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den301095 [7]
3 years ago
13

I need to find the LCD of fractions 3/4 + 6/7 and how to solve

Mathematics
1 answer:
alexira [117]3 years ago
7 0

The least common denominator of two fraction is the least common multiple of the two denominator.

The least common multiple of 4 and 7 is their product 28, because 4 and 7 have no common factor.

Now, we need to manipulate both fractions so that they have denominator 28. Recalling that you can multiply numerator and denominator of a fraction by the same number without affecting its value, we have

\dfrac{3}{4}=\dfrac{3\cdot 7}{4\cdot 7}=\dfrac{21}{28},\quad \dfrac{6}{7}=\dfrac{6\cdot 4}{7\cdot 4}=\dfrac{24}{28}

So, the sum becomes

\dfrac{3}{4}+\dfrac{6}{7}=\dfrac{21}{28}+\dfrac{24}{28}=\dfrac{21+24}{28}=\dfrac{45}{28}

In fact, when two fractions have the same denominator, you can directly sum their numerators.

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A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performanc
Anni [7]

Answer:

A.) At α = 0.05, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline.

B.)<u><em>The advantage of attempting to remove the block effect is</em></u>

The completely randomized designs does not prove that H0 is incorrect only that it cannot be rejected.

Step-by-step explanation:

<em><u /></em>

<em><u>Using Two-way ANOVA method</u></em>

Given problem

<em><u>Observation              I          II       III          Row total (xr)</u></em>

A                              18 21 20            59

B                            24 26 27             77

C                            30 29 34             93

D                            22 25 24            71

<u>E                            20 23 24           63                      </u>

Col total (xc)             114 124 129        367

∑x²=9233→(A)

∑x²c/r

=1/5(114²+124²+129²)

=1/5(12996+15376+16641)

=1/5(45013)

=9002.6→(B)

∑x²r/c

=1/3(59²+77²+93²+71²+67²)

=1/3(3481+5929+8649+5041+4489)

=1/3(27589)

=9196.3333→(C)

(∑x)²/n

=(367)²/15

=134689/15

=8979.2667→(D)

Sum of squares total

SST=∑x²-(∑x)²/n

=(A)-(D)

=9233-8979.2667

=253.7333

Sum of squares between rows

SSR=∑x²r/c-(∑x)²/n

=(C)-(D)

=9196.3333-8979.2667

=217.0667

Sum of squares between columns

SSC=∑x²c/r-(∑x)²/n

=(B)-(D)

=9002.6-8979.2667

=23.3333

Sum of squares Error (residual)

SSE=SST-SSR-SSC

=253.7333-217.0667-23.3333

=13.3333

<u>ANOVA table</u>

Source                 Sums         Degrees      Mean Squares

of Variation       of Squares   of freedom

<u>                               SS                 DF              MS       F p-value</u>

B/ w     SSR=217.0667              4 MSR=54.2667    32.56 0.0001

rows

B/w     SSC=23.3333         c-1=2 MSC=11.6667        7 0.01

columns

<u>Error (residual)SSE=13.3333 (r-1)(c-1)=8 MSE=1.6667                  </u>

<u>Total SST=253.7333 rc-1=14                                                        </u>

Conclusion:

<u> 1. F for between Rows</u>

The critical region for F(4,8) at 0.05 level of significance=3.8379

The calculated F for Rows=32.56>3.8379

Therefore H0 is rejected

<u>2. F for between Columns</u>

The critical region for F(2,8) at 0.05 level of significance=4.459

We see that the calculated F for Colums=7>4.459

therefore H0 is rejected,and concluded that there is significant differentiating between columns

<u><em>Part B:</em></u>

To analyze the data for completely  randomized designs click on anova two factor without replication  in the data analysis dialog box of the excel spreadsheet.

The following table is obtained

Source DF             Sum                  Mean           F Statistic

<u>                 (df1,df2)    of Square (SS) Square (MS)                    P-value</u>

Factor A       1 1496.5444 1496.5444 769.6514          0.001297

Rows

Factor B -     2 19.4444           9.7222               5                  0.1667

Columns

Interaction

AB               2    3.8889   1.9444        0.1013         0.9045

<u> Error     12   230.4            19.2                                           </u>

<u>Total 17 1750.2778 102.9575                                                         </u>

<u />

<u>Factor - A- Rows</u>

Since p-value < α, H0 is rejected.

<u>Factor - B- Columns</u>

Since p-value > α, H0 can not be rejected.

The averages of all groups assume to be equal.

<u>Interaction AB</u>

Since p-value > α, H0 can not be rejected.

<u><em>The advantage of attempting to remove the block effect is</em></u>

The completely randomized designs does not prove that H0 is incorrect only that it cannot be rejected.

3 0
3 years ago
Suppose you're given the formula R=s+2t and s is three times greater than t, how could you rewrite the formula
sattari [20]

Answer:

R = 5t

Step-by-step explanation:

given s is three times t then s = 3t and

R = 3t + 2t = 5t


4 0
3 years ago
I need helpppppppppp!!!!!!!!!!
Genrish500 [490]

Answer:

m MN = 70°

Step-by-step explanation:

∠MLN is an angle formed by the chords ML and LN and is calculated as

∠MLN = 0.5( m arc MN ), that is

35° = 0.5 arc MN ( multiply both sides by 2 )

arc MN = 2 × 35° = 70°

4 0
3 years ago
What is the value of x?
Fittoniya [83]

Answer:

a

Step-by-step explanation:

6^2+8^2=100

sqrt of 100 = 10

4 0
3 years ago
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What is the slope of the line through (-9,6) and (-3, 9)?
Artyom0805 [142]
To find slope, y2-y1/x2-x1
9-6/-3-(-9)=
3/6= 1/2
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