Part 1) The radius of the circle is r=17 units. Part 2) The points (-15,14) and (-15,-16) are situated on this circle. Step-by-step explanation: Step 1 Find the radius of the circle. We know that the distance from the center of the circle to any point on its circumference equals the radius of the circle. The formula to determine the distance between two points is equal to......we have (-7, -1) and (8, 7) substitute... Step 2 Determine the y-coordinate of point (-15,y). The standard form of the circle's equation is given by... where (h,k) represents the center, and r is the radius. Replace the values, substituting x=-15 in the equation... square root both sides... ultimately, we find two solutions: point (-15,14) and point (-15,-16) refer to the attached figure for a clearer understanding of the problem.
Respuesta:
P = 2/7 = 0.2857 o 28.57%
Explicación paso a paso:
En primer lugar, sabemos que hay 15 bolas y necesitamos identificar cuáles son pares y superiores a 10.
Por lo tanto, debemos calcular inicialmente la probabilidad de que el número obtenido sea par.
Los números pares son 2, 4, 6, 8, 10, 12, 14
Contamos 7 números de 15 ---> P(B) = 7/15
De esos números, solo dos son mayores a 10, que son 12 y 14, así que: P(A|B) = 2/15
Para encontrar la probabilidad de obtener un número par mayor que 10:
P(A/B) = P(A|B) / P(B)
P(A/B) = 2/15 / 7/15 = 2/7 = 0.2857
Para calcular el porcentaje: 0.2857 * 100 = 28.57%.
The diagrams for parts A and C are included here. For part B, we have circle O. We begin by drawing two radii OA and OC, connecting points A and C to create chord AC. The radius intersects chord AC at point B, bisecting AC into equal segments AB and BC. This gives us two triangles, ΔOBA and ΔOBC, where OA equals OC (since they're radii), OB equals OB (by the reflexive property), and AB is equal to BC (as stated in the question). By applying the SSS triangle congruence criterion, we conclude that ΔOBA is congruent to ΔOBC, allowing us to deduce that ∡OBA equals ∡OBC, both measuring 90°. Thus, OB is perpendicular to AC. Moving on to part D, we again work with circle O and draw the two radii OA and OC, joining points A and C to create chord AC. The radius intersects AC at point B, where AB is perpendicular to AC, meaning ∡B equals 90°. We then consider the right triangles ΔOBA and ΔOBC, and given OA equals OC (the radii), and OB equals OB (reflexive property), we conclude through the HL triangle congruence that ΔOBA is congruent to ΔOBC. Consequently, we find BA equal to BC, thus OB bisects AC.
Answer:
The P-value signifies that the likelihood of obtaining a linear correlation coefficient that is as extreme or more extreme is 3.5%, which is considered significant at α=0.05. Thus, we have sufficient evidence to assert that there exists a linear correlation between the weight of automobiles and their highway fuel consumption.
Step-by-step explanation:
The correlation coefficient demonstrates the relationship between the weights and highway fuel consumption values across seven distinct types of automobiles.
The P-value expresses the significance of this connection. If the p-value is beneath a significance level (e.g., 0.05), it indicates that the relationship is indeed significant.
