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3 years ago

28/29 and 30 plz short explanation thanks

Mathematics

1 answer:

zzz [600]3 years ago

5 0

Integers are numbers like ...-3, -2, -1, 0, 1, 2, 3... and so on. So, according to this definition, let's solve this problem:

28. We know that the product of three integers is -3. So, the statement states that we have three factor, so:

a.b.c = -3

The possible values of the factors are:

Factors are: 3, 1 and -1 in which case:

(3)(1)(-1) = -3

Factors are: -3, 1 and 1 in which case:

(-3)(1)(1) = -3

29. In this problem we know two nonzero integers, that is, they cannot be equal to zero. Thus, they must have different sign, that is, one of them must be positive and the other negative. For instance:

-9 and 2

(-9)(2) = -18, So -18 is less than -9 and 2

Another example:

1 and -8

(1)(-8) = -8, So -8 is equal to -8 and -8 is less than 1.

30. The sign of the product of two integers with the same sign is positive, that is:

(+)(+) = (+) and

(-)(-) = (+)

So, the sign of the product of three integers with the same sign are two options:

<u>Option 1.</u> The three integers are positive in which case:

(+)(+)(+) = (+), So the sign of the product is positive

<u>Option 2.</u> The three integers are negative in which case:

(-)(-)(-) = (-), So the sign of the product is negative.

This option two gives us that result because:

(-)(-) = (+) and (+)(-) = (-)

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Anastasy [175]

Answer:

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Step-by-step explanation:

See the diagram attached.

We have to prove Δ ABC ≅ Δ ADC

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Between Δ ABC and Δ ADC

1. CA bisects ∠ BAD, and hence, ∠ CAB = ∠ CAD {Given}

2. ∠ B = ∠ D {Given}

3. Side AC is common to both the triangles.

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3 years ago

Equation for the sum of 27 and a number is 50

8_murik_8 [283]

27 + X = 50 is the equation

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3 years ago

Read 2 more answers

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and

masya89 [10]

Answer:

a) There is a 100% probability that the (sample) average time waiting in line for these customers is less than 10 minutes.

b) There is a 100% probability that the (sample) average time waiting in line for these customers is between 5 and 10 minutes.

c) There is a 0% probability that the (sample) average time waiting in line for these customers is less than 6 minutes.

d) Because there are less observations, it would be less accurate.

e) Because there are moreobservations, it would be more accurate.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. This means that $\mu = 8.2, \sigma = 1.5$ .

Suppose that a random sample of n = 49 customers is observed

This means that $s = \frac{1.5}{\sqrt{49}} = 0.21$ .

(a) Less than 10 minutes.

This probability is the pvalue of Z when $X = 10$ . So:

$Z = \frac{X - \mu}{s}$

$Z = \frac{10 - 8.2}{0.21}$

$Z = 8.57$

$Z = 8.57$ has a pvalue of 1.

This means that there is a 100% probability that the (sample) average time waiting in line for these customers is less than 10 minutes.

(b) Between 5 and 10 minutes.

This probability is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 5.

From a), we have that the zscore of X = 10 has a pvalue of 1.

For X = 5.

$Z = \frac{X - \mu}{s}$

$Z = \frac{5 - 8.2}{0.21}$

$Z = -15.24$

$Z = -15.24$ has a pvalue of 0.

Subtracting, we have that there is a 100% probability that the (sample) average time waiting in line for these customers is between 5 and 10 minutes.

(c) Less than 6 minutes.

This probability is the pvalue of Z when X = 6. So:

$Z = \frac{X - \mu}{s}$

$Z = \frac{6 - 8.2}{0.21}$

$Z = -10.48$

$Z = -10.48$ has a pvalue of 0.

This means that there is a 0% probability that the (sample) average time waiting in line for these customers is less than 6 minutes.

(d) If you only had two observations instead of 49 observations, would you believe that your answers to parts (a), (b), and (c), are more accurate or less accurate? Why?

The less observations there are, the less acurrate our results are.

So, because there are less observations, it would be less accurate.

(e) If you had 1,000 observations instead of 49 observations, would you believe that your answers to parts (a), (b), and (c), are more accurate or less accurate? Why?

The more observations there are, the more acurrate our results are.

So, because there are moreobservations, it would be more accurate.

8 0

3 years ago

Find the greatest common factor of 15x 2 y 3 and -20x 3 yz.

Andre45 [30]

You multiply the GCF of the numerical part 3 and the GCF of the variable part x^2y to get 3x^2y

7 0

3 years ago

Read 2 more answers

Please and thank you help me

Art [367]

9514 1404 393

Answer:

your graph is correct
y = 3x -5

Step-by-step explanation:

The graph shows you the line has a "rise" of 1-(-2) = 3 for a "run" of 2-1 = 1, so the slope is 3/1 = 3.

The y-intercept is seen to be -5, so the equation is ...

y = mx +b . . . . . where m is the slope (3) and b is the y-intercept (-5)

y = 3x -5

The points and line are plotted correctly, so you already have your graph.

4 0

3 years ago