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3 years ago

The average brain is about 2% of a persons total body weight which fraction is equivalent to 2%

1 answer:

3 0

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}\qquad \stackrel{\textit{2\% of anything}}{\left( \cfrac{2}{100} \right)anything}\implies \left( \cfrac{1}{50} \right)anything\implies(0.02)anything$

in short, we can change any percent formatted number to a decimal or fraction formatted one by simply dividing it by 100.

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An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the near

tino4ka555 [31]

Answer:

The height of the triangle is 5.2 inches

Step-by-step explanation:

we know that

An equiangular triangle is a triangle where all three interior angles are equal in measure

Remember that an equilateral triangle has three equal sides and three equal interior angles

An equiangular triangle Is the same that an equilateral triangle. The measure of its interior angles is equal to 60 degrees

Let

h ----> the height of triangle

b ---> the length side of the triangle

Applying Pythagoras Theorem

$h^2=b^2-(b/2)^2$

we have

$b=6\ in$

substitute

$h^2=6^2-(6/2)^2$

$h^2=36-9$

$h^2=27$

$h=\sqrt{27}\ in$

$h=5.2\ in$

see the attached figure to better understand the problem

5 0

3 years ago

HELP ASAP BRAINLIEST FOR FIRST CORRECT ANSWER In triangle ABC, m∠A=(5x−10)∘, m∠B=(12x)∘, and the exterior angle at C is (16x)∘.

kirill [66]

Answer:

160

Step-by-step explanation:

5x-10+12x=16x

17x-16x=10

x= 10

exterior angle at C = 16x= 16×10 = 160°

5 0

3 years ago

Read 2 more answers

A certain article indicates that in a sample of 1,000 dog owners, 610 said that they take more pictures of their dog than of the

lbvjy [14]

Answer:

(a) The 90% confidence interval is: (0.60, 0.63) Correct interpretation is (3).

(b) The 95% confidence interval is: (0.42, 0.46) Correct interpretation is (1).

(c) First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

Step-by-step explanation:

(a)

Let X = number of dog owners who take more pictures of their dog than of their significant others or friends.

Given:

X = 610

n = 1000

Confidence level = 90%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{610}{1000}=0.61$

The critical value of z for a 90% confidence level is:

$z_{\alpha/2}=z_{0.10/2}=z_[0.05}=1.645$

Construct a 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.61\pm 1.645\sqrt{\frac{0.61(1-0.61}{1000}}\\=0.61\pm 0.015\\=(0.595, 0.625)\\\approx(0.60, 0.63)$

Thus, the 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends is (0.60, 0.63).

Interpretation:

There is a 90% chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within the interval (0.60, 0.63).

Correct option is (3).

(b)

Let X = number of dog owners who are more likely to complain to their dog than to a friend.

Given:

X = 440

n = 1000

Confidence level = 95%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{440}{1000}=0.44$

The critical value of z for a 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Construct a 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.44\pm 1.96\sqrt{\frac{0.44(1-0.44}{1000}}\\=0.44\pm 0.016\\=(0.424, 0.456)\\\approx(0.42, 0.46)$

Thus, the 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend is (0.42, 0.46).

Interpretation:

There is a 95% chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within the interval (0.42, 0.46).

Correct option is (1).

(c)

The confidence interval in part (b) is wider than the confidence interval in part (a).

The width of the interval is affected by:

The confidence level
Sample size
Standard deviation.

The confidence level in part (b) is more than that in part (a).

Because of this the critical value of z in part (b) is more than that in part (a).

Also the margin of error in part (b) is 0.016 which is more than the margin of error in part (a), 0.015.

First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

4 0

3 years ago

Write one-half times a number minus 4. use x as a variable

alexdok [17]

Answer:

$\frac{1}{2}$ x-4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

How well can you apply Boyle’s law to this sample of gas that experiences changes in pressure and volume? Assume that temperatur

emmasim [6.3K]

Answer:

A = 1.0 L

B = 0.50 atm

C = 0.60 atm

D = 4.0 L

Step-by-step explanation:

According to the Boyle's law, the volume of a gas is inversely proportional to its volume. If we consider an initial state (1) and a final state (2):

P₁ × V₁ = P₂ × V₂

P₁ × V₁ = P₂ × V₂

1.5 atm × 2.0 L = 3.0 atm × A

A = 1.0 L

P₁ × V₁ = P₂ × V₂

1.5 atm × 2.0 L = B × 6.0 L

B = 0.50 atm

P₁ × V₁ = P₂ × V₂

1.5 atm × 2.0 L = C × 5.0 L

C = 0.60 atm

P₁ × V₁ = P₂ × V₂

1.5 atm × 2.0 L = 0.75 atm × D

D = 4.0 L

4 0

4 years ago

Read 2 more answers