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2 years ago

There are 30 businesses with 4 executives each for the new office building. Each business needs one office for each of its

Mathematics

1 answer:

Zanzabum2 years ago

8 0

Answer:

Step-by-step explanation:

B is the right one because the question says that every 4 executives can go into 1 office

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Michael earns $21 per hour and works 40 hours per week. How many overtime hours would he have to worky in a week for his time-an

Alex73 [517]

Answer:

27 hours

Step-by-step explanation:

The regular hours are paid normally, 21/hr hence working for 40 hours, Michael earns 40*21=$840

To work x hours paid overtime as 1.5 of the normal rate, the rate would be $21*1.5=$31.5/hr

X hours multiplied by rate of $31.5/hr should be at least equal to $840

31.5x>=840

X>=840/31.5>=26.6667 hours and when rounded off

X is 27 hours

6 0

2 years ago

Charlie bought a pair of shorts at the store when they were having a 45% off sale. If the regular price of the pair of shorts wa

spayn [35]

Answer:

$13.20

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

A given set of values is found to be a normal distribution with a mean of 140 and a standard deviation of 18.0. Find the value t

Alisiya [41]

Answer:

The value that is greater than 45% of the data values is approximately 137.84.

Step-by-step explanation:

The key is transforming values from this distribution to a z-score range and finding the corresponding value using a z-score table.

We are looking for a value x which attains a critical z-score that corresponds to the (100-45)%=55-th percentile:

$z_{0.55} = \frac{x-\mu}{\sigma}=\frac{x-140}{18}\implies x = 18\cdot z_{0.55}+140$

The critical z value (from z-score table, online) is: -0.12, so:

$x = 18\cdot z_{0.55}+140=18\cdot(-0.12)+140\approx137.84$

The value that is greater than 45% of the data values is approximately 137.84.

5 0

1 year ago

Read 2 more answers

Solve the recurrence relation: hn = 5hn−1 − 6hn−2 − 4hn−3 + 8hn−4 with initial values h0 = 0, h1 = 1, h2 = 1, and h3 = 2 using (

musickatia [10]

(a) Suppose $h_n=r^n$ is a solution for this recurrence, with $r\neq0$ . Then

$r^n=5r^{n-1}-6r^{n-2}-4r^{n-3}+8r^{n-4}$
$\implies1=\dfrac5r-\dfrac6{r^2}-\dfrac4{r^3}+\dfrac8{r^4}$
$\implies r^4-5r^3+6r^2+4r-8=0$
$\implies (r-2)^3(r+1)=0\implies r=2,r=-1$

So we expect a general solution of the form

$h_n=c_1(-1)^n+(c_2+c_3n+c_4n^2)2^n$

With $h_0=0,h_1=1,h_2=1,h_3=2$ , we get four equations in four unknowns:

$\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}$

So the particular solution to the recurrence is

$h_n=-\dfrac8{27}(-1)^n+\left(\dfrac8{27}+\dfrac{7n}{72}-\dfrac{n^2}{24}\right)2^n$

(b) Let $G(x)=\displaystyle\sum_{n\ge0}h_nx^n$ be the generating function for $h_n$ . Multiply both sides of the recurrence by $x^n$ and sum over all $n\ge4$ .

$\displaystyle\sum_{n\ge4}h_nx^n=5\sum_{n\ge4}h_{n-1}x^n-6\sum_{n\ge4}h_{n-2}x^n-4\sum_{n\ge4}h_{n-3}x^n+8\sum_{n\ge4}h_{n-4}x^n$
$\displaystyle\sum_{n\ge4}h_nx^n=5x\sum_{n\ge3}h_nx^n-6x^2\sum_{n\ge2}h_nx^n-4x^3\sum_{n\ge1}h_nx^n+8x^4\sum_{n\ge0}h_nx^n$
$G(x)-h_0-h_1x-h_2x^2-h_3x^3=5x(G(x)-h_0-h_1x-h_2x^2)-6x^2(G(x)-h_0-h_1x)-4x^3(G(x)-h_0)+8x^4G(x)$
$G(x)-x-x^2-2x^3=5x(G(x)-x-x^2)-6x^2(G(x)-x)-4x^3G(x)+8x^4G(x)$
$(1-5x+6x^2+4x^3-8x^4)G(x)=x-4x^2+3x^3$
$G(x)=\dfrac{x-4x^2+3x^3}{1-5x+6x^2+4x^3-8x^4}$
$G(x)=\dfrac{17}{108}\dfrac1{1-2x}+\dfrac29\dfrac1{(1-2x)^2}-\dfrac1{12}\dfrac1{(1-2x)^3}-\dfrac8{27}\dfrac1{1+x}$

From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of $x^n$ , ideally matching the solution found in part (a).

3 0

1 year ago

Which expressions are equivalent to 4^{-2} \cdot 7^{-2}4 −2 ⋅7 −2 4, start superscript, minus, 2, end superscript, dot, 7, start

PolarNik [594]

Answer:

Step-by-step explanation:

Given the expression 4^{-2}•7^{-2}. The following expression are equivalent to given expression on simplification.

Generally from indices, a^-b = 1/a^b. Applying this to the given expression we have:

4^{-2}•7^{-2} = 1/4^2 • 1/7^2

= 1/(4×4) • 1/(7×7)

= 1/16 • 1/49

= 1/(16×49)

= 1/784

4 0

1 year ago