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4 years ago

Write in standard form

"2.96 \times 10 {}^{7} " alt="2.96 \times 10 {}^{7} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

atroni [7]4 years ago

4 0

$\bf 2.96\times 10^7\impliedby \textit{we move the dot 7 slots over to the right}
\\\\\\
2\underline{9600000}$

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FIND the product<br>(5a³-3a²+8)(3a-4)

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3 years ago

What is the equation of the line through (-6, -5) and (-4, -4)?

Norma-Jean [14]

Answer:

y = 1/2x -2

Step-by-step explanation:

The 2-point form of the equation for a line is useful for answering questions like this.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . equation of a line through (x1, y1) and (x2, y2)

Filling in the given points, the equation becomes ...

y = (-4 -(-5))/(-4 -(-6))/(x -(-6)) -5

y = 1/2(x +6) -5

y = 1/2x -2

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4 years ago

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

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4 years ago

32% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and a

Tems11 [23]

Answer:

a) $P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211$

b) $P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668$

c) $P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.32)$