solve 3x - 2x + 4 = 5x - 4x - 8
no solution

6

-3

infinitely many solutions.

3
​

Answer:

-4

Step-by-step explanation:

We can use slope formula m = (y2-y1)/(x2-x1)

So just substitute those two points in it.

m = (11- 3)/(0-2)

m = 8/(-2)

m= -4

The required probabilities for the events in question are:

Based on the parameters given :

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

A.)

Probability of green slots 2 or more times :

(2/38)² × (36/38)²³ = 0.00080

B.)

Probability of ball not entering the green slots

1 - P(green slots)

P(not entering green slot ) = 1 - 0.0008 = 0.9992

C.)

probability that ball falls into black slot 15 or more times :

(18/38)¹⁵ * (20/38)¹⁰ = \(2.21\times10^{-8}\)

D.)

Probability that ball falls into red slot 10 or less times :

(10/38)¹⁰ * (28/38)¹⁵ = \(1.63\times10^{-8}\)

Therefore, the required probabilities are :

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Out of 50 beings surveyed, 34 of them preferred tott juice.

What is survey?

If 68% of beings on planet Dubble preferred tott juice, it means that 68 out of every 100 beings preferred tott juice. This can be written as a fraction: 68/100, which can be simplified to 17/25.

If 50 beings were surveyed in total, we can find the number of beings who preferred tott juice by multiplying the total number of beings by the fraction who preferred tott juice:

50 x 17/25 = 34

Therefore, out of 50 beings surveyed, 34 of them preferred tott juice.

What is fraction?

A fraction is a way of expressing a part of a whole or a ratio of two numbers. It consists of two numbers separated by a line, where the number on top is called the numerator and the number on the bottom is called the denominator. The denominator represents the total number of equal parts that make up a whole, while the numerator represents the number of those parts being considered. For example, the fraction 3/4 represents three parts out of four equal parts that make up a whole. Fractions can be used to represent numbers between 0 and 1, and they can also be used to represent division or ratios in mathematical operations.

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Answer:

1/12

Step-by-step explanation:

1/4 *1/3=1/12

Answer:

The letter E

20 ounces

Step-by-step explanation:

no exceptions

The value of x is a counter example to the student's conjecture (x = 2).

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that x is a non-negative number, a student conjectured that x + 4 < x².

Since x is a non-negative number, A and B are eliminated.

This leaves C and D at the value of x = 2,

2 + 4 < 2²

6 < 4 is false.

Therefore, the value of x is a counterexample to the student's conjecture (x = 2).

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Answer:

A. 22

b. Yes. Because there are 23 woman and they are all under 18 and there are 22 males. In which we don't know if they are underage, but it doesn't really matter because there is one more girl in the room than boys. And all woman are underage so there for there are more underage students in the room.

Step-by-step explanation:

Hope this helps :)

Pls make brainliest :p

And have an amazing day <3

Answer:

there would be 21.6 males. That doesn't work, so you'd have 21 or 22(probably 22)

yes, most of the students are minors. 52% percent at least are under 18 years. 52% is more than half, so that would make it so most are minors.

Step-by-step explanation:

For the first question:

The correct answer is C. The mean of the sampling distribution of the sample mean is 150 hot dogs.

This is because the mean of the sample means will be equal to the population mean in the case of a random sampling.

For the second question:

The correct answer is B. 2.7−4.2=−1.5

The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is equal to the difference between the population means, which is 2.7 - 4.2 = -1.5 minutes.

For the third question:

The correct answer is D. 2.9225−2.92210

The standard deviation σ(\(x^{-1} - x^{-2}\)) of the sampling distribution of the difference in sample means \(x^{-1} - x^{-2}\) is equal to the square root of [(\(σ1^2\)/n1) + (\(σ2^2\)/n2)], which in this case is √[(2.92/5) + (2.92/10)] = 1.5.

For the first question, option C is correct because the sampling distribution of the sample mean tends to have the same mean as the population mean.

For the second question, option B is correct because the mean of the sampling distribution of the difference in sample means is equal to the difference between the population means.

For the third question, option D is correct because the standard deviation of the sampling distribution of the difference in sample means is calculated as the square root of the sum of the variances of the two sample means.

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Answer:

Inequality Form:

x > 11

Interval Notation:

(11,∞ )

Susan can make 8 distinct arrangements, according to the question.

Generally speaking, an arrangement of objects is just a collection of them. A combination (order is ignored) or permutation is used to determine the number of "arrangements" of the components (order is significant).

The number of possible arrangements or orders for a set of items is known as an arrangement number, also known as a permutation number or just a permutation.

The following formula calculates the number of combinations of n objects taken r at a time: C(n,r)=n! (n−r)! r!

According to the question,

We have the given information:

6 Tulips, 6 Roses, and 8 Daisies

Total number of plants to be arranged= 20

It means 20! ways

Dividing it by 6! 6! and 8! ways,

Total number of ways= 20!/6!6!8!

                                   = 116396280

Therefore, the total number of ways 116396280.

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The volume between the paraboloids can be found by integrating the difference between the two equations over the limits of the region. The resulting volume is approximately 7.87 cubic units.

The volume lying between the paraboloids z=x^2 + y^2 and 3z=4-x^2-y^2 can be found by integrating the difference between the two equations over the limits of the region.

To find the limits of the region, we need to set the two equations equal to each other and solve for the value of z, which gives us 3z=4. Therefore, the limits of integration for z are 0 to 4/3. For x and y, we can use cylindrical coordinates, where r^2=x^2+y^2, and integrate over the entire x-y plane, which gives us a limit of 0 to 2π. Finally, for the radius, we need to find the maximum radius of the paraboloid z=x^2+y^2, which is at the vertex, where x=y=0 and z=0, so the radius is 0.

Putting all this together, we can set up the integral as:

V = ∫∫∫ (4/3 - (x^2+y^2)) dV, where the limits of integration are 0 to 2π for φ, 0 to 4/3 for z, and 0 to √(4/3-z) for r.

Evaluating this integral gives us the volume between the two paraboloids, which is approximately 7.87 cubic units.

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a) The probability that there will be an accident on Highway 48 today is 0.36%.

b) The probability that the weather today was wet given that there was an accident on Highway 48 is approximately 55.56%.

a) To find the probability that there will be an accident on Highway 48 today, we need to consider both the probability of an accident when it's dry and when it's wet, and the probability of each type of weather. We can use the formula: P(A) = P(A|B) × P(B) + P(A|B') × P(B'), where A represents an accident, B represents wet weather, and B' represents dry weather.
P(A) = P(Accident|Wet) × P(Wet) + P(Accident|Dry) * P(Dry)
P(A) = (0.01) × (0.2) + (0.002) × (0.8)
P(A) = 0.002 + 0.0016
P(A) = 0.0036
b) To find the probability that the weather was wet given that there was an accident on Highway 48, we can use Bayes' theorem: P(B|A) = (P(A|B) × P(B)) / P(A)
P(Wet|Accident) = (P(Accident|Wet) × P(Wet)) / P(Accident)
P(Wet|Accident) = (0.01 × 0.2) / 0.0036
P(Wet|Accident) = 0.002 / 0.0036
P(Wet|Accident) = 0.5556

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The solution for the -

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

is (1, 1)

AND

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

is (0, 1)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following set of equations

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graphs that the solution is given for first set is of simultaneous equations as (1, 1) and the second set of simultaneous equations as (0, 1)

Refer to the two graphs attached.

Therefore, the solution for the -

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

is

(1, 1)

AND

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

is

(0, 1)

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a = -2 is the value of linear equation .

What are examples of linear equations?

Step 1 - Write the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 2 - rewrite the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 3 - Take the LCM.

3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4

Step 4 - Further simplify the above expression

3a - 6 - a - 2/a² - 4 = 6a/a² - 4

Step 5 - Cancel out the denominator of both sides and then further simplify.

2a - 8 = 6a

a = -2

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The complete question is -

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

3/a + 2 − 6a/a2 − 4 = 1/a − 2

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

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Answer:

Yes

Step-by-step explanation:

You have to add 4 on both sides to get X by itself. Then, you solve for X by multiplying the Denominator.

Answer:

Step-by-step explanation:

6

No, not quite. The inequality graphed should look something like this:

A valid assignment of probabilities for the number of heads observed in two flips is D) All of the above.

The exact qualities of the coin being used determine the appropriate attribution of probabilities for the number of heads observed in two coin flips. In this situation, the probability assigned to each option must be determined and then the best choice must be decided.

A) Number of heads: 0 1 2

Probability: 1/4 2/4 1/4

Thus,

1/4 + 2/4 + 1/4

= 4/4

= 1

Therefore, option A is a valid assignment of probabilities.

B) Number of heads: 0 1 2

Probability: 1/3 1/3 1/3

Thus,

1/3 + 1/3 + 1/3

= 3/3

= 1

Therefore, option B is a valid assignment of probabilities.

C) Number of heads: 0 1 2

Probability: 1/10 5/10 4/10

Thus,

1/10 + 5/10 + 4/10

= 10/10

= 1

Therefore, option C is a valid assignment of probabilities.

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82%(percent) of the sample as a whole are region 1 bunny owners.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage."

Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

Hundredths are also referred to as percents.

As a result, 1% is one hundredth of a percent, or 1%=1/100=0.01.  

According to our question-

Total people  = 390

390*18/100

=70.2

Hence, 82%(percent) of the sample as a whole are region 1 bunny owners.

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K-means clustering is the process of organizing observations into one of a number of groups based on a measure of similarity. It is a type of unsupervised learning algorithm that sorts data points into groups, called clusters, based on their similarity to one another. This technique is commonly used in pattern recognition, image analysis, and data mining.

K-means clustering begins by randomly assigning each data point to one of k clusters. Then, the algorithm iteratively moves each data point to the cluster whose mean is closest to it. The process continues until there are no more changes in cluster membership or some other stopping criterion is met.

K-means clustering is not used to agglomerate observations into a series of nested groups based on a measure of similarity, nor is it used to estimate the value of a continuous outcome variable. It also does not reduce the number of variables to consider in a data-mining approach. Rather, it is a technique for clustering data points based on their similarity to one another.

In conclusion, K-means clustering is the process of organizing observations into one of a number of groups based on a measure of similarity. The algorithm sorts data points into groups called clusters based on their similarity to one another.

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By evaluating the formula for the sequence, we will get the terms:

Here we want to find the second, fourth, and eleventh terms in the sequence:

A(n) = -9 + (n - 1)*3

n defines the "number" of the term in the sequence.

So to get the second term, we need to use n = 2, we will get.

A(2) = -9 + (2 - 1)*3

A(2) = -9 + 3 = -6

The fourth term is what we get if we evaluate in n = 4, then:

A(4) = -9 + (4 - 1)*3

A(4) = -9 + 9 = 0

And the eleventh term is what we get when we use n = 11, we will get:

A(11) = -9 + (11 - 1)*3

A(11) = -9 + 30 = 21

These are the 3 terms of the sequence that we wanted to find.

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The true proportion of the side lengths of the quadrilaterals is A'B'/AB

From the question, we have the following parameters that can be used in our computation:

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

Substitute the known values in the above equation, so, we have the following representation

k = A'B'/AB

Hence, the proportion is A'B'/AB

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These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

Gregory most likely took an intelligence test, specifically the Wechsler Adult Intelligence Scale (WAIS). The WAIS is designed to measure an individual's cognitive abilities and is commonly used in psychological assessments. It consists of a full scale or total score, which is a combination of the verbal score and the performance score. The verbal score measures an individual's language and communication skills, while the performance score measures an individual's ability to solve problems and complete tasks. These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

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Answer:

A. (4, 18)

Step-by-step explanation:

The "y" coordinate of the midpoint will be equal to the average of the y coordinates of the endpoints, and the x coordinate of the midpoint will be equal to the average of the x coordinates of the endpoints, and so we get that...

The x coordinate of the midpoint = (5 + 3) / 2 = 8 / 2 = 4

The y coordinate of the midpoint = (21 + 15) / 2 = 36 / 2 = 18

So the right answer is A (4, 18)

Answer: 67,500

Step-by-step explanation:

75,000 divided by 10% = 7,500

75,000 - 7,500 = 67,500

N(x, y, z) = [-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0and O(x, y, z) = [-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0 respectively.

The equations of the normal plane and osculating plane of the curve at the given point are given by N = 0 and O = 0.

Here is the step-by-step explanation for finding equations of the normal plane and osculating plane of the curve at the given point for X= sin 2t, y=-c0s 2t, z =(0, 1, 2x) and 150:

Given that X= sin 2t, y=-c0s 2t, z =(0, 1, 2x) and t = 150.

Let us first find the first derivative of the given function.

f (t) = [X(t), Y(t), Z(t)] = [sin 2t, -cos 2t, 2 sin 2t]f'(t) = [2 cos 2t, 2 sin 2t, 4 cos 2t]

Again, let us find the second derivative of the given function.

f''(t) = [-4 sin 2t, 4 cos 2t, -8 sin 2t]At t = 150, we have

f'(t) = [2 cos 300, 2 sin 300, 4 cos 300] = [-1, √3, 2]f''(t) = [-4 sin 300, 4 cos 300, -8 sin 300] = [-2 √3, -2, 4 √3]

At the given point [X(150), Y(150), Z(150)] = [sin 300, -cos 300, 2 sin 300] = [√3/2, -1/2, √3]

The equation of the normal plane can be found as

N(x, y, z) = [f'(150)] . [x - X(150), y - Y(150), z - Z(150)] = 0[-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0

The equation of the osculating plane can be found as

O(x, y, z) = [f''(150)] . [x - X(150), y - Y(150), z - Z(150)] = 0[-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0

Hence, the equations of the normal plane and osculating plane of the curve at the given point are given by

N(x, y, z) = [-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0and O(x, y, z) = [-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0 respectively.

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The solution to the given differential equation as required is; y = √(x² + 4).

As evident in the task content;

dy / dx = x / y, y(0) = -2

Therefore, we have that;

dy (y) = dx (x)

By integration of both sides indefinitely;

y² / 2 = x²/2 + C

y² = x² + 2c

y = √(x² + 2c)

Hence, using the initial conditions;

-2 = √(0² + 2c)

-2 = √2c

2c = 4

c = 2.

Hence, the required solution of the differential equation as given is; y = √(x² + 4) since c = 2.

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