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Leona [35]
3 years ago
10

I need help on this question

Mathematics
2 answers:
AnnZ [28]3 years ago
5 0
Using the fact that the triangles shown are similar, we can set up a proportion between the lengths of the sides. 

The side length in question is QR, or "x". To find its corresponding side in the larger triangle let's look at the similarity.

MNO is similar to PQR
Vertices are always written in order of correspondence when stating similarities. Since QR are the last two letters of the triangle's name, and NO are the last two letters of the larger triangle's name, we know that QR and NO are corresponding sides. We can apply this same method to any other side.

NO/QR = MN/PQ
(MN and PQ are also corresponding sides)
Now we can substitute the side names with their values.
4.5/x = 5/2
Cross multiply
5x = 9
Divide both sides by 5
x = 9/5 or 1.8 or 1 4/5

Hope this helps!

lutik1710 [3]3 years ago
5 0
Hello!

ΔMNO ≈ ΔPQR

MN ≈ PQ

MN = 5
PQ = 2

NO = QR

4 1/2 = 9/2

\frac{2}{5} \times  \frac{9}{2} =  \frac{18}{10} = 1  \frac{8}{10} = 1  \frac{4}{5}

Answer ⇒ 3rd choice
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mrs lemke has 10 2/3 ounces of fertilizer for her plants. She plans to use 3/4 ounce of fertilizer om each plant. After she put
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What we know:
Mrs Lemke has a total of 10 2/3 oz of fertilizer
3/4 oz fertilizer per plant

What we need to find is left over fertilizer after equally distributing as much 3/4 oz of fertilizer per plant.

10 2/3 oz must be divided into groups of 3/4 oz
Those groups will show how many plants can be fertilized with each receiving 3/4 oz of fertilizer and the remainder will be the left over fertilizer in ounces we need to find.

First we must change 10 2/3 into an improper fraction of 32/3.
Now, we divide 32/3 by 3/4.
(32/3)/(3/4)=(32/3)x(4/3)
(32x4)/(3x3)=128/9

128/9 equals to 14 with a remainder of 2/9
That means Mrs Lemke can fertilize 14 plants with 3/4 oz of fertilizer each and have left over of 2/9 ounces.
Your answer is the remainder which is 2/9 ounces.
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3 years ago
A digit's ________ value is the value it signifies when written as part of a number.
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1. Consider the system of equations consisting ol' x + y = 3 and 3x - y = 5.
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Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly becaus
const2013 [10]

Answer:

Step-by-step explanation:

Hello!

Given the variable

X:  Ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloth.

The researcher's claim is that the ratio of the SC of the sloths is more variable than in other animal species that are more active.

For more active species the standard deviation of the ratio is σ= 0.09

1)

To calculate the sample standard deviation you have to calculate the sample variance first:

S^2= \frac{1}{n-1} [sumX^2-\frac{(sumX)^2}{n} ]

n=7; ∑X= 8.91; ∑X²= 11.8599

S^2= \frac{1}{6} [11.5899-\frac{(8.91)^2}{7} ]= 0.0287= 0.029

S= √S²= √0.029= 0.169≅ 0.17

The sample standard deviation of the ratio is 0.17

2)

The parameter of interest is the population standard deviation. To calculate a confidence interval for the standard deviation of a population you have to estimate the population variance first. Then calculate the square root of both limits of the interval for the variance to obtain the interval for the standard deviation.

The statistic to use is the Chi-Square and the formula for the interval is:

[\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ]

X^2_{n-1;\alpha /2}= X^2_{6; 0.025}= 1.2373

X^2_{n-1;1-\alpha /2}= X^2_{6; 0.975}= 14.449

[\frac{6*0.029}{14.449} ;\frac{6*0.029}{1.2373} ]\\

[0.0120; 0.1406]

Using a 95% confidence level you'd expect the interval [0.0120; 0.1406] to include the true value of the population variance of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.

Now you have to calculate the square root of each limit:

[√0.0120; √0.1406]

[0.1097; 0.3750]

Using a 95% confidence level you'd expect the interval [0.1097; 0.3750] to include the true value of the population standard deviation of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.

3)

As you can see the calculated interval doesn't include the value obtained for the other species.

I hope this helps!

5 0
2 years ago
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