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3 years ago

A collection of animals including both birds and beasts has 43 heads and 120 feet how many based are there in the collection

Mathematics

1 answer:

DaniilM [7]3 years ago

8 0

Step-by-step explanation:

x = number of birds

y = number of beasts

x + y = 43 (as each of these creatures had only 1 head).

2x + 4y = 120 (birds have 2 feet, beasts 4 feet).

x + 2y = 60 (divided both sides by 2)

so, second equation minus the first equation is

(x-x) + (2y-y) = 60-43

y = 17

x + y = 43

x + 17 = 43

x = 26

so, there are 17 beasts and 26 birds.

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alekssr [168]

The similarity ratio of ΔABC to ΔDEF = 2 : 1.

Solution:

The image attached below.

Given ΔABC to ΔDEF are similar.

To find the ratio of similarity triangle ABC and triangle DEF.

In ΔABC: AC = 4 and CB = 5

In ΔDEF: DF = 2, EF = ?

Let us first find the length of EF.

We know that, If two triangles are similar, then the corresponding sides are proportional.

⇒ $\frac{AC}{DF} =\frac{BC}{EF}$

⇒ $\frac{4}{2} =\frac{5}{EF}$

⇒ $4EF=5\times2$

⇒ $EF=\frac{5\times 2}{4}$

⇒ $EF=\frac{5}{2}$

Ratio of ΔABC to ΔDEF = $\frac{AC}{DF} =\frac{4}{2}=\frac{2}{1}$

Similarly, ratio of ΔABC to ΔDEF = $\frac{BC}{EF} =\frac{5}{\frac{5}{2}}=\frac{2}{1}$

Hence, the similarity ratio of ΔABC to ΔDEF = 2 : 1.

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3 years ago

If you have 7x^2 + 3 if the input is 4 what is the output

Usimov [2.4K]

7x^2 + 3
7(4)^2 + 3
7(16) + 3
112 + 3
115.

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3 years ago

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What type of polynomial is 2x+10

Romashka-Z-Leto [24]

AnswerAnswer:

Binomial

Step-by-step explanation:

there are 2 terms

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2 years ago

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For every 5 yard you run jill run 6 yard if you have run 30 yard then how far jill run.

liubo4ka [24]

Jill has ran 36 yards.
We run 5, 10, 15, 20, 25, 30
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3 years ago

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The amount of time it takes a bat to eat a frog was recorded for each bat in a random sample of 12 bats. The resulting sample me

spin [16.1K]

Answer: a. CI for the mean: 17.327 < μ < 26.473

b. CI for variance: 29.7532 ≤ $\sigma^{2}$ ≤ 170.9093

Step-by-step explanation:

a. To construct a 95% confidence interval for the mean:

The given data are:

mean = 21.9

s = 7.7

n = 12

df = 12 - 1 = 11

1 - α = 0.05

$\frac{\alpha}{2}$ = 0.025

t-score = $t_{0.025,11}$ = 2.2001

Note: since the sample population is less than 30, it is used a t-score.

The formula for interval:

mean ± $t.\frac{s}{\sqrt{n} }$

Substituing values:

21.9 ± 2.200. $\frac{7.7}{\sqrt{12} }$

21.9 ± 4.573

The interval is: 17.327 < μ < 26.473

b. A 95% confidence interval for the variance:

The given values are:

$s^{2}$ = $7.7^{2}$

$s^{2}$ = 59.29

α = 0.05

$\frac{\alpha}{2}$ = 0.025

$1-\frac{\alpha}{2}$ = 0.975

$\chi^{2}_{0.025,11}$ = 21.92

$\chi^{2}_{0.975,11}$ = 3.816

Note: To find the values for $\chi^{2}_{\alpha/2,n-1}$ and $\chi^{2}_{1-\alpha/2,n-1}$ , look for them at the chi-square table

The formula to calculate interval:

( $\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}}$ )

are the lower and upper limits, respectively.

Substituing values:

( $\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816}$ )

(29.7532, 170.9093)

The interval for variance is: 29.7532 ≤ $\sigma^{2}$ ≤ 170.9093

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3 years ago