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3 years ago

What is the total surface area of the solid?

Mathematics

2 answers:

mash [69]3 years ago

6 0

Answer:

Step-by-step explanation:

The formula for determining the total surface area of a rectangular prism is expressed as

Total surface area = 2lw + 2wh + 2lh

Where

l represents the length = 16

w represents the width = 11

h represents the height = 10

Total surface area = (2 × 16 × 11) + (2 × 11 × 10) + (2 × 16 × 10) = 352 + 220 + 320 = 892 mm²

The formula for determining the total surface area of a triangular prism is expressed as

Total surface area = ph + 2b

p represents perimeter of base

h represents height of prism

b represents base area

From the information given,

h = 16

b = 1/2base × height = 1/2 × 11 × 8 = 44 mm²

to determine the perimeter of the base, we would determine the slant height, l by applying Pythagoras theorem.

Hypotenuse² = opposite side² + adjacent side²

l² = 11² + 8² = 185

l = √185 = 13.6

p = 13.6 + 11 + 8 = 32.6 mm

Total surface area = (32.6 × 16) + (2 × 44) = 521.6 + 88 = 609.6 mm²

alexandr402 [8]3 years ago

3 0

Answer:

I thinks its B

Step-by-step explanation:

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il63 [147K]

To solve our questions, we are going to use the kinematic equation for distance: $d=vt$
where
$d$ is distance
$v$ is speed
$t$ is time

1. Let $v_{w}$ be the speed of the wind, $t_{w}$ be time of the westward trip, and $t_{e}$ the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so $d=2400$ . We also know that the speed of the plane is 450 mi/hr, so $v=450$ . Now we can use our equation the relate the unknown quantities with the quantities that we know:

<span>Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
</span> $d=vt$
$2400=(450-v_{w})t_{w}$

Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
$d=vt$
$2400=(450+v_{w})t_{e}$

We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate: $450-v_w$ Time: $t_w$
Going eastward -Distance: 2400 Rate: $450+v_w$ Time: $t_e$

2. Notice that we already have to equations:
Going westward: $2400=(450-v_{w})t_{w}$ equation(1)
Going eastward: $2400=(450+v_{w})t_{e}$ equation (2)

Let $t_{t}$ be the time of the round trip. We know from our problem that the round trip takes 11 hours, so $t_{t}=11$ , but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so $t_{t}=t_w+t_e$ . Using this equation we can express $t_w$ in terms of $t_e$ :
$t_{t}=t_w+t_e$
$11=t_w+t_e$ equation
$t_w=11-t_e$ equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns:
$2400=(450-v_{w})t_{w}$
$2400=(450-v_{w})(11-t_e)$

We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
$2400=(450-v_{w})(11-t_e)$ equation (1)
$2400=(450+v_{w})t_{e}$ equation (2)

3. Lets solve our system of equations to find the speed of the wind:
$2400=(450-v_{w})(11-t_e)$ equation (1)
$2400=(450+v_{w})t_{e}$ equation (2)

Step 1. Solve for $t_{e}$ in equation (2)
$2400=(450+v_{w})t_{e}$
$t_{e}= \frac{2400}{450+v_{w}}$ equation (3)

Step 2. Replace equation (3) in equation (1) and solve for $v_w$ :
$2400=(450-v_{w})(11-t_e)$
$2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )$
$2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )$
$2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} )$
$2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}}$
$2400(450+v_{w})=1147500+2400v_w-11(v_w)^2$
$1080000+2400v_w=1147500+2400v_w-11(v_w)^2$
$(11v_w)^2-67500=0$
$11(v_w)^2=67500$
$(v_w)^2= \frac{67500}{11}$
$v_w= \sqrt{\frac{67500}{11}}$
$v_w=78$

We can conclude that the speed of the wind is 78 mi/hr.

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Many people believe that the daily change of price of a company's stock on the stock market is a random variable with mean 0 and

Tomtit [17]

Answer:

Step-by-step explanation:

We can use normal aproximation, assuming that the random variables are a lot of that means the sample size is large.

$P(x>105) = P(z>\frac{105-100}{1})=P(z>5)$

Using the normal distribution table,

P(z>5) = 0.00005

Hence, we can conclude that the probability that the stock’s price will exceed 105 after 10 days is very small.

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drek231 [11]

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A TV that usually sells for $192.74 is on sale for 25% off. If sales tax on the TV is 5%, what is the price of the TV, including

Mashutka [201]

Answer:

Step-by-step explanation:

If you are saving 25%, you are still paying 75%, right? So the cost of the TV with a discount of 25% is 192.74(.75) which is $144.56

That's the cost of the TV on sale. Now we need to find the sales tax amount, if the sales tax is .05 as a decimal. We are paying $144.56 for the TV, which is 100% of the cost. On top of that, we are paying another 5%. So altogether, for the TV, we are paying 105% of the TV. Therefore,

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Inessa [10]

Answer:

Step-by-step explanation:

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