One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?
A biology student wants to determine if using a fertilizer would help promote growth of new babies in spider plants. The student chooses 100 baby spider plants to be used in the study. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. Fifty of the plants will be given the fertilizer treatment and the other 50 plants will not receive any fertilizer. After one year, the shoots will be counted for each plant.
What is written as a single logarithm?
What are the solutions to
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking volunteers to participate in the study, and 100 subjects replied. They are informed that one group will receive a new cream and the other group will receive a cream with no active ingredient. The researchers believe that sun exposure may affect the cream’s effectiveness. The subjects are then asked about their outdoor activity, and 42 of the subjects state they spend more than 50% of their day outside. The 42 subjects are randomly assigned to the two treatments. The remaining 58 subjects are also randomly assigned to the two treatments. All subjects are exposed to poison ivy and given their cream. They are asked to return in three days and report their level of irritation.
The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?
A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 20 different vehicles and wants to use a randomized block design for the experiment.Which of the following variables would be the best to block the experimental units?
Hugo reflects a vector v across the line y = –x. Nemo rotates a vector v 180° counterclockwise about the origin. Which of the following vectors would have the same image for Hugo and Nemo?
Which image is a reflection over the line y = x of triangle 1?
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
The bottom of a 12-foot ladder is placed on the ground 7 feet from the base of a pipe sticking out of the ground. The top of the ladder is placed an unknown distance off the ground, leaning on the pipe. The ladder and the ground meet at a 56.4° angle. At what angle does the pipe meet the ground?
A statistics teacher has 4 periods of introductory statistics. She wants to get students’ opinions on a new homework policy. To get a sample, the teacher randomly selects 1 period and surveys all of the students in that class. Which sampling method was used?
A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a point 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?
Which is the graph of ?
A therapist wants to study the effects of yoga and meditation on stress relief. She has 60 volunteers who experience varying levels of stress. Half of the participants will be assigned to practice yoga for one month and the other half will practice meditation. Before the experiment begins, all of the participants will be asked to rate their stress levels on a scale from 0 to 10, with 0 representing "no stress” and 10 representing "highest level of stress.” At the end of one month, the participants will be asked to rate their stress levels again. The differences in stress levels will be compared.
Let q = ⟨15, –3⟩, r = ⟨–5, 8⟩, and s = ⟨10, –1⟩. What is r – q + 2s?
Which expression is equivalent to ?
A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a continuous quantitative variable that might be included in the brochure?
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop by using a random digit table. What is the fewest number of digits that should be used, given that there are 100 plants in total?
The equation of the piecewise function f(x) is below. What is the value of f(–2)?
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