Tüm alıştırma soruları

A straight ramp connects a driveway to a loading dock that is $10$ feet above the ground. The ramp forms an angle $\theta$ with the flat ground such that $\tan(\theta) = \frac{5}{12}$. What is the length, in feet, of the ramp?

A solar power system generated a total of $450$ kilowatt-hours (kWh) of electricity during a 3-day period. On Day 1, the system generated $\frac{2}{9}$ of the total 3-day electricity. On Day 2, it generated $40\%$ of the remaining electricity after Day 1. How many kilowatt-hours of electricity were generated on Day 3?

A community library's summer program requires participants to create a 3-book reading list consisting of exactly $1$ biography, $1$ science fiction novel, and $1$ history book selected from a featured list. The featured list contains $5$ biographies (2 of which have over $400$ pages), $6$ science fiction novels (3 of which have over $400$ pages), and $4$ history books (1 of which has over $400$ pages). If a participant selects $1$ book of each genre at random from the featured list, what is the probability that at least $1$ of the selected books has over $400$ pages? Express your answer as a decimal.

A high school science club organized a daily recycling drive over a 10-day period. The frequency table below summarizes the number of aluminum cans collected per day:

What is the positive difference between the mean number of cans collected per day and the median number of cans collected per day?

A circle in the standard $(x, y)$ coordinate plane is represented by the equation $x^2 + y^2 + 4x - 6y - 12 = 0$. What is the distance between the two points where this circle intersects the $x$-axis?

A team of plant physiologists investigated the transpiration rate of four plant species (Species W, X, Y, and Z) under two distinct light conditions—Low Intensity ($150\text{ }\mu\text{mol/m}^2\text{/s}$) and High Intensity ($800\text{ }\mu\text{mol/m}^2\text{/s}$)—at a controlled temperature of $25^\circ\text{C}$. The measured rates are shown in the table below:

Based on the table, what was the average increase in transpiration rate (in $\text{mg H}_2\text{O/cm}^2\text{/hr}$) across all four plant species when light condition was increased from Low Intensity to High Intensity?

Experiment 1
Students conducted a gravimetric analysis to determine the phosphate concentration in a water sample by precipitating magnesium ammonium phosphate hexahydrate ($\text{MgNH}_4\text{PO}_4 \cdot 6\text{H}_2\text{O}$). The apparatus included a Büchner funnel, a heavy-walled filter flask attached to a vacuum aspirator line, filter paper, a wash bottle filled with ice-cold dilute ammonia solution, and an oven.

To ensure quantitative transfer, efficient impurity removal, and accurate final mass measurement of the precipitate without losing product, in what chronological order should the students perform the following steps of the filtration and drying procedure?

A technician is installing a straight support beam for a solar panel array mounted on a flat roof. The beam forms a right triangle with the horizontal roof and a vertical panel frame. The vertical frame is $24$ inches tall, and the angle $\theta$ between the support beam and the horizontal roof satisfies $\sin(\theta) = \frac{12}{13}$. What is the horizontal distance, in inches, along the roof from the bottom of the vertical frame to the anchor point of the support beam?

A soil scientist investigated the effect of varying soil copper ($\text{Cu}^{2+}$) concentrations on the rate of nitrate uptake in spinach roots. Five groups of ten plants each were grown in identical hydroponic solutions containing $\text{Cu}^{2+}$ concentrations of $0\text{ }\mu\text{M}$, $5\text{ }\mu\text{M}$, $10\text{ }\mu\text{M}$, $25\text{ }\mu\text{M}$, and $50\text{ }\mu\text{M}$, respectively. Throughout the 14-day experiment, all plant groups were maintained at $22^\circ\text{C}$ under a constant 16-hour light / 8-hour dark cycle. At the conclusion of the experiment, the researcher recorded the total nitrate concentration ($\mu\text{mol/g}$) remaining in the nutrient solutions.

In this investigation, which factor serves as the independent variable?

Astrophysicists measured the transit depth (percentage of starlight blocked) for four exoplanets orbiting a host star at two observation wavelengths ($0.5\ \mu\text{m}$ and $1.5\ \mu\text{m}$), as recorded in the table below:

True or False: The mean transit depth across all four exoplanets measured at $1.5\ \mu\text{m}$ is $0.4\%$ greater than the mean transit depth measured at $0.5\ \mu\text{m}$.

While studying historical climate patterns, dendrochronologists collected core samples from ancient bristlecone pines, they measured the ring widths with microscopes, and cross-dated the growth patterns against established regional master chronologies.

Which choice provides the correct punctuation and grammatical structure for the underlined portion?

A community theater group allocated a total budget of $\$1,500$ to create costumes for an upcoming production. Exactly $\frac{1}{4}$ of the budget was spent on fabric, $0.30$ of the budget was spent on specialized footwear, and $\frac{1}{5}$ of the budget was spent on sewing accessories. The remaining amount of the budget was spent on theatrical wigs. What amount, in dollars, did the theater group spend on theatrical wigs?

Read the passage below:

When volcanologist Dr. Helen Vance published her definitive report on Mount Searing's tephra stratigraphy in 2012, few realized how many years of groundwork had preceded the milestone. Her interest in the island crater was originally sparked back in 2004, when she unexpectedly detected anomalous glass shards while analyzing archived sediment cores in her university laboratory. To prepare for direct field sampling, Dr. Vance secured a specialized micro-X-ray fluorescence spectrometer in 2005. This crucial acquisition allowed her to launch her initial expedition to Mount Searing in 2006. It was not until her 2009 follow-up survey, however, that she collected the basaltic samples that ultimately validated her eruption timeline.

According to the passage, which of the following events occurred FIRST chronologically?

During nocturnal field observations in tropical rainforests, entomologists recorded firefly species that produced rhythmic bright flashes, and they transmitted these signals across the dense canopy. Which choice best completes the sentence according to the conventions of standard written English?

In right triangle $UVW$, the right angle is located at vertex $V$. The length of hypotenuse $UW$ is $85$ centimeters. If $\sin(U) = \frac{15}{17}$, what is the length, in centimeters, of leg $UV$?

A specialty coffee roasting facility packages a batch of $c$ pounds of dark roast coffee beans into retail bags. Each bag is filled with exactly $1.5$ pounds of coffee. If the facility completely fills $28$ bags with no coffee left over, which of the following equations can be used to find the total weight, $c$, in pounds, of the coffee batch?

A circle in the standard $(x, y)$ coordinate plane is described by the equation $x^2 + y^2 - 6x + 10y + 18 = 0$. A second circle is concentric with the first circle (meaning they share the exact same center) but has an area that is $4$ times the area of the first circle. Which of the following is an equation of the second circle?

A security code consists of four characters generated in order: a letter, a digit, a letter, and a digit.

- The 1st character is a letter chosen from the 5-element set $\{A, B, C, D, E\}$.
- The 2nd character is a digit chosen from the 9 non-zero digits $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$.
- The 3rd character is a letter chosen from $\{A, B, C, D, E\}$, but it cannot be the same as the 1st character.
- The 4th character is an even digit chosen from $\{2, 4, 6, 8\}$, but it cannot be the same as the 2nd character.

How many different security codes can be formed following these rules?

A biology student recorded the mass, in grams, of 6 plant specimens after three weeks of growth: $14$, $9$, $22$, $18$, $12$, and $15$. If a 7th plant specimen is added to the data set, what must its mass be, in grams, so that the mean mass of all 7 specimens equals the median mass of the original 6 specimens?

A commercial printing press produces $420$ color brochures every $15$ minutes. If the press operates continuously at this constant rate, how many hours will it take to produce a total of $5,040$ brochures?