At a local concert, the cost for 3 adults and 2 children was $32.00. The cost for 8 adults and 5 children

Solve for c. 3 − 7c − 20c = 7(–7c − 19) + 14c c =

OleMash [197]

Answer:

$\boxed{c = -17}$

Step-by-step explanation:

$= > 3 - 7c - 20c = 7( - 7c - 19) + 14c \\ \\ = > 3 - 27c = ( - 7c \times 7) - (7 \times 19) + 14c \\ \\ = > 3 - 27c = - 49c - 133 + 14c \\ \\ = > 3 - 27c = - 35c - 133 \\ \\ = > 3 - 27c + 35c = - 133 \\ \\ = > 3 + 8c = - 133 \\ \\ = > 8c = - 133 - 3 \\ \\ = > 8c = - 136 \\ \\ = > c = - \frac{136}{8} \\ \\ = > c = - 17$

7 0

3 years ago

Read 2 more answers

You invest in a new play. The cost includes an overhead of $30,000, plus production costs of $2500 per performance. A sold-out p

Alchen [17]

Answer: 48 sold-out performances must be played in order for you to break even.

Step-by-step explanation:

Let x represent the number of sold-out performances must be played in order for you to break even.

You invest in a new play. The cost includes an overhead of $30,000, plus production costs of $2500 per performance. This means that the total cost of x sold out performances would be

2500x + 30000

A sold-out performance brings you $3125. This means that he total revenue from x sold out performances would be

3125x

To break even, cost = revenue

Therefore,

2500x + 30000 = 3125x

3125x - 2500x = 30000

625x = 30000

x = 30000/625

x = 48

8 0

3 years ago

The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o

timurjin [86]

Answer:

a) Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

b) $p_v =2*P(t_{(24)}$

c) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

The values obtained are:

$\bar X=85272$ represent the mean annual salary for the sample

$s=11039.23$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =90000$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean salary differs from 90000, the system of hypothesis would be:

Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(24)}$

Part c: Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

6 0

3 years ago

X +81=75 Hi hello bonjour hi

dedylja [7]

Answer:

x= -6

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Solve for a: g=ca Urgent help please

777dan777 [17]