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kkurt [141]
3 years ago
9

If juliana and brody hiked both trails, how far did they hike? 3 2/3 and 2 5/6

Mathematics
1 answer:
Andreyy893 years ago
8 0

Juliana trails = 3\frac{2}{3}

Brody trails = 2\frac{5}{6}.

In order to find total how far they hiked, we need to add Juliana trails and Brody trails.

Juliana trails + Brody trails  = 3\frac{2}{3} +2\frac{5}{6}.

Adding whole number in front 3+2 = 5.

Now, adding fractions 2/3 and 5/6 by taking common denominator (lcd).

Least common denominator(lcd) of 3 and 6 is = 6.

So, we need to make both denominator = 6.

Muilplying 2/3 by 2 in top and bottom we get 2*2/3*2 = 4/6.

Now, adding 4/6 and 5/6.

We got the common denominator 6. So, we can just add numerators.

\frac{4}{6} +\frac{5}{6}  = \frac{4+5}{6} = \frac{9}{6}

Converting 9/6 into improper fraction:

If we divide 9 by 6, we get quotent 1 and 3 remainder.

So, we get fraction 1 \frac{3}{6} .

3/6 could also be reduced to 1/2 by dividing 3 and 6 by 3.

We get,

\frac{3}{6}  = \frac{1}{2}

Therefore, 1 \frac{3}{6}  = 1 \frac{1}{2}

Adding 5 into 1\frac{1}{2}.

We get,

6\frac{1}{2}.

So, we could say

They hiked total 6\frac{1}{2} far.

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Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, co
sineoko [7]

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Step-by-step explanation:

The given is,

               Initial investment - $5000

               Future amount - $6000

               Interest rate - 7.5% (compounded quarterly)

Step:1

           Formula to calculate the Future amount with compound interest,

                                   F = P(1+\frac{r}{n} )^{nt}...................................(1)

          Where, F - Future amount

                           P - Initial amount

                            r - Rate of interest

                           n - No. of compounding in a year

                            t - Time period

          From given,

                      F = $6000

                      P = $5000

                       r = 7.5%

                       n = 4 (compounded quarterly)

        Equation (1) becomes,

                              6000=5000(1+\frac{0.075}{4} )^{(t)(4)}

                               \frac{6000}{5000} =(1+0.01875)^{4t}

                                 1.2 = (1.01875)^{4t}

         Take log on both sides,

                            log 1.2 = 4(t) log 1.01875

         Substitute log values,

                       0.07918 = 4(t) (0.0080676)

                                      = (t) (0.0322705)

                                   t = \frac{0.07918}{0.0322705}

                                      = 2.45

                                   t ≅ 2.5 years

Result:

         2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

3 0
3 years ago
Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Sea-hawks when they won Su
weeeeeb [17]

Answer:

No. These measures show a thinner team of NFL players according to the mean, variance, standard deviation, and quartiles.

Step-by-step explanation:

1) The measures of variation, namely The Range, Variance, Quartiles, Interquartiles, Sum of Squares, etc. shows us how the data are dispersed.

The Range Δ is calculated:

\Delta =305-189=116 Maximum value - Minimum value for weight

Mean:

\bar{x}=\frac{189+254+235+225+190+305+202+190+252+305}{11}\approx 231.09 \:pounds

Variance:

s^{2}=\frac{\sum_{i=1}^{n} (x_i-\bar{x})^{2}}{n-1}\Rightarrow s=1923.69\\

The Standard Deviation of the sample

s=\sqrt{s^{^{2}}}\Rightarrow s\approx 43.86\\

2) Since there is no preceding exercise, the comparison was made to a recent study in which a NFL player average weight is about 245 pounds (average),

Since 25% of this list are player whose weight is 192.5 lbs and 50% (2nd Quartile) =225 lbs , finally only at the 3rd Quartile we have players above the regular NFL average with 253. This, added with the other data, allow us to say that this list is not a typical of all NFL players.

4 0
3 years ago
Find two positive numbers satisfying the given requirements.
Umnica [9.8K]

Answer:

8 and 19

Step-by-step explanation:

To some this, let's first list all the factors of 152. They are;

1, 2, 4, 8, 19, 38, 76, 152.

Now, let's arrange them to reflect being multiplied to get 152.

Thus;

1 × 152 = 152

2 × 76 = 152

4 × 38 = 152

8 × 19 = 152

Also, let's do the same for their sum;

1 + 152 = 153

2 + 76 = 78

4 + 38 = 42

8 + 19 = 27

Looking at the figures above, the ones that their product is 152 but have the least sum are 8 and 19

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Please answer fast! (10 points)
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Answer:

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Step-by-step explanation:

8 0
3 years ago
Write the equation of a parabola with a vertex and (-5, 2) and a directrix y = -1
mrs_skeptik [129]

Answer:

y=(x+5)²/6 + 1/3

Step-by-step explanation:

Use the distance formula to plug in the values you know:

√(y+1)² =√(x+5)² +( y-2)²

the square roots cancel out

(y+1) ²= (x+5)² +(y-2)²

(y+1) (y-1)= (x+5)² + (y-2) (y-2)

y²+2y+1= (x+5)² + y² -4y+4

the y² cancel out

2y+ 4y = (x+5)² + 4-1

6y= (x+5)² +3

y= (x+5)² /6+ 1/3

4 0
3 years ago
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