Algebra 1 EOC Practice Test Questions And Answers

The correct answer is 25 because the median age is the middle value when the ages are arranged in ascending order. Since there are four ages given, the median would be the average of the two middle values, which are 24 and 27. Adding them together and dividing by 2 gives us 25.

The correct answer is Next = Now + 5. This equation represents the sequence because it shows that each subsequent term is obtained by adding 5 to the previous term. Starting with -9 and adding 5 repeatedly gives us the sequence -9, -4, 1, 6, 11, ...

√16 = √4² = 4

24/3=8

Therefore, √16-23/8+2³=4

In other words, the square root of 16 is 4. 2 to the power of 3 is 8. Then you will add and subtract from left to right. Thus, 4+8-8 = 4.

To find the number for which 18 is 24% of, you can set up an equation and solve for the unknown. Let's use N as the unknown number. 



According to the question:

24% of N = 18

0.24 * N = 18



To solve for N, divide both sides by 0.24:

N = 18 / 0.24

N = 75



So, the number 18 is 24% of 75.

To find the mean, you first add up all the ages of the family members to get the total sum. In this case, the sum of all the ages is 435. Then, you count how many family members there are, which is 15. Finally, you divide the total sum (435) by the number of members (15) to get the average age. So, 435 divided by 15 equals 29. This means the average, or mean, age of the family members is 29 years.

The product of the given expression can be found by multiplying the coefficients of the terms with the same degree of x. In this case, the expression is 2x³ + 2x - 10x. The product of this expression is D.

The graph of y=x^2 - 2 would differ from y=x^2 by shifting 2 units down. This means that every point on the graph of y=x^2 - 2 would be 2 units lower than the corresponding point on the graph of y=x^2.

Based on the scatterplot, we can observe a general trend that as age increases, the number of minutes exercised per week tends to decrease. Since the data for people who are 30 to 39 years old are not displayed, we can estimate their expected exercise time by looking at the trend. The scatterplot shows that individuals in their 40s tend to exercise around 80-100 minutes per week. Therefore, it is reasonable to expect that a 30- to 39-year-old person would also exercise in a similar range, leading to the answer of 80-100 minutes.

When the slope of the line is doubled, the equation becomes y = 4x - 4. The x-intercept is the value of x when y is equal to zero. In the original equation y = 2x - 4, the x-intercept is x = 2. However, in the new equation y = 4x - 4, the x-intercept is x = 1. Therefore, the x-intercept changes. On the other hand, the y-intercept is the value of y when x is equal to zero. In both the original and new equations, the y-intercept remains the same at y = -4. Therefore, the correct comparison is that the x-intercept changes, and the y-intercept is the same.

The fractions are arranged in order from least to greatest based on their decimal equivalents. When converting the fractions to decimals, we get 0.6, 0.615, 0.621, 0.667, and 0.75. Therefore, the correct order from least to greatest is 3/5, 24/39, 18/29, 12/18, 3/4.

When comparing the equations y=x²+1 and y=x²+3, we can observe that both equations represent parabolas because they have the form y=ax²+c, where a represents the coefficient of the quadratic term and c represents the constant term.

The equation y=x²+1 represents a parabola that opens upwards and has its vertex at the point (0, 1) on the coordinate grid. This means that Beth's graph is shifted upward by 1 unit compared to the standard parabola 2y=x².

Now, when Jacob graphs y=x²+3, the constant term in the equation is 3 instead of 1. This indicates that his graph will be vertically shifted upward by an additional 2 units compared to Beth's graph. Therefore, Jacob's graph will have its vertex at the point (0, 3) on the coordinate grid, 2 units higher than Beth's graph.

In summary, Jacob's graph y=x²+3 will be positioned above Beth's graph y=x²+1 at every point on the coordinate grid due to the vertical shift of 2 units upward.

The correct answer is a normal or "bell"-shaped curve. This is because a normal distribution is characterized by a symmetrical shape, with the majority of the data clustered around the mean and tapering off towards the tails. In a bell-shaped curve, the data is evenly distributed on both sides of the mean, indicating a balanced distribution of test scores among the students.

The given information states that the population of bacteria triples every minute. This indicates exponential growth, as the population is increasing at an exponential rate. Exponential functions have a constant ratio of change, and in this case, the population is tripling every minute, which is a consistent rate of growth. Therefore, the correct answer is exponential.

The solution to the equation is -27. The solution to the equation is -27. This can be determined by solving the equation and finding the value that satisfies it. You will subtract 6 on both sides of the equation then multiply (3/2) (this is the reciprocal of 2/3) on both sides of the equation to get -27. 

The area to be planted with grass can be found by subtracting the area of the circular swimming pool from the total area of the rectangle. The area of the rectangle is calculated by multiplying the length and width, which gives us 10 yds * 8 yds = 80 yd2. The area of the circular swimming pool is calculated by using the formula for the area of a circle, which is π * (radius)2. The radius of the circular swimming pool is half of the diameter, so it is 5 yds / 2 = 2.5 yds. Plugging this into the formula, we get π * (2.5 yds)2 = 19.63 yd2. Subtracting this from the total area of the rectangle, we get 80 yd2 - 19.63 yd2 = 60.37 yd2. Rounding to the nearest tenth, the area to be planted with grass is approximately 60.4 yd2. Therefore, the correct answer is C.

High School R is increasing its enrollment by 20 students per year, while High School T is decreasing its enrollment by 30 students per year. The difference between the two schools' enrollments is currently 200 students (400 - 200). Since High School R is gaining 20 students per year and High School T is losing 30 students per year, the difference between their enrollments will decrease by 50 students each year (20 + 30). Therefore, it will take 4 years for the two schools to have the same enrollment, as the difference will decrease by 200 students (50 x 4) in that time.

The bar graph (Option B) best represents the number of students preferring each type of music because it visually displays the exact number of students (out of 500) who selected each category. The heights of the bars correspond directly to the calculated numbers: 110 for Rock, 130 for Hip Hop, 145 for Pop, and 115 for Other. This makes it easy to compare the popularity of each music type, unlike the pie chart or line graph.

To solve for x, add 7 to both sides of the equation:

3x - 7 + 7 = 20 + 7 3x = 27

Now, divide both sides by 3 to isolate x:

3x / 3 = 27 / 3 x = 9

So, the solution to the equation is x = 9.

The two equations have different slopes because the coefficients of x (-8 and 4) are different. They also have different y-intercepts because the constants on the right side of the equations (6 and 12) are different. Therefore, the correct answer is different slope, different y-intercept.

The line of best fit represents the trend or relationship between the variables in a scatterplot. In this case, the line y = 100 is a possible line of best fit because it is a horizontal line that passes through the y-axis at the value of 100. This suggests that there is a consistent relationship between the x and y variables where y is always equal to 100, regardless of the value of x.

The equation represents the total cost of the notebooks, where x is the number of least expensive notebooks ($2.50 each) and (8-x) is the number of more expensive notebooks ($3.25 each). The total cost of the least expensive notebooks is $2.50x, and the total cost of the more expensive notebooks is $3.25(8-x). The sum of these two costs equals the total cost of $24.50.

The probability of obtaining "H6" is not 2 out of 12. In the diagram, there are 2 possible outcomes for flipping a coin (H or T) and 6 possible outcomes for rolling a die (1, 2, 3, 4, 5, or 6). Therefore, the total number of possible outcomes is 2 * 6 = 12. However, "H6" is only one specific outcome out of these 12 possibilities, so the probability of obtaining "H6" is 1 out of 12, not 2 out of 12.

The expression 3(2x − 3) (x + 4) is the factored form of the given expression. It is factored completely because all the factors within the expression cannot be further simplified or factored.

Table 1 represents a linear relation because the values in the second column increase by a constant rate (2) for each corresponding value in the first column. This indicates a linear relationship where the dependent variable (second column) changes at a constant rate with respect to the independent variable (first column). On the other hand, Table 2 does not exhibit a constant rate of change between the columns, indicating that it does not represent a linear relation.

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Simplify 4/8 to 1/2. Use the exponent rule of division. If you have the same variable, and they want to divide then you subtract the exponents. We have two exponents for the x-variable. So you subtract the exponents which is 3-5 = -2.  Since the exponent is negative we put the variable back in the denominator for it to be positive. We will do the same for the y-variable. Subtract the exponents which is 3-2 = 1. Since the exponent is positive we keep it in the numerator. Thus, our answer should be A. 

Analyzing the Stem-and-Leaf Plot:

1 | 0 0 3 4 4 4 4 2 | 2 2 4 9 3 | 1 1 2 3 4 | 6 7 8 8 8 8 9 5 | 0 0 1 2 5 7 19 | 8

Frequency Count:

10: 2 times

13: 1 time

14: 4 times

22: 2 times

24: 1 time

29: 1 time

31: 2 times

32: 1 time

33: 1 time

46: 1 time

47: 1 time

48: 4 times

49: 1 time

50: 2 times

51: 1 time

52: 1 time

55: 1 time

57: 1 time

198: 1 time

Mode:

The mode is the number that appears most frequently. In this data set, the numbers 14 and 48 both appear four times each. Therefore, the mode of the data set is 14 and 48.

The slope, m, of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates of the two points are (-3, 1) and (7, -5). Plugging these values into the formula, we get (1 - (-5)) / (-3 - 7) = 6 / (-10) = -3/5. Therefore, the slope, m, is -3/5. The y-intercept, b, can be found by substituting the slope, m, and the coordinates of one of the points into the equation y = mx + b. Using the point (-3, 1), we have 1 = (-3/5)(-3) + b. Simplifying this equation, we get 1 = 9/5 + b. Solving for b, we find b = -4/5. Therefore, the slope, m, is -3/5 and the y-intercept, b, is -4/5.

If the length of the rectangle is 4 times its width, let's assume the width is x. Therefore, the length would be 4x. The original perimeter would be 2(length + width), which is 2(4x + x) = 10x. If the length is cut in half, the new length would be 2x. The new perimeter would be 2(new length + width), which is 2(2x + x) = 6x. To find the percentage, we need to calculate (new perimeter / original perimeter) * 100, which is (6x / 10x) * 100 = 60%.

To find the solution for the system of equations, we can solve them simultaneously. By substituting the value of y from the first equation into the second equation, we get 4x - 3(2x - 3) = 31. Simplifying this equation gives us 4x - 6x + 9 = 31. Combining like terms yields -2x + 9 = 31. By subtracting 9 from both sides, we get -2x = 22. Dividing both sides by -2 gives us x = -11. Substituting this value of x into the first equation gives us y = 2(-11) - 3 = -25. Therefore, the solution for the system of equations is (-11, -25).