A total of

A collection of coins contains a total of sixteen dimes and quarters. It is worth $2.20 in all. How many dimes are in the collec

grin007 [14]

9514 1404 393

Answer:

12 dimes

Step-by-step explanation:

Let q represent the number of quarters. Then the number of dimes is 16-q and the total value is ...

0.25q +0.10(16 -q) = 2.20

0.15q +1.60 = 2.20 . . . . . . . simplify

0.15q = 0.60 . . . . . . . . subtract 1.60

q = 4 . . . . . . . . . . . divide by 0.15

16-q = 12

There are 12 dimes in the collection.

5 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

3 years ago

Geraldine is an accrual basis taxpayer who has the following transactions during the current calendar tax year: Accrued business

Artyom0805 [142]

Answer:

Total: $69,500

Step-by-step explanation:

Income:

Other than rental: 220,000

Rental: 21,000

Expenses:

Other than rental: (170,000)

Rental (9,000/6): (1,500)

Total: $69,500

3 0

3 years ago

A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company Credit Union, bu

m_a_m_a [10]

Answer:

a) 0.4770

b) 3.9945

c) z-statistics seem a large value

Step-by-step explanation:

a. Find the standard deviation of the sample proportion based on the null hypothesis

Based on the null hypothesis:

$p_{0}$ : 0.35

and the standard deviation σ = $\sqrt{p_{0} *(1-p_{0}) }$ = $\sqrt{0.35 *0.65 }$ ≈0.4770

b. Find the z statistic

z-statistic is calculated as follows:

z= $\frac{X-p_{o} }{\frac{s}{\sqrt{N} } }$ where

X is the proportion of employees in the survey who take advantage of the Credit Union ( $\frac{138}{300}=0.46$ )
$p_{0}$ is the proportion in null hypothesis (0.35)
s is the standard deviation (0.4770)
N is the sample size (300)

putting the numbers in the formula:

z= $\frac{0.46-0.35} }{\frac{0.4770}{\sqrt{300} } }$ = 3.9945

c. Does the z statistic seem like a particularly large or small value?

z-statistics seem a large value, which will cause us to reject the null hypothesis.

4 0

3 years ago

(2x - 1) ft (x + 4) ft 7 ft

anygoal [31]

What is the question?

7 0

3 years ago