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alina1380 [7]
3 years ago
7

Is 19/3 a rational number

Mathematics
2 answers:
Mashcka [7]3 years ago
8 0

Answer:

Yes

Step-by-step explanation:

19/3 is equal to 6.3333 repeating which is rational (repeating decimals are rational)

nexus9112 [7]3 years ago
8 0

Answer:

yes

Step-by-step explanation:

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You read 9.75 pages in your science book and 24.5 pages of a play for English class
Marizza181 [45]

Answer: 1. You have to multiply 9.75x1.2= 11.7

2.You have to multiply 24.5x0.8= 20.4

3. Add the to products 11.7+20.4= 32.1

4. Answer is- 31.3 minutes

Step-by-step explanation: Hopefully this helped a lot ;D

6 0
3 years ago
Simplify the problem below and write in standard<br> form:<br> –725 + 8x3 – 6x2 – 10x3 – 9<br> -7x5
ValentinkaMS [17]
You combine like terms

Your answer will be -7x^5 - 2x^3 - 6x^2 -9
3 0
2 years ago
4. A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution. How many
solniwko [45]

Given:

A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.

To find:

The quantity of the 60% solution in the mixture.

Solution:

Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.

Quantity of mixture is 234. So,

x+y=234

x=234-y                  ...(i)

The mixture has 43% fertilizer. So,

\dfrac{60}{100}x+\dfrac{21}{100}y=\dfrac{43}{100}\times 234

Multiply both sides by 100.

60x+21y=10062            ...(ii)

Using (i) and (ii), we get

60(234-y)+21y=10062

14040-60y+21y=10062

-39y=10062-14040

-39y=-3978

Divide both sides by -39.

\dfrac{-39y}{-39}=\dfrac{-3978}{-39}

y=102

Putting this value in (i), we get

x=234-102

x=132

Therefore, 132 liters of the 60% solution must be used.

3 0
2 years ago
Suri is buying fruit to make a fruit salad.She buys x pounds of strawberries that cost $3.99 per pound and y pound of blueberrie
Scilla [17]

Answer: Cost of strawberries and blueberries in the fruit salad,

C= 3.99x +4.99y

Step-by-step explanation:

Let the amount of strawberry be x pounds

Let the amount of blueberries be y

The fruit salad contains x pounds of strawberry and y pounds of blueberries

Cost of strawberries and blueberries in the fruit salad ,

C= 3.99x +4.99y

This is the algebraic expression to represent this situation.

8 0
3 years ago
The temperature, H, in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation. H = 70 + 1
Alex73 [517]

Answer:

The temperature a t = 0 is 190 °F

The temperature a t = 1 is 100 °F

The temperature a t = 2 is 77.5 °F

It takes 1.5 hours to take the coffee to cool down to 85°F

It takes 2.293 hours to take the coffee to cool down to 75°F

Step-by-step explanation:

We know that the temperature in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation:

H(t)=70+120(\frac{1}{4})^t

a) To find the temperature a t = 0 you need to replace the time in the equation:

H(0)=70+120(\frac{1}{4})^0\\H(0)=70+120\cdot 1\\H(0) = 70+120\\H(0)=190 \:\°F

b) To find the temperature after 1 hour you need to:

H(1)=70+120(\frac{1}{4})^1\\H(1)=70+120(\frac{1}{4})\\H(1) = 70+30\\H(1)=100 \:\°F

c) To find the temperature after 2 hours you need to:

H(2)=70+120(\frac{1}{4})^2\\H(2)=70+120(\frac{1}{16})\\H(2) = 70+\frac{15}{2} \\H(2)=77.5 \:\°F

d) To find the time to take the coffee to cool down 85 \:\°F, you need to:

85 = 70+120(\frac{1}{4})^t\\70+120\left(\frac{1}{4}\right)^t=85\\70+120\left(\frac{1}{4}\right)^t-70=85-70\\120\left(\frac{1}{4}\right)^t=15\\\frac{120\left(\frac{1}{4}\right)^t}{120}=\frac{15}{120}\\\left(\frac{1}{4}\right)^t=\frac{1}{8}

\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)

\ln \left(\left(\frac{1}{4}\right)^t\right)=\ln \left(\frac{1}{8}\right)

\mathrm{Apply\:log\:rule}=\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)

t\ln \left(\frac{1}{4}\right)=\ln \left(\frac{1}{8}\right)

t=\frac{\ln \left(\frac{1}{8}\right)}{\ln \left(\frac{1}{4}\right)}\\t=\frac{3}{2} = 1.5 \:hours

e) To find the time to take the coffee to cool down 75 \:\°F, you need to:

75=70+120\left(\frac{1}{4}\right)^t\\70+120\left(\frac{1}{4}\right)^t=75\\70+120\left(\frac{1}{4}\right)^t-70=75-70\\120\left(\frac{1}{4}\right)^t=5\\\left(\frac{1}{4}\right)^t=\frac{1}{24}

\ln \left(\left(\frac{1}{4}\right)^t\right)=\ln \left(\frac{1}{24}\right)\\t\ln \left(\frac{1}{4}\right)=\ln \left(\frac{1}{24}\right)\\t=\frac{\ln \left(24\right)}{2\ln \left(2\right)} \approx = 2.293 \:hours

3 0
3 years ago
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