Please help. In plus only answer if know the answer

The number of students who took the test on Monday is found to be 15, hence the correct option is B.

Let us assume that the number of student taking test on Monday is n. The total score for Monday's test is n times the average score of 80.4,

Monday's total score = 80.4n

When the student who missed the test on Monday took the test on Tuesday and scored 90, the total score became,

Total score = 80.4n + 90

The new average score of 81 can be expressed as,

81 = Total score / (n+1)

Substituting the value of the total score, we get,

81 = (80.4n + 90)/(n+1)

Multiplying both sides by n+1, we get,

81(n+1) = 80.4n + 90

Expanding the brackets,

81n + 81 = 80.4n + 90

Simplifying,

0.6n = 9

n = 15, so, the number of students who took the test on Monday is 15.

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Two algebraic expressions that have the same value for all values of their variable(s) are called Equivalent expression.

Algebraic expression is an expression which is made up of variables and constants along with algebraic operation (addition, subtraction etc. )

Variables are values that can change over time.

Constant are the quantities that have fixed numerical value.

Two algebraic expression are equivalent expression if they have the same value for all values of their variable(s).

Equivalent algebraic expression are those expression which on simplification give the same resulting expression.

or

Two expression are said to be equivalent if their values obtained by substituting the values of the variable are same

For example:

Let,

\(f(x)=3(x+2)\\g(x)=3x+6\)

Substituting the \(x=4\) in the both equation..

\(f(x)=3(x+2)=3(4+2)=3(6)=3*6=18\)

\(g(x)=3x+6=3*4+6=12+6=18\)

\(3(x+2)\) and \(3x+6\) are the equivalent expression because the value of both equation remain same for any value of \(x\)

Two algebraic expressions that have the same value for all values of their variable(s) are called Equivalent expression.

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The singular points of the given differential equation are x = 0 and x = 1, corresponding to options a) 0 and b) 1.

To find the singular points of the given differential equation x²(x-1)y'' - 2xy' + y = 0, we will identify the values of x where the equation becomes singular or undefined.

The equation is in the form of a second-order linear differential equation: x²(x-1)y'' - 2xy' + y = 0.

A singular point occurs when the leading coefficient of the highest-order derivative becomes zero or undefined.

In this case, the leading coefficient is x²(x-1).

To find the singular points, we set the leading coefficient to zero:
x²(x-1) = 0

Now, we solve for x:
x² = 0  =>  x = 0

x - 1 = 0  =>  x = 1
So, options a) and b) are correct.

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Answer:

30

Step-by-step explanation:

The problem involves a rocket launched from a platform, traveling directly upward at a constant speed of 15 feet per second. the rocket's height above the ground 7 seconds after it was launched is 204 feet.

The height of the rocket above the ground can be expressed using a formula that relates the height to the time since the rocket was launched. We need to find the time elapsed when the rocket's height is 210 feet and determine the rocket's height 7 seconds after launch.

(a) To express the rocket's height above the ground, h, in terms of the number of seconds t since the rocket was launched, we can use the formula:

h(t) = 99 + 15t

(b) To find the number of seconds elapsed when the rocket's height is 210 feet, we can solve the equation:

210 = 99 + 15t

Simplifying the equation, we get:

15t = 210 - 99

15t = 111

t = 111/15

t ≈ 7.4 seconds

(c) To determine the rocket's height 7 seconds after it was launched, we can substitute t = 7 into the formula:

h(7) = 99 + 15(7)

h(7) = 99 + 105

h(7) = 204 feet

Therefore, the rocket's height above the ground 7 seconds after it was launched is 204 feet.

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Answer:

C, I got it right

Step-by-step explanation:

The two major types of series are the arithmetic series and the geometric series. The arithmetic series is characterized by common difference, while the geometric series has common ratio between two successive terms.

The sum of the given series is:

\(\lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )\)

The given series is a geometric series. So, we first calculate the common ratio (r) using:

\(r = T_2 \div T_1\)

From the series, we have:

\(T_1 = \frac{1}{4}\)

\(T_2 = \frac{1}{16}\)

So, the equation becomes

\(r = \frac{1}{16} \div \frac{1}{4}\)

Rewrite as product

\(r = \frac{1}{16} * \frac{4}{1}\)

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

The formula to calculate the sum of a geometric series of is:

\(S_n = \frac{a(1 - r^n )}{1-r}\)

Where

\(a = T_1 =\frac{1}{4}\) -- the first term

\(S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{1-\frac{1}{4}}\)

Simplify the denominator

\(S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{\frac{3}{4}}\)

Divide 1/4 by 3/4

\(S_n = \frac{1}{3}(1 - \frac{1}{4}^n )\)

We can conclude that, the sum of the series is:

\(S_n = \lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )\)

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Answer:

21

Step-by-step explanation:

Answer:

Point D

Step-by-step explanation:

Any angle with negative notation represents the measurement of the angle in clockwise direction.

Therefore, rotation of a point Q when rotated by -165° about the origin (0, 0) means rotation of the point in clockwise direction by 165°.

So the image point will lie in 4th quadrant represented by point D.

(As shown in the picture attached).

The average of the sample ranges for the weight of packages of Skittles is 0.11. So, the correct answer is (e) 0.11.

To find the average of the sample ranges for the weight of packages of Skittles, we first calculate the range for each sample. The range is the difference between the maximum and minimum values in each sample.

Sample 1: Range\(= 3.62 - 3.58 = 0.04\)

Sample 2: Range\(= 3.65 - 3.49 = 0.16\)

Sample 3: Range \(= 3.65 - 3.45 = 0.20\)

Sample 4: Range \(= 3.64 - 3.54 = 0.10\)

Sample 5: Range\(= 3.62 - 3.49 = 0.13\)

Next, we calculate the average of these sample ranges:

A\(verage = (0.04 + 0.16 + 0.20 + 0.10 + 0.13) / 5 = 0.11\)

Therefore, the average of the sample ranges for the weight of packages of Skittles is \(0.11\). So, the correct answer is (e) \(0.11.\)

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The missing angle measures for the similar triangles are given as follows:

Similar triangles share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle C is obtained as follows:

m < C + 22 + 75 = 180

m < C = 180 - 97

m < C = 83º.

The equivalent vertices on the similar triangles share the same angle measures, hence:

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Answer:

  -1 ≤ x ≤ 2

Step-by-step explanation:

You want the solution to |x +1| +|x -2| = 3.

We find it convenient to solve these absolute value equations using a graphing calculator. When we subtract 3 from both sides, we have ...

  |x +1| +|x -2| -3 = 0

The solutions will show on the graph as places where the expression has a value of 0, that is, the x-intercepts.

The left-side expression has a value of 0 for all values of x between -1 and +2, inclusive. That is, the solution is ...

  -1 ≤ x ≤ 2

The absolute value function is piecewise defined:

  |x| = x . . . . for x ≥ 0

  |x| = -x . . . . for x < 0

That is, the behavior of the function changes at x=0.

In the given equation the absolute value function arguments are zero at ...

  x +1 = 0   ⇒   x = -1

  x -2 = 0   ⇒   x = 2

These x-values divide the domain of the equation into three parts.

In this domain, both arguments are negative, so the equation is actually ...

  -(x +1) -(x -2) = 3

  -2x +1 = 3

  -2x = 2

  x = -1 . . . . . . not in the domain

In this domain, the argument (x+1) is positive, but the argument (x-2) is negative. That means the equation is ...

  (x +1) -(x -2) = 3

  1 +2 = 3

True for all x in this domain.

In this domain, both arguments are positive, so the equation is ...

  (x +1) +(x -2) = 3

  2x -1 = 3

  2x = 4

  x = 2 . . . . in the domain (this point was excluded from x < 2).

The solution is -1 ≤ x ≤ 2.

Answer:36

Step-by-step explanation:

6x6

Answer:

Step-by-step explanation:

To calculate the number of Democrats and Republicans who voted for the Clean Water bill, we need to use the information provided in the question.

First, we can calculate the number of Democrats who voted for the bill by multiplying the total number of Democrats by the percentage who voted for it:

46% of 205 Democrats = 0.46 x 205 = 94.3 Democrats (rounded to the nearest tenth)

Therefore, approximately 94 Democrats voted for the Clean Water bill.

Next, we can calculate the number of Republicans who voted for the bill by multiplying the total number of Republicans by the percentage who voted for it:

48% of 230 Republicans = 0.48 x 230 = 110.4 Republicans (rounded to the nearest tenth)

Therefore, approximately 110 Republicans voted for the Clean Water bill.

Note that these are approximations since we rounded to the nearest tenth.

To determine the optimal order size for tomato sauce for Mama Rosa, we need to use the economic order quantity (EOQ) formula. This formula is given as:

Economic Order Quantity (EOQ) = sqrt(2DS/H)

Where: D = Annual demand

S = Cost per order

H = Holding cost per unit per year

Since the EOQ is the optimal order size, Mama Rosa should order 4,648 quarts of tomato sauce each time she orders.  For Mama Rosa's tomato sauce ordering:

D = 360*120

= 43,200 Cost per order,

S = $50 Holding cost per unit per year,

H = 20% of

$1 = $0.20 Substituting the values in the EOQ formula,

we get: EOQ = sqrt(2*43,200*50/0.20)

= sqrt(21,600,000)

= 4,647.98 Since the EOQ is the optimal order size, Mama Rosa should order 4,648 quarts of tomato sauce each time she orders.  

LT = Lead time

V = Variability of demand during lead time Lead time is given as 5 days and variability of demand is the standard deviation, which is given as 50 quarts.

To determine the reorder point, we Using the z-score table, the z-score for a 2% service level is 2.05. Substituting the values in the safety stock formula. use the formula: Reorder point = (Average daily usage during lead time x Lead time) + Safety stock Average daily usage during lead time is the mean, which is given as 120 quarts. Substituting the values in the reorder point formula, we get: Reorder point = 622.9 quarts Therefore, Mama Rosa should order tomato sauce when her stock level reaches 622.9 quarts.

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Answer:

C.

Step-by-step explanation:

-x^2 - 5x + 7.

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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2 will be the output of the following code snippet.

What is a snippet in coding?

What does a code snippet look like?

The output will be 2 because when two integers are divided in Java, the decimal portion is always truncated.

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The complete question is -

The following snippet of code would produce what outcome? public static void main(String 2 [] args) { int day = 5; switch (day) { case 1: System.out.println("Monday "); case 2: System.out.println("Tuesday "); case 3: System.out.println("Wednesday "); case 4: System.out.println("Thursday "); case 5: System.out.println("Friday "); case 6: System.out.println("Saturday "); case 7: System.out.println("Sunday "); break; default: System.out.println("Invalid Day "); } } Invalid Day Friday Saturday Sunday Invalid Day Friday Friday Saturday Sunday What will be the output of the following code: int x = 20; int y = 40; if (x > 10) { if (y > 50) { System.out.println("Hello, Friend."); } else { System.out.println("Goodbye, Friend."); } } else { if (y > 50) { System.out.println("Hello, Enemy:"); } else { System.out.println("Goodbye, Enemy."); } } Hello, Friend. Hello, Enemy. Goodbye, Friend. Goodbye, Enemy.

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].

Explanation:

We can approximate f(x) as a Fourier series, as follows:

\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)

If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.

We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:

\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)

For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.

However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.

Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:

\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)

Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].

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To calculate the number of four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit, we need to consider the following:

1. Selecting the suits: There are 4 suits in a deck (hearts, diamonds, clubs, and spades). We need to choose two suits out of these four.

2. Selecting the two cards of one suit: Once we have chosen the two suits, we need to select two cards from one of the chosen suits. There are 13 cards in each suit, so we can choose 2 cards from the 13 available.

3. Selecting the two cards of another suit: After selecting the first suit, we need to choose two cards from the remaining suit. Again, there are 13 cards to choose from.

To calculate the total number of four-card hands satisfying these conditions, we multiply the number of choices at each step. Therefore, the total number of such hands is:

4C2 * 13C2 * 13C2 = (4! / (2! * 2!)) * (13! / (2! * 11!)) * (13! / (2! * 11!))

= 6 * (13 * 12 / (2 * 1)) * (13 * 12 / (2 * 1))

= 6 * 78 * 78

= 36,432.

Therefore, there are 36,432 four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit.

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Answer:

72,072

Step-by-step explanation:

To determine the number of different ways the committee can be formed, we need to calculate the combination of selecting 5 teachers out of 10 and 3 students out of 13.

The number of ways to choose 5 teachers out of 10 is given by the combination formula:

C(10, 5) = 10! / (5! * (10 - 5)!) = 252

Similarly, the number of ways to choose 3 students out of 13 is:

C(13, 3) = 13! / (3! * (13 - 3)!) = 286

To find the total number of ways the committee can be formed, we multiply the number of ways to choose teachers by the number of ways to choose students:

Total number of ways = 252 * 286 = 72,072

Therefore, there are 72,072 different ways the committee can be formed.

The company's extraction rate of contaminated water from a deep well is modeled by the function N(t) = 61¹ - 720r³ + 21600r², where t represents the number of days since the extraction began.

The given function N(t) = 61¹ - 720r³ + 21600r² represents the extraction rate of contaminated water, measured in gallons per day, from the deep well. The variable t represents the number of days since the extraction process started. The function is defined in terms of the variable r.

To understand the behavior of the extraction rate, we need to analyze the properties of the function. The function is a polynomial of degree 3, indicating a cubic function. The coefficient values of 61¹, -720r³, and 21600r² determine the shape of the function.

The first term, 61¹, is a constant representing a base extraction rate that is independent of time or any other variable. The second term, -720r³, is a cubic term that indicates the influence of the variable r on the extraction rate. The third term, 21600r², is a quadratic term that also affects the extraction rate.

The cubic and quadratic terms introduce variability and complexity into the extraction rate function. The values of r determine the specific rate of extraction at any given time. By manipulating the values of r, the company can adjust the extraction rate according to its requirements.

In summary, the company's extraction rate of contaminated water from the deep well is modeled by the function N(t) = 61¹ - 720r³ + 21600r², where t represents the number of days since the extraction began. The function incorporates a cubic term and a quadratic term, allowing the company to control the extraction rate by manipulating the variable r.

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Answer:

y = 2/3

Step-by-step explanation:

14 = 6(2) + 3y

14 = 12 + 3y

2 = 3y

y = 2/3

Answer:

-9

Step-by-step explanation:

Given :-

And we need to find out the common difference of the Arithmetic sequence . The common difference of a Arithmetic sequence is the number which is added to a term to obtain the next term of the sequence . And it can be obtained by subtracting the consecutive terms.

Sequence :-

\(:\implies\) -5 , -14 , -23

Common difference :-

\(:\implies\) CD = -14 -(-5) = -14+5=-9

\(:\implies\) CD = -23-(-14) = -23+14=-9

Hence the common difference is (-9) .

Answer:

. 8 + (7 + 3) = (8 + 7) + 3

Step-by-step explanation:

commutative property of addition

a(b+c)=(a+b)+c

Answer:

c

(8 + 7) + 3 = 3 + (8 + 7

Step-by-step explanation: