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tangare [24]
2 years ago
11

.....................​

Mathematics
1 answer:
tankabanditka [31]2 years ago
6 0

Answer:

God bless you all and always

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A population of lizards decreases exponentially at a rate of 12.5% per year. What is the equivalent monthly rate to the nearest
soldier1979 [14.2K]

Answer:1.04%


Step-by-step explanation:

12.5/12 = 1.04166667

when we round this to the nearest hundredth its 1.04%


3 0
3 years ago
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Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
2 years ago
a bag contains colored gumdrops 5 are cherry 3 are strawberry 2 are grape. a gumdrop will be randomly selected from the bag what
weqwewe [10]

Answer:

probablity of grapes = 0.2

Step-by-step explanation:

here's the solution : -

probablity of grapes =

\frac{number \: of \: grapes}{total \: fruits}

=》

\frac{2}{2 + 3 + 5}

=》

\frac{2}{10}

=》

0.2

6 0
3 years ago
6 times the sum of a number and 5 is 16
Ulleksa [173]
The equation would be 6 times x+5=16. This would be kinda Impossible. But a really close answer is 1.833
8 0
3 years ago
WILL MARK BRAINLEST
Snowcat [4.5K]

Answer:

109.0125 dollars, rounded is 109.01$

Step-by-step explanation:

6 0
3 years ago
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