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USPshnik [31]
3 years ago
14

Select the mixed number or fraction that is equivalent to 32.029.

Mathematics
1 answer:
lubasha [3.4K]3 years ago
6 0
32 29/999 >>>>>>>>>>>>>>>>>>>>>>>>>>>>
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PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)
Anvisha [2.4K]
1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
\left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right  \\   \\ \Rightarrow  \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right  \\  \\ \Rightarrow10x=320 \\  \\ \Rightarrow x=32 \\  \\ \Rightarrow y=80-32=48
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.


2.) Volume of alcohol in the original mixture
\frac{35}{100} \times 40=14 quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
\frac{48}{100} \times (40+x)=14+x \\  \\ \Rightarrow19.2+0.48x=14+x \\  \\ \Rightarrow0.52x=5.2 \\  \\ \Rightarrow x=10

Therefore, 10 quarts of pure alcohol should be added


3.) Original proportion of white paint in the mixture
=\frac{5}{5+11}=\frac{5}{16}

Let x be the number of gallons of white paint to be added, then
\frac{5+x}{16+x}=\frac{2}{3} \\  \\ \Rightarrow3(5+x)=2(16+x) \\  \\ \Rightarrow15+3x=32+2x \\  \\ \Rightarrow x=32-15=17
Therefore, 17 gallons of white paint should be added.


4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
x - 2 + x + x + 2 = 25 \\  \\ \Rightarrow3x=25\Rightarrow x=8.33
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.


5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
\frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\  \\ \Rightarrow t= \frac{180}{23} =7.83
Therefore, it will take 7.83 hours to get the tank filled up.
3 0
3 years ago
535=5 hundreds+how many tens +5 ones<br> 535= how many tens + 5 ones<br> 535=535 ones
weqwewe [10]
4 hundreds 13 tens 5 ones = 4*100+13*10+5*1=400+130+5= \boxed {535}
8 0
3 years ago
Read 2 more answers
Please help!! With step by step
Sever21 [200]

Answer:

R=\$145.12

Step-by-step explanation:

<u>Compound Interest</u>

This is a well-know problem were we want to calculate the regular payment R needed to pay a principal P in n periods with a known rate of interest i.

The present value PV or the principal can be calculated with

P=F_a\cdot R

Solving for R

\displaystyle R=\frac{P}{F_a}

Where Fa is computed by

\displaystyle F_a=\frac{1-(1+i)^{-n}}{i}

We'll use the provided values but we need to convert them first to monthly payments

i=7\%=7/(12\cdot 100)=0.00583

n=3*12=36

\displaystyle F_a=\frac{1-(1+0.00583)^{-36}}{0.00583}

F_a=32.386

Thus, each payment is

\displaystyle R=\frac{4,700}{32.386}=145.12

\boxed{R=\$145.12}

4 0
3 years ago
A small class has 10 students, 4 of whom are girls and 6 of whom are boys. The teacher is going to choose two of the students at
Vinil7 [7]

Answer:

1/3

Step-by-step explanation:

Dividing the amount of boys (6) by the amount of students (10), and then reiterating that, subtracting 1 from both, you get:
(6/10) x (5/9) which equals a third.

7 0
2 years ago
I need help please help!
Blababa [14]

Answer:

50.5 m^3

Step-by-step explanation:

Volume of pyramid = 1/3 × base area × height.

  • Height: 11
  • Base Dimensions: 4.3 and 3.2

Area of Base:

  • 4.3 * 3.2
  • 13.76  

Next, we multiply 13.76 by 11.

  • 13.76 × 11
  • 151.36

Lastly, divide by 3 and round to nearest tenth.

  • 151.36 ÷ 3  
  • 50.453333..
  • ≈ 50.5

Therefore, the answer is 50.5 m^3

4 0
2 years ago
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