Math riddle.

I am 3-digit number.

I am an even number.

If you deduct 1 from me, I become 2-digit number.

What am I?

Answer:

y= -1/2x+3

Step-by-step explanation:

math

The quadratic equation y = x² - 3 · x + 6 fits the points (0, 6), (2, 4) and (3, 6).

Herein we find a set of three points that fits in a quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. It is possible to find a quadratic equation as the number of points is equal to the numbers of real coefficients.

First, obtain the system of linear equations by substituting the values of x and y on each case:

(x, y) = (0, 6)

a · 0² + b · 0 + c = 6

c = 6

(x, y) = (2, 4)

a · 2² + b · 2 + c = 4

4 · a + 2 · b + c = 4

(x, y) = (3, 6)

a · 3² + b · 3 + c = 6

9 · a + 3 · b + c = 6

Second, solve the system of linear equations by numerical methods:

(a, b, c) = (1, - 3, 6)

Third, write the resulting quadratic equation:

y = x² - 3 · x + 6

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Answer:

45.00%

Step-by-step explanation:

The total answers count 40 - it's 100%, so we to get a 1% value, divide 40 by 100 to get 0.40. Next, calculate the percentage of 18: divide 18 by 1% value (0.40), and you get 45.00% - it's your percentage grade.

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(a) Approximated velocity of the object when t = 2 is (2.4,4,0) m/s.

(b) Approximated acceleration of the object when t = - 2.75 is (-4,-4,4) m/s^2.

(c) Approximated position of the object when t = 3.25 is (6,3,4) m.

(a) To approximate the velocity of the object when t = 2, we can use the data for t = 2.0 and t = 2.25. The change in time is 0.25 seconds.

To find the change in position, we subtract the coordinates of r(1) at t = 2.0 from those at t = 2.25, which gives us:

(3,2,0) - (2.4,1,0) = (0.6,1,0).

To find the velocity, we divide the change in position by the change in time, which gives us:

(0.6,1,0) / 0.25 = (2.4,4,0) m/s.

Therefore, the approximate velocity of the object when t = 2 is (2.4,4,0) m/s.

(b) To approximate the acceleration of the object when t = -2.75, we can use the data for t = 2.5 and t = 2.75. The change in time is 0.25 seconds.

To find the change in velocity, we subtract the coordinates of v(1) at t = 2.5 from those at t = 2.75, which gives us:

(1,1,2) - (2,2,1) = (-1,-1,1).

To find the acceleration, we divide the change in velocity by the change in time, which gives us:

(-1,-1,1) / 0.25 = (-4,-4,4) m/s^2.

Therefore, the approximate acceleration of the object when t = -2.75 is (-4,-4,4) m/s^2.

(c) To approximate the position of the object when t = 3.25, we can use the data for t = 3.0 and t = 3.25. The change in time is 0.25 seconds.

To find the change in position, we subtract the coordinates of r(1) at t = 3.0 from those at t = 3.25, which gives us:

(6,3,4) - (3,2,0) = (3,1,4).

To find the position, we add the change in position to the coordinates of r(1) at t = 3.0, which gives us:

(3,2,0) + (3,1,4) = (6,3,4).

Therefore, the approximate position of the object when t = 3.25 is (6,3,4) m.

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Answer:

6 combinations

Step-by-step explanation:

You could have a total of 6 combinations.  2 shirts, and 3 pants 2 x 3 =6

                - shorts                                               - shorts

1 red shirt - slacks                            1 blue shirt - slacks      

                - jeans                                                 - jeans

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The possible number of shirt-and-pant combinations John can wear is 6.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks. Therefore, he has two shirts, while he only has 3 pants.

The number of possible combination that John can make is,

Number of possible combination = 2 × 3 = 6

Further, the list of all the possible shirt-and-pant combinations can be written as,

Hence, the possible number of shirt-and-pant combinations John can wear is 6.

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Answer:

-----------------

Use slope formula and solve for y:

The value of y is 4.

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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Answer:

x = 5

Step-by-step explanation:

Step 1: Write equation

5x - 6 = 3x + 4

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

5(5) - 6 = 3(5) + 4

25 - 6 = 15 + 4

19 = 19

Answer:

X= 5

Step-by-step explanation:

5*5-6=19

3*5+4=19

Consider the given lines, y= 3, x= −1, x= , and y= 3x - 5 as possible asymptotes of a rational function y= f(x). This is how you can find the probable expressions for f(x) for each case when some or all of these asymptotes are present: Case 1: Only y= 3 is an asymptote It is possible to find a function with only the y= 3 asymptote.

Step by step answer:

If there is only the y = 3 asymptote, then the denominator of f(x) should have a root at x= 4. Therefore, we can write the function as f(x) = (A/(x-4)) + 3, where A is a constant to be determined. As we are dealing with rational functions, this is possible as the denominator cannot be zero.

Case 2: Only x= -1 is an asymptote It is possible to find a function with only x = -1 as an asymptote. For example,

\($$ f(x) = \frac{x-3}{x+1} $$\)

The denominator is zero at x= -1, and the numerator is nonzero, which results in the vertical asymptote at x= -1.

Case 3: Only x= 2 is an asymptote It is not possible to have only x= 2 as an asymptote for a rational function as there is no vertical asymptote in the form of x= a for any a.

Case 4: Only y= 3x - 5 is an asymptote

The line y= 3x - 5 cannot be an asymptote as it is not a horizontal or vertical line.

Case 5: Both y= 3 and x= -1 are asymptotes It is possible to have both y= 3 and x= -1 asymptotes. To find the corresponding f(x), we can use the following equation:

\($$ f(x) = \frac{A}{x+1} + 3 $$\)

where A is a constant. Here, the denominator has a root at x= -1, and the numerator is not zero.

Case 6: Both y= 3 and  

x= 2 are asymptotes It is not possible to have both

y= 3 and

x= 2 asymptotes. A rational function has a vertical asymptote if and only if the denominator of f(x) is zero at the point x = a. The denominator must be (x-2) in this case, indicating that x= 2 is a vertical asymptote. However, there is no horizontal asymptote y= 3 to be found. Therefore, this case is impossible for rational functions.

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The required answer is the equation of the tangent line to the function at the point (2, f(2)) = (2, 4) is y = 6x - 8.

To find the equation of the tangent line to the function at the point (2, f(2)) = (2, 4), we need to first find the derivative of the function at x = 2.
Assuming we have the original function loaded in content, we can find the derivative as follows:
f(x) = x^2 + 2x
f'(x) = 2x + 2

The tangent line touched the a curve can be made more explicit by considering the sequence of straight lines passing through two points, A and B, those that lie on the function curve. The tangent at is the limit when points ,approximates or tends .

If two circular arcs meet at a sharp point  then there is no uniquely defined tangent at the vertex because the limit of the progression of secant lines depends on the direction in which "point B" approaches the vertex.

The existence and uniqueness of the tangent line depends on a certain type of mathematical smoothness, known as "differentiability."
Now we can plug in x = 2 to find the slope of the tangent line at that point:
f'(2) = 2(2) + 2 = 6
So the slope of the tangent line is m = 6.
To find the y-intercept (b) of the tangent line, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Plugging in the point (2, 4) and the slope we just found, we get:
y - 4 = 6(x - 2)
Simplifying and solving for y, we get the equation of the tangent line in slope-intercept form:
y = 6x - 8
Therefore, the equation of the tangent line to the function at the point (2, f(2)) = (2, 4) is y = 6x - 8.

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Answer:

96

Step-by-step explanation:

4^2(PENDAS)=16

6*16=96

11.4

Step-by-step explanation:

Answer:

(3x+5)(7x^2+3)

Step-by-step explanation:

Factor : 21x^3+35x^2+9x+15

21x^3+35x^2+9x+15

=(3x+5)(7x^2+3)

______________________

Hope this helps!

Bootstrap sampling is a resampling technique used to estimate the sampling distribution of a statistic. In this case, we have a sample of weight changes (kg) of college students in their freshman year: 11, 5, 0, -8.

We generate ten bootstrap samples by randomly selecting observations with replacement from the original sample. The bootstrap samples obtained are: {11, 11, 11, 0}, {11, -8, 0, 11}, {11, -8, 5, 0}, {5, -8, 0, 11}, {0, 0, 0, 5}, {5, -8, 5, -8}, {11, 5, -8, 0}, {-8, 5, -8, 5}, {-8, 0, -8, 5}, {5, 11, 11, 11}. These samples represent possible alternative scenarios for the weight changes based on the observed data, allowing us to estimate the sampling variability and make inferences about the population.

Bootstrap sampling involves randomly selecting observations from the original sample with replacement to create new samples. Each bootstrap sample has the same size as the original sample. In this case, the original sample of weight changes is {11, 5, 0, -8}.

For each bootstrap sample, we randomly select four observations with replacement from the original sample. For example, in the first bootstrap sample {11, 11, 11, 0}, we randomly selected the numbers 11, 11, 11, and 0 from the original sample. This process is repeated for each bootstrap sample.

The purpose of generating bootstrap samples is to estimate the sampling distribution of a statistic, such as the mean or standard deviation. By examining the variability of the statistic across the bootstrap samples, we can make inferences about the population from which the original sample was drawn.

In this case, the bootstrap samples represent alternative scenarios for the weight changes of college students. Each sample reflects a possible combination of weight changes based on the observed data. By studying the distribution of weight changes across the bootstrap samples, we can gain insights into the variability and potential range of weight changes in the population.

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Answer:

  (x, y) = (1, -6)

Step-by-step explanation:

The expression for y given by the first equation can be substituted into the second equation.

  11x +(-8x +2) = 5 . . . substitute for y

  3x +2 = 5 . . . . . . . simplify

  3x = 3 . . . . . . . . . subtract 2

  x = 1 . . . . . . . . . divide by 3

  y = -8×1 +2 = -6 . . . . use the first equation to find y

The solution is (x, y) = (1, -6).

We have to find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1.

To find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1, we have to integrate x^(1/2) and x^(1/3) with respect to x. That is, Area = ∫0¹ [x^(1/2) - x^(1/3)] dx= [2/3 x^(3/2) - 3/4 x^(4/3)] from 0 to 1= [2/3 (1)^(3/2) - 3/4 (1)^(4/3)] - [2/3 (0)^(3/2) - 3/4 (0)^(4/3)]= 0.2857 square units

Therefore, the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1 is 0.2857 square units. Note: The question  but the answer has been provided in the format requested.

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Given: The bearing and distance of a ship from Akron(A) through Bellville(B) to Compton(C)

To Determine: The distance travelled and the angles

Solution

The diagram of the journey can be represented as shown below

Let us solve for BC using cosine rule

The total distance travelled is

Using sine rule, we can determine the measure of angle C

Also know that the sum of angles in a triangle is 180 degree. Therefore

The bearing of Compton from Bellville(B) is

The bearring of Akron(A) from Compton(C) is

In summary

The total distance travelled is 676km

The bearing of Compton from Bellville is 124.4 degrees, and the bearing of Akron from Compton is 304.4 degrees

Answer:

inequality: x > -3

Set notation: {x: x> -3}

Interval notation: [-3, ∞)

The interval can be described as inequality is x>-3, the set notation is {x: x>-3}, and the interval notation is [-3, α).

The positive, negative, whole, and rational numbers can be mark on a number line. Numbers appearing on the right side of 0 are positive, and those reflected on the left side are negative.

The thick line on the picture starts at -3 and tends towards positive infinity.  So, it can be represented as inequality by x>-3.

The set notation can be described for x-axis elements since it is a line. The elements greater than -3 are present in it. So it can represented as {x :x> -3}.

The interval ranges from -3 to positive infinity; hence, it can be represented as [-3,α).

So we can conclude that the interval can be represented by an inequality as x > -3, the set notation contains elements greater than -3, and the interval ranges from -3 to positive infinity.

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The decimal system value of the binary floating point representation [1, 1, 1, 0, 1, 1, 0, 1] with three bits used to represent the magnitude of the characteristic is -13.

To determine the decimal value of the given binary representation, we need to separate it into its three components: sign, characteristic, and mantissa.

The sign bit is the leftmost bit, which is 1, indicating a negative value.

The characteristic is the next three bits, which are [1, 1, 1]. To determine the decimal value of the characteristic, we convert it from binary to decimal. In this case, [1, 1, 1] in binary is equal to 7 in decimal.

The mantissa is the remaining bits, which are [0, 1, 1, 0, 1]. To determine the decimal value of the mantissa, we convert it from binary to decimal. In this case, [0, 1, 1, 0, 1] in binary is equal to 0.375 in decimal.

The decimal system value, v, can be calculated using the formula: v = (-1)^sign * (1 + mantissa) * 2^(characteristic - bias), where the bias is 2^(n-1) - 1, and n is the number of bits used to represent the characteristic.

In this case, the bias is 2^(3-1) - 1 = 3, and the values we have are:

sign = 1 (negative)

characteristic = 7

mantissa = 0.375

Plugging these values into the formula, we get:

v = (-1)^1 * (1 + 0.375) * 2^(7 - 3)

 = (-1) * 1.375 * 2^4

 = -1.375 * 16

 = -22

The decimal system value of the binary floating point representation [1, 1, 1, 0, 1, 1, 0, 1], with three bits used to represent the magnitude of the characteristic, is -13.

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Step-by-step explanation:

3^2 + 4^2 = 5^2

9 + 16 = 25

Therefore, 25 = 25

\(\\ \sf\longmapsto 3^2+4^2=5^2\)

Let's verify

\(\\ \sf\longmapsto 9+16=25\)

\(\\ \sf\longmapsto 25=25\)

Verified

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

linear

Step-by-step explanation:

We can write this  in the form

y = mx+b

where m is the .75 per mile and b is the 39 dollars

y = .75x + 39

Answer:

8.7

Step-by-step explanation:

a = side of a regular hexagon inscribed in a circle = radius of the circle

Area of a hexagon = (3√3 / 2)a² =  (3√3 / 2)4² = 41.57

Acircle = πr² = π4² = 50.27

Area of shaded region = Acircle - Ahexagon = 50.27 - 41.57 = 8.7

Answer:

The answer is -512

Step-by-step explanation

8*8*8= 512 and the cube root of 512 is 8 and the cube root answer is negative so 512 is negative

Answer:

B

Step-by-step explanation:

total area minus white area give you shaded area

Answer:

reggie made an error

the correct scale factor is 2/3

Step-by-step explanation:

we want to get from A to A', B to B', and ultimately C to C'

to get there, we must multiply each value in each point by the scale factor.

let's start out with reggie's scale factor. he multiplies each value in C by 3/2 to get to C'. we can try this out with one point, e.g. A

for A: 3/2 * (-12, -6) = (-18, -9). this is not A' = (-8, -4)! thus, 3/2 cannot be the scale factor

now, onto hillary's scale factor of 2/3

for A: 2/3 * (-12, -6) = (-8, -4). this is A'! thus, hillary is correct and reggie made an error

the correct scale factor is thus hillary's: 2/3

we cannot provide the specific value among the given options (A) Ο, (B) 1.162, (C) 1.465, (D) 1.845).

To find the value of x where the function f attains its maximum value on the closed interval 0 < x < 2, we need to analyze the behavior of the function using the given first derivative.

The maximum value of f can occur at critical points where the derivative is either zero or undefined, as well as at the endpoints of the closed interval.

Given that f'(x) = sin(x^3) for 0 < x < 2, we can find the critical points by setting the derivative equal to zero:

sin(x^3) = 0.

Since sin(x^3) is equal to zero when x^3 = 0 or when sin(x^3) = 0, we need to solve for these cases.

Case 1: x^3 = 0.

This case gives us x = 0 as a critical point.

Case 2: sin(x^3) = 0.

To find the values of x for which sin(x^3) = 0, we need to find when x^3 = nπ, where n is an integer.

x^3 = nπ

x = (nπ)^(1/3).

We are interested in values of x within the closed interval 0 < x < 2. Therefore, we consider the integer values of n such that (nπ)^(1/3) falls within this interval.

For n = 1, (1π)^(1/3) ≈ 1.464.

For n = 2, (2π)^(1/3) ≈ 1.847.

So, the critical points for sin(x^3) = 0 within the interval 0 < x < 2 are approximately x = 1.464 and x = 1.847.

Additionally, we need to consider the endpoints of the interval: x = 0 and x = 2.

Now, we evaluate the function f(x) at these critical points and endpoints to find the maximum value.

f(0) = ?

f(1.464) = ?

f(1.847) = ?

f(2) = ?

Unfortunately, the original function f(x) is not provided in the question. Without the explicit form of the function, we cannot determine the exact value of x where f attains its maximum on the given interval.

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Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

we can see that there is no stem value of 4 and therefore no department store with 49 pairs of glasses.

To find the largest number of pairs of glasses at any one department store, we need to examine the stem-and-leaf plot provided.

The stem-and-leaf plot shows the number of pairs of glasses at each store, with the first digit (the stem) indicating the tens place and the second digit (the leaf) indicating the ones place.

Looking at the plot, we can see that the largest stem is 4, which corresponds to the number 40. The largest leaf for stem 4 is 8, which corresponds to the number 48. Therefore, the largest number of pairs of glasses at any one department store is 48.

We can also verify this by scanning through the leaves in the plot and looking for the largest value. The largest leaf value is 9, which corresponds to the number 49. However, we can see that there is no stem value of 4 and therefore no department store with 49 pairs of glasses.

The largest number of pairs of glasses at any one department store is indeed 48.

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The two variables are said to have a correlation.

Correlation is a statistical measure of the relationship between two variables. When two variables are correlated, changes in one will be associated with changes in the other. For example, as the temperature increases, ice cream sales will also increase.

The correlation coefficient is a measure of the strength of the relationship between two variables. If the coefficient is close to +1, there is a strong positive correlation.

This means that as one variable increases, the other also increases. If the coefficient is close to -1, there is a strong negative correlation. This means that as one variable increases, the other decreases. If the coefficient is close to zero, the variables are said to have no correlation.

Correlation does not necessarily imply causation. It only indicates that two variables are related and does not necessarily explain why.

For example, two variables can be correlated because of a third variable. Therefore, correlation does not always indicate a causal relationship between two variables.

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