At the movies, a couple bought 2 medium drinks and a large popcorn for $13.85. At the same theater, a family bought 3 medium dri
2 answers:
Answer:
A medium drink costs $3.8
A large popcorn is priced at $6.25
Step-by-step explanation:
Let’s denote the medium drink's price as m and the large popcorn's price as p. The equations can be represented as follows:
--- (1)
--- (2)
Now, we need to determine the prices of both items.
Using equation (1), we can find .
We then replace this value of in equation (2):
Next, using this new value of , we can solve for
:
p=
. Consequently, the price of a medium drink is $3.8 and a large popcorn is $6.25.
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Answer:
a) In this case, we have a z-score of 1.57, characterized as:
This signifies that our score is 1.57 standard deviations above the average of all test scores.
b)
Using the normal standard distribution or Excel, we computed:
This represents 2.275% of the dataset.
Step-by-step explanation:
Previous concepts
Normal distribution denotes a "probability distribution that is symmetric around the mean, indicating that data close to the mean occurs more frequently than data further from it".
The Z-score serves as "a statistical measurement representing a value's relation to the average (mean) of a set, calculated in terms of standard deviations away from the mean".
Solution to the problem
Part a
For this instance, we hold a z-score of 1.57, which is defined as:
This shows that our score is 1.57 deviations above the overall test score average.
Part b
A z-score of z=-2 indicates that your friend's score is 2 deviations below the other test scores.
Assuming a normal distribution, we can derive the percentage:
Using the normal standard distribution or Excel, we discovered:
This represents 2.275% of the data.
Answer:
The variable x lies within the interval of all positive real numbers less than 5 cm.
Detailed solution:
Problem statement:
Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.
Refer to the provided diagram for clarity.
Define:
x → length in centimeters of each square cutout side
The volume of the box with open top can be written as:
Given this, we have:
By substitution:
Determine the domain of x:
Because:
Therefore:
Domain is the interval (0,5)
That means all real numbers strictly greater than zero and less than 5 cm are valid for x.
Hence, the volume V as a function of x is:
Answer:
∠ R 90°
Explicación paso a paso:
Dado que en el triángulo RST
Ahora, según la condición, un ángulo es mayor que la suma de los otros dos ángulos.
En un triángulo, la suma de los tres ángulos es 180°
Por lo tanto, si un ángulo mide 90°, la suma de los otros dos debe ser igual a 90°
Y si uno de los ángulos es de 90°, solo los otros dos pueden ser de 45° cada uno.
Aquí suponiendo que el ángulo s = ángulo T = 30°, entonces con esta condición el ángulo r sería de 120°, que es mayor que 90°.
De lo anterior, se concluye que
Para,
∵ ∠ R = 120°, por lo tanto es mayor que 90°.
Es decir, ∠ R 90°
Respuesta