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3 years ago

Scientist finds that for every in of rainfall at a lake, the level of the

Mathematics

1 answer:

Serga [27]3 years ago

8 0

Answer:

0.8 cm

Step-by-step explanation:

I divided 0.6 by 3 and then multiplied by 4 because 0.6 is 3/4 of the portion and we need the other 1/4.

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What is the variance of the data set (4,6,7,10)

crimeas [40]

Answer:

4.6875

Step-by-step explanation:

Given data set

(4,6,7,10)

To find

Variance

Solution

The Variance is defined as the average of the squared differences from the mean.

The mean is:

x = (4 + 6 + 7 + 10)/4 = 6.75

The variance is:

σ² = [(4 - 6,75)² + (6 - 6.75)² + (7 - 6.75)² + (10 - 6.75)²]/4 = 4.6875

4 0

3 years ago

Solve the following quadratic equation for all values of x in simplest form. 3(4x + 1)2 – 37 = 5

motikmotik

Answer:

Step-by-step explanation:

Add 37 to both sides (to combine like terms):

3(4x + 1)^2 = 42

Reduce this by dividing both sides by 3:

(4x + 1)^2 = 14

Taking the square root of both sides results in:

4x + 1 = ± √14, or

4x = -1 ± √14

Solve for x by dividing both sides by 4:

-1 ± √14

x = ----------------

8 0

3 years ago

You deposit $1,000 in a savings account that earns 0.5% each month. Assuming you do not deposit or withdraw any money from the a

Firdavs [7]

0.5% is 5$ so 5$ x 12 = 60 60 x 3 is 180 180 is your answer

3 0

3 years ago

Read 2 more answers

Angela is carpeting a rectangular conference room that measures 20

lisov135 [29]

$a = lw$

$a = (30)(20)$

$a = 600 \: {ft}^{2}$

The conference room has an area of 600 ft²

$a = lw$

$a = (5)(4)$

$a = 20 \: {ft}^{2}$

The carpet has an area of 20 ft²

$\frac{600}{20} = 30$

She would need 30 pieces to carpet the entire room.

5 0

3 years ago

A candle is burning. It starts out 12 inches long. After 1 hour, it is 10 inches long. After 3 hours, it is 5.5 inches

lubasha [3.4K]

Answer:

The equation of the burning of the candle is

$y = -2x + 12$

It would take 6 hours for the candle to burn out completely.

Step-by-step explanation:

A candle is burning. It starts out 12 inches long.

After 1 hour, it is 10 inches long.

After 3 hours, it is 6 inches (5.5 must be a typing error)

2. Is the height of the candle a function of time? If yes, is it a linear function? Explain your thinking,

The burning of this candle can be modeled by a linear equation of the form

$y = mx + b$

where y is the length of the candle in inches, x is the time in hours, m is the slope and b is the y-intercept.

The height of the candle is clearly a function of time since it changes with time.

The slope m is given by

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1, y_1) = (0, 12) \\\\(x_2, y_2) = (1, 10) \\\\$

$m = \frac{10 - 12}{1 - 0}$

$m = -2$

The slope of negative 2 means that the length of the canlde is decreasing by a factor of 2.

To find the value of the y-intercept (b),

substitute (x, y) = (0, 12)

which means that at x = 0 the length of the candle is 12 inches.

$y = mx + b \\\\12 = -2(0) + b \\\\b = 12$

So the equation of burning of the candle becomes

$y = mx + b \\\\y = -2x + 12 \\\\$

1. When do you think the candle will burn out completely?

Since we have the equation now we can find the length of the candle for any given time and also find the time required for a specific length of the candle.

Burn out completely means the length of the candle becomes zero.

$y = -2x + 12 \\\\0 = -2x + 12 \\\\-2x = -12 \\\\x = 12/2 \\\\x = 6 \: hours \\\\$

Therefore, it would take 6 hours for the candle to burn out completely.

3 0

3 years ago