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2 years ago

Which expression correctly represents “nine less than the quotient of a number and four, increased by three

Mathematics

1 answer:

Natasha2012 [34]2 years ago

3 0

The required expression is $\frac{x}{4}-9+3$

Step-by-step explanation:

We need to identify the expression correctly represents “nine less than the quotient of a number and four, increased by three"

Solving:

Let the number is x

The quotient of number and four: $\frac{x}{4}$

nine less than the quotient of a number and four: $\frac{x}{4}-9$

Increased by 3 : $\frac{x}{4}-9+3$

So, nine less than the quotient of a number and four, increased by three is:

$\frac{x}{4}-9+3$

So, The required expression is $\frac{x}{4}-9+3$

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The number of calls coming per minute into a hotel reservation center is Poisson random variable with mean 3.

natima [27]

Answer:

a) 0.05

b) 0.9826

c) 0.000039308

Step-by-step explanation:

a) $P_X(0) = \frac{e^{-3}3^0}{0!} = e^{-3} = 0.05$

b) For two minutes, the mean is doubled, hence it is 6. In order to calculate the probability of al least two calls arriving, we calculate first the probability of the complementary event: At most 1 call will arrive. For that probability, we need to sum the probabilities of 0 and 1.

$P_X(0) = e^{-6}$

$P_X(1) = \frac{e^{-6}*6^1}{1!} = 6*e^{-6}$

Hence,

$P(X \geq 2) = 1-P(X < 2) = 1- 7*e^{-6} = 0.9826$

c) For five minutes the mean is 15. We need to sum the probabilities of 0, 1 and 2.

$P_X(0) = e^{-15}$

$P_X(1) = e^{15}*15$

$P_X(2) = \frac{e^{-15}*15^2}{2!} = 112.5*e^{-15}$

As a result,

$P(X \leq 2) = e^{-15}(1+15+112.5) = 0.000039308$

Practically 0

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2 years ago

The graph shows the solution to the initial value problem y'(t)=mt, y(t0)= -4

Charra [1.4K]

$y'(t)=mt
\\
\\ y=\int {mt} \, dt=m \int{t} \,dt=m \frac{t^2}{2} +C \\ \\y= \frac{mt^2}{2}+C$

Now find equation of the graph. It passes through the point (2,3), and intersects y-axis at -2.

$y=at^2+b
\\
\\3=a\times 2^2-2
\\
\\3=4a-2
\\
\\5=4a
\\
\\a= \frac{5}{4} 
\\
\\y=\frac{5}{4} t^2-2 \\ \\y= \frac{m}{2} t^2+C
\\ \\ \frac{m}{2} = \frac{5}{4} 
\\
\\m= \frac{5}{2} 
\\
\\C=-2
\\
\\y(t_0)=-4
\\
\\-4= \frac{5}{4} t_0^2-2
\\
\\ -2= \frac{5}{4} t_0^2
\\
\\ t_0^2=- \frac{8}{5} 
\\
\\t_0=\pm \sqrt{- \frac{8}{5} }$

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2 years ago

A poll stated that 32% of those polled think the economy is getting worse. An economist wanted to check this claim so she survey

zysi [14]

Answer:

$z=\frac{0.30 -0.32}{\sqrt{\frac{0.32(1-0.32)}{750}}}=-1.174$

The p value for this case would be given by:

$p_v =2*P(z$

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %

Step-by-step explanation:

Information given

n=750 represent the random sample taken

$\hat p=0.30$ estimated proportion of people who thought the economy is getting worse

$p_o=0.32$ is the value that we want to verify

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to check if the true proportion of interest is equal to 0.32 or not.:

Null hypothesis: $p=0.32$

Alternative hypothesis: $p \neq 0.32$

The statistic would be given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.30 -0.32}{\sqrt{\frac{0.32(1-0.32)}{750}}}=-1.174$

The p value for this case would be given by:

$p_v =2*P(z$

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2 years ago

If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –5 – 6i 5 – 6i 6 – 5i 6

san4es73 [151]

Answer: 5-6i

The rule is that if f(x) has real number coefficients, then a root of x = a+bi pairs up with its conjugate pair of x = a - bi. In this case, a = 5 and b = 6.

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2 years ago

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Marina CMI [18]

Answer:

The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

= -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

= -31.72x^2 + 2,030x+126.96x - 26,391

Combine like terms

= -31.72 x^2 + 2156.96 x - 26391

This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391

-36668.32+73336.64-26391

10277.32

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2 years ago

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