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anastassius [24]
2 years ago
8

WILL GIVE BRAINLIEST Mr. and Mrs. Bailey hope to send their son to college in eleven years. How much money should they invest no

w at an interest rate of 9% per year, compounded continuously, in order to be able to contribute $7500 to his education?
Do not round any intermediate computations, and round your answer to the nearest cent.
Mathematics
1 answer:
Ronch [10]2 years ago
7 0

Mr. and Mrs. Bailey need to invest $2906.50 so as to send their son to college.

<h3>Compound interest</h3>

Compound interest is given by:

A=P(1+\frac{r}{n})^{nt}

where A is the amount after t years, P is initial amount, r is the rate and n is the times compounded per period

Given that n = 1, r = 9% = 0.09, A = $7500 t = 11. Hence:

7500=P(1+\frac{0.09}{1} )^{1*11}\\\\P=\$2906.50

Mr. and Mrs. Bailey need to invest $2906.50 so as to send their son to college.

Find out more on Compound interest at: brainly.com/question/24924853

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Answer:

2  ,   3

Step-by-step explanation:

5 0
3 years ago
To which sets of numbers does 1 1/2 belong to
baherus [9]

Answer:

A rational number because it's negative it can't be natural and cuz it's fraction it can't be whole nor integers.

<em>p.s. thanks to salma1148 for the answer</em>

7 0
3 years ago
12 out of 30 people chose their favourite colour as blue caculate the angle you would use for blue on a pie chart
GrogVix [38]

Answer:

The angle = 144 degrees.

Step-by-step explanation:

Look at it this way (it is a proportion question)

30 people would require a pie chart made of a full circle (360 degrees)

12 people would require x part of the pie chart.


30/360 = 12 / x            Cross multiply

30x = 360 * 12             Simplify the right

30x = 4320                  Divide by 30

30x/30 = 4320/20      

x = 144                           Answer

6 0
3 years ago
Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left o
solniwko [45]

Answer and Step-by-step explanation:

Not p = ¬p

P or q = p ∨ q  

P and q = p ∧ q

If p then q = p → q

P if and only if q = p ↔ q

Existential quantification:  There exist an element x in the domain such that p(x).

Universal quantification: p(x) for all values of x in the domain.

(a)  No one has lost more than one thousand dollars playing the lottery.

Let A(x) means ‘x has lost more than one dollars playing the lottery’

It can also write as “there does not exists a person that lost more than one thousand dollars playing”

                     ¬Ǝ x A (x)

Negation of this statement:  

By using double negation law:

                               ¬ [¬Ǝ x A (x)]  ≡ Ǝ x A(x)

(b) There is a student in this class who has chatted with exactly one other student.

Let B(x,y) means “ x has chatted with y” and domain is all students of this class.

We can write the given sentence as:

“There is a student in the class who has chatted with one student and this student is not himself and for all people the student chatted with, this student has to be himself or the one student he chatted with”

Ǝ x Ǝ y[B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x,y) → ( z = x v z = y))]

The negation:

               ¬ Ǝ x Ǝ y[B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]

By using De Morgan’s law for quantifiers:

≡∀x ¬ Ǝ y [B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]

≡∀x ∀ y [B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]

De Morgan’s law:

≡∀x ∀ y [¬  B ( x, y) v  ¬ ( x ≠ y) v ∀ z (B(x ,y) → ( z = x v z = y))]

By using De Morgan’s law for quantifiers:

≡∀x ∀ y [¬  B ( x, y) v  x=  y  v Ǝ z¬ (B(x ,z) → ( z = x v z = y))]

(c)  No student in this class has sent e-mail to exactly two other students in this class

Let c(x, y) means “ x has sent email to y” and the domain is all student of class.

Using double negation law:

Ǝ x Ǝ y Ǝ z [c(x, y) ∧c(x ,z) ∧ x≠ y ∧ x ≠z ∧ y ≠ z ∀ w (c(x,w) → ( w = x v w = y v w = z)]

There is a student in class that has sent email to exaxtly two other students in class.

(d)  One student has solved every exercise in this book

Let D(x , y) mean student x has solved exercise y in this book.

The negation:  

Ǝx∀yD(x,y)

Use De Morgan’s law for qualifiers:

    ≡∀ x Ǝ y ¬D(x, y)  

(e). No student has solved at least one exercise in every section of this book.

Let E(x, y,z) be student x has solved exercise y in section z of this book.

We can write “there does not exist a student that solved at least one exercise in all sections of this book”

¬Ǝ x Ǝ y ∀ Z E(x, y, z)  

Negation:

                      ≡¬ [¬ Ǝ x Ǝ y ∀ Z E(x, y, z)  ]

Use double negation law:

                                     ≡ Ǝ x Ǝ y ∀ Z E(x, y, z)  

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7 0
3 years ago
What is the value of q² - p² for q = 4 and p = 2?​
valentina_108 [34]

Answer:

um so here it is. 12

Step-by-step explanation:

4 ×4 - 2×2 = 16-4=12

6 0
3 years ago
Read 2 more answers
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