Selvi deposited RM8 000 in a fixed deposit
account with a simple interest of 3.5% per annum
for a term of a year. Calculate the amount of
Selvi's money at the end of the term.​

Answer:

D. 2144.6

Step-by-step explanation:

volume of a sphere is 4/3 * pi * r^3

we've been given the value of our radius as 8 and also the value for pi is 3.142 so in you solve using the formula you get 2144

\(\\ \rm\Rrightarrow V=4/3\pi r^3\)

\(\\ \rm\Rrightarrow V=4/3\pi (8)^3\)

\(\\ \rm\Rrightarrow V=4/3\pi 512\)

\(\\ \rm\Rrightarrow V=170.6(4)\pi\)

\(\\ \rm\Rrightarrow V=682.4cm^3\)

Step-by-step explanation:

f(g(x))=(3x+1)^2 +2(3x+1) -4

=9x^2 +6x +1 +6x +2 -4

=9x^2 +12x +(-1)

Answer:

160 dollars

Step-by-step explanation:

Using Bionomial probability distribution,

the probability of getting all 10 times suceess or we will leave with $20 is 0.000104.

we have provide the following information

let the winning or success occour when heads come as result on toss of coin.

probability of winning (p) = 40% = 0.40

probability of failure (q) ,= 60% = 0.60

betting rate is $1 at a time . So, for turn $10 into $20 we have to toss a coin 10 times . After 10 toss either we complete $20 or bankrupt .

we have to calculate the probability that we winning the bet in all 10 rounds or turn $10 to $20. i.e probability of comming head in all toss of a biased coin as a result .

Using Bionomial distribution formula,

P(X= x) = ⁿCₓ(p)ˣ (q)⁽ⁿ⁻ˣ⁾

where , n---> total number of tossed a coin

x ---> number of times we have succes

Here, n= 10 and x= 10 ,p= 2/5 , q = 3/5

putting all the values in above formula we get,

P(X= 10) = ¹⁰C₁₀(2/5)¹⁰(3/5)⁰

=> P(X= 10) = (2/5)¹⁰ = 0.000104

Hence, the probability we will leave with $20 is 0.000104..

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Leaving the TV on for two weeks while on vacation would cost you approximately $4.46.

To calculate the cost, we need to determine the total energy consumed by the TV while you were on vacation and then convert it to dollars.

First, let's calculate the energy consumption in kilowatt-hours (kWh):

Power (in kilowatts) = Voltage (in volts) * Current (in amps) / 1000

Power = 120 V * 0.96 A / 1000 = 0.1152 kW

Now, we need to find the total energy consumed in kilowatt-hours (kWh) over the two-week period:

Energy (in kilowatt-hours) = Power (in kilowatts) * Time (in hours)

Energy = 0.1152 kW * 24 hours/day * 14 days = 38.4512 kWh

Next, let's calculate the cost of this energy consumption:

Cost = Energy (in kilowatt-hours) * Cost per kilowatt-hour

Cost = 38.4512 kWh * $0.116/kWh = $4.46 (rounded to two decimal places)

Therefore, leaving the TV on for two weeks while on vacation would cost you approximately $4.46.

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The probability of the randomly selected bank being a) guilty of fraud is 0.1 and b) guilty of fraud, it is given it is a private bank is 0.15

Here

let A be the event of the Bank being a fraud

Let B be the event of the bank being private

Here we see that 100 banks have been sampled.

a)

Probability = no. of favorable outcomes/total no. of outcomes

Here we see that under the row of Bank Fraud and Yes section there are

6 + 4

= 10 banks.

Hence,

n(A) = 10

n = 100

Therefore,

P(A) = 10/100

= 0.1

b)

The conditional Probability

P(X|Y) = P(X ∩ Y) / P(Y)

Here,

we need to find the bank is a fraud given that it is a private bank. Hence we need to find,

P(A|B)

= P(A ∩ B) / P(B)

Here we see that the private banks that are fraud are given to be 6.

Hence,

n(A ∩ B) = 6

Therefore,

P(A ∩ B) = 6/100

n(B) = 6 + 34 = 40

P(B) = 40/100

Hence P(A|B) = (6/100) / (40/100

= 6/40

= 3/20

= 0.15

Complete Question

(Information attached as an image)

if an audit company picks a bank at random for audit what is the probability that a bank

(a) is guilty of fraud?

(b) is guilty of fraud given it is a private bank?

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Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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The solution to the equation is x = 8.

To solve this equation, we can use the properties of logarithms to simplify it.

Recall that:

log a^b = b log a (the logarithm of a power is equal to the exponent times the logarithm of the base)

log a + log b = log(ab) (the logarithm of a product is equal to the sum of the logarithms of its factors)

log a - log b = log(a/b) (the logarithm of a quotient is equal to the difference of the logarithms of its terms)

Using these properties, we can rewrite the equation as:

2log2(x) - log2(2x) = 3

log2(x^2) - log2(2x) = 3

log2(x^2/2x) = 3

log2(x) = 3

x = 2^3

x = 8

Therefore, the solution to the equation is x = 8.

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1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

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the answer of course is bobbies

Answer

the answer if b in the above

Answer:

= 3

/3 + 5a/12 = 9/4

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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The equation that represents the situation is y = x + 6.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=) and can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

The equation that represents the situation is B. y = x + 6.

The problem states that the total cost, y, is the book price, x, plus a $6 shipping fee. We can express this as:

y = x + 6

Option A, y = 6x, suggests that the total cost is only determined by the book price multiplied by 6, which is not what the problem states.

Option C, y = , is not a valid equation as it does not include any terms to determine the value of y.

Option D, y = x - 6, suggests that the total cost is the book price minus $6, which is not what the problem states either.

Therefore, the equation that represents the situation is y = x + 6.

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The equation would be -x+10.2-\(\frac{1}{2}\)x+y

The equation contains:

-decimals

-variables

-negatives

-fractions

-like-terms

Answer:

The algebraic expression has one constant, 10.2, which is a number by itself. The variables, which are letters that stand for unknown values, are x and y. The coefficients, which are numbers that are multiplied to the variables, are

-1, -1/2, and 1. The terms that have an x are like terms.

Step-by-step explanation:

The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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Answer:

Acute

Step-by-step explanation:

It should be acute as its less than 90 (right angle) and that also mean its not obtuse ( any angle more than 90.

The marginal frequencies are 35 people have a limited data plan. 64 people have an unlimited data plan. 52 people use Company A. 47 people use Company B. 482 people were surveyed.

By dividing the sum or total of a row or the sum or total of a column by the overall number of observations in a dataset, the marginal relative frequency of a data set is determined. A two-way table is used to represent the dataset under consideration here. Both a decimal and a percentage value can be used to indicate the marginal relative frequency, though percentage values are typically preferred.

The total of the given table is:

78 + 94 + 175 + 135 = 482

From the given table of the data plan, we see that;

78 + 94 / 482 = 0.35 = 35 people have a limited data plan.

175 + 135/ 482 = 0.64 = 64 people have an unlimited data plan.

78 + 175 / 482 = 0.52 = 52 people use Company A.

94 + 135 / 482 = 0.47 = 47 people use Company B.

78 + 94 + 175 + 135 = 482 people were surveyed

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Answer:

6.66 miles

Step-by-step explanation:

Miles run in 27 minutes = 3 miles

Miles run in 1 minute = 3÷27 miles = \(\frac{1}{9}\)

1 hour = 60 minutes

Therefore,

Miles run in 60 minutes = \(\frac{1}{9}\) × 60

                                        = \(\frac{20}{3}\) miles OR 6.66 miles

Answer:

Yes

Step-by-step explanation:

Substitute:

Calculate the product or quotient:

Calculate the sum or difference:

Obtain a simplified relation:

Determine true or false: True

Answer: True

The correct answer is A) Yes.

The law of constant composition or the law of definite proportions, also recognized as

Proust's Law

, is a law that states that the components of a pure compound are always combined in the same proportion by weight.

As a result, the

compound

will always have the same relative mass of the components.

Let's use this law to solve the problem.

Firstly, we have to calculate the percentage of Na and Cl in both samples as follows:

Mass

percent of Na = (Mass of Na / Total mass of compound) × 100

Mass percent of Cl = (Mass of Cl / Total mass of compound) × 100

First sample:

Mass percent of Na = (9.3 g / (9.3 + 14.3) g) × 100 = 39.37%

Mass percent of Cl = (14.3 g / (9.3 + 14.3) g) × 100 = 60.63%

Second sample:

Mass percent of Na = (3.78 g / (3.78 + 5.79) g) × 100 = 39.53%

Mass percent of Cl = (5.79 g / (3.78 + 5.79) g) × 100 = 60.47%

As you can see, the percentage of Na and Cl in both samples are almost the same. It means the ratios of Na to Cl are the same.

Thus, these results are consistent with the law of constant composition.

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Answer:

..........................

Answer:

123

Step-by-step explanation:

insert 2 everywhere you see an x

11^2 +2 = 121+2 = 123

HOPE THIS HELPS!!!

The two data sets that meet the given conditions for in centers, and variability is in the explanations.

Data Set 1 - Heights of Adults in a City:

Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62

Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.

Data Set 2 - Salaries of Employees in a Corporation:

Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55

Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.

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Answer:A function f(x) is even if f(-x) = f(x). The function is odd if f(-x) = -f(x). An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.

Step-by-step explanation:

The function is even when f(-x) = f(x) and is odd when f(-x) = -f(x).This has been obtained using even-odd functions.

What are even-odd functions?

When the output value of a real-valued function, f(x), is equal to f(x), for all values of x inside the domain of f, the function is said to be an even function.

It is claimed that a real-valued function f(x) is an odd function when, for all values of x in the domain of f, the output value of f(-x) is equal to the negative of f(x).

We have an even function if we have an expression that is equivalent to f(x) and we have an odd function if we obtain an expression that is equivalent to -f(x).

If we take a function and substitute x for -x, simplify the result, and then compare it to what you started with, you can "determine algebraically" if the function is even, odd, or neither.

The function is even if you come out with exactly what you started with (i.e., if f (-x) = f (x), in which case all of the signs are the same. If you come out with exactly the opposite of what you started with (i.e., if f(-x) = -f (x), in which case all of the signs are switched), it is an odd function.

Hence, the function is even when f(-x) = f(x) and is odd when f(-x) = -f(x).

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Answer:

4

Step-by-step explanation:

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:   They need to drive 154 miles before they stop for the night.

Step-by-step explanation:

Given: Total distance for trip = 440 miles

Halfway distance = \(\dfrac{440}{2}=220\)

Let x be the distance they need to drive to reach halfway from the current position.

Since, they already drove 66 miles, so

x+66 = 220

⇒ x = 220-66

⇒ x = 154 miles

Hence, they need to drive 154 miles before they stop for the night.

Answer:

B

Step-by-step explanation:

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional