Mary wants to buy a mobile phone; the least expensive one she's spotted so far is $15. Mary has $4.25 saved for a mobile phone. If Mary works at a rate of $2.15 per hour, how many hours (H) will she have to work in order to afford a mobile phone?

Answer: [tex]7.93[/tex]

Step-by-step explanation:

Given

[tex]f(x)[/tex] is an exponential function. Suppose [tex]f(x)[/tex] is [tex]ae^{bx}[/tex]

[tex]f(1.5)=5\ \text{and}\ f(7.5)=79[/tex]

[tex]\Rightarrow 5=ae^{1.5b}\\\Rightarrow \ln 5=\ln a-1.5b\quad \ldots(i)[/tex]

Similarly,

[tex]\Rightarrow 79=ae^{7.5b}\\\Rightarrow \ln(79)=\ln a+7.5b\quad \ldots(ii)[/tex]

Subtract (i) and (ii)

[tex]\Rightarrow \ln (79)-\ln (5)=9b\\\Rightarrow \ln (\frac{79}{5})=9b\\\\\Rightarrow b=\dfrac{\ln (\frac{79}{5})}{9}\\\\\Rightarrow b=0.3066[/tex]

Insert the value of [tex]b[/tex]

[tex]\Rightarrow 5=ae^{0.46}\\\Rightarrow a=5\times 0.6312\\\Rightarrow a=3.156\approx 3.16[/tex]

So, the function becomes

[tex]\Rightarrow f(x)=3.16e^{0.3066b}[/tex]

[tex]\Rightarrow f(3)=3.16e^{0.3066\times 3}\\\Rightarrow f(3)=7.927\approx 7.93[/tex]

Answer:

7.93

General Exponential Form: y=ab^x

Plug in both points

divide the equations

cancel out a, subtract exponent of b

Answer: -cos(a)+cos(b)

Step-by-step explanation:

To integrate is the same as saying to find the antiderivative.

[tex]\int\limits^a_b {sin(x)} \, dx[/tex]         [antiderivative of sinx is -cosx]

[tex]-cos(x)|_b^a[/tex]           [include boundaries]

[tex]-cos(a)+cos(b)[/tex]

Therefore, the integral would be -cos(a)+cos(b).

d=10

Answer:

Solution given:

[tex]\sqrt{25+3x}=d+2x[/tex]

squaring both side

25+3x=(d+2x)²

when x=-3

25+3*-3=(d+2*-3)²

25-9=(d-6)²

16=(d-6)²

[tex]\sqrt{16}=d-6[/tex]

4=d-6

d=4-6

d=10

Answer:

d = 6

Step-by-step explanation:

[tex] \sqrt{25 + 3( - 3)} = d + 2( - 3) \\ 4 = d - 6 \\ d = 10[/tex]

hopefully this makes sense

:)

Answer:

leading coefficient -3

constant 2

Step-by-step explanation:

Standard from is from largest power to smallest power

-3x^2 +5x +2

The leading coefficient is the number in front of the largest power of x

-3

The constant is the number without a power of x ( or x^0)

2

Answer:

0

Step-by-step explanation:

Tan 30 and Sin 60 are in first quadrant and so their values will be positive.

Cos 180 is in Second quadrant. In second quadrant , value of cos is negative.

Cos 180 = -1 ; Tan 30 = 1/√3  & Sin 60 = √3/2.

Cos 180 + 2 tan 30 + Sin 60 =  [tex]-1 + 2* \frac{1}{\sqrt{3}}*\frac{\sqrt{3}}{2}[/tex]

                                              = [tex]-1 + 1 = 0[/tex]

Answer:

[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]

Answer:

A

Step-by-step explanation:

A

The number of sides for a regular polygon that will not form a regular tessellation is 7. The correct option is C.

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

A tessellation or tiling is the seamless covering of a surface, frequently a plane, with one or more geometric shapes, known as tiles. One regular polygon can be used to create a single regular tessellation. Two or more regular polygons are used in a semi-regular tessellation.

Triangles, squares, and hexagons are the only three regular tessellations.

Now, the name of the polygon having 3, 4, and 6 sides is triangle, square, and Hexagon. Therefore, the only regular polygon that will not form a regular tessellation is heptagon, which has 7 sides.

Hence, the number of sides for a regular polygon that will not form a regular tessellation is 7.

Learn more about Polygon here:

https://brainly.com/question/10441863

#SPJ2

To find the inverse of a function, switch the x's and y's, then solve for y again.

y = 2/3x - 17

SWITCH

x = 2/3y - 17

2/3y = x + 17

y = 3(x + 17) / 2

y = x - 10

SWITCH

x = y - 10

y = x + 10

y = cuberoot(2x)

SWITCH

x = cuberoot(2y)

x^3 = 2y

y = x^3 / 2

y = x/5

SWITCH

x = y/5

y = 5x

Hope this helps!

Answer:

b.

[tex]{ \tt{(6x + 7 + {x}^{2})(2 {x}^{2} - 3) }} \\ = { \tt{(2 + 1) {x}^{2} + 6x + (7 - 3) }} \\ = { \tt{3 {x}^{2} + 6x + 4 }}[/tex]

Answer:

4.5 hours in minutes = 270

Every 45 minutes, bacteria triples

You start with 50

Divide 270 (total time) by 45 (every time bacteria triples)

270/45 = 6

36,450 bacteria

Answer:

i think its 30

Step-by-step explanation:

Answer:

length ≈ 2.6 ft

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{30}{360}[/tex]

      = 2π × 5 × [tex]\frac{1}{12}[/tex]

      = 10π × [tex]\frac{1}{12}[/tex]

     = [tex]\frac{10\pi }{12}[/tex]

     ≈ 2.6 ft ( to the nearest tenth )

Answer:

(x-9)^2 +(y-12)^2 = 225

Step-by-step explanation:

First find the length of the radius

If is the distance from the center to the point

d = sqrt( (x2-x1)^2 + (y2-y1)^2 )

   = sqrt( (0-9)^2 + (0-12)^2)

   = sqrt ( 81+144)

  = sqrt(225)

  = 15

The equation for a circle is

( x-h) ^2+ (y-k)^2 = r^2

(x-9)^2 +(y-12)^2 = 15^2

(x-9)^2 +(y-12)^2 = 225

Answer:

no solution

Step-by-step explanation:

Supplementary angles add to 180

Let x be the supplement

x+69 = 180

x = 180-69

x =111

The complement of an angle means they add to 90

111+y = 90

y = 90-111

y =-21

But an angle cannot be negative so there is no solution

Answer:

21 degrees.

Step-by-step explanation:

To find the complementary angle you have to subtract the given angle from 90.

so,

90 - 69 = 21.

Extra info: if you need to find the supplementary angle you need to subtract the given angle from 180.

Answer:

Step-by-step explanation:

The domain are all the x values in order, no repeats allowed:

D = {-2, 2, 5}

Same thing for the range, except these are the y values:

R = {-7, 2, 4}

The coordinates stated this way don't match up to what they are in coordinate form, but they don't have to.

Answer:

Domain : {-2,2,5}

Range:{ -7,2,4}

Step-by-step explanation:

The domain is the inputs

Domain : {-2,2,5}

The range is the outputs

Range:{ -7,2,4}

Answer:

2187 = [tex]3^{7}[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex] , then

[tex]log_{3}[/tex] 2187 = 7

2187 = [tex]3^{7}[/tex]

Answer:

3 ^7 = 2187

Step-by-step explanation:

log3 2187 = 7

log a (b) = c

a^c = b

3 ^7 = 2187

Answer:

12+27k

Step-by-step explanation:

distribute the 3

Answer:

[tex]R_1>R_2>R_3[/tex]

Step-by-step explanation:

As per Ohm's law,

V = IR

I = Current

R = Resistance

V = Voltage

This law states → R = [tex]\frac{V}{I}[/tex]

If we graph the relation between Voltage and Current, linear graph represents the Resistance.

Greater the slope of the line will represent greater resistance.

Therefore, [tex]R_1>R_2>R_3[/tex]

Answer:

it would be

D.

(7,-4)

Mark me as brainliest pleases

Answer:

it would be A (-7,-4)

Step-by-step explanation:

Answer:

Maybe, there is a chance, but I don't know for sure.

It might matter, but I wouldn't worry or stress about it too much.

My only advice to you is do not procrastinate and if you need help don't be afraid to ask.

Answer:

It matters but not like you think.

GPA, extracurricular activities, and SAT/ACT are the biggies. Truthfully it won't change a thing if you took accelerated pre-algebra versus normal. In fact, spoiler alert, the SAT/ACT (I'm assuming your american) will matter more than your courses ever did. I took two years of college physics in highschool and i made more off my SAT. Not only that, but an A in an easy class looks better than a C in a hard one on transcripts.

My advise is slow down, relax, and learn it well. Better to learn the concept fully in normal so that you can apply it, than half learn it in advance and struggle in future applications. After all, math ALWAYS builds. Take it slow, take it easy.

I would recommend talking to a school guidance counselor about your academic stress. Im sure their professional insight will help put you at ease. It may also help to get you going in the right direction so that you achieve your goals.

Good luck. Enjoy life

Answer:

[tex]\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx = xln|x| - x + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Logarithmic Differentiation

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Logarithmic Integration

Integration by Parts:                                                                                               [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for integration by parts using LIPET.

Step 4: Integrate Pt. 3

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

1766 using 3.14 for pi

1767 using the pi button

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

we need to know the radius

r =d/2 = 15/2 = 7.5

V = 4/3 (pi)( 7.5)^3

V =562.5 pi

Approximating pi by 3.14

V = 562.5 (3.14)

V =1766.25

To the nearest whole number

V = 1766

If you use the pi button

1767.14586

To the nearest whole number

1767

Answer:

[tex]V=1767[/tex]

Step-by-step explanation:

Step 1:  Find the volume of the sphere

Volume of a Sphere:  [tex]V=\frac{4}{3}\pi r^{3}[/tex]

Find the radius

[tex]Radius = Diameter / 2[/tex]

[tex]Radius = 15 / 2[/tex]

Plug in the values and solve

[tex]V=\frac{4}{3}\pi * \frac{15}{2}^{3}[/tex]

[tex]V=\frac{4}{3}\pi * \frac{3375}{8}[/tex]

[tex]V=\frac{1125}{2}\pi[/tex]

[tex]V=1767[/tex]

Answer:  [tex]V=1767[/tex]

Answer:

4 containers.

Step-by-step explanation:

Since Noelle collected 3 quarts 1 pint of liquid from the first table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.

She also collected 4 quarts from the second table, 2 quarts from the third table.

Finally, she collected collected 3 quarts 1 pint of liquid from the fourth table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.

So, the total amount of liquid she collected in quarts is V = 3.5 quarts + 4 quarts + 2 quarts + 3.5 quarts = 7.5 quarts + 5.5 quarts = 13 quarts

We now convert this value to gallons to know the amount of containers Noelle needs since she has one gallon containers.

13 quarts = 13 × 1 quarts = 13 quarts × 1 gallon/4 quarts = 13/4 gallons = 3.25 gallons

Since the total amount of liquid is 3.25 gallons = 3 gallons + 0.25 gallons, Noelle would need 4 containers since 3 containers would contain the first 3 gallons and the fourth container would contain the remaining 0.25 gallons.

So, Alyssa would need 4 containers.

Answer:

I think its 1.4

Step-by-step explanation:

if you divide 42 by 1.4 it makes 30 and if u multiply 30 by 1.4 it makes 42

Answer:

the scale factor is 7/5

Step-by-step explanation:

42/30=

42/30=

then you find a common factor between the two is 6, so you divide both sides of the fraction by 6 to get 7/5. and because they both are the same you know that they both have the same scale factor. Which is 7/5. I am not quite sure if you need to find the missing side length but in case you do multiply 40 by 7/5 so it looks like 40/1 x 7/5. 40 x 7 = 280. 280/5 = 56. so your side length is 56.

Answer:

Option A

Step-by-step explanation:

[tex]\frac{1}{a^{-m}}=a^{m}\\[/tex]

[tex]\frac{m^{7}n^{3}}{mn^{-1}}=\frac{m^{7}n^{3}n^{1}}{m}=\frac{m^{7}n^{3}n}{m}[/tex]

Answer:

X = 276°

Step-by-step explanation:

Divide X into x1 and x2

then then using the trick of co-interior angles, find the answer of x1 and x2 . then add x1 and x2