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Rashid [163]
2 years ago
12

Snow Dome Ski Resort has 65 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resor

t has 74 inches of snow. Currently it is snowing there at a rate of ½ inch per hour.
a) Write equations that show the amount of snow at each resort as a function of the number of hours of snow.

b) If the snow continues at this rate, when will Snow Dome have more snow than Mt. Winterpark? Show your solution process clearly.
Mathematics
1 answer:
34kurt2 years ago
7 0

Answer:

a) Equation for Snow Dome Ski Resort:

I_s = 65+t

Equation for Mt. Winterpark Ski Resort:

I_m = 74+\frac{t}{2}

b) After 19 hours, Snow dome will have more snow.

Step-by-step explanation:

Given that:

Initial snow at Snow Dome Ski Resort = 65 inches

Snowing rate at Snow Dome Ski Resort = 1 inch per hour

Initial snow at Mt. Winterpark Ski Resort = 74 inches

Initial snow at Mt. Winterpark Ski Resort = \frac{1}{2} inch per hour

a) To write equations that show amount of snow at each resort.

Let the time in hours be represented by t.

Snow increased in t hours by snowing at Snow Dome Ski Resort = 1\times t = t inches per hour

Snow increased in t hours by snowing at Mt. Winterpark Ski Resort = \frac{1}{2}\times t = \frac{t}{2} inches per hour

Equation for Snow Dome Ski Resort:

I_s = 65+t

Equation for Mt. Winterpark Ski Resort:

I_m = 74+\frac{t}{2}

b) Time at which Snow Dome has more snow.

Using the above equations, we can write the following inequality:

65+t>74+\dfrac{t}{2}\\\Rightarrow t-\dfrac{t}{2}>74-65\\\Rightarrow \dfrac{t}{2}>9\\\Rightarrow t>18\ hours

After 18 hours have passed, they will have equal amount of snow.

After 19 hours, Snow dome will have more snow.

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Geometry and I need help
Yanka [14]

Answer:

y = 11

Step-by-step explanation:

We use the definition of Supplementary Angles and Adjacent Angles.

Step 1: Set up equation 1 (Definition of Supplementary Angles)

5x - 4 +7x - 8 = 180

Step 2: Solve for <em>x</em>

12x - 4 - 8 = 180

12x - 12 = 180

12x = 192

x = 16

Step 3: Plug in <em>x</em>

5(16) - 4

80 - 4

76°

Step 4: Set up equation 2 (Definition of Supplementary Angles)

76 + 9y + 5 = 180

Step 5: Solve for <em>y</em>

9y + 81 = 180

9y = 99

y = 11

3 0
3 years ago
Read 2 more answers
The pulse rates of 174 randomly selected adult males vary from a low of 39 bpm to a high of 111 bpm. Find the minimum sample siz
Daniel [21]

Answer:

a. The sample size is approximately 97 adults

Step-by-step explanation:

The given parameters are;

The number of adults surveyed, n = 174

The lowest value of the pulse rate = 39 bpm

The highest value of the pulse rate = 111 bpm

The level of confidence used for determining the sample size = 90%

The given sample mean = 3 pm of the population mean

a. The range rule of thumb states that the standard deviation is approximately one quarter (1/4) of the range

The range = 111 bpm - 39 bpm = 72 bpm

Therefore, the standard deviation, σ = 72 bpm/4 = 18 bpm

The sample size, 'N', is given as follows;

N = \dfrac{z^2 \cdot p \cdot q}{e^2}

Where;

N = The sample size

z = The confidence level, 90% (z-score at 90% = 1.645)

p·q = σ² = 18² = 324

e² = 3² = 9

N = \dfrac{1.645^2  \times 324}{3^2} = 97.4169

Therefore the appropriate sample size, N ≈ 97 adults.

8 0
3 years ago
Find the area of the largest square contained by a circle of radius r = 1cm. Explain your answer and justify that it is correct.
Elena-2011 [213]

Answer:

2 square cm

Step-by-step explanation:

Given :

A square is inscribed in a circle whose radius is r = 1 cm

Therefore, the diameter of the circle is 2 r = 2 x 1

                                                                      = 2 cm.

So the diagonal of the square is 2r.

Using the Pythagoras theorem, we find each of the side of the triangle is $r \sqrt 2$.

Therefore, the area of the square is given by $\text{(side)}^2$

                                                                         = $(r\sqrt 2)^2$

                                                                         $= 2 r^2$

                                                                         $= 2 (1)^2$

                                                                         $=2 \ cm^2$

Hence the area of the largest square that is contained by a circle of radius 1 cm is 2 cm square.

7 0
3 years ago
A CD usually sells for $18.00. If the CD is 30% off, and sales tax is 6%, what is the total price of the CD, including tax?
natali 33 [55]
Ok first find out what it will cost after the 30% discount

18*.30=
$5.40 discount 
$18.00-$5.40=
$12.60
Now lets figure out the sales tax
$12.60*.06=
76 cents
total price including tax is $13.36
6 0
3 years ago
Value of x for 12(x-2)+3x=1/2(x+6)+2​
Damm [24]

Answer:

The value of x = 2

Step-by-step explanation:

Given the equation

12\left(x-2\right)+3x=\frac{1}{2}\left(x+6\right)+2

  • Expand 12(x-2) = 12x - 24
  • Expand 1/2(x+6) = 1/2x + 3

so the equation becomes

12x-24+3x=\frac{1}{2}x+3+2

simplifying

15x-24=\frac{1}{2}x+5

15x=\frac{1}{2}x+29

multiplying both sides by 2

30x = x + 58

subtracting x from both sides

30x - x = 58 - x

29x = 58

divide both sides by 29

\frac{29x}{29}=\frac{58}{29}

simplifying

x = 2

Therefore, the value of x = 2

4 0
3 years ago
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