Mathematics College

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to represent the first three terms, respectively.] The three number are __, __, and __

Answers

Answer 1
ooh, fun

geometric sequences can be represented as
[tex]a_n=a(r)^{n-1}[/tex]
so the first 3 terms are
[tex]a_1=a[/tex]
[tex]a_2=a(r)[/tex]
[tex]a_2=a(r)^2[/tex]

the sum is -7/10
[tex]\frac{-7}{10}=a+ar+ar^2[/tex]
and their product is -1/125
[tex]\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3[/tex]

from the 2nd equation we can take the cube root of both sides to get
[tex]\frac{-1}{5}=ar[/tex]
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
[tex]\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r[/tex]
subsituting -1/5 for ar
[tex]\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r[/tex]
which simplifies to
[tex]\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}[/tex]
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
so
for 2r²-5r+2=0
a=2
b=-5
c=2

[tex]r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}[/tex]
[tex]r=\frac{5 \pm \sqrt{25-16}}{4}[/tex]
[tex]r=\frac{5 \pm \sqrt{9}}{4}[/tex]
[tex]r=\frac{5 \pm 3}{4}[/tex]
so
[tex]r=\frac{5+3}{4}=\frac{8}{4}=2[/tex] or [tex]r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}[/tex]

use them to solve for the value of a
[tex]\frac{-1}{5}=ar[/tex]
[tex]\frac{-1}{5r}=a[/tex]
try for r=2 and 1/2
[tex] a=\frac{-1}{10}[/tex] or [tex]a=\frac{-2}{5}[/tex]


test each
for a=-1/10 and r=2
a+ar+ar²=[tex]\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}[/tex]
it works

for a=-2/5 and r=1/2
a+ar+ar²=[tex]\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}[/tex]
it works


both have the same terms but one is simplified

the 3 numbers are [tex]\frac{-2}{5}[/tex], [tex]\frac{-1}{5}[/tex], and [tex]\frac{-1}{10}[/tex]
Answer 2

Answer:

2r²-5r+2=0

a=2

b=-5

c=2

Step-by-step explanation:

   

Related Questions

Use synthetic division and the Remainder Theorem to find P(a)

P(x)=x^4+10x^3+8x^2+4x+10 ; a=2


2


–114


56


146

Answers

  P(x) =  x^4+10x^3+8x^2+4x+10

Synthetic dicision:

           ! 1        10       8        4    10
x=a=2 !             2     24      64  136
----------------------------------------------
             1         12    32      68  146=Remainder

P(a)=P(2)=146

Answer: Fourth option. 146

if you laid 9 bolts end-to-end that each measure seven eighths of an inch, how long would that row of bolts be?

Answers

That's easy, the answer is 7.875

A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is h = -16t2 + 272t + 1344. When will the ball strike the ground?

Answers

The answer is -16(t+4)(t-21)

Answer:

Time taken to reach the ball to the ground is 21 seconds.                  

Step-by-step explanation:

Given : A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is [tex]h = -16t^2 + 272t + 1344[/tex].

To find : When will the ball strike the ground?

Solution :

The equation for the ball's height 'h' at time 't' is given by,

[tex]h(t)= -16t^2 + 272t + 1344[/tex]

When the ball strike the ground the height of the ball became zero.

Substitute h=0 in the given equation,

[tex]-16t^2 + 272t + 1344=0[/tex]

Taking 16 common,

[tex]16(-t^2 + 17t + 84)=0[/tex]

or [tex]t^2-17t-84=0[/tex]

Solve by middle term split,

[tex]t^2-21+4t-84=0[/tex]

[tex]t(t-21)+4(t-21)=0[/tex]

[tex](t-21)(t+4)=0[/tex]

[tex]t=21,-4=0[/tex]

Reject t=-4 as time can never be negative.

Therefore, Time taken to reach the ball to the ground is 21 seconds.

Find the magnitude and direction (in degrees) of the vector. v = ‹ - sqrt(7)/9, - sqrt(2)/3 ›

Answers

The magnitude is given by:
 lvl = root ((- root (7) / 9) ^ 2 + (- root (2) / 3) ^ 2)
 lvl = 0.555555556
 The address is given by:
 cos (theta) = (- root (7) / 9) / (0.555555556)
 Clearing theta:
 theta = acos ((- root (7) / 9) / (0.555555556))
 theta = 121.95 degrees
 Answer:
 The magnitude and direction (in degrees) of the vector are:
 lvl = 0.555555556
 theta = 121.95 degrees

What is the area of the given circle in terms of pi? Diameter 6.6. Please Help

Answers

i believe the answer is 10.362
hope this helps

area=π*r^2
r=radius
2r=d -> d/2=r


we are given d, the diameter
we need r
so
d/2=6.6/2=3.3=r

therefore
area=π*r^2
area=π*(3.3)^2
area=π*10.89
area=10.89π square units

plz help and explain thanks

Answers

[tex] \dfrac{x^0}{q^{-3}} = \dfrac{5^0}{(-6)^{-3}}= \dfrac{1}{(-6)^{-3}} = (-6)^3 = -216[/tex]
hey there!:


for q = - 6 and x = 5 :

   5⁰
------
(-6)⁻³ 


Apply rule :  a⁰ = 1  , a≠0

5⁰ = 1     :    

    1
* -------
   (-6)⁻³


Apply exponent rule:  (-a)ⁿ = - aⁿ  , if  " n " is  odd :

(-6)⁻³   = -6⁻³


     1
* -------
   -6⁻³


Apply fraction rule : a/-b  = - a/b


= - 1 /  -6⁻³

Apply exponent rule: a⁻ᵇ =  1 / ab


6⁻³ = 1 / 6³

=> ( - 1/1 ) / ( 6³ )

= - 6³ / 1

Apply rule a/1  = a

= - 6³

* 6 * 6 * 6 => 216

a = -216

hope this helps!
  



x 13 16 18 21 23 25 26 31
p(x) .07 .21 .17 .25 .05 .04 .13 .08
the mean of the discrete random value variable x is the 20.59. What is the variance of X?
Round your answer to the nearest hundredth
a 27.89
b27.89
c33.15
d23.18

Answers

First compute the second moment:

[tex]\mathbb E[X^2]=\displaystyle\sum_x x^2p(x)=13^2\cdot0.07+\cdots+31^2\cdot0.08\approx447.13[/tex]

Then the variance of [tex]X[/tex] is

[tex]\mathbb V[X]=\mathbb E[X^2]-\mathbb E[X]^2\approx447.13-20.59^2\approx23.18[/tex]
Final answer:

The variance of a discrete random variable calculation involves working out (x-µ)^2 * p(x) for each x value and summing them up. Using given data and mean as 20.59, variance ≈ 27.89 (options a and b).

Explanation:

To calculate the variance of a discrete random variable, we use the formula: Variance = Σ[(x-µ)^2 * p(x)] where 'x' is each value of the variable, 'µ' is the mean and 'p(x)' is the probability of 'x'

Given that the mean µ is 20.59 we perform the calculation, (x-µ)^2 * p(x) for each value of 'x' and sum them all up:

(13-20.59)^2 * .07 = 14.08(16-20.59)^2 * .21 = 4.38Continuing this process for all given values of 'x' and summing them up, we find that the variance ≈ 27.89.

So, the correct answer is 27.89, which corresponds to option a and b.

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At the end of the past month the cash account of a company had an ending balance of 6750. During the last month the account was debited for a total of 11350 and credited for a total of 10500. What was the balance in the cash account at the of the last month

Answers

Debits are subtracted from the previous balance and credits are added to find the new balance.

6750 -11350 +10500 = 5900

At the end of last month, the cash account balance was 5900.

A pound of chocolate costs 7 dollars. Tiffany buys p pounds. Write the equation to represent the total cost c that Tiffany pays.

Answers

The answer to this question is 7p=c

Final answer:

The equation to represent the total cost c that Tiffany pays for p pounds of chocolate, when a pound costs 7 dollars, is c = 7 × p. This is a simple linear equation with 7 as the price per pound.

Explanation:

The question asks to write an equation to represent the total cost c that Tiffany pays for p pounds of chocolate, with the knowledge that a pound of chocolate costs 7 dollars.

To find the total cost c, we simply need to multiply the cost per pound of chocolate by the number of pounds Tiffany buys. If each pound costs $7, then the equation showing the total cost for p pounds would be:

c = 7 × p

Where:

c represents the total cost

p represents the number of pounds of chocolate

This is a straightforward linear equation with the coefficient 7 representing the price per pound of chocolate.

PLEEZ HELP ME I AM STUCK AND I REALLY NEED THE ANSWER ASAP!!
A wooden block in the shape of a rectangular prism is cut into two congruent pieces. Which statement best compares the surface areas of the pieces to the surface area of the original block?

A. The surface area of each piece is equal to 1/2 surface area of the original block.

B. The surface area of each piece is equal to the sum of half the surface area of the original block plus half the area of the face created by the cut.

C. The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.

D. The surface area of each piece is equal to the surface area of the original block minus the area of the face created by the cut.

Answers

C. The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.

The option c is correct

What is rectangular prism ?

A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

According to the question,

The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.

Hence, option c is correct for given condition.

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If f(x) = x^2 and g(x) = 1/2x + 3, find g(f(-1)).
A.) -1
B.) 1/25
C.) 1/5
D.) 1

Answers

f(x)=x^2
x=-1→f(-1)=(-1)^2→f(-1)=1

g(x)=1/(2x+3)
g(f(-1))=g(1)→x=1→g(1)=1/[2(1)+3]=1/(2+3)→g(f(-1))=1/5

Answer: Option C.) 1/5

What is the probability that celia is first in line and felicity is last in line?

Answers

If there is only Celia and Felicity in the line:

There are 2 solutions that Celia and Felicity can be organised in:

Celia 1st in the line, Felicity last in the lane.
Felicity 1st in the line, Celia last in the line.

So, there is a 50% chance that Celia would be 1st in the line and Felicity would be last in the line.


If there is 1 other person in the line:
(The other person will be referred to as Bob)

There are 6 solutions that Bob, Celia and Felicity can be organised in:
(Correct way is in bold)

Bob 1st in line, Celia 2nd in line, Felicity last in line.
Bob 1st in line, Felicity 2nd in line, Celia last in line.
Felicity 1st in line, Bob 2nd in line, Celia last in line.
Felicity 1st in line, Celia 2nd in line, Bob last in line.
Celia 1st in line, Bob 2nd in line, Felicity last in line.
Celia 1st in line, Felicity 2nd in line, Bob last in line.

There is only 1 correct solution, so there is a 16.7% chance that Celia is first in line and Felicity is last in line.
(rounded to 1 decimal place) 

If there are more people, you do what is underneath.

From the 1st section of answers (There were only Celia and Felicity in the line), there were 2 people in the line. The 2nd section of answers showed that 3 people were in the line. So, you times 2 and 3 to make 6. There were 6 solutions in the 2nd section. 

From there, you get the next consecutive number of the people in the line, which is 4 (NOT 7) and times 6 by 4, which is 24. There are 24 solutions to having 4 people in the line. 

Do this again and you get 24 times 5, which is 120. So there are 120 solutions to having 5 people in the line. 

Keep on doing this until you get the number of people in the line you need.

Hopefully this helps!

By the way, this took around 12 minutes to type out.

Edit: Convert the number to a percentage by doing 1/120 times 100.
This gets you 0.83 (rounded to 2 decimal places)
(using the answer of 5 people in the line)

The probability of Celia being first and Felicity last in a line is found by multiplying the probabilities of each independent event. For a line of n people, it would be [tex](1/n) \(*\) (1/(n-1))[/tex]. For 10 people, this probability would be 1/90.

The scenario implies that there's a line of people, and we are interested in the probability of Celia being the first and Felicity being the last in this line. This is a combinatorial probability problem. To calculate the probability, we must first acknowledge that each person in the line is equally likely to be in any position. If we assume there are n people in total, the probability that Celia is first is 1/n, and once Celia is in place, assuming Felicity is not first, the probability that Felicity is last is 1/(n-1). Since these two events are independent (Celia being first does not affect the probability of Felicity being last), we multiply these probabilities together to find the combined probability.

Using the formula for independent events:

P(Celia first and Felicity last) = P(Celia first) * P(Felicity last given that Celia is first)P(Celia first and Felicity last) = (1/n) * (1/(n-1))

If there are 10 people in the line, for example, the probability would be (1/10) * (1/9) = 1/90.

Bristol is analyzing positive daily customer feedback on different restaurants to find the perfect place to invest. She would like to choose a restaurant with a high median of positive mark counts and a small interquartile range. She constructed box plots shown in the diagram below. Which restaurant has a median positive mark count above 75 and the smallest interquartile range? Burrito bros, pasta pals, make your own pie, pap smurfys

Answers

The Answer is A) Burrito Bros

Answer:

A. Burrito Bros

Annie is planning a business meeting for her company. her budget is 1,325 for renting the meeting room at the local hotel and providing lunch. she expects 26 people to attend the meeting the room cost $270 which inequality show how to find the amount × Annie can spend for lunch on each person

Answers

$1325 - $270 = $1055

Annie has $1055 to spend on 26 lunches.

Let the cost of a lunch be x.

26x < 1055     

x <  $40.58

Answer: x <  $40.58

Answer:

26x + 270 ≤ 1,325

Step-by-step explanation:

Suppose x be the amount ( in dollars ) of lunch of each person,

So, the cost of lunch for 26 people = 26x,

Also, the cost of meeting room = $ 270,

Thus, the total cost = total cost of lunch + meeting room cost

= 26x + 270,

According to the question,

The budget of meeting is $ 1,325,

That is, the total cost can not exceed to $ 1325,

[tex]\implies 26+270 \leq 1325[/tex]

Which is the required inequality that will used to find the cost of each lunch.

Milt built a prism using a 3 unit cubes. He adds two more layers of 3 unit cubes each.how many unit cubes are used for the prism?

Answers

we know that
1) Milt built a prism using a 3 unit cubes
total unit cubes is 3

2) He adds two more layers of 3 unit cubes each
total unit cubes=3+2*3----> 9 unit cubes

the answer is
9 units cubes
Final answer:

Milt used a total of 9 unit cubes to build his prism. This was calculated by multiplying the quantity of unit cubes in each layer (3 cubes) by the total number of layers (3).

Explanation:

This is a Mathematics question about the concept of volume in prisms, specifically a cube. Milt starts by building a prism using 3 unit cubes and then adds 2 more layers of 3 unit cubes each. This means he has 3 layers of 3 cubes each.

We can calculate the total number of unit cubes used by multiplying the number of cubes in each layer by the number of layers. Here's the step-by-step calculation:

Start with quantity in a single layer: 3 unit cubes.

Multiply by the total number of layers to get the total quantity: 3 layers * 3 cubes/layer = 9 unit cubes.

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PLZZZ HELP NOOOOWWW!!!

Answers

Hello!

You can use the Pythagorean Theorem

[tex] a^{2} + b^{2} = c^{2} [/tex]

C is the hypotenuse which is the line across the diameter
a and b are the other sides

You have to find the bottom side of the triangle

9 - 6 = 3

Put in the values you know

[tex] 9^{2} + 3^{2} = c^{2} [/tex]

Square the numbers

[tex]81 + 9 = c^{2} [/tex]

Add

[tex]90 = c^{2} [/tex]

take the square root of both sides

[tex] \sqrt{90} = c[/tex]

The answer is [tex]C) \sqrt{90} [/tex]

Hope this helps!

PLZ HELP ASAP TANGENTS OF CIRCLES PROBLEMS

Answers

Since all these lines are tangents: the unknown length along BC is also equal to 3.3 units. The first segment from C going towards D is also 5.1, meaning that the segment on CD closer to D is 7 units. This is the same length of the first segment from D going towards A, meaning that the segment on DA that is nearest A is 5.2 units long, which is also the length of the unknown segment along AB.
Therefore the perimeter is: 12.2 + 12.1 + 5.1 + 3.3 + 3.3 + 5.2 = 41.2 units

What are the zeros of the function f(x) =(x^2 - 3x - 10)(x + 4)
!!Please help!!!

Answers

f(x) = (x² - 3x - 10)(x + 4) becomes (x - 5)(x + 2)(x + 4) when completely factored. Now set each binomial equal to zero. 

x - 5 = 0
x = 5

x + 2 = 0
x = - 2

x + 4 = 0
x = - 4

Your zeros are at x = - 4, - 2, and 5. Or at (- 4, 0), (- 2, 0), and (5, 0). 

What number should be added on both sides of the equation to complete the square x2 -6x =5

Answers

The Answer wouldn't be any other number but 9. I took this test and got it right.

Answer:

We should add 9 on the both sides of the given equation.

Step-by-step explanation:

Since, for making a perfect square on the left side of a quadratic equation,

We add the square of the half of the coefficient of x on both sides,

The given equation,

[tex]x^2-6x = 5[/tex]

Here, the coefficient of x is 6,

Half of 6 = 3

Square of 3 = 9,

Thus, we should add 9 on the both sides of the given equation.

Verification :

[tex]x^2 - 6x + 9 = 5 + 9[/tex]

[tex](x-3)^2 = 14[/tex]

What is the area of this composite figure? 12ft2 80 ft2 88 ft2 100 ft2

Answers

Look at the picture.

[tex]x=10ft-2ft=8tf\\\\A_1=10ft\cdot8ft=80ft^2\\\\y=10ft-6ft=4ft\\\\A_2=4ft\cdot2ft=8ft^2\\\\A_F=A_1+A_2\to A_F=80ft^2+8ft^2=88ft^2[/tex]

[tex]Answer:\ \boxed{88ft^2}[/tex]

I need help on this please

Answers

The correct answer is the option number 1, which is:

 a(v)=√(3V/8)

 The explanation is shown below:

 To solve this problem you must apply the following proccedure:

 1. You must use the formula for calculate the volume of a square pyramid, which is:

 V=a²h/3

  2. Therefore, when you clear a, you obtain:

 3V=a²h
 3V/h=a²
 a=√(3V/h)

 3. You have that heigth is 8, then:

 a(v)=√(3V/8)

 4. So, as you can see, the correct answer is the option mentioned above.

A card is selected at random from a standard 52-card deck. (a) what is the probability that it is an ace? 4/52 (b) what is the probability that it is a heart? .25 (c) what is the probability that it is an ace or a heart

Answers

Part (a) is relatively straight forward.

There are 4 aces in a standard 52-card deck. So the probability that AN ace is picked is just 4/52.

Part (b):
Note that there are 4 suits in a standard 52-card deck. So picking hearts will be 13/52 or 1/4.

Part (c):
The probability condition OR means we need to add the two probabilities because we do not want them simultaneously. So, we end up getting Pr(ace) + Pr(heart).

From part (a), we found that picking an ace had a probability of 4/52, which is reduced down to 1/13.

From part (b), we found that picking a heart had a probability of 1/4.

So, the probability of an ace OR a heart is 1/13 + 1/4 = 4/52 + 13/52 = 17/52.

What is 9.8 divided by 7

Answers

[tex] \frac{9.8}{7} [/tex] :    1.4

9.8 ÷ 7 = 1.4

So, the answer to your question is 1.4.

Which of the following represents the zeros of f(x) = 6x3 − 35x2 + 26x − 5?
the answer choices are
A. -5, one third, one half
B. 5, negative one third, one half
C. 5, one third, negative one half
D. 5, one third, one half

Answers

Given the function:
f(x)=6x³-35x²+26x-5
to get the zeros we need to factorize the polynomial given:
to factorize we look for a number such that when we substitute in the equation we get a zero:
first number is:
x=5
thus:
to get the rest of the number we shall have:
(6x³-35x²+26x-5)÷(x-5)
=(3x-1)(2x-1)
thus the other roots are:
x=1/3 and x=1/2
hence the answer will be:
C. 5, one third, negative one half

For either linear regression or multiple regression, the standard error of estimate can be computed as ____.​
a. ​the square root of msresidual
b. ​the square root of msregression
c. ​msresidual/(n – 2)
d. ​msregression/(n – 2)

Answers

The standard error of the estimate is a measure of the accuracy of predictions. 

It is given by the square root of the mean square residual.

Therefore, for either linear regression or multiple regression, the standard error of estimate can be computed as ​the square root of msresidual.

The correct computation for the standard error of estimate in regression analysis is the square root of the residual mean square (MSresidual), which is option a. This metric represents the average distance that data points fall from the regression line.

The standard error of estimate in regression analysis, whether it's linear regression or multiple regression, provides us with a measure of the accuracy of predictions made with the regression equation. It represents the average distance that the observed values fall from the regression line.

The correct formula for computing the standard error of the estimate is the square root of the residual mean square (MSresidual), which can be denoted as the square root of MSE or RMS/RMSE. Therefore, the correct answer to the question is a. the square root of msresidual.

This is because the MSE or MSresidual is the average of the squares of the residuals (or deviations of points from the regression line), while the standard error of the estimate is its square root, providing a measure of these residuals in the original units of the dependent variable.

Q # 13, write a rule for the linear function in the graph

Answers

From the two points first we need to find the slope (m)

[tex]m= \frac{3+1}{4-3}=4 [/tex]

Using the slope and a point (4,3) we can write the equation in slope intercept form as:

y - 3 = 4(x-4)

y = 4x -16 + 3

y = 4x - 13

So the correct answer is option A

Two balls are drawn in succession out of a box containing 6 red and 6 white balls. find the probability that the second ball was​ red, given that the first ball​ was:

Answers

Final answer:

The probability that the second ball is red, given the color of the first ball, is 11/22.

Explanation:

To find the probability that the second ball was red, given that the first ball was either red or blue, we need to consider two cases:

If the first ball drawn was red: In this case, there are 5 red balls and 11 balls remaining. So, the probability of drawing a red ball as the second ball is 5/11.If the first ball drawn was blue: In this case, there are 6 red balls and 11 balls remaining. So, the probability of drawing a red ball as the second ball is 6/11.

Since the first ball can be either red or blue with equal probability, we need to consider both cases. Thus, the total probability is (1/2) * (5/11) + (1/2) * (6/11) = 11/22.

simple interest $4000 at 7% for 8 mo.

Answers

I = p(rt + 1)
I = (4000 x .07 x [tex] \frac{8}{12} [/tex]) + 4000
I = 186.67 + 4000
I = around $4186.67

*hope this helped!

In​ 2012, the population of a city was 6.81 million. the exponential growth rate was 1.61​% per year. ​a) find the exponential growth function. ​b) estimate the population of the city in 2018. ​c) when will the population of the city be 10 ​million? ​d) find the doubling time.

Answers

For this case we have a function of the form:
 y = A * (b) ^ t
 Where,
 A: initial amount
 b: growth rate
 t: time
 For each of the questions we must make use of this equation in the following way:
 
 Part A:
 y = 6.81 * (1.0161) ^ t

 Part B:
 y = 6.81 * (1.0161) ^ 6
 y = 7.49 million

 Part C:
 10 = 6.81 * (1.0161) ^ t
 log1.0161 ((1.0161) ^ t) = log1.0161 ((10 / 6.81))
 t = log1.0161 ((10 / 6.81))
 t = 24.05 years

 Part D:
 2 * 6.81 = 6.81 * (1.0161) ^ t
 log1.0161 ((1.0161) ^ t) = log1.0161 ((2 * 6.81 / 6.81))
 t = log1.0161 (2)
 t = 43.40 years

hayden delivers pizza for papa john's. His average tip is $1.50 for each pizza that he delivers. How many pizzas must he deliver to earn at least $20 in tips?

Answers

14 pizzas, you will get $20.50

let us assume that the number of pizzas he must deliver = x

The tip obtained for one pizza = $1.50

Total tips that he must earn = 20

So, we frame the equation as shown below:

1.50*x = 20

1.50x = 20

x = 20/1.5 = 13.333

So he must deliver 13.333 pizzas

Since he cannot deliver fractional pizzas, the number of pizzas he must deliver = 14 pizzas

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