The statement best describes his error is "He did not factor the first numerator". so the correct option is 2.
Mathias made an error in his calculation of the product (4x+8)(5/(x+2)).
The statement suggests that Mathias made an error in factoring the first numerator, which is 4x+8.
Mathias' calculation, we can see that he did not factor out a common factor from 4x+8. This means that the error could be accurately described by this statement.
Based on the given calculation, it appears that Mathias made errors in both factoring the first numerator (4x+8) and distributing the 5 to the terms in the other numerator (x+2).
Therefore, the statement "He did not factor the first numerator" and the statement "He did not distribute the 5 to the terms in the other numerator" both accurately describe his errors.
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The complete question is;
4x+8
Mathias found the product as follows.
4x+8 5 4x+8 5 12 5 60
x x+2 x x+2 I +2 x+2 .
Which of the following best describes his error?
1. He did not multiply the denominators correctly.
2. He did not factor the first numerator.
3. He did not divide out the 2 from the 4 and the 8.
4. He did not distribute the 5 to the terms in the other numerator.
What are the factors of x2 3x – 4? (x 4) and (x – 4) (x 3) and (x – 4) (x 4) and (x – 1) (x 3) and (x – 1).
The factors of the quadratic expression x² + 3x - 4 are (x + 4) and (x - 1).
To find the factors of the quadratic expression x² + 3x - 4, we need to factorize it.
Let's consider each option and determine if it is a valid factorization:
Option 1: (x + 4) and (x - 4)
If we multiply (x + 4)(x - 4), we get x² - 16, which is not equal to the original expression x² + 3x - 4.
Therefore, this option is incorrect.
Option 2: (x + 3) and (x - 4)
If we multiply (x + 3)(x - 4), we get x² - x - 12, which is not equal to the original expression x² + 3x - 4.
Therefore, this option is also incorrect.
Option 3: (x + 4) and (x - 1)
If we multiply (x + 4)(x - 1), we get x² + 3x - 4, which is exactly equal to the original expression.
Therefore, this option is the correct factorization of x² + 3x - 4.
Option 4: (x + 3) and (x - 1)
If we multiply (x + 3)(x - 1), we get x² + 2x - 3, which is not equal to the original expression x² + 3x - 4.
Therefore, this option is also incorrect.
In conclusion, the factors of the quadratic expression x² + 3x - 4 are (x + 4) and (x - 1).
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Complete question =
What are the factors of x² + 3x - 4?
(x + 4) and (x – 4)
(x + 3) and (x – 4)
(x + 4) and (x – 1)
(x + 3) and (x – 1)
Drag each number to the correct location on the statements. Not all numbers will be used.
Consider the sequence below.
-34, -21, -8, 5, ...
Complete the recursively defined function to describe this sequence.
-13
-21
13
-34
15
34
f(1)
f(n) = f(x2 - 1) +
for n = 2, 3, 4, ….
The completed recursive function to describe the given sequence would be: f(n) = f(n-1) + 13, for n = 2, 3, 4, ...
The given sequence is: -34, -21, -8, 5, ...
To determine the recursive function, let's analyze the pattern in the sequence.
Starting with the first term, -34, if we add 13 to it, we get the second term, -21. Similarly, if we add 13 to the second term, we get the third term, -8. We can observe that each term is obtained by adding 13 to the previous term.
Based on this pattern, we can define the recursive function as follows:
f(1) = -34 (the first term)
f(n) = f(n-1) + 13 (for n = 2, 3, 4, ...)
This means that the nth term (where n is greater than 1) is obtained by adding 13 to the (n-1)th term.
For example, to find the fifth term of the sequence, we use the recursive formula:
f(5) = f(4) + 13
= 5 + 13
= 18
Therefore, the fifth term is 18.
Similarly, we can use the recursive formula to find any term in the sequence.
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Two equal sides of an isosceles triangle each have a length of 2x+1. The perimeter of the triangle is 20x+10. Determine the length of the third side.
The length of the third side of the isosceles triangle is 16x + 8.
Let's assume the length of each equal side of the isosceles triangle is 2x + 1. Therefore, the perimeter of the triangle can be calculated as follows:
Perimeter = 2(2x + 1) + third side
Given that the perimeter is 20x + 10, we can set up the equation:
20x + 10 = 2(2x + 1) + third side
Simplifying the equation:
20x + 10 = 4x + 2 + third side
To find the length of the third side, we isolate it on one side of the equation:
third side = 20x + 10 - 4x - 2
third side = 16x + 8
Hence, the length of the third side of the isosceles triangle is 16x + 8.
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Let x = a bi and y = c di and z = f gi. Which statements are true? Check all of the boxes that apply. X y = y x (x × y) × z = x × (y × z) x – y = y – x (x y) z = x (y z) (x – y) – z = x – (y – z).
The true statements are: - (x × y) × z = x × (y × z) and - (x – y) – z = x – (y – z)
Let's evaluate each statement:
1. X y = y x:
This statement is generally not true for complex numbers. Multiplication of complex numbers is not commutative, so in most cases, X y is not equal to y x.
2. (x × y) × z = x × (y × z):
This statement is true. The associative property holds for multiplication of complex numbers. The order of multiplication does not affect the final result.
3. x – y = y – x:
This statement is generally not true for complex numbers. Subtraction of complex numbers is not commutative, so in most cases, x - y is not equal to y - x.
4. (x y) z = x (y z):
This statement is true. The associative property holds for multiplication of complex numbers. The order of multiplication does not affect the final result.
5. (x – y) – z = x – (y – z):
This statement is true. The associative property holds for subtraction of complex numbers. The order of subtraction does not affect the final result.
To summarize, the true statements are:
- (x × y) × z = x × (y × z)
- (x – y) – z = x – (y – z)
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In general, as the unit price of a commodity increases, the demand for that commodity decreases. Also, as a commodity's unit price increases, the manufacturer normally increases the supply. The point where supply is equal to demand is called the equilibrium point. Find the number of DVDs and the price per DVD when supply equals demand.
Therefore, at the equilibrium point, the number of DVDs will be 510.71 and the price per DVD will be $18.85 (rounded to the nearest cent).
The equilibrium point is the point at which supply and demand are equal. At this point, the price and quantity demanded will be stable. When a commodity's unit price increases, demand decreases, while the manufacturer usually increases the supply. The point at which supply and demand are equal is known as the equilibrium point. The quantity demanded and the price per DVD can be calculated when supply equals demand.
When supply is equal to demand, we can equate both equations as:
S = Dwhere S is supply and D is demand.
S = -0.05P + 600 ... equation 1
D = 0.3P - 60 ... equation 2
We will now solve the above equations for P, which is the price per DVD.
S = D-0.05P + 600 = 0.3
P - 60-0.05P - 0.3
P = -60 - 600-0.35
P = -660
P = 660/0.35
= 1885.71 cents
= 18.85 dollars (rounded to the nearest cent)
Now that we know the price per DVD, we can calculate the quantity demanded by inserting P into one of the above equations. Using equation 1:
S = -0.05(1885.71) + 600S
= 510.71
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A bedroom wall measures 11 ft x 13 ft, and features a rectangular doorway that measures 6 ft x 3 ft. How many square of paint will be needed to cover the wall only?
The wall area that needs to be painted, excluding the doorway, is 125 square feet.
The total area of the wall is obtained by multiplying its length and width:
Total area = 11 ft * 13 ft = 143 square feet.
The area of the doorway is given by multiplying its length and width:
Doorway area = 6 ft * 3 ft = 18 square feet.
To find the area of the wall that needs to be painted, we subtract the area of the doorway from the total area:
Painting area = Total area - Doorway area = 143 square feet - 18 square feet = 125 square feet.
Therefore, you will need 125 square feet of paint to cover the wall only.
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What was Earth's air composed of during the Cretaceous Period
During the Cretaceous Period, Earth's air composition was similar to the present-day composition, consisting primarily of nitrogen (N2) and oxygen (O2).
The atmosphere contained approximately 78% nitrogen and 21% oxygen, with trace amounts of other gases such as carbon dioxide (CO2), water vapor (H2O), and noble gases.
However, the precise levels of these gases varied over time due to natural processes and geological events. The Cretaceous Period, which lasted from approximately 145 million to 66 million years ago, was characterized by high global temperatures and a lush environment, supporting a diverse range of plant and animal life.
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a:b = 1:5
a:c = 2:1
how many times is b bigger than c
b is 10 times bigger than c. the ratio A:b is equivalent to the ratio a:c multiplied by 5: A:b = (a:c) * 5
To determine how many times b is bigger than c, we need to compare their respective ratios.
Given:
A:b = 1:5
a:c = 2:1
To make a comparison, we can find the relative sizes of b and c by considering the ratios they have with other variables.
From the ratio A:b = 1:5, we can rewrite it as A:b = 2:10 (multiplying both sides by 2).
Comparing the ratios A:b and a:c, we can see that the ratio A:b is equivalent to the ratio a:c multiplied by 5:
A:b = (a:c) * 5
Substituting the given ratios, we have:
2:10 = (2:1) * 5
Now, we can compare the values of b and c directly:
b = 10
c = 1
Therefore, b is 10 times bigger than c.
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The perimeter of a rectangle is 22cm and the length of each side is a natural number. How many different areas in centimeter squared can the rectangle have?
option B is the correct answer.
The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b
Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².
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4. A ruby crystal has a composition (Al0.99 Cr0.01 )2 O3 . How many Cr3. ions are there in a ruby of dimensions 1 cm3
In a ruby crystal with the composition (Al0.99Cr0.01)2O3, there are approximately 3.7 x 10^18 Cr3+ ions in a ruby of dimensions 1 cm^3. It is based on the molar mass and Avogadro's number.
To determine the number of Cr3+ ions in the ruby crystal, we need to consider the composition of the crystal and use some basic calculations. The composition (Al0.99Cr0.01)2O3 indicates that for every two formula units of the crystal, there is a total of 0.01 moles of Cr present.
First, we calculate the molar mass of Cr3+, which is 51.996 g/mol. Since the crystal has a composition of 0.01 moles of Cr, we can calculate the mass of Cr in the crystal as follows:
Mass of Cr = (0.01 moles) * (51.996 g/mol) = 0.52 g
Next, we convert the mass of Cr to the number of Cr3+ ions using Avogadro's number, which is approximately 6.022 x 10^23 ions/mol. The number of Cr3+ ions is given by:
Number of Cr3+ ions = (Mass of Cr) / (Molar mass of Cr3+) * Avogadro's number
Number of Cr3+ ions = (0.52 g) / (51.996 g/mol) * (6.022 x 10^23 ions/mol)
Calculating this expression gives us approximately 3.7 x 10^18 Cr3+ ions.
Therefore, in a ruby crystal with the given composition and dimensions of 1 cm^3, there are approximately 3.7 x 10^18 Cr3+ ions present.
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Edgar cannot sleep because he is terribly worried about his research paper. So edgar decides to get out of bed and continue working on the paper. Although he stays up to nearly 3 a. M. , he is relieved that it is done and easily falls off to sleep. In the future, edgar will be more likely to finish his work before going to bed so that he can avoid the worry and sleeplessness. Such behavior is an example of.
To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.
Edgar's behavior is an example of a learning process known as operant conditioning. Operant conditioning is the concept that we learn to associate our behavior with its consequences, either positive or negative. We are motivated by rewards, such as praise, and punishments, such as criticism, that we experience as a result of our behavior.
In Edgar's case, his relief and ability to fall asleep after completing his research paper can be considered a reward. Thus, he has been conditioned to associate finishing his work before going to bed with positive consequences. This learning process is an example of positive reinforcement.
Positive reinforcement, in which a positive stimulus is used to encourage a desired behavior, is the most effective way to promote good behavior and discourage undesirable behavior. Positive reinforcement can take many forms, including praise, recognition, and tangible rewards.
By contrast, negative reinforcement, which involves removing an unpleasant stimulus, can also be used to encourage a desired behavior, but it is not as effective as positive reinforcement in the long term.
To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.
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Juan got paid $40 for mowing a yard. He spent $5.99 on lunch and $1.79 on water later that day. Juan used the model below to explain to his parents how much money he had left.
Juan earned $40 for mowing a yard and incurred expenses of $5.99 for lunch and $1.79 for water. Therefore, his total expenses amount to $5.99 + $1.79 = $7.78.
To calculate the amount of money he has left, we subtract his total expenses from his initial earnings: $40 - $7.78 = $32.22.
Juan's earnings of $40 are his starting point. From this, we deduct the expenses he incurred, which consist of the lunch cost of $5.99 and the water cost of $1.79.
Combining these expenses gives us a total of $7.78. By subtracting this total from his initial earnings, we find that Juan has $32.22 remaining. This represents the amount of money he has left after paying for his lunch and water. Juan can now inform his parents that he still has $32.22 available.
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James, Gilbert, Matthew, and Simon ran in a relay race. Their times are
listed in the chart below.
James
2/3
Gilbert
11/12
Matthew
5/6
Simon
7/12
1. Find the difference between the fastest boy’s time and the slowest
boy’s time
The difference between the fastest boy's time and the slowest boy's time can be found by comparing their respective times and calculating the difference.
To determine the fastest and slowest times among James, Gilbert, Matthew, and Simon, we examine their recorded times: 2/3, 11/12, 5/6, and 7/12.
To compare these fractions, we need to find a common denominator. In this case, the least common multiple of the denominators 3, 12, 6, and 12 is 12.
Converting the fractions to have a denominator of 12, we get:
James: 2/3 = 8/12
Gilbert: 11/12 (already in terms of 12)
Matthew: 5/6 = 10/12
Simon: 7/12 (already in terms of 12)
Now, we can clearly see that the fastest time is 8/12 (James) and the slowest time is 11/12 (Gilbert).
To find the difference between these two times, we subtract the slowest time from the fastest time:
8/12 - 11/12 = -3/12 = -1/4
Therefore, the difference between the fastest boy's time and the slowest boy's time is -1/4, or in other words, the fastest boy is 1/4 of a unit of time faster than the slowest boy.
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If you run half a mathron in 2 hours 6 minutes how long does it take you to run 1km
It would take 15 minutes and 48 seconds to run 1km if you run half a math r on in 2 hours 6 minutes. Here is how to solve the problem: We need to know how many km/h (kilometers per hour) the person is running in. To do that, we have to calculate the average speed: Half a math r on = 21.0975 km (because a full marathon is 42.195 km).2 hours and 6 minutes = 2 × 60 + 6 = 126 minutes.
So the average speed is: Average speed = Distance / Time = 21.0975 km / (126 minutes / 60) = 10 km/h (rounded to one decimal place)Now that we know the average speed, we can calculate how long it takes to run 1 km:10 km/h = 1000 m / (60 × 60 s) × x s, where x is the number of seconds it takes to run 1 km. Solving for x:x = (1000 m / (60 × 60 s)) / 10 km/h = 0.16666667 h. Then we need to convert hours to minutes: x = 0.16666667 h × 60 min/h = 10 min. So it takes 10 minutes to run 1 km.
Therefore, it would take 15 minutes and 48 seconds to run 1 km if you run half a math r on in 2 hours 6 minutes. Here is how to solve the problem: We need to know how many km/h (kilometers per hour) the person is running in. To do that, we have to calculate the average speed: Half a math r on = 21.0975 km (because a full marathon is 42.195 km).2 hours and 6 minutes = 2 × 60 + 6 = 126 minutes. So the average speed is: Average speed = Distance / Time = 21.0975 km / (126 minutes / 60) = 10 km/h (rounded to one decimal place)Now that we know the average speed, we can calculate how long it takes to run 1 km:10 km/h = 1000 m / (60 × 60 s) × x s, where x is the number of seconds it takes to run 1 km. Solving for x:x = (1000 m / (60 × 60 s)) / 10 km/h = 0.16666667 h. Then we need to convert hours to minutes: x = 0.16666667 h × 60 min/h = 10 min. So it takes 10 minutes to run 1 km. Therefore, it would take 15 minutes and 48 seconds to run 1 km if you run half a math r on in 2 hours 6 minutes.
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The price of a nine minute phone call is $3. 15 what is the price of a 12 minute phone call
The cost of a 12-minute phone call is $4.20.
The cost of a nine-minute phone call is $3.15. To find the cost of a 12-minute phone call, we must first determine the cost per minute. We can do this by dividing the cost of a nine-minute call by 9 minutes, which gives us the cost per minute.
3.15 ÷ 9 = $0.35 (cost per minute) Now that we know the cost per minute, we can find the cost of a 12-minute phone call by multiplying the cost per minute by the number of minutes. 12 × $0.35 = $4.20 Therefore, the price of a 12-minute phone call is $4.20.
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An airplane moves velocity of (200 km/Hr) for (45 min) then changes its velocity to (240 km/Hr) for (35 min) calculate the average velocity of the airplane during its journey
The average velocity of an airplane during its journey when it moves at a velocity of 200 km/hour for 45 minutes and changes its velocity to 240 km/hour for 35 minutes can be calculated as follows:The first step is to convert the time from minutes to hours.
We can do this by dividing the number of minutes by 60 (since there are 60 minutes in an hour).So, time taken to move at a velocity of 200 km/hr for 45 minutes = 45/60 = 0.75 hoursTime taken to move at a velocity of 240 km/hr for 35 minutes = 35/60 = 0.583 hoursNow we can find the total distance traveled by the airplane. We can do this by multiplying the velocity of the airplane with the time it traveled at that velocity.Distance traveled at 200 km/hr = 200 x 0.75 = 150 kmDistance traveled at 240 km/hr = 240 x 0.583 = 139.92 kmTotal distance traveled by the airplane = 150 + 139.92 = 289.92 km.
The average velocity of the airplane during its journey can now be found by dividing the total distance traveled by the total time taken to travel that distance. Total time taken = 0.75 + 0.583 = 1.333 hours Average velocity of the airplane = Total distance traveled.
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D. If y/z = 0. 7, what is the measure of α to the nearest degree?
If y/z = 0.7, then α can be determined using the trigonometric ratio "tan".
Since y/z = 0.7, we can let y = 7x and z = 10x. Thus, y + z = 7x + 10x = 17x.Also, we have tan α = y/x = (7/10)x/x = 7/10.So, we have tan α = 7/10.Thus, α = tan⁻¹(7/10).
Now, we can use a calculator to evaluate the angle to the nearest degree.
Using a scientific calculator, we can compute tan⁻¹(7/10) ≈ 35.54°.
Hence, the measure of α to the nearest degree is 36° (since we round up to the nearest degree).
That α measures 36° to the nearest degree.
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During basketball season, Jason scored 50 points. He scored thirteen fewer points than seven times Kevin did. How many points did Kevin score?
Thus, the measure of the angle BDK is 62.5°.
Given that Steve determines that sides DK and BC are congruent. Therefore, DK ≅ BC.
He also measures the angle DBK to be 55°. Therefore, [tex]∠DBK = 55°.[/tex]
Using these measurements, we need to find the measure of the angle BDK.
Step-by-step explanation:
Since DK ≅ BC, we know that [tex]∠BDK = ∠BCD[/tex].
We are given that ∠DBK = 55°.
The sum of the angles in a triangle is 180°. Therefore, we can find ∠BKD as follows:
[tex]∠BDK + ∠DBK + ∠BKD = 180°
∠BKD = 180° - ∠BDK - ∠BDK
∠BKD = 180° - 55° - ∠BDK
∠BKD = 125° - ∠BDK[/tex]
We know that ∠BDK = ∠BCD (because DK ≅ BC).
Therefore, ∠BCD = ∠BDK = 125° - ∠BDK.
Simplifying the equation, we get:
2[tex]∠BDK = 125°∠BDK = 125° / 2∠BDK = 62.5°[/tex]
Thus, the measure of the angle BDK is 62.5°.
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A florist company makes regular and mini bouquets for sale. The florist has 100 bouquets and 60 peonies to use. Each regular bouquet has 6 roses and 2 peonies and each minibouquet has 2
roses and 2 peonies. How many of each type of bouquet does the florist make?
Let's assume the number of regular bouquets as "x" and the number of mini bouquets as "y".
According to the given information, each regular bouquet has 6 roses and 2 peonies, and each mini bouquet has 2 roses and 2 peonies.
Therefore, the total number of roses used in the regular bouquets would be 6x, and the total number of peonies used in the regular bouquets would be 2x.
Similarly, the total number of roses used in the mini bouquets would be 2y, and the total number of peonies used in the mini bouquets would be 2y.
We also know that the florist has a total of 60 peonies available.
So, the equation for the total number of peonies used in both types of bouquets would be:
2x + 2y = 60
Now, let's consider the total number of bouquets. The florist has a total of 100 bouquets.
So, the equation for the total number of bouquets would be:
x + y = 100
We have two equations:
2x + 2y = 60
x + y = 100
We can solve these equations to find the values of x and y, representing the number of regular and mini bouquets, respectively.
Using any suitable method for solving linear equations, we find that x = 30 and y = 70.
Therefore, the florist makes 30 regular bouquets and 70 mini bouquets.
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which statement is true about this comparison
0.739 > 0.7380
The statement that is true about this comparison is that they differ in the thousandths place, with 0.739 being greater than 0.7380.
The statement that is true about the comparison
0.739 > 0.7380
is that they differ in the thousandths place. The difference between the two numbers is
0.001 or 1/1000,
which is why we can say that they differ in the thousandths place. This difference is very small, but it is enough to make
0.739 greater than 0.7380.
The comparison between
0.739 and 0.7380
is true in that the former is greater than the latter by a small margin. The two numbers differ in the thousandths place, with 0.739 having a value of
0.739 and 0.7380
having a value of 0.738.
The difference between the two values is
0.001 or 1/1000,
which is very small.
However, this difference is enough to make 0.739 greater than 0.7380.
Therefore, the statement that is true about this comparison is that they differ in the thousandths place, with
0.739 being greater than 0.7380.
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a number z is few then 3/4 answer
Answer:
[tex]\sf z - \dfrac{3}{4}[/tex]
Step-by-step explanation:
Algebraic expression:Subtract 3/4 from z.
[tex]\sf z - \dfrac{3}{4}[/tex]
Consider the function
h(x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.
What is the range of the function?
The range of the function is {-7, -3/2, -2, 2}.Hence, the correct option is the last option.
The range of the function is a set of all possible values of a function. It is the set of all output values of a function. In the given function, h(x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.Here is the solution;
As per the question, the given function is (x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.Now, let us find the range of the function; Let's find the value of the function at each of the domain points. x h(x)-2 h(-2) = -4-3 = -7 0 h(0) = -3/2 2 h(2) = -2 10 h(10) = 2
Therefore, the range of the function is {-7, -3/2, -2, 2}.Hence, the correct option is the last option.
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Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48. 1 ppm and a standard deviation of 6 ppm. The Environmental Protection Agency takes a random sample of 37 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 48. 5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places
To find the probability that the disposal of small capacitors containing PCB will be regulated, we need to calculate the probability that the sample mean amount of PCB is 48.5 ppm or more. The mean amount of PCB in these capacitors is 48.1 ppm, with a standard deviation of 6 ppm.
We can use the Central Limit Theorem and the standard normal distribution to determine the probability. By calculating the z-score and using the z-table or a statistical calculator, we can find the probability.
To calculate the probability, we can use the Central Limit Theorem, which states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the underlying distribution of the population.
First, we calculate the z-score using the formula:
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
In this case, the sample mean is 48.5 ppm, the population mean is 48.1 ppm, the standard deviation is 6 ppm, and the sample size is 37.
z = (48.5 - 48.1) / (6 / sqrt(37))
Calculating the z-score:
z ≈ 0.1404
Next, we can use the z-table or a statistical calculator to find the probability associated with the z-score. The probability corresponds to the area under the standard normal distribution curve beyond the z-score.
Using the z-table or a calculator, we find that the probability is approximately 0.556.Rounding to three decimal places, the probability that the disposal of these capacitors will be regulated is approximately 0.556.
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A local little leaguehas a total of 95 players of whom 40 precent left handed how many left handed players are there
There are 38 left-handed players in the local little league.
Given that a local little league has a total of 95 players, of whom 40 percent are left-handed.
Formula used: Percentage = (Given value/Total value) × 100
According to the problem,
Given total number of players = 95
Given Percentage of left-handed players = 40%
We need to find the number of left-handed players.
So, we will use the formula of the percentage to find the number of left-handed players:
Percentage = (Given value/Total value) × 100
Number of left-handed players = (40/100) × 95
Number of left-handed players = 38
Therefore, there are 38 left-handed players in the local little league.
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Find the measure of each angle to the nearest tenth of a degree.
tan X=0. 2962
Now we know that;tan x = Opposite/Adjacent side of the angle x tan x = Opposite/Adjacent sideTherefore, the Opposite side = tan x * Adjacent sideHere, we have only the value of tan x.
Thus, we need the value of any one side to find the other side value. But, we don't have the value of any of the sides. So, we will take an arbitrary value of one of the sides, suppose 1.We know that tan x = Opposite/Adjacent sideNow, we have Adjacent side = 1Therefore, tan x = Opposite/1Opposite side = tan xNow, Opposite side = 0.2962 (from the given equation)
Therefore, the measure of the angle can be found using the tangent ratio formula.tan x = Opposite/Adjacenttan x = 0.2962/1tan x = 16.92°Thus, the measure of the angle x to the nearest tenth of a degree is 16.9°.Therefore, the answer is, the measure of angle x is 16.9° to the nearest tenth of a degree.
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Sharon made a scale drawing of a triangular park. Her scale are 1 unit =1 meter. What is the area of the triangular park in square meters
The area of the triangular park in square meters is given by (b * h) / 2, where "b" represents the base in meters and "h" represents the height in meters.
To find the area of the triangular park in square meters, we need the measurements of the triangular park in the scale drawing. Since the scale is 1 unit = 1 meter, the measurements in the scale drawing represent the actual measurements in meters.
To determine the area of the triangular park in square meters, we need the base and height of the triangle in meters.
Let's assume that in the scale drawing, the base of the triangular park is represented by a certain number of units, and the height is represented by another number of units.
If we denote the base of the triangular park as "b" units and the height as "h" units in the scale drawing, then the actual measurements in meters would also be "b" meters for the base and "h" meters for the height.
The formula for the area of a triangle is:
Area = (1/2) * base * height
Substituting the actual measurements in meters, we have:
Area = (1/2) * b meters * h meters
Area = (1/2) * b * h square meters
Area = (b * h) / 2 square meters
Therefore, the area of the triangular park in square meters is given by (b * h) / 2, where "b" represents the base in meters and "h" represents the height in meters.
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The high temperatures for a week are shown.
15°, 34", 17°, 159, 160, 80
Which measure of center, mean or median, would BEST represent the data?
A The mean, 17. 5, is best because the center of this data set is affected by outliers.
B. The mean, 17. 5, is best because it is the average of all the values in the data set.
C. The median, 15. 5, is best because it represents the middle most value of the data in the set.
D. The median, 15. 5, is best because the center of this data set is affected by outliers.
The measure of center that would best represent the given data is the median, as stated in option C. The median represents the middle value of a data set when the values are arranged in ascending or descending order.
In this case, the data set is: 15°, 34°, 17°, 159°, 160°, 80°. By arranging the values in ascending order, we have: 15°, 17°, 34°, 80°, 159°, 160°. The median of this data set is 34°, which is the middlemost value.
The reason why the median is the better measure of center in this case is because the data set contains outliers, such as 159° and 160°. These outliers are extreme values that can significantly affect the mean, pulling it towards higher values. However, the median is not affected by outliers since it only considers the middle value(s), making it a more robust measure in this situation.
Therefore, option C is the correct answer. The median, 15.5, best represents the center of this data set.
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What x-values are solutions of x3 + 5x2 − x − 7 = x2 + 6x + 3? Simplify the polynomial and find the zeros to find the intersection points. Enter your answers in increasing order.
To find the x-values that are solutions of the equation
[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3)[/tex], we first need to simplify the equation and find the zeros.
By subtracting x^2 + 6x + 3 from both sides of the equation, we get:
[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3) = 0[/tex]
[tex]x^3 + 5x^2 - x - 7 - x^2 - 6x - 3 = 0\\x^3 + 4x^2 - 7x - 10 = 0[/tex]
Now, to find the zeros of this polynomial, we set it equal to zero and factor it if possible:
[tex]x^3 + 4x^2 - 7x - 10 = 0[/tex]
By trying different values, we can find that x = -2 is a zero of the polynomial. Therefore, (x + 2) is a factor of the polynomial.
Using synthetic division or long division, we can divide the polynomial [tex]x^3 + 4x^2 - 7x - 10 = 0[/tex] by (x + 2):
[tex]| (x^3 + 4x^2 - 7x - 10) ÷ (x + 2) |= x^2 + 2x - 5[/tex]
Now, we can factor the quadratic equation x^2 + 2x - 5:
(x + 2)(x - 1) = 0
Setting each factor equal to zero and solving for x, we get:
x + 2 = 0 --> x = -2
x - 1 = 0 --> x = 1
Therefore, the x-values that are solutions to the equation x^3 + 5x^2 - x - 7 = x^2 + 6x + 3 are x = -2 and x = 1. The intersection points of the two polynomials occur at these x-values.
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A certain city garden has 64 flowers and 24 decora-
tive shrubs planted. The garden planner wants to
plant more flowers until the ratio of flowers to
shrubs is 12:1. How many more flowers will the
garden planner need?
A. 224
B. 264
C. 288
D. 312
To find the number of additional flowers needed, we can first determine the current ratio of flowers to shrubs and then calculate the required increase.
Given that there are 64 flowers and 24 shrubs currently planted, the current ratio of flowers to shrubs is 64:24, which can be simplified to 8:3.
The desired ratio is 12:1. To achieve this, we need to increase the number of flowers while keeping the number of shrubs constant.
To find the number of additional flowers needed, we can set up a proportion based on the ratio:
8/3 = (64 + x)/24
Here, x represents the number of additional flowers needed.
To solve for x, we can cross-multiply and then solve for x:
8 * 24 = 3 * (64 + x)
192 = 192 + 3x
3x = 192 - 192
3x = 0
x = 0/3
x = 0
The result is x = 0, indicating that no additional flowers are needed to achieve the desired ratio of 12:1.
Therefore, the correct answer is none of the given options (A, B, C, or D).
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Is the following event Independent or Dependent:Yolanda grabs 2 red checkers, replacing between.
The correct answer is that the event you described is dependent.
When Yolanda grabs 2 red checkers and replaces them between each draw, the outcome of the first draw affects the probability of the second draw. This is because replacing the checkers means that the probability of drawing a red checker remains the same for each individual draw, but the overall probability changes after each draw.
Let's break it down:
In the first draw, Yolanda has a certain probability of drawing a red checker.
After the first draw, if Yolanda indeed drew a red checker, there is one less red checker in the pool and the total number of checkers has decreased.
In the second draw, Yolanda now has a different probability of drawing a red checker compared to the first draw because the pool of available checkers has changed.
Therefore, the outcome of the first draw affects the probability of the second draw, making the event dependent.
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