ERROR ANALYSIS 2
Solving Equations
Look at the students working below. Identify and explain the error that was
made when working the problem. Once completed re-work the problem
correctly in the space provided.
Identity & explain the error
WORKING
Sore the equation -
x-7-4
5
X5 XS
Re-work the problem
x-7-4
+7 +7
x=11

The tangent function is defined as the ratio of the sine function to the cosine function. It is periodic with a period of pi and has vertical asymptotes at odd multiples of pi/2. An equation for a tangent function with a domain of all real numbers and n as an integer is given by the following equation:
y = tan(x + n(pi))


The tangent function is defined as the ratio of the sine function to the cosine function, and it is periodic with a period of pi. It has vertical asymptotes at odd multiples of pi/2.
The tangent function can be represented by the following equation:
y = tan(x)
Where x is the angle measured in radians.
If we want to shift the graph of the tangent function by a certain amount, n, in the horizontal direction, we can use the following equation:
y = tan(x + n(pi))
Where n is an integer.
For example, if n = 2, then the graph of the tangent function would be shifted 2pi units to the left, and the equation would be:
y = tan(x - 2pi)
If n = 3, then the graph of the tangent function would be shifted 3pi units to the left, and the equation would be:
y = tan(x - 3pi)
And so on for any integer value of n.

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Examining the figure of a right angle triangle,  the required values are

information given in the question consist of right angle triangle

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the figure

x is the hypotenuse

opposite = 5

adjacent  = 8

= √(5² + 8²)

= √(25+ 64)

= √(89)

solving for the hypotenuse y

opposite = 5

adjacent  = 8 + 4 = 12

=√(5² + 12²)

=√(25 + 144)

= √(169

= 13

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To find the logarithm of 0.4 without using a calculator, we can use the properties of logarithms and some approximations. Here's a step-by-step approach:

Recall the property of logarithms: log(a * b) = log(a) + log(b).

Express 0.4 as a product of powers of 10: 0.4 = 4 * 10⁻¹.

Take the logarithm of both sides: log(0.4) = log(4 * 10⁻¹).

Use the property of logarithms to separate the terms: log(4) + log(10⁻¹).

Evaluate the logarithm of 4: log(4) ≈ 0.602.

Determine the logarithm of 10⁻¹: log(10⁻¹) = -1.

Add the results from step 5 and step 6: 0.602 + (-1) = -0.398.

Round the answer to two decimal places: -0.398 ≈ -0.39.

Therefore, the approximate value of log(0.4) is -0.39, as expected. Remember that this is an approximation and may not be as precise as using a calculator or logarithm tables.

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Answer:

-11

Step-by-step explanation:

let (2,1)be x1 and y1 respectively

(3,-10) be x2 and y2 respectively

From,slope= (y2-y1)/(x2-x1)

=(-10-1)/(3-2)

= -11/1

= -11

To calculate the company's annual holding cost, we need to multiply the annual average inventory by the holding cost per unit.

First, we need to calculate the annual average inventory. The formula for the average inventory is (Q/2), where Q represents the order quantity.

Given:

Annual requirements (Demand) = 7500 units

Ordering cost = BD 12

Order quantity (Q) = 150, 300, 45000 (Assuming these are different order quantities)

Holding cost per unit = BD 0.5

For each order quantity, we can calculate the annual average inventory using the formula (Q/2). Then, we multiply the average inventory by the holding cost per unit.

For order quantity Q = 150:

Average Inventory = Q/2 = 150/2 = 75 units

Holding Cost = Average Inventory * Holding cost per unit = 75 * 0.5 = BD 37.5

For order quantity Q = 300:

Average Inventory = Q/2 = 300/2 = 150 units

Holding Cost = Average Inventory * Holding cost per unit = 150 * 0.5 = BD 75

For order quantity Q = 45000:

Average Inventory = Q/2 = 45000/2 = 22500 units

Holding Cost = Average Inventory * Holding cost per unit = 22500 * 0.5 = BD 11250. Now, we sum up the holding costs for each order quantity:

Annual Holding Cost = BD 37.5 + BD 75 + BD 11250 = BD 11362.5 Therefore, the company's annual holding cost is BD 11362.5.

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Answer:

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

=

9

7

= 1.2857142857143

θ =

arctan( ΔY )

ΔX

= 52.125016348902°

ΔX = 49 – 21 = 28

ΔY = 63 – 27 = 36

Distance (d) = √ΔX2 + ΔY2 = √2080 = 45.607017003966

Equation of the line:

y = 1.2857142857143x – 3.5527136788005E-15

When x=0, y = -3.5527136788005E-15

When y=0, x = 2.7632217501782E-15

If 1 Point and the Slope are Known:0.75

Answer: To solve it you have to use subtraction

Step-by-step explanation:

You have to use subtraction since you don't know x,you have to do the opposite of what it's showing.

The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

Answer:

d) 2p° and (p+15) ° are complementary angles.

2p° + p° + 15° = 90°

3p° = 90° - 15°

p° = 75°/3

p = 25°

Now, 2p° = 2×25° = 50°

(p+15)° = 25°+15° = 40°

e) x° and x°÷4 are supplementary angles.

x° + x°÷4 = 180°

4x + x = 180°×4

5x = 180°×4

x = 180°×4/5

x° = 36° × 4 = 144°

And x°÷4 = 144/4 = 36°

f) Complementary angles in the ratio 4:11

Let the angles be 4x and 11x .

4x + 11x = 90°

15x = 90°

x = 6°

Now, 4x = 4×6 = 24°

11x = 11×6 = 66°

g) Supplementary angles in the ratio 7:5.

Let the angles be 7x and 5x.

7x + 5x = 180°

12x = 180°

x = 180°/12

x = 15°

Hence, 7x = 7×15 = 105°

5x = 5×15 = 75°.

by using the condition for orthogonality between surfaces and applying it to the given equation  \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\) are orthogonal at every point of intersection.

Let's consider the surfaces F(x, y, z) = 0 and G(x, y, z) = 0, where the gradients of F and G are non-zero at the point of intersection P. To prove that the surfaces are orthogonal at P, we need to show that their dot product, FxGx + FyGy + FzGz, is equal to zero at P.

The dot product of the gradients can be written as FxGx + FyGy + FzGz. If this expression evaluates to zero at P, it implies that the gradients are perpendicular, and therefore the surfaces are orthogonal at P.

Now, let's apply this result to the surfaces \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\). Taking the gradients of these surfaces, we find that the dot product FxGx + FyGy + FzGz is equal to 2\(z^{2}\) + 2(\(x^{2}\) + \(y^{2}\) + \(z^{2}\)), which simplifies to 3\(z^{2}\) + 2(\(x^{2}\) + \(y^{2}\)).

Since this expression is equal to zero for all points (x, y, z) satisfying the equation of the second surface, \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\), we can conclude that the surfaces \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\)+ \(z^{2}\) = \(r^{2}\) are orthogonal at every point of intersection

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Answer:

(a+b)^2 = a^2 + 2ab + b^2

(a-b)^2 = a^2 - 2ab + b^2

(a-b)(a+b) = a^2 - b^2

Step-by-step explanation:

Answer:

Here is the diagram that Han drew to represent 0.25. Draw a different diagram that represents 0.25. Explain why your diagram and Han's diagram represent the same number. Figure \(\Page Index{9}\) For each of these numbers, draw or describe two different diagrams that represent it. \(0.1\) \(0.02\) \(0.43\) Use diagrams of base-ten units to.

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation:

We can actually write an equation to find what should be added to get -1.

\(-\frac{5}{4}+x=-1\)

We get this equaiton because the problem asks what should be added to -5/4 to get -1. We put x in place to see what number fits. X is being added to the -5/4.

\(x=-1+\frac{5}{4}\)

\(x=-\frac{4}{4}+\frac{5}{4}\)

\(x=\frac{1}{4}\)

Answer:

The correct answer is \(\frac{1}{4}\).

Step-by-step explanation:

Method #1: Converting the given fraction to a decimal

If we convert \(-\frac{5}{4}\) to a decimal, we will get \(-1.25\). We can then see that we only need to add \(0.25\) to obtain our final needed value of \(-1\).

The mathematical process that I used to find this answer is shown here (of course, you may have learned another way than I have adapted to - if this is the case, please stick with the method that you know for adding and subtracting decimals!):

\(-1.25 + 1 = -0.25\\1.25 - 1 = 0.25\)

I always use the operation that I showed above to obtain my values. This may not work for you, and that is perfectly okay. Adding and subtracting decimals can be very tedious, but it comes as an easier obstacle throughout practice and time.

Method #2: Converting all integers to fractions

This method is much easier to use because the math is laid out for you in a more organized way.

To start, integers are any whole number that is not a fraction (they can be positive or negative). So, our value of \(-1\) qualifies as an integer.

Together, we are going to convert this value to a fraction in order to obtain fractions for ALL of our values and figure out what fraction we need in order to fulfill the requirements of our question.

To start, we already have \(-\frac{5}{4}\) in fraction form. We need to convert \(-1\) to a fraction. This is really easy to do. To transform a whole number to a fraction, follow these steps:

→ 1. If the number is negative, install the negative sign in front of the fraction. If the number is positive, you may ignore this step (fractions without a leading operation sign are always inferred to be positive without the sign).

→ 2. The numerator and the denominator will be the same value as the integer (i.e., if the integer is \(2\), the simplified fractional form is always going to be \(\frac{2}{2}\) - you can use multiples of the numerator to obtain unsimplified versions of the fraction, but it is best to keep it simplified to make our operations much easier to deal with).

With this information, we can convert \(-1\) to \(-\frac{1}{1}\).

Now, we need to find a least common multiple so that our denominators can be equal to each other and make our operations even easier to work with (once you see these steps multiple times with your own practice, you will be able to see how easy it is to do without it - just like stated earlier, this skill comes with time and much more math to come).

The denominator of \(-\frac{5}{4}\) is \(4\). We need to get the denominator of \(-1\) equivalent to follow these steps:

→ 1. Figure out what the fractional form of the denominator is (i.e., if the denominator of a fraction is \(2\), that value has a fractional form of \(\frac{2}{2}\)).

→ 2. Now, multiply the value that you get from completing the previous step by the newly converted fraction to get the common denominator and easier operations.

Using these steps, we now convert the newly converted fraction \(-\frac{1}{1}\) to \(-\frac{4}{4}\).

Here's the math worked out for this step:

\(-\frac{5}{4}\) has a denominator of 4 - get the fractional form of this value: \(\frac{4}{4}\)

\(\frac{4}{4} * -\frac{1}{1} = -\frac{4}{4}\)

Finally, we can now figure out what we need to add to \(-\frac{5}{4}\) to get \(-1\). To do this, we are going to use the keep-change-change (KCC) shortcut to solve this much quicker (this is the only way that I will demonstrate because the other way is just a reciprocal operation). I will show the math for this step below:

\(-\frac{5}{4} + \frac{4}{4} = \frac{1}{4}\)

Knowing that we have two different values that we have solved for (one in decimal form and one in fractional form), we can see that they are equivalent to each other and therefore have both options as final answers depending on the demanded format for submission.

I hope this is very helpful. If anything is unclear, please let me know so I may clear it up! Best of luck!

Values are in matrix det(A¹) = -3; det(A-¹) = -1/3; det(-2A) = 96; det (4²) = -3072(b) det(B) = 3

Given the following :Suppose A € M5,5 (R) and det(A) = -3.

Find each of the following : (a) det(A¹), det(A-¹), det(-2A), det (4²) (b) det(B), where B is obtained from A by performing the following 3 rows interchange.1.

Calculation of Determinants

The determinant of a matrix is a number obtained from a matrix. It is frequently used in linear algebra to solve problems.

The determinant of the given matrix A is det(A) = -3.2.

Calculation of det(A¹)Given that det(A) = -3

We know that det(A¹) = |A| = -3.3. Calculation of det(A-¹)

We know that A-¹ exists if and only if det(A) ≠ 0The given det(A) = -3 ≠ 0∴ A-¹ exists

Now, det(A-¹) = 1/det(A) = 1/-3= -1/3Thus det(A-¹) = -1/3.4.

Calculation of det(-2A)

Since we have a scalar value -2, it can be written as -2I.

Thus det(-2A) = det(-2I * A) = (-2I)⁵*|A| = -2⁵*(-3) = 96.

The determinant of -2A is 96.5.

Calculation of det (4²)Given that det(A) = -3

We know that det(4A) = 4⁵*|A| = 1024*(-3) = -3072Thus det(4²) is equal to -3072.6.

Calculation of det(B) where B is obtained from A by performing the following 3 rows interchange.

The determinant of B is equal to the determinant of A with the rows interchanged.

Thus det(B) = -det(A) = -(-3) = 3.

Hence the answer is :
(a) det(A¹) = -3; det(A-¹) = -1/3; det(-2A) = 96; det (4²) = -3072(b) det(B) = 3

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9514 1404 393

Answer:

Step-by-step explanation:

Let b represent the speed of runner B. then the ratio of speeds is ...

  b/(b+5) = 8/18

  18b = 8(b +5) . . . . cross multiply

  10b = 40 . . . . . . . . subtract 8b

  b = 4 . . . . . . . . . . . divide by 10

Runner B's speed is 4 mph; runner A's speed is 5 mph more.

Runner A is running at 9 mph; Runner B is running at 4 mph.

Based on the information in the graph, it can be inferred that team B scores 4 more goals per game.

To compare the populations using measures of center and median we must carry out the following procedure:

Team A

Median = 3

Q₁ = 2

Q₃ = 4

IQR = Q₃ - Q₁ = 4 - 2 = 2

Team B

Median = 7

Q₁ = 6

Q₃ = 8

IQR = Q₃ - Q₁ = 8 - 6 = 2

According to the information above, the variation in goals scored is the same. However, team B usually scores 4 more goals than team A for each game.

Additionally, the difference in the mean of these two values is 2.

Note: This question is incomplete. Here is the complete information:

Attached image

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Answer:

x > 2

Step-by-step explanation:

-4 > 10-7x

-4 - 10 > -7x

-14 > -7x

Inequality reverses when dividing or multiplying a negative number.

-14/-7 < x

2 < x

x > 2

Answer:

that formula is known as the Pythagorean theorem

Answer:

Step-by-step explanation:

Answer:

Hello There. ☆~---~--___●♡●__~--☆ Since p = x² - 7, you can substitute/plug in p for x² - 7

So:

(x² - 7)² - 4x² + 28 = 5

(p)² - 4x² + 28 = 5   You can factor out -4 from (-4x² + 28)

p² - 4(x² - 7) = 5        Plug in p

p² - 4p = 5        Subtract 5

p² - 4p - 5 = 0  And, your correct answer is C.

Hope It Helps!~

ItsNobody~ ☆

the correct notation to represent the probability of event A given event B is P(A|B).

The correct notation for the probability of event A given event B is P(A|B), which is read as "the probability of A given B." This notation represents the conditional probability of event A occurring, given that event B has already occurred.

On the other hand, OP (A or B) represents the probability of either event A or event B occurring, or their union. This is not the same as the probability of A given B.

Similarly, OP (A and B) represents the probability of both event A and event B occurring, or their intersection. This is also different from the probability of A given B.

OP(A/B) and OP(BIA) are not standard notations in probability theory and are not commonly used to represent conditional probabilities. The correct notation for conditional probability is P(A|B).

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The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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Claire experiences apprehension and fear during the anticipatory socialization phase of socialization when her boss proposes putting her on a task force at work, due to her negative group experiences in college.

Anticipatory socialization is the phase in the socialization process where individuals anticipate and prepare for their future roles and experiences in a particular social group or setting.

It involves forming expectations, attitudes, and behaviors based on past experiences and knowledge.

In Claire's case, her negative group experiences in college, where she often ended up doing most of the work and faced poor communication within the group, have shaped her expectations and attitudes towards group work.

As a result, when her boss proposes putting her on a task force at work, Claire immediately feels apprehensive and fearful.

She anticipates that she may face similar challenges, such as an uneven distribution of workload and ineffective communication, which could negatively impact her experience in the task force.

During the anticipatory socialization phase, individuals rely on their past experiences and perceptions to anticipate what they may encounter in a new social setting.

Claire's negative group experiences in college have influenced her apprehension and fear, as she expects the same difficulties to arise in the task force at work.

These emotions and concerns may impact her willingness to fully engage in the new group and could influence her interactions and behavior within the task force.

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Answer:

9 marbles

Step-by-step explanation:

He got 47 marbles, after keeping 2 of his marbles, he got 47-2 = 45 marbles left

To divide equally between his 5 friends, each of his friend should get 45 :5 = 9 marbles each

Enjoy your prize :D

Answer:

\(105+25n\)

where \(n\) is the number of weeks

Step-by-step explanation:

Initial money available with Tom = $105

Allowance given to Tom every week = $25

To find:

Equation for money available with Tom given a number of weeks.

Money available with Tom after first week = $105+ $25 = $130

Money available with Tom after second week = $130+ $25 = $155 OR 105+ 2 \(\times\) 25

Money available with Tom after third week = $155 + $25 = $180 OR 105+ 3 \(\times\) 25

and so on.

Money available with Tom after \(n\) weeks = $105 + $25 \(\times n\)

Therefore, the equation is:

\(105+25n\)

Answer: 7

This is kind of a trick question. Each daughter has one brother- the same brother.

Answer:

14 people

Step-by-step explanation:

6(2) = 12

12 + 2= 14

Answer:

73u/ - 11

Step-by-step explanation:

Answer:

-5.05. U -6

Step-by-step explanation:

Distribute the Negative Sign:=3.65u−11+−1(−5+8.7u)=3.65u+−11+(−1)(−5)+−1(8.7u)=3.65u+−11+5+−8.7uCombine Like Terms:=3.65u+−11+5+−8.7u=(3.65u+−8.7u)+(−11+5)=−5.05u+−6