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Just 5 quick algebra 1 questions for 50 points!

Answer:

The formula for the solution to the initial value problem x'' + 25x = f(t) is given by the inverse Laplace transform of [(F(s) + sx0 + v0) / (s^2 + 25)].

Step-by-step explanation:

To obtain a formula for the solution to the initial value problem x'' + 25x = f(t), we can use the convolution theorem. The convolution theorem states that the Laplace transform of the convolution of two functions is equal to the product of their individual Laplace transforms.

Let's denote the Laplace transforms of x(t) and f(t) as X(s) and F(s) respectively. The Laplace transform of the differential equation x'' + 25x = f(t) is given by:

s^2X(s) - sx(0) - x'(0) + 25X(s) = F(s)

Rearranging the Laplace transform and substituting the initial conditions x(0) = x0 and x'(0) = v0, we have:

s^2X(s) - sx0 - v0 + 25X(s) = F(s)

Now, let's solve for X(s):

(s^2 + 25)X(s) = F(s) + sx0 + v0

X(s) = (F(s) + sx0 + v0) / (s^2 + 25)

Applying the inverse Laplace transform to X(s), we obtain the solution x(t):

x(t) = L^(-1) [(F(s) + sx0 + v0) / (s^2 + 25)]

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Answer:

D) 18

Step-by-step explanation:

2x² - 6x = 540

2x² - 6x - 540 = 0

(2x + 30)(x - 18) = 0

x - 18 = 0

x = 18

2x + 30 = 0

2x = -30

x = -15; this cannot be the answer as it is negative

The best value to use as x0 when determining the value of f(5.5) by the method of linear approximation The method of linear approximation is based on the fact that for small changes in x, the change in f(x) is approximately proportional to the change in x, and this relationship can be expressed using the derivative of f(x) at x0.

The power rule tells us that the derivative of 2x^2 is 4x, and the chain rule tells us that the derivative of √(8) is 1/(2√(8)). So, the derivative of f(x) is:
f'(x) = 4x - 1/(2√(8))


Based on these calculations, the best value to use as x0 is 5.495, since f'(5.495) gives us the closest estimate to f(5.5). Therefore, we can use the equation of the tangent line to f(x) at x=5.495 to estimate f(5.5):
f(x) ≈ f(5.495) + f'(5.495)(x - 5.495)
Plugging in the values we know, we get:
f(5.5) ≈ f(5.495) + f'(5.495)(5.5 - 5.495)
f(5.5) ≈ (2(5.495)^2 - 8√(5.495)) + (4(5.495) - 1/(2√(8)))(0.005)
f(5.5) ≈ 5.506

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Answer:

10x3=30

Step-by-step explanation:

X=2 is 10 and x=5 is 30.

10 is the factor of 30, and 10 could be multiplied by 3 to get 30.

OR 30 could be divided by 10, and you‘ll get 3.

Hope this helped! :)

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Answer:

B for sure

Step-by-step explanation:

Therefore, to ensure with probability 0.9 that the class average would be within 5 of 60, the professor would need 118 students to take the final exam.

The Central Limit Theorem states that the distribution of the sum or average of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.

Therefore, in this example we can use the Central Limit Theorem to approximate the mean of the test scores of the students taking the final exam. If the professor knows that the mean of the test scores is 60 and the standard deviation is 16, then the professor can calculate the sample size necessary to ensure that the class average is within 5 of 60 with a probability of 0.9.

Using the formula \(n = (zα/2 * σ/ε)2\), where zα/2 is the z-score associated with a confidence level of 0.9, σ is the standard deviation of the population, and ε is the margin of error desired, we can calculate the sample size necessary for this professor.

\(n = (1.645 * 16/5)2 = 118.03\)
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Answer:

yes

Step-by-step explanation: k

Answer:

r+a+e+f^31+b

Step-by-step explanation:

Self-explanatory

If Homer can travel the same distance on the moving walkway as he can on the floor in the same amount of time, then his walking speed and the speed of the moving walkway must be the same. Therefore, Homer's walking speed is 4 mph.

Let's say that the distance Homer needs to travel to get to his gate is D. If he walks on the floor next to the moving walkway, he will travel this distance at his walking speed, which we'll call W. If he walks on the moving walkway, he will travel this distance at the speed of the walkway plus his walking speed, or W + 4 mph.

Since the time it takes for Homer to travel the distance D is the same in both cases, we can set the two equations equal to each other:

D/W = D/(W + 4)

Cross-multiplying gives us:

D(W + 4) = DW

Distributing the D gives us:

DW + 4D = DW

Subtracting DW from both sides gives us:

4D = 0

Dividing both sides by 4 gives us:

D = 0

Since the distance D cannot be zero, this means that the only way for the two equations to be equal is if W and the speed of the moving walkway are the same. Therefore, Homer's walking speed is 4 mph.

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Answer:

The answer is -285

Step-by-step explanation:

Answer:

Since the pole is in the shape of a cylinder, its volume can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length in this case). We are not given the radius, so we cannot calculate the exact volume. However, we can use an approximation assuming a reasonable radius.

Let's assume a radius of 1 foot. Then, the volume would be V ≈ π(1)²(15) = 15π ≈ 47.1 cubic feet.

The closest answer choice to this approximation is D) 141 ft². However, note that volume is measured in cubic units (feet cubed or ft³), not square units (feet squared or ft²). Therefore, none of the answer choices are in the correct units for the volume of a cylinder.

Answer:

A term is a single mathematical expression. ... Examples of single terms: 3x is a single term. The "3" is a coefficient. The "x" is the variable.

Answer:

X is the variable.

Step-by-step explanation:

In this expression, there are three types here: Fraction, variable and coefficient. 1/2 and 1/8 are the fraction;proper fraction. 3 is the coefficient and x is the variable. A number is always the coefficient while that alphabet are the variable.

Answer:

It costs $90 dollars afterwards.

Step-by-step explanation:

Answer:

y=40/183x

Step-by-step explanation:

y = Rise/Run multiplied plus y intercept by x or Y= mx + b

There is no b

m = 40/183

Y = 40/183x

The required sample size is determined by finding the z-score that corresponds to a 90% confidence interval and then using that z-score to calculate the sample size. In this case, the z-score is 2.24 and the sample size is 467.

In order to determine the required sample size to be 90% certain that we are within 4 IQ points of the true mean, we must first calculate the z-score that corresponds to a 90% confidence interval. This z-score is calculated by subtracting the lower bound of the interval from the mean, and then dividing this difference by the standard deviation. In this case, the z-score is 2.24. We then use this z-score to calculate the required sample size, which is calculated by taking the z-score, squaring it, and then multiplying it by the sample variance. In this case, the sample size is 467. This means that we need at least 467 samples in order to be 90% certain that we are within 4 IQ points of the true mean.

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Answer: x = 150

Step-by-step explanation:

See the liner pair of angle 70 will be 110 degrees.

Then using angle sum property third angle will be

Third angle = 180 - 150

Third angle of the triangle = 30

Now linear pair of the 30 degree angle

30+x = 180

x = 180-30

x = 150

Therefore answer is option e x = 150.

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The measure of the value of angle x is 150°, and the correct option is E

Linear pair of angles are formed when two lines intersect each other at a single point.

The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.

BY applying linear pair angles;

\(\rm \angle 1+\angle 2=180\\\\70 +\angle 2=180\\\\ \angle 2=180-70\\\\ \angle 2=110\\\\\)

The sum of the three angles is 180.

\(\rm \angle 1+\angle 2+ \angle 3=180\\\\ 110+40 +\angle 3=180\\\\150+\angle 3= 180\\\\\angle 3=180-130\\\\\angle 3=30\)

The measure of the value of angle x is;

\(\rm 30+x = 180\\\\x = 180-30\\\\x = 150\)

Hence, the measure of the value of angle x is 150°, and the correct option is E.

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Answer:

\(5x^{4}\)

Step-by-step explanation:

lmk if you need an explanation  :)

The main effects are room illumination and room temperature. Therefore, 2 main effects are there.

Generally speaking, room temperature refers to a range of air temperatures that people favor indoors. When someone is dressed in regular indoor attire, they feel at ease. Depending on humidity, air circulation, and other factors, human comfort can go beyond this range. Neither heated nor chilled, food or beverages may be served at room temperature.

Temperature ranges are defined as room temperature for certain products and processes in industry, science, and consumer goods.

In a study examining the effect of room illumination (low, medium, high) and room temperature (cold, warm, hot) on test performance, there are 2 main effects possible. The main effects are room illumination and room temperature.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

0.969

Step-by-step explanation:

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (18 - 31) / 7

= -1.857

area in z-score table (this is area to left of <18) is 0.0314.

P(>18) = 1 - 0.0314 = 0.969

Answer:

D.

Step-by-step explanation:

You can see it in the graphs after you plot it.

We have defined the criteria for SAS congruency of triangles.

What is SAS?

The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."

According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.

Hence, we have defined the criteria for SAS congruency of triangles.

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The cost of resurfacing her driveway will be $384.00.

A square is a quadrilateral having all equal sides and the sum of the for angles is equal to 360. the lines of the square are perpendicular to each other.

It is given in the question that:-

The total area of the squares will be:-

A    =    Side² x 48  =   10²   x   48    =   4800  square feet

The total cost will be:-

Cost  =  4800   x    0.08   =   $384.00

Hence the cost of resurfacing her driveway will be $384.00.

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We would require 400 square tiles, each measuring one square foot, to cover the whole surface of the square room.

If the perimeter of the room is 80 feet, we know that all four sides of the square room have the same length. To find the length of each side, we can divide the perimeter by 4: 80 feet / 4 = 20 feet.

Now that we know the length of each side of the room, we can find the area of the room by squaring that measurement: 20 feet x 20 feet = 400 square feet.

To find the number of floor tiles needed to cover the area of the room, we divide the total area of the room by the area of each tile: 400 square feet / 1 square foot/tile = 400 tiles.

So, to cover the entire area of the square room, we would need 400 square tiles of one square foot each.

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Answer:

option 2 : y-7 = 2(x-1)

Step-by-step explanation:

the fastest way is to simply put the x- and y-values of both points into the equations, and see, which one is true for both points.

the first option is only true for the second point

7-7 = 4(1-1)

0 = 4×0 = 0

but for the first point

3-7 = 4(-1 - 1)

-4 = 4×-2 = -8

-4 = -8 is false

the second option then is true for both points

7-7 = 2(1-1)

0 = 0

3-7 = 2(-1 - 1)

-4 = 2×-2 = -4

Learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called Adaptive learning

Adaptive learning platforms utilize algorithms to tailor the learning experience for individual students based on their needs, abilities, and learning progress.

By analyzing data and feedback, adaptive learning systems can dynamically adjust the content, pace, and difficulty level to optimize learning efficiency and personalize the educational journey for each student.

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Let the number = x

The sum of five times a number and 2

Since, the number = x

five times the number = 5 * x

Fivetimes the number = 5x

The sum of five times a number and 2 = 5x + 2

Answer:

4 + 9 = 13

Step-by-step explanation:

Start by prime factorizing 108. 108 is equal to \(2^2 \cdot 3^3\). This conveniently makes the a and b we need, as we are looking for \(a^2 \cdot b^3\). We get \(a=2,b=3\). Now, plug this into \(2a+ 3b\). We get \(2 \cdot 2 + 3 \cdot 3 = 4 + 9 = 13\).

Answer:

1/2

Step-by-step explanation:

1.0 :1/2

The town's population in thousands in 2007 as per the function was 16.56 thousand.

The base value in an exponential function determines how quickly the function rises or falls. If the base value is more than 1, the function increases exponentially; if the base value is between 0 and 1, it decreases exponentially. A higher base value indicates faster growth or degradation.

Given that,

y = 8.5(1.1) ˣ

The value of x is calculated as:

x = 2007 - 2000

= 7 years.

After substituting the value of x in the given function:

y = 8.5(1.1) ⁷

y = 16.56

Hence, the town's population in thousands for 2007 is 16.56 thousand.

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