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3 years ago

Convert the decimal to a fraction. 0.02

Mathematics

2 answers:

kotykmax [81]3 years ago

7 0

You times 0.02 with a hundred and that’s it

Blizzard [7]3 years ago

3 0

Step-by-step explanation: To turn 0.02 into a fraction, let's first multiply the numerator and the denominator by 100 to remove the two decimal places. Next, we want to find the greatest common factor which is 2. So, we can reduce the fraction by dividing both numerator and denominator by 2.

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. Tommy gives baseball cards to four of his friends. He gives Kiana 3 cards less than he gives Gary.

Licemer1 [7]

We need to write system of equations for this problem. Reading text we write 1 equation by 1.
first lets name our variables
x - Kiana cards
y - Gary cards
z - Monty cards
m - Willa cards

x = y-3 which we can write as y = x+3
z = x + 7
m = 2z
x + y + z + m = 74

I think easiest way to solve this is to express all variables in last equation and solve for x.
x + x+3 + x + 7+ 2x + 14= 74
5x = 50
x = 10
now we just calculate cards given to each friend

y = 13
z = 17
m = 34

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3 years ago

Which relationship in the triangle must be true?

Paul [167]

We'll assume this is an arbitrary triangle ABC.

A) No, the sines of two different angles can be whatever they want

B) sin(B)=cos(90-B)

Yes, that's always true. The "co" in cosine means "complementary" as in the complementary angle, which adds to 90. So the sine of an angle is the cosine of the complementary angle.

C) No, the correct identity is sin(180-B)=sin B. Supplementary angles share the same sine.

D) Just like A, different triangle angles often have different cosines.

Answer: Choice B

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3 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

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forsale [732]

The correct answer is

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3 years ago