what is u=k/a,for a ?

Answer:

a.8x^2+18x+9

8x^2+(9+2)x+9

8x^2+2x+9x+9

2x(4x+1)+9(x+1)

(2X+9)+(4x+1)+(x+1)

Statements 2, 4 and 5 are true.

Let us check each statement one by one-

1. The square root of a positive number cannot be negative-

This statement is false. Let us take an example. If we take a number, say 4, 4 has 2 square roots- 2 and -2. This is because 2 × 2 = -2 × -2 = 4. Thus, the square root of a positive number can be negative.

2. All positive numbers have two square roots.

This statement is true. It follows from the example in 1 that any positive number has 2 square roots- one negative and one positive.

3. √18 = 9 because 9(2) = 18

The given statement is false. √18 ≠ 9. If √18 was equal to 9, then 9 × 9 must be 18. But 9 × 9 is 81. Hence, false.

4. √49 = 7 because 7(7) = 49

The given statement is true. √49 = 7 as 7 × 7 = 49

5. √25 = 5 because 5²= 25

The given statement is true. √25 = 5 as 5 × 5 = 25

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Answer:

.

Step-by-step explanation:

Answer:

50°

Step-by-step explanation:

Sum of interior angle is equal to the sum of exterior angle

Production: 168,500 units.

Direct materials: 337,000 pounds.

Direct labor: Calculated based on units produced.

Factory overhead: Calculated based on direct labor hours.

1. Production Budget for the Third Quarter:

BLACK DIAMOND COMPANY Production Budget (in units) Third Quarter

Budgeted sales units: 170,000

Add: Desired ending inventory units: 5,500

Total required units: 175,500

Less: Beginning inventory units: 7,000

Units to produce: 168,500

2. Direct Materials Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Materials Budget Third Quarter

Units to produce: 168,500

Materials needed for production (pounds): 2 pounds per snowboard

Total materials required (pounds): 337,000 pounds

Materials to purchase (pounds): Total materials required - Beginning inventory pounds - Desired ending inventory pounds

3. Direct Labor Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Labor Budget Third Quarter

Units to produce: 168,500

Direct labor hours needed: 0.5 hour per snowboard

Cost of direct labor: Direct labor hours needed * Direct labor rate

4. Factory Overhead Budget for the Third Quarter:

BLACK DIAMOND COMPANY Factory Overhead Budget Third Quarter

Direct labor hours needed: Calculated from the direct labor budget

Budgeted variable overhead: Direct labor hours needed * Variable overhead rate

Budgeted total factory overhead: Budgeted fixed overhead + Budgeted variable overhead

Note: The specific rates for direct materials, direct labor, and variable overhead were not provided in the given information and would need to be included in the calculations based on the company's specific cost structure.

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Answer:

The gradient of the line segment between the points (1,-1) and (3,-13) is -6

Step-by-step explanation:

We need to find the gradient of the line segment between the points (1,-1) and (3,-13)

The gradient is basically the slope of line.

The formula used to calculate slope\gradient is: \(Slope=\frac{y_2-y_1}{x_2-x_1}\\\)

We have \(x_1=1, y_1=-1, x_2=3, y_2=-13\)

Putting values and finding slope

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\\\Slope=\frac{-13-(-1)}{3-1} \\Slope=\frac{-13+1}{2} \\Slope=\frac{-12}{2}\\Slope=-6\)

So, gradient of the line segment between the points (1,-1) and (3,-13) is -6

Answer:

（1）：

angle1/2/3/4=90

angle6=51

angle7=40

angle8=89

angle9=51

angle10=40

angle12=50

angle13=130

angle14=50

Step-by-step explanation:

Q1：

angle1 2 3 4 divided 360 into four equal parts

so 360/4=90

angle11=110degree

so angle12 is 180-130=50 degree

because angle 12 3 10 are in triangle

their sum is 180

so angle 10=180-90（angle3）-50（angle12）=40

because angle 10 5 6 sum is 180

so angle 6 is=180-89（angle5）-40（angle10）=51

because angle 5 6 7 sum is 180

angle7=180-51（angle6）-89（angle5）=40

angle8=angle5=89

angle9=angle6=51

angle12 &13sum is 180

so angle13=180-50=130

angle14=angle12=50

The correct answer is D. 7 is the square root of 49.

The equation 7 * 7 = 49 demonstrates that the product of multiplying 7 by itself equals 49. We can analyze the options provided to determine which one accurately represents the equation.

Option A states that 49 is an even number. However, this is incorrect. An even number is divisible by 2 without a remainder. Since 49 is not divisible by 2 (49 ÷ 2 = 24 remainder 1), it is an odd number, not an even number.

Option B suggests that 49 is a prime number. A prime number is a number that is only divisible by 1 and itself. In the case of 49, it can be divided evenly by 7 and 1, making it a composite number, not a prime number. Therefore, option B is incorrect.

Option C claims that 7 is the square of 49. This is incorrect because the square of a number is the result of multiplying the number by itself. In this case, the square of 7 is 49, not the other way around.

Option D states that 7 is the square root of 49. This is the correct interpretation. The square root of a number is a value that, when multiplied by itself, results in the original number. In this case, √49 = 7.

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The histogram in Figure 2.16 shows that the distribution of waiting times is skewed to the right and not symmetrical.

Histograms are visual representations of the distribution of a dataset.

In order to determine whether the empirical rule is appropriate for describing the distribution of bank customer waiting times, we need to examine the histogram in Figure 2.16.

Looking at the histogram, we can see that the distribution of waiting times is not perfectly symmetrical.

The shape of the histogram is not exactly bell-shaped, which is what we would expect if the data were normally distributed. Instead, it is skewed to the right.

In conclusion, the histogram in Figure 2.16 indicates that the empirical rule is not appropriate for describing the distribution of bank customer waiting times. This is because the waiting times are not normally distributed and do not follow a symmetrical, bell-shaped curve.

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Answer:

The numbers are 36 and 68.

Step-by-step explanation:

Let the smaller number be x.

"The larger number is four less than two times the smaller

number."

The larger number is

2x - 4

The sum of the numbers is x + 2x - 4, or 3x - 4.

"The sum of the numbers is 104."

3x - 4 = 104

3x = 108

x = 36

The smaller number is 36.

The larger number is 2x - 4, or

2x - 4 = 2(36) - 4 = 72 - 4 = 68

The larger number is 68.

Answer: The numbers are 36 and 68.

The correct answer is: 3 premises and 1 conclusion.

A syllogism is a logical argument that consists of three parts: two premises and one conclusion. The premises are statements that provide evidence or reasons, while the conclusion is the logical outcome or deduction based on those premises. In a hypothetical syllogism, the premises and conclusion are based on hypothetical or conditional statements. By analyzing the premises and applying logical reasoning, we can determine the validity or soundness of the argument. It is important to note that the number of conclusions in a syllogism is always one, as it represents the final logical deduction drawn from the given premises.

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Answer:

It would require 40 teaspoons

Step-by-step explanation:

Given that;

A cookie recipe requires 3 teaspoons of baking soda for 36 cookies

The amount of teaspoons of baking soda required per cookie is;

r = 3/36 teaspoons per cookie

So, for 480 cookies i would require;

N = r × 480 cookies

Substituting r, we have;

N = 3/36 teaspoons per cookie × 480 cookies

N = 40 teaspoons

It would require 40 teaspoons

PCA (Principal Component Analysis) is an unsupervised learning technique used to reduce dimensionality. It is a commonly used dimensionality reduction technique. This technique is used to discover patterns in data that have multiple features. PCA is used to reduce the dimensionality of data.

Compute the mean of each feature. For every feature, compute the mean μ=1/nΣxi where n is the number of data points and xi is the feature vector. Calculate the covariance matrix compute the covariance matrix from the mean-adjusted data: X=X−μ,Covariance matrix: C=1/nXTX where X is the mean-adjusted data matrix.

Now find the eigenvectors and eigenvalues of the covariance matrix. Sort the eigenvectors in order of decreasing eigenvalues. These eigenvectors represent the principal components. The first eigenvector represents the direction of the maximum variance.

Create the projection matrix. Only the top k principal components are used for dimensionality reduction. The projection matrix can be computed by stacking the eigenvectors of the top k principal components: W=[u1u2…uk]where ui represents the eigenvector.

Project the data onto the lower-dimensional subspace. The original data can be projected onto the lower-dimensional subspace using the projection matrix: Z=X×WPCA is a commonly used dimensionality reduction technique that involves computing the principal components of a dataset. This technique can be used to find the most important patterns in the data.

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Answer:

x=−4 and y=1

Step-by-step explanation:

Rewrite equations:

y=−2x−7;−3x+4y=16

Step: Solvey=−2x−7for y:

y=−2x−7

Step: Substitute−2x−7foryin−3x+4y=16:

−3x+4y=16

−3x+4(−2x−7)=16

−11x−28=16(Simplify both sides of the equation)

−11x−28+28=16+28(Add 28 to both sides)

−11x=44

-11x/-11=44/-11

x=−4

Step: Substitute−4forxiny=−2x−7:

y=−2x−7

y=(−2)(−4)−7

y=1(Simplify both sides of the equation)

x=−4 and y=1

Answer:

Step-by-step explanation:

Answer:

k > 8

Step-by-step explanation:

Step 1: We know in order for a quadratic equation to have 2 distinct solutions the discriminant has to be positive

Important formula: Discriminant = \(b^{2}-4ac\)

Step 2: Input information into discriminant

\(b^{2}-4ac\) > 0

\(k^{2}-4(2)(8)\) > 0

\(k^{2}-64\) > 0

\(k^{2}\) > 64

\(\sqrt{ k^{2}}>\sqrt{64}\)

k > 8

Therefore in order for the equation to have 2 distinct solutions is to have k > 8

(b²-4ac) > 0

where Z is an integer

(-k)²-4(2)(8) > 0

k²-64 > 0

k²>64

k>8

Therefore the sum of all values of k is infinite

8/19 or 42.1%

add all values up to a total, then find the percentage from that total.

8 + 2 + 1 + 3 + 5 = 19 balls total

8 tennis valls to 19 total.

8/19 or 42.1%

There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Hey there!☺

\(Answer:\boxed{y=\frac{-1}{2}}\)

\(Explanation:\)

\(\frac{y}{-8}=\frac{1}{16}\)

In our first step, we will use the cross multiply method:

\(\frac{y}{-8}=\frac{1}{16}\\ y*(16)=(1)*(-8)\\16y=-8\)

In our second/last step, we will divide both sides by 16:

\(\frac{16y}{16}=\frac{-8}{16}\\y=\frac{-1}{2}\)

Hope this helps!☺

Answer:

Step-by-step explanation:

16y = -8

y = -8/16

y = -1/2

Answer:

0.625

Step-by-step explanation:

You must first calculcate what is in between the parentheses. Firstly, you add 3/8 + 3/4 (as shown in the beginning) to get 1.125. Second, you add 1/3 plus 1/6 (shown in the second part of the equation) to get 0.5. Lastly, you're left with 0.625 after subtracting 0.5 from 1.125.

Rounding to the nearest person, we estimate the city's population in 2025 to be 303,977 based on rate proportional.

When two quantities are directly proportional to one another with regard to time or another variable, this circumstance is referred to as being "rate proportional" in mathematics. For instance, if a population's rate of growth is proportionate to its size, the population will increase in size at an increasingly rapid rate. Similar to this, if an object's speed and applied force are proportionate, then increasing the force will increase an object's speed. Linear equations or differential equations can be used to describe proportional relationships, which are frequently found in many branches of science and mathematics.

To estimate the city's population in 2025, we can use the formula:

\(P(t) = P(0) * e^(kt)\)

where P(0) is the initial population (123,580 in 1990), t is the time elapsed (in years), k is the growth rate (which we need to find), and P(t) is the population at time t.

To find k, we can use the fact that the population is increasing at a rate proportional to the existing population. This means that the growth rate (k) is constant over time. We can use the following formula to find k:

\(k = ln(P(t)/P(0)) / t\)

where ln is the natural logarithm.

Plugging in the given values, we get:

k = ln(152,918/123,580) / 10 = 0.026

This means that the city's population is growing at a rate of 2.6% per year.

Now we can use the formula\(P(t) = P(0) * e^(kt)\) to estimate the population in 2025:

\(P(35) = 123,580 * e^(0.026*35) = 303,977\)

Rounding to the nearest person, we estimate the city's population in 2025 to be 303,977.

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Answer: The meausre is 25°

Step-by-step explanation:

Supplementary angles add up to 180 degrees. So if one of the angles measure 155 degrees then the other has to be added to it for it to equal 180 degrees. We can represent that by the equation  155 + x =180 where x is the measing angle.

155 + x = 180   solve for x  by subtracting 155 from both sides

-155        -155

x = 25  

Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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The given quadratic equation has no real solutions.

Given expression is 3x² + 7x = 10, and the solution to the quadratic equation using the quadratic formula is required.

Let us solve it as follows:

Step 1: Identify the values of a, b, and c. Here, a = 3, b = 7, and c = 10.

Therefore, we have: a = 3, b = 7, c = 10

Step 2: Plug in the values of a, b, and c in the quadratic formula \(X = [-b \pm \sqrt{(b^{2} -4ac)]/2a. }\)

We get X = [-7 ± √(7²-4(3)(10))]/(2×3)

Step 3: Simplify the equation obtained in Step 2.

We get\(X = [-7 \pm \sqrt{(49-120)]/6} = [-7 \pm \sqrt{(-71)]/6}\ ]\)

Now, we cannot have the square root of a negative number since the square of any real number is always positive.

Therefore, the given quadratic equation has no real solution.

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i) I was proven innocent by virtue of the law.

ii) Don’t leave without your coat.

In sentence (i), the prepositional phrase "by virtue of" introduces the reason or cause for being proven innocent. It indicates that the law is the basis or foundation for the proof.

In sentence (ii), the prepositional phrase "without your coat" indicates the absence or lack of something. It specifies that the action of leaving should not occur unless the person has their coat with them.

Prepositional phrases consist of a preposition (such as "by," "of," or "without") followed by a noun or pronoun object. They provide additional information about location, time, manner, or other relationships in a sentence. Recognizing and understanding prepositional phrases helps in comprehending the structure and meaning of sentences.

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Answer:

it helps you know what to divide

Answer:

C and D

Step-by-step explanation:

You can just divided the numerator by the denominator and find which answers are the same as 9/10