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Alex Ar [27]
3 years ago
10

Ms. Ferguson is considering reserving a room at the Abraham Hotel. The Abraham Hotel charges $239 a night.

Mathematics
1 answer:
skad [1K]3 years ago
6 0
A) 1000/239 = 4.something
Ms. Ferguson could book the room for 4 nights
B) 6 x 239 = 1434
1450/1434 = 1.01
Ms Ferguson was off by 1%
C) 2075/1589 = 1.3058
The price increase was by 31%
D) 2075/1.3 = 1596.153
The price that was found was $1596.15
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If 4sintheta = -3, solve for theta given 0°>_theta>_360°
Soloha48 [4]

Answer:

311.41 degrees

Step-by-step explanation:

If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).

Let's assume we're in Quadrant IV.  Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.

According to the Pythagorean Theorem,  (-3)^2 + x^2 = 4^2, or,

x^2 = 16 - 9 = 7.

Then x is either √7 or -√7.

To find the angle Ф, use the inverse sine function:

Ф = arcsin (-3/4).  Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees.  We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."  

6 0
3 years ago
Q2. A train travels at a constant speed of 45 m/s. a) Calculate the distance travelled by the train in:
alex41 [277]

Answer:

i) 1350 m

ii) 5400 m

Step-by-step explanation:

<u>Formula for Speed</u>

\boxed{\sf Speed=\dfrac{Distance}{Time}}

Rearrange the formula so that Distance is the subject:

\implies \sf Distance = Speed \times Time

<h3><u>Question (i)</u></h3>

Given:

  • Speed = 45 m/s (meters per second)
  • Time = 30 seconds

Substitute the given values into the formula for distance:

\implies \sf Distance = 45 \times 30 = 1350\:m

<h3><u>Question (ii)</u></h3>

Given:

  • Speed = 45 m/s (meters per second)
  • Time = 2 minutes

As the time is given in a different unit of time as the speed, we must first convert the time into seconds:

1 minute = 60 seconds

⇒ 2 minutes = 60 × 2 = 120 seconds

Therefore:

  • Speed = 45 m/s (meters per second)
  • Time = 120 seconds

Substitute the values into the formula for distance:

\implies \sf Distance = 45 \times 120 = 5400\:m

3 0
1 year ago
Read 2 more answers
F(x)=1/2(x-2)(x+3)^3
KatRina [158]

Answer:y=

1

2

x4+

7

2

x3+

9

2

x2+

−27

2

x−27

Step-by-step explanation:

5 0
3 years ago
In the first year of a 10,000 investment the interest rate was 6%. All earned interest remained invested for the second year, an
Aleks04 [339]

Answer:

13.4%

Step-by-step explanation:

First year:

$10,000*6% = $600

New balance = $10,600

Second Year:

$10,600*7% = $742

$10,600+ $742 = $11,342

Total Return:

Final Balance - Initial balance

$11,342 - $10,000 = $1,342

$10,000*x ÷ $1,342

x = $1,342/$10,000

x = 0.1342

0.134 = 13.4%

7 0
3 years ago
The measure of an angle is 6° less than the measure of its complement.
kogti [31]
It’s 3 less then measure of its complement 6°
7 0
3 years ago
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