A group of friends went to lunch. The bill, before sales tax and tip was $35.55. A sale tax of 6% was added. The group then tipped 15% on the amount after the sales tax was added. What was the amount, in dollars, of the total cost?

Given:

f(x) is an exponential function.

[tex]f(-3.5)=25, f(6)=33[/tex]

To find:

The value of f(6.5).

Solution:

Let the exponential function is

[tex]f(x)=ab^x[/tex]         ...(i)

Where, a is the initial value and b is the growth factor.

We have, [tex]f(-3.5)=25[/tex]. So, put x=-3.5 and f(x)=25 in (i).

[tex]25=ab^{-3.5}[/tex]         ...(ii)

We have, [tex]f(6)=33[/tex]. So, put x=6 and f(x)=33 in (i).

[tex]33=ab^{6}[/tex]         ...(iii)

On dividing (iii) by (ii), we get

[tex]\dfrac{33}{25}=\dfrac{ab^{6}}{ab^{-3.5}}[/tex]

[tex]1.32=b^{9.5}[/tex]

[tex](1.32)^{\frac{1}{9.5}}=b[/tex]

[tex]1.0296556=b[/tex]

[tex]b\approx 1.03[/tex]

Putting b=1.03 in (iii), we get

[tex]33=a(1.03)^{6}[/tex]

[tex]33=a(1.194)[/tex]

[tex]\dfrac{33}{1.194}=a[/tex]

[tex]a\approx 27.63[/tex]

Putting a=27.63 and b=1.03 in (i), we get

[tex]f(x)=27.63(1.03)^x[/tex]

Therefore, the required exponential function is [tex]f(x)=27.63(1.03)^x[/tex].

Answer:

1/5

Step-by-step explanation:

its probability there is only 1 orange ball out of 5 balls altogether so the probability of picking 1 orange ball is 1/5

Answer:

4y-3x or -3x+4y

Step-by-step explanation:

first you have to distribute so you will do -1/3*9x and then -1/3*-12y

1. -1/3*9x=-3x

2. -1/3*-12y = 4y

then you have your answer 4y-3x or -3x+4y

Hope this helps!!!

Answer:

Step-by-step explanation:

t=s+(s+5)

t=s+s+5

t=2s+5

Answer:

The expression is:

y=500x+550p, where

y is the amount earned

x is the quantity of Xboxes sold

p is the amount of Playstations sold

Step-by-step explanation:

With the information provided, you can say that the amount of money they will earn for selling Playstations and Xboxes is equal to the sum of the result of multiplying the price per Xbox Series X for the quantity sold plus the result of multiplying the price per Playstation 5 for the quantity sold, which can be expressed as:

y=500x+550p, where

y is the amount earned

x is the quantity of Xboxes sold

p is the amount of Playstations sold

Answer:

A

Step-by-step explanation:

019eheiehejeeiejehehhehe

Answer:

I got you, give me a few minutes

1st one: 6x+12+6y

2nd one: -12a-20b

4th one: 2x times 18

Step-by-step explanation:

1: -4x + 2y + 10

2: -12a^2 + 20ab

3: i didnt know it sorry

4: x^2 - 9x + 18

all you need to do is the order of operations

Answer:

We cannot draw graphs in brainly. we could send a pic or screenshot of where we could draw it though if u wanted

Step-by-step explanation:

blue

What grade are you in? this is really easy!  you are definitely not a middle schooler, and forget high school . the reason you don't get this  is that you're wasting your time

playing  r 0 B I o x and  going on discord  now pull yourself together and study!!!

AND THATS ON PERIODT!!!

Answer:

-4.5-5.2 and -4.5+(-5.2)

Step-by-step explanation:

True:

Her lowest score is 40

(one of them)

Answer:

side = 16.97 cm

Step-by-step explanation:

24²/2 = side²

side = 16.97 cm

Area of rhombus :-

[tex] \bf \star \: \: \boxed{ \bf \dfrac{d_{1}d_{2}}{2} }[/tex]

[tex] \sf \longrightarrow d_{1} = 4 \sqrt{3} + 4 \sqrt{3} = 8 \sqrt{3} [/tex]

[tex] \sf \longrightarrow d_{2} = 4 + 4 = 8[/tex]

Area of rhombus :-

[tex] : \implies \sf \dfrac{8 \sqrt{3} \times 8 }{2} [/tex]

[tex] : \implies \sf 8 \sqrt{3} \times 4[/tex]

[tex]: \implies \bf 32 \sqrt{3} \: {m}^{2} [/tex]

Answer:

the last one

Step-by-step explanation:

the answer is d which it's the last one

Answer:

A.

Step-by-step explanation:

got it on edge assignment

Answer: English please

Step-by-step explanation:

Answer:

The missing angle is 40 degrees

Step-by-step explanation:

Tan = opposite / adjacent

Tan ? = 24 / 29

24 / 29 = 0.8275

Tan-1 of 0.8275 is 39.610

Round to the nearest degree

39.610 = 40

Answer:

Step-by-step explanation:

Here you have a right triangle with the side lengths 24 and 29 and are asked to find the measure of the smallest angle.

In cases like this you should ask yourself which trig function includes the lengths of the legs (that is, the lengths of the side opposite the angle and the side adjacent to the angle).  That would be the tangent function, and so:

tan (?) = (opposite side) / (adjacent side)

Here, tan x = 24/29 = 0.691.  Note:  I used my TI-83Plus calculator to determine that the measure of angle x in radians is 0.691.

The unknown angle is 0.691 radians, or (multiplying that by the conversion factor (180/pi) ) 39.6 degrees.  To the nearest degree, that'd be 40 degrees.

Answer:

answer is 11.9...... have a good day

Answer:

11.9

Step-by-step explanation:

TU=TV-UV

TU=17.7-5.8=11.9

Answer: 28x+15

Step-by-step explanation:

Answer: 5.320311

Step-by-step explanation: hope this helps!

Answer:

5.3203112212

Step-by-step explanation:

Answer:

x

Step-by-step explanation:

Answer:

12 divided by 1 can be 12. If thats what you mean and if not, just tell me by explaining with more detail

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Use rise over run, (y2 - y1) / (x2 - x1)

Plug in the points and simplify:

(y2 - y1) / (x2 - x1)

(70 - 56) / (5 - 4)

14 / 1

= 14

So, the slope of the line is 14.

Answer:

m=14

Hope it helped if it did mark as brainliest!

Answer:

The value of w is 7.

Step-by-step explanation:

According to Pythagoras theorem,

Hypotenuse²=Perpendicular²+Base²

H²=P²+B²

Here,

Hypotenuse given=7√2

w=y

Perpendicular=Base=x

(7√2)²=x²+x²

49*2=2x²

(49*2)/2=x²

49=x²

√49=x

7=x

Perpendicular=x=7

Answer:

1) 60 miles

2) 7 dollars

Step-by-step explanation:

1) Question 1

Let x be equal to the full distance of the trip

[tex]0.4x=24[/tex]

Divide both sides by 0.4

[tex]\frac{0.4x}{0.4}=\frac{24}{0.4} \\x=60[/tex]

Therefore, the trip is 60 miles long.

2) Question 2

Let y be equal to the price that Marco paid for the doll.

[tex]35*0.2=y[/tex]

We multiply 35 by 1-0.8 because the doll is 80% off, meaning he's paying for 20% of the original price

[tex]7=y[/tex]

Therefore, Marco paid $7 for the doll.

I hope this helps!

Answer:

y+3=-11/7(x-2)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(8-(-3))/(-5-2)

m=(8+3)/-7

m=11/-7

y-y1=m(x-x1)

y-(-3)=-11/7(x-2)

y+3=-11/7(x-2)

Answer:

the first one

35 (that symbol i cant find it on the computer) 5

Answer:

Exact Form:

77 /8

Decimal Form:

9.625

Mixed Number Form:

9  5 /8

Step-by-step explanation:

I AM SO SORRY IF THIS IS WRONG

Answer:

fraction form: 77/8

decimal form: 9.625

Step-by-step explanation:

if you change 11 into 11/1 you get

11/1*7/8

11*7=77

1*8=8

77/8

hope this helps!

Answer:

mixed number form 1 1/9

decimal form 1.11111111111111 it goes on forever

percent form 111.111111111111% it goes on forever (again)

Step-by-step explanation:

i hope that helps!

Answer:

1  1/9

Step-by-step explanation:

10/9, you get 1 as the whole number.

You have a 1 left over when dividing 10 and 9. the 1 will be over 9.

Giving you 1 as the whole number and 1/9 next to it.