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3 years ago

What multiples to 42 and adds to -2

Mathematics

1 answer:

solniwko [45]3 years ago

4 0

Answer:

Step-by-step explanation:

xy = 42

x+y = - 2 Substitute into the top equation

y = -2 - x Put in for y

x(-2 - x) = 42 Remove the brackets

-2x - x^2 = 42 Subtract 42 from both sides.

-2x - x^2 - 42 = 0 Put in the more normal order.

-x^2 - 2x - 42 = 0 Multiply by -1

x^2 + 2x + 42 = 0

This cannot be factored. It gives complex roots as it is written. I will give you the answer but I kind of doubt the question is correct.

x1 = - 1 + 6.40i

x2 = -1 - 6.40i

Leave a comment if you have a correction.

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Thickness measurement ancient prehistoric Native American Pot Shards discovered in Hopi Village are approximately normally distr

beks73 [17]

Answer:

a) $P(X$

And we can find this probability using the normal standard table and we got:

$P(z$

b) $P(X>7)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z>\frac{7-5.1}{0.9})=P(z>2.11)$

And we can find this probability using the complement rule and the normal standard table and we got:

$P(z>2.11)=1-P(Z$

Step-by-step explanation:

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".

Solution to the problem

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

$X \sim N(5.1,0.9)$

Where $\mu=5.1$ and $\sigma=0.9$

Part a

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table and we got:

$P(z$

Part b

We are interested on this probability

$P(X>7)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>7)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z>\frac{7-5.1}{0.9})=P(z>2.11)$

And we can find this probability using the complement rule and the normal standard table and we got:

$P(z>2.11)=1-P(Z$

4 0

3 years ago

Find an exponential function with a horizontal asymptote y equals=2 whose graph contains the points (0,3) and (1,6).

Andrew [12]

$\bf y=a(b)^x\qquad \qquad (\stackrel{x}{0}~,~\stackrel{y}{3})\implies 3=a(b)^0\implies 3=a
\\\\\\
therefore\qquad y=3(b)^x\\\\
-------------------------------\\\\
(\stackrel{x}{1}~,~\stackrel{y}{6})\implies 6=3(b)^1\implies \cfrac{6}{3}=b^1\implies 2=b
\\\\\\
therefore\qquad y=3(2)^x$

now, exponential functions have a horizontal asymptote at the x-axis, namely when y = 0, however, if you just move this one with a vertical translation of 2, then the horizontal asymptote will be at 2 instead. y = 3(2)ˣ + 2

6 0

3 years ago

Given the diameter of a circle is 17 1/2cm, find its area (use π = 22/7)

vladimir2022 [97]

Answer:

240.625 is full value. you can use sigfigs if you need.

Area is (pi)(r)^2 so (22/7)(8.75)^2

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2 years ago

mike observed that 75% of the students of a school liked skating. if 35 students of the school didn't like skating, the number o

bezimeni [28]

Cross multiply.

75 / x = 25 / 35
25x = 35(75)
25x = 2625
/25 /25
x = 105

Therefore 105 students liked skating.

Proof:

105 + 35 = 140.
140 * 0.75 = 105
140 * 0.25 = 35

140 (total) split into quarters.

35 + 35 + 35 + 35 = 140
35 + 35 + 35 = 105 (3 quarters liked)
35 = 35 (1 quarter disliked)

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3 years ago

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Airida [17]

Answer: a

Step-by-step explanation:

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2 years ago