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3 years ago

Benito wrote the equations shown about the figure. Explain Benito’s errors.

Mathematics

1 answer:

Minchanka [31]3 years ago

7 0

Answer:

Benito's error was using the equal sign (=) instead of the congruency symbol (≅).

Explanation:

Benito's error was using the equal sign (=) instead of the congruency symbol (≅).

The congruency symbol (≅) means that the elements (segments, angles or figures in general) have the same measure, i.e. they have equal lengths for the segments or equal measure for the angles.

For instance, it is an error saying that the segment AB is equal to the segment BC because, as you clearly see in the picture, they are not same; they have the same length but they are joining different points, that makes them different in essence, although they have the same length. They would be equal only if they are the same figure.

In mathematics, you must not say that two different segments or two different angles are equal but they are congruent, which means that their lengths are equal. The use of equal is reserved for numbers and variables, not for figures like segment, points, angles, polygons.

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The probability that John receives junk mail is 11 percent. If he receives 94 pieces of mail in a week, about how many of them c

SVETLANKA909090 [29]

Answer:

10 (10.34 rounded down)

Step-by-step explanation:

11% is the same as .11

Multiply by 94 for your answer.

.11 x 94 = 10.34

10 pieces

5 0

3 years ago

Solve the following equation 5(3x+5)=3(5x+1)

rjkz [21]

Answer:

No solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

5(3x+5)=3(5x+1)

Step 1: Simplify both sides of the equation.

5(3x+5)=3(5x+1)

(5)(3x)+(5)(5)=(3)(5x)+(3)(1)(Distribute)

15x+25=15x+3

Step 2: Subtract 15x from both sides.

15x+25−15x=15x+3−15x

25=3

Step 3: Subtract 25 from both sides.

25−25=3−25

0=−22

Answer:

There are no solutions.

6 0

2 years ago

Read 2 more answers

At Southside Middle School, 30% of the students play an instrument. There are 310 students. How many students play an instrument

rodikova [14]

93 students play an instrument because you would take 310 (the total amount of students) and multiply it by 0.3 (the thirty percent) and get 93

5 0

3 years ago

N^2- 5n +4=0 quadratic equation

luda_lava [24]

Answer:

n = 1, 4

Step-by-step explanation:

Step 1: Write equation

n² - 5n + 4 = 0

Step 2: Solve for n

Factor: (n - 4)(n - 1) = 0

Find roots: n = 1, 4

Step 3: Check

Plug in n to verify if it's a solution.

1² - 5(1) + 4 = 0

1 - 5 + 4 = 0

-4 + 4 = 0

0 = 0

4² - 5(4) + 4 = 0

16 - 20 + 4 = 0

-4 + 4 = 0

0 = 0

7 0

2 years ago

Read 2 more answers

The Insurance Institute reports that the mean amount of life insurance per household in the US is $110,000. This follows a norma

nata0808 [166]

Answer:

a) $\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}= \frac{40000}{\sqrt{50}}= 5656.85$

b) Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

c) $P( \bar X >112000) = P(Z>\frac{112000-110000}{\frac{40000}{\sqrt{50}}}) = P(Z>0.354)$

And we can use the complement rule and we got:

$P(Z>0.354) = 1-P(Z$

d) $P( \bar X >100000) = P(Z>\frac{100000-110000}{\frac{40000}{\sqrt{50}}}) = P(Z>-1.768)$

And we can use the complement rule and we got:

$P(Z>-1.768) = 1-P(Z$

e) $P(100000< \bar X$

And we can use the complement rule and we got:

$P(-1.768$

Step-by-step explanation:

a. If we select a random sample of 50 households, what is the standard error of the mean?

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the amount of life insurance of a population, and for this case we know the distribution for X is given by:

$X \sim N(110000,40000)$

Where $\mu=110000$ and $\sigma=40000$

If we select a sample size of n =35 the standard error is given by:

$\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}= \frac{40000}{\sqrt{50}}= 5656.85$

b. What is the expected shape of the distribution of the sample mean?

Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

c. What is the likelihood of selecting a sample with a mean of at least $112,000?

For this case we want this probability:

$P(X > 112000)$

And we can use the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$P( \bar X >112000) = P(Z>\frac{112000-110000}{\frac{40000}{\sqrt{50}}}) = P(Z>0.354)$

And we can use the complement rule and we got:

$P(Z>0.354) = 1-P(Z$

d. What is the likelihood of selecting a sample with a mean of more than $100,000?

For this case we want this probability:

$P(X > 100000)$

And we can use the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$P( \bar X >100000) = P(Z>\frac{100000-110000}{\frac{40000}{\sqrt{50}}}) = P(Z>-1.768)$

And we can use the complement rule and we got:

$P(Z>-1.768) = 1-P(Z$

e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000

For this case we want this probability:

$P(100000$

And we can use the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$P(100000< \bar X$

And we can use the complement rule and we got:

$P(-1.768$

8 0

3 years ago