Answer:
There are different methods to find the horizontal asymptote of a function, but one common approach is to take the limit of the function as x approaches positive or negative infinity. If the limit exists and is a finite number, then that is the horizontal asymptote.
To apply this method to the given function:
y = (-4x^6+6x +3)/(8x^2+9x+3)
As x becomes very large (either positive or negative), the highest power of x in the numerator and denominator dominates the other terms. This is because exponential functions grow or shrink much faster than polynomials as x goes to infinity or negative infinity.
Therefore, we can simplify the function by dividing both numerator and denominator by x^6:
y = (-4 + 6/x^5 + 3/x^6)/(8/x^4 + 9/x^5 + 3/x^6)
As x approaches infinity, all the terms with negative powers of x go to zero, leaving:
y ≈ (-4 + 0 + 0)/(0 + 0 + 0)
This is an indeterminate form of 0/0, which suggests that we need to do more algebraic simplification. One way to do this is to factor out the highest power of x in both numerator and denominator:
y ≈ (-4/x^6 + 6/x^11)/(8/x^4 + 9/x^5 + 3/x^6)
y ≈ (-4/x^6)(1 - 6x^5)/(8/x^4)(1 + 9x/x^4 + 3/x^2)
Now, as x approaches infinity, the fraction becomes dominated by the leading terms:
y ≈ (-4/x^6)(-6x^5)/(8/x^4)(9x/x^4)
y ≈ (24/72)(1/x)
As x goes to infinity, 1/x goes to zero, so:
y ≈ 1/3x
Therefore, the horizontal asymptote of the graph of y = (-4x^6+6x +3)/(8x^2+9x+3) is y = 1/3x.
4) Hansen attaches his A+ test to the refrigerator with a circular magnet. Out of curiosity,
he measures the magnet and calculates that it has a diameter of 2 inches. What is the
magnet's area?
() Use 3.14 for л. If necessary, round your answer to the nearest hundredth.
square inches
Submit
The magnet's area is approximately 3.14 square inches.
What is circle?
Every point in a horizontal surface that is a certain distance above another point forms a circle (center).
The area of a circle is given by the formula:
[tex]A = \pi r^2[/tex]
where π is approximately equal to 3.14 and r is the radius of the circle. Since the diameter of the magnet is given as 2 inches, the radius is half of that, or 1 inch.
Plugging this value into the formula, we get:
[tex]A = 3.14 * 1^2[/tex]
A = 3.14 square inches
Therefore, the magnet's area is approximately 3.14 square inches.
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smo help me fill in the charts, will give brainliest
Answer:
In the explanation
Hope this helps!
Step-by-step explanation:
a.
1. LCM of 2 & 5 is 10
2. [tex]\frac{15x}{10} =\frac{12}{10}[/tex] -> 15x = 12
3. x = [tex]\frac{12}{15}[/tex] or [tex]\frac{4}{5}[/tex]
b.
1. LCM of 3 & 9 is 9
2. 2x - [tex]\frac{6}{9}[/tex] = [tex]\frac{4}{9}[/tex] -> 2x = [tex]\frac{10}{9}[/tex] -> [tex]\frac{18}{9} x[/tex] = [tex]\frac{10}{9}[/tex] -> x = [tex]\frac{10}{9}[/tex] × [tex]\frac{9}{18}[/tex] -> x = [tex]\frac{10}{18}[/tex] -> x = [tex]\frac{5}{9}[/tex]
3. x = [tex]\frac{5}{9}[/tex]
Which of the following equations represents a linear function?
y equals two thirds times x squared
x = 5
y equals negative one fourth times x plus 5
2x + 7 = 12
The equation "y equals negative one fourth times x plus 5" represents a linear function.
Selecting the linear functions?A linear function is a function whose graph is a straight line. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
Out of the given equations, only "y equals negative one fourth times x plus 5" can be written in the form y = mx + b, where m = -1/4 and b = 5.
Therefore, the equation "y equals negative one fourth times x plus 5" represents a linear function.
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Find the perimeter of the figure below.
Figure not drawn to scale
According to the given information, the perimeter of the given right-angle triangle is 30ft.
What is Pythagoras' Theorem?Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
According to the given information:We can use the Pythagorean theorem to find the length of the missing side of the right triangle, BC:
[tex]BC^2 = AB^2 - AC^2\\BC^2 = 13^2 - 12^2\\BC^2 = 169 - 144\\BC^2 = 25[/tex]
BC = 5
Now that we know all three sides of the triangle, we can find the perimeter by adding them together:
Perimeter = AB + AC + BC
Perimeter = 13 + 12 + 5
Perimeter = 30
Therefore, according to the given information, the perimeter of the given right-angle triangle is 30ft.
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Which inequality represents the values of that ensure triangle ABC exists?
A
2x + 4
B
18
6x
O A. < x < 1/1
OB. -< < 1/1
O C.
1 < x < 5
OD. 2 < x < 6
C
The Inequality which ensure triangle exists is 22 > 4x > 7.
What is inequality ?Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Theorem used In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
.
Substitute the value in the inequality to ensure triangle exists we get 4x > 7 and 22 > 4x.
From (1) and (2) inequality of triangle we get 22 > 4x > 7.
Hence, Inequality which ensure triangle exists is 22 > 4x > 7.
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Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the 1000-pound legal limit, and the standard deviation to be less than 40. A random sample of 31 helmets was tested and the sample mean and variance were found to be 825 pounds and 2350 pounds2, respectively. The manufacturer wants to know if the data provides sufficient evidence to indicate that the standard deviation is significantly less than 40.
Step 1 of 5: Calculate the test statistic for this problem. Round your answer to two decimal places.
Step 2 of 5: Determine the p-value for a lower one-sided alternative hypothesis (left-tail test). The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 3 of 5: What is the rejection region at the 10% level of significance for the test on the variance for a left-tailed alternative hypothesis? The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 4 of 5: State your conclusion using a significance level of 0.05. The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 5 of 5: Calculate a 90% confidence interval for the variance of force on the helmets. Round your answers to four decimal places.
Step 1: The test statistic is 56.56.
Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.
Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.
Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.
Step 5: The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]
What is Variance?In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.
Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: [tex]σ^{2}[/tex] ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb[tex]s^{2}[/tex]. The test statistic is:
chi-square = (n - 1) *[tex]s^{2}[/tex] / [tex]σ^{2}[/tex]
where n is the sample size, [tex]s^{2}[/tex] is the sample variance, and [tex]σ^{2}[/tex] is the population variance under the null hypothesis.
Substituting the given values, we have:
chi-square = (31 - 1) * 2350 / 1600 = 56.56
Rounding to two decimal places, the test statistic is 56.56.
Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.
Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.
Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.
Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:
[(n - 1) * [tex]s^{2}[/tex]/ chi-square upper, (n - 1) * [tex]s^{2}[/tex] / chi-square lower]
where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:
chi-square upper = 45.722
chi-square lower = 18.307
[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]
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One angle of a parallelogram measures 37°. What are the measures of the other three angles in the parallelogram?
The measures of the other two angles in the parallelogram are both 143 degrees.
what is a parallelogram?A parallelogram is a quadrilateral with two sides that are parallel to one another. A parallelogram has equal-length opposite sides and equal-length opposite angles. The internal angles that are extra to the transversal on the same side. A parallelogram's total interior angles add up to 360 degrees.
A parallelogram is formed by the junction of two parallel lines, and its opposite angles are equal.
Then, there are two 35 degree angles. Two further angles that are equivalent are noted: A parallelogram's angles add up to 360 degrees. Following that, x+x+37+37=360
2x=360-74
2x=286
x=143.
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PLSSSSSSSSSSSSSSSS HELP I WILL MARK YOU BRAINLYEST
The interior angles formed by the sides of a regular octagon have measures that total 1080. What is the measure of each angel
Step-by-step explanation:
Welll.... there are EIGHT of them that total 1080
1080 / 8 = 135 degrees each
Explica por qué las siguientes expresiones representan el mismo valor.
a) 10 - (-2)
b) -10 +2
after calculating both the expressions we can conclude that both expressions represent the same value of 12.
what is expression ?Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.
given,
Since subtracting a negative integer is equivalent to adding its positive counterpart, the expressions "10 - (-2)" as well as "-10 + 2" have the same meaning.
To be more precise, "10 - (-2)" denotes starting with a value of 10 and then deducting a negative value of -2. The positive value of an amount that is negative may be subtracted without affecting it, and vice versa. Therefore, "10 - (-2)" equals "10 + 2," making 12 the result.
The expression "-10 + 2" on the opposite hand suggests that we start with an amount of -10 and subsequently add a value of 2.
A positive number is equal to its negative counterpart when added to a negative number. Because of this, "-10 + 2" equals "-10 - (-2)", which also equals 12.
Therefore, both expressions represent the same value of 12.
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4. One of the players scored 13. 7 points per game with 4. 1 free throw attempts per game. How does this compare to what the model predicts for this player?
The model predicts that the player should score around 17.47 points per game based on their 4.1 free throw attempts per game. However, the player's observed score of 13.7 points per game suggests that they may be underperforming compared to what would be expected based on this relationship.
Let us assume that the model predicts a linear relationship between points per game and free throw attempts per game, we can calculate the predicted value of points per game for this player using the regression equation
points per game = slope * free throw attempts per game + intercept
From the given data, we know that the slope of the regression line is 2.6 and the intercept is 7.1. Plugging in the values for this player, we get:
points per game = 2.6 * 4.1 + 7.1 = 17.47
So the model predicts that this player should score approximately 17.47 points per game, which is higher than the observed value of 13.7 points per game. This suggests that this player may be underperforming compared to what would be expected based on their free throw attempts per game.
However, just one player and there may be other factors that could affect their performance beyond just free throw attempts per game.
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Find the area under the χ 2 -curve with 5 degrees of freedom to the right of 9.24.
The area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.
What is area?Area is a two-dimensional measure of a surface, such as a length multiplied by a width. It is used to measure the size of a space, such as a room, or a piece of land. Area can also be used to measure the size of a shape, such as a circle or a square. Area is usually measured in units such as square meters (m2) or square feet (ft2).
(a)1.61
The area under the X2 curve with 5 degrees of freedom to the right of 1.61 can be calculated using the following formula:
Area = 1 - Φ(x; df)
Where Φ(x; df) is the cumulative distribution function of the chi-square distribution, and df stands for the degrees of freedom.
For df = 5, Φ(1.61; 5) = 0.922.
Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 1.61 is equal to 1 - 0.922 = 0.078.
(b) 9.24
For df = 5, Φ(9.24; 5) = 0.9999.
Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 9.24 is equal to 1 - 0.9999 = 0.0001.
(c) 15.09
For df = 5, Φ(15.09; 5) = 1.
Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 15.09 is equal to 1 - 1 = 0.
In conclusion, the area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.
Complete questions as follows-
find the area under the x2 -curve with 5 degrees of freedom to the right of (a) 1.61 (b) 9.24 (c) 15.09.
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Help me calculate this integral!
Answer:
Step-by-step explan 456
What is a measure of the differences of all observations from the mean, expressed as a single number
The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.
The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.
It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.
A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.
The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.
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On a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 4 inches and one with a side length of 5 inches.
Which statement is true about the two triangles?
Responses
The two triangles are the same size but not the same shape.
The two triangles are the same shape but not the same size.
It is impossible to construct equilateral triangles with these side lengths.
The two triangles are the same size and same shape.
The correct statement is "The two triangles are the same shape but not the same size."
How to determine Which statement is true about the two trianglesBoth triangles will have three congruent sides and three congruent angles, which means they will be equilateral and equiangular. However, since the side lengths are different, the triangles will be different in size. In other words, one triangle will be larger than the other.
To see why they cannot be the same size, imagine drawing a line from one vertex of each triangle to the opposite side. Since both triangles are equilateral, these lines will bisect the opposite side and form two congruent right triangles. The hypotenuse of the larger triangle (with side length 5) will be longer than the hypotenuse of the smaller triangle (with side length 4), which means the two triangles are not the same size.
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obability and Sampling: End-of-Unit
Assessment (B)
Illustrative
iM
İM Mathema
Do not use a calculator. A standard number cube has the numbers 1 through 6 on its
faces.
1. Elena would like to know the average speed that people drive on her street. She
tracks the speed of 30 random cars that drive through with a speedometer. The
mean of Elena's sample is 30 miles per hour, and the MAD (mean absolute deviation)
is 3.
Select all the true statements.
A. Elena would be more likely to get an accurate estimate of the mean speed of
the population by sampling 60 cars instead of sampling 30 cars.
B. The median speed of the sample must be between 25 and 35 miles per hour.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36
miles per hour.
D. The mean speed of these 30 cars is likely to be the same as the mean speed of a
second sample of 30 cars.
E. The mean speed of these random 30 cars is likely to be the same as the mean of
all cars that drive in a residential area.
The true statements are:
A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.
What is Mean Absolute Deviation (MAD)?Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.
Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars. This statement is true. The larger the sample size, the more accurate the estimate of the population mean.Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour. This statement is true. The mean of a random sample of 30 cars is likely to be within one MAD of the population mean.Learn about mean here https://brainly.com/question/1136789
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Make up two data sets. list all the values in each data set and write a story to describe where they come from. The data sets should meet the following conditions:
The data set should come from random samples from a population
The centers of the distribution should be similar
The variabilities of the distributions should be different
The two data sets that meet the given conditions for in centers, and variability is in the explanations.
What are the two datasets?Data Set 1 - Heights of Adults in a City:
Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62
Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.
Data Set 2 - Salaries of Employees in a Corporation:
Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55
Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.
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Solve for a. -3.7a 1.7 = -6.07
Answer:
a = 2.1
Step-by-step explanation:
-3.7a + 1.7 = -6.07
-3.7a = -7.77
a = 2.1
Solve for x Trigonometry
Answer:
31.97⁰ to the nearest hundredth.
Step-by-step explanation:
sin x = opposite side / hypotenuse
= 9/17
x = 31.9657
If you buy fast food 4 times per week and it costs you about $850 each time, then what should your monthly budget be for fast food?
A. $136
B. $35
C. $100
D. $148
The Monthly Budget for fast food is Option A. $136.
To determine how much money you should budget for fast food, we need to calculate the total amount of money you spend on fast food each week. To do this, we simply multiply the cost of one fast food meal by the number of meals you buy in a week, which is four in this case.
$850 x 4 = $3400 per week
Next, we need to figure out how much money you spend on fast food per month. To do this, we need to multiply the weekly amount by the number of weeks in a month. Most months have around four weeks, so we will use that as an estimate.
$3400 x 4 = $13600 per month
Therefore, the answer is Option A. $136. You should budget around $136 per month for fast food if you buy it four times a week and it costs you about $850 each time.
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At a local store, 2 bagels and 2 cups of coffee cost $4.40. The cost of 3 bagels and 4 cups of coffee is $7.80.
Part A:
Write a system of equations to represent this situation.
Part B:
Solve the system of equations by substitution and interpret its meaning.
answer these questions please
The difference in the two figure's areas is 96 square units.
The height of the horse trough is 4 feet.
How to find the difference in the two figure's areas?No. 11
The area of Figure A is:
A = l * w = 12 * 8 = 96 square units
The area of Figure B is:
B = l * w = 16 * 12 = 192 square units
The difference in the two figure's areas is:
B - A = 192 - 96 = 96 square units
Therefore, the difference in the two figure's areas is 96 square units.
No. 12
We are given that the base area is 24 square feet, and the volume is 96 cubic feet.
Volume = base area * height
96 = 24 * height
height = 96/24
height = 4 feet
Therefore, the height of the horse trough is 4 feet.
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Answer:...............
Step-by-step explanation:
...................
The set of values for x that satisfies a quadratic inequality is x < -0.5 or x > 1.5
Write down a possible quadratic inequality. Can u show me working it how to do this please. Thanks
Answer:
To write a possible quadratic inequality, we first need to determine which quadratic function has roots at x = -0.5 and x = 1.5.
We know that the solution to the quadratic inequality is x < -0.5 or x > 1.5, which means that the parabola associated with our quadratic function should not intersect the x-axis between x = -0.5 and x = 1.5.
One quadratic function with roots at x = -0.5 and x = 1.5 is:
(x + 0.5)(x - 1.5) ≤ 0
To see why this is the case, we can use a graphing calculator to graph the quadratic function y = (x + 0.5)(x - 1.5) and observe that the function is negative (i.e., has a y-value less than zero) when x is less than -0.5 or greater than 1.5.
Alternatively, we can use the fact that the product of two factors is less than or equal to zero if and only if one factor is positive and the other is negative.
Since (x + 0.5) is positive for x > -0.5 and negative for x < -0.5, and (x - 1.5) is positive for x > 1.5 and negative for x < 1.5, the inequality (x + 0.5)(x - 1.5) ≤ 0 is true for x < -0.5 or x > 1.5, but false for -0.5 < x < 1.5.
Therefore, a possible quadratic inequality that satisfies the given set of values for x is:
(x + 0.5)(x - 1.5) ≤ 0
Help 44 PONITS
Graph the inverse for each relation below ‐ show answers right over the existing graph on the same
plane. 3 points each
The inverse of the graphs are added as an attachment
Plotting the inverse of the graphTo plot the inverse of a graph, you can follow these steps:
Start with a function f(x).Replace f(x) with y.Swap the x and y variables so that the equation is in terms of x and y.Solve for y to get y = f^(-1)(x), which represents the inverse function.Plot the original function f(x) on a coordinate plane.Reflect the graph of f(x) across the line y = x to get the graph of fSee attachment for the graphs
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HELPPPP Question 10 of 10
Which of the following are characteristics of the graph of the reciprocal
parent function?
Check all that apply.
A. It does not go through the origin.
B. It is a parabola.
C. It is a hyperbola.
D. It is in quadrants I and II.
The correct options are:
C. It is a hyperbola.
D. It is in quadrants I and II.
How to determine the characteristics of the graph of the reciprocal parent functionThe reciprocal parent function is given by:
f(x) = 1/x
The graph of this function is a hyperbola, which opens up and down, and has vertical asymptotes at x = 0 (the y-axis).
The graph is in quadrants I and II, since x > 0 for positive values of y, and x < 0 for negative values of y.
The graph does not go through the origin (0,0), since f(0) is undefined. It is not a parabola, since a parabola is a U-shaped curve, which is not the shape of the reciprocal parent function.
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Solve the simultaneous equations:
y=x² + 3x - 18
x + 2y + 14 = 0
!!PLEASE HELPPPPP MEEE!!
Using simple interest his interest is $ 1165.50
What is simple interest?Simple interest is given by I = PRT/100 where
P = principal, R = rate and T = timeGiven that Tucker deposits an amount of $7400 in an account that pays 3.15 % simple interest. Since he keep the amount in the account for 5 years without making any withdrawal or deposits, we need to find the amount of interest after 5 years.
Using the simple interest formula,
I = PRT/100
Given that
P = $ 7400, R = 3.15 % and T = 5 yearsSo, substituting the values of the variables into the equation, we have that
I = PRT/100
I = $ 7400 × 3.15 % × 5/100
= $ 74 × 315 × 5/100
= $ 116550/100
= $ 1165.50
So, his interest is $ 1165.50
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Question 14(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
The correct graph for the given data is given by option The bar graph x axis labeled sport and the y axis labeled number of students, with each having value as basketball -17, baseball-12, soccer - 27, and tennis - 44.
Which graph represents the given data?Because the data shows discrete categories (sports) and their related frequencies, the correct graph is a bar graph (number of students).
The x-axis is to be named "Sports" to represent the various sports (Basketball, Baseball, Soccer, and Tennis), and the y-axis has to be labelled "Number of Students" to reflect the frequency. The graph's bars will show the frequency of each sport, with the heights of the bars giving the number of students who identified each sport as their favourite. The right values for the bars should be based on the data provided:
[tex]Basketball: 17\\Baseball: 12\\Soccer: 27\\Tennis: 44[/tex]
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Students mesured different amounts of water into their beakers for an experiment. If the total amount of water is redistributed equally, how much water will be in the beaker?
1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4
However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.
what is volume ?Typically, it is expressed in geometric units, which including cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3), depending on the length unit being used. A formula that is based on an object's shape can be used to determine its volume. The volume of such a rectangular prism, for instance, can be determined by utilizing the formula V = lwh, where l stands for length, w for width, and h for height. A cylinder's volume can be calculated using the formula V = r2h, where r denotes the circle of the base and h the height.
given
We can simply sum the numbers supplied to determine the total volume of water in all the beakers:
1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4
= 1.5 + 1.5 + 0.5 + 1.25 + 1.5 + 1.75 (converting mixed values to improper fractions)
= 8.5
8.5 units of water are therefore present in all of the beakers.
Each beaker will have 8.5 divided by the number of beakers if this water is distributed equally among them.
We are unable to provide a precise response since we are unsure of the number of beakers.
However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.
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Which of the following options have the same value as 72%, percent of 50?