Answer:
Step-by-step explanation:
Hello!
To determine whether boys excel in math classes compared to girls, two random samples were collected:
Sample 1
X₁: score achieved by a boy in calculus
n₁= 15
X[bar]₁= 82.3%
S₁= 5.6%
Sample 2
X₂: score obtained by a girl in calculus
n₂= 12
X[bar]₂= 81.2%
S₂= 6.7%
To estimate a confidence interval for the difference between the average percentages of boys and girls in calculus, it's essential that both variables come from normally distributed populations.
For utilizing a pooled variance t-test, it is also required that the population variances, though unknown, are assumed to be equal.
The confidence interval can then be calculated with:
[(X[bar]_1 - X[bar]₂) ±
*
]


[(82.3 - 81.2) ± 1.708 * (6.11 *
]
[-2.94; 5.14]
Using a 90% confidence level, the interval [-2.94; 5.14] is expected to encompass the true difference between the average percentages achieved by boys and girls in calculus.
I hope this is of assistance!
Answer:
The measure of arc GH is 80 degrees.
Step-by-step explanation:
Circles F and J are congruent.

Given that: m∠DFE = 80°
Angle DFE serves as the central angle of circle F.
Arc GH's measurement corresponds with the central angle from Circle J.
Since the two circles are congruent

The measure of arc GH, therefore, is 80 degrees.
Answer: El lado mayor del rectángulo mide 10cm
Step-by-step explanation:
El perímetro de un rectángulo está dado por:
P = 2*L + 2*A
Donde L es la longitud y A es el ancho.
Como sabemos que un lado es 6cm más largo que el otro, podemos expresar esto como:
L = A + 6cm.
Por lo tanto, P = 28cm = 2*L + 2*A
Sustituyendo la primera ecuación en la segunda tenemos:
28cm = 2*(A + 6cm) + 2*A
28cm = 12cm + 4*A
28cm - 12cm = 4*A
16cm/4 = A
4cm = A.
Así que el ancho es 4 cm y la longitud se calcula como L = 4cm + 6cm = 10cm
Answer:
$82.3
Step-by-step explanation:
82 multiplied by 25 equals 2050.
Adding 90 gives 2140.
Dividing 2140 by 26 results in 82.3.