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3 years ago

7

A plane is flying at an altitude of 10,000 feet begins to descending when the end of the runway is below a point 60,000 feet awa

y. Find the angle of descent (depression) to the nearest degree.

1 answer:

yan [13]3 years ago

6 0

Answer:

The angle of descent is 81°

Step-by-step explanation:

We have to think of the problem as a right triangle where the height of the plane is the leg adjacent to the angle of descent and the distance from the ground is the opposite leg

well to start we have to know the relationship between angles, legs and the hypotenuse in a right triangle

α = ?

a: adjacent = 10,000ft

o: opposite = 60,000

h: hypotenuse

sin α = o/h

cos α = a/h

tan α = o/a

we see that it has (angle, adjacent, opposite)

is the tangent

tan α = o/a

tan α = 60,000/10,000

tan α = 6

α = tan^-1(6)

α = 80.5377

if we want to round to the nearest degree

α = 80.5377° = 81°

The angle of descent is 81°

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The USDA conducted tests for salmonella in produce grown in California. In an independent sample of 252 cultures obtained from w

Marat540 [252]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 252$

The number that tested positive is $k_1 = 18$

The second sample size is $n_2 = 476$

The number that tested positive is $k_2 = 20$

The level of significance is $\alpha = 0.01$

Generally the first sample proportion is mathematically represented as

$\^ p _1 = \frac{k_1 }{ n_1 }$

=> $\^ p _1 = \frac{18 }{ 252 }$

=> $\^ p _1 = 0.071$

Generally the second sample proportion is mathematically represented as

$\^ p _2 = \frac{k_2 }{ n_2 }$

=> $\^ p _2 = \frac{20 }{ 476}$

=> $\^ p _2 = 0.042$

The null hypothesis is $H_o : p_1 - p_2 = 0$

The alternative hypothesis is $H_a : p_1 - p_2 \ne 0$

Generally the test statistics is mathematically represented

$z = \frac{ \^ p_1 - \^ p_2 - ( p_ 1 - p_2 )}{ \sqrt{\frac{\^ p_1 (1-\^ p_1)}{ n_1 } + \frac{\^ p_2 (1-\^ p_2)}{ n_2 } } }$

=> $z = \frac{ 0.071 - 0.042 - 0 }{ \sqrt{\frac{0.071 (1-0.071)}{ 252 } + \frac{0.042 (1-\^ 0.042)}{ 476 } } }$

=> $z = 1.56$

From the z table the area under the normal curve to the right corresponding to 1.56 is

$P(Z > 1.56 ) =0.05938$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.56 )$

=> $p-value = 2 * 0.05938$

=> $p-value = 0.1188$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

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3 years ago

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AysviL [449]

B, if they would breath in the air it would mess up there lungs

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3 years ago

What is the product of 7.5 and 1000

madam [21]

Answer:

7500 is the answer

Step-by-step explanation:

Product means a quantity obtained by multiplying quantities together, so if you multiply 7.5 and 1000 you get that answer :)

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3 years ago

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For a track meet, Tara ran the 1,600 m event at constant speed in 5 minutes and 20 seconds. What was her speed?

Arlecino [84]

Distance ran by Tara = 1600 m

Time taken by Tara to ran 1600 m = 5 min 20 seconds

We have to calculate the speed.

Firstly, we will convert the unit of time in one unit.

Time = 5 min 20 seconds

= 5 min + $\frac{20}{60}$ min (Because 1 min = 60 sec)

= $5+\frac{1}{3}$

= $\frac{15+1}{3}$

= $\frac{16}{3}$ min

Now we will use Distance speed formula which states,

Distance = speed $\times$ time

1600 m = speed $\times$ $\frac{16}{3}$

speed = $\frac{1600 \times 3}{16}$

Speed = 300 m/min

So, the speed of Tara was 300 meter/min.

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4 years ago

Write an equation in slope-intercept form of the line that contains the point (-2, 2) and has the slope = -5.

vichka [17]

Answer:

$y=-5x-8$

Step-by-step explanation:

Given the following question:

To calculate the slope intercept of a line/point we need to use the formula for slope intercept, substitute, and solve for b.

<u>Formula for slope intercept:</u>
$y=mx+b$
$m=-5$
$y=2$
$x=-2$
$2=-5(-2)+b$

<u>Solve for b:</u>
$2=-5(-2)+b$
$-5(-2)=10$
$2=10+b$
$10-10=0$
$2-10=-8$
$-8=b$
$b=-8$

<u>Substitute for the following:</u>
$y=mx+b$
$b=-8$
$m=-5$
$y=-5x-8$

Your answer is "y = -5x - 8."

Hope this helps.

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2 years ago