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3 years ago

Please help me with these, find the missing side. Thank yu only if you know

Mathematics

1 answer:

abruzzese [7]3 years ago

8 0

Answer:

7.48m (3s.f.)

Step-by-step explanation:

Let the missing side be x m.

Applying Pythagoras' Theorem,

x² +5²= 9²

x² +25= 81

x²= 81 -25 (-25 on both sides)

x²= 56

$x = \sqrt{56}$

$x = 2 \sqrt{14}$

x= 7.48 (3 s.f.)

∴ The missing side is 7.48 m (3s.f.)

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When converting a fraction to a decimal, the numerator is the A dividend. B quotient. divisor. product.

Andrei [34K]

Answer:

Dividend

Step-by-step explanation:

When converting a fraction to a decimal, the numerator is the dividend.

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3 years ago

The sum of seven and the quotient of a number xxx and eight.

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Answer:

7 + $\frac{x}{8}$

Since 7 + x/8 is true since it's adding each other only after they divided.

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4 years ago

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Consider Statement A and Statement B below:

wlad13 [49]

Answer:

These two statements are equivalent because statement A is the contrapositive of statement B.

Step-by-step explanation:

In logic, when we have an "if" statement we can have its contrapositive or its converse.

Given a "if p, then q" (p is the hypothesis and q is the conclusion), the converse is "if q, then p", in other words, we interchange the hypothesis and the conclusion.

Now, given a "if p, then q", the contrapositive is "if not q, then not p". In other words, we take the negation of both the hypothesis and the conclusion and then we interchange them.

Now, let's take a look at our statements:

If a and b are two real numbers, and if ab = 0, then either a = 0 or b = 0.

In this case:

p = a and b are two real numbers and ab=0

q = either a = 0 or b = 0

Now, let's take the negative of p and q:

The negative of p would be: a and b are two real numbers and their product is not zero.

The negative of q would be: neither of the two real numbers is zero

Now, given than the contrapositive is "if not q, then not p" we would have:

If neither of two real numbers is zero, then their product is not zero.

We can see that this last sentence is the contrapositive of the first one and thus:

These two statements are equivalent because statement A is the contrapositive of statement B.

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3 years ago

The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. a. Find the pro

MrMuchimi

Answer:

a. 0.313% (0.003134842261), b. 237.79 days (237.788095878)

Step-by-step explanation:

In this case, the length of pregnancies is a normally distributed variable, with a mean of 266 days, and a standard deviation of 15 days.

A graph showing the distribution, with regions of interest for the answer, is presented below.

<h3>First Part: Find the probability of a pregnancy lasting 307 days or longer.</h3>

To answer the question regarding the probability of a pregnancy lasting 307 days or longer, it is necessary to calculate what the cumulative probability distribution value is at 307 days. By the way, according to the graph below, 307 days are quite far from the population mean (266 days).

Using the function normaldist(266,15).cdf(307), from free Desmos software on Internet, we find that, at this length (307 days), the sum of all probabilities for all cases at this value is 99.69% (0.996865157739).

Considering that the total area of the curve is 1, then the probability of pregnancy lasting 307 days or longer is 1 - 0.996865157739 or 0.003134842261 (or 0.00313), approximately 0.313%, a very low probabilty.

This probability is showed as the "light blue" region at the right extreme of the graph.

<h3>Second Part: Find the length that separates premature babies from those who are not premature.</h3>

To find the length that separates premature babies from those who are not premature, it is a question about find the days related with the probability of 3% (or 0.03) to find such premature babies. So, it is a question of finding a percentile (or 100-quantiles): given the cumulative normal distribution curve, what is the value (length of pregnancies) that represents this 3%.

Using the function quantile(normaldist(266,15), 0.03), from free Desmos software on Internet, we obtained a value of 237.79 days (237.788095878) for the length of pregnacies of premature babies. In other words, those babies whose mothers have a length of pregnancy lower than 237.79 days are considered premature, or this is "the length that separates premature babies from those who are not premature".

The area below 237.79 days is the blue shaded region in the graph below, at the left extreme of it.

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The remainder will be;
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4 years ago