A copy machine makes 32 coples per minute. How many copies does it make in 4 minutes and 15 seconds?

Answer:

5 ml of 50% syrup solution will be used to create the final solution

Step by step Explanation:

Let the amount of 50% solution that was used = b

Which means ( 30 - b ) is the amount of 1/200 solution used then we can derive an equation as follows,

set up will then be,

0.5b +0.05(30 -b) = 1/8 (30)

We can simplifiy this as

0.5b+ 1.5 -0.05b = 3.75

Then make b the subject of the formula we have

0.45b = 2.25

b= 2.25/0.45

b = 5 ml

Therefore, 5ml of 50% syrup solution will be used to create the final solution

To find the roots of a third-degree polynomial, also known as a cubic polynomial, we can use a method called factoring or apply the cubic formula.

The first step is to check if there are any common factors that can be factored out. Next, we can use the rational root theorem to determine potential rational roots. By applying synthetic division or long division, we can divide the polynomial by the potential roots to see if they are indeed roots.

If a rational root is found, we can then use synthetic division to factor out the corresponding quadratic equation. Finally, we can solve the quadratic equation using methods like factoring, completing the square, or using the quadratic formula to find the remaining roots.

It's important to note that not all cubic polynomials can be easily factored or solved algebraically. In such cases, numerical methods or approximation techniques may be used to find the roots.

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To find the roots of a third degree polynomial, you can follow these steps: 1) Check for rational roots using the Rational Root Theorem. 2) Use synthetic division to divide the polynomial by a linear factor. 3) Factor the resulting quadratic equation. 4) Solve for the roots by setting each factor equal to zero.

To find the roots of a third degree polynomial, we can follow these steps:

Remember, the Fundamental Theorem of Algebra states that every polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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Raven bought 1/3 kg of turkey ham, and Chisa bought 2/9 kg less. The total amount of turkey ham they bought together is 1/3 + 1/9 = 3/9 + 1/9 = 4/9 kg. Together, they bought a total of 4/9 kg of turkey ham.

A fraction is a mathematical symbol that represents a portion of a whole or a component of a number. It is made up of two numbers divided by a horizontal line, with the number above the line (numerator) indicating the portion under consideration and the number below the line (denominator) indicating the entire or the total number of equal parts in the whole.

From the given information, we know that Raven bought 1/3 kg of turkey ham, and Chisa bought 2/9 kg less than Raven. This means that Chisa bought:

1/3 kg - 2/9 kg = 3/9 kg - 2/9 kg = 1/9 kg

Now we can find the total amount of turkey ham they bought together by adding Raven's purchase and Chisa's purchase:

1/3 kg + 1/9 kg = 3/9 kg + 1/9 kg = 4/9 kg

Therefore, Raven and Chisa bought a total of 4/9 kg of turkey ham together.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

now, we only need to calculate :

9 × 16 / 2 = 9 × 8 = 72 m²

Answer: 72

Hope this helps!

When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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Answer:

D. sqrt 13

Step-by-step explanation:

took on edge :)

The required magnitude of the vector is √13. Option D is correct.

A graph is given, that shows the vector, the magnitude of the vector is to be determined.

Vector form is defined as representing any point in space that has both magnitude and direction.  A point k in space is represented as a vector OKi + OKj, which denotes the vector line, OK joining the line from the origin O to the point k. The vector form is used to define a line or a plane in a 3D space.

From the figure,
given vector can be expressed as,
\(\bar v = 3\bar i+2\bar j\)
now the magnitude of vactor,
\(|\bar v| = \sqrt{3^2+2^2}\\|\bar v| = \sqrt{9+4}\ \\|\bar v| = \sqrt{13}\\)

Thus, the required magnitude of the vector is √13. Option D is correct.

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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Answer:

The slope is 2/3x and the y-intercept is 5.

Answer:6 cars

Step-by-step explanation:

Since he gave away 19 total (6+5+8) and had 25,he has 6 remaining. (25-19)

10.0 x 0.01 0 . 1

----------------- = -------------

0.01 x 0.01 0 . 0001

To find the multiple regression model, you can use statistical software like R or Python with packages such as statsmodels, scikit-learn, or MATLAB.

The actual implementation may vary depending on the specific software or programming language you are using.

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The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.

To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:

\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:

\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)

        \(= [2(3) - (0)(3)] / (3)^2\)

        = 6/9

        = 2/3

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,  
y - 0 = (2/3)(x - 1)

y = (2/3)x - 2/3

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.

Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.

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The complete question is:

Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).

Answer: 77

Step-by-step explanation:

\(g(2)=2(2)+3=7 \\\\\implies f(g(2))=f(7)\\\\f(7)=7^2 +4(7)=49+28=77\)

If demand has averaged 6105 units with a standard deviation of 243. the company currently has 6647 units in stock ,the service level is approximately 1.28%, which is option b.

To calculate the service level, we need to determine the probability that the demand does not exceed the available stock. We can use the Z-score formula to calculate this probability.

Given:

Average demand (μ) = 6105 units

Standard deviation (σ) = 243 units

Available stock (X) = 6647 units

First, we calculate the Z-score using the formula:

Z = (X - μ) / σ

Substituting the values, we get:

Z = (6647 - 6105) / 243

Z = 542 / 243

Z ≈ 2.231

Next, we need to find the corresponding probability using the Z-table or a statistical calculator. The Z-score of approximately 2.231 corresponds to a probability of approximately 0.988.

Since we are interested in the probability that the demand does not exceed the available stock, we subtract the obtained probability from 1:

1 - 0.9882 = 0.0128

Converting the probability to a percentage, we get 0.012 * 100 = 1.28%.

Therefore, correct option is B.

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Answer:

0.017

Step-by-step explanation:

The probability for 8 times will be equal to 0.16.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

That an online retailer determines that people click on a particular advertisement 2% of the time it appears.

The probability will be calculated as,

Probability = Number of favourable outcomes / Number of sample

Probability = 2% x 8

Probability = 0.02 x 8

Probability = 0.16

Therefore, the probability for 8 times will be equal to 0.16.

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Using the slope concept, it is found that the balloon's vertical distance above the ground is of 437.4 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem:

Hence, applying the concept:

tan (36º) = x/602

x = 602 x tan(36º)

x = 437.4.

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For a. 10.2,

For b. 70,

For c. 0.15,

For d. 4,

For e. 13.02,

For f. 45.4

Answer:

494,615

Step-by-step explanation:

Strategy 1.

Line up 5,819 on the top, and 85 on the bottom. Multiply 9 x 5, and if there are any carry-ons, put them above the top line of numbers. Once done with multiplying the top by 5, go under the line and write a 0. Then continue to multiple with 8, in the same way. Then add the top and bottom line (your answers), and you should get 494,615.

Strategy 2.

Use a calculator.

Step 1

Find the equation of both lines using

Where,

Hence,

For the second line we will have

Step 2

Hence expressed the graphed solution as a piecewise function

The total height of the building in question is;

600 ft

The ledge of a wall is simply a projection from a building.

Now, we are told that this ledge is 300 ft from the building.

Now, from the attached image, the distance from the ledge on the building wall to the top of the building is x.

x/300 = tan 60

x = 300 × 1.732

x ≈ 520 ft

y/300 = tan 15

y = 300 × 0.2679

y ≈ 80

Thus;

Height of building = 520 + 80

Height of building = 600 ft

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:

\(\mathrm{a=-50,\ d=7,\ general\ formula=7(n-1)-50}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Given,}\\\mathrm{15^{th}\ term(t_{15})=48}\\\mathrm{or,\ a+14d=48.........(1)}\\\mathrm{And\ 40^{th}\ term(t_{40})=223}\\\mathrm{or,\ a+39d=223......(2)}\\\mathrm{n^{th}\ term(t_n)=\ ?}\\\mathrm{Subtracting\ equation(1)\ from\ (2),}\\\mathrm{25d=175}\\\mathrm{or,\ d=7}\\\mathrm{Now,\ a+14d=48\ or,\ a=48-14d=48-14(7)}\\\mathrm{\therefore a=-50}\)

\(\mathrm{t_n=a+(n-1)d}\\\mathrm{or,\ t_n=-50+(n-1)7}\\\mathrm{\therefore general\ formula=7(n-1)-50}\)

The answer is C.) (0, 5)

Explaintion is in the pictures

I believe this is the answer if it isn't I'm sorry for wasting your time by answering.

Hope this helps!

you didnt put a number line tho :/

Answer:

25

Step-by-step explanation:

that one spongebob meme

haha

:(

theres no number line

The matrix in its reduced row echelon form is:[4, -1 | 2] [0, 1 | 2]

Given the system of equations is:4x - y = 2 and -x + y = 4To solve the given system of equations using the augmented matrix and elementary row operations, we represent the system as a matrix equation of the form AX = B, where A is the coefficient matrix of the variables, X is the matrix of the variables, and B is the constant matrix.

Therefore, we get the matrix as:⇒ [4, -1 | 2] [ -1, 1 | 4]To simplify this matrix into its reduced row echelon form, we perform elementary row operations as follows:R2 → R2 + R1Hence the matrix in its reduced row echelon form is:[4, -1 | 2] [0, 1 | 2]

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The equation that Rae should use to determine the width of a pen is 280 = w(w + 6)

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilateral are kite, rhombus, rectangle, square, parallelogram.

A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other. Each angle measure 90 degrees and diagonals bisect each other.

The area of rectangle is:

area = length * width

Let w represent the width of the rectangle

Given that length is 6 feet longer than the width, length = w + 6. Hence:

Area = length * width

substituting:

280 = w(w + 6)

w² + 6w - 280 = 0

The equation is 280 = w(w + 6)

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