GACE science/math 088

A certain high school class consists of juniors and seniors. There are 23 students in the class, and the number of seniors is 7 less than twice the number of juniors. How many seniors are in the class?

13 Option (B) is correct. To solve the problem, let j be the number of juniors in the class. Since the number of seniors is 7 less than twice the number of juniors, the number of seniors can be represented by 2j−7, and the number of juniors and seniors would be j+(2j−7)=3j−7. Since the class consists of juniors and seniors and the number of students is 23, the equation 3j−7=23 can be solved to find the number of juniors in the class. Adding 7 to both sides of the equation and then dividing both sides by 3 gives the answer that there are 10 juniors in the class. Therefore, the number of seniors in the class is 2(10)−7=13.

In the xy-plane, what is the distance between the origin (0,0) and the point with coordinates (−5,12)?

13 Option (D) is correct. To move from (0,0) to (−5,12) in the xy-plane, one could move 5 units to the left and then 12 units up. These two distances would form the legs of a right triangle that has a hypotenuse equivalent to the distance between (0,0) and (−5,12), so the Pythagorean theorem can be used to find the distance between the points. 5^2+12^2=25+144=169, and 169‾‾‾√=13, so the distance between the points is 13 units.

When the integer x is divided by 6, the remainder is 4. When x is divided by 8, the remainder is 0. Which of the following is a possible value of x ?

136 Option (D) is correct. Since the remainder is 0 when the integer is divided by 8, the integer is a multiple of 8. Since 80 is a multiple of 8, 78 is not a multiple of 8. Since 96 is a multiple of 8 (8×12=96), 94 is not a multiple of 8. Both 120 (8×15) and 136 (8×17) are multiples of 8, so the next step is to determine which of the two integers has a remainder of 4 when it is divided by 6. One way to determine this is to see if each number is 4 more than a multiple of 6. An integer is a multiple of 6 if it is even and a multiple of 3, so 120 is a multiple of 6, which means it is not 4 more than a multiple of 6. However,136−4=132, and since 132 is even and a multiple of 3 (3×44=132), 132 is divisible by 6, which means that 136 is both a multiple of 8 and 4 more than a multiple of 6.

In the figure above, each circle is tangent to the other two circles. The points X, Y, and Z are the centers of the circles. If the circles have radii of 3, 4, and 5, respectively, what is the perimeter of triangle XYZ?

24 Option (D) is correct. To find the perimeter of triangle XYZ, it is important to realize that each side of the triangle has length equal to the sum of the radii of the two circles that have centers at the endpoints of that side. The length of segment XY equals 7, since the radius of the circle centered at X is 3 and the radius of the circle centered at Y is 4. Similarly, the length of segment ZY is 5+4=9, and the length of segment ZX is 3+5=8. Therefore, the perimeter of triangle XYZ is 7+9+8=24.

Half of the students included in the table shown are girls, but only 40 percent of the fourth-grade students are girls. According to the table, how many of the girls are not in the fourth grade? Grade Number of Students First 112 Second 96 Third 100 Fourth 105 Fifth 92 Sixth 95 Total 600

258 Option (A) is correct. The number of girls included in the table is 12(600)=300. If 40 percent of the fourth-grade students are girls, then the number of girls who are not in the fourth grade is 300−(40100)(105)=300−42=258.

Mr. Sloan left his house at 8:30 A.M., arrived at the airport in Boston 50 minutes later, and waited another hour and 45 minutes before his plane took off for Salt Lake City. The plane landed in Salt Lake City 5 hours and 10 minutes later. The local time in Boston is 4:00 P.M. when the local time in Salt Lake City is 2:00 P.M. What was the local time in Salt Lake City when his plane landed?

2:15 P.M. Option (A) is correct. Mr. Sloan left his house at 8:30 A.M. and arrived at the airport at 9:20 A.M. The plane took off at 11:05 A.M. local time in Boston and landed in Salt Lake City when the local time in Boston was 4:15 P.M. Since the local time in Salt Lake City is two hours behind the local time in Boston, the plane landed at 2:15 P.M. local time in Salt Lake City.

The population of Country X is 0.36 billion persons, and the population of Country Z is 12 million persons. The population of Country X is how many times that of Country Z ?

30 Option (B) is correct. The numbers 0.36 billion and 12 million can be written as 360,000,000 and 12,000,000, respectively, and since 360,000,000/12,000,000=30, the population of Country X is 30 times the population of Country Z.

Betty owns x CDs. Ginny owns 5 more CDs than Betty and 8 fewer than Allison. Which of the following represents the total number of CDs the three girls own?

3x+18 Option (D) is correct. Since Betty owns x CDs, Ginny owns x+5, and Allison owns x+5+8. The total number of CDs the girls own is x+x+5+x+5+8=3x+18.

A scale drawing of an automobile is being created in which a length of 13inch on the drawing is equivalent to an actual length of 1 foot. If the actual length of the car is 14 feet, which of the following is closest to the length, in inches, of the car in the drawing?

4.7 Option (B) is correct. The scale drawing has a ratio of 1/3 inch1 foot. Thus, a drawing of a car of length 14 feet will be scaled to be 1/3 inch1 foot(14 feet)=14/3 in=4 2/3 in, which is 4.7 inches, rounded to the nearest tenth of an inch.

A cash drawer contains a total of $1,240 in five-dollar bills and twenty-dollar bills. If the drawer contains 8 more five-dollar bills than twenty-dollar bills, which of the following systems of equations can be used to determine the number of five-dollar bills and the number of twenty-dollar bills in the drawer?

5x+20y=1,240 x−y=8 Option (D) is correct. Let x represent the number of five-dollar bills, and let y represent the number of twenty-dollar bills. Each of the five-dollar bills is worth 5 dollars, so the value of all of the five-dollar bills is 5x dollars. Similarly, the value of all of the twenty-dollar bills is 20y dollars. Since the value of all of the money is $1,240, the value of the five- and twenty-dollar bills together is 5x+20y and the equation is 5x+20y=1,240. Since there are 8 more five-dollar bills than twenty-dollar bills, the other equation is x−y=8, and these are the two equations shown in option (D).

Marta has $88 in a jar. If she adds $6 each week to the money already in the jar without withdrawing any money, in how many weeks will she have a total of $142 in the jar?

9 Option (C) is correct. The problem can be written as the equation 6w+88=142 with w representing the number of weeks. The problem can be solved by subtracting 88, the amount Marta already has, from 142, her goal, and then dividing the difference by 6, the amount she plans to add each week. The final result is 9.

Which of the following laboratory instruments is most appropriate to use for determining the volume of a large rectangular block of wood of unknown density?

A metric ruler' Option (A) is correct. To find the volume of a large rectangular block of wood, first use the metric ruler to find the length, width, and height of the block. Then use the formula for the volume of a rectangular solid — length × width × height — to determine the volume.

Starlings, a type of bird, were introduced into the United States from Europe in the nineteenth century. Since then, starlings have spread throughout the country and become a nuisance, or pest species, especially in urban areas. They often drive native birds out of their habitats. Factors that have contributed to the starlings' success in the United States include which of the following? Select all that apply.

A. Appropriate locations for nesting B. A suitable range of temperatures D. The availability of a variety of food sources Options (A), (B), and (D) are correct. Both biotic factors, such as the availability of food sources or lack of predators, and abiotic factors, such as a suitable range of temperatures, contribute to the success of a species in a certain habitat. European starlings build nests in natural or artificial cavities and commonly displace other cavity-nesting birds to do so. They largely feed on insects, but also eat grains, seeds, fruits, and food waste. Urban and suburban areas throughout the United States provide suitable habitats to the extent that the original population of 60 starlings in 1890 has multiplied to approximately 150 million birds. The starlings' behavior of flying in huge flocks deters predators.

The graph above shows the levels of primary productivity for different ecosystems. Based on the data, which of the following is the most likely conclusion?

Abundance of water is important to achieve high primary productivity levels. Option (B) is correct. The graph illustrates the relative net primary productivity of selected ecosystems. Net primary productivity refers to the amount of organic matter that is produced by photosynthesis and that is available to support consumers and decomposers, but provides no information about the number and types of species in an ecosystem. Based on the graph, ecosystems with an abundance of water — tropical rain forest, freshwater wetland, and salt marsh — have the highest primary productivity. Therefore, the most likely conclusion is that abundance of water is important to achieve high productivity levels.

Order the polygons below from the polygon with the least number of lines of symmetry to the polygon with the greatest number of lines of symmetry. An equilateral triangle A square A regular hexagon An isosceles triangle A rectangle that is not a square

An isosceles triangle A rectangle that is not a square An equilateral triangle A square A regular hexagon The correct order of the polygons is as follows: an isosceles triangle, a rectangle that is not a square, an equilateral triangle, a square, and a regular hexagon. It is easier to order the polygons as requested if the number of lines of symmetry of each polygon is known. In an equilateral triangle, a line from each vertex to the base of the opposite side bisects the length of that side. Therefore, an equilateral triangle has 3 lines of symmetry. Each of the 2 diagonals of a square is a line of symmetry. The line that bisects one side of a square will also bisect the opposite side; therefore, it is a line of symmetry. Therefore, 2 lines of symmetry will bisect the 2 pairs of opposite sides of the square. This makes 4 lines of symmetry for a square. A regular hexagon has 6 congruent sides and 6 congruent angles. There are 3 lines of symmetry that can be drawn from a vertex to an opposite vertex and 3 lines of symmetry that can be drawn from the midpoint of a side to the midpoint of an opposite side, for a total of 6 lines of symmetry. An isosceles triangle has 1 line of symmetry running from the vertex of the congruent sides to, and bisecting the base of, the triangle. A rectangle that is not a square has 2 lines of symmetry, each of which bisects the 2 pairs of opposite sides.

Which of the following actions decrease the energy consumption of a residential house? Select all that apply.

B. Reducing hot water use C. Adding insulation to a poorly insulated house D. Replacing incandescent lightbulbs with compact fluorescent bulbs Options (B), (C), and (D) are correct. Reducing hot water use results in a decrease in the amount of energy consumed to heat incoming, cold water as the outgoing, hot water is used. Increasing the insulation in a poorly insulated house reduces heat loss through the roof and outside walls, so less energy is consumed to maintain a comfortable temperature in the house. A compact fluorescent bulb produces the same amount of visible light as an incandescent lightbulb, but uses significantly less electricity. Lowering, not raising, the thermostat setting in cold weather reduces the energy consumption of a house.

An organism that is unicellular, lacks membrane-bound organelles, and reproduces asexually is most likely classified as which of the following?

Bacterium Option (A) is correct. Bacteria are prokaryotic organisms that are unicellular, lack a nucleus and other membrane-bound organelles, and reproduce through binary fission, a type of asexual reproduction.

Which of the following chemical equations is balanced?

CaO + SiO2 → CaSiO3 Option (C) is correct. An equation is balanced when the number of atoms of each element is the same on both the reactant and product sides of the equation.

According to many scientists, Earth's average surface temperature is rising largely because of an enhanced greenhouse effect. An increase in the atmospheric concentration of which of the following gases is considered to be primarily responsible for the enhanced greenhouse effect?

Carbon dioxide Option (D) is correct. Although there are other gases, such as methane and water vapor, that are considered to be greenhouse gases, it is the increase in the atmospheric concentration of carbon dioxide that is considered to be primarily responsible for the enhanced greenhouse effect. The increase in concentration is largely attributed to the burning of fossil fuels.

In a classroom, there are 11 boys and 13 girls. Two different students will be selected at random to compete in a contest. What is the probability that both of the students selected will be girls? Give your answer as a fraction.

Correct Answer: 13/46 The correct answer is 1346. There are a total of 24 students in the class, made up of 11 boys and 13 girls. The probability that the first student selected will be a girl is 1324. The probability that the second student selected will be a girl (out of the remaining 12 girls among 23 students) is 1223. Therefore, the probability that both of the students selected will be girls is 1324∙1223=156552=1346. Please note that you do not need to simplify the fraction to get the answer correct.

Based on its position on the periodic table, which of the following elements is most likely to have luster and malleability?

Cs Option (A) is correct. Luster and malleability are physical properties of metals. Metallic character generally decreases from left to right across the periodic table and increases down a row of the periodic table. Therefore, based on its position on the periodic table, the metal cesium, Cs, is most likely to have luster and malleability.

Which of following biological molecules are used to transmit genetic information?

Deoxyribonucleic acids Option (C) is correct. Deoxyribonucleic acids (DNA) are biological molecules consisting of four different nucleotides that are linked together to form long chains, or strands. Genetic information is encoded by the sequence of the nucleotides. DNA usually exists as complementary pairs of strands that form a double helix and are organized into chromosomes.

The bending of a sound wave around the wall of a building is an example of which of the following phenomena?

Diffraction Option (D) is correct. Diffraction is the bending of waves around small obstacles and the spreading out of waves past small openings. The phenomenon is observed with both light and sound waves.

Earth's 24-hour solar day is primarily a result of

Earth's rotation on its axis Option (C) is correct. Earth's 24-hour solar day is primarily a result of Earth's rotation on its axis. Solar noon is the time of day at which the Sun is at its highest point in the sky at a given location. A solar day is based on the length of time between two consecutive solar noons.

The major reason that it is warmer in the United States in summer than in winter is that

Earth's rotational axis is tilted so that the Northern Hemisphere receives more direct sunlight in summer than in winter Correct Answer: D Option (D) is correct. Seasonal variations in temperature occur because Earth's rotational axis is tilted. During summer in the Northern Hemisphere, when the northern end of the axis is tilted toward the Sun, regions in the Northern Hemisphere receive more direct sunlight, resulting in warmer temperatures compared to temperatures in winter.

For many people, a warm, humid day is much less comfortable than a warm, dry day because the high humidity decreases the rate of which of the following?

Evaporation of water from the skin Option (C) is correct. On a humid day, the amount of water vapor in the air is approaching the saturation point, the maximum amount of water vapor that air can hold at a given temperature. As a result, the rate of evaporation of water from the skin decreases, and people are less comfortable because of the lack of evaporative cooling that occurs when water undergoes a phase change from liquid to vapor.

A light display for a festival consists of a string of 1,000 lightbulbs in the colors red, yellow, green, and blue repeated consecutively in that order for the entire display. The bulb of the 543rd light needs to be replaced. If the 1st bulb is red, what is the color of the bulb that needs to be replaced?

Green Option (C) is correct. The 1st bulb is red, the 2nd is yellow, the 3rd is green, and the 4th is blue. There are 4 bulbs in the pattern, so the blue bulbs will be the 8th, 12th, 16th, etc. Thus, the blue bulbs will all be the bulbs numbered 4n, where n is a positive integer. The last blue bulb in the string before bulb 543 is bulb 540, since 540 equals 4 times 135. So, bulb 540 is blue, bulb 541 is red, bulb 542 is yellow, and bulb 543 is green.

Which of the following statements best describes Copernicus' major contribution to the field of science?

He proposed the first modern theory that the Sun is the center of the universe and that Earth and the planets revolve around the Sun. Option (C) is correct. Copernicus' major contribution to science is that he proposed the first modern heliocentric theory that the Sun, not Earth, is the center of the universe and that Earth and the planets revolve around the Sun. Observations by other astronomers later established that the Sun is not the center of the universe, which has no real center, and that the Sun is only the center of our solar system.

The Moon's gravitational pull on Earth causes water on the side of Earth facing the Moon to bulge toward the Moon. Which of the following usually results at locations where the bulge is large?

High tides Option (B) is correct. High tides usually result in locations where the bulge is large. Water on the opposite side of Earth, where the gravitational pull is exceeded by inertia, also bulges. Therefore, coastal areas generally experience two high tides and two low tides each day, as Earth makes one complete rotation.

Which of the following best describes the overall topography of the ocean floor?

It has many flat areas such as plains, but it also has features such as ridges and canyons. Option (C) is correct. The ocean floor has a variety of features. In many locations there is a progression from shoreline to continental shelf, then continental slope, then continental rise, then abyssal plain. The deepest parts of the oceans are not in the center, but are in deep-sea trenches where tectonic plates are being subducted (for example, the Mariana Trench). The oceans also have mid-ocean ridges (chains of undersea mountains), submarine canyons, seamounts, etc.

After Mr. Shaw graded the tests for his second-period class, he determined that the class average (arithmetic mean) was 75. A student who had been ill took the test at a later date and earned a grade that is 10 points higher than the class average. Which of the following statements must be true about the new class average?

It is less than 10 points higher than before. Option (B) is correct. To solve this problem, it may be helpful to use the definition of average (arithmetic mean). Given a set of test grades for a class, the class average is equal to the sum of the grades divided by the number of grades. Therefore, to find the sum of the grades, multiply the class average by the number of grades. Let n denote the number of students who originally took the test. Then, the sum of the grades on the tests for which the class average is 75 is 75×n. Therefore, the sum of these grades plus the new grade of 85 can be expressed as (75×n)+85, and so the new class average is given by (75×n)+85/n+1. By writing 85 as 75+10, the new class average can be expressed as (75×n)+75+10/n+1=75×(n+1)+10n+1=75×(n+1)n+1+10/n+1=75+10/n+1. Note that since n+1 represents an integer greater than 1, the fraction 10/n+1 is a number less than 10. Thus, the new class average must be less than 10 points higher than before.

Which of the following best describes the process of transpiration in the water cycle?

It is the evaporation of water through the leaves and stems of plants. Option (C) is correct. Transpiration is the evaporation of water from the leaves and stems of a plant to the atmosphere. Transpiration is one process in the water cycle by which liquid water is changed to atmospheric water vapor. Evaporation from bodies of water is the primary source of water vapor in the atmosphere.

If the value of w in the equation p=3(w+5)+7 above is increased by 1, how will the value of p change?

It will increase by 3. Option (B) is correct. The value of p can be written as p=3w+15+7=3w+22. If w is increased by 1, the value of p becomes p=3(w+1+5)+7=3(w+6)+7=3w+18+7=3w+18+25. Since 3w+25 is 3 more than 3w+22, the value of p will increase by 3 if the value of w is increased by 1.

A student recorded the height of a single plant every day over the course of a year. Of the following types of graphs, which is most appropriate for the student to use to present the data?

Line graph option (C) is correct. A line graph is most appropriate for the student to use to present the data. A line graph compares two variables, each plotted along one of two perpendicular axes and connected by straight line segments. When time is plotted along the x-axis, the graph illustrates the change of a variable, or trend, over a period of time.

Which of the following organelles are directly involved in cellular respiration, the breakdown of sugars for energy?

Mitochondria Option (B) is correct. Cellular respiration takes place in the cytoplasm and mitochondria. Energy that is released by the breakdown of sugars is used for the formation of ATP molecules, which are the primary source of energy for many cellular processes.

Using which of the following to produce electricity contributes most to the incidence of acid rain in North America?

Power plants that burn fossil fuel Option (B) is correct. Acid rain is caused by the reaction of sulfur oxides and nitrogen oxides with water in the atmosphere to form acids. The burning of fossil fuels is a major source of these oxides.

The invention of the first known practical telescopes in the seventeenth century enabled astronomers to observe rings around which of the following planets?

Saturn Option (C) is correct. Saturn, the second largest planet in the solar system, has the most extensive ring system in the solar system. Saturn's disklike rings were first observed and described in the seventeenth century after the invention of the first known practical telescopes.

If a six-inch bar magnet is cut crosswise into three equal pieces, what is the total number of magnetic poles among the three pieces?

Six Option (D) is correct. A bar magnet has two poles, a north pole and a south pole, that cannot be isolated. Each piece of bar magnet that is cut in half has a north pole and a south pole. Therefore, a bar magnet that is cut crosswise into three pieces has a total of 6 poles

Which of the following best explains the necessity of completing the entire course of an antibiotic prescribed for a bacterial infection?

Some bacteria are more difficult to eliminate and require a longer antibiotic exposure. Option (D) is correct. In the beginning of a course of treatment, antibiotics kill or inhibit the growth of the more susceptible bacteria. The remaining bacteria are more resistant to the action of the antibiotic and longer exposures are required. Discontinuing use of an antibiotic before the resistant bacteria are eliminated may lead to increasingly antibiotic-resistant strains of bacteria. Antibiotics are only effective against bacterial infections.

At a thrift store, each shirt costs $4, each pair of pants costs $7, and there is no sales tax on clothing purchases. Jason bought some shirts and some pairs of pants at the thrift store and paid exactly $41. How many shirts and how many pairs of pants did Jason buy at the thrift store?

The correct answer is 5 shirts and 3 pairs of pants. One of the ways to solve the problem is to set up a table similar to the following. Number of Pairs of Pants Bought Amount Spent on Pairs of Pants Amount Left for Shirts 1 $7 $34 2 $14 $27 3 $21 $20 From the table, it is seen that when 3 pairs of pants are bought at a cost of $21, there is $20 left to buy 5 shirts, since each shirt costs $4.

To answer the question of whether matter is conserved in a chemical reaction that produces a gas and a solid, a student will need to measure which of the following?

The initial mass of reactants and the total mass of products and any remaining reactants Option (B) is correct. The law of conservation of matter states that matter cannot be created or destroyed in a chemical reaction. According to the law, the mass of the reactants consumed should be equal to the mass of the products. Thus, the initial mass of the reactants should be equal to the total mass of the products plus any unconsumed reactants that remain.

A group of students measured the boiling point of three different samples of pure water. Each measurement was made by a different student using the same thermometer. Their measurements were 94ºC, 99ºC, and 104ºC. Which of the following most likely accounts for the discrepancy in the measurements?

The students misread the markings on the thermometer. Option (B) is correct. The error that most likely accounts for the discrepancy in the measurements is that the students misread the markings on the thermometer. The temperature at which water boils (100ºC at a pressure of 1 atmosphere) is the same regardless of what hot plate is used and how long the water is heated. If the thermometer had inaccurate markings, the students' measurements would likely all be either above or below the known boiling point.

A sailor watches ships at sea and notes that they always appear to be sinking as they sail toward the horizon. Which of the following statements best explains the sailor's observation?

The surface of the ocean is curved. Option (D) is correct. As the distance between an observer, such as the sailor, and a ship increases, the curved surface of the ocean prevents the observer from seeing greater portions of the lower part of the ship, and so it appears that the ship is sinking.

Which of the following is most likely true about organisms that are producers in an ecosystem?

They contain chlorophyll. Option (A) is correct. Organisms that are producers use energy from the Sun to synthesize sugar through the process of photosynthesis. Chlorophyll is a green pigment that absorbs light energy that is required for photosynthesis. It is found in cyanobacteria and in chloroplasts of algae and plants. Energy stored in sugar molecules is transferred to organisms, called primary consumers, in the next trophic level, who feed on the producers.

Which of the following is always true about the atoms of two different isotopes of an element?

They have the same number of protons. Option (A) is correct. Isotopes of an element have the same number of protons but a different number of neutrons and different mass numbers.

Which of the following occurs at divergent plate boundaries?

Two plates move away from each other. Option (A) is correct. Divergent plate boundaries occur where two tectonic plates are moving apart from each other. A mid-ocean ridge is an example of a divergent plate boundary.

Some human traits are carried by genes on the Y chromosome. A man will transmit the traits to

all of his male offspring Option (C) is correct. Human males generally have one X and one Y chromosome. A male offspring will receive only the Y chromosome from his father, while a female offspring will receive only the X chromosome from her father. Therefore, traits that are carried by genes on the Y chromosome are transmitted from a father to all of his male offspring.

When a small amount of an unknown solution is added to a sample of baking soda, the mixture begins to bubble and fizz. It can be concluded from these results that the liquid is

an acidic solution Option (B) is correct. Baking soda, NaHCO3(s), is a weak base and it reacts with an acid to form carbonic acid, H2CO3(aq), which decomposes to water and carbon dioxide gas according to the reaction H+(aq) + NaHCO3(s) → H2CO3(aq) → H2O(l) + CO2(g).

Igneous rock is formed when preexisting rock melts and the molten rock is then

crystallized Option (A) is correct. Igneous rock is formed when molten rock (magma or lava) cools and crystallizes (solidifies). As the temperature of the molten rock decreases, crystals of different minerals form.

A block is accelerating along a flat surface under the action of a force applied parallel to the surface. If the magnitude of the applied force is doubled, then the magnitude of the block's acceleration will

double Option (B) is correct. According to Newton's second law of motion, the acceleration of the block is directly proportional to the applied force acting on the block. If the applied force is doubled in magnitude, then the block's acceleration will double in magnitude.

The white feathers of the white-tailed ptarmigan in winter plumage make it nearly invisible against its snowy surroundings. The phenomenon is an example of

evolutionary adaptation Option (D) is correct. The white feathers of the white-tailed ptarmigan in winter plumage are an example of camouflage, an evolutionary adaptation that increases the survival rates of organisms with certain traits. Ptarmigans with winter plumage that blends with the snow are not as likely to be preyed on by predators that use vision to hunt and are more likely to survive to reproduce and pass along the genes for white winter plumage.

The number of bacteria in a culture doubles every hour. If the culture started with 10 bacteria, which of the following functions models the number of bacteria in the culture after t hours?

f(t)=10(2)^t Option (D) is correct. There are 10 bacteria in the culture at time t=0. After 1 hour, the number of bacteria would be doubled to 2(10)=20. After 2 hours, the number of bacteria would be 2(20)=2(2(10))=2^2(10)=40. After 3 hours, the number of bacteria would be 23(10)=80. After t hours, the number of bacteria would be 2^t(10), or 10(2)^t.

The expression 1/2n(n−3) gives the number of diagonals in a polygon with n sides, where n is an integer. Which of the following expressions is equivalent to the expression shown?

n^2/2−3n/2

A student conducts an investigation at home to test how using different strengths of a water-soluble fertilizer affects the growth of bean plants. The student plants bean seeds in three different types of potting soils, sets the pots randomly on windowsills around the home, where they receive different amounts of light, and waters the bean plants with random volumes of the fertilizer solutions. Which of the following statements expresses the major concern about the experimental design?

the type of soil, amount of light, and volume of fertilizer solution may affect plant growth and should be the same for each plant. Option (D) is correct. When conducting an investigation, only a single independent variable, in this case, the strength of the fertilizer solution, should be manipulated. If more than one independent variable is manipulated, it is impossible to determine which variable is responsible for any observed changes in the dependent variable, which is, in this case, the growth of the bean plants.

Peggy is in charge of ordering classroom materials for all the teachers in her unit. The company from which the school district orders materials charges 6% of the catalog price for sales tax, plus $8.50 shipping on each order. Since Peggy orders materials frequently, she would like to use an equation to simplify her computations. If the total of the catalog prices for an order is x dollars, which of the following equations gives the total price, y, for the order?

y=x+(.06)x+8.50 Option (A) is correct. The total price, y, for the order must include the total of the catalog prices, x, the tax on the total of the catalog prices, which is 6% or .06 times x, and the shipping cost of $8.50. Therefore, y is equal to the sum of those three quantities.