If 3 + w=b, which expression is equivalent to w?

True.

If the equation Ax=0 has a nontrivial solution, then the columns of A are linearly dependent.

If the equation Ax=0 has a nontrivial solution, then the columns of A are linearly dependent. This means that there exist constants c1, c2, ..., cn, not all zero, such that the vector

v = c1*a1 + c2*a2 + ... + cn*an

is the zero vector, where a1, a2, ..., an are the columns of A.

This implies that A has a non-pivot column, since we can write the vector v as a linear combination of the other columns. Therefore, A has fewer than n pivot columns, or equivalently, fewer than n pivot points.

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Answer:

8

Step-by-step explanation:

8-15=-7

-7/7=-1

y = [5 -9] = [1 1] + [4 -10]

To write y as the sum of two orthogonal vectors, we can decompose y into two components: one component in the span of vector u, and another component orthogonal to u. Let u = [1 1].

To find the component in the span of u, we can project y onto u using the formula: ((y · u) / (u · u)) * u.

Calculating the dot product of y and u: (5 * 1) + (-9 * 1) = -4.

Calculating the dot product of u and u: (1 * 1) + (1 * 1) = 2.

(((-4) / 2) * [1 1]) = [(-4/2) (-4/2)] = [-2 -2].

To find the component orthogonal to u, we can subtract the projected component from y: y - [-2 -2] = [5 -9] - [-2 -2] = [5 -9] + [2 2] = [7 -7].

Therefore, y can be written as the sum of two orthogonal vectors: x₁ = [-2 -2] in Span(u) and x₂ = [7 -7] orthogonal to u.

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Step-by-step explanation:

a=90

e=45

f=45

plzzzz mark me brainliest if it helps you then

Answer:

iiiii

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

An exponential function can represent growth or decay.

The graph represents an exponential growth function is given by  \(y = ab^{x}\).

An exponential function is represented as:

\(y = ab^{x}\)

Where:

a represents any constant value.

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

Graph shown below represents an exponential growth function.

Hence, the graph representing an exponential growth function is graph traced by \(y = ab^{x}\).

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\(\bold{Heya...}\)

3x + y = 11.

Let's solve for x ~

3x + y = 11

Step 1: Add -y to both sides.

\(\mathtt{3x \: + \: y \: + \: -y \: = \: 11 \: + \: -y}\)

\(\mathtt{3x \: = \: -y \: + \: 11}\)

Step 2: Divide both sides by 3.

\(\mathtt{\frac{3x}{3} \: = \: \frac{-y \: + \: 11}{3}}\)

↓ \(\underline{A \: n \: s \: w \: e \: r :}\) ↓

\(\bold{x \: = \: \frac{-1}{3}y \: + \: \frac{11}{3}}\)

Let's solve for x ~

5x - y = 21.

Step 1: Add y to both sides.

\(\mathtt{5x \: - \: y \: + \: y \: = \: 21 \: + \: y}\)

\(\mathtt{5x \: = \: y \: + \: 21}\)

Step 2: Divide both sides of 5.

\(\mathtt{\frac{5x}{5} \: = \: \frac{y \: + \: 21}{5}}\)

↓ \(\underline{A \: n \: s \: w \: e \: r :}\) ↓

\(\bold{x \: = \: \frac{1}{5}y \: + \: \frac{21}{5}}\)

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Answer:

Circumference is about 182.21

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is 29. Plug 29 into the formula 2(pi)r to find the Circumference. The answer is 182.21

The equation of the circle is \(\rm(x-3)^2+(y+2)^2=29^2\).

The equation of the circle is given by;

\(\rm (x-h)^2+(y-k)^2=r^2\)

Where r is the radius and h and k are the centre of the circel.

The radius of the circle is;

\(r=\sqrt{(23-3)^2+(19-(-2))^2} \\\\r=\sqrt{(20)^2+(21)^2} \\\\r=\sqrt{400+441}\\\\r =\sqrt{841}\\\\r=29\)

The equation of the circle is;

\(\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-3)^2+(y-(-2))^2=29^2\\\\ (x-3)^2+(y+2)^2=29^2\)

Hence, the equation of the circle is \(\rm(x-3)^2+(y+2)^2=29^2\).

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Therefore, The probability that the customer likes neither hot nor iced coffee is 0. This can be calculated by subtracting the probability of the customer liking hot coffee or iced coffee from 1.

The probability that the customer likes neither hot nor iced coffee can be calculated by subtracting the probability of the customer liking hot coffee or iced coffee from 1. Let A be the event that the customer likes neither hot nor iced coffee. Then, P(A) = 1 - P(H) - P(I). If P(H) = 0.6 and P(I) = 0.4, then P(A) = 1 - 0.6 - 0.4 = 0. Therefore, the probability that the customer likes neither hot nor iced coffee is 0.
To find the probability of an event, we need to divide the number of favorable outcomes by the total number of possible outcomes. Here, the customer can either like hot coffee, iced coffee, or neither. Since the customer can only like one of the two options, we can use the complement rule to find the probability of the customer not liking either. We subtract the sum of probabilities of the customer liking hot and iced coffee from 1.
Therefore, The probability that the customer likes neither hot nor iced coffee is 0. This can be calculated by subtracting the probability of the customer liking hot coffee or iced coffee from 1.

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Using a sample mean of a specific size would be beneficial in situations where it is impractical or impossible to gather data from an entire population. By taking a sample and calculating the mean, we can make reliable inferences about the population mean, saving time and resources.

1. Limited Resources: In some cases, it may be infeasible or too costly to collect data from an entire population. For example, if you want to determine the average height of all people in a country, it would be impractical to measure every single person. Instead, you can select a representative sample.

2. Time Constraints: Conducting a study on an entire population might require a significant amount of time. For time-sensitive situations, using a sample mean of a specific size allows for quicker data collection and analysis. This is especially true when immediate decisions or interventions are necessary.

3. Accuracy: Sampling can provide accurate estimates of the population mean when done properly. By ensuring that the sample is representative and randomly selected, statistical techniques can be applied to estimate the population mean with a desired level of confidence.

4. Cost-Effectiveness: Collecting data from an entire population can be expensive and time-consuming. By using a sample, you can significantly reduce the costs associated with data collection, analysis, and other resources required for a full population study.

5. Feasibility: In certain cases, accessing the entire population might be logistically challenging. For instance, if you want to determine the average income of all households in a country, it would be difficult to gather data from every single household. A representative sample can provide reliable estimates without the need for accessing the entire population.

In conclusion, utilizing a sample mean of a specific size is beneficial when resources, time, accuracy, cost, and feasibility considerations make it impractical to collect data from an entire population. By employing statistical techniques on a well-designed sample, we can make valid inferences about the population mean, saving resources while still obtaining reliable results.

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The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.

According to the statement

we have given that If 15 actuators have failed and we have to find the probabilities on some conditions.

we know that the formula of probabilities is

probability = possible outcomes / total outcomes

So,

at least 10 are repairable = 1 - 10/15

at least 10 are repairable = (15 - 10)/15

at least 10 are repairable = (5)/15

at least 10 are repairable = 1/3

from 3 to 8 are repairable = 1/5 *8/15

exactly 5 are repairable = 1/3

These are the probabilities of the given conditions.

So, The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.

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The period of simple harmonic motion is T = 4.19 seconds:

For given question,

A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.

So, we have mass (m) = 16 pounds

spring constant (k) = 36 lb/ft.

Let T be the period of simple harmonic motion.

Using the formula for the period of simple harmonic motion,

⇒ T = 2π√(m/k)

⇒ T = 2 × π × √(16/36)

⇒ T = 2 × π × √(0.444)

⇒ T = 2 × π × 0.666

⇒ T = 1.333 × π

⇒ T = 4.19 seconds

Therefore, the period of simple harmonic motion is T = 4.19 seconds

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Answer:

$5.32

Step-by-step explanation:

I think its $5.32 because there is at least 6 yogurts in the pack, and its not to expensive as the first one. Plus it has 2 more yogurts then the third one.

(i am so sorry if this dosent make sense)

The "independent-variable" in statement, "Allison wants know that if deer-population in area is influenced by coyote-population" is "Coyote-Population".

The "Independent-Variable" is the factor that is controlled by the researcher in an experiment to observe its effects on the dependent variable. In this case, Allison wants to determine if the deer-population is influenced by the coyote-population.

So, she would manipulate or observe changes in the coyote-population to understand its impact on the deer-population. By controlling or varying the coyote population, Allison can analyze the resulting changes in the deer-population, which serves as the dependent variable.

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The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.

A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.

While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.

Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.

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Answer:

A,B,C,

Step-by-step explanation:

PLATO

Answer:

the additive inverse of 12 is -12

Step-by-step explanation:

The number of ways that a cook can arrange 8 of 12 spice jars on a spice rack is; 495 ways.

We want to find the number of ways that a cook can arrange 8 of 12 spice jars on a spice rack.

This is a Combination Problem which follows the formula;

nCr = n!/(r!(n - r)!

12C8 = 12!/(8!(12 - 8)!

Solving this gives;

12C8 = 495 ways

Thus, the number of ways that a cook can arrange 8 of 12 spice jars on a spice rack is 495 ways.

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Answer:

The correct answer is: 19,958,400.

Step-by-step explanation:

I hope this helps! :)

False. The statement "Solving the system of linear equations by elimination -2x+y=3 and 3x+2y=-15" is not a true or false statement. It is a method used to solve the given system of equations.

The process of solving a system of linear equations by elimination involves eliminating one variable by adding or subtracting the equations to create a new equation with only one variable. The goal is to eliminate one variable so that the resulting equation becomes solvable for the remaining variable.

In the given system of equations -2x+y=3 and 3x+2y=-15, the process of elimination can be used to eliminate one variable and solve for the other. By multiplying the first equation by 3 and the second equation by 2, the coefficients of the x term can be made equal, allowing the x variable to be eliminated. Adding the resulting equations will eliminate x, and solving the resulting equation will yield the value of y.

Therefore, the statement provided in the question is not a true or false statement but rather a method used to solve the system of linear equations. The actual solution to the system can be determined by applying the elimination method and finding the values of x and y that satisfy both equations.

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Answer:

The two complex numbers that make the equation true are 1 + i  and 3 + 2i

(1 + i) + (3 + 2i) = 4 + 3i

Step-by-step explanation:

(1 + i) + (3 + 2i)

Combine the real and imaginary parts in numbers 1 + i and 3 + 2i

1 + 3 + (1 + 2)i

Add 1 to 3. Add 1 to 2.

4 + 3i

The two complex numbers that make the equation true are 1 + i  and 3 + 2i

The formula to calculate the common sum of the interior angles of an n-sided polygon is as follows: Sum = (n-2) × 180The problem states that the polygon is regular. As a result, all angles in the polygon have the same degree.

To discover the degree of each angle, divide the sum of the angles by the number of angles in the polygon.

Say, for instance, that the polygon has 150 sides. The formula for the sum of the interior angles of a polygon with 150 sides is:S = (n-2) × 180 = (150-2) × 180 = 148 × 180 = 26640 degrees

To determine the size of each interior angle, we must now divide the sum by the number of angles in the polygon: Each angle size = S/n = 26640/150 = 177.6 degrees Therefore, each interior angle in a regular 150-sided polygon has a degree of 177.6.

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The probability of picking an orange or a cherry flavored candy from the bag is \(\frac{8}{15}\).

Given that, total number of candies=15, banana flavoured candies=4, strawberry flavoured candies=3, cherry flavoured candies=6 and orange flavoured candies=2.

We need to find out what would be the probability of picking an orange or a cherry-flavoured candy from the bag.

According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.

The probability of an event\(=\frac{Number of favourable outcomes}{Total Number of outcomes}\).

Now, the probability of picking an orange flavored candy from the bag \(=\frac{2}{15}\)

The probability of picking a cherry flavored candy from the bag \(=\frac{6}{15}\)

The probability of picking an orange or a cherry flavored candy from the bag \(=\frac{2}{15}+\frac{6}{15}=\frac{8}{15}\).

Therefore, the probability of picking an orange or a cherry flavored candy from the bag is \(\frac{8}{15}\).

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Answer:the triangles are similar to each other by AA rule and EF = 8.

Step-by-step explanation:

the triangles are similar to each other by AA rule and EF = 8.

this should help if wrong sorry im in middle school so

Answer:

In the state of Kansas, the density of people per square mile is 34.3

Step-by-step explanation:

According to US topographers, the state of Kansas has an area of ​​213 096 km².

If 1 km² is equal to 0.39 mi², then how much is 213 096 km².

If 1 km²   :   0.39 mi².

213,096 km²  :   83,107.44 mi²

If the state of Kansas has a population of 2.85 million people, then:

2.85 x10^6 people / 83 107.44 mi² =

34.3 people per square mile.

Answer:

x(3+9)=72

or, x(12)=72

or, x=72÷12

or, x = 6 ans.

Answer: x=6

Step-by-step explanation:

Let's solve your equation step-by-step.

x(3+9)=72

Step 1: Simplify both sides of the equation.

12x=72

Step 2: Divide both sides by 12.

12x/12=72/12

x=6

Answer:

x=6

If the equation of the absolute value function is f(x) = |x + 1| + 7, then the range of the function is -∞ < y ≤ 7

The question is incomplete, so I will provide a general explanation

Assume that the absolute value function is given as:

f(x) = |x + 1| + 7

Set the absolute value to 0

f(x) ≥ 0 + 7

Evaluate

f(x) ≥ 7

This means that the smallest value of the function is 7

Hence, the range of the absolute value function is -∞ < y ≤ 7

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Answer:  that person is right

Step-by-step explanation:

i got it right on a test

Answer:

Hello! Your answer would be BELOW

Step-by-step explanation:

A)

D)

C)

Hope I helped! Ask me anything if you have more questions! Brainiest plz! Have a nice mourning! Hope you make an 100%! -Amelia♥

Answer:D. y = 3/4x + 1

Answer:

16

Step-by-step explanation:

Answer:

To find the slope of the parallel and perpendicular lines to the equation y = 3/4x + 4, we need to use the fact that parallel lines have the same slope, while perpendicular lines have opposite reciprocal slopes.

The given equation is in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

Therefore, the slope of the given line y = 3/4x + 4 is 3/4.

To find the slope of a line parallel to this one, we know that it must have the same slope. Therefore, the slope of the parallel line is also 3/4.

To find the slope of a line perpendicular to this one, we need to take the opposite reciprocal of the slope. The opposite reciprocal of 3/4 is -4/3. Therefore, the slope of the perpendicular line is -4/3.

In summary, the slope of the parallel line is 3/4, and the slope of the perpendicular line is -4/3.

This is true that √(6a + 3) < a + 2 for all a > 1, using the Mean Value Theorem.

To prove that √(6a + 3) < a + 2 for all a > 1 using the Mean Value Theorem,

we can define a function f(x) = √(6x + 3) and apply the theorem.

By the Mean Value Theorem, there exists a c in the interval (1, a) such that:

f(a) - f(1) = f'(c)(a - 1)

where f'(x) is the derivative of f(x).

The derivative of f(x) is:

f'(x) = (3 / √(6x + 3))

So, we have:

Since 1 < c < a, we have:

Substituting this into the previous equation, we get:

√(6a + 3) - 3 < 3(a - 1) / √(6c + 3) < 3(a - 1) / √(6a + 3)

We want to show that:

√(6a + 3) < a + 2

Adding 3 to both sides, we get:

√(6a + 3) - 3 < a - 1

Dividing by 3, we get:

(√(6a + 3) - 3) / 3 < (a - 1) / 3

Substituting this into the previous inequality, we get:

(√(6a + 3) - 3) / 3 < 3(a - 1) / √(6c + 3) < 3(a - 1) / √(6a + 3)

Since 1 < c < a, we have:

√(6a + 3) - 3 < 3(a - 1) / √(6a + 3)

Multiplying both sides by √(6a + 3) + 3, we get:

(√(6a + 3) - 3)(√(6a + 3) + 3) < 3(a - 1)

Simplifying, we get:

6a < 3a + 6

This is true for all a > 1.

Hence, we have shown that √(6a + 3) < a + 2 for all a > 1 using the Mean Value Theorem.

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