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3 years ago

8

Mrs. chin paid a 20 percent tip on the bill for lunch.if the tip amount was $2.75, what was the bill for lunch before the tip wa

s added to it?

2 answers:

bija089 [108]3 years ago

8 0

The original bill for the lunch was $13.75

nexus9112 [7]3 years ago

7 0

Answer:

the bill before for the lunch before the tip was $13.75

Step-by-step explanation:

Let bill before for the lunch before the tip was $x.

Now, it has been given that Mrs. chin paid a 20 percent tip on the bill for lunch.

Hence, the equation for the situation is

$0.20x=2.75$

Now, solve the equation for x

Divide both sides by 0.20

$x=\frac{2.75}{0.20}\\\\x=13.75$

Hence, the bill before for the lunch before the tip was $13.75

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A farmer has 240 acres to plant. He needs to decide how many acres of corn to plant and how many of oats. He can make $40 per ac

Gala2k [10]

Answer:

The acres of each the farmer must plant to obtain the maximum profit is:

<u>160 acres of oat.</u>
<u>80 acres of corn.</u>

Step-by-step explanation:

First, we're gonna take the data of the exercise:

Area: 240 acres.
Profit of the corn: $40/acre
Profit of the oat: $30/acre
Time spent by corn: 2 hour per acre.
Time spent by oat: 1 hour per acre.
Total working time available: 320 hours.

Now, we're gonna suppose that all the area could be planted with corn (the most profitable), in this form, we obtain the highest profit to take this how reference:

Total profit with corn = area * profit of the corn
Total profit with corn = 240 acres * $40/acre
Total profit with corn = $9600

How you can see, $9600 is the highest profit that the farmer can obtain, but, as each acre of corn needs 2 hours, the farmer would need 480 hours of labor to plant all the area with corn, with the 320 hours availables, the farmer just could plant 160 acres of corn, therefore, the real profit would be:

Total profit with corn = 160 * $40
Total profit with corn = $6400

Now, we're gonna make the same exercise but with the oats, to obtain the total profit with this:

Total profit with oat = area * profit of the oat
Total profit with oat = 240 acres * $30/acre
Total profit with oat = $7200

Taking into account the hours of labor availables, <em>the oat gives $800 more profit than the corn, but in that case we'd lose 80 hours of labor that could be used to make a better profit</em>, but, as the oat per hour of labor is more profitable, we're gonna use 2/3 of the area to plant oat and 1/3 to plant corn:

Area used for oat = 240 acres * 2/3
<u>Area used for oat = 160 acres</u>
Area used for corn = 240 acres * 1/3
<u>Area used for corn = 80 acres</u>

How you can see, with 160 acres of oat, the farmer would need 160 hours of labor and, with 80 acres of corn, the farmer would need 160 hours of labor too, by this, we know all the available time will be used, now, we're gonna calculate the profit in each case:

Real profit with oat = used area * profit of the oat
Real profit with oat = 160 acres * $30/acre
<u>Real profit with oat = $4800</u>
Real profit with corn = 80 acres * $40/acre
<u>Real profit with corn = $3200</u>

The total profit to the farmer with this plan is:

Total profit = Corn profit + Oat profit
Total profit = $3200 + $4800
<u>Total profit = $8000</u>

<u>The profit with the given plan is $8000</u>, that is better than the profit only with oat or corn separately and, this is the maximum profit the farmer can make.

7 0

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Ronch [10]

Answer:

P(0, 1)

Step-by-step explanation:

Using the section formula

$x_{P}$ = $\frac{(3(-2))+(2(3))}{2+3}$ = $\frac{-6+6}{5}$ = 0

$y_{P}$ = $\frac{(3(5))+(2(-5))}{2+3}$ = $\frac{15-10}{5}$ = 1

Hence P(0, 1)

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3 years ago

Find the Lateral Surface Area of the triangular prism. Question 5 options: 420 cm2 462 cm2 581 cm2 503 cm

tamaranim1 [39]

Answer:

1400 cm²

Step-by-step explanation:

10 x 10 x 14

100 x 14

1400 cm²

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3 years ago

At a baseball game, 89% of people attending were supporting the home team, while 11% were supporting the visiting team. If 2314

pickupchik [31]

Answer:

2600

Step-by-step explanation:

2314 ÷ 89% = 2600

2314 is 89% of 2600.

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3 years ago

A random sample of 180 microbiology students were asked how many science classes he or she was enrolled in August 1990. The resu

frutty [35]

Answer:

$z=\frac{1.83-1.94}{\sqrt{\frac{1.48^2}{180}+\frac{1.62^2}{180}}}}=-0.673$

$p_v =2*P(z$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the two means

Step-by-step explanation:

Data given and notation

$\bar X_{1}=1.83$ represent the mean in 1990

$\bar X_{2}=1.94$ represent the mean for 2005

$s_{1}=1.48$ represent the sample deviation for 1990

$s_{2}=1.62$ represent the sample standard deviation for 2005

$n_{1}=180$ sample size for 1990

$n_{2}=180$ sample size for 2005

t would represent the statistic (variable of interest)

$\alpha=0.05$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{1}=\mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$z=\frac{1.83-1.94}{\sqrt{\frac{1.48^2}{180}+\frac{1.62^2}{180}}}}=-0.673$

What is the p-value for this hypothesis test?

Since is a bilateral test the p value would be:

$p_v =2*P(z$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the two means

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4 years ago