Mr. Barth is creating an arrow across the school parking lot. The area covered by the arrow is calculated to be 70 square units. Step-by-step explanation: I've marked the points on a coordinate grid and connected them with a rough red line, which is shown in the attached image. The arrow's shape consists of a triangle and a rectangle. Therefore, the total area of the arrow equals the triangle's area plus the rectangle's area. The triangle's area is determined using the formula 0.5 * base * height, where the base measures 12 units while the height is 7 units, giving an area of 42. The rectangle's area is calculated as length * height, where length equals 7 and height equals 4, resulting in an area of 28. Hence, the total area of the arrow equals 42 + 28 = 70 square units.
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.
The x-axis is nearer to point B. Since the ratio PB:AB = 2/7 is positive, this indicates internal division of the line. We utilize the coordinate formula for a point dividing a line internally. Thus, x = (mx₂ + nx₁)/(m + n) and y = (my₂ + ny₁)/(m + n), where PB/AB = 2/7 translates to n/m, giving n = 2 and m = 7. With point A at (0,0) and point P at (10, -5), we substitute these coordinates to find x and y. The calculations yield coordinates for B at 7⁷/₉ and -3⁸/₉. Therefore, B is -3⁸/₉ units from the x-axis and 7⁷/₉ from the y-axis, confirming that the x-axis is closer to B.
Answer: The hourly charge for the rototiller is $3.
Step-by-step explanation:
Let h denote the hourly rate for the rototiller rental.
The rental provider imposed a base fee of $43 in addition to a charge per hour. Assuming the rototiller was rented for x hours, the cost incurred would total
43 + hx.
If they paid $64 for 7 hours of rental, the equation representing this situation would be
43 + 7h = 64.
Resolving gives us 7h = 64 - 43 = 21.
Therefore, h = 21/7 = $3.
It is not possible, as there are just 2 sides, and they likely flipped it in various ways. They experienced some 'luck'.
