find the principle which amount 10 birr 142.83 in 5 year as 3% peryear​

Answer:

I belive the answer is 96 ft.

Step-by-step explanation:

Hope that helps!

Answer:

245 miles per hour

Step-by-step explanation:

1470 divided by 6

Total number of employee working for four hours per shift for the manager is 2 people.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event. The probability of an event can not be more than the number 1.

The probability of failure of an event is equal to the difference of the 1 to the success of the event.

Here, the manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution below.

Probability Distribution

Hours Worked: X     Probability: P(X)

           3                         0.1

           4                           ?

           5                        0.14

           6                         0.3

           7                        0.36

           8                       0.06

As, the probability of an event can not be more than the number 1. Thus, the sum of all the probabilities will be equal to 1.

Let suppose the probability of people working for four hour is x. Therefore,

\(0.1+x+0.14+0.3+0.36+0.06=1\\x+0.96=1\\x=1-0.96\\x=0.04\)

Now, the total number of people work for the manager is 50. Therefore, total number of people working for 4 hours are,

\(0.04\times50=2\)

Hence, total number of employee working for four hours per shift for the manager is 2 people.

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Answer:

Step-by-step explanation:

The first one :

3/10 + 4/14 = 3.7/10.7 + 4.5/14.5 = 21/70 + 20/70 = (21+20)/70 = 41/70

The first step is, to make the 2 denominators of the 2 fractions to be the LCM.

10 = 2.5
14 = 2.7
So, the LCM of these 2 will be 2.5.7 = 70

In 3/10, we multiply both the nominator and the denominator by 7 to make the denominator 70.

And in 4/14, we multiply both the nominator and the denominator by 5 to make the denominator 70

And so we have : 21/70 + 20/70
Add the nominators together, the denominator stay the same, we'll have 41/70.


The second one : 5/12 = 6/13 = 5.13/12.13 - 6.12/13.12 = 65/156 - 72/156 = (65-72)/156 = -7/156

So, we find the LCM of 12 and 13 again. And since 13 is a prime number and 12 is not a factor of 13, the LCM will be 12x13=156

Multiply both the nominator and the denominator of 5/12 by 13, and 6/13 by 12, we'll get 65/156 and 72/156

Subtract the nominators, the denominator stay the same, we get -7/156.

Answer:

$3,700

Step-by-step explanation:

12% of 9,250 is 1,110

so each year 1,110 is subtracted from the original price of the tractor.

So if you subtract 1,110 five times from 9,250 you get 3,700.

Answer:

y = 5/3x - 2

Step-by-step explanation:

Slope = 5/3

y-intercept: - 2

Answer:

where is the rest of the context?

Answer:

\(\frac{2x^2-4x-12}{x^2+3x}\)

Step-by-step explanation:

=> \(\frac{2x}{x+3} - \frac{4}{x}\)

LCM = x(x-3)

=> \(\frac{2x^2-4(x+3)}{x(x+3)}\)

=> \(\frac{2x^2-4x-12}{x^2+3x}\)

This is the required simplest form and can't be simplified further.

Hope this Helps!

Don't hesitate asking any question regarding this.

The height of the actual building, given the height of the model, can be found to be 1, 455 feet

The model is such that every inch of the building on the model is 75 feet of the actual building.

This means that if the height of the building in the model is 19 ² / ₅ inches, then the height of the actual building would be:

= Height of building in model x Scale factor per inch

= 19 ² / ₅  x 75

= 97 / 5 x 75

= 1, 455 feet

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The graph for the three selected points can be found in the photos section. Good luck!

(i)The number of distinct words that can be made using all the letters from the word EXAMINATION is 99,792.

(ii) The number of words that can be made when "AA" must not occur is 97,978

(i)The word EXAMINATION has a total of 11 letters. However, there are repeating letters: two 'A's and two 'I's.

P = n! / (n1! * n2! * ... * nk!)

n = 11 (total number of letters) n1 = 2 ('A's) n2 = 2 ('I's)

Putting these values into the formula

P = 11! / (2! * 2!)

P = 399,1680 / 4

P = 99,792

Therefore, the number of distinct words that can be made using all the letters from the word EXAMINATION is 99,792.

(ii) The number of words that can be made when "AA" must not occur, we need to subtract the number of words containing "AA" from the total number of distinct words.

Using the result from part (i), which is 99,792, we need to subtract the number of words that have "AA."

The number of words with "AA" can be found by treating "AA" as a single entity, so the remaining letters can be rearranged in (11 - 1) = 10 positions.

Therefore, the number of words with "AA" is equal to the number of distinct words that can be made using 10 letters, which is calculated as

P = 10! / 2!

P = 3,628 / 2

P = 1,814

Number of words = Total number of distinct words - Number of words with "AA"

Number of words = 99,792 - 1,814

Number of words = 97,978

Therefore, the number of words that can be made when "AA" must not occur is 97,978.

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Answer:

  they are the same

Step-by-step explanation:

The number of guests seated were, in each case, ...

  (guests per table) × (number of tables)

__

For Santa, this product is ...

  X × Y

For Mrs. Claus, this product is ...

  Y × X

The commutative property of multiplication tells you that ...

  XY = YX

The numbers of guests were the same.

The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High  .

In the question ,

it is given that

the Summer is planning to build a small snow cone shed .

the distance from north junior high = 7/8 miles = 0.875 miles

the distance from South elementary = 0.680 miles

the distance from West Side elementary = 5/6 miles = 0.833 miles

From , above result we see that

the farthest from summer snow cone is north junior high which is 0.875 miles .

the nearest from summer snow cone is South Elementary which is 0.680 miles .

So , the order from closest to farthest is

South Elementary < West Side Elementary < North Junior High

Therefore , The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High  .

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Answer:

x=3

Step-by-step explanation:

Check the picture

The sum of the first 10 terms of the sequence -5, 15, 45, 135 is 295240.

We can use the following formula to determine the sum of a geometric sequence:

S = a(1 - r^n) / (1 - r) (1 - r)

where an is the first term, r is the common ratio, and n is the total number of terms, S is the sum of the sequence.

We can see that the first term in the series -5, 15, 45, 135 is -5, and the common ratio is 3. (since each term is obtained by multiplying the previous term by 3). The series contains 4 terms, hence n is equal to 4. Adding these values to the formula yields the following results:

S = -5(1 - 3^4) / (1 - 3) (1 - 3)

S = -5(1 - 81) / (-2) (-2)

S = 5(80) (80)

S = 400

The total of the numbers 5, 15, 45, and 135 equals 400.

We may once more use the following formula to determine the sum of the first 10 entries in the same sequence:

S = a(1 - r^n) / (1 - r) (1 - r)

Instead, we will use a = -5, r = 3, and n = 10 this time. By replacing these values, we obtain:

S = -5(1 - 3^10) / (1 - 3) (1 - 3)

S = -5(1 - 59049) / (-2) (-2)

S = 5(59048) (59048)

S = 295240

The result is 295240 for the first 10 terms in the series, which are -5, 15, 45, and 135.

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Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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\(\huge\fbox{Answer ☘}\)

number of marks available = 140

percentage secured = 70%

therefore marks secured =

\(70\% \: \: of \: 140 \\\\ =>\frac{70}{100} \times 140 \\ \\ = > 98 \: marks\)

hope helpful~

The probability that a randomly selected girl does not have brown hair is 34.54%.

Given that in a certain school, 45% of the students are boys, and 80% of the boys have brown hair while 50% of those with brown hair are girls, to determine what is the probability that a randomly selected girl does NOT have brown hair, the following calculation must be performed:

Therefore, the probability that a randomly selected girl does not have brown hair is 34.54%.

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The median of X is 1;  P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and  the value of q such that P(X < q) = 0.95 is 1.9.

(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.

Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.

For 0 < x < 2, the CDF is:

F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x

Setting (1/2) * x = 0.5 and solving for x:

(1/2) * x = 0.5;  x = 1

Therefore, the median of X is 1.

(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.

For x > 2, the PDF is 0, so P(X > x) = 0.

Therefore, P(X > 2) = 0.

(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.

P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)

Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.

Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.

(d) The variance of X can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:

E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3

To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:

E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Now we can calculate the variance:

Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33

Therefore, Var(X) is approximately 0.33.

(e) The expected value of X, E(X), is given by:

E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Therefore, E(X) is 1.

(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:

∫(0 to q) f(x) dx = 0.95

Since the PDF is constant at 1/2 for 0 < x < 2, we have:

(1/2) * (x) | (0 to q) = 0.95

(1/2) * q = 0.95

q = 0.95 * 2 = 1.9

Therefore, the value of q such that P(X < q) = 0.95 is 1.9.

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Answer:   30 / 6

                =5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

step by step explanation

Approximate probability that at least 30 have used a discount broker: 0.918

In this scenario, we are given that 28% of all individual investors have used a discount broker. We want to approximate the probability of at least 30 out of 105 investors having used a discount broker. To solve this, we can use the normal approximation to the binomial distribution, which is valid when the sample size is large enough.

To apply the normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution. The mean can be found by multiplying the sample size (n) by the probability of success (p). In this case, μ = n * p = 105 * 0.28 = 29.4. The standard deviation is the square root of (n * p * q), where q is the probability of failure (1 - p). So, σ = sqrt(n * p * q) = sqrt(105 * 0.28 * 0.72) = 4.319.

Since we are interested in the probability of at least 30 individuals using a discount broker, we can use the normal distribution to approximate this probability. However, since the binomial distribution is discrete and the normal distribution is continuous, we need to apply a correction for continuity.

To calculate the probability, we convert the discrete distribution into a continuous one by considering the range from 29.5 (30 - 0.5, applying the continuity correction) to infinity. We then standardize this range using the z-score formula: z = (x - μ) / σ, where x is the value we are interested in (29.5) and μ and σ are the mean and standard deviation, respectively.

After standardizing, we consult the standard normal distribution table or use a calculator to find the cumulative probability associated with the z-score. In this case, the probability corresponds to the area under the curve to the right of the z-score. We find that the z-score is approximately 0.0348. Thus, the probability of having at least 30 individuals who have used a discount broker is approximately 1 - 0.0348 = 0.9652.

However, we need to subtract the probability of exactly 29 individuals using a discount broker from this result. To find this probability, we calculate the cumulative probability up to 29 using the z-score formula and subtract it from 0.9652. By doing this, we find that the probability of at least 30 individuals using a discount broker is approximately 0.918.

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The sum of 5/6 and 2/9 is: C. 1 1/18.

The sum of 1/2 and 2/3 is 7/6.

The fraction of the boys that have either blue or hazel eyes is: B. 1/2.

The sum of 7/10 and 1/4 is: D. 19/20.

The sum of 3/5 and 1/5 is 11/10.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, each of the sums can be calculated as follows;

Fraction = 5/6 + 2/9

Fraction = (15 + 4)/18

Fraction = 19/18 = 1 1/18.

Fraction = 1/2 + 2/3

Fraction = (3 + 4)/6

Fraction = 7/6

Fraction = 1/5 + 3/10

Fraction = (2 + 3)/10

Fraction = 1/2

Fraction = 1/4 + 7/10

Fraction = (5 + 14)/20

Fraction = 19/20

Fraction = 3/5 + 1/2

Fraction = (6 + 5)/10

Fraction = 11/10

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Answer:

Length = 26 ft, Width = 21 feet

Step-by-step explanation:

Area of the rectangular floor is Width(W) x Length(L).  Area = 546 ft^2

L = W + 5

Area = W*L

546 ft^2 = W*(W+5)

W^2 + 5W - 546 = 0

W = 21 (and - 26)  ft

If W = 21 ft, L is 26 ft

(21 ft)*(26 ft) = 546 ft^2

The dimension of the rectangular floor is 21 ft and 26 ft.

A rectangle is a type of parallelogram, having all the angle, right angle and congruent, parallel opposite side.

Given that, The rectangular floor of a storage shed has an area of 546 square feet. The length of the floor is 5 feet more than its width

Area of rectangular floor = lengthxwidth

Let the width be x, therefore, length = (x+5)

Area = x(x+5) = 546

x²+5x = 546

x²+5x-546 = 0

Factorizing,

x²+5x-546 = 0

x²-21x+26x-546 = 0

(x-21)(x+26) = 0

x = 21 or x = -26

Since, a measurement can not be negative, so considering x = 21

Hence, length = 21+5 = 26 feet and width = 21 feet

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The order in which the kids sit is an illustration of arrangement.

We understand that: Bella is two seats away from Ella.

This arrangement is represented as: (E)_ (B)

Freddy sits between Bella and Ella.

This arrangement is represented as: (E) (F) (B)

Danielle does not sit next to Ella, and Charlie is at the end of the table.

This arrangement is represented as: (D) _ (E) (F) (B) (C)

So, Adam will occupy the seat between Danielle and Ella

This arrangement is represented as: (D) (A) (E) (F) (B) (C)

Hence, the order in which the 6 kids sit is: Danielle, Adam, Ella, Freddy, Bella and Charlie

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Answer:

Y = 3x - 1

Step-by-step explanation:

Sorry it’s late but hope this helps. Pls give brainliest.

The expected utility of Marlee with the ticket from Fony is 28.

The utility function of Marlee is given by u(x) = x+k. Here, k equals 100 if Marlee gets to go to the concert and equals 0 otherwise.

Marlee has $100 to buy tickets to the Fleet Foxes concert in Atlanta. She found two different websites selling tickets, Fony Front Seats and Best Tickets. If she buys a $20 ticket from Fony, there is a 60% chance that the ticket is fake, but she won't know until she gets to the concert.

If she buys a $60 ticket from Best Tickets, the ticket is certainly real. The seat placements for both tickets are identical and it costs $10 in gas to get to the concert.

Marlee's utility function is given as u(x) = x+k, where k equals 100 if Marlee gets to go to the concert and equals 0 otherwise. Her goal is to maximize her utility function.

Marlee is facing a trade-off between the cost of the ticket and the probability of getting a real ticket.

If she buys a $20 ticket from Fony, there is a 60% chance that the ticket is fake, but she won't know until she gets to the concert. Thus, there is a 40% chance that the ticket is real.

So, the expected utility of Marlee with the ticket from Fony is given by,

0.6u(0)+0.4u(100-20-10)=0.6(0)+(0.4)(70)=28

Therefore, the expected utility of Marlee with the ticket from Fony is 28. This indicates that Marlee will not be able to go to the concert if she buys the ticket from Fony Front Seats.

If she buys a $60 ticket from Best Tickets, the ticket is certainly real. Therefore, the expected utility of Marlee with the ticket from Best Tickets is,

u(100-60-10)=u(30)=30+100=130

Therefore, the expected utility of Marlee with the ticket from Best Tickets is 130.

This indicates that Marlee should buy the ticket from Best Tickets to get the maximum utility.

Therefore, Marlee should buy her ticket from Best Tickets because she will receive the maximum utility if she buys the ticket from Best Tickets.

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Answer:

Exact form - x=277/90

Decimal form - x=3.07

Mixed number - x=3  7/90

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).