4. Find the compound interest on 3000 at the rate


of 12% per annum for 12 months when interest is


compounded half-yearly.


(a) ₹370. 8


(c) 7310. 80


(b) 331


(d) 7308

Therefore, the possible rational zeros of C(x) are -1/2, 1/2, -1, 1, -2, and 2.

To find the rational zeros of the function C(x), we need to find the factors of the constant term -1 and the factors of the leading coefficient 2. Then we can form all possible fractions that can be obtained by dividing the factors of the constant term by the factors of the leading coefficient.

The factors of -1 are ±1 and ±1/2, and the factors of 2 are ±1 and ±2. Therefore, the possible rational zeros of C(x) are:

±1/2, ±1, ±1/2, ±1/1, ±2/2

Simplifying these fractions, we get:

±1/2, ±1, ±2

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Answer: The very last one 5y +5y +10

Step-by-step explanation:

Answer:

29.79 should be the answer

Step-by-step explanation:

200 copies 19.50 + 9.00 for 100 copies = 28.50 + 4% = 29.79

The cost of the resumes c(r) algebraically as a piecewise function will be: c(r)=$19.5 if r < 2 and  =$29.78 is the cost of 300 copies including a sales tax of 4 1/2

Two or more expressions with an Equal sign is called as Equation.

Given,

Dakota Printing charges 19.50$ for the first 200 copies and 9$ for every 100 additional copies.

Let r be the  number of sets of 100 resumes.

c(r)=$19.5 when r represent an integer and is less than 2

c(r)=$19.5+(r-2) ($9) (1+0.045)

c(r)=$19.5+(r-2) ($9) (1.045) when r represent an integer and is greater than 2

the cost of the resumes c(r) algebraically as a piecewise function will be: c(r)=$19.5 if r < 2

c(r)=$19.5+(r-2) ($9) (1.045) if r ≥ 2

Cost of 300 copies=($19.5+$9)+($19.5+$9) (0.045)

=$28.5+$28.5(0.045)

=$28.50+$1.28

=$29.78

Hence, the cost of the resumes c(r) algebraically as a piecewise function will be: c(r)=$19.5 if r < 2 and  =$29.78 is the cost of 300 copies including a sales tax of 4 1/2

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Answer: ...

Step-by-step explanation: Find the hypotenuse x. Suppose angle A = 50°, angle B = 60°, and angle C = x are the angles of a triangle. ABC. By using the angle sum property we can find the value of x. angle A + angle B + angle C = 180 degrees. Solve for x in fractions, we simply do the cross multiplication and simplify the equation to find x.

Answer:

26,400

Step-by-step explanation:

Just got this question.

A mile is a unit of measurement for length. The yards of cable used will be 26400. Therefore, option b is correct.

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. Such as to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

The length of cable is given as 15 miles.

Since one mile =  1760 yards

15 miles = 15 × 1760 yards

             = 26400 yards.

Hence, the yards of cable to be used is 26400 yards.

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We know that the score is obtained by subtracting the number of incorrect answers from twice the number of correct answers. Let's use "x" to represent the number of correct answers.

According to the question, the player answered 40 questions in total. This means that the number of incorrect answers is 40 - x.
Now we can use the formula for the score:
Score = 2x - (40 - x)
We also know that the player obtained a score of 50. So we can set up the equation:
50 = 2x - (40 - x)
Simplifying the equation:
50 = 3x - 40
90 = 3x
x = 30
Therefore, the player answered 30 questions correctly.
To check, we can plug this value back into the formula for the score:
Score = 2x - (40 - x)
Score = 2(30) - (40 - 30)
Score = 60 - 10
Score = 50
So the score of 50 is correct and the player answered 30 questions correctly.

To find out how many questions the player answered correctly in the trivia game with a score of 50, we can use the given information to set up an equation:
Let x be the number of correct answers and y be the number of incorrect answers. According to the question, the score is calculated by subtracting the number of incorrect answers (y) from twice the number of correct answers (2x). The player answered 40 questions in total, so we have:
x + y = 40
2x - y = 50
Now we can solve this system of equations step-by-step:
1. Solve the first equation for x:
x = 40 - y
2. Substitute this expression for x in the second equation:
2(40 - y) - y = 50
3. Simplify the equation:
80 - 2y - y = 50
4. Combine like terms:
80 - 3y = 50
5. Subtract 80 from both sides:
-3y = -30
6. Divide both sides by -3:
y = 10
7. Substitute the value of y back into the expression for x:
x = 40 - 10
x = 30
The player answered 30 questions correctly in the trivia game with a score of 50.

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Answer:

the answer is 8700

Step-by-step explanation:

(87 x 63) + (87 x 37)= 8700

hope this helps :-)

Now we have the constant of proportionality, we can fill the table in (1)

if t=6,

6 = 1/6 x d

d = 36 ft

if d = 60 ft

t = 1/6 x 60

t = 10 mins

If d =18 ft

t = 1/6 x 18

t = 3 mins

If t = 1

1= 1/6 x d

d = 6 ft

Now let me draw the table and insert the values we just got

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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Answer:

Step-by-step explanation:

Quadratic: binomial

Cubic: trinomial

Quartic: four terms

Quintic: five terms

8th degree: six terms

There are generally  \(6.776 x 10^{35}\)  particular combinations of 29 inflatables(balloons) that can be chosen from the store. 

Given data,

Since there are 8 colors of balloons,

 we need to select 29 balloons from each color to

Calculate a total of 29 x 8 = 232 balloons.

We need to find the number of different combinations of 29 balloons

that can be chosen from this set of 232 balloons.

Able to utilize the condition for combinations:  

we know that,

 C(n, r) = n! / (r! * (n - r)!) ...........(1)

where n is the complete number of things

and C is the combination of given(29) balloons.

 r is the number of things to choose.

Substituting the above values into equation (1)

 we get   

C(232, 29) = 232! / (29! * (232 - 29)!) = \(6.776 x 10^{35}\)

 Along these lines, there are generally \(6.776 x 10^{35}\)  particular combinations of 29 inflatables(balloons) that can be chosen from the store.

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Vertical asymptote: x = 2

Domain: (2, ∞)

Key point: (3/2, 16)

An asymptote is a straight line or a curve that a mathematical function approaches but never touches. In other words, as the input value of the function gets very large or very small, the function gets closer and closer to the asymptote, but it never actually intersects with it.

There are two main types of asymptotes: vertical and horizontal. A vertical asymptote occurs when the function approaches a specific x-value, but the function's output value approaches either positive or negative infinity. A horizontal asymptote, on the other hand, occurs when the function approaches a specific output value (y-value) as the input value (x-value) becomes very large or very small.

Asymptotes can be found in various mathematical contexts, including in functions like rational functions, exponential functions, logarithmic functions, and trigonometric functions. They have numerous applications in science, engineering, and other fields where mathematical modeling is required.

Vertical asymptote: x = -5

Domain: (-5, ∞)

Key point: (-4, -3)

Vertical asymptote: x = 3

Domain: (3, ∞)

Key point: (4, 1)

Vertical asymptote: x = 4

Domain: (4, ∞)

Key point: (5, 2)

Vertical asymptote: x = 1

Domain: (1, ∞)

Key point: (2, 5)

Vertical asymptote: x = 6

Domain: (6, ∞)

Key point: (7, -5)

Vertical asymptote: x = 2

Domain: (2, ∞)

Key point: (3/2, 16)

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The percentage change in the staff strength of the grocery store is 10.53%.

We are given;

Number of employees in store = 38 employees

Number of additional people hired = 4 employees

Thus, percentage change in their staff is;

4/38 * 100% = 10.53%

Thus, the percentage change in the staff strength of the grocery store is 10.53%.

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According to the information given, the correct hypotheses for a one-sample z-test for a population proportion p are:

\(H_0: p = 0.9\)

\(H_1: p < 0.9\)

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Answer:

12 hours(105km)

13.64 hours (120 km)

16 hours (141 km)

40 hours ( 352km)

Answer:

12 hours ( 105 km )

13.64 hours ( 120 km )

16 hours ( 141 km )

40 hours ( 352 km ) .

Answer:

104

Step-by-step explanation:

8x = 7x + 13

x = 13

m<U = 7(13) + 13 = 91 + 13 = 104 degrees

If person A and person B have equal positive amounts of goods X and Y and person A values good X more than good Y and person B values good Y more than good X, there are mutually beneficial trades available.

Mutually beneficial trades are the kind of trades that benefit both parties in a trade agreement. A mutually beneficial trade occurs when two countries or individuals trade and both benefit from the transaction. In the case where person A and person B have equal positive amounts of goods X and Y and person A values good X more than good Y and person B values good Y more than good X, there are mutually beneficial trades available. This is because person A would be more willing to trade his good Y for Person B’s good X since person A values good X more than good Y and person B would be more willing to trade his good X for person A’s good Y since person B values good Y more than good X. In this way, both parties would benefit from the transaction because they would be trading the goods they value less for the ones they value more.

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Answer:

Here you go

Step-by-step explanation:

A) 3x

B) -2p + 9

C) 13+6w

D) 2(5d + 3c +1)

E) 2(4g - 3)

F) 11a

Answer:

a. 3x

b. -2p+9

c. 6w+13

d. 6c+10d+2

e. 2(4g-3)

d. 11a

Step-by-step explanation:

The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.857 or 85.7%.

The random variable X represents the outcome of the first test, where it takes on a value of 1 if the student passes and 0 if the student fails.

Similarly, the random variable Y represents the outcome of the second test, taking on a value of 1 if the student passes and 0 if the student fails. Given that the joint probability of passing both tests is 0.6, we can interpret this as the probability of X=1 and Y=1.

The marginal probability of failing the first test is 0.3, which can be represented as P(X=0). To find the conditional probability of passing the second test, given that the student passed the first test, we use the formula \(P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1).\)

Since we know that \(P(X=1 and Y=1) = 0.6, and P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7\), we can substitute these values into the formula:
\(P(Y=1 | X=1) = 0.6 / 0.7\)

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The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.8571 or 85.71%.

The conditional probability of passing the second test, given that the student passed the first test, can be calculated using the formula for conditional probability:

P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1)

We are given that the joint probability of passing both tests is 0.6, which means P(X=1 and Y=1) = 0.6.

To find P(X=1), we need to use the marginal probability of failing the first test, which is given as 0.3. Since the marginal probability of passing the first test is the complement of failing the first test (i.e., 1 - 0.3 = 0.7), we can say P(X=1) = 0.7.

Now we can substitute these values into the conditional probability formula:

P(Y=1 | X=1) = 0.6 / 0.7

Simplifying this expression, we have:

P(Y=1 | X=1) = 0.8571

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

Step-by-step explanation:

a) The potential inside the sphere is constant and equal to V₀.

b) The electric field inside the sphere is zero.

a) The given electric potential function, V(θ) = V₀sin²(2θ), represents the potential on the surface of the hollow sphere. To find the potential inside the sphere, we need to consider that there are no additional free charges inside or outside the sphere. In this case, the electric potential inside a hollow sphere is constant and equal to the potential on its surface. Therefore, the potential inside the sphere is V₀.

b) To determine the electric field inside the sphere, we can use the relationship E = -∇V, where E represents the electric field and ∇V is the gradient of the potential. Since the potential inside the sphere is constant (V₀), its gradient is zero. Hence, the electric field inside the sphere is also zero.

The electric potential inside a hollow sphere is constant because, according to the given conditions, there are no additional free charges inside or outside the sphere. This implies that the electric field inside the sphere is zero. The absence of an electric field indicates that there are no forces acting on charged particles placed inside the sphere. As a result, the potential inside the sphere remains constant at the same value as the potential on its surface, which is V₀.

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Answer:

215

Step-by-step explanation:

The solution to the quadratic equation 2x²−3x−5=0 are x=5/2 or x=-1/2

The quadratic formula can be used to solve the quadratic equation 2x²−3x−5=0. Here’s how to do it:

First, identify the coefficients of the equation. In this case, a=2, b=-3, and c=-5.

Next, plug these values into the quadratic formula: x = (-b ± √(b²-4ac)) / 2a,Substitute the values in the equation: x = (-(-3) ± √((-3)²-4(2)(-5))) / 2(2)

Simplify the equation to get:x = (3 ± √(9+40)) / 4,

x = (3 ± √49) / 4
x = (3 + 7) / 4 or x = (3 - 7) / 4
x = 5/2 or x = -1/2

In summary, the quadratic formula can be used to solve quadratic equations with ease. It is important to know the values of the coefficients of the equation and substitute them into the quadratic formula. The formula will simplify the equation and give the solutions.

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Answer:

1/2 × |AB| × |OE|

Step-by-step explanation:

use the formula for finding the area of a triangle.

Answer:

k = 5

Step-by-step explanation:

The straight angle is 180º

The right angle is 90º

Therefor

(8k + 1) + 90 + 49 = 180

combine like terms

8k + 140 = 180

Subtract 140 from both sides

8k = 40

Divide both sides by 8

k = 5

Answer:

16.25

Step-by-step explanation: