An equivalent fraction for 10/14 is _____.

Answers

Answer 1

Answer:

$(10)/(14)=(10:2)/(14:2)=(5)/(7)\n\n(10)/(14)=(10\cdot2)/(14\cdot2)=(20)/(28)\n\n(10)/(14)=(10\cdot3)/(14\cdot3)=(30)/(42)\n\n(10)/(14)=(5)/(7)=(5\cdot5)/(7\cdot5)=(25)/(35)\n\vdots$

Answer 2

Answer:

Answer:

5/7

Step-by-step explanation:

Find the GCD of the numerator and denominator

GCD of 10 and 14 is 2

Divide both the numerator and denominator by the GCD

10 ÷ 2

14 ÷ 2

Reduced fraction:

5/7

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Answers

Answer:

132.56

Step-by-step explanation:

John, Sally, and Natalie would all like to save some money. John decides that itwould be best to save money in a jar in his closet every single month. He decides
to start with $300, and then save $100 each month. Sally has $6000 and decides
to put her money in the bank in an account that has a 7% interest rate that is
compounded annually. Natalie has $5000 and decides to put her money in the
bank in an account that has a 10% interest rate that is compounded continuously.

How much money have after 2 years?

How much money will sally have in 10 years?

What type of exponential model is Natalie’s situation?

Write the model equation for Natalie’s situation

How much money will Natalie have after 2 years?

How much money will Natalie have after 10 years

Answers

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^(t)$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^(0.10t)$ or $A=5,000(1.1052)^(t)$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+(r)/(n))^(nt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\n r=7\%=0.07\nn=1$

substitute in the formula above

$A=6,000(1+(0.07)/(1))^(1*t)\n A=6,000(1.07)^(t)$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^(10)=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^(2)=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^(rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\nr=10\%=0.10$

substitute in the formula above

$A=5,000(e)^(0.10t)$

Applying property of exponents

$A=5,000(1.1052)^(t)$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^(0.10t)$ or $A=5,000(1.1052)^(t)$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^(0.10*10)=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^(0.10*2)=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

What is the value of 9 in the number 9.173

Answers

9.000 is the answer so 9 because 9.173 is part of a number or a unit.

The value is in the ones value

(analyze) Which total cost is less:25 tickets for 5$ each or 20 tickets for 6$ each

Answers

20 tickets for $6 is less because when you multiply 25×5 you get 125 which is bigger.
When you multiply 20×6 you get 80.
So 80 is less than 125

How do you convert 18/5 into a mixed number

Answers

Ok, so first, see how many times 5 goes into 18. It goes into it 3 times so know the leftover numbers become the fraction (numerator). Your answer is 3 3/5

The mixed number equivalent of 18/5 is 3 3/5.

Converting improper fraction into mixed fraction.

To convert the fraction 18/5 into a mixed number, you can divide the numerator 18 by the denominator 5.

The quotient will become the whole number part of the mixed number, and the remainder will become the numerator of the fraction part. Here's the process:

18/5 = 3 3/5

The remainder becomes the numerator of the fraction part, which is 3.

The denominator of the fraction part remains the same, which is 5.

Therefore, the mixed number equivalent of 18/5 is 3 3/5.

Learn more mixed and improper fraction here: brainly.com/question/970872

#SPJ6

(k^4_3_3k^3)+(-5k^3+6k^3_8k^5)

Answers

Answer:

(k4+3+3k3)+(-5k3+6k3+8k5)

Final result :

8k5 + k4 + 4k3 + 3

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(((k4)+3)+(3•(k3)))+(((0-(5•(k3)))+(6•(k3)))+23k5)

Step 2 :

Equation at the end of step 2 :

(((k4)+3)+(3•(k3)))+(((0-(5•(k3)))+(2•3k3))+23k5)

Step 3 :

Equation at the end of step 3 :

(((k4)+3)+(3•(k3)))+(((0-5k3)+(2•3k3))+23k5)

Step 4 :

Equation at the end of step 4 :

(((k4) + 3) + 3k3) + (8k5 + k3)

Step 5 :

Checking for a perfect cube :

5.1 8k5+k4+4k3+3 is not a perfect cube

Trying to factor by pulling out :

5.2 Factoring: 8k5+k4+4k3+3

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: k4+3

Group 2: 8k5+4k3

Pull out from each group separately :

Group 1: (k4+3) • (1)

Group 2: (2k2+1) • (4k3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.3 Find roots (zeroes) of : F(k) = 8k5+k4+4k3+3

Polynomial Roots Calculator is a set of methods aimed at finding values of k for which F(k)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers k which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 8 and the Trailing Constant is 3.

The factor(s) are:

of the Leading Coefficient : 1,2 ,4 ,8

of the Trailing Constant : 1 ,3

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -8.00

-1 2 -0.50 2.31

-1 4 -0.25 2.93

-1 8 -0.13 2.99

-3 1 -3.00 -1968.00

-3 2 -1.50 -66.19

-3 4 -0.75 -0.27

-3 8 -0.38 2.75

1 1 1.00 16.00

1 2 0.50 3.81

1 4 0.25 3.07

1 8 0.13 3.01

3 1 3.00 2136.00

3 2 1.50 82.31

3 4 0.75 6.90

3 8 0.38 3.29

Polynomial Roots Calculator found no rational roots

Final result :

8k5 + k4 + 4k3 + 3

Step-by-step explanation:

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