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Following are the number of grams of carbohydrates in a sample of 12-ounce espresso beverages offered at Starbucks. 6 , 9, 10, 2

marusya05 [52]

Answer:

x=6, 9, 10, 20, 22, 25, 27, 40 , 48, 59

i= 1, 2 , 3, 4, 5, 6, 7, 8, 9, 10

And as we can see here the position for x=40 is 8, so then we can calculate the percentile for 40 grams like this:

$p=\frac{8}{10} *100 = 80$

So the the vale of 40 gr correspond to the 80th percentile of the data since accumulates 80% of the values below.

Step-by-step explanation:

We can define a percentile as "a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it"

For this case we have the following data given:

6 , 9, 10, 20, 22, 25, 27, 40 , 48, 59

And we want to calculate the percentile for the value of 40 grams

Since the dataset is on increasing way there is no problem to calculate this percentile.

We see that we have a total of n =10 observations, and we can rank the position of each observation (i) like this:

x=6, 9, 10, 20, 22, 25, 27, 40 , 48, 59

i= 1, 2 , 3, 4, 5, 6, 7, 8, 9, 10

And as we can see here the position for x=40 is 8, so then we can calculate the percentile for 40 grams like this:

$p=\frac{8}{10} *100 = 80$

So the the vale of 40 gr correspond to the 80th percentile of the data since accumulates 80% of the values below.

3 0

3 years ago

If Florist B increases the cost per rose to $5.20,for what number of roses is it less expensive to order from Florist A? From Fl

Alenkinab [10]

Answer:

For 38 roses at $5.15 per rose, Florist A is Less Expensive then Florist B

For 34 roses at $5.20 per rose, Florist A is Less Expensive then Florist B

Step-by-step explanation:

The Full Question Reads:

Derek wants to order some roses online. Florist A charges $4.75 per blue rose plus $40 delivery charge. Florist B charges $5.15 per red rose plus $25 delivery charge. If Florist B increases the cost per rose to $5.20, for what number of roses is it less expensive to order from Florist A? From Florist B?

To begin we need to understand our given information and what we are actually looking for.

Given Information

Florist A:

charges $4.75 per blue rose

charges $40 per delivery

Florist B:

charges $5.15 per red rose

charges $25 per delivery

Note: in this problem we ignore the colour of the rose (red or blue) as it does not affect our solution or contributes to it. Therefore we shall call our first variable representing the number of roses as $x$ .

The next step is to construct a system of equations representing our problem and our given information. Here we are looking at linear relationships so a linear function of the form:

$y=ax+b$ Eqn(1).

will suffice where

$y$ : represents the total cost from the Florists (i.e. number of roses and delivery charges). Dependent Variable

$x$ : represents the number of roses purchased from the Florists. Independent Variable

$a$ : is our relationship factor between $y$ and $x$

$b$ : is our constant which in this problem is the delivery charge value for each florist.

Since we have two Florists, we will construct two equations, one for each florist, by employing Eqn(1). and our given information as follow:

Florist A: $y=4.75x+40$ Eqn(2).

Florist B: $y=5.15x+25$ Eqn(3).

By employing both equations above and writing them as an inequality since we are looking for which value of $x$ (i.e. number of roses) will the less expensive Florist be and then solving for $x$ we have:

$4.75x+40$

$4.75x-5.15x$ Gathering all similar terms together

$-0.4x$ Simplifying

$x>\frac{-15}{-0.4}\\$ Solving for x

$x>37.5$

(note how < changes to > since any multiplication/devision process of negative sign in an Inequality will change the order of < to > and vice versa).

Since a rose has to be sold as a whole and not half we will say that $x>38$ So we can then plug in the value of $x$ in Eqn(2) and Eqn(3) and find the cost of buying more than 38 roses from each:

Eqn(2): Florist A: $y(x>38)=4.75*38+40=220.5$

Eqn(3): Florist B: $y(x>38)=5.15*38+25=220.7$

Which tells us that Florist A is less expensive than Florist B by $0.20 for a purchase of more than 38 roses.

Next the question tells us that Florist B increases the cost from $5.15 to $5.20 per rose, which in Eqn(3) denotes our $a$ value and thus Eqn(3). now becomes:

Florist B: $y=5.20x+25$ Eqn(3).

Applying the same method like before and solving for the value of $x$ we have:

$4.75x+40$

$4.75x-5.20x$ Gathering all similar terms together

$-0.45x$ Simplifying

$x>\frac{-15}{-0.45}\\$ Solving for x

$x>33.3$

Similarly as a rose has to be sold as a whole and not half we will say that $x>34$ So we can then plug in the value of $x$ in Eqn(2) and Eqn(3) and find the cost of buying more than 34 roses from each:

Eqn(2): Florist A: $y(x>34)=4.75*34+40=201.5$

Eqn(3): Florist B: $y(x>34)=5.15*34+25=201.8$

Which tells us that Florist A is again less expensive than Florist B by $0.30 for a purchase of more than 34 roses. It was also shown that as the cost of the rose increased by $0.05 the number of roses for purchase decreased.

4 0

3 years ago

What is the equation of the line that passes through the points (3,8) and (6,2)?

vodka [1.7K]

Answer:

y = −2x+14

plot the points on a graph, and find the slope :)

8 0

3 years ago

The expression 21 - (2x + 3)2 + 4 (1 - 1) + z3 can be simplified into the form

mr Goodwill [35]

Answer:

A=z

B=-2

C=0

D=30

Step-by-step explanation:

First lets simply the equation

21 - (2x +3)2 + 4(1-1) + z^3

21 - (2x^2 + 9) + 4(0) + z ^3

21 - 2x^2 + 9 + z^3

- 2x^2 + z ^3 + 30

This means that:

A=z

B=-2

C=0

D=30

5 0

4 years ago

Help please and thank you

Akimi4 [234]

-6×-6=36
f-34=36
34+36=70
f=70

7 0

3 years ago