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2 years ago

A quadrilateral has vertices A(3,5), B(2,0), C(7,0) and D(8,5). Which statement about the quadrilateral is true?

Mathematics

2 answers:

ioda2 years ago

3 0

Answer:

ABCD is a rhombus with non-perpendicular adjacent sides

Step-by-step explanation:

A rhombus is a quadrilateral with four sides equal in length and non-perpendicular adjacent sides.

In the given case, when we plot the quadrilateral having vertices A(3,5), B(2,0), C(7,0) and D(8,5) then the length of each side comes out to be 5 i.e.

AB=BC=CD=AD=5

hence given quadrilateral ABCD is a rhombus with non-perpendicular adjacent sides.

posledela2 years ago

3 0

Answer: ABCD is a parallelogram with non-perpendicular adjacent sides

Step-by-step explanation:

As we have two points on y=0 and two points on y=5 we can soy it has two parallel sides.

BC on y=0 has a length of 7-2=5 units

AD on y=5 has a is 8-3=5 units long

As the quadrilateral has 2 parallel sides that mesure the same, it has to be a parallelogram.

To be a rectangle the other two sides should be parallel to the y-axis, and their points should share their x coordenate. So it’s a non rectangular parallelogram.

To be a rhombus it should have 4 sides with the same lenght. AB is $\sqrt{1+5^{2} }$ that’s different to 5. Then its not a rhombus.

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Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

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 sums, we have that the mean is $\mu*n$ and the standard deviation is $s = \sigma \sqrt{n}$

In this problem, we have that:

$\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160$

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

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

$Z = \frac{4000 - 3500}{160}$

$Z = 3.13$

$Z = 3.13$ has a pvalue of 0.9991

X = 3000

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

$Z = \frac{3000 - 3500}{160}$

$Z = -3.13$

$Z = -3.13$ has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

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2 years ago

A store manager records the total visitors and sales, in dollars, for 10 days. The data is shown in the scatter plot. What concl

pickupchik [31]

Answer:An increase in visitors is correlated with an increase in sales.

Step-by-step explanation:

From the given scatter plot we can see that variables are positively correlated because they are moving in the same direction.

Since we know that the positive correlation is a relationship between two variables such that they increase or decrease together.

Since, the two variables given her is " number of visitors" and "Total sales"

Therefore, based on the given data it can be observed that "An increase in visitors is correlated with an increase in sales."

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2 years ago

Identify the rule of inference that is used to derive the conclusion "You do not eat tofu" from the statements "For all x, if x

Arturiano [62]

Answer:

1(b) ∀ (A(x) ⇒ B(x) )

2(b) ∀ (B(x) ⇒ C(x) )

3(b) ∀ (B(x) ⇒ E(x) )

Step-by-step explanation:

1) Tofu is healthy

2) Tofu is healthy to eat

3) Tofu eats what taste good

1a) For all x, if x is healthy to eat

2a) For all x, if x is not healthy to eat, then x does not taste good.

3a) For all x, if x is healthy to eat, then x is healthy to eat what tastes good

For all x in order to symbolize the statement

1(a) 2(a) 3(a)

If we use:

A(x): Tofu is healthy

B(x): Tofu is healthy to eat

C(x): Tofu eats what taste good

E(x): Tofu only eat what tastes good

If we symbolize "For all x" by the symbol ∀ then then the propositions 1(a), 2(a) and 3(a) can be written as:

1(b) ∀ (A(x) ⇒ B(x) )

2(b) ∀ (B(x) ⇒ C(x) )

3(b) ∀ (B(x) ⇒ E(x) )

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2 years ago

When a problem involves more than one unit for a characteristic ( such as length) how can you tell which unit use is more approp

Art [367]

In the absence of clues, it is a judgment call.

Often, the problem statement or answer choices will tell you the desired units.

In general, units are available so that you can express dimensions in 4 or fewer digits with appropriate units. There are a few gaps, but the reason units are what they are is to make expressing everyday values easy to do.

SI units are easy to work with on this score, as the various available prefixes ensure that you can always express a quantity using a number between 1 and 1000. This is generally what you want to do (in the absence of direction otherwise).

For some things, there are customary units that are expected. Vehicle speed is unusally miles (or kilometers) per hour, for example. Land area is usually square feet, acres, or square miles in US units, or square meters, hectares, or square kilometers in SI units.

Generally, too, it is appreciated by your reader if the units you choose are ones they are familiar with. In most applications, you'd choose feet or yards or miles instead of furlongs, for example (unless your audience is familiar with racetrack distances).

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2 years ago

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Sati [7]

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