Which graph matches the exponential function f(x) = (3)x?

A restaurant has fixed costs of $147.50 per day and an average unit cost of $5.75 for each meal served. If a typical meal costs

Nikolay [14]

Answer:

The answer is 118.

Step-by-step explanation:

First we need to subtract the meal cost from average unit cost for each meal:

$7-5.75=1.25$

A restaurant profits 1.25$ for each meal. If we divide fixed cost to profit for each meal:

$147.5/1.25=118$

The restaurant have to sell 118 meals at least each day for the owner to break even

5 0

3 years ago

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

$X=1$ number of citrus trees that are infected with the citrus red mite.

$n=5$ random sample taken

$\hat p=\frac{1}{5}=0.2$ estimated proportion of citrus trees that are infected with the citrus red mite.

$p$ true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56$

And rounded up we have that n=6147

5 0

3 years ago

A person invested $6,000, some at 7% and the rest at 5%. The income from the 7% investment is equal to the income from the 5% in

8090 [49]

Answer:

The person invested $3500 at 7% and $2500 at 5%

Step-by-step explanation:

We can say that $0,07x+0,05x=6000$ because the investment is equal both in one as in another, where x is the income from the investment.

Solving the equation we have:

$0,12x=6000\\x=50000$

Then to get the incomes:

At 7%: $I=0.07*50000\\I=$3500$

And at 5%: $I=0.05*50000\\I=$2500$

Finally we can demonstrate the answer because the income at 7% + income at 5% are 3500+2500=$6000

6 0

3 years ago

If it takes 5 men 20hours to brick a house, how long will it take 2 men to do the job if they work at the same rate?

Elden [556K]

To find the contribution of each man (this is a sexist problem as women could work as well, but that’s besides the point) take 5/2 and then multiply that value by 20 and you’ll find it takes 50 hours for two men to do it.

Answer: 50 hours

4 0

3 years ago

Read 2 more answers

if took john 12 hours riding his bike to make the round trip to his uncles if he averaged 20 mph out and 40 mph back how long di

slega [8]

I think 320 miles. i think

5 0

3 years ago