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2 years ago

9

Franks credit card has no annual fee, 23.99% interest rate. Switch to new card 16.99% rate. $35 annual fee. How much average bal

ance would frank have to make switching cards worth it?

1 answer:

Luda [366]2 years ago

7 0

Answer:

<em>The minimum average balance that makes the switching worth it is $500</em>

Step-by-step explanation:

<u>Equations</u>

We know Frank's credit card has no annual fees and charges an interest rate of 23.99% of his average balance B. He wants to switch to a new card with $35 annual fees but less interest rate of 16.99%.

The total annual payment Frank actually has to pay is given only by the interest of his annual average balance. That is

$P_1=23.99\%\cdot B=0.2399\cdot B$

With the new card, he'll have to pay a fixed fee of $35 plus the annual interest:

$P_2=35+16.99\%\cdot B=35+0.1699\cdot B$

To make switching cards worth it, both payments will need to be (at least) equal:

$0.2399\cdot B=35+0.1699\cdot B$

Rearranging

$0.2399\cdot B-0.1699\cdot B=35$

$0.07B=35$

Solving

$B=35/0.07=500$

$B=\$500$

The minimum average balance that makes the switching worth it is $500. If his balance is more than $500, he'll save by using the new card.

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Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. In a random sample of 12 drivers driving between 1

Lesechka [4]

Answer:

(a) 0.28347

(b) 0.36909

(c) 0.0039

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

$P(x=r)=^nC_rp^rq^{n-r}$

(a) Exactly two will be drunken drivers.

$P(x=2)=^{12}C_{2}(0.2)^{2}(0.8)^{12-2}$

$P(x=2)=66(0.2)^{2}(0.8)^{10}$

$P(x=2)=\approx 0.28347$

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

$P(x=3\text{ or }x=4)=P(x=3)\cup P(x=4)$

$P(x=3\text{ or }x=4)=P(x=3)+P(x=4)$

Using binomial we get

$P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}$

$P(x=3\text{ or }x=4)=0.236223+0.132876$

$P(x=3\text{ or }x=4)\approx 0.369099$

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

$P(x\geq 7)=1-P(x$

$P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]$

$P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]$

$P(x\leq 7)=1-[0.9961]$

$P(x\leq 7)=0.0039$

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

$P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)$

$P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315$

$P(x\leq 5)=0.9806$

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

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3 years ago

A car travels 50 km in 2 liters find

Savatey [412]

It can travel 125km with 5 liters
And 6 liters to travel 150 :)

5 0

2 years ago

Read 2 more answers

I GIVEEEEE BRAINLILSTTTT

Georgia [21]

Answer:

Step-by-step explanation:

englargment

4 0

2 years ago

Read 2 more answers

3/4 is 1/3 of what number? Write a division expression to match this expression

WITCHER [35]

It would be 9/4. To find 1/3 of something you have to multiply it by 3. 9/4 should be considered as a division expression. Hope this helped!

7 0

2 years ago

Just number 3 is fine please but if you could also 4

PIT_PIT [208]

Answer:

3. r = -8

4. x = -5

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

2(-5r + 2) = 84

<u>Step 2: Solve for </u><em><u>r</u></em>

Divide 2 on both sides: -5r + 2 = 42
Subtract 2 on both sides: -5r = 40
Divide -5 on both sides: r = -8

<u>Step 3: Check</u>

<em>Plug in r into the original equation to verify it's a solution.</em>

Substitute in <em>r</em>: 2(-5(-8) + 2) = 84
Multiply: 2(40 + 2) = 84
Add: 2(42) = 84
Multiply: 84 = 84

Here we see that 84 does indeed equal 84.

∴ r = -8 is a solution of the equation.

<u>Step 4: Define equation</u>

264 = -8(-8 + 5x)

<u>Step 5: Solve for </u><em><u>x</u></em>

Divide both sides by -8: -33 = -8 + 5x
Add 8 to both sides: -25 = 5x
Divide 5 on both sides: -5 = x
Rewrite: x = -5

<u>Step 6: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

Substitute in<em> x</em>: 264 = -8(-8 + 5(-5))
Multiply: 264 = -8(-8 - 25)
Subtract: 264 = -8(-33)
Multiply: 264 = 264

Here we see that 264 does indeed equal 264.

∴ x = -5 is a solution of the equation.

8 0

2 years ago