19. Find 3 consecutive integers such that twice
the least integer is 12 more than the greatest
integer.

Answer:

a. Jared and Ali

Step-by-step explanation:

b. Molly make mistake when he/she divide all equation by 4 but left the 8x remain 8x, it should be 2x.

Mark make mistake in changing the sign whitout changing side/ passing trough equal sign. FYI, + can be - and also - can be + if they move to the other side

i.e.

2 + 3 = 5

2 = 5 - 3

The curve of the equation x³ + 9x² = 0 is sketched.

To begin, we can start by finding the x-intercepts of the function. The x-intercepts occur when F(x) = 0, so we can set the equation equal to zero and solve for x:

x³ + 9x² = 0

x²(x + 9) = 0

This equation has two solutions: x = 0 and x = -9. These values correspond to the x-intercepts of the function.

Next, we can find the y-intercept by evaluating the function at x = 0:

F(0) = 0³ + 9(0)² = 0

So the y-intercept is 0.

We can also analyze the behavior of the function as x approaches positive or negative infinity. As x becomes very large (either positive or negative), the x³ term in the equation will dominate and the function will behave like x³. This means that the function will increase without bound as x approaches infinity, and decrease without bound as x approaches negative infinity.

To sketch the curve, we can use these points and information to plot the general shape of the function. We know that the function has two x-intercepts, at x = 0 and x = -9, and a y-intercept at the origin. We also know that the function behaves like x³ as x becomes very large (either positive or negative).

Then we get the graph like the following.

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The resulting marks on the number line would represent the positions of the square roots of different numbers. The distance between each mark would correspond to the value of the square root.

To represent the square root (√) on a number line, we can mark the positions of the square root of different numbers.

Starting from the origin (0), we can mark the position of the square root of various positive numbers by measuring the distance from the origin based on their square root value. For example, the square root of 1 (√1) is 1, so we can mark a point at 1 unit away from the origin. Similarly, the square root of 4 (√4) is 2, so we can mark a point at 2 units away from the origin.

We can continue this process for other numbers, marking the positions of their square roots on the number line. For instance, the square root of 9 (√9) is 3, so we can mark a point at 3 units away from the origin.

The resulting marks on the number line would represent the positions of the square roots of different numbers. The distance between each mark would correspond to the value of the square root.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

In various settings, such as work or school, measures of location, measures of variability, and measures of association can provide valuable insights and aid in interpreting data.

Let's consider an example from a work setting where employee performance data is collected

Measures of location, such as the mean or median, can illustrate an important aspect of employee performance. By calculating the mean performance score, we can identify the average level of performance across the organization. This measure helps us understand the central tendency of the data and provides a benchmark to assess individual employee performance against the average. If the mean performance score is low, it indicates the need for improvement in overall performance.

Measures of variability, such as the standard deviation, can indicate the spread or dispersion of performance scores. A high standard deviation suggests a wide range of performance levels among employees, indicating a lack of consistency. This insight prompts organizations to investigate the underlying factors contributing to the variability and identify areas for improvement in training, resources, or performance management processes.

Furthermore, measures of association, such as correlation coefficients, can help identify relationships between variables. For example, we can explore the correlation between employee performance scores and factors like years of experience, education level, or training hours. Understanding these associations can guide decision-making processes, such as designing targeted training programs for employees who exhibit a lower correlation between training hours and performance.

By applying these measures and interpreting the data, organizations can gain valuable insights into employee performance. This understanding can lead to improved decision-making, such as identifying areas for performance improvement, optimizing resource allocation, and implementing targeted interventions to enhance overall productivity and success within the work setting.

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The sample space for choosing one card is, S={I, L, L, M, P, T, U, Y}

Since, We know that;

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given that,

A set of eight cards were labeled with M, U, L, T, I, P, L, Y.

Here, the sample space is;

{ S, U, B, T, R, A, C, T}

Now, Elements in order is,

⇒ S = {I, L, L, M, P, T, U, Y}

Therefore, the sample space for the given cards is,

S = {I, L, L, M, P, T, U, Y}

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Answer:

\(f(1.2)=1.221\)

Step-by-step explanation:

From the question we are told that

\(dy/dx = xy\)

Initial condition\(f(1) = 1.\)

\(x = 1\)

\(Step\ Size\ of\ 0.1\)

Generally equation for \(y_1\) is given mathematically as

\(f_0=F(1,1)=1\)

Therefore

\(y_1=y_0+hf_0\)

\(y_1=y_0+(0.1)(1)\)

\(y_1=1.1\)

Generally the approximation of the solution is mathematically given by

\(x=1+h\\x=1+0.1\\x=1.1\)

\(y=1.1\)

Generally the \(f_1\) is mathematically given by

\(F_1=f(1.1,1.1)\\F_1=1.21\)

Generally the \(y_2\) is mathematically given by

\(y_2=y_1+hf_1\\y_2=1.1+0.121\\y_2=1.221\)

Generally the approximation to the solution

at

\(y_2=1.221\)

\(x_2=1.1+0.1\\x_2=1.2\)

Therefore

\(f(1.2)=1.221\)

Answer:

14x-4w+14y

Step-by-step explanation:

9x+5x-8w+4w+9y+5y

=14x-4w+14y

Graphing this equation x³ - 3x² - 4 = 1/(x - 1) + 5 we get one solution of approximately x = 0.91 and another one x = 3.689.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, An equation of degree 3 which is,

x³ - 3x² - 4 = 1/(x - 1) + 5.

Now by graphing this equation we get one solution of approximately x =

0.91 and another one x = 3.689.

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The rotation matrix R corresponding to a quaternion q=(a,b,c,d) is given by the formula shown.

To prove the given formula for the rotation matrix R corresponding to quaternion q=(a,b,c,d), we can use the properties of quaternions and matrix operations.

A quaternion can be represented as q=a+bi+cj+dk, where a, b, c, and d are real numbers. The rotation matrix R represents a linear transformation that can rotate a vector in three-dimensional space.

To derive the formula for R, we consider the rotation of a unit vector u=(x,y,z) in three-dimensional space using the quaternion q. The rotated vector can be obtained by performing quaternion multiplication between q and the quaternion representation of u.

Using quaternion multiplication rules, the rotated vector can be expressed as quq_conjugate, where q_conjugate is the conjugate of q. The result of this multiplication is another quaternion, which can be represented as r=(x', y', z', w').

The rotation matrix R can be constructed using the components of the quaternion r. The elements of R are derived from the quaternion components using specific formulas.

By performing the necessary calculations, it can be shown that the rotation matrix R is given by the formula provided:

[2(a^2+b^2)-1, 2(bc+ad), 2(bd-ac);

2(bc-ad), 2(a^2+c^2)-1, 2(cd+ab);

2(bd+ac), 2(cd-ab), 2(a^2+d^2)-1].

This formula expresses the relationship between the quaternion q and the rotation matrix R. It allows for the transformation of vectors using quaternion multiplication and provides a way to represent rotations in three-dimensional space using matrices.

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Answer:

Step-by-step explanation:

numbers to find perimeter = perimeter

Side + Side + 2 unknown sides = perimeter

12 + 7.8 + 2t = 50.2

19.8 + 2t = 50.2

19.8 + 2t = 50.2

-19.8        - 19.8

2t = 30.4

12 + 7.8 + t + t = 50.2

12 + 7.8 + (15.2) + (15.2) = 50.2

Hope this helped,

Kavitha

Answer:

t = 15.2 miles

Step-by-step explanation:

First, let's add the top and bottom numbers together.

7.8 + 12 = 19.8 mi

Next, we subtract that from 50.2 to get the combined value of both t's.

50.2 - 19.8 = 30.4 mi

Finally, we can divide 30.4 by 2 to get the value of t.

30.4 ÷ 2 = 15.2 mi

To check our answer, we can add all the sides up to see if they equal to 50.2. 15.2 + 15.2 = 30.4

30.4 + 12 + 7.8 = 50.2

Answer:

The distance from Durham to Fuquay-Varina is 30 miles.

Step-by-step explanation:

Given that the cities of Raleigh, Durham, and Fuquay-Varina approximate a right triangle, and the distance from Raleigh to Durham is 24 miles, while the distance from Raleigh to Fuquay-Varina is 18 miles, to determine what is the distance from Durham to Fuquay-Varina, the following calculation must be performed, applying the Pythagorean theorem:

18 ^ 2 + 24 ^ 2 = X ^ 2

324 + 576 = X ^ 2

√ 900 = X

30 = X

Therefore, the distance from Durham to Fuquay-Varina is 30 miles.

Answer:

twice

Step-by-step explanation:

\(\frac{4/6}{1/3} =\frac{(4)(3)}{(1)(6)} =12/6 = 2\)

Hope this helps

The number of times that Gabriel needs to use his measuring scoop to make the bread will be 2 times.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Gabriel is making bread, and his recipe calls for 4/6 cups of flour. in any case, he has just a 1/3 cup estimating scoop.

Then the number of times that Gabriel needs to use his measuring scoop to make the bread will be given as,

⇒ (4/6) / (1/3)

⇒ (4/6) x (3/1)

⇒ 4 x 3 / 6

⇒ 12 / 6

⇒ 2 times

The number of times that Gabriel needs to use his measuring scoop to make the bread will be 2 times.

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Sally's conclusion that high school GPA is an excellent and useful predictor of performance ratings at work is not entirely supported by the correlation coefficient of 0.09 with a significance level of p<.01.

Although a significant correlation suggests a positive association between high school GPA and performance ratings, the strength of the relationship is weak. The practical significance of such a weak correlation may be limited in real-world scenarios where multiple factors can influence job performance.

It is also important to note that correlation does not imply causation.

Therefore, even if high school GPA is significantly correlated with performance ratings at work, it does not necessarily mean that high school GPA is a causative factor in better job performance. Other variables such as work experience, motivation, and personality may also contribute to predicting job performance, and their effects should also be taken into account when assessing the usefulness of high school GPA as a predictor.

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The 95% upper bound represents the value below which 95% of the data falls. In this case, we have X ~ N(70,38), which means that X follows a normal distribution with a mean of 70 and a standard deviation of 38.

To find the 95% upper bound, we need to find the z-score associated with the 95th percentile.

The z-score can be calculated using the formula:
z = (x - μ) / σ

Where:
x is the value we want to find the z-score for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.

In this case, we want to find the z-score corresponding to the 95th percentile, which is 1.645. However, the critical value given is 1.69, which is slightly higher than 1.645. Therefore, we will use the critical value of 1.69 instead.

Now, we can rearrange the formula to solve for x:
x = z * σ + μ

Plugging in the values, we have:
x = 1.69 * 38 + 70

Calculating this, we find that the 95% upper bound is approximately 135.1.
Therefore, we can say with 95% confidence that X will be less than approximately 135.1.

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The data which is given by the historian is used to find the population, variable, parameter, sample, data, and statistic. He estimated the mean number of children per household in New York City in 1900.

Population - all of the households in New York City in 1900.

Variable - a quantity equivalent to the number of children in a randomly selected household

Parameter -  the mean number of children per household in New York City in 1900

Sample - the 200 households selected by the historian

Data - the 200 records collected by the historian

Statistic -  the mean number of children per household in the historian's sample.

Complete question:

Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.

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y= -2/5x

1) Since we have the point (5,-2) and also the slope m= -2/5. Let's find the linear coefficient, "b". By plugging into that equation: y=mx+b the following values

(x, y)

(5,-2)

m= -2/5

2) Plugging into that

y=mx+b

-2=-2/5 (5) +b

-2=-2 +b

-2+2=b

b=0

3) Finally, the equation that passes through the point (5,-2) with a slope of -2/5 is

y = -2/5x

The number of units x =  1500 units produce a maximum revenue r found using the given function.

To find the number of units x that produces a maximum revenue r, we need to differentiate the given revenue function with respect to x.

Then equate the derivative to zero to find the critical points which will be the maximum or minimum point for the function.

r = 180x² - 0.08x³

Let's differentiate the above revenue function with respect to x.

Using the Power Rule and the Chain Rule, we get:

dr/dx = d/dx [180x² - 0.08x³]

dr/dx = 360x - 0.24x²

To find the critical points, we need to solve the equation 360x - 0.24x² = 0

Factorizing x from the above equation, we get:x (360 - 0.24x) = 0x = 0 or 360 - 0.24x = 0

Solving for x, we get:x = 0 or x = 1500

We need to verify whether these critical points correspond to a maximum or minimum value of the function.To find out, we'll take the second derivative of the revenue function.

Using the Power Rule and the Chain Rule, we get:

d²r/dx² = d/dx [360x - 0.24x²]d²r/dx²

= 360 - 0.48x

The second derivative test states that if d²r/dx² > 0, the function has a minimum at that point; and if d²r/dx² < 0, the function has a maximum at that point.

At x = 0, d²r/dx² = 360 which is greater than 0, therefore, the function has a minimum value at x = 0.

At x = 1500, d²r/dx² = 360 - 0.48(1500)  = -360 which is less than 0, therefore, the function has a maximum value at x = 1500.

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This vector equation represents all the points that lie on the line passing through (-1, -1, -1) and (8, -1, 7) for any value of t. As t varies over the real numbers, the points P(t) trace the line in three-dimensional space.

The line passing through the points (-1, -1, -1) and (8, -1, 7) can be described using vector notation. Let's denote the position vector of a point on the line as P(t), where t is a real number that represents a parameter along the line. The vector equation for the line can be written as: P(t) = (-1, -1, -1) + t[(8, -1, 7) - (-1, -1, -1)].

Simplifying the equation: P(t) = (-1, -1, -1) + t(9, 0, 8) = (-1 + 9t, -1, -1 + 8t). This vector equation represents all the points that lie on the line passing through (-1, -1, -1) and (8, -1, 7) for any value of t. As t varies over the real numbers, the points P(t) trace the line in three-dimensional space.

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A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector. Therefore, option C is the correct answer

Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.

A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.

A) Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

B) An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.

C) Perpendicular bisector: A line that bisects a line segment in two equal parts.

D) Median: The middle number; found by ordering all data points and picking out the one in the middle.

A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector. Therefore, option C is the correct answer

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Answer:

B or second option.

Step-by-step explanation:

Answer:

I think the answer would be B..

Hope this helped...

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Answer:

He has 45 kids now.

Step-by-step explanation:

Answer:

I chose "Gallon Of Gas"

Percent of Change is (19.8C:CENTS:)per year

Average price of the item (Gas Gallon) this year (2021) is $3.744

Does It Match The Trend ? NO!

Disease in 2021 ranked the gas prices up a ton in 2021 almost by $2 in some states.

Predicted Gas Prices For Future Year !

$4 dollars per gallon / Capital price at the average rate of change and economic fixtures (Real-Life Problems)

Step-by-step explanation:

Calculate the percent of change of the item's price each decade, and use your results to determine the average rate of change from 1960–2000.

A common search on the web shows the expideited increase in gas prices incoming for the next decade.

Down below is the line graph recorded date sheet !

Answer:

6x+2

Step-by-step explanation:

First you have to do the parenthesis.

The equation should be now,

7x+3x-6-4x+8

I would now add the variables

6x-6+8

6x+2

Answer:

sorry i am trying but i don't know what to do

Step-by-step explanation:

Answer:

The answer is 10.4 :)

Step-by-step explanation:

125 + 5 x 10.4 will give you your 180 degree angle, therefore 10.4 should be the correct answer! Hope I could help <3