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3 years ago

A summer camp counselor wants to find a length x in feet across a lake as represented in the sketch to the left

Mathematics

1 answer:

Nata [24]3 years ago

8 0

The question is incomplete and without a picture. I found similar question as follows:

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

Answer:

1600ft

Step-by-step explanation:

Angle AEB and CBD is the same value.

Referring to the picture, since ABC and DBE are straight lines and crosses each other at B, the angle DBC and EBA are equal.

Since we have 2 equal angle, the third angle must be the same as well.

Therefore we can conclude that both ABE and CBD are similar triangle but with different factor with;

AB similar to BC

EB similar to BD

AE similar to CD

To find the factor between ABE and CBD,

EB / BD = 1400 / 700 = 2

So x, which is AE must be a factor of 2 to CD

AE = 2*800 =1600ft

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A line that contains the point (-8,-1) and is perpendicular to -15x +3y = 9

zaharov [31]

Put the other line in point slope form...(solve for y :D )

3y=15x+9

y=5x+3, so this line has a slope of 5

For a line to be perpendicular to another the slopes have to be negative reciprocals of each other...mathematically...

s1*s2=-1

So for the other line to be perpendicular to the first:

5m=-1, m=-1/5, thus our other line (so far) is:

y=b-x/5, now we can use the point (-8,-1) to solve for the y-intercept, "b":

-1=b-(-8)/5

-1=b+8/5

-1=b+1.6

b=-2.6

So the perpendicular line that contains the point (-8,-1) is:

y=-0.2x-2.6

7 0

2 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.)The advantage of attempting to remove the block effect is

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

Step-by-step explanation:

Using Two-way ANOVA method

Given problem

Observation I II III Row total (xr)

A 18 21 20 59

B 24 26 27 77

C 30 29 34 93

D 22 25 24 71

E 20 23 24 63

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

ANOVA table

Source Sums Degrees Mean Squares

of Variation of Squares of freedom

SS DF MS F p-value

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

Error (residual)SSE=13.3333 (r-1)(c-1)=8 MSE=1.6667

Total SST=253.7333 rc-1=14

Conclusion:

1. F for between Rows

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

2. F for between Columns

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

Part B:

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

(df1,df2) of Square (SS) Square (MS) P-value

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

Error 12 230.4 19.2

Total 17 1750.2778 102.9575

Factor - A- Rows

Since p-value < α, H0 is rejected.

Factor - B- Columns

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

The averages of all groups assume to be equal.

Interaction AB

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

The advantage of attempting to remove the block effect is

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

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2 years ago

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Sladkaya [172]

14-5+20÷2∧2+4

exponent first: 14-5+20÷4+4

Divide: 14-5+5+4

Solve left to right: 9+5+4

add all: 14+4 = 18

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3 years ago

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Ghella [55]

Answer:

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