Answer: No he does not meet both of his expectation by cooking 10 batches of spaghetti and 4 batches of lasagna.
Step-by-step explanation:
Since here S represents the number of batches of spaghetti and L represents the total number of lasagna.
And, the chef planed to use at least 4.5 kilograms of pasta and more than 6.3 liters of sauce to cook spaghetti and lasagna.
Which is shown by the below inequality,
----------(1)
And,
--------(2)
By putting S = 10 and L = 4 in the inequality (1),

⇒
(true)
Thus, for the values S = 10 and L = 4 the inequality (1) is followed.
Again By putting S = 10 and L = 4 in the inequality (2),

⇒
( false)
But, for the values S = 10 and L = 4 the inequality (2) is not followed.
Therefore, Antonius does not meet both of his expectations by cooking 10 batches of spaghetti and 4 batches of lasagna.
Answer:
1. $109.20 2. $46.80
Step-by-step explanation:
Doing the math, we find that 30% of 156 (138+18) is 46.80, which answers the second part of this problem. Plugging this value into the first part of the equation gives us what Stefan originally paid.
Good luck! Hope this helps!
Answer:
Type I error
Step-by-step explanation:
A type I error occurs if the null hypothesis is rejected when it is actually true.
Type I Type II
Reject null when true Fail to reject null when not true
Null hypothesis: ∪ = 30%
Alternative hypothesis: ∪ > 30%
The researchers concluded that more than 30% of first-grade students at this school have entered the concrete operational stage of development and they rejected the null hypothesis.
However, a census actually found that in the population of all first graders at this school, only 28% have entered the concrete operational stage.
A type I error has been made because in actuality the null hypothesis was true but was rejected.
Answer:
(-1.703, 2.396)
(1.37, 6.493)
Step-by-step explanation:
We can easily solve this question by using a plotting tool or any graphing calculator,
The solution to the system of equation is given by the intersection points between the graphs of
y1 = −x^2 + x + 7
y2 = x^2 + 3x + 7
Please, see attached picture below.
The solutions are:
(-1.703, 2.396)
(1.37, 6.493)