The balance A for P dollars invested at a rate r for t years and compounded n times per year can be calculated using the formula: A = P (1 + r/n)^(n*t)
where:
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the number of years the money is invested
n = the number of times the interest is compounded per year
A = the total amount including principal and interest
To solve for the balance A, simply substitute the given values for P, r, t, and n into the formula and evaluate:
For example, let's say we invest $5000 at an annual interest rate of 4.5% for 3 years, compounded monthly (n=12).
P = $5000
r = 0.045 (4.5% expressed as a decimal)
t = 3 years
n = 12 (compounded monthly)
A = 5000 (1 + 0.045/12)^(12*3)
= 5000 (1.00375)^36
= $5,838.27
Therefore, balance A is $5,838.27 after 3 years of investing $5000 at an annual interest rate of 4.5%, compounded monthly.
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a quality control inspector has drawn a sample of 11 light bulbs from a recent production lot. suppose that 60% of the bulbs in the lot are defective. what is the standard deviation of the number of defective bulbs in the sample? round your answer to two decimal places.
The standard deviation of the number of defective bulbs in a sample of 11 light bulbs, where 60% are defective, is 1.53, rounded to two decimal places.
The number of defective bulbs in a sample of 11 light bulbs follows a binomial distribution with parameters n = 11 and p = 0.6, where n is the sample size and p is the probability of a defective bulb.
The standard deviation of the binomial distribution is given by the formula:
σ = sqrt(np(1-p))
where σ is the standard deviation, n is the sample size, p is the probability of success (defective bulb), and (1-p) is the probability of failure (non-defective bulb).
Substituting the values into the formula, we get:
σ = sqrt(11 * 0.6 * 0.4) = 1.53
Therefore, the standard deviation of the number of defective bulbs in the sample is 1.53, rounded to two decimal places.
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In ∆DEF, m∠D=42°, m∠E=63°, and EF=24 in. What is DE to the nearest tenth of an inch? *Hint: Law of Sines
DE is approximately 30.3 inches to the nearest tenth of an inch.
Describe Law of Sines?The Law of Sines is a trigonometric formula used to find unknown sides and angles in any triangle, whether it is acute, obtuse, or right-angled. It relates the lengths of the sides of a triangle to the sine of the opposite angle.
The formula for the Law of Sines is:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the opposite angles.
We can use the Law of Sines to solve for DE.
The Law of Sines states that for any triangle ABC,
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths opposite the angles A, B, and C, respectively.
In this case, we know that:
m∠D = 42°
m∠E = 63°
EF = 24 in.
Let x be the length of DE.
Then, applying the Law of Sines to ∆DEF, we have:
x/sin(63°) = 24/sin(42°)
Solving for x, we get:
x = (24*sin(63°))/sin(42°) ≈ 30.3
Therefore, DE is approximately 30.3 inches to the nearest tenth of an inch.
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the graph of f(x) to answer the question.
f(x) 18
16-
(-10, 14)
10-
6
(-6, 1.2)
-14-12-10-8-6-4-2
(-5, -1)
(10, 14)
(8, 6.8)
6 8 10 12 14
(5, -1)
(0, -6)
©2018 StrongMind. Created using GeoGebra.
What is the output off when x = -6?
Enter your answer as the numerical value shown in the graph
The output of the graphed function when x = 6 is given as follows:
y = 1.2.
How to define a quadratic function according to it's vertex?The coordinates of the vertex are (h,k), meaning that:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.Considering a leading coefficient a, the quadratic function is given as follows:
y = a(x - h)² + k.
The vertex is the turning point of a quadratic equation, hence it's coordinates for this problem are given as follows:
(0, -6).
Meaning that the function is defined as follows:
y = ax² - 6.
When x = 5, y = -1, hence the leading coefficient a is obtained as follows:
-1 = 25a - 6
a = 0.2.
Hence the function is:
y = 0.2x² - 6.
Hence the output when x = -6 is given as follows:
y = 0.2(-6)² - 6
y = 1.2.
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what is the value of x ?
Answer: 98.5 if this is wrong im sry.
Step-by-step explanation:
Each prism has the same volume. Which has the least surface area? Explain or show your
reasoning.
This means that the cube will have less surface area than the rectangular prism.
What is surface area?Surface area is a measure of the total exposed area of an object, or the total area of its two-dimensional surface. It is a measurement of the total exposed area of a three-dimensional object and is used to calculate the amount of material needed to cover a given area. Surface area is commonly used in physics, chemistry, engineering, and mathematics.
The prism with the least surface area of the same volume is the cube. This is because a cube has equal length, width, and height, allowing for all of the sides to be equal in size. This means that the area of each side is the same and all six sides of the cube are congruent. This creates the least amount of surface area for a given volume, as compared to any other prism. To illustrate this, take a cube and a rectangular prism with the same volume. The cube will have 6 smaller sides, while the rectangular prism will have 5 larger sides and 1 smaller side. This means that the cube will have less surface area than the rectangular prism.
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can sombody help me
Simplify. (4k2−12)−(6k2−3k−10)
Answer:
n
Step-by-step explanation:
n
Answer: -2k^2+3k-2
Step-by-step explanation:
distribute
add
combine like terms
rearrange
the radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.5 in/s. at what rate is the volume of the cone changing when the radius is 136 in. and the height is 110 in.?
When the radius is 136 in. and the height is 110 in., the volume of the cone is changing at a rate of 109.76 in³/s.
The volume of a right circular cone is given by the formula V = (1/3)*πr²h, where r is the radius and h is the height. Thus, when the radius is increasing at a rate of 1.6 in/s and the height is decreasing at a rate of 2.5 in/s, the rate of change of the volume (dV/dt) is given by:
dV/dt = (1/3)*π(1.6r + 2.5h)
Substituting r = 136 in. and h = 110 in., we get
dV/dt = (1/3)*π(216 + 275) = 109.76 in³/s
Therefore, when the radius is 136 in. and the height is 110 in., the volume of the cone is changing at a rate of 109.76 in³/s.
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a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 139 like snickers, 184 like twix, 181 like reese's peanut butter cups, 129 like snickers and twix, 109 like twix and reese's peanut butter cups, 71 like snickers and reese's peanut butter cups, and 70 like all three kinds of chocolate candy. how many students like at most 2 kinds of these chocolate candies?
433 students like at most two types of these chocolate candies.
A survey of 500 high school students was conducted to determine their favorite chocolate candy.
139 students liked snickers, 184 liked Twix, 181 liked Reese's Peanut Butter Cups, 129 liked Snickers and Twix, 109 liked Twix and Reese's Peanut Butter Cups, 71 liked Snickers and Reese's Peanut Butter Cups, and 70 liked all three types of chocolate candy. So, how many students like at most two types of these chocolate candies?
Step-by-step explanation:
If you use the Principle of Inclusion-Exclusion, you can figure out how many students enjoy two or fewer candies. The PIE formula is as follows:
n(Snickers U Twix U Reese's) = n(Snickers) + n(Twix) + n(Reese's) - n(Snickers ∩ Twix) - n(Snickers ∩ Reese's) - n(Twix ∩ Reese's) + n(Snickers ∩ Twix ∩ Reese's)n(Snickers U Twix U Reese's)
= 139 + 184 + 181 - 129 - 109 - 71 + 70
n(Snickers U Twix U Reese's) = 503
Students who liked two or fewer types of candies can be found by subtracting the number of people who liked all three from the total number of individuals in the study who like any one candy.
503 - 70 = 433 students
Therefore, 433 students like at most two types of these chocolate candies.
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The triangle shown is rotated about line m.
A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters.
What is the approximate base area of the resulting three-dimensional figure?
Area of a circle: A = πr2
38 sq. cm
113 sq. cm
201 sq. cm
314 sq. cm
Answer:
Step-by-step explanation:
When the triangle is rotated about the side with a length of 8 cm, it forms a cone with a base radius equal to 4 cm and height equal to 6 cm.
Using the formula for the volume of a cone, V = 1/3 * πr^2h, where r is the radius and h is the height, we can find the volume of the resulting solid:
V = 1/3 * π * 4^2 * 6
V ≈ 100.53 cubic centimeters
To find the approximate base area, we need to calculate the area of the circle with a radius of 4 cm (the base of the cone):
A = πr^2
A ≈ 50.27 sq. cm
Therefore, the approximate base area of the resulting three-dimensional figure is about 50.27 sq. cm.
So, the closest option available in the given choices is 38 sq. cm, but the correct answer based on calculations is approximately 50.27 sq. cm.
Answer:
I just did the quiz. Look below.
Step-by-step explanation:
A cylinder has a height of 20 feet. Its volume is 7,598.8 cubic feet. What is the radius of the cylinder?
Answer:
The radius is approximately 11 feet. More exactly 10.997 when rounded to the nearest thousandth.
Step-by-step explanation:
A cylinder has a height of 20 feet.
h = 20
Its volume is 7,598.8 cubic feet.
V = 7598.8
The formula for the volume of a cylinder is:
V = pi•r^2•h
Fill in what is given.
7598.8 = pi•r^2•20
Now there is only one variable in the equation, r and we can solve for it.
Divide both sides by 20pi.
120.938658 = r^2
We will have to square root both sides to find r.
10.997 = r
So the radius is 10.997 feet (to the nearest thousandth) or round to 11 feet.
On social issues, _____ think people should be liberated from the ways of the past and able to decide for themselves about how to live
On social issues, progressives think people should be liberated from the ways of the past and able to decide for themselves about how to live.
Progressivism is a political and social philosophy that emphasizes individual liberty, equality of opportunity, and the role of government in protecting citizens from social and economic abuses.Progressives believe that people should be free to make their own choices about how to live their lives and that the government should not interfere with their decisions. They believe that individuals should have the right to make choices regarding their personal lives, including decisions about marriage, sexuality, and reproductive health.Progressives also advocate for the protection of the environment and the promotion of sustainable practices.
They believe that it is the government's responsibility to protect the natural world and to ensure that future generations have access to clean air, water, and food.In addition, progressives advocate for social justice and the elimination of discrimination on the basis of race, gender, sexuality, and religion. They believe that everyone should have equal access to education, healthcare, and other basic services, regardless of their background or socioeconomic status.Overall, progressives believe in the power of individuals to make positive changes in their own lives and in the world around them. They believe that by working together and advocating for social and economic justice, we can create a better future for ourselves and for future generations.
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a bag contains 3 black ,4 red and 2 green balls if two balls are drawn at random what's the probability of getting exactly 2 balls
Answer:9 red
Step-by-step explanation:
which of the following statements is true? a. the sum of the squared deviations from the arithmetic mean is always zero b. the sum of the deviations from the arithmetic mean is always zero c. the standard deviation is always less than the variance d. the distance between the first and third quartiles is twice the distance between the first quartile and the median e. the arithmetic mean is always less than the geometric mean if two data sets have the same range: a. the distances from the smallest to largest observations in both sets will be the same b. the smallest and the largest observations are the same in both sets c. both sets will have the same mean d. both sets will have the same interquartile range
Suppose you were given the function F(x) = x4 - 2x³ + 3x² - 10x + 3 and
the factor (x - 2). What is the value of a?
The value of x =is 7.5.
What are function?Any subset of a Cartesian product is a relation.
For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."
These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.
A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).
A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.
As you can see from these definitions, every function is a relation from X to Y, but not vice versa .
F(x)=x^4-2x^3+3x^2 - ax+3
F(2) = 2^4-2(2)^3+3(2)^2 - a(2) +3
F(2) = 16 - 16 + 12 - 2a +3
F(2) = 15 - 2a
15 - 2a = 0
15 = 2a
a = 7.5
Hence, The value of x =is 7.5.
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sin 30° = 0.5 Using the equality above, copy and complete the following: sin-¹ (0.5) =
However, sin⁻¹ is defined to return an angle between -90° and 90°, so it returns the angle that is closest to 30° (which is 30° in this case).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.
Here,
If sin 30° = 0.5, then sin⁻¹(0.5) is the angle whose sine is 0.5. In other words, we are looking for the angle whose sine is 0.5. Since sin 30° = 0.5, we know that one possible answer is 30 degrees. However, there are other angles that also have a sine of 0.5. One way to find the other angles is to use the inverse sine function, denoted as sin⁻¹. This function takes a value between -1 and 1 as its input and returns an angle between -90° and 90° as its output. So, if we want to find sin⁻¹(0.5), we are asking: what angle has a sine of 0.5?
The answer is: sin⁻¹(0.5) = 30°.
Note that there are other angles that also have a sine of 0.5, such as 150°, 390°, etc.
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Complete question:
Using the equality above, copy and complete the following:
The value of sin⁻¹ (0.5) when sin 30° = 0.5.
jeff had $20. he spent 38 of his money on lunch. how much money does jeff have left? a. $12.50 b. $7.50 c. $8.25 d. $16.75
Answer:
$12.50
Step-by-step explanation:
62% would be left,so
[tex]\frac{62}{100}[/tex] × $20
=$12.50
Simon is making a frame for a photo that measures 6 inches by 8 inches. He wants the frame to be the same width all the way around and the total area of the frame and photo to be 120 square inches. Which quadratic equation represents the area of the picture and frame?
Answer: A
Step-by-step explanation:
if 10 friends are going to occupy 10 seats in shuttle on the way to the airport, how many different ways can they arrange themselves in the shuttle? provide your answer below:
If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.
Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.
Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800
Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.
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does the confidence interval suggest that the difference, if any, observed in this sample will also generalize to the larger population?
In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.
What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.
A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.
A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.
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suppose that each party must select a speaker and a vice speaker. how many ways are there for the speaker and vice speaker to be selected in the demonstrators party?
There are n x (n-1) number of ways for the speaker and vice speaker to be selected in the demonstrator's party, where n is the number of members in the party.
For the demonstrator's party, the first position of the speaker can be filled by any of the n members. After the speaker is chosen, there are n-1 members left to select from for the position of vice speaker. Therefore, the total number of ways the speaker and vice speaker can be selected is n x (n-1).
For example, if the demonstrator's party has 4 members, there are 4 choices for the speaker position. After the speaker is chosen, there are 3 choices left for the position of vice speaker. So, the total number of ways to select a speaker and vice speaker in the party is 4 x 3 = 12.
This formula can be applied to any size of the party to determine the total number of possible ways to select a speaker and vice speaker.
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after weeks of practice, mrs. carroll recalculated the free throw percentages of the team and found that the 3 players with the highest free throw percentage increased it by 4 points. if mrs. carroll recalculates the statistical measures, which of the measures would stay the same?
The measures such as overall team free throw percentage, the percentages of the other players, the median, the mean, and the shape of the distribution would remain the same.
The 3 players with the highest free throw percentage increased their percentage by 4 points, but all other statistical measures, such as overall team free throw percentage and the percentages of the other players, would stay the same.
The overall team free throw percentage is calculated by adding the percentages of all players and dividing the total by the number of players. Since the percentages of the other players remain the same, the overall team free throw percentage would remain unchanged.
Additionally, since only the 3 players with the highest percentages increased theirs, the median and mean of the free throw percentages would remain the same.
The increase in free throw percentage of the 3 players affects the free throw percentage distribution, but the shape of the distribution would remain the same.
That is, the distribution will still have the same range, but the 3 players with the highest free throw percentage would have a slightly higher percentage.
In conclusion, the only statistical measure that would change after Mrs. Carroll recalculates the free throw percentages of the team is the percentage of the 3 players with the highest free throw percentage, which would increase by 4 points.
All other measures, such as overall team free throw percentage, the percentages of the other players, the median, the mean, and the shape of the distribution would remain the same.
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two people start from the same point. one walks east at 9 mi/h and the other walks northeast at 8 mi/h. how fast is the distance between the people changing after 15 minutes? (round your answer to three decimal places.) mi/h
The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.
We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:
x = (9 mi/h) * (0.25 h) = 2.25 mi
y = (8 mi/h) * (0.25 h) = 2 mi
The distance between the two people is given by:
[tex]d = sqrt(x^2 + y^2)[/tex]
Taking the derivative with respect to time t, we get:
[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]
Substituting the values we found earlier, we get:
[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]
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i need help on all of this
Answer: 1 1/12
Step-by-step explanation:
so you would subtract 2-1=1
Then you do 1/3-1/4=1/12
The answer would be 1 1/12
UR WELCOME
I need this done for me please
The system of inequalities 3 and 4 have no solutions, while other solutions are computer below
Solving the system of inequalitiesThe given system of inequalities can be solved by graph
To solve a system of inequalities by graph, you will need to follow these steps:
Graph each inequality on the same coordinate plane.Identify the region that satisfies all of the inequalities. This region is the solution to the system of inequalities.If the region is bounded (i.e., has a finite area), then the solution is a set of points within the region. If the region is unbounded (i.e., has an infinite area), then the solution is a set of points that lie in a specific direction.The graphs are added as an attachment, and the some points in the system are as follows:
System 1: (0, 5)System 2: (5, -5)System 3 and 4: No solutionSystem 5, 6 and 7: (5,4)System 8: (0, 0)Read more about system of inequalities at
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if y = 2, then -3y(1-5)
[tex] \: [/tex]
Solution:-[tex] \rm{-3y( 1 - 5)}[/tex][tex] \: [/tex]
put the value of y = 2 in equation
[tex] \rm \: -3( 2 ) ( 1 - 5 )[/tex][tex] \: [/tex]
[tex] \rm \: -6 ( 1 - 5 )[/tex][tex] \: [/tex]
[tex] \rm \: -6 - 5[/tex][tex] \: [/tex]
[tex] \underline{ \rm{ \red{ \: \: -11 \: \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
Help me find the slope of the line for each one it’s ok if you don’t know all of them
Answer:
1. 1/2
2. -4/1
3. 1/1
Step-by-step explanation:
Answer:
1 y=2/1+2
2 y=.25x+3
3 y=x-2
Step-by-step explanation:
Step-by-step
y=mx+b
1. 2
2. .25
3. 1
suppose that 65% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection. consider groups of 17 trucks and let x be the number of trucks in a group that have passed the inspection. what is the probability that at least 9 but fewer than 12 trucks pass the inspection?
There is a 55.75% probability that at least 9 but fewer than 12 trucks pass the inspection out of a group of 17 trucks undergoing a brake inspection at the inspection facility with a pass rate of 65%.
We can utilize the binomial distribution formula to resolve this issue. Out of a group of 17 trucks, let X represent the proportion of trucks that pass the inspection, and let p represent the probability of passing the test, which is 0.65. A binomial distribution with n = 17 and p = 0.65 is then followed by X.
Calculating the cumulative chance of receiving 9, 10, or 11 trucks passing the inspection can help us determine the likelihood that at least 9 but fewer than 12 trucks will pass the test. The binomial distribution formula can be used for this as follows:
P(X=9, X=10, X=11) = P(X=9, X=10, X=11)
Using the binomial distribution formula, we can get the probabilities for each of the following:
[tex]P(X=9) = (17 pick 9) (17 choose 9) * 0.65^9 * 0.35^8[/tex] = [tex]0.1837 \sP(X=10)[/tex] = [tex](17 select 10) (17 choose 10) P(X=11)[/tex] = [tex](17 select 11) * 0.65*10 * 0.35*7[/tex] = [tex]0.2197 * 0.65*11 * 0.35*6 = 0.1541[/tex]
In light of this, the likelihood that at least 9 but not all 12 vehicles pass the inspection is:
P(9 ≤ X < 12) = 0.1837 + 0.2197 + 0.1541 = 0.5575
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Charlotte invested $730 in an account paying an interest rate of 3≥% compounded continuously. Khalil invested $730 in an account paying an interest rate of 33 % compounded daily. After 8 years, how much more money would Khalil have in his account than Charlotte, to the nearest dollar?
Answer:
Khalil would have $1,845 more than Charlotte, to the nearest dollar.
Step-by-step explanation:
Behaviors are executed when neurons from the ___ send instructions to muscles along a descending neural network called the ___, which decussates in the ____.
The corticospinal tracts carry information from the motor cortex, which is responsible for coordinating the movement of muscles, to the lower motor neurons. The extra-pyramidal tracts are made up of several types of neurons that play a role in modulating and fine-tuning the movement of muscles.
Neurons in the central nervous system (CNS) send instructions to muscles along a descending neural network called the descending motor pathways, which decussate in the medulla oblongata. This means that information from the brain travels down the spinal cord on both sides of the body, and crosses over to the opposite side at the medulla. The descending pathways start from the brainstem and motor cortex, and control the contraction of skeletal muscles, which are responsible for body movements.
The descending motor pathways are a series of neurons that connect the CNS to the muscles, transmitting the information required for voluntary body movements. Through the descending pathways, the brain can communicate with the muscles and control them. The pathways are divided into two parts, the corticospinal tracts and the extra-pyramidal tracts.
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an open rectangular gutter is made by turning up the sides of a piece of metal 20 in wide. the area of the cross section of the gutter is 50 in^2 find the depth of the gutter