The year 1915 marks a population of 15,689. In 1940, it increased to 39,381. The required time to reach this figure is t = 137.9 years. Step-by-step explanation: To answer, we apply an exponential growth formula: A = P (1 + r) t, where P is the original number of individuals, r is the growth rate in decimal, and t is the time in years. Plugging in provided values: A = 6,250 (1 + 0.0375)^t. For the year 1915, as 1915-1890 translates to 25 years: A = 6,250 (1.0375)^25 yields 15,689. For 1940, as 1940-1890 indicates 50 years passed: A = 6,250 (1.0375)^50 results in 39,381. To find when the population hits 1,000,000, substitute A=1,000,000 and solve for t. This leads to 1,000,000/6,250 = (1.0375)^t implying log(160) = t * log(1.0375) results in t being approximately 137.9 years.
The accurate selections are: 1. For both families, the graph representing the connection between the number of pizzas (x) and the amount of slices (y) intersects at the origin (0, 0) and forms a straight line. 2. If the Wilson family orders 3 large pizzas from the same pizza shop as the Hernandez family, they will have a greater number of slices than the Hernandez family once the pizzas are sliced. The equations for the relationships between total slices (y) and pizzas ordered (x) are as follows: y = a × x, where 'a' indicates slices per pizza. For the Hernandez family, we have y = 24 when x = 3, resulting in a = 24/3 = 8 slices per pizza, producing the equation y = 8 × x. For the Wilson family, the relationship is represented by y = 10 × x. When both families’ equations are plotted, the result is straight-line graphs with a y-intercept of 0, meaning they pass through (0, 0). Thus, if the Wilsons order 3 large pizzas, they will have y = 10 × 3 = 30 slices, exceeding the Hernandez family's 24 slices.
Answer:
The length AB equals length TU.
Step-by-step explanation:
Procedure: Replicate angle <QPR so that;
<QPR matches <TSU
Set the compass so that each leg touches points A and B to replicate the distance AB.
Next, position the compass at T to draw an arc that marks point U. Draw a straight line from S to U.
Consequently,
<QPR is congruent to <TSU
This method guarantees that angles are congruent by maintaining the same radius, thus AB = TU.
Answer:
Step-by-step explanation:
The initial scenario is a specific case of the subsequent one, so we will address the second case first.
Consider 
. Through the utilization of derivatives and trigonometric function properties, it is determined that
The equation is represented as 
. It's important to note that since 
it leads to the equation
,
which signifies that 
. Consequently, 
It's notable that in this instance, the value of k is independent of A and B. Thus, it applies universally to any values of A and B. The first scenario is included since it corresponds to A=0 and B=1.
