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scoundrel [369]

2 years ago

14

A tax preparation firm is interested in comparing the quality of work at two of its regional offices. the observed frequencies s

howing the number of sampled returns with errors and the number of sampled returns that were correct are as follows.
regional office
return office 1 office 2
error 35 28
correct 217 274

1 answer:

Veronika [31]2 years ago

7 0

The sample proportion of returns with errors at the two tax offices will be 0.1389 and 0.0927 respectively.

<h3>How to calculate the sample proportion?</h3>

From the information, the the observed frequencies showing the number of sampled returns with errors and the number of sampled returns were given.

The sample proportion will be:

P1 = 35/(35 + 217)

= 35/252

= 0.1389

P2 = 28/(28 + 274)

= 28/302

= 0.0927

Learn more about sample proportion on:

brainly.com/question/24232216

#SPJ1

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286 children enter the brass band competition.There are 27 teachers who accompany them and 19 parents.How many people visit the

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Answer:

332

Step-by-step explanation:

286+27+19

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A road 4 inches long on a map is 80 miles long in real life. A river is 2 ½ inches long on the map and is 50 miles long in real

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Not Proportional. Sorry if it’s wrong

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3 years ago

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

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Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ <em>(Approximated)</em>

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago

At the city museum, child admission is $6.10 and adult admission is $9.90. On Friday, 142 tickets were sold for a total sales of

antoniya [11.8K]

Answer:

no of child tickets sold were 58

Step-by-step explanation:

Let the number of child ticket sold be x

cost of 1 child ticket = $6.10

Total cost of x child ticket = x*cost of 1 child ticket = = $6.10x

Let the number of adult ticket sold be y

cost of 1 adult ticket = $9.90

Total cost of y adult ticket = y*cost of 1 adult ticket = = $9.90y

Given total ticket sold = 142

Thus,

number of child ticket sold + number of adult ticket sold = 142

x + y = 142 - equation 1

x = 142 -y

Total sales of ticket = $1185.40

total sales of ticket = Total cost of x child ticket + Total cost of x a dult ticket

6.10x + 9.90y = 1185.40

in this equation substituting x = 142 - y from equation 1

6.10(142 - y ) + 9.90y = 1185.40

=>866.2 - 6.10y + 9.90y = 1185.40

=> 3.80y = 1185.40 - 866.2

=> 3.80y = 319.2

=> y = 319.2/3.80 = 84

Thus, y = 84

x = 142 - y = 142 - 84 = 58

Thus, no of child tickets sold were 58

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3 years ago

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