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3 years ago

Find the surface area of the following prism.

Mathematics

1 answer:

Alex3 years ago

3 0

Answer:

226 11/20 cm^2.

Step-by-step explanation:

This consists of 2 trapezoids and 4 rectangles.

Area of the 2 trapezoids = 2 * 4 *(6 1/2 + 5 1/4 ) /2

= 47 cm^2.

Area of the 4 rectangles = 4*9 + 6 1/2 * 9 + 4 1/5 * 9 + 9* 5 1/4

= 36 + 117/2 + 189/5 + 189/4

= 3591/20 cm^2

Total surface area = 47 + 3591/20

= 4531/20

= 226 11/20 cm^2.

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6) Two coastguard stations P and Q are 17km apart, with due East of P. A ship S is observed in distress on a bearing 048° fromP

adelina 88 [10]

Answer:

The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Step-by-step explanation:

Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.

But,

<P = 048°

<Q = $360^{o}$ - $324^{o}$

= 0 $36^{o}$

Sum of angles in a triangle = $180^{o}$

<P + <Q + <S = $180^{o}$

048° + 0 $36^{o}$ + <S = $180^{o}$

$84^{o}$ + <S = $180^{o}$

<S = $180^{o}$ - $84^{o}$

= $96^{o}$

<S = $96^{o}$

Applying the Sine rule,

$\frac{y}{Sin P}$ = $\frac{x}{Sin Q}$ = $\frac{z}{Sin S}$

$\frac{y}{Sin P}$ = $\frac{z}{Sin S}$

$\frac{y}{Sin 48^{o} }$ = $\frac{17}{Sin 96^{o} }$

$\frac{y}{0.74314}$ = $\frac{17}{0.99452}$

⇒ y = $\frac{12.63338}{0.99452}$

= 12.703

y = 12.70 km

$\frac{x}{Sin Q}$ = $\frac{z}{Sin S}$

$\frac{x}{Sin 36^{o} }$ = $\frac{17}{Sin 96^{o} }$

$\frac{x}{0.58779}$ = $\frac{17}{0.99452}$

⇒ x = $\frac{9.992430}{0.99452}$

= 10.0475

x = 10.05 km

Thus,

the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.

6 0

3 years ago

The lengths of lumber a machine cuts are normally distributed with a mean of 106 inches and a standard deviation of 0.3 inch. (

Vinvika [58]

Answer:

a) $P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)$

And we can find this probability with the complement rule:

$P(z>0.37)=1-P(z$

b) $z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}= 2.431$

And if we use the z score we got:

$P(z>2.431) =1-P(z$

Step-by-step explanation:

Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:

$X \sim N(106,0.3)$

Where $\mu=106$ and $\sigma=0.3$

Part a

We are interested on this probability

$P(X>106.11)$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And using this formula we got:

$P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)$

And we can find this probability with the complement rule:

$P(z>0.37)=1-P(z$

Part b

For this case we select a sample of n =44 and the new z score formula is given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score we got:

$z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}= 2.431$

And if we use the z score we got:

$P(z>2.431) =1-P(z$

6 0

3 years ago

How can the zero product be applied to real life

ddd [48]

Answer:

The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.

The Zero Product Property simply states that if ab=0 , then either a=0 or b=0 (or both). A product of factors is zero if and only if one or more of the factors is zero.

Step-by-step explanation:

hope it helps

7 0

2 years ago

The solution set of the inequality 2x − y > 2 consists of all the points __ ? the line __ ?

GalinKa [24]

Answer:

b - below; y = 2x − 2

Step-by-step explanation:

2x − y > 2
2x - y + y - 2 > 2 + y - 2
2x - 2 > y
y < 2x - 2

Solution is the points below the line y = 2x - 2

<u>Correct option is:</u>

b - below; y = 2x − 2

7 0

3 years ago

A salesperson's commission rate is 6%. What is the commission from the sale of 42,000 worth of furnaces? Use pencil and paper

pickupchik [31]

Answer:

42,000 X 6 % = $2520.00

42,000 x 2 = 84,000

84,000 x 6% = $5,040

Step-by-step explanation:

3 0

2 years ago