what is the least common multiple of 24 and 32?
i need an answer asap ​

Answer:  the value of f′′′(4) is 3/256.

Step-by-step explanation:

Given the third-degree Taylor polynomial:

f(x) = (x−4)³/512 − (x−4)²/64 + (x−4)⁴/2

To find the value of f′′′(4), we need to differentiate the polynomial three times and evaluate it at x = 4.

First derivative:

f'(x) = 3(x−4)²/512 − 2(x−4)/64 + 4(x−4)³/2

Second derivative:

f''(x) = 6(x−4)/512 − 2/64 + 12(x−4)²/2

Third derivative:

f'''(x) = 6/512 + 24(x−4)/2

Now, substitute x = 4 into f'''(x):

f'''(4) = 6/512 + 24(4−4)/2

= 6/512 + 0

= 6/512

= 3/256

Therefore, the value of f′′′(4) is 3/256.

The Construction is shown below.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

a) Steps for perpendicular line:

b) Perpendicular Bisector for triangle

So, if we extend the bisector they can meet inside, at center and outside the triangle.

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Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer:

f(x)=x/2 +8

if x =10

10/2 +8

5+8=13

Step-by-step explanation:

option c

Answer:

It would be 2x-y=3.

Answer:

y = 3/4 x + 8

Step-by-step explanation:

y-5 = 3/4 (x-(-4)

y - 5 = 3/4 (x+4)

y - 5 = 3/4 x + 3

Y = 3/4 x + 3 + 5

y = 3/4 x + 8

Answer:

(-4,5) x = -4 and y = 5

use y = mx + c formula

so 5 = 3/4 (-4) +c

5 = -3 + c

5 + 3 = c

so c = 8

y = 3/4x + 8

The velocity vector (-2, -2) points in the direction of the line joining the point (7, -4) to the point (5, -3).

To determine the direction in which the particle is moving as it passes through the point (3, -2), we need to find the velocity vector of the particle at that point.

The velocity vector is given by the derivative of the position vector with respect to time:

v(t) = (x'(t), y'(t))

where x'(t) and y'(t) are the derivatives of x(t) and y(t) with respect to t, respectively.

Taking the derivatives of x(t) and y(t), we get:

x'(t) = -2

y'(t) = 2t

So the velocity vector at time t is:

v(t) = (-2, 2t)

To find the velocity vector at the point (3, -2), we substitute t = -1 into the expressions for x(t) and y(t), since the particle passes through the point (3, -2) at time t = -1:

x(-1) = 5 - 2(-1) = 7

y(-1) = (-1)2 - 3 = -4

So the particle is at position (7, -4) when it passes through the point (3, -2).

Substituting t = -1 into the expressions for x'(t) and y'(t), we get:

x'(-1) = -2

y'(-1) = 2(-1) = -2

So the velocity vector at the point (7, -4) is:

v(-1) = (-2, -2)

The velocity vector (-2, -2) points in the direction of the line joining the point (7, -4) to the point (5, -3), which is to the left and slightly down from the point (7, -4). Therefore, the particle is moving in a direction that is slightly to the left and slightly down as it passes through the point (3, -2).

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Answer:

c = 4(d) + .43(m)

Step-by-step explanation:

We can test this by plugging in numbers for each of the variables. Let's say Jamal drove 5 miles over 2 days.

c = 4(2) + .43(5)

c = 8 + 2.15

c = $10.15

Have a nice day!

Answer:

gg

Step-by-step explanation:

hug js at Udinehebdg sorry this is for points , lol I wish I knew but sorry I dontbut good luck !

The simplified form of the given exponential notation is 2¹² = 4096.

Exponential notation is used to express any large number or very small number into a small form by using powers.

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation. This maths operation can be addition, subtraction, multiplication, or division.

For examples, - 2³, a², -9ⁿ are some kind of exponential notations.

Given is an exponential notation, (2⁻⁴)⁻³

Using exponential identity, (aⁿ)ᵇ = aⁿᵇ

(2⁻⁴)⁻³ = 2⁻⁴⁽⁻³⁾

= 2⁴⁽³⁾

= 2¹²

= 4096

Hence, the simplified form is (2⁻⁴)⁻³ = 2¹² = 4096

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A z-score of 2.2 for Test 1 indicates that a score of 750 is more than 2 standard deviations of the mean, is quite rare.

A z-score of 1.5 for Test 2 indicates that a score of 29 is only 1.5 standard deviations above the mean, is relatively less rare.

The more unusual score is the Test 1 score of 750. A.

To determine which score is more unusual, we need to calculate the z-scores for both scores.

For Test 1, if a student has a score of 750, their z-score would be:

z = (750 - 530) / 100 = 2.2

For Test 2, if a student has a score of 29, their z-score would be:

z = (29 - 23) / 4 = 1.5

The z-score tells us how many standard deviations a data point is away from the mean of the distribution.

A higher absolute value of the z-score indicates that the data point is further away from the mean and hence more unusual.

A z-score of 2.2 for Test 1 indicates that a score of 750 is more than 2 standard deviations above the mean, is quite rare.

A z-score of 1.5 for Test 2 indicates that a score of 29 is only 1.5 standard deviations above the mean, is relatively less rare.

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Answer: complementary

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees

The sum of the measure of angles 1 and 2 is the right angle which is 90 degrees. Then the correct option is C.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Angles 1 and 2 form a right angle.

2 lines form a right angle.

Another line extends between the 2 lines to form 2 angles.

The top angle is labeled 1, and the bottom angle is labeled 2.

Then the sum of the measure of the angle 1 and 2 is the right angle which is 90 degrees. Then the angles are known as complementary angles.

Then the correct option is C.

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In the question, the independence assumption may have been violated, while the Nearly Normal Condition is likely justified. Therefore, the use of the Student-t model for inference may be unreliable.

a) In order to perform a hypothesis test on the claim made by the diet guide, we need to assess the assumptions and conditions required for reliable inference. The independence assumption states that the observations are independent of each other. In this case, it is not explicitly mentioned whether the yogurt samples were independent or not. If the samples were obtained from the same batch or were not randomly selected, the independence assumption could be violated.

Regarding the Nearly Normal Condition, which assumes that the population of interest follows a nearly normal distribution, it is reasonable to assume that the distribution of calorie counts in vanilla yogurt is approximately normal. However, since we do not have information about the population distribution, we cannot definitively justify this condition.

b) The appropriate hypotheses for testing the claim made by the diet guide would be:

H0: The average calories per serving of vanilla yogurt is 120.

HA: The average calories per serving of vanilla yogurt is not equal to 120.

To test these hypotheses, we can use a t-test for a single sample. The test statistic (t) can be calculated by taking the mean of the sample calorie counts and subtracting the claimed average (120), divided by the standard deviation of the sample mean. The p-value can then be determined using the t-distribution and the degrees of freedom associated with the sample.

Without the actual sample mean and standard deviation, it is not possible to provide the specific test statistic and p-value for this scenario. These values need to be calculated using the given data (calorie counts) in order to draw a conclusion about the claim made by the diet guide.

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Answer:

2πr

Step-by-step explanation:

The function f(x) = ((x+1)/(x-1))^3 is bijective as it is both injective and surjective, meaning it has a one-to-one correspondence between its domain and codomain.

To prove that f(x) = \(((x+1)/(x-1))^3\)is bijective, we need to show that it is both injective and surjective.

Injectivity: To prove injectivity, we assume that f(x1) = f(x2) and show that it implies x1 = x2. So, let's assume f(x1) = f(x2) and substitute the function values:

\(((x1+1)/(x1-1))^3 = ((x2+1)/(x2-1))^3\)

Taking the cube root of both sides, we get:

(x1+1)/(x1-1) = (x2+1)/(x2-1)

Cross-multiplying and simplifying, we have:

x1 + 1 = x2 + 1

This implies x1 = x2, which shows that the function is injective.

Surjectivity: To prove surjectivity, we need to show that for every y in the codomain, there exists an x in the domain such that f(x) = y. In this case, the codomain is R - {1}.

Let y be an arbitrary element in R - {1}. We can solve the equation f(x) = y for x:

\(((x+1)/(x-1))^3\)= y

Taking the cube root of both sides, we get:

\((x+1)/(x-1) = y^(1/3)\)

Cross-multiplying and simplifying, we have:

\(x + 1 = y^(1/3)(x - 1)\)

Expanding and rearranging terms, we get:

\((x - y^(1/3)x) = y^(1/3) - 1\)

Factoring out x, we have:

\(x(1 - y^(1/3)) = y^(1/3) - 1\)

Dividing both sides by (1 - y^(1/3)), we get:

\(x = (y^(1/3) - 1)/(1 - y^(1/3))\)

This shows that for any y in R - {1}, we can find an x in the domain such that f(x) = y, proving surjectivity.

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The dot product of vectors x and y with magnitudes 5 and 4 units, respectively, is 20 units, indicating that they are parallel to each other and in the same direction.

From the given information, we know that the magnitudes of vectors x and y are 5 and 4 units, respectively, and their dot product is 20 units.

To find the angle between vectors x and y, we can use the formula:

cos(theta) = (x.y) / (|x| * |y|)

Substituting the given values, we get:

cos(theta) = 20 / (5 * 4)
cos(theta) = 1

This implies that the angle between vectors x and y is 0 degrees, which means that they are parallel to each other.

Thus, we can conclude that vectors x and y are parallel and in the same direction.



Given the magnitudes of vectors x and y and their dot product, we can determine their relationship and direction. The dot product is the product of their magnitudes and the cosine of the angle between them. Using this formula, we found that the angle between vectors x and y is 0 degrees, indicating that they are parallel to each other. Therefore, we can conclude that vectors x and y are parallel and in the same direction. This information can be useful in various mathematical and physical applications, such as determining the force required to move an object in a particular direction.



In conclusion, the dot product of vectors x and y with magnitudes 5 and 4 units, respectively, is 20 units, indicating that they are parallel to each other and in the same direction. This information can be useful in various mathematical and physical applications.

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Hence,  when \(n=10\) the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.

So,

\(2(n + 2) < 5(n-1)\)

When

\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)

Hence,  when \(n=10\) the given inequality is true.

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Thus, the radius of convergence of the series is 4. That shows  that the series converges absolutely for all values of x such that |x| < 4, and diverges for all values of x such that |x| > 4.

To find the radius of convergence of the given series, we can use the ratio test.

The ratio test states that for a series ∑an, if the limit of |an+1/an| as n approaches infinity is L, then the series converges absolutely if L < 1, diverges if L > 1, and inconclusive if L = 1.

So, applying the ratio test to the given series, we get:

|a(n+1)/an| = |(n+1)!x^(n+1) 3 · 7 · 11 · ⋯ · (4n + 3) / n!x^n 3 · 7 · 11 · ⋯ · (4n − 1)|
= |(n+1)x / (4n+3)|
= |x/(4 + 3/n)|

Taking the limit as n approaches infinity, we get:
lim n→∞ |a(n+1)/an| = |x/4|

Since we want this limit to be less than 1, we have:
|x/4| < 1

Solving for x, we get:
-1 < x < 4

Therefore, the radius of convergence of the series is 4. This means that the series converges absolutely for all values of x such that |x| < 4, and diverges for all values of x such that |x| > 4. When |x| = 4, the series may converge or diverge, and further analysis is needed to determine this.

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Answer:

\(5^{-2}\)

Step-by-step explanation:

Primd factorize 25

25 = 5*5 = 5²

\(\sf \dfrac{1}{25}=\dfrac{1}{5^{2}} \\\\= 5^{-2}\)

HINT:

\(\dfrac{1}{a^{m}}=a^{-m}\)

The dimension of the length of the classroom in the drawing is calculated to be 7 ft

The scale of a map represents by how much a map is reduced or increased. Most of the times the map is smaller than what is being represented hence the scale is usually a reduction.

Give that

1 in in drawing represent 7 ft in actual length

If the actual length of your classroom is 49 feet then we solve as follows to get the dimension in the drawing:

1 in = 7 ft

? in = 49 ft

cross multiplying gives

7 * ? = 49 * 1

? = 49 / 7

? = 7 in

Hence, the conclusion is that the unknown dimension in the drawing represented as ? is equal to 7 in.

This implies that 7 in in the drawing represents actual distance of 49 ft and this is a reduction

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30 ÷ (15÷2.5) + 7

Given: 16 · (4.5 + 3) ÷ 10= ____

First let us do PEMDAS (Parenthesis, Equation, Multiply, Divide. Add, Subtract) upon the given value.

16 · (7.5) ÷ 10 = ____

       120 ÷ 10 = ____

                     = 12

We now understand that the given is equal to the value of 12, now we will calculate each equation with PEMDAS until we find the equivalent value.

20.8 + (3 · 4) ÷ 4 =

   20.8 + 12 ÷ 4   =

          20.8  +  3  =

                            = 23.8

24 ÷ (8 − 4) + 8.2 =

       24 ÷ 4 + 8.2 =

               6 + 8.2 =

                            = 14.2

30 ÷ (15 ÷ 2.5) + 7 =

            30 ÷ 6 + 7 =

                     5 + 7 =

                              = 12

36 ÷ (9 − 4.2) + 3 =

       36 ÷ 4.8 + 3 =

                7.5 + 3 =

                            = 10. 5

It is safe to say the following:

16 · (4.5 + 3) ÷ 10 ≠ 20.8 + (3 x 4) ÷ 4

16 · (4.5 + 3) ÷ 10 ≠ 24 ÷ (8 − 4) + 8.2

16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7

16 · (4.5 + 3) ÷ 10 ≠ 36 ÷ (9 − 4.2) + 3

Therefore, the answer is:

16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7

Hope this helps =D, happy learning !

We obtained the solutions by solving the system via substitution:

x = 2/3, y = 8/3.

We should probably start by solving problem number 5 in the system of equations.

The set of equations is as follows:

y = x + 2

3x + 3y = 6

We must isolate one of the variables from one of the equations before substituting it in the other equation to solve it via substitution.

Since "y" is already isolated in the first equation, for instance, we can utilize it to replace it in the second equation.

3x + 3y = 6

3x + 3*(y = x + 2) = 6

3x + 3*(x + 2) = 6

We now have an equation that depends just on x, allowing us to solve it:

3x + 3x + 2 = 6

6x + 2 = 6

6x = 6 - 2 = 4

x = 4/6 = 2/3.

The value of y can now be determined using the first equation:

y = x + 2 = 2/3 + 2 = 2/3 + 6/3 = 8/3.

The answer is then:

x = 2/3 and y = 8/3.

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The Complete Question

Unit 5: Systems of Equations & Inequalities Homework 2: Solving Systems by Substitution

The alternative Hypothesis is that at least one of the mean total cholesterol levels is different from the others in the four groups of subjects.

A researcher can use an analysis of variance (ANOVA) parametric statistical method to determine if the mean total cholesterol level of the population is the same for four groups of subjects (Group 1 = Diet Restriction; Group 2 = Exercise; Group 3 = Both Diet and Exercise; Group 4 = None).

a. Statistical Test is ANOVA.
b. Null Hypothesis is that the mean total cholesterol level of the population is the same for all four groups.
c. Alternative Hypothesis is that the mean total cholesterol level of the population is different for at least one group.

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The vertex form of the quadratic equation \(\(y = x^2 - 6x + 2\) is \(y = (x - 3)^2 - 7\)\) represents a minimum at \(\((3, -7)\)\).

To rewrite the quadratic equation \(\(y = x^2 - 6x + 2\)\) in vertex form, we complete the square by adding and subtracting the appropriate constant term.

Starting with \(\(y = x^2 - 6x + 2\)\), we proceed as follows:

\(\[y = (x^2 - 6x) + 2\]\)

Now, we complete the square by adding the square of half the coefficient of \(\(x\)\) to both sides:

\(\[y = (x^2 - 6x + 9) - 9 + 2\]\)

Simplifying further:

\(\[y = (x^2 - 6x + 9) - 7\]\)

The expression inside the parentheses can be rewritten as a perfect square:

\(\[y = (x - 3)^2 - 7\]\)

Now we have the equation in vertex form, which is \(\(y = a(x - h)^2 + k\)\), where \(\((h, k)\)\) represents the vertex of the parabola.

Comparing the equation to the vertex form, we can identify where the vertex is at \(\((h, k) = (3, -7)\)\).

Therefore, the correct answer is:

b. minimum at \(\((-3, -7)\)\)

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Answer:

Step-by-step explanation:

The value of x in the secant intersection is 16 units.

Secant is a line that intersects a curve at a minimum of two distinct points. Therefore, the product of secant segment is equals to the product of the other secant segment and its external segment.

Hence, using the rule for secant intersection,

let's find x

8 × (8 + 4) = (x - 10)x

8(12) = x² - 10x

96 = x² - 10x

x² - 10x - 96 = 0

x² - 16x + 6x - 96 = 0

x(x - 16) + 6(x - 16) = 0

(x + 6)(x - 16) = 0

Therefore,

x = -6 and x = 16

Therefore, we can only use positive number.

Hence,

x = 16 units

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Answer:

$2511.674254, rounded to $2512

Step-by-step explanation:

1700x1.05^8

Answer:

X= 43/3

Step-by-step explanation:

-1/4 x 5 = 3/4x - 12

-5/4=3/4x -12

-5=3x - 48

-3x-5 = -48

-3x = -48 + 5

-3x= -43

-3 x= -43

X= 43/3