Pls answer correctly fasttt!!

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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Using the binomial distribution, it is found that there is a 0.1008 = 10.08% probability that exactly 18 of them say job applicants should follow up within two weeks.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The values of the parameters are given as follows:

n = 25, p = 0.62.

The probability that exactly 18 of them say job applicants should follow up within two weeks is P(X = 18), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 18) = C_{25,18}.(0.62)^{18}.(0.38)^{7} = 0.1008\)

0.1008 = 10.08% probability that exactly 18 of them say job applicants should follow up within two weeks.

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Answer:

ok so what i think your trying to ask is if we roll two dice that the sum will be more then 6

Two dice

Assuming that the dice are unbiased or not " loaded".

Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.

How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?

These are the possibilities

Case 1.

D1 =1 & D2=5

Or

D1= 5 & D2=1

Case 2.

D1 =2 & D2=4

Or

D1= 4 & D2= 2

Case 3. D1=3, D2=3

P3 =0.027778

Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.

The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.

P1= 0.02778+ 0.02778 =0.055558

P2= 0.02778+0.02778 =0.055558

Same way,

P3=0.027778, when there is only one way to get the sum 6.

So, P = 0.138894

Based on truncating at the sixth decimal place.

A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.

Hope This Helps!!!

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

488

Step-by-step explanation:

You divide 28453 by 58.3053278689 and get 488.

Answer: in a region with a letter

Step-by-step explanation:

we cannot predict for sure what will happen when we plot the random point.

Answer:

A certain answer would be  in a region with a letter

Step-by-step explanation:

All the sections have letters so, no matter what letter, the point would land in a section with a letter.

The value of the inequality is x ≥ 3/7

The relationship between two values that are not equal is defined by inequalities. When two terms are not equal, they can either be:

greater than >

less than <

greater than or equal to ≥

less than or equal to ≤

6(x-2)≥-5+5x+6

12x-2 ≥ 5x + 6-5

collect like terms

12x -5x ≥ 6-5+2

7x ≥ 3

divide both sides by 7

x ≥ 3/7

therefore the value of the inequality is x ≥ 3/7

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The value of the expression is -4

The cube root of a number can be defined as the factor multiplied by three times by itself  to get that number.

Cube root is represented using the formula, '∛'

From the information given,

c³ = -64

Take the cube root of both sides

∛c³ = ∛ - 64

c = - 4

Thus, the value of the expression is -4

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Answer:

The sale price of item is 63.05 dollars

Step-by-step explanation:

Given that the price of item is $97

Let P be the price

\(P = 97\)

It is also mentioned in the question that on sale the item costs 65% of the original price so we have to calculate 65% of the item's original price to find the sale price.

Mathematically,

\(Sale\ Price = 65\%\ of\ P\\= 0.65 * 97\\= 63.05\)

Hence,

The sale price of item is 63.05 dollars

Answer:

to solve a system of linear equations graphically we graph both equations in the same coordinate system, the solution to the system will be in the point where the 2 lines intersect.

the circumference of circle of area 2122.64 sq. cm. is 163.36 cm.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Area of circle is calculated using formula :

A = πr²

It is given that Area of circle is 2122.64 sq cm. then the radius will be :

A = πr²

2122.64 = π(r)²

r = √2122.64 / π

r = 26 cm

Now, calculating the circumference of the circle using formulae :

C = 2πr

C = 2π x 26

C = 163.36 cm

Therefore, the circumference of circle of area 2122.64 sq cm is 163.36 cm.

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Therefore , width of rectangle is 9 cm and length is 13cm

What does a rectangle's area equal?

The territory a rectangle occupies inside its four sides or limits is referred to as its area.

The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Thus, we can say that the area of a rectangle equals the space enclosed by its perimeter. The area of a square will, however, be equal to the square of side-length in the case of a square because all of its sides are equal.

Length x Breadth = Area of rectangle

Let’s start by defining the width of the rectangle as w.

From the problem statement, we know that the length of the rectangle is 5 inches less than twice its width. So, we can represent the length as

2w - 5.

The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width.

Substituting l = 2w - 5, we get:

A = (2w - 5) * w

A = 2w² - 5w

Now, we can use this equation to find the width of the rectangle when its area is 117 square inches.

A = 117

2w² - 5w = 117

2w² - 5w - 117 = 0

We can solve this quadratic equation using the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -5, and c = -117.

w = (-(-5) ± √((-5)² - 4(2)(-117))) / (2 * 2)

w = (5 ± √(25 + 936)) / 4

w = (5 ± √(961)) / 4

We can ignore the negative root since we are looking for a positive value for the width.

w = (5 + 31) / 4

w = 9

so, length  l=2w-5

put value of w

2×9-5

=18-5=13

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Length =l

Height = h

Area function = l * h = 924

Perimeter function = 2i + 2h = 122

Divide by 2

I + h = 61.

Plug in I or h for the other variable

I * (61 - I) = 924

61i - i^2 = 924

Factor the function

(-I + 28)(I - 33) = 0

l = 33 as l cannot be negative

61 - 33 = 28

h = 28

Difference between h and l is 33-28=5

The end behavior of the polynomials are as follows;

(a) y = x³ - 9·x² + 8·x - 14

End behavior; y → ∞ as x → ∞

\({}\)                        y → -∞ as x → -∞

(b) y = -8·x⁴ + 13·x + 800

End behavior; y → -∞ as x → -∞

\({}\)                        y → -∞ as x → ∞

The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.

The factors that effect the end behavior of a polynomial are;

The degree of the polynomial, (even or odd)

The sign of the leading coefficient of the polynomial (positive or negative)

The leading coefficient is the coefficient of the term with the highest degree.

(a) The polynomial, function, y = x³ - 9·x² + 8·x  - 14

The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;

y tends to positive infinity as x tends to positive infinity

y tends to negative infinity as x tends to negative infinity

End behavior;

y → ∞ as x → ∞

y → -∞ as x → -∞

(b) The polynomial function can be expressed as follows;

y = -8·x⁴ + 13·x + 800

The above polynomial of degree 4 is an even degree polynomial

The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative

The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;

y-values approaches negative infinity as x approaches negative infinity

y-values approaches negative infinity as x approaches positive infinity

End behavior;

y → -∞ as x → -∞

y → -∞ as x → ∞

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Answer:

The value of an expression doesn't change when it is expanded. When one expands an expression, one is writing out such that one can see every term in it. This doesn't change the value of the expression, it just rewrites it.

Step-by-step explanation:

There are different patterns that could be used to determine the next number in this sequence, so there is not necessarily one correct answer. However, one possible pattern is to look at the differences between the numbers and see if there is a consistent change.

If we look at the differences between the numbers, we can see that:

12 - 16 = -4

9 - 12 = -3

The differences are decreasing by 1 each time, so we might expect the next difference to be -2. Therefore, to find the next number in the sequence, we can subtract 2 from 9:

9 - 2 = 7

So one possible answer to "what comes next" in the sequence 16, 12, 9 is 7.

There are different ways to approach this sequence, but one possible pattern is that each term is the result of subtracting a decreasing odd number from the previous term:

Starting from 16: 16 - 4 = 12

Starting from 12: 12 - 3 = 9

Starting from 9: 9 - 2 = 7

Therefore, the next term could be 6, which is obtained by subtracting 1 from 7. However, it's important to note that this is just one possible pattern, and there could be other valid ways to continue the sequence.

Answer:

d. The slope of the relationship between firstfloorsquarefootage and price is moresteep for homes near the beach than elsewhere in Tampa.

Step-by-step explanation:

In this regression model, we have a positive slope. This positive slope is indicative of an increase. So to interpret this slope, we would say that the slope of the relationship that exists between the two variables (price and firstfloorsquarefootage) is steeper for the homes that are closer to the beach compared to the ones that are elsewhere. Therefore option D is our answer.

The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:

-------------------------

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Answer:

Step-by-step explanation:

Given

Solve for h

Answer:

Area = 40

Perimeter = 26

Step-by-step explanation:

length = 8

width = 5

Area = 8 x 5 = 40

Perimeter = 2(8 + 5) = 26

Answer:

Following the rules the coordinate pairs are: (1,0), (5,1), (17,3), (53,7), (161,15)

Step-by-step explanation:

Nicole's Pattern: Multiply by 3 then add 2, starting from 1

Ion's Pattern: Add 1/2 then multiply by 2 starting from 0

So, Nicole's pattern is generated starting from 1, we multiply by 3 and then add 2 to get the next number

While Ion's pattern is generated starting from 0, we add 1/2 to it and then multiply by 2 to get the next number

Nicole's Pattern               Ion's Pattern          Coordinate pairs

1                                          0                               (1,0)

5                                          1                                (5,1)

17                                         3                              (17,3)

53                                        7                               (53,7)

161                                        15                              (161,15)