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3 years ago

Find the slope of the line.

Mathematics

2 answers:

Aleksandr-060686 [28]3 years ago

7 0

A simple way of finding the slope is counting the spaces. the graph is going downwards to the right so it's clear the slope is negative, and if you count you'll see it takes going down 3, over 5 to get to the next point. therefore, the slope is -3/5

weqwewe [10]3 years ago

6 0

Its negative as its slopes down from the right
slope = rise / run = -5/8

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Select the correct answer. Every dimension of a triangular pyramid is multiplied by 10 to produce a new figure that is geometric

BaLLatris [955]

Answer:

C. The surface area of the pyramid is multiplied by 100

Step-by-step explanation:

The area is the function of the two dimensions.

If each dimension has changed by 10 times, the the area will change by:

10*10 = 100 times

Correct choice is C

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3 years ago

An article reports on an experiment in which each of five groups consisting of six rats was put on a diet with a different carbo

loris [4]

Answer:

H0 is rejected, Hence the true average DNA content is affected by the type of carbohydrate in the diet between samples

Step-by-step explanation:

A B C D E

2.58 2.63 2.13 2.41 2.49

∑A=2.58 ∑B=2.63 ∑C=2.13 ∑D=2.41 ∑E=2.49

A² B² C² D² E²

6.6564 6.9169 4.5369 5.8081 6.2001

∑A²=6.6564 ∑B²=6.9169 ∑C²=4.5369 ∑D²=5.8081 ∑E²=6.2001

Calculations

Group A B C D E Total

N n1=1 n2=1 n3=1 n4=1 n5=1 n=5

∑xi T1=2.58 T2=2.63 T3=2.13 T4=2.41 T5=2.49 ∑x=12.24

∑x²i 6.6564 6.9169 4.5369 5.8081 6.2001 ∑x²=30.1184

Mean xi 2.58 2.63 2.13 2.41 2.49 Total2.448

Σ Σ xij^2 = 185.4 given

Let k = the number of different samples = 5

n=n1+n2+n3+n4+n5=1+1+1+1+1=5

Overall ˉx=12.24/5 =2.448

∑x=T1+T2+T3+T4+T5=2.58+2.63+2.13+2.41+2.49=12.24----1

Correction Factor=(∑x)²/n=12.242/5=29.9635--------(2)

∑T²i/ni=(2.582/1+2.632/1+2.132/1+2.412/1+2.492/1)=30.1184------(3)

∑x²=∑x²1+∑x²2+∑x²3+∑x²4+∑x²5

=6.6564+6.9169+4.5369+5.8081+6.2001=30.1184-------(4)

ANOVA:

Step-1 : sum of squares between samples

SSB=(∑T2i/ni)-(∑x)2/n

=(3)-(2)

=30.1184-29.9635

=0.1549

Step-2 : Total sum of squares

SST=SSB-CF

= 185.4-2.488

=182.952

Step-3 : Sum of Squares Within Samples

SSW=∑x²-(∑T²i/ni)=SST- SSB=

= 182.952-0.1549=182.7971

Step-4 : variance between samples

MSB=SSB/k-1

=0.1549/4

=0.0387

Step-5 : variance within samples

MSW=SSW/n-k

=182.7971/5-5

=36.55942

Step-6 : test statistic F for one way ANOVA test

F=MSB/MSW

=0.0387/36.55942 = 0 .001058

ANOVA table

Source Sums Degrees Mean

of Variation of Squares of freedom Squares

SS DF MS F

B/w samples SSB = 0.1549 k-1 = 4 MSB = 0.0387 0.001

Within samples SSW = 0 n-k = 0 MSW = 36.55942

Total SST = 0.1549 n-1 = 4

H0 : The true average DNA content is not affected by the type of carbohydrate in the diet between samples

Ha : The true average DNA content is affected by the type of carbohydrate in the diet between samples

F(4,0) at 0.05 level of significance =0.5

As calculated F=0.001 >0.5

So, H0 is rejected, Hence the true average DNA content is affected by the type of carbohydrate in the diet between samples

6 0

3 years ago

Determine all numbers at which the function is continuous

Kay [80]

Answer

Please see attached image for full understanding of the solution

If we plot the function we can see that it has a discontinuity at x = 1.

Also,

If we evaluate at x = -9, we see that the values of the piecewise function in both cases are completely different.

Therefore, x = -9 is also a discontinuity.

The right answer is option a

(discontinuity at x = 1 and x = -9)

6 0

3 years ago