The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.
To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:
P(X > $429.35) = 0.011
Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:
-2.33 = ($429.35 - $395) / σ
Solving for σ, we get:
σ = ($429.35 - $395) / (-2.33) = $14.57
Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.
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What is the volume in cubic inches of a rectangular prism with a height of a 11 inches width of 15 inches and a length of 2 inches
Answer:
330 cubic inches
Step-by-step explanation:
The formula for a rectangular prism is l x w x h
so, let's input the numbers:
2 x 15 x 11
and solve:
330
So, the volume of a rectangular prism is 330 cubic inches
PLEASE HELP FASTTT LIKW IN LESS THAN 30 MINUTES PLSS IM GIVING BRAINLIEST
Answer:
Each student will have passed 17 tests; It will take 3 weeks.
Step-by-step explanation:
The explanation is in the picture.
What’s the answer? I need help please what’s the answer
The complex number with the greatest modulus is given as follows:
z1.
What is a complex number?A complex number is a number that is composed by a real part and an imaginary part, as follows:
z = a + bi.
In which:
a is the real part.b is the imaginary part.The modulus of the complex number is obtained as follows:
|z| = sqrt(a² + b²).
On the coordinate plane, we have that:
The x-axis is the real axis.The y-axis is the imaginary axis.In this problem, we have that the complex number z1 has both the highest absolute value in the x-coordinate and in the y-coordinate, thus it has the largest modulus.
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This table shows statistics about the US population in 2010. A table titled U S Population by age group (2010). Column 1 labeled age group: under 18, 18 to 24, 25 to 44, 45 to 64, 65 and older. Column 2 labeled percent of population: 24, 9.9, 26.6, 26.4, 13. Column 3 labeled total number: 74,181,467, 30,672,088, 82,134,554, 81,489,445, 40,267,984. What percent of the population was under the age of 18? nearly 10 percent nearly 25 percent nearly 50 percent nearly 75 percent
According to the table, the "Under 18" age group constitutes 24% of the total population, which is nearly 25 percent. Therefore, the answer is "nearly 25 percent".
The percentage of the population under the age of 18 can be calculated by dividing the total number of people in that age group by the total population, then multiplying by 100 to obtain a percentage.
From the table, we see that the total number of people under 18 is 74,181,467.
The total population is the sum of the total numbers in all age groups, which is 74,181,467 + 30,672,088 + 82,134,554 + 81,489,445 + 40,267,984 = 308,745,538.
Dividing the total number of people under 18 by the total population and multiplying by 100 gives
(74,181,467 / 308,745,538) × 100 ≈ 24%.
Therefore, nearly 25% of the population was under the age of 18 in 2010.
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Jerome is a photographer. He earns $125 per hour
(d) Part D
Create a graph of the data from the table.
The graph of the data from the table is added as an attachment
Creating a graph of the data from the table.From the question, we have the following parameters that can be used in our computation:
Jerome is a photographer. He earns $125 per hour
This means that the equation of the function is
f(x) = 125x
Where x is the number of hours he works
Using the above as a guide, we have the following table of values
x f(x)
1 125
2 250
3 375
4 500
5 625
6 750
Next, we plot the graph from the table of values and the function f(x) = 125x
The graph of the function is added as an attachment
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the average temperature for a random sample of 56 covid patients was 101.2 with a known population standard deviation of 6. test at a 10% alpha level if the true average temperature of covid patients exceeds 100. what type of error could have occurred? and what are the chances of that happening?
We reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100, with a type I error rate of 10% and a p-value of 0.0068 indicating a low probability of obtaining the observed sample mean if the null hypothesis were true.
To test if the true average temperature of COVID patients exceeds 100, we can use a one-sample z-test.
The null and alternative hypotheses are
Null hypothesis: The true average temperature of COVID patients is less than or equal to 100.
Alternative hypothesis: The true average temperature of COVID patients exceeds 100.
We can calculate the test statistic as
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean, μ is the hypothesized population mean (100 in this case), σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get
z = (101.2 - 100) / (6 / sqrt(56))
z = 2.47
We can find that the p-value is 0.0068. This means that if the true average temperature of COVID patients is actually 100, there is only a 0.68% chance of getting a sample mean of 101.2 or higher.
Since the alpha level is 10%, and the p-value is less than 10%, we reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100.
The type of error that could have occurred is a type I error, which is rejecting the null hypothesis when it is actually true. The probability of a type I error is equal to the chosen alpha level, which is 10% in this case.
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If you spin the spinner below 75 times, how many times would you expect to spin a number that is less than 5?
ANSWER FAST PLEASE!
An account is opened with an intial deposit of $7,500 and earns 3. 4% interest compounded semi-annually. Round all answers to the nearest dollar
The accumulated amount 54675 ([tex]2.7^{t}\\[/tex]) in dollars of an account with an initial deposit of $7,500 and earns 3. 4% compound interest semi-annually.
A compound interest is calculated by the formula,
[tex]A = P [ 1 + ( r/n )]^{nt}[/tex]
where, A is the accumulated amount at the end of the period ,
P is the initial amount of deposit,
r is the rate of interest earned on the initial deposit in the period
t is the time periods elapsed
and n is the number of times interest is applied per time period
Here the account has an initial deposit , P = $7500 and earns 3.4% rate of interest, say r, compounded semi- annually, that is n= 2 ( as rate of interest is applied twice a year or twice per time period) in time period, say t.
Therefore by the formula of compound interest we get,
Accumulated amount, A = [tex]7500[ 1 + 3.4/2]^{2t}[/tex]
⇒ A = [tex]7500[ 1 + 1.7]^{2t}[/tex] in dollars
⇒ A = [tex]7500(2.7)^{2t}[/tex] in dollars
⇒ A = 7500 (2.7)² ([tex]2.7^{t}[/tex] ) in dollars
⇒ A = 54675 ([tex]2.7^{t}\\[/tex]) in dollars
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Find the surface area of the cylinder. Round your answer to the nearest tenth if necessary 2 cm 2 cm
The surface area of the cylinder is approximately 50.2 square cm
Finding the surface area of the cylinderThe formula for the surface area of a cylinder is:
Surface area = 2πr^2 + 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
In this case, the radius is 2 cm and the height is also 2 cm.
Substituting these values into the formula, we get:
Surface area = 2π(2)^2 + 2π(2)(2)
Surface area = 8π + 8π
Surface area = 16π
So, we have
Surface area ≈ 16(3.14)
Surface area ≈ 50.2
Therefore, the surface area of the cylinder is approximately 50.2 square cm when rounded to the nearest tenth.
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three circles of radius are drawn in the first quadrant of the -plane. the first circle is tangent to both axes, the second is tangent to the first circle and the -axis, and the third is tangent to the first circle and the -axis. a circle of radius is tangent to both axes and to the second and third circles. what is ?
The value of r/s is equal to 9.
There exists a theorem that states that the square of a hypotenuse in a right-angled triangle is equal to the sum of squares of the perpendicular side and the base side. This theorem is known as Pythagoras theorem. By applying Pythagoras' theorem in this right-angled triangle formed in our image, we obtain the given formula
[tex]H^2 = P^2 + B^2[/tex]
[tex](r + s)^2 = (r - s)^2 + (r - 3s)^2[/tex]
[tex]r^2 + 2r.s + s^2 = 2r^2 - 8r.s + 10.s^2[/tex]
[tex]r^2 - 10.r.s + 9s^2 = 0[/tex]
(r - 9s) (r - s) = 0
Now we will equate these two factors to 0.
By equating, we get r/s = 9 and r/s = 1.
r/s = 1 does not apply to the geometry in this question.
So, r/s = 9 is the solution for the given equation.
Therefore, our answer is 9.
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The complete question is -
"Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius r>s is tangent to both axes and to the second and third circles. What is r/s? "
Simplify 9/12x1/12=?
Answer: Exact Form:
1/16
Decimal Form:
0.0625
Step-by-step explanation:
The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = 1 and x =
8. Use the line segment to determine the average rate of
change of the function f(x) on the interval 1 ≤ x ≤ 8.
The average rate of change of the function f(x) on the interval 1 ≤ x ≤ 8 is given as follows:
5.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
The parameters for the function are given as follows:
For an input of 1, the output is of -10.For an input of 8, the output is of 25.Hence the average rate of change for the function is given as follows:
r = (25 - (-10))/(8 - 1) = 35/7 = 5.
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A sphere has a radius of 2. 1 cm. What is the volume of sphere in cm3 (use 3. 14 for π? round to the nearest whole number
The volume of the sphere is approximately 39 cm³.
A sphere is a three-dimensional shape that is perfectly round, just like a ball. It is characterized by its radius, which is the distance from its center to any point on its surface. In your problem, the sphere has a radius of 2.1 cm, which means that every point on its surface is exactly 2.1 cm away from its center.
To find the volume of a sphere, we use the formula V = (4/3)πr³, where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
Plugging in the values from your problem, we get:
V = (4/3)π(2.1)³
V = (4/3)π(9.261)
V = 39.082 cm³
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abag contains 8 green balls and 5 red balls. the following events occur in sequence: i aball is randomly drawn and its color is recorded. then, it is returned to the bag. ii 3 balls of the opposite color recorded in step (i) are added to the bag. (for example, if a red ball was drawn in step (i), 3 green balls would be added to the bag) iii a ball is randomly drawn from the bag. what is the probability that the second ball drawn is red?
A bag contains 8 green balls and 5 red balls. Then the probability that the moment ball is drawn is ruddy is 23.1%.To fathom this issue, able to utilize the law of adding up to likelihood and consider:
A ruddy ball is drawn in step (i)The likelihood of drawing a ruddy ball in step (i) is 5/13, as there are 5 ruddy balls out of 13 adding up to balls within the pack.
After step (ii), there will be 5 ruddy balls (unique) + 3 green balls (inverse color) = 8 ruddy balls within the pack. So, the likelihood of drawing a ruddy ball in step (iii) given that a ruddy ball was drawn in step (i) is 8/11.
Presently, we will apply the law of adding up to likelihood to discover the general likelihood of drawing a ruddy ball in step (iii):
P(Red ball in step iii) = P(Green ball in step i) x P(Red ball in step iii | Green ball in step i)
P(Red ball in step i) x P(Red ball in step iii | Ruddy ball in step i)
= (8/13) x (3/11) + (5/13) x (8/11)
= 0.231 or roughly 23.1%.
thus, the likelihood that the moment ball is drawn is ruddy is 23.1%
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Use the binomial theorem to expand (2x^2+5y)^5
The expanded form of (2x² + 5y)⁵ using the binomial theorem is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.
Expand the expression using binomial theorem?Given the expression in the question:
(2x² + 5y)⁵
To expand (2x² + 5y)⁵ using the binomial theorem, we need to apply the following formula:
(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + C(n, 2)a⁽ⁿ⁻²⁾ b² + ... + C(n, r)[tex]a^{(n-r)}[/tex] [tex]b^r[/tex] + ... + C(n, n)a⁰ bⁿ
Where C(n, r) is the binomial coefficient, which represents the number of ways to choose r items from a set of n distinct items.
(2x² + 5y)⁵
Here: a = 2x² and b = 5y, so we have:
Plug into the above formula
(2x² + 5y)⁵ = C(5, 0)(2x²)⁵ (5y)⁰ + C(5, 1)(2x²)⁴ (5y)¹ + C(5, 2)(2x²)³ (5y)² + C(5, 3)(2x²)² (5y)³ + C(5, 4)(2x²)¹ (5y)⁴ + C(5, 5)(2x²)⁰ (5y)⁵
Simplifying each term using the binomial coefficient formula C(n, r) = n! / (r! (n-r)!):
(2x² + 5y)⁵ = 1(32x¹⁰)1(1) + 5(16x⁸)1(5y)¹ + 10(8x⁶)2(25y²) + 10(4x⁴)3(125y³) + 5(2x²)4(625y⁴) + 1(1)5(3125y⁵)
Simplifying the coefficients and the exponents of x and y:
(2x² + 5y)⁵ = 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵
Therefore, the expanded form is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.
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Two similar solids have edges of 4 feet in 24 feet if the smaller saw that has a volume of 16 ft.³ find the volume of the other solid?
The volume of the other solid (Solid B) is 3456 cubic feet.
How to solve for the volumeSolid A has edges of 4 feet, and its volume is given as 16 cubic feet. Solid B has edges of 24 feet.
Since the solids are similar, they have the same shape, and their corresponding lengths are proportional. To find the ratio of their corresponding lengths, we can divide the length of an edge of Solid B by the length of an edge of Solid A:
Ratio = (length of edge of Solid B) / (length of edge of Solid A)
Ratio = 24 feet / 4 feet
Ratio = 6
Now that we have the ratio of their corresponding lengths, we can find the ratio of their volumes. The ratio of the volumes of similar solids is the cube of the ratio of their corresponding lengths:
Volume ratio = (length ratio)³
Volume ratio = 6³
Volume ratio = 216
Now we can use the volume ratio to find the volume of Solid B:
Volume of Solid B = (Volume of Solid A) × (Volume ratio)
Volume of Solid B = 16 ft³ × 216
Volume of Solid B = 3456 ft³
So, the volume of the other solid (Solid B) is 3456 cubic feet.
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If three staff of Chukwudi and Sons Ltd. agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is ₦120,000.00K, How much does the second staff receive?
The second staff member receives ₦40,000.
what is Ratio?In mathematics, a ratio is a comparison of two or more quantities of the same kind or unit. It is expressed as the quotient or fraction of one quantity to another. Ratios are used to compare and express the relationship between different quantities, such as distance, time, weight, or money.
To solve this problem, we need to first determine the total ratio of the ages of the three staff, which is 18 + 20 + 22 = 60.
Next, we need to calculate the share of each staff member by multiplying their age ratio with the total amount of money collected:
The first staff member's share = (18/60) x ₦120,000 = ₦36,000
The second staff member's share = (20/60) x ₦120,000 = ₦40,000
The third staff member's share = (22/60) x ₦120,000 = ₦44,000
Therefore, the second staff member receives ₦40,000.
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Solve the quadratic equation 9x2 − 16 = 0
The resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.
What is a quadratic equation?Any equation in algebra that can be written in standard form where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
An algebraic equation of the second degree in x is a quadratic equation.
The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
So, we have the quadratic equation:
9x² − 16 = 0
Now, solve as follows:
a = 9
b = 0
c = -16
Now,
c = -0 ± √0² - 4-9(-16)/2*9
x = ±4/3
Therefore, the resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.
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what is the correct order of the numbers from least to greatest 1\2, 0.6,6%,6\5
Thus, the correct order of the numbers from least to greatest: 6% < 1/2 < 0.6 < 6/5
Explain about the ascending order:In an ascending list, the item that is smallest, first, or oldest will be at the top:
The order of a number or amount is from smallest to largest. The list will be arranged with lower values at the top.The alphabetical order of the sort is A to Z for letters and words.With data that includes both numbers and letters or words, like address lines, the sort is probably alphanumeric, which means that 0–9 is sorted first, then A–Z, and so on.Given number-
1\2, 0.6,6%,6\5
convert all numbers in its fraction form:
1\2 = 0.5
0.6 = 0.6
6% = 0.06
6\5 = 1.2
Order from least to greatest: 0.06, 0.5, 0.6 1.2
Or,
Thus, the correct order of the numbers from least to greatest 6% < 1/2 < 0.6 < 6/5
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Help please!!!
It would be much appreciated! <3
Workout of the fastest person's total time is 2 minutes 34 seconds.
What about time?Time is a concept used to describe the sequence and duration of events or changes that occur in the universe. It is a measure of the interval between two events or occurrences, and it allows us to describe and understand the order and duration of events.
In physics, time is often described as a dimension, along with the three spatial dimensions, and is often measured in units such as seconds, minutes, or hours. Time is also relative, meaning that its perception and measurement can vary depending on factors such as motion and gravity.
Overall, time is a fundamental concept in many fields, including physics, philosophy, and everyday life, and its study and understanding are crucial to our understanding of the world around us.
According to the given information:
From the given table we can observe that Ben is the fastest
Total time =53.44 + 49.79+ 50.50
= 153.73 seconds.
Hence, total time = 2 minutes 34 seconds
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6 3/7 + 1 2/5 fraction.
The sum of 6 3/7 and 1 2/5 as a mixed fraction is 7 29/35.
What is the addition of the given fractions?Given the mixed fraction in the question:
6 3/7 + 1 2/5
To add mixed fractions, we first need to convert them into improper fractions.
First, convert 6 3/7 to an improper fraction:
6 3/7 = (6 × 7)/7 + 3/7
= 42/7 + 3/7
= 45/7
Convert 1 2/5 to an improper fraction:
1 2/5 = (1 × 5)/5 + 2/5
= 5/5 + 2/5
= 7/5
Now we can add the fractions:
45/7 + 7/5
(45 × 5)/(7 × 5) + (7 × 7)/(5 × 7)
= 225/35 + 49/35
= 274/35
= 7 29/35.
Therefore, the sum is 274/35 or 7 29/35.
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which of the following probability distribution types has a mean, median, and mode that are all equal? constant symmetric positively skewed negatively skewed
Answer: B symmetric
Step-by-step explanation:
Since every value in a constant-distribution has the same chance of happening, the distribution is symmetric. The mean and median are both identical to this value because there is only one value, which also makes it the mode.
The mode may or may not be equal to the mean and median for a symmetric distribution, but they are always equal. The mean is often higher than the median and the mode may be lower than the median in a positively skewed distribution. The mode may be higher than the median and the mean is often lower in a negatively skewed distribution.
A constant-probability distribution is a form of probability distribution in which the likelihood of each possible result is the same. In other words, there is an equal chance of each outcome.
Therefore , The Constant-distribution is a sort of probability distribution where the mean, median, and mode are all equal.
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Please help it’s due really soon!!!
The values of x that makes line segment m parallel to n (m ║ n) are as follows;
13. x = 107°.
14. x = 133°.
15. x = 20°.
16. x = 23°
The outer strings of the oud are parallel because they are all cut or intersected by a transversal.
What are corresponding angles?In Mathematics and Geometry, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.
By applying corresponding angles theorem, we have the following:
x + 73 = 180° (sum of all interior angles)
x = 180 - 73
x = 107°.
x + 14 = 147 (vertical angles theorem).
x = 147 - 14
x = 133°.
3x + 2x + 20 = 180° (sum of all interior angles)
5x = 180 - 20
x = 60/3
x = 20°.
7x - 11 = 4x + 58 (corresponding angles theorem)
7x - 4x = 58 + 11
3x = 69
x = 23°
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Determine the absolute value of the complex number colon open vertical bar 6 straight i close vertical bar
Answer:
√37 ≈ 6.083
Step-by-step explanation:
You want the modulus of the complex number 6 -i.
ModulusThe modulus of a number is written using absolute value bars:
|6 -i|
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts:
|6 -i| = √(6² +(-1)²)
|6 -i| = √37 ≈ 6.083
PLEASE HELP!!!!!!!!
The box plots below show attendance at a local movie theater and high school basketball games:
Two box plots shown. The top one is labeled Movies. Minimum at 60, Q1 at 65, median at 95, Q3 at 125, maximum at 150. The bottom box plot is labeled Basketball games. Minimum at 90, Q1 at 95, median at 125, Q3 at 145, maximum at 150. Which of the following best describes how to measure the spread of the data?
a. The IQR is a better measure of spread for movies than it is for basketball games.
b. The standard deviation is a better measure of spread for movies than it is for basketball games.
c. The IQR is the best measurement of spread for games and movies.
d. The standard deviation is the best measurement of spread for games and movies.
a) 'The IQR is a better measure of spread for movies than it is for basketball games' best describes how to measure the spread of the data
According to the information provided, the box plots for movies and basketball games indicate that both have the same range of attendance data, with a minimum of 60 and a maximum of 150. However, when comparing the interquartile ranges (IQRs) of the two box plots, it can be seen that the IQR for movies is smaller than the IQR for basketball games.
The IQR represents the middle 50% of the data, and the smaller IQR for movies suggests that the attendance data for movies is more closely clustered around the median than the attendance data for basketball games. Therefore, the IQR is a better measure of spread for movies than it is for basketball games, as it gives a more accurate representation of the variability of the data for movies.
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Which number line shows the solution to the inequality n + 3 > 4?
The number line which correctly shows the solution to the given inequality as required is as attached.
What is the solution of the inequality represented on a number line?It follows from the task content that the number line which correctly shows the solution to the given inequality is to be determined.
First, we must solve the inequality as follows;
n + 3 > 4
n > 4 - 3
n > 1.e
Ultimately, the number line which represents the solution of the inequality as required is as in the attached image.
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An athlete has decided to track how many minutes they exercise each day. During the first day, the athlete exercised for 30 minutes. For each day after that, the athlete increased their exercise time by 3 minutes. Which equation in point-slope form models the number of minutes the athlete exercises, y, based on the day, x?
A: y-30=3(x-1)
B: y+30=3(x+1)
C: y-1=3(x-30)
E: y+1=3(x+30
The initial exercise time is 30 minutes, so the y-intercept of the line is 30. The athlete increases their exercise time by 3 minutes each day, which means the slope of the line is 3. The correct answer is option: A.
We use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the first day's exercise time as our point, we get (1, 30) as our (x1, y1) values. Substituting these values into the point-slope form and simplifying, we get y - 30 = 3(x - 1), that is option A. Hence option A is correct.
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PLEASE HELP ME!!!!
A toy American Eskimo dog has a mean weight of 8 pounds with a standard deviation of 1 pound. Assuming the weights of toy Eskimo dogs are normally distributed, what range of weights would 95% of the dogs have?
a. Approximately 7–9 pounds
b. Approximately 6–10 pounds
c. Approximately 5–11 pounds
d.Approximately 4–12 pounds
Answer:
Step-by-step explanation:
A cuz if we do 7-9=1 and he has one pound of each
PLEASE HELP!!!!! Select all the correct answers.
If you graph the system of inequalities given below, which points would lie in the solution set? Select all the correct answers.
x-y>-4
2x-y<5
2y + x>1
(-2,3)
(-1,3)
(0, 0)
(2,-2)
(3,5)
Answer:
To determine which points lie in the solution set of the system of inequalities x-y>-4, 2x-y<5, and 2y + x>1, we can graph the inequalities on a coordinate plane and look for the region that satisfies all three inequalities.
To graph the inequality x-y>-4, we can first graph the line x-y=-4 by plotting the points on the line:
x y
0 -4
-4 0
Then, we can shade the region above the line, since all points above the line will satisfy the inequality x-y>-4:
|
-4 | x
| /
| /
| /
|/
-8 +------
-4 0
To graph the inequality 2x-y<5, we can first graph the line 2x-y=5 by plotting the points on the line:
x y
0 5
2.5 0
Then, we can shade the region below the line, since all points below the line will satisfy the inequality 2x-y<5:
|
5 | x
| / |
| / |
| / |
|/ |
0 +----|--
0 2.5
To graph the inequality 2y + x>1, we can first graph the line 2y + x = 1 by plotting the points on the line:
x y
0 0.5
1 0
Then, we can shade the region above the line, since all points above the line will satisfy the inequality 2y + x>1:
|
2 | x
| |
1|-----
| /
| /
| /
|/
0 +------
0 1
The solution set of the system of inequalities is the region that satisfies all three inequalities, which is the shaded region in the graph below:
|
5 |
|
| x
2| |
| |
| |
| /|
| / |
0+------+------
-4 0 2.5
So the points that lie in the solution set are:
(-2,3), (-1,3), (2,-2)
Therefore, the correct answers are:
(-2,3), (-1,3), and (2,-2)
alarming levels of mercury are starting to creep into our food chain: our fish are showing up with levels of mercury in them that used to be absent. are the mercury levels the same in all fish? the dataset mercury (found on canvas module 9 under data) gives mercury levels in parts per million for four types of fish.
The mercury will not be the same in all the fishes it will depend on various factors such as the species of fish, the location where it was caught, and the size of the fish.
In any case, in common, the mercury levels in angle can change broadly depending on different components such as the species of angle, the area where it was caught, and the measure of the angle.
A few angle species are known to construct up">to construct up more mercury in their tissues than others.
whereas a few angles caught in certain ranges may be uncovered to higher levels of mercury due to contamination or other environmental factors.
It is additionally worth noticing that the U.S. Food and Drug Administration (FDA) has issued rules on the greatest levels of mercury that are considered secure for utilization in angle.
The FDA exhorts that pregnant ladies, nursing moms, and youthful children ought to dodge devouring angles that are known to be tall in mercury, such as shark, swordfish, ruler mackerel, and tilefish.
Other sorts of angles that are lower in mercury, such as salmon, shrimp, pollock, and catfish, can be devoured in balance.
By and large, it is vital to be aware of the potential dangers of expanding fish which will contain tall levels of mercury, and to form educated choices approximately which sorts of angle to expend.
learn more about Food and Drug Administration (FDA)
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