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Answer:
The thrid one
Step-by-step explanation:
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Dominic's grandfather is teaching him how to make cornbread. Dominic pours it into the pan shown. Dominic's grandfather tell him he should stop when it is 1/2 inch from the top, to allow room for the cornbread to rise in the oven. what is the volume?
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Answer:
Step-by-step explanation:
Answer:
115.5
Step-by-step explanation:
did the iready
the of a node is the height of its right subtree minus the height of its left subtree. question 24 options: a) balance factor b) depth c) length d) degree
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a) balance factor
The balance factor of a node in a binary tree is defined as the height of its right subtree minus the height of its left subtree. It is commonly used in balance algorithms for maintaining balanced binary trees, such as AVL trees.
What is balance factor?
The balance factor is a keyword that represents the measure of the height difference between the left and right subtrees of a node in a binary tree. It is calculated by subtracting the height of the left subtree from the height of the right subtree
Certainly! In a binary tree, the balance factor of a node is a measure of the difference in height between its right subtree and left subtree. It is calculated by subtracting the height of the left subtree from the height of the right subtree.
The balance factor helps in determining the balance or imbalance of a node in a binary tree. It is used as a criterion for tree balancing algorithms, such as the AVL tree. By checking the balance factor of each node, these algorithms ensure that the tree remains balanced and avoids degeneration into a skewed or unbalanced structure.
A balance factor of 0 indicates that the heights of the left and right subtrees are equal, meaning the node is balanced. A positive balance factor means the right subtree is taller than the left subtree, indicating a right-heavy or right-skewed tree. Conversely, a negative balance factor implies the left subtree is taller, indicating a left-heavy or left-skewed tree.
By maintaining balanced trees using the balance factor, efficient search and retrieval operations can be achieved, ensuring optimal performance in various tree-based data structures.
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in an election, suppose that 45% of voters support a new tax on fast food. if we poll 105 of these voters at random, the probability distribution for the proportion of the polled voters that support a new tax on fast food can be modeled by the normal distibution pictured below. complete the boxes accurate to two decimal places
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The normal distribution curve represents the probability distribution for the proportion of voters who support the new tax on fast food when polling 105 voters at random.
Since the proportion of voters who support a new tax on fast food follows a normal distribution, we can model it using the normal distribution curve. Given that 45% of voters support the tax, the mean proportion of voters who support the tax is 0.45.
The standard deviation can be calculated using the formula:
Standard Deviation = sqrt[(p * (1 - p)) / n]
where p is the proportion of voters who support the tax (0.45) and n is the sample size (105).
Substituting the values, we get:
Standard Deviation = sqrt[(0.45 * (1 - 0.45)) / 105] ≈ 0.0497 (rounded to four decimal places)
Now, we can complete the boxes:
Mean = 0.45 (given)
Standard Deviation = 0.0497 (calculated)
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a dance cd has 12 songs on it - 9 are slow, and 3 are fast. when the dj at a dance plays a song it is not played again. all songs from the cd are played at random. what is the probability that the first two songs played are slow songs?
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The probability of the first two songs played being slow songs is approximately 0.5454.
The probability that the first two songs played are slow songs can be calculated by dividing the number of favorable outcomes (two slow songs) by the total number of possible outcomes.
Since there are 9 slow songs out of 12 total songs, the probability of selecting a slow song as the first song is 9/12. After the first slow song is played, there are 8 slow songs left out of the remaining 11 songs. Therefore, the probability of selecting a slow song as the second song, given that the first song was slow, is 8/11.
To find the probability of both events occurring (selecting a slow song first and then selecting a slow song second), we multiply the probabilities of each event:
P(First song slow) * P(Second song slow | First song slow) = (9/12) * (8/11) = 72/132 = 0.5454 (rounded to four decimal places).
The probability that the first two songs played are slow songs is 0.5454.
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A ball of radius r rolls on the inside of a track of radius R (see figure below). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping? (Answer: V ,(Ro-ro)) 90°
Answers
The speed of the ball when it reaches the lowest point of the track is V = sqrt(2g(R-r))
The potential energy of the ball at the starting position is equal to its kinetic energy at the lowest point of the track. Therefore, we can use the conservation of energy principle to solve for the speed of the ball at the lowest point of the track.
The potential energy of the ball at the starting position is mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the starting position above the lowest point of the track. Since the ball starts from rest, its initial kinetic energy is zero.
At the lowest point of the track, the ball has both translational and rotational kinetic energy. The translational kinetic energy is equal to (1/2)mv^2, where v is the speed of the ball at the lowest point. The rotational kinetic energy is equal to (1/2)Iω^2, where I is the moment of inertia of the ball and ω is its angular velocity.
Since the ball is rolling without slipping, the speed of the ball is related to its angular velocity by the equation v = ωR, where R is the radius of the track. The moment of inertia of the ball is (2/5)mr^2, where r is the radius of the ball.
Setting the initial potential energy equal to the final kinetic energy, we have:
mgh = (1/2)mv^2 + (1/2)(2/5)mr^2(v/R)^2
Solving for v, we get:
v = sqrt((10/7)g(R-h))
Substituting the values given in the problem, we get:
v = sqrt((10/7)(9.8 m/s^2)(2 - 1)) = 6.08 m/s
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Toasters again In a batch of 10,000 toasters, what are the chances that fewer than 450 need to be returned?
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The number of trials is n = 10,000 and we want to find the probability of having fewer than 450 faulty toasters, which is equivalent to finding the probability of having 0, 1, 2, ..., 449 faulty toasters.
Using a binomial distribution calculator or software, we can find that the probability of having 0 faulty toasters is about 0.0379, the probability of having 1 faulty toaster is about 0.1584, the probability of having 2 faulty toasters is about 0.3095, and so on. If we add up all these probabilities for 0 to 449 faulty toasters, we get a total probability of about 0.9999.
Therefore, the probability of having fewer than 450 faulty toasters is about 0.9999 or 99.99%. This means that it is highly likely that fewer than 450 toasters need to be returned in a batch of 10,000.
I'll provide a general explanation using the given terms:
1. First, determine the defect or return rate. Let's assume it is given as "p" (e.g., 0.05 would represent a 5% defect rate).
2. Next, find the expected number of defective toasters in the batch by multiplying the total number of toasters (10,000) by the defect rate "p": Expected_Defects = 10,000 * p.
3. Then, use a statistical method, such as the binomial distribution or normal approximation, to calculate the probability of having fewer than 450 defective toasters. This will involve finding the cumulative probability (sum of probabilities) for 0 to 449 defective toasters.
4. Finally, the resulting probability will represent the chances that fewer than 450 toasters need to be returned in the batch of 10,000.
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URGENT!!
In words I need the answer to this for my geometry class
Create a conditional and it’s converse where the conditional is TRUE but the converse is False.
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The conditional statement with a false converse is :
Conditional: If an animal is a dog, then it is a mammal.Converse: If an animal is a mammal, then it is a dog.How to write the statement ?A conditional statement consists of an if-then structure, and its converse can be formed by swapping the hypothesis and conclusion. To illustrate, "If A, then B," becomes "If B, then A" in converse form. Our aim is to devise a truthful condition while simultaneously ensuring that its converse yields a falsehood.
Thus, for instance, we may use the fact that all dogs are classified as mammals to offer a valid conditional statement; regrettably, such a proposition fails under converse statement, since not all mammals share this canine trait. Consider cats, elephants, and whales - they render our converse false.
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Find the volume of a right circular cone that has a height of 5.9 in and a base with a
diameter of 11.2 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
in
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attempt 1 out of 2
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The volume of the given cone is 193.65 in³.
Given is a cone of height 5.9 in and radius of 5.6 in, we need to find the volume of the cone,
V(cone) = π × radius² × height / 3
= 3.14 × 5.6² × 5.9 / 3
= 193.65 in³
Hence the volume of the given cone is 193.65 in³.
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A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively.
a. Draw the density function.
b. Determine P(35 < X < 45).
c. Draw the density function including the calculation of the probability in part (b).
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```
|
|
|
|
| ___________
| | |
| | |
|_____|___________|
20 35 60
```
b. To find P(35 < X < 45), we need to find the area of the rectangle between x = 35 and x = 45. The height of the rectangle is 1/40 and the width is 45 - 35 = 10. Therefore, the area is:
P(35 < X < 45) = (1/40) * 10 = 1/4
c. Here is the density function with the shaded area representing the probability from part (b):
```
|
|
|
|
| ___________
| | |
| | |
|_____|___________|
20 35 60
|
|
|
|
| ___________
| | |
| | |
|_____|___________|
35 45
```
The shaded area represents the probability P(35 < X < 45), which is 1/4.
If the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], what is nullity(A)?
Answers
If the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], then the nullity of A is 0, meaning there are no linearly independent vectors that satisfy the equation Ax = 0.
To determine the nullity of matrix A, we need to find the number of linearly independent vectors that satisfy the equation Ax = 0. Since the set {u1, u2, u3} spans R3, we know that any vector in R3 can be expressed as a linear combination of these three vectors. Thus, the equation Ax = 0 has a nontrivial solution if and only if the three vectors u1, u2, and u3 are linearly dependent. If they are linearly dependent, then one of them can be expressed as a linear combination of the other two, and we can eliminate that vector from the matrix A. This means that the nullity of A is equal to the number of linearly dependent vectors in the set {u1, u2, u3}. Since the set spans R3, it must contain three linearly independent vectors, and therefore the nullity of A is 0.
In summary, if the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], then the nullity of A is 0, meaning there are no linearly independent vectors that satisfy the equation Ax = 0.
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Find the volume of the solid enclosed by the paraboloid z = 2 + x2 + (y - 2)2 and the planes z = 1, x = ?2, x = 2, y = 0, and y = 3.
Answers
Main Answer:The volume of the solid enclosed by the paraboloid and the planes is 18.67 cubic units.
Supporting Question and Answer:
How do we calculate the volume of a solid bounded by surfaces using triple integration?
To calculate the volume of a solid bounded by surfaces using triple integration, we set up a triple integral with the integrand equal to 1, representing the infinitesimal volume element. The bounds of integration are determined by the equations defining the surfaces that enclose the solid. By evaluating the triple integral over the specified region, we can find the volume of the solid.
Body of the Solution: To find the volume of the solid enclosed by the paraboloid z = 2 + x^2 + (y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 3, we can set up a triple integral in the given region.
To find the volume,using the triple integral:
V = ∫∫∫ R (1) dz dy dx
where R is the region bounded by the given planes and the paraboloid.
The bounds of integration for x are -2 to 2, for y are 0 to 3, and for z are the lower bound function z = 1 and the upper bound function z = 2 + x^2 + (y - 2)^2.
Setting up the triple integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 ∫ from z = 1 to 2 + x^2 + (y - 2)^2 (1) dz dy dx
Integrating the innermost integral with respect to z:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [(2 + x^2 + (y - 2)^2) - 1] dy dx
Simplifying the expression inside the integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [x^2 + (y - 2)^2 + 1] dy dx
Integrating the inner integral with respect to y:
V = ∫ from x = -2 to 2 [x^2(y) + ((y - 2)^3)/3 + y] evaluated from y = 0 to 3 dx
Substituting the limits of integration for y:
V = ∫ from x = -2 to 2 [x^2(3) + (3 - 2)^3/3 + 3 - (x^2(0) + (0 - 2)^3/3 + 0)] dx
Simplifying further:
V = ∫ from x = -2 to 2 [3x^2 +2/3] dx
Integrating the final integral with respect to x:
V = [(x^3) + (2/3)x] evaluated from x = -2 to 2
Evaluating the expression at the limits:
V = [(2^3) +(2/3) 2] - [((-2)^3) + (2/3)(-2)]
V = (8 +4/3) - (-8 - 4/3)
V = 16+8/3
V =56/3
Final Answer:Therefore, the volume of the solid enclosed by the paraboloid and the given planes is 56/3 cubic units.
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The volume of the solid enclosed by the paraboloid and the planes is 18.67 cubic units.
How do we calculate the volume of a solid bounded by surfaces using triple integration?To calculate the volume of a solid bounded by surfaces using triple integration, we set up a triple integral with the integrand equal to 1, representing the infinitesimal volume element. The bounds of integration are determined by the equations defining the surfaces that enclose the solid. By evaluating the triple integral over the specified region, we can find the volume of the solid.
Body of the Solution: To find the volume of the solid enclosed by the paraboloid z = 2 + x^2 + (y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 3, we can set up a triple integral in the given region.
To find the volume,using the triple integral:
V = ∫∫∫ R (1) dz dy dx
where R is the region bounded by the given planes and the paraboloid.
The bounds of integration for x are -2 to 2, for y are 0 to 3, and for z are the lower bound function z = 1 and the upper bound function z = 2 + x^2 + (y - 2)^2.
Setting up the triple integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 ∫ from z = 1 to 2 + x^2 + (y - 2)^2 (1) dz dy dx
Integrating the innermost integral with respect to z:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [(2 + x^2 + (y - 2)^2) - 1] dy dx
Simplifying the expression inside the integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [x^2 + (y - 2)^2 + 1] dy dx
Integrating the inner integral with respect to y:
V = ∫ from x = -2 to 2 [x^2(y) + ((y - 2)^3)/3 + y] evaluated from y = 0 to 3 dx
Substituting the limits of integration for y:
V = ∫ from x = -2 to 2 [x^2(3) + (3 - 2)^3/3 + 3 - (x^2(0) + (0 - 2)^3/3 + 0)] dx
Simplifying further:
V = ∫ from x = -2 to 2 [3x^2 +2/3] dx
Integrating the final integral with respect to x:
V = [(x^3) + (2/3)x] evaluated from x = -2 to 2
Evaluating the expression at the limits:
V = [(2^3) +(2/3) 2] - [((-2)^3) + (2/3)(-2)]
V = (8 +4/3) - (-8 - 4/3)
V = 16+8/3
V =56/3
Therefore, the volume of the solid enclosed by the paraboloid and the given planes is 56/3 cubic units.
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what will be the shape of the sampling distribution of the difference in sample proportions, and why?
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The sampling distribution of the difference in sample proportions will be approximately normal, provided that the sample sizes are large enough and certain conditions are met.
The shape of the sampling distribution can be determined by the Central Limit Theorem (CLT), which states that when sampling from a population, the sampling distribution of a sample statistic approaches a normal distribution as the sample size increases. In the case of the difference in sample proportions, the CLT applies if the sample sizes are large enough for each proportion and if the samples are independent.
When these conditions are met, the sampling distribution of the difference in sample proportions will be approximately normal. The exact shape of the distribution will depend on the population proportions and the sample sizes, but it will be symmetric and bell-shaped. This allows for the use of statistical tests and confidence intervals based on the normal distribution to make inferences about the difference in proportions.
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the single factor anova tests for mean differences between 3 or more groups by comparing ____
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The single factor ANOVA tests for mean differences between 3 or more groups by comparing the variance within groups to the variance between groups.
It examines whether the differences between the means of the groups are greater than what would be expected due to chance. The ANOVA test uses the F-statistic to calculate the ratio of the variance between groups to the variance within groups. If the F-statistic is significant, it indicates that there is a significant difference in the means between the groups, and post-hoc tests can be conducted to determine which specific groups differ significantly. In conclusion, the single factor ANOVA tests are an essential statistical tool for determining whether there are significant differences between multiple groups and are used widely in various fields of research.
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Pepe tiene 2 veces la edad de su hermano. Hace 4 años tenía cuatro veces la edad de su hermano, que edad tiene cada uno?
Answers
The solution is: the present age of the man is 40 years and the present age of the son is 8 years.
Let us assume the age of the son now = x
Then
The age of the man now = 5x
Now we have to calculate the age of the son and father 9 years ago
Age of the son 4 years ago = x - 4
Age of the man 4 years ago = 5x - 4
Then
5x - 4 = 9(x - 4)
5x - 4 = 9x - 36
5x - 9x = -36 + 4
- 4x = - 32
MUltiplying both sides of the equation by -1 we get
4x = 32
x = 32/4
= 8
So the present age of the son is 8 years
Present age of the man = 5x
= 5 * 8
= 40 years
So the present age of the man is 40 years and the present age of the son is 8 years.
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complete question:
A man is five times as old as his son. Four years ago, he was nine times as old. Find their present ages.
let f(x)=x^3, g(x)=sqrt x, and h(x)=x/3. Find each of the following.
h(f(g(1/2)))
h(f(g(x)))
Answers
The value of the functions are;
h(f(g(1/2))) = (√1/2)³/3
h(f(g(x))) = = (√x)³/3
How to determine the valueIt is important to note that a function is an equation that shows the relationship between two variables
From the information given, we have that;
f(x) = x³
g(x) = √x
h(x) = x/3
To determine the composite function, we need to substitute the value of one function as the value of x in the other, we have that
f(g(1/2) =
g(1/2) = √1/2
Substitute the value
f(g(1/2) = (√1/2)³
Now, substitute the value as x in h(x)
h(f(g(1/2))) = (√1/2)³/3
f(g(x)) = (√x)³
Then, h(f(g(x))) = = (√x)³/3
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Use the Standard Normal Distribution to answer the
following problems:
A normal distribution has a mean of 30 and a standard
deviation of 4. Find the probability that a randomly
selected x-value from the distribution is in the given
interval. Represent your answer as a decimal to the
nearest ten-thousandth place.
Between 24 and 32
Between 31 and 37
Between 20 and 35
At least 27
At least 19
At most 29
Answers
The probabilities of the normal distribution are:
Between 24 and 32 is 0.7745.
Between 31 and 37 is 0.2580.
Between 20 and 35 is 0.8962.
At least 27 is 0.7734.
At least 19 is 0.9970.
At most 29 is 0.4013.
We have,
To find the probabilities using the standard normal distribution, we need to standardize the given values using the formula z = (x - μ) / σ, where z is the standardized value, x is the given value, μ is the mean, and σ is the standard deviation.
Between 24 and 32:
Standardized value for 24: z = (24 - 30) / 4 = -1.5
Standardized value for 32: z = (32 - 30) / 4 = 0.5
Using a standard normal distribution table or a calculator, we can find the corresponding probabilities:
P(24 < x < 32) = P(-1.5 < z < 0.5)
Between 31 and 37:
Standardized value for 31: z = (31 - 30) / 4 = 0.25
Standardized value for 37: z = (37 - 30) / 4 = 1.75
P(31 < x < 37) = P(0.25 < z < 1.75)
Between 20 and 35:
Standardized value for 20: z = (20 - 30) / 4 = -2.5
Standardized value for 35: z = (35 - 30) / 4 = 1.25
P(20 < x < 35) = P(-2.5 < z < 1.25)
At least 27:
Standardized value for 27: z = (27 - 30) / 4 = -0.75
P(x ≥ 27) = P(z ≥ -0.75)
At least 19:
Standardized value for 19: z = (19 - 30) / 4 = -2.75
P(x ≥ 19) = P(z ≥ -2.75)
At most 29:
Standardized value for 29: z = (29 - 30) / 4 = -0.25
P(x ≤ 29) = P(z ≤ -0.25)
Using a standard normal distribution table or a calculator, you can look up the probabilities corresponding to the standardized values and find the answers to each of the above expressions.
So,
Between 24 and 32:
P(24 < x < 32) = P(-1.5 < z < 0.5) ≈ 0.7745
Between 31 and 37:
P(31 < x < 37) = P(0.25 < z < 1.75) ≈ 0.2580
Between 20 and 35:
P(20 < x < 35) = P(-2.5 < z < 1.25) ≈ 0.8962
At least 27:
P(x ≥ 27) = P(z ≥ -0.75) ≈ 0.7734
At least 19:
P(x ≥ 19) = P(z ≥ -2.75) ≈ 0.9970
At most 29:
P(x ≤ 29) = P(z ≤ -0.25) ≈ 0.4013
Thus,
The probabilities of the normal distribution are:
Between 24 and 32 is 0.7745.
Between 31 and 37 is 0.2580.
Between 20 and 35 is 0.8962.
At least 27 is 0.7734.
At least 19 is 0.9970.
At most 29 is 0.4013.
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Th graph shows a relationship between the balance of a gift card, y, and the number of lunches purchased with the gift card x. Write an equation in slope intercept form to represent this situation.
Answers
The equation in slope intercept form to represent this situation is y = -7.5x + 30
Writing the equation in slope intercept form to represent this situation.From the question, we have the following parameters that can be used in our computation:
The graph
A linear equation si represented as
y = mx + c
Where
m = slope
c = y when x = 0
From the graph, we have
c = 30
So, we have
y = mx + 30
Using the other points, we have
4m + 30 = 0
So, we have
m = -7.5
This gives
y = -7.5x + 30
Hence, the equation in slope intercept form to represent this situation is y = -7.5x + 30
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►Solving equation x+1 3 || X 2 can anyone please give me a question and the answers which is related to algebra solving equation
Answers
The solution for the given equation is x = 2.
Given is an equation, x+1 / 3 = x/2, we need to solve it,
So, in the questions like this, our first step should be of cross-multiplication,
x+1 / 3 = x/2
Cross-multiplying,
2(x+1) = 3x
Using the distributive law,
2x+2 = 3x
Combining the like terms,
3x-2x = 2
x = 2
There can be many equations made like this,
For example,
1) 9 = 3 + x/4
Solution = 9-3 = x/4
6 = x/4
x = 24
2) 2x+2 / 4 = x-3 / 3
Using Cross-multiplying,
6x+6 = 4x-12
2x = -12-6
2x = -18
x = -9
Hence there are many equations made.
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Which of the following conditions are necessary, and which conditions are sufficient for the natural number n to be divisible by 6. The natural numbers are N={0,1,2,...,}.
a. n is divisible by 3.
b. n is divisible by 9.
c. n is divisible by 12.
d. n = 24.
e. n^2 is divisible by 3.
f. n is even and divisible by 3.
Answers
Conditions (a) and (c) are necessary for n to be divisible by 6, but neither is sufficient. Condition (d) is both necessary and sufficient for n to be divisible by 6.
(a) and (c) are necessary conditions because 6 is a multiple of 3 and 12, so any number that is divisible by 6 must also be divisible by 3 and 12. However, being divisible by 3 or 12 does not guarantee divisibility by 6. For example, 9 is divisible by 3 but not by 6, and 12 is divisible by 12 but not by 6.
Condition (d) is both necessary and sufficient for divisibility by 6 because 6 is the product of 2 and 3, and 24 is the product of 2, 3, and 4. Any number that is divisible by 2, 3, and 4 is also divisible by 6.
Conditions (e) and (f) are not necessary or sufficient for divisibility by 6. For example, 9^2 is divisible by 3 but 9 is not divisible by 6, and 6 is even and divisible by 3 but not all even numbers divisible by 3 are also divisible by 6.
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pls help i dont know
the answer too
Answers
Answer:
The sum of the exterior angles of a polygon is always 360 degrees, regardless of the number of sides. So, if we know the measures of two exterior angles, we can find the measure of the third exterior angle by subtracting the sum of the first two angles from 360 degrees.
In this case, we know that the measures of exterior angles R and P are 80 degrees and 72 degrees, respectively. So, the measure of exterior angle W is
Code snippet
360 - 80 - 72 = 108 degrees
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Therefore, the missing exterior angle is 108 degrees.
Step-by-step explanation:
Can I hv help with this pls!!
Answers
The conversion of the recurring decimals 0.027 and 0.037 to fractions in its simplest form are 0.243/9 and 0.333/9
How to convert recurring decimals to fractions?Let
the fraction = x
0.027
Multiply by 10
0.027 × 10 = x
= 0.27
Subtract 0.027 from 0.27
0.27 - 0.027 = x
0.243 = x
divide by 9
0.243/9 = x
0.037
= 0.037 × 10
= 0.37
Subtract 0.037 from 0.37
0.333 = x
divide by 9
x = 0.333/9
Hence, 0.243/9 and 0.333/9 is the fraction for the recurring decimals 0.027 and 0.037.
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40% of jams 60 classmates enjoy watching football . 35% of his 20 relatives enjoy football . how many more classmates enjoy football ?
Answers
out of jams 60 classmates, 40% OR 24 Classmates enjoy watching football. out of jams 20 relatives, 35% or 7 relatives enjoy watching football. therefore there are 25-7=17 more classmates who enjoy football than relatives
5. Jake drew a model on grid paper
of a kite that he wants to make.
Each grid line represents 10 cm.
His drawing has coordinates (1,
5), (3, 6), (5, 5), and (3, 0). Sketch
Jake's kite, and calculate the area
of the real kite.
Answers
Based on the information given ,it should be noted that the area of the real kite will be 1615.548 cm²
How to calculate the areaThe given coordinates are:
(1, 5) -> (10 cm, 50 cm)
(3, 6) -> (30 cm, 60 cm)
(5, 5) -> (50 cm, 50 cm)
(3, 0) -> (30 cm, 0 cm)
Base = Distance between (10 cm, 50 cm) and (30 cm, 0 cm)
= ✓((30 cm - 10 cm)² + (0 cm - 50 cm)²)
= ✓(400 + 2500)
= ✓(2900) cm
Height = Distance between (30 cm, 60 cm) and (30 cm, 0 cm)
= 60 cm - 0 cm
= 60 cm
Area of Triangle 1 = (1/2) * Base * Height
= (1/2) * ✓(2900) cm * 60 cm
= 1615.548 cm²
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can you help me with this math
Answers
Answer: B
Step-by-step explanation:
203.95-11.95=192
192/4=48
One ticket cost 48 dollars, and the service fee is $11.95. Therefore, c=11.95+48t
Which expression is equal to x−9x−4+x2−x+5x−4 ?
Responses
x2−42x−8
x2−4x−4
x2−x−42x−8
x2−x−4x−4
Answers
Starting with the x terms:
X - 9x - x = -9x
Next, the constants:
-4 + 5(-4) = -4 - 20 = -24
Putting it all together:
X-9x-4+×2-x+5×-4 = -8x - 24
Therefore, none of the expressions listed is equal to X-9x-4+×2-x+5×-4.
what is the ratio for COS A?
Answers
The ratio of cos A in the right triangle is 12 / 13.
How to find the angle of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the ratio of cos A using trigonometric ratios.
Using cosine ratio,
cos A = adjacent / hypotenuse
Therefore,
adjacent side = 12
hypotenuse side = 13
cos A = 12 / 13
Therefore, the ratio is 12 / 13
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please help question 12
Answers
The magnitude is 4√(10) and the direction of vector w is approximately 18.4° (in standard position) above the negative x-axis.
How to calculate magnitude and direction?Find the components of vectors ũ and v.
Vector u has magnitude 2 and direction 90°, so its components are:
u₁ = 2 cos(90°) = 0
u₂ = 2 sin(90°) = 2
Vector v has magnitude 4 and direction 180°, so its components are:
v₁ = 4 cos(180°) = -4
v₂ = 4 sin(180°) = 0
Now find the components of vector w:
w₁ = 2u₁ + 3v₁ = 2(0) + 3(-4) = -12
w₂ = 2u₂ + 3v₂ = 2(2) + 3(0) = 4
The magnitude of vector w is given by:
|w| = √(w₁² + w₂²) = √((-12)² + 4²) = √(160) = 4√(10)
The direction of vector w is given by the angle it makes with the positive x-axis:
θ = arctan(w₂/w₁) = arctan(-4/(-12)) = arctan(1/3)
So the direction of vector w is approximately 18.4° (in standard position) above the negative x-axis.
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what is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron
Answers
The cross section formed by a plane containing a vertical line of symmetry for a tetrahedron can take various shapes, including polygons or curved shapes, depending on the orientation and angle of the intersecting plane.
What is tetrahedron?A tetrahedron is a three-dimensional geometric shape with four triangular faces. If a plane containing a vertical line of symmetry intersects a tetrahedron, the resulting cross section would depend on the orientation and position of the plane relative to the tetrahedron.
In general, there are several possible cross sections that can be formed by a plane containing a vertical line of symmetry for a tetrahedron. The specific shape and characteristics of the cross section would vary based on the angle and position of the intersecting plane.
For example, if the plane intersects the tetrahedron perpendicular to its vertical line of symmetry, the resulting cross section would be a vertical slice through the tetrahedron. This cross section would typically be a polygon with sides formed by the intersecting edges of the tetrahedron's faces.
On the other hand, if the intersecting plane is at an angle to the vertical line of symmetry, the resulting cross section would have a different shape. It could be a tilted polygon or even a curved shape, depending on the orientation of the intersecting plane and the specific angles of intersection.
In summary, the cross section formed by a plane containing a vertical line of symmetry for a tetrahedron can take various shapes, including polygons or curved shapes, depending on the orientation and angle of the intersecting plane.
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Which equation represents a line which is perpendicular to � = 0 x=0? � = − � x=−y � = − 5 x=−5 � = � + 2 y=x+2 � = 1 y=1
Answers
The equation y=1 represents a line Perpendicular to x=0.
The equation x=0 represents a vertical line passing through the point (0,0) on the x-axis. A line perpendicular to this line will be a horizontal line passing through the point (0, c) where c is a constant.
So, the equation of the line perpendicular to x=0 is y = c, where c is any constant.
Among the given options, the equation that represents a horizontal line is:
� = 1 y=1
Therefore, the equation y=1 represents a line perpendicular to x=0.
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What are the transformations applied to f(x) = to change it to the graph
2
of g(x) = 2
2
+ 12 + 20?
Answers
The transformations applied to f(x) to obtain the graph of g(x) can be summarized as a vertical stretch by a factor of 2, followed by a vertical shift upward by 12 units, and a horizontal shift to the left by 20 units.
Assuming that the expression 2 2 refers to 2 raised to the power of 2, the transformations applied to f(x) to change it to the graph of g(x) can be identified as follows:
Vertical stretch: The coefficient 2 in front of the function f(x) indicates that the graph of f(x) is stretched vertically by a factor of 2 to obtain the graph of 2f(x).
Vertical shift: The term +12 added to the function 2f(x) shifts the graph vertically upward by 12 units.
Horizontal shift: The term +20 added to the function 2f(x) shifts the graph horizontally to the left by 20 units.
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Note The full question is :
"What are the specific transformations applied to the function f(x) to obtain the graph of g(x)?"
