Response: Annabelle is employing the statistical concept known as Mode.
Detailed explanation: A central tendency measure, in its most basic sense, is a singular value or measure that effectively represents all elements of a particular data set. As such, one number can serve to essentially represent 99 other numbers in a data set of one hundred figures.
Commonly acknowledged measures of central tendency include mean, median, and mode.
The mode denotes the value that appears most often in a data set. Therefore, the modal value is statistically suitable as a representative of the entire group of values or data points.
If Annabelle measures the sides of 15 right triangles and concludes that the sum of the squares of the two legs is equal to the square of the hypotenuse for any right triangle, she is identifying the most frequently occurring value, and in her analysis, the most common data observed aligns with the Pythagorean Theorem.
This is why Annabelle's assumption is made with confidence.
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
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
The P-value to evaluate the claim that the mean length of pencils produced in this factory equals 18.0 cm is 0.00736. Step-by-step explanation: In this case, a quality control specialist extracted a random sample of 45 pencils from the assembly line, which exhibited a mean length of 17.9 cm. With a known population standard deviation of 0.25 cm, we denote by the population mean length for pencils produced in the factory. Thus, Null Hypothesis: = 18.0 cm (indicating that the population mean length equals 18.0 cm). Alternate Hypothesis: ≠ 18.0 cm (suggesting different from 18.0 cm). We apply the one-sample z-test since the population standard deviation is known. The test statistic yields: T.S. ~ N(0,1), with the sample mean length 17.9 cm and population standard deviation 0.25 cm for a sample size of 45. Hence, the calculated test statistic is -2.68. The corresponding P-value is derived from P(Z < -2.68) = 1 - P(Z > 2.68), equating to 1- 0.99632 = 0.00368. For a two-tailed test, the resulting P-value computes to 2 * 0.00368 = 0.00736.
