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Since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year. Predict th

BaLLatris [955]

Answer:

20,158 cases

Step-by-step explanation:

Let $t=0$ represent year 2010.

We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.

Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.

We can represent this information in an exponential decay function as:

$F(t)=102,390(1-0.15)^t$

$F(t)=102,390(0.85)^t$

To find number of cases in 2020, we will substitute $t=10$ in our decay function as:

$F(10)=102,390(0.85)^{10}$

$F(10)=102,390(0.1968744043407227)$

$F(10)=20,157.970260446597\approx 20,158$

Therefore, 20,158 cases will be reported in 2020.

3 0

3 years ago

Please help?

Mazyrski [523]

Answer:

$23\sqrt{3}\ un^2$

Step-by-step explanation:

Connect points I and K, K and M, M and I.

1. Find the area of triangles IJK, KLM and MNI:

$A_{\triangle IJK}=\dfrac{1}{2}\cdot IJ\cdot JK\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 2\cdot 3\cdot \dfrac{\sqrt{3}}{2}=\dfrac{3\sqrt{3}}{2}\ un^2\\ \\ \\A_{\triangle KLM}=\dfrac{1}{2}\cdot KL\cdot LM\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 8\cdot 2\cdot \dfrac{\sqrt{3}}{2}=4\sqrt{3}\ un^2\\ \\ \\A_{\triangle MNI}=\dfrac{1}{2}\cdot MN\cdot NI\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 3\cdot 8\cdot \dfrac{\sqrt{3}}{2}=6\sqrt{3}\ un^2\\ \\ \\$

2. Note that

$A_{\triangle IJK}=A_{\triangle IAK}=\dfrac{3\sqrt{3}}{2}\ un^2 \\ \\ \\A_{\triangle KLM}=A_{\triangle KAM}=4\sqrt{3}\ un^2 \\ \\ \\A_{\triangle MNI}=A_{\triangle MAI}=6\sqrt{3}\ un^2$

3. The area of hexagon IJKLMN is the sum of the area of all triangles:

$A_{IJKLMN}=2\cdot \left(\dfrac{3\sqrt{3}}{2}+4\sqrt{3}+6\sqrt{3}\right)=23\sqrt{3}\ un^2$

Another way to solve is to find the area of triangle KIM be Heorn's fomula, where all sides KI, KM and IM can be calculated using cosine theorem.

7 0

3 years ago

If a cube has a side length of 4 1/2 cm, what is one way to write the volume of the cube?

atroni [7]

For this case we have that by definition, the volume of a cube is given by: $V = s ^ 3$

Where,

<em>s: Side of the cube </em>

We have that the cube side is given by:

$s = 4 \frac {1} {2} cm$

Therefore, replacing values we have:

$V = (4 \frac {1} {2}) ^ 3 cm ^ 3$

Answer:

One way to write the volume of the cube is:

$V = (4 \frac {1} {2}) ^ 3 cm ^ 3$

3 0

3 years ago

Read 2 more answers

Find the area of the given trapezoid.

tatyana61 [14]

Answer:

40 inches

Step-by-step explanation:

To find the area of a trapezoid, you have to multiply the longest base (10 inches in this case) by the highth (i can't spell lol) (the highth is 4 inches in this case). So, A= Bh Area=10*4 Area =40 inches.

7 0

3 years ago

6pi= M over 360, 2 times pi times 18

Lelu [443]

$\dfrac{M}{360}\cdot2\pi\cdot18=6\pi\ \ \ \ |:\pi\\\\\dfrac{M}{360}\cdot36=6\\\\\dfrac{M}{10}=6\ \ \ \ |\cdot10\\\\\boxed{M=60}$

7 0

3 years ago