Math
Solve for x:
2(3x – 1) – 2(x + 5) = 12
1. 4
2. 6
3. 0
4. 5
What is 2
When solving equations remember to use:
Step 1: Distribute
In this problem, we are first going to remove the parentheses from the equation. To do this we must multiply the term in front of each parenthesis by each term inside its respective parenthesis.
2(3x – 1) – 2(x + 5) = 12
6x – 2 – 2x – 10 = 12
Step 2: Combine Any Like Terms
Now we can rearrange the equation so that we can combine all whole numbers and all terms with the same variable. Also, remember to include the sign IN FRONT of each term.
6x – 2 – 2x – 10 = 12
If we rearrange, it becomes:
6x – 2x – 2 – 10 = 12
This simplifies to:
4x – 12 = 12
Step 3: Solve the Equation
When we solve equations, we can start by applying the inverse of the constant term on both sides of the equation. The constant is the term with no variable attached to it.
We see that 12 is being subtracted from 4x, the -12 is the constant term because there is no x attached, so we have to undo subtraction using addition. Therefore we are going to add 12 to both sides.
4x – 12 + 12 = 12 + 12
Which then becomes:
4x = 24
Now we can solve:
Since 4 is being multiplied by x, we have to undo the multiplication using division. Therefore we are going to divide both sides by 4.
(4x/4) = (24/4)
This simplifies to:
1x = 6
Since 1x and x are the same thing, our final answer is:
x = 6
Living in one of the warmest countries on Earth poses many challenges, as its inhabitants need not only to find inventive ways to stay cool, but they also require innovative strategies that allow them to grow their own food. Since 1985, Dmitry Ivanov has been researching hydroponic farming systems, a way to grow crops directly in nutrient-rich water. Among its many advantages, Dmitry remarks on the fact that hydroponics offers a decrease in water usage in agriculture: to grow 1 kilogram of tomatoes using intensive farming methods requires 400 liters of water, whereas hydroponic methods need only 70 liters. Nevertheless, climate change and land degradation will render all of Ivanov’s efforts useless.
Which of the following sentences from the passage does not follow the overall tone of the passage?
1. Among its many advantages, Dmitry remarks on the fact that hydroponics offers a decrease in water usage in agriculture: to grow 1 kilogram of tomatoes using intensive farming methods requires 400 liters of water, whereas hydroponic methods need only 70 liters.
2. Since 1985, Dmitry Ivanov has been researching hydroponic farming systems, a way to grow crops directly in nutrient-rich water.
3. Living in one of the warmest countries on Earth poses many challenges, as its inhabitants need not only to find inventive ways to stay cool, but they also require innovative strategies that allow them to grow their own food.
4. Nevertheless, climate change and land degradation will render all of Ivanov’s efforts useless.
What is 4
This is correct because the overall tone is objective, whereas this sentence uses a pessimistic tone that doesn’t appear in the rest of the text.
Which of the following anatomical terms is correctly matched with its meaning?
1. cervical/wrist
2. cranial/skull
3. inguinal/neck
4. carpal/foot
What is 2
Cranial refers to the bone comprising the skull.
Carpal refers to the bone comprising the wrist.
Cervical refers to the region of vertebrae in the neck.
Inguinal is the superior region of the thigh.
Which of the following words is spelled correctly?
1. absense
2. absents
3. absence
4. abcense
What is 3
Absence is correct. Ab- as a prefix means away, so absent is the adjective that describes someone who is away from a certain place. Replacing the –t in absent with –ce creates the noun form absence (the state/condition of being away from a place). This principle applies to other words like different and difference.
An emergency room patient’s heart rate dropped 30% to 63 beats per minute. What was the patient’s heart rate prior to the drop in beats per minute?
1. 19
2. 44
3. 210
4. 90
What is 4
Step 1: Interpret the Problem
Calculating the patient’s original heart rate before the drop requires some manipulation of the percentages. We need to consider that the original heart rate represents 100%. If the original heart rate represents 100% we must calculate how much of the original heart rate is remaining after a percent drop.
Given the heart rate dropped by 30%, we know,
100% – 30% = 70%
Therefore, the remaining heart rate percent is 70%.
Step 2: Turn The Percent Into a Decimal
We never use percentages in our actual math problems, so we first must turn our percentages into a decimal.
To turn a percentage into a decimal, we divide by 100, which is the same as moving the decimal point two spaces to the left.
70% = 70.%
70.% ÷ 100 = .70
70% as a decimal is .70. Remember, zeros at the end of a number after a decimal do not add any value, so we can just write it as .70.
.70 = .7
Step 3: Determine the Original Heart Rate
We know 63= 70%, and that we are looking for the value that represents 100%. This means whatever 100% is, will be more than 63.
Once you calculate the percent paid and turn that to a decimal, we can use the rule below to calculate the original price of an item by using division.
Current Heart Rate ÷ Decimal = Original Heart Rate
63 ÷ .7 = 90
The patient’s heart rate before the drop was 90 beats per minute.
Olympic runners
Depending on the type of track running, Olympic runners have different dietary requirements. Sprinters, for example, run for short lengths and need short, sharp bursts of energy. In contrast, long-distance or marathon runners need slow-releasing nutrients that provide energy for a longer period of time. For this reason, they require a similar amount of calories as swimmers. During training sessions close to their race, marathon runners follow a high-carb diet. They eat a very high percentage of carbohydrates three days before the race, but an average portion the night before. On the other hand, carb-loading the day before the event could compromise their performance, leaving the runners feeling bloated and lethargic.
What is the main idea of the passage?
1. Different types of runners burn energy in different ways.
2. Swimmers need a high-carb diet before their performance.
3. High-carb diets can negatively affect a runner’s abilities.
4. Runners eat more carbohydrates during training.
What is 1
Different types of runners burn energy in different ways is correct because it provides a reason as to why Olympic runners “have different dietary requirements”, which is supported by details throughout the paragraph such as “Sprinters, for example, run for short lengths and need short, sharp bursts of energy. In contrast, long-distance or marathon runners need slow-releasing nutrients that provide energy for a longer period of time.”
Which of the following is happening during a contraction of the diaphragm?
1. A decrease in the volume of the thoracic cavity
2. Forced expiration
3. A decrease in alveolar pressure
4. An increase in alveolar pressure
What is 3
When the diaphragm is contracting, it is moving downward and allowing the lungs to inflate. During inhalation, alveolar pressure is decreased because the expansion of the lungs increases the surface area or number of alveoli available for gas exchange, thus reducing the pressure at the alveoli.
Since air is being inhaled, the volume of air in the thoracic cavity is increased, not decreased.
Alveolar pressure increases during exhalation, because the lungs are slightly collapsing, reducing the surface area of the alveoli.
Forced expiration is not occurring during diaphragm contraction, because this indicates inhalation.
The principle of the high school was debating whether to pursue the issue any further.
Which of the following corrects an error in the sentence above?
1. Replace debating with debateing
2. Replace whether with weather
3. Replace further with farther
4. Replace principle with principal
What is 4
Replace principle with principal is the correct answer.
This is correct because a principle is an idea or rule. In this case, the principal (meaning “the most important”) is a person.
What is the largest number that still rounds to 154?
1. 153.62
2. 154.23
3. 154.52
4. 153.61
What is 2
Step 1: Remember Your Rounding Rules
Step 2: Check Out Each Answer Choice To Determine Which Was Rounded Correctly and is the largest number
Answer choice: 153.62
Underline 3 to round the number to the nearest whole number.
153.62
Since the number to the right of 3 is 6, 3 goes up to 4. Any number to the right of 4 turns to 0 and any number to the left stays the same.
154.00
153.62 does round to 154 but must be compared to the other answer choices to see if it is the largest number that rounds to 154.
Answer choice: 154.52
Underline 4 to round the number to the nearest whole number.
154.52
Since the number to the right of 4 is 5, 4 goes up to 5. Any number to the right of 5 turns to 0 and any number to the left stays the same.
155.00
To the nearest whole number, 154.52 rounds to 155 not 154 so, this answer choice is not correct.
Answer choice: 153.61
Underline 3 to round the number to the nearest whole number.
153.61
Since the number to the right of 3 is 6, 3 goes up to 4. Any number to the right of 4 turns to 0 and any number to the left stays the same.
154.00
153.61 does round to 154 but must be compared to the other answer choices to see if it is the largest number that rounds to 154.
Answer choice: 154.23
Underline 4 to round the number to the nearest whole number.
154.23
Since the number to the right of 4 is 2, 4 stays the same. Any number to the right of 4 turns to 0 and any number to the left stays the same.
154.00
154.23 does round to 154 but must be compared to the other answer choices to see if it is the largest number that rounds to 154.
Step 3: Compare the numbers in the answer choices that round to 154 to see which is the largest.
Comparing answers, we have 153.62 < 153.61< 154.23 – Therefore, 154.23 is the correct answer.
Because she paid attention, took notes, and looked up unfamiliar words, she was able to discern the speaker’s meaning.
1. Determine
2. Obfuscate
3. Ignore
4. Describe
What is 1
Determine is correct. It means to draw a conclusion. The sentence states things that could reasonably help someone figure something out (such as paying attention, taking notes, and looking up unfamiliar words). Like the word determine, when you discern something, you perceive or recognize meaning — you figure the thing out.
Which of the following lists the respiratory passageways in order from largest diameter to smallest diameter?
1. Trachea, bronchioles, bronchi
2. Trachea, bronchi, bronchioles
3. Bronchioles, bronchi, trachea
4. Bronchi, trachea, bronchioles
What is 2
The trachea is the largest airway of the lower respiratory system and is composed of a single tube. It splits into two smaller tubes, a left and right bronchi. These bronchi further split into small bronchioles.
Which of the following demonstrates correct punctuation?
1. We will study three sources of electrical power that are: solar, wind, and tidal energy.
2. We will be studying three sources of electrical power, solar, wind, and tidal energy.
3. We will study three sources of electrical power; solar, wind, and tidal energy.
4. We will be studying three sources of electrical power: solar, wind, and tidal energy.
What is 4
We will be studying three sources of electrical power: solar, wind, and tidal energy is correct. When adding a list that gives the details of a claim in the sentence, use a colon. The colon must follow an independent clause. In other words, the part in front of the colon should be able to stand on its own as a sentence. “Will study/will be studying” are both grammatically correct and do not affect the solution.
Ivy spends $5.85 for 3 pounds of fruit and $9.00 for 2.7 pounds of vegetables. Approximate the average cost per pound Ivy spent on the fruits and vegetables.
1. $3.50
2. $6.60
3. $5
4. $10
What is 3
Step 1: Interpret the question
To find the average in this scenario, we need to take the ratio of the total cost of the fruits and vegetables to the total number of pounds of them. Therefore, we have a division relationship between the total cost and the total number of pounds.
The total cost of the fruits and vegetables will be the sum of their costs.
Total cost:
5.85 + 9
The total number of pounds of fruits and vegetables will be the sum of their weights.
Total number of pounds:
3.2 + 2.7
To get the average cost per pound for the fruits and vegetables, we divide the 2 totals.
Average cost per pound= (Total cost) ÷ (Total number of pounds)
Step 2: Round our numbers
Since the question asks “approximate total cost…” we have to round some of these numbers before we add them together. The numbers 5.85 and 2.7 will need to be rounded.
5.85 will be rounded to the nearest ones place.
Let’s round 5.85.
We underline the place value we are rounding to:
5.85
When we look to the right of the 5 we see an 8, which tells us the underlined digit goes up by one. So, 5 goes to 6.
Everything to the right of 6 turns to 0.
6.00
Since the zero after the decimal has no value we can get rid of it.
5.85 rounds to 6.
2.7 will also be rounded to the nearest ones place.
Let’s round 2.7.
We underline the place value we are rounding to:
2.7
When we look to the right of the 2 we see a 7, which tells us the underlined digit goes up by one. So, 2 goes to 3.
Everything to the right of 3 turns to 0.
3.0
Since the zero after the decimal has no value we can get rid of it.
2.7 rounds to 3.
Step 3: Solve
First, find the total cost of the fruits and vegetables.
6 + 9 = 15
So, the total cost of the fruits and vegetables is $15.
Next, find the total weight of the fruits and vegetables.
3 + 3 = 6
So, the total weight of the fruits and vegetables is 6 pounds.
Finally, we get the average cost per pound of the fruits and vegetables by dividing the total cost by the number of pounds.
15 ÷ 3 = 5
So, the average cost per pound for the fruits and vegetables is $5.
Which of the following statements indicates a stereotype?
1. Before starting the school year, teachers usually take a preparation course in their subjects.
2. It is important to study hard in high school.
3. Algebra is usually the first mathematics course taken by high school students.
4. All students find the transition from junior high to high school difficult.
What is 4
This is a stereotype of students coming from junior high and does not allow for the fact that some students may be adequately prepared for the shift in levels.
Remember, a stereotype is a fixed, widely held belief about a particular group of people or things. However, these beliefs are over-generalized. When we stereotype someone or something, we are drawing the conclusion that this person or thing possesses an entire range of characteristics we assume all members of that group have.
The ______________ is a double layered membrane that lines the lungs.
1. pleura
2. pleural cavity
3. pericardium
4. alveolus
What is 1
The pleura of the lungs is composed of two layers of tissue that separate the lungs from the thoracic cavity. There as an inner visceral pleura which lines all of the folds of the lungs, and an outer parietal pleura. A pleural cavity exists between the two layers of the pleura.
The pericardium is the lining of the heart.
An alveolus is a single air sac that makes up the alveoli, where the majority of gas exchange occurs in the lung.
My ______________________ has many tips on finding deals at the grocery store.
Which of the following options correctly completes the sentence above?
1. sister, a single mother of two,
2. sister. A single mother of two,
3. sister a single mother of two
4. sister: a single mother of two
What is 1
sister, a single mother of two, is correct. The information inside of the commas is nonessential to the meaning of the sentence. It is simply extra information for the reader.
If 17 dollars is equivalent to 266 Egyptian Pounds, how many Pounds would you get with $121?
1. 1,893.3
2. 54,716.2
3. 5,281.8
4. 37.4
What is 1
Step 1: Interpret the Problem and Set Up a Proportion
In this problem, we know that $17 is equivalent to 266 Egyptian Pounds. We are trying to find the number of pounds that could be obtained with $121 at the same exchange rate.
When we set up the proportion, the units must match. Since we are dealing with dollars per pound, dollars will be in the numerator and pounds will be in the denominator.
Let X be the number of pounds that is equivalent to 121 dollars.
So we have:
$17 ⇒ $121
266 pounds ⇒ X pounds
17/266 = 121/X
Step 2: Cross Multiply & Solve the Equation
To find the X, we multiply one denominator by the opposite numerator.
(17 × X) = (121 × 266)
This gets simplified to:
17 X = 32,186
Now we can solve for X:
17X/17 = 32,186/17
32,186 ÷ 17 = 1,893.3
X = 1,893.3
$121 can buy 1,893.3 Egyptian Pounds.
Julie is conducting a research project that seeks to understand how confident teachers who have recently graduated from college feel in a classroom setting. She will interview teachers who have recently graduated from college and are teaching in a middle school.
Which of the following answer choices best describes the appropriateness of Julie’s data sample in the following vignette?
1. The sample is not biased and is appropriate for the study.
2. The sample is biased because the size is too large.
3. The sample is biased because the size is too small.
4. The sample is biased because it is limited to a specific grade level.
What is 1
This is correct because Julie’s purpose for the study involves understanding “how confident teachers who have recently graduated from college feel in a classroom setting”. So, she is interviewing teachers “who have recently graduated from college”. This is appropriate. The fact that they are teaching in a middle school provides further detail, but does not limit the scope of the project, nor does it make the scope too large.
Remember that bias is showing favor toward (or prejudice against) a thing, person, or group when compared to another. This type of comparison, upon examination, is usually considered to be unfair in some way and will impact the outcome or reflection of an experiment, study, or observation.
Which of the following best describes the mechanical process of normal breathing during expiration?
1. The diaphragm relaxes and moves downward, while the intercostal muscles relax and move the ribs downward.
2. The diaphragm relaxes and moves upward, while the intercostal muscles relax and move the ribs downward.
3. The diaphragm contracts and moves upward, while the intercostal muscles relax and contract upward.
4. The diaphragm relaxes and moves upward, while the intercostal muscles contract and move the ribs upward.
What is 2
During exhalation, two primary components drive the mechanical process- the diaphragm and the intercostal muscles. During inhalation, the lungs fill with air with the help of the intercostal muscles moving up and outward to expand the chest cavity. The diaphragm contracts and pushes downward to make room for the expanded lungs.
During expiration, the opposite movements occur in order to help push air out of the lungs. Thus during exhalation, the diaphragm moves up and the intercostal muscles move the ribs downward.
_________ register with a valid email address.
Which of the following options correctly completes the sentence above?
1. First; please
2. First: please
3. First, please
4. First please
What is 3
First, please is correct. The comma after our introductory word is grammatically correct as it sets off our introductory adverb from the rest of the sentence.