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4vir4ik [10]
2 years ago
7

Joan is filling a 2-liter soda bottle with different colors of sand to make an art project for her class. She has 1,000 millilit

ers of
red sand, 35 centiliters of blue sand, and 2,5 deciliters of yellow sand in the bottle, but it is not full yet. How many liters of
purple sand will she need to use to have the bottle completely full?
Mathematics
1 answer:
Marrrta [24]2 years ago
6 0

Answer:

0.4 l of purple sand

Step-by-step explanation:

<u>Volume to be filled in:</u>

  • 2 liter = 2000 ml

<u>Red sand</u>

  • 1000 ml

<u>Blue sand</u>

  • 35 centiliters = 35*10 ml = 350 ml

<u>Yellow sand</u>

  • 2.5 deciliters = 2.5*100 ml = 250 ml

<u>Total volume filled:</u>

  • 1000 + 350 + 250 = 1600 ml

<u>Purple sand needed:</u>

  • 2000 - 1600 = 400 ml = 0.4 l

<u>Answer is</u> 0.4 l of purple sand required

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Sauron [17]
Since it's 3 people splitting 10 oz, we get:
\frac{10}{3}

Which can then be simplified to a mixed fraction:
3 \frac{1}{3}

So, yes, you got it right! Good job!
5 0
2 years ago
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A construction explosion has an intensity I of 1.25 x 10–4 W/m2. Find the loudness of the sound in decibels if W/m2. Round to th
bezimeni [28]
We solve this problem by using the decibels formula which is expressed as:

dB = 10 x log (Isig/Iref)

where dB is decibels, Isig is the intensity of the signal and Iref is the intentsity of the softest sound the human ear can hear which has a value of 10^-12.

We solve as follows:
dB = 10 x log (<span>1.25 x 10–4 </span>/ 10^-12 ) = 80.97 decibels

Therefore, the correct answer is option A, 81 decibels.
7 0
1 year ago
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In ΔTUV, the measure of ∠V=90°, TV = 56, UT = 65, and VU = 33. What is the value of the tangent of ∠U to the nearest hundredth?
mamaluj [8]

Answer: The tangent of angle U equals 1.69 (to the nearest hundredth)

Step-by-step explanation: The triangle TUV has one of the angles (angle V) measuring 90 degrees. That makes it a right angled triangle. Also line TV equals 56. Note that the third angle (angle U) would be facing line TV, that makes line TV opposite angle U, since angle U is the reference angle. Line VU measures 33. If angle U is the reference angle and angle V is the right angle, then line VU is the adjacent (line between the right angle and the reference angle).

The trigonometric ratio can be applied in a right angled triangle. Where the opposite and adjacent have been given, the ratio is as follows;

Tan X = opposite/adjacent

Tan U = 56/33

Tan U 1.696969

Rounded off to the nearest hundredth, the tangent of angle U is 1.69

5 0
2 years ago
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Which quadratic equation has solutions x=8 and x=−1?
andrezito [222]
There are two ways you can do this

Using the formula


{x}^{2}  - (sum \: of \: roots)x + poduct \: of \: roots = 0

{x}^{2}  - (8+-1)x +  - 1 \times 8 = 0


{x}^{2}  - 7x  - 8 = 0


Working backwards


x = 8 \: or \: x =  - 1
\Rightarrow x-8=0  \: or  \: x+1=0

\Rightarrow (x-8)(x + 1)=0
\Rightarrow  {x}^{2}   + x -8x - 8 = 0
\Rightarrow  {x}^{2}  - 7x - 8 = 0
7 0
2 years ago
If u (x) = negative 2 x squared and v (x) = StartFraction 1 Over x EndFraction, what is the range of (u circle v) (x)?
Sindrei [870]

Answer:

The range is negative numbers.

The interval for the range is (-\infty,0).

***You might want to look at your functions again because I don't see a choice that matches.

Step-by-step explanation:

Given functions:

u(x)=-2x^2

v(x)=\frac{1}{x}

We are asked to find the range of (u \circ v)(x).

I'm also going to look at the domain just to see if this possibly might change my range .

v(x) is the inner function. So we will consider the domain of that function first.

You only have to worry about division by zero for the function v.

Since we are dividing by x, we don't want x to be zero.

So far the domain is all real numbers except x=0.

Now let's move out.

u(x)=-2x^2 exists for all numbers, x. So we didn't want to include x=0 from before.

Now let's put it together:

(u \circ v)(x)

u(v(x))

u(\frac{1}{x})

-2(\frac{1}{x})^2

-2(\frac{1^2}{x^2})

-2(\frac{1}{x^2})

\frac{-2}{x^2}

So the domain is still all real numbers except at x=0 since we cannot divide by 0 and x^2 is 0 when x=0.

y=\frac{-2}{x^2} with x \neq 0.

x^2 is positive for all numbers except x=0.

So \frac{-2}{x^2} is negative for all numbers since negative divided by positive is negative.

So the range is only negative numbers.

Let's also look at the inverse:

y=\frac{-2}{x^2}

Multiply both sides by x^2:

yx^2=-2

Divide both sides by y:

x^2=\frac{-2}{y}

Take the square root of both sides:

x=\pm \sqrt{\frac{-2}{y}}.

So y can't be 0 and it also can't be positive because the inside of the square root will be negative (since negative divided by positive results in negative).

7 0
2 years ago
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