholas started babysitting to earn extra spending money. Over the summer, he tracked how much money he earned at ea
Ierofanga [76]

Answer:

25%

Step-by-step explanation:

The 5 values of the given box plot are;

The minimum value = 20

The first quartile, the 25th percentile point, Q₁ = 25

The median or second quartile, the 50th percentile point, Q₂ = 30

The third quartile, the 75th percentile point, Q₃ = 40

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The range = The maximum value - The minimum value

∴ The range = 55 - 20 = 35

We note that Nicholas earned $25 or less from the minimum value up to first quartile, Q₁, which is the 25th percentile point, where we have 25 percent of the data points

Therefore, the percent of the time Nicholas earned $25 or less is 25 percent of the time.

8 0
2 years ago
What are the coordinates of the hole in the graph of the function f(x) ?
Vinvika [58]
ANSWER

(3, \infty )

EXPLANATION

The given function is

f(x) = \frac{ {x}^{2} - 9}{x - 3}

When we plug in x=3 into this function, we obtain,

f(3) = \frac{0}{0}

This means that the function is discontinuous at x=3.

We need to simplify the function to obtain,

f(x) = \frac{(x - 3)(x + 3)}{(x - 3)}

This implies that,

f(x) = x + 3

The graph this function is a straight line that is continuous everywhere.

To graph

f(x) = \frac{ {x}^{2} - 9}{x - 3}
we draw the graph of

f(x) = x + 3
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See diagram in attachment.

Hence the coordinates of hole is

(3, \infty )

6 0
3 years ago
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pishuonlain [190]

Answer: kindly check explanation

Step-by-step explanation:

Given the data :

5 3 3 1 4 4 5 6 4 2 6 6 6 7 1 1 14 1 2 4 4 4 5 6 3 5 3 4 5 6 8 4 7 6 5 9 11 3 12 4 7 6 5 15 1 1 10 8 9 2 12

Frequency and relative frequency table can be found in the attachment below.

b. Where do the data tend to cluster?

3 up to 6

7 0
3 years ago
caleb and emily are standing 100 yards from each other. caleb looks up at a 45 degree angle to see a hot air balloon. Emily look
Sunny_sXe [5.5K]
Check the picture below.

thus then

\bf \begin{cases}
y=100-a\\
y=a\sqrt{3}
\end{cases}\implies 100-a=a\sqrt{3}\implies 100=a+a\sqrt{3}
\\\\\\
100=a(1+\sqrt{3})\implies \boxed{\cfrac{100}{1+\sqrt{3}}=a}
\\\\\\
\textit{what is the altitude \underline{y} then?}\qquad y=100-a
\\\\\\
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3 years ago
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