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Lelechka [254]
3 years ago
13

Which statement is the converse of the following statement? If planes are parallel, then they do not intersect.

Mathematics
2 answers:
Lilit [14]3 years ago
6 0
The <em>converse</em> of a statement is one in which<em> its hypothesis and conclusion are reversed. </em>A statement of the form p⇒q (p implies q) becomes the statement q⇒p (q implies p).

Here, if we let p be the statement "planes are parallel" and let q be the statement "they do not intersect," then q⇒p would be "If planes do not intersect, then they are parallel."
Brut [27]3 years ago
4 0
If two planes are not parallel, they will intersect (in a line).
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The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What ar
Degger [83]

Answer:

The minimum value of the bill that is greater than 95% of the bills is $37.87.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

\mu = 28, \sigma = 6

What are the minimum value of the bill that is greater than 95% of the bills?

This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

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

1.645 = \frac{X - 28}{6}

X - 28 = 6*1.645

X = 37.87

The minimum value of the bill that is greater than 95% of the bills is $37.87.

4 0
3 years ago
4x^2-5x-15=0 how to find the vertex and y intercept
mezya [45]
ax^2+bx+c=0\\\\the\ vertex:\left(\frac{-b}{2a};\frac{-(b^2-4ac)}{4a}\right)\\\\y-intrcept=c\\=======================================\\\\4x^2-5x-15=0\\\\a=4;\ b=-5;\ c=-15\\\\\frac{-b}{2a}=\frac{-(-5)}{2\cdot4}=\frac{5}{8};\ \frac{-(b^2-4ac)}{4a}=\frac{-[(-5)^2-4\cdot4\cdot(-15)]}{4\cdot4}=-\frac{265}{16}\\\\\boxed{the\ vertex:\left(\frac{5}{8};-\frac{265}{16}\right)}\\\\\boxed{y-intercept:-15}
5 0
4 years ago
4,12,20, 28 nth term
Anna007 [38]

Answer:

8n - 4

Step-by-step explanation:

The numbers here go up in 8, so you have 8n. Afterwards, use the term and the 8 times tables. Eg. 4 is the first term and the first 8 multiple is 8, so 4-8. You have to subtract 4 from 8 to get the first term. Sorry if this didn't help but yeah...

3 0
3 years ago
Multiply (2x^3 + 1)(5x^2 +4) and write your result in simplest form.
tatyana61 [14]
(2x^3)*(5x^2)+(2x^3)*(4)+(1)*(5x^2)+(1)*(4)
10x^5+8x^3+5x^2+4

8 0
3 years ago
Six​ stand-up comics,​ A, B,​ C, D,​ E, and​ F, are to perform on a single evening at a comedy club. The order of performance is
kiruha [24]

Answer:

a) 1/6

b) 1/36

c) 1/720

d) 1/3

Step-by-step explanation:

a) Any of the six comics can perform in the fourth place, so there is one chance in six that Comic F is the one that performs fourth.

P(F=4th)=1/6

b) In this case, we have two conditions. Both are independent of each other, so the probability of both happening is the product of the probabilities of each happening individually:

P(D=4th \&B=2nd)=P(D=4th)\cdot P(B=2nd)=(1/6)\cdot(1/6)=1/36

c) This combination is one in all possible orders of perform. The amount of combinations of orders is n!=6!=720 possible combinations. So the probability of this specific order is:

P(F, D, B, A, C, E)=1/720

d) In this case, of the six possible comics performing in the last place, we calculate the probability of 2 of them being in that place. So the probability is:

P(C=6th\,or\, E=6th)=2/6=1/3

8 0
4 years ago
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