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2 years ago

9

Two joggers run 12 miles north and then 5 miles west. What is the shortest distance they must travel to return to their starting

point

1 answer:

Lera25 [3.4K]2 years ago

3 0

Answer:

13 miles

Step-by-step explanation:

It may be easier to use a diagram but I am going to try my best to explain without one.

Picture their journey north as one side of a right angle triangle (a). Now picture their journey west as another side (b).

The shortest journey back is the hypotenuse of the triangle (c).

Using pythagoras you can work out the answer

$a^{2} + b^{2} = c^{2}$

$5^{2} + 12^{2} = c^{2}\\25 + 144 = c^{2} \\\\169 = c^{2}\\\sqrt{169} = c^{2} \\13 = c^{2}$

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the length of a rectangle is 3 times its width. the perimeter is 55. find the length and width of the rectangle

Shkiper50 [21]

Answer:

Step-by-step explanation: L= length w= width p= perimeter

L=3W p=55CM

P. of rectangle= 2(l+w)=55cm

L+w= 55/2= 27.5 cm

3w+w=27.5cm

4w=27.5cm

w=27.5/4=6.875cm w=6.875cm L= 3w=6.875*3=20.625cm

4 0

2 years ago

The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed

algol [13]

Answer:

$\chi^2 = \frac{(27-33.33)^2}{33.33}+\frac{(31-33.33)^2}{33.33}+\frac{(42-33.33)^2}{33.33}+\frac{(40-33.33)^2}{33.33}+\frac{(28-33.33)^2}{33.33}+\frac{(32-33.33)^2}{33.33} =5.860$

$p_v = P(\chi^2_{5} >5.860)=0.32$

Since the p value is higher than the significance level assumed 0.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we can assume that we have equally like results.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Number: 1, 2 , 3 , 4 , 5 ,6

Frequency: 27, 31, 42, 40, 28, 32

We need to conduct a chi square test in order to check the following hypothesis:

H0: The outcomes are equally likely.

H1: The outcomes are not equally likely.

The level of significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The observed values are given:

$O_{1}=27$ $O_{2}=31$

$O_{3}=42$ $O_{4}=40$

$O_{5}=28$ $O_{6}=32$

The expected values are given by:

$E_{1} =\frac{1}{6}*200=33.33$ $E_{2} =\frac{1}{6}*200=33.33$

$E_{3} =\frac{1}{6}*200=33.33$ $E_{4} =\frac{1}{6}*200=33.33$

$E_{5} =\frac{1}{6}*200=33.33$ $E_{6} =\frac{1}{6}*200=33.33$

And now we can calculate the statistic:

$\chi^2 = \frac{(27-33.33)^2}{33.33}+\frac{(31-33.33)^2}{33.33}+\frac{(42-33.33)^2}{33.33}+\frac{(40-33.33)^2}{33.33}+\frac{(28-33.33)^2}{33.33}+\frac{(32-33.33)^2}{33.33} =5.860$

Now we can calculate the degrees of freedom for the statistic given by:

$df=Categories-1=6-1=5$

And we can calculate the p value given by:

$p_v = P(\chi^2_{5} >5.860)=0.32$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(5.860,5,TRUE)"

Since the p value is higher than the significance level assumed 0.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we can assume that we have equally like results.

4 0

3 years ago

Friends needs this anwsered help

olya-2409 [2.1K]

Answer:

3, 8, 14, 30, 58

Step-by-step explanation:

As with all formulas, put the numbers in place of the corresponding variables, and do the arithmetic.

$a_1=3\qquad\text{given}\\\\a_2=8\qquad\text{given}\\\\a_3=2a_1+a_2=2(3)+8=14\\\\a_4=2a_2+a_3=2(8)+14=30\\\\a_5=2a_3+a_4=2(14)+30=58$

The first 5 terms of the sequence are 3, 8, 14, 30, 58.

4 0

2 years ago

2k to the power of 6 over 8k to the power of 2

Readme [11.4K]

Answer:

1000000000000

Step-by-step explanation:

2000^6/8000^2=1000000000000

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3 years ago

Read 2 more answers

What equation is graphed in this figure? HELP PLEASE

UkoKoshka [18]

I believe that would be b

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3 years ago

Read 2 more answers