The risk of down syndrome, in terms of the percentage of births per year, is changing at a rate given by the equation r(x) = 0.004641x² - 0.3012x + 4.9 for the range 20 ≤ x ≤ 45, where x signifies the maternal age at delivery. To derive the risk function as a percentage of births relative to maternal age x, we integrate r(x), leading to the function f(x) = 0.001547x³ - 0.1506x² + 4.9x + c. When x is 30, f evaluates to 0.14%. This means that 0.001547(30³) - 0.1506(30²) + 4.9(30) + c equals 0.14. Solving gives 41.769 - 135.54 + 147 + c = 0.14, which simplifies to c = -53.089. As a result, we establish that f(x) = 0.001547x³ - 0.1506x² + 4.9x - 53.089 for 20 ≤ x ≤ 45. The graph corresponding to this function is illustrated below.
The correct answer is option D. Detailed explanation: As per the attached image. Observing the image, the coordinates are outlined. To determine the reflection of a point across a line, the distances from the points to the line must be equal. Point A(1,1) sits on the line x = 1, meaning its reflection A' remains at A'(1,1). Point C(2,5) is a distance of 1 from x = 1 on the right, hence its reflected position C' shifts left by the same distance — subtracting 1 from its x-coordinate places it at C'(1 - 1, 5) or C'(0, 5). Point B(4,1) is positioned 3 from x = 1 on the right; therefore, its reflection B' would also move left by 3 – leading to B'(1 - 3, 1) or B'(-2, 1). Plotting A', B', and C' confirms option D as the correct choice.
No, Mike presented the ratio based on the change compared to the new amount. He ought to have utilized the ratio of the change against the original amount, which is represented as 55/275, or 20%.
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
The solution is C. Let’s start by identifying the equations without inequalities. Since there's a dotted line at y = 1, options A and B can be disregarded. Dotted lines indicate exclusivity, so they do not encompass the = sign. Therefore, the answer must be C.
