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3 years ago

Find the sum 3 + (-6)

Mathematics

2 answers:

adoni [48]3 years ago

8 0

The answer was in the problem, -3.

Gennadij [26K]3 years ago

6 0

To find the sum of two numbers, we must add them together. However, in this case we are adding a negative number. Addition of a negative number can also be written as subtraction, and this method is easier for most people to compute and understand, so we are going to rewrite the expression as follows:

3 - 6

Next, we must just perform the subtraction.

3 - 6 = -3

Therefore, your answer is -3.

Hope this helps!

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2 years ago

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Andrea is given triangle ABC and told that a ^ 2 + b ^ 2 = c ^ 2 draws right triangle RTS with legs measuring a and b and hypote

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Complete question is;

Andrea is given ABC and told that a² + b² = c². She draws right triangle RTS with legs measuring a and b and hypotenuse measuring 2. Which best describes what Andrea should

do in order to prove that ABC is a right triangle?

Answer:

Andrea should show that c = 2, so: ∡ABC = ∡RTS and ∡C = ∡S. Hence, ∡C is a right angled triangle, hence ΔABC is a right triangle

Step-by-step explanation:

In this question, we are told that the given sides of the triangle are a, b and c. Now, Andrea is able to draw the two sides of the right triangle with sides = a and b and the third, hypotenuse equal to 2. Since the length of the hypotenuse = 2, then we have;

2² = a² + b²

However, we are told that c² = a² + b²

Therefore, c = 2

Hence, Andrea should show that c = 2 so ΔABC = ΔRTS and ∡C = ∡S hence ∡C is a right angled triangle since it is the angle opposite to the hypotenuse c and therefore, ΔABC is a right triangle.

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2 years ago

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

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2 years ago

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Answer:

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A duck is going to fly from the coordinates (1, 3) then go 3 units right. And 6 units down

That means -----> The rule of the translation is

3 units right ----> x+3

6 units down ---> y-6

(x,y) ----> (x+3,y-6)

To find out the the coordinates of the duck’s final position, apply the rule of the translation to the duck’s original position

(1,3) ------> (1+3,3-6)

(1,3) ------> (4,-3)

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2 years ago

2.11 as a mixed number in simplest form

Elis [28]

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2 years ago

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