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mrs_skeptik [129]
3 years ago
10

Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon. You need to purchase at least 9 gallons of drinks for a n

eighborhood picnic, but have at most $55 to spend. Model the scenario with a system of inequalities. Which of the following options represents a possible solution to the system of inequalities?

Mathematics
2 answers:
egoroff_w [7]3 years ago
7 0

Answer:

The system of inequalities is equal to

x+y\geq 9

4x+6y\leq 55

The graph in the attached figure

Step-by-step explanation:

Let

x------> the number of gallons of iced tea

y-----> the number of gallons of lemonade

we know that

x+y\geq 9 -----> inequality A

4x+6y\leq 55 -----> inequality B

using a graphing tool

the solution is the shaded area

see the graph in the attached figure

USPshnik [31]3 years ago
7 0

The answer is 10,1

The explanation is below. The graph is correct and the point 10,1 is in the shaded area that is covered by both equations.

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There are 45 male teachers and 75 female teachersin a school. Find the percentage of male teachers, female teachers in the schoo
Zielflug [23.3K]

Answer:

37.5% are male

62.5% are female

Step-by-step explanation:

in total 120 teachers (45 male+75 female)

therefore:

for male

120 - 100%

45 - x%  (we need to find x)

by using the butterfly method (or cross multiply) we get:

120x=100*45

x=4500/120=37.5% (male teachers)

we do the same for female but instead of using 45 we will use 75(the quantity of female theachers in school)

120x=100*75

x=7500/120=62.5%

5 0
3 years ago
Consider the following hypothesis test:H0: 20Ha: < 20A sample of 60 provided a sample mean of 19.6. The population standard d
elixir [45]

Answer:

a: z = -1.936

b: 0.0265

d: z < -1.645

Reject H0 if z < -1.645

Step-by-step explanation:

We are given:

H0:  µ = 20

HA:  µ < 20

n = 60, sample mean: 19.6, σ = 1.6

Since the alternate hypothesis has a < sign in it, it is a left tailed test.  The < or > sign in the alternate hypothesis points towards the rejection region.

For a:  We need to calculate the test statistic for our situation.  This is done with a z-score formula for samples.  

For b:  we need to use the z-score table to look up the p-value for the score we calculate in part a.  The p-value is 0.0265.  This means that there is only about a 2.65% chance that the sample values were a result of random chance.

For d:  Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645.  This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis

See attached photo for all the calculations!

4 0
3 years ago
The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking.assume
Assoli18 [71]

Answer:  d=18t

Step-by-step explanation:

By definition, Direct proportion equations have the following form:

y=kx

Where "k" is the constant of proportionality.

In this case you know that the distance (in meters) that an ant can travel varies directly with the amount of time (in hours) the ant spends walking.

With this information you can write the following equation:

d=kt

According to the exercise, the constant of proportionality is:

k=18

Therefore, substituting the value of the constant of proportionality into the equation, you get that  the equation that represents the proportional relationship between "d" and "t" is:

d=18t

4 0
3 years ago
Mary’s mother invested in an internet stock the price went up and down over the next few months: +32, -10 +13 -25 at the end of
babunello [35]

Answer:

higher

Step-by-step explanation:

add all of these numbers, if the sum is positive it is higher, if the sum is negative it is lower

32-10+13-25=10, this is positive so it is higher

8 0
3 years ago
Find the area of the shape, show work pls ill give brainiest
andre [41]

Answer:

6.2

Step-by-step explanation:

Although there's multiple ways to solve this problem, my method will be to simply find the area for the full triangle (the empty + orange triangles) and subtract the area of the smaller, empty triangle.

Now, you that area for a triangle is 1/2*base*height.

To find the measurements for the full triangle, you must add up the bases for the two smaller triangles:

Base_{total}  = Base_{empty} + Base_{orange}  \\Base_{total} = 1.9ft + 3.1 ft\\Base_{total} = 5 ft

Height is the same for both triangles so Height total = 4 ft.

Now the total area can be calculated:

Area total= 1/2* base_total * height_total

Area total = 1/2 * 5ft * 4 ft  

Area total = 20 / 2 = 10 ft squared

Lastly, subtract the area of the empty triangle from the total triangle to find the orange triangle.

Area Empty Triangle = 1/2 * base_empty * height_empty

Area Empty Triangle = 1/2 * 1.9ft * 4 ft = 7.6 ft / 2 = 3.8 ft squared

Area total - Area empty = 10ft^2 - 3.8ft^2 = 6.2 ft squared

8 0
3 years ago
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