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2 years ago

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25 9 start fraction, 9, divided by, 25, end fraction of Polly's co-workers prefer tea over coffee. What percent of Polly's co-

workers prefer tea over coffee?

1 answer:

MrRa [10]2 years ago

8 0

Answer: $36\%$

Step-by-step explanation:

<h3> The complete exercise is: " $\frac{9}{25}$ of Polly's co-workers prefer tea over coffee. 25 What percent of Polly's co-workers prefer tea over coffee".</h3>

In order to solve this exercise, you need to follow the steps shown below:

<em>Step 1:</em> Divide the numerator 9 of the fraction by the denominator 25. Then:

$9\div25=0.36$

<em>Step 2: </em>To calculate the percent of Polly's co-workers that prefer tea over coffee, you must multiply the quotient obtained before (this is $0.36$ ) by 100.

Therefore, you get the following result:

$Percent=(0.36)(100)\\\\Percent=36\%$

Then, you can conclude that 36% of Polly's co-workers prefer tea over coffee.

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A cake has a mass of 2.5kg. It contains 275g of fruit. What percentage of fruit is there in the cake

Travka [436]

The answer is: "11 %" .
__________________________________
There is 11% of fruit in the cake.
______________________________
Explanation:
____________________________________

275g is what percent of 2.5 kg?

First, convert "275 g" into "kg".

Note the exact conversion: 1000 g = 1 kg .

So 275 g = (275/1000) kg = 0.275 kg .

0.275 kg = (n/100) * 2.5 kg ;

→ (n/100) * 2.5 = 0.275 ;
____________________________
Divide each side by "(2.5)"
______________________
→ (n/100) = (0.275) / (2.5) ;

→ (n/100) = 0.11 ;

Multiply each side by "100" ;

n = 11 .
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The answer is: 11 % .
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8 0

2 years ago

Read 2 more answers

There are some nickels dimes and quarters in a large piggy bank for every two nickels there are 3 dimes for every two dimes that

creativ13 [48]

We are given

piggy bank has nickels , dimes and quarters

Let's assume

number of nickels =n

every two nickels there are 3 dimes

so, number of dimes are

$=\frac{3}{2}n$

$=1.5n$

every two dimes that are 5 quarters there

so, number of quarters are

$=\frac{5}{2}\times 1.5n$

$=3.75n$

so, total number of coins = number of nickels + number of dimes +number of quarters

total number of coins =n+1.5n+3.75

there are 500 coins

so, we get

$n+1.5n+3.75n=500$

now, we can solve for n

$6.25n=500$

divide both sides by 6.25

so, we get

$n=80$

number of dimes is 1.5n

$=1.5\times 80$

$=120$

number of quarters is 3.75n

$=3.75\times 80$

$=300$

so,

Number of nickels =80

Number of dimes =120

Number of quarters =300............Answer

6 0

2 years ago

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

2 years ago

3. Standard deviation is ________. a mean of squared differences the square root of the variance unit-free the covariance 4. Sta

Ksenya-84 [330]

Answer:

3. Standard deviation is the square root of the variance.

4. Standard deviation is useful because it has the same units as the underlying data.

Step-by-step explanation:

3. In statistics, the dispersion in a given data with respect to its mean distribution can be determined or measured by standard deviation and variance. The standard deviation of a distribution can also be determined as the square root of variance.

4. Standard deviation is measured in the same units as that of the original data. Thus it has the same units as the underlying data.

5 0

2 years ago

A rectangular pool 18 meters by 12 meters is surrounded by a walkway of width x

vesna_86 [32]

Answer:

x=3 meters

Step-by-step explanation:

step 1

Find the area of the rectangular pool

$A=LW$

we have

$L=18\ m\\W=12\ m$

substitute

$A=18(12)=216\ m^2$

step 2

Find the area of rectangular pool including the area of the walkway

Let

x ----> the width of the walkway

we have

$L=(18+2x)\ m\\W=(12+2x)\ m$

substitute

$A=(18+2x)(12+2x)$

step 3

Find the area of the walkway

To find out the area of the walkway subtract the area of the pool from the area of rectangular pool including the area of the walkway

so

$A=(18+2x)(12+2x)-216$

step 4

Find the value of x if the area of the walkway equal the area of the pool

so

$(18+2x)(12+2x)-216=216$

Solve for x

$(18+2x)(12+2x)=432\\216+36x+24x+4x^{2}=432\\4x^{2} +60x-216=0$

Solve the quadratic equation by graphing

The solution is x=3 meters

see the attached figure

8 0

2 years ago