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3 years ago

Find sec θ if tan θ = 15/8 and θ terminates in QIII.

1 answer:

5 0

Tangent = opposite/adjacent
tangent = 15 / 8
If opp = 15 and adj = 8 then
hypotenuse^2 = 15^2 + 8^2
hypotenuse^2 = 225 + 64
hypotenuse^2 = 289
hypotenuse = 17

secant = hypotenuse / adjacent
secant = 17 / 8
secant = 2.125

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How to find the rule for the nth term of a geometric sequence with changing common ratio?

ki77a [65]

Hmmm... a geometric sequence MUST have a fixed common ratio. If it is changing, then the sequence you are looking at might not be a geometric sequence at all. We'd need to see an example to be sure.

6 0

3 years ago

1. A new brand of hot dog claims to have a lower sodium content than the leading brand.

kherson [118]

Answer:

(a) Population mean = 314.5mg

(b) Margin of error = 21.281mg

The new brand of hot dog has a lower sodium content on average than the leading brand

(d) Yes

Step-by-step explanation:

(a) Population mean = (370+326+322+297+326+289+293+264+327+331)/10 = 3145/10 = 314.5mg

(b) Margin of error = t×sd/√n

sd = 29.73, n = 10, degree of freedom = n-1 = 10-1 = 9

Assuming 95% confidence level

t-value corresponding to 9 degrees of freedom and 95% confidence level is 2.262

Margin of error = 2.262×29.73/√10 = 21.281mg

Lower limit of new brand = 314.5 - 21.281 = 293.219mg

Upper limit = 314.5 + 21.281 = 335.781mg

The range of sodium content for the new brand of hot dog is between 293.219mg and 335.781mg which is lower than the leading brand (350mg)

(d) Margin of error = t×sd/√n

From the formula above, margin of error varies inversely as the square root of sample size

The smaller the sample size (n = 10) the larger the margin of error and the less accurate is the population mean

The larger the sample size (n = 40) the smaller the margin of error and the more accurate is the population mean

8 0

4 years ago

Area of the figure: A)128 B)136 C)153 C)258

GarryVolchara [31]

Answer: 153

Step-by-step explanation:

area of rectangle= 16 x 3= 48

area of trapezium= 1/2(a+b)h

=1/2(16+5)x 10

=105

105+48= 153 in^2

3 0

3 years ago

nlexa [21]

So say we have the number: 54,321

The 5 would be worth 50,000 meaning it's in the ten thousands place.

The 4 would be worth 4,000 meaning it's in the thousands place.

The difference between them is a zero, so the ten thousands place is 10 times bigger than the thousands place

Hope that helps :)

7 0

3 years ago

Two objects were lifted by a machine. One object had a mass of 2 kilograms and was lifted at a speed of 2m/sec. the other had a

OLga [1]

Sadly, after giving all the necessary data, you forgot to ask the question.
Here are some general considerations that jump out when we play with
that data:

For the first object:
The object's weight is (mass) x (gravity) = 2 x 9.8 = 19.6 newtons
The force needed to lift it at a steady speed is 19.6 newtons.
The potential energy it gains every time it rises 1 meter is 19.6 joules.
If it's rising at 2 meters per second, then it's gaining 39.2 joules of
potential energy per second.
The machine that's lifting it is providing 39.2 watts of lifting power.
The object's kinetic energy is 1/2 (mass) (speed)² = 1/2(2)(4) = 4 joules.

For the second object:
The object's weight is (mass) x (gravity) = 4 x 9.8 = 39.2 newtons
The force needed to lift it at a steady speed is 39.2 newtons.
The potential energy it gains every time it rises 1 meter is 39.2 joules.
If it's rising at 3 meters per second, then it's gaining 117.6 joules of
potential energy per second.
The machine that's lifting it is providing 117.6 watts of lifting power.
The object's kinetic energy is 1/2 (mass) (speed)² = 1/2(4)(9) = 18 joules.

If you go back and find out what the question is, there's a good chance that
you might find the answer here, or something that can lead you to it.

4 0

3 years ago