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Cerrena [4.2K]
3 years ago
7

Perimeter of a mirror is 260. The length is x cm. Find the height of the mirror in terms of x

Mathematics
1 answer:
Elenna [48]3 years ago
4 0

\bf \textit{perimeter of a rectangle}\\\\ P=2(L+h)~~ \begin{cases} L=length\\ h=height\\[-0.5em] \hrulefill\\ P=260\\ L=x \end{cases}\implies 260=2(x+h) \\\\\\ \cfrac{260}{2}=x+h\implies 130=x+h\implies 130-x=h

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Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0.85t. Local taxes are a
kolezko [41]
What its saying is that u have a discount price and that goes up by 8% so we know its not greater than 1
8 0
3 years ago
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
2 years ago
Evaluate square root of 16 minus x end root when x = 8.
My name is Ann [436]
\sqrt{16-x}
x=8
16-8=8
\sqrt{8}

Use a calculator to find the square root of 8.

7 0
3 years ago
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4
Firdavs [7]

The expression cos⁴ θ in terms of the first power of cosine is <u>[ 3 + 2cos 2θ + cos 4θ]/8.</u>

The power-reducing formula, for cosine, is,

cos² θ = (1/2)[1 + cos 2θ].

In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.

We can do it as follows:

cos⁴ θ

= (cos² θ)²

= {(1/2)[1 + cos 2θ]}²

= (1/4)[1 + cos 2θ]²

= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}

= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)

= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]

= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8

= 3/8 + cos 2θ/4 + cos 4θ/8

= [ 3 + 2cos 2θ + cos 4θ]/8.

Thus, the expression cos⁴ θ in terms of the first power of cosine is <u>[ 3 + 2cos 2θ + cos 4θ]/8</u>.

Learn more about reducing trigonometric powers at

brainly.com/question/15202536

#SPJ4

5 0
2 years ago
A cake is shared between 5 people. What percentage of the cake does each person get. SOMEONE HELP ASAP
abruzzese [7]

Answer:

20%

Step-by-step explanation:

100% shared between 5 peoples.

100/5 = 20%

Yeah_Boi ;)

Follow me on Insta,

khuturr_

6 0
2 years ago
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