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3 years ago

Please help!!!

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

6 0

The composite shape's area is 61.12.

Step-by-step explanation:

Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.

Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.

Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.

Area of the composite shape = 36 + 25.12 = 61.12.

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Divide using synthetic division (x^2 +9)÷(x-3) =

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SOLUTION:

Case: Hypothesis testing

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$\begin{gathered} H_0:\mu=P127.50 \\ H_1:\mu\leq P127.50 \end{gathered}$

Step 2: T-test analysis

$\begin{gathered} t=\frac{\hat{x}-\mu}{\frac{s}{\sqrt{n}}} \\ t=\frac{135-127.5}{\frac{75.25}{\sqrt{450}}} \\ t=2.144 \end{gathered}$

Step 3: t-test with the significance level

$\begin{gathered} t_{\alpha}=? \\ \alpha=0.05 \\ From\text{ }tables \\ t_{0.05}=1.654 \end{gathered}$

Step 4: Comparing

$t>t_{\alpha}$

So tail to reject the null hypothesis. There is enough evidence at a 0.05 level of significance to claim that the mean spent is greater than P127.50.

Final answer:

Yes, there is evidence sufficient to conclude that the mean amount spent is greater than P127.50 per month at a 0.05 level of significance.

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1 year ago

What is the probability that a person who is above 35 years old has a hemoglobin level of 9 or above?

lorasvet [3.4K]

Answer:

Option C. $P=0.531$

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

Let

x------> size of the event space (total person's hemoglobin level of 9 or above with age above 35 years)

y-----> size of the sample space (total person's age above 35 years)

$P=\frac{x}{y}$

In this problem we have

$y=162$

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Let

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substitute the values

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3 years ago

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Find the solutions for a triangle with a = 16, c =12, and B = 63º.

maks197457 [2]

Answer:

b. A = 71.6°; C = 45.40°; b =15.0

Step-by-step explanation:

The missing values can be found with the help of the Law of Cosine and properties of triangles:

Side b (Law of Cosine)

$b = \sqrt{a^{2}+c^{2}-2\cdot a \cdot c \cdot \cos B}$

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Angle A (Law of Cosine)

$\cos A = -\frac{a^{2} - b^{2}-c^{2}}{2\cdot b \cdot c}$

$\cos A = - \frac{16^{2}-15.022^{2}-12^{2}}{2\cdot (15.022)\cdot (12)}$

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$A \approx 71.639^{\circ}$

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$C = 180^{\circ} - 63^{\circ} - 71.639^{\circ}$

$C = 45.361^{\circ}$

Hence, the right answer is B.

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