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 Resort 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.

Answers

Answer 1

Answer:

a) Equation for Snow Dome Ski Resort:

[tex]I_s = 65+t[/tex]

Equation for Mt. Winterpark Ski Resort:

[tex]I_m = 74+\frac{t}{2}[/tex]

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 = [tex]\frac{1}{2}[/tex] inch per hour

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

Let the time in hours be represented by [tex]t[/tex].

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

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

Equation for Snow Dome Ski Resort:

[tex]I_s = 65+t[/tex]

Equation for Mt. Winterpark Ski Resort:

[tex]I_m = 74+\frac{t}{2}[/tex]

b) Time at which Snow Dome has more snow.

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

[tex]65+t>74+\dfrac{t}{2}\\\Rightarrow t-\dfrac{t}{2}>74-65\\\Rightarrow \dfrac{t}{2}>9\\\Rightarrow t>18\ hours[/tex]

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

After 19 hours, Snow dome will have more snow.


Related Questions

us
Figure ABCD is a kite. Find the
value of x.
B
X + 20
X + 10
А
С
X = [?]
Enter

Answers

Answer:

x = 30

Step-by-step explanation:

Since this is a right triangle,

90 = (x + 20) + (x + 10)

90 = x + x + 20 + 10

90 = 2x + 30

90 - 30 = 2x

60 = 2x

60/2 = 2x/2

30 = x

Check:

x + 20

30 + 20 = 50

x + 10

30 + 10 = 40

50 + 40 = 90

Hope this helps!

BLINKS!! WHAT ALBUM SHOULD I GET
Theres more but not all fit in one pic ​

Answers

Answer: Idc u pick

Step-by-step explanation:

Answer:

square up

Step-by-step explanation:

its the best (blink fan for 3 years)

which one is greater 140% or 0.14

Answers

140% because you can convert 0.14 to 14% or u can convert 140% to 1.4.

three less than the total of a number and
nine

Answers

Answer:

(x+9)-3

Step-by-step explanation:

Find the quotient. 3,482 ÷ 9 = *

Answers

Answer:

386.8

Step-by-step explanation:

pretty sure thats it

Answer:

386.8888 .. ...

Step-by-step explanation:

3482/9

What is the rate of change for the line that goes through the points (8,14) and (11, 19.25)​

Answers

Answer:

1.75

Step-by-step explanation:

The rate of change for the line that goes through the points (8,14) and (11, 19.25)​ is known as the slope expressed as;

slope m = y2-y1/x2-x1

Substitute the coordinate pairs into the formula;

m = 19.25-14/11-8

m = 5.25/3

m = 1.75

Hence the rate of change for the line is 1.75.

1
After becoming completely blind at the age of
sixty-four, what did Leonhard Euler do?

Answers

Answer:

his remarkable mathematical flow continued without interruption – in fact, it increased.

Step-by-step explanation:

Please help it would mean alot!
Points and brinliast!

Answers

Answer:

Maybe because what about the other votes that were supposed to be left.

Step-by-step explanation:

Set up an equation and solve for x

Answers

Answer:

x=22

Step-by-step explanation:

3x+3+27+x+3+2x+18=180

6x+48=180

6x=132

x=22

Options:
- does not
- does

Answers

Answer: does not

Step-by-step explanation: I think a linear equation is y=mx+b

Consider the following hypothesis test:
H0: µ = 20
Ha: µ < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic (to 2 decimals).
b. What is the p-value (to 3 decimals)?
c. Using a = .05, can it be concluded that the population mean is less than 20?
d. Using a = .05, what is the critical value for the test statistic?
e. State the rejection rule: Reject H0 if z is the critical value.
f. Using a = .05, can it be concluded that the population mean is less than 20?

Answers

Answer:

a

 [tex]z = - 2.12[/tex]

b

 [tex]p- value = 0.017003[/tex]

c

There is sufficient evidence to show that the population mean is less than 20

d

 [tex]z_{0.05} =- 1.645[/tex]

e

   The decision rule is  

Reject the null hypothesis

f

The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Step-by-step explanation:

From the question we are told that

   The null hypothesis  is  [tex]H_o: \mu = 20[/tex]

    The alternative hypothesis is  Ha: µ < 20

    The sample size is  n  =  50  

    The sample mean is  [tex]\= x = 19.4[/tex]

    The level of significance is  [tex]\alpha = 0.05[/tex]

      The population standard deviation is  [tex]\sigma = 2[/tex]

Generally the test statistics is mathematically represented as

       [tex]z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]

=>    [tex]z = \frac{19.4 - 20 }{ \frac{2}{ \sqrt{50 } } }[/tex]

=>    [tex]z = - 2.12[/tex]

From the z table  the area under the normal curve to the left corresponding to  -2.12  is  

       [tex](P< -2.12) = 0.017003[/tex]

Generally the p-value is  

        [tex]p- value = 0.017003[/tex]

From values obtained we see that [tex]p-value < \alpha[/tex] hence  

   The decision rule is  

Reject the null hypothesis

   The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Generally form the normal distribution table the critical value at a level of significance of  [tex]\alpha = 0.05[/tex] is

        [tex]z_{0.05} =- 1.645[/tex]

Generally given that  [tex]z < z_{0.05}[/tex]

   The decision rule is  

Reject the null hypothesis

   The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

PLEASE ANSWER ME!
What is the result when the number 65 is increased by 53%?

Answers

Answer:

The result when 65 is increased by 53% is 34.45

Step-by-step explanation:

Hope this helps and have a great day :)

Answer:

34.45

Step-by-step explanation:

i hope you get it right

Yesterday, the temperature in a city dropped from 9°C to –9°C, as shown below.



The expression 9 + (–18) represents the final temperature. Which of the following is an equivalent way to describe this temperature?

|–18| degrees in a negative direction from 9 degrees

|–18| degrees in a positive direction from 9 degrees

|–9| degrees in a negative direction from 9 degrees

|–9| degrees in a positive direction from 9 degrees

Answers

Answer:

b

Step-by-step explanation:

absoulute value is never negative.

What is the slope of function 3x-5y=17

Answers

Answer:

y=5/3x-3.4

Step-by-step explanation:

slope is 5/3

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

In slope-intercept form of linear equation y = mx + b , "m" is the slope

3x - 5y = 17

- 5y = - 3x + 17

y = [tex]\frac{3}{5}[/tex] x - [tex]\frac{17}{5}[/tex]  

m = [tex]\frac{3}{5}[/tex]

Celeste wants to have her hair cut and
permed and also go to lunch. She knows
she will need $95. The perm costs twice
as much as her haircut and she needs $5
for lunch.
How much does the perm cost?

Answers

Answer:

the perm will cost $60

Step-by-step explanation:

take away $5 from the total because Its a set amount that's already known

which leaves 90 which if you  take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped

help please 20 points to who answers not 10 points 20

Answers

Answer:

b c and a

Step-by-step explanation:

Answer:

A, B, C

Step-by-step explanation:

What is the slope of line m?

Answers

Answer:

Slope= -0.5

Step-by-step explanation:

Answer:

1/2x

Step-by-step explanation:

You go down one step and run 2 steps

A rectangle a photo with dimension 3 inches wide by 4 inches long is enlarged to a length of 12 inches what is the width of the enlarged print

Answers

It should be 9 inches wide

Eighteen less than 9 times a number is the same as 14 more than the number.
Comply the equation

Answers

Answer:

x=4

Step-by-step explanation:

9x-18 = x+14

9×-× = 14+18

8× = 32

X = 4

as
Complete the equation describing how x
and y are related.
ху
-2
-1
0
1
2
3
-8
-5
-2
1
4
y = [? ]x +
Enter the answer that
belongs in [?].

Answers

Answer:

[tex] y = 3x - 2 [/tex]

Step-by-step explanation:

The equation that describes how x

and y are related is given in the slope-intercept form, [tex] y = mx + b [/tex]

Where, m = slope, and b = y-intercept.

Let's find the value of m and b using the table of values given.

Using two of the pairs given, (-2, -8) and (-1, -5),

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-8)}{-1 -(-2)} = \frac{3}{1} = 3 [/tex]

Substitute x = -2, y = -8, and m = 3 in [tex] y = mx + b [/tex] to find the value of b.

Thus:

[tex] -8 = (3)(-2) + b [/tex]

[tex] -8 = -6 + b [/tex]

Add 6 to both sides

[tex] -8 + 6 = b [/tex]

[tex] -2 = b [/tex]

Substitute m = 3 and b = -2 in [tex] y = mx + b [/tex].

The equation that describes how x

and y are related would be:

[tex] y = 3x - 2 [/tex]

a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes. What is the snails rate in Minutes per Meters

Answers

Answer:

Step-by-step explanation

Given

a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.

Solution

So

the snails rate =11/8÷11/2

= 1/4Minutes per Meters

So the answer is 1/4 minute per meter

It is the quantity of an amount of something at a rate of one of another quantity.

If a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.

The snail's rate in minutes per meter is 4/3 minutes.

What is a unit rate?

It is the quantity of an amount of something at a rate of one of another quantity.

Example:

3 miles in 60 minutes.

1 mile in 20 minutes.

We have,

Snail travels:

[tex]1\frac{1}{8}[/tex] meters = [tex]1\frac{1}{2}[/tex] minutes

9/8 meters = 3/2 minutes

Multiplying 8/9 on both sides.

1 meters = 8/9 x 3/2 minutes

1 meter = 4/3 minutes

This means that the snail's rate in minutes per meter is 4/3 minutes.

Thus,

If a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.

The snail's rate in minutes per meter is 4/3 minutes.

Learn more about unit rates here:

https://brainly.com/question/11258929

#SPJ5

Look at the long division problem shown on the right. Complete the division to determine what the remainder will be.

What is the remainder?

–10

–7

7

10
x + 4 StartLongDivisionSymbol 4 x Superscript 4 Baseline + 18 x cubed + 3 x squared minus 18 x + 15 EndLongDivisionSymbol. minus 4 x Superscript 4 Baseline + 16 x cubed to get a remainder of 0 x Superscript 4 Baseline + 2 x cubed + 3 x squared. minus 0 x Superscript 4 Baseline + 2 x cubed + 8 x squared to get a remainder of 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 18 x. minus 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 20 x to get a remainder of blank and a quotient of 4 x cubed + 2 x squared minus 5 x + c.

Answers

Answer:

The remainder is...

7

Hope this helps!!

Step-by-step explanation:

Answer: it’s c

Step-by-step explanation:

5
y=2x+5y, equals, 2, x, plus, 5
Complete the missing value in the solution to the equation.
(
2
,

Answers

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[tex]y = f(x) = 2x + 5[/tex]

[tex]f(2) = 2(2) + 5[/tex]

[tex]f(2) = 4 + 5[/tex]

[tex]f(2) = 9[/tex]

Thus ;

[tex]( \: 2 \: , \: 9 \: )[/tex]

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Answer:

9

Step-by-step explanation:

The purchase price of a camcorder is $818 what is the total price if the sales tax rate is 8.5%

Answers

I believe it would be $887.53 because the tax would be $69.53

help with number 1 & number 2 please !

Answers

Step-by-step explanation:

2vt= (ht²/2) - 2c - r

v= ((ht²/2) -2c -r) / 2t

v= ht/4 - c/t - r/2t

Can you please give me more answers?

Answers

Answer:

more answers on wht

Step-by-step explanation:

Answer:

wdym more answers ? there isn't a question

Step-by-step explanation:

AB = BC
5(2x + 2).
3(3x - 1)
Find x:
2
4
-10
16
None of the other answers are correct

Answers

Answer:

Step-by-step explanation:

holdup im gonna help

Answer:

x = 2

Step-by-step explanation:

2[3(3x - 1)] = 5(2x + 2)

18x - 6 = 10x + 10

8x = 16

x = 2

Is the sum of any 2 consecutive prime numbers also prime?

Answers

Answer:

Yes! (it’s making me write 20 letters so yes is ur answer ok cool)

Yes beachside I really don’t know you it juts is

Calculate Valume of cones and spheres

Answers

Answer:

v = 1808,64cm³

Step-by-step explanation:

big cone:

a = pi.r²

a = 3,14x12²

a = 452,16cm²

v = a.h/3

v = 452,16x12/3

v = 1808,64cm³ (that's a three)

you got the point, now you can do the others... kinda of

Interest paid on £2500 at an interest at an interest rate of 15%

Answers

Answer:

£375

Step-by-step explanation:

Amount = £2500Interest rate = 15%

Interest

£2500*15/100 = £375
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