Janice really likes potatoes. Potatoes cost $1.00 per pound, and she has $6.00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30. how many pounds of potatoes will she purchase?

Answer:

The domain in each case is the set of real numbers

Step-by-step explanation:

There is no restriction on what values can be used for x.  The domain in each case is the set of real numbers

Answer:

a) 12

b) 129

Step-by-step explanation:

a)

\(w, x \in \mathbb{Z}_{\ge 0}\)

\(w>50\\x<40\)

For the smallest value of \(w-x\), we gotta figure out the smallest value for w and the highest value for x.

\(w>50 \Rightarrow \text{ smallest value is } 51\)

For \(x\), once \(-(-x)=x\), we conclude that \(x\) cannot be negative and therefore, \(x=39\).

\(51-39=12\)

b)

\(y, z \in \mathbb{Z}_{\ge 0}\)

\(y<70\\z\leq 60\)

For the largest value of \(y+z\), we gotta figure out the highest value for y and z.

\(y<70 \Rightarrow \text{ highest value is } 69\)

\(z\leq 60 \Rightarrow \text{ highest value is } 60\)

\(y+z=69+60=129\)

Therefore , the solution of the given problem of expressions comes out to be  potential energy at 550 metres of altitude is roughly 2,798.46 Joules.

Instead of producing estimates at random, it is preferable to use expanding, decreasing, & blocking moving numbers. They were only able to assist one another by exchanging resources, knowledge, or answers to problems. In addition to arithmetic operations like addition, negation, synthesis, and combination, a truth statement may also contain formulas, components, and notations. It is feasible to evaluate and analyse both sentences as words.

Here,

The gravitational potential energy of the bird at a height of 550m can be determined using the following formula, assuming you meant to say "0.52 kg bird" instead of "0.52k bird":

Mass times gravity times height equals gravitational potential energy.

where mass is measured in kilogrammes, gravity is the force of gravity, which accelerates objects near the Earth's surface at a rate of around 9.81 m/s2, and height is measured in metres.

Inputting the values provided yields:

The gravitational potential energy is equal to

=> 0.52 kg * 9.81 m/s2 *550 m,

=> 2,798.46 joules.

Hence, the bird's gravitational potential energy at 550 metres of altitude is roughly 2,798.46 Joules.

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The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.

First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;

(a+a+2+a+4+a+6+a+8+a+10)/6 = b

6b=6a+30

b=a+5

Also, let the average of the consecutive intergers ending with b be denoted by; x.

(b+b-1+b-2+b-3+b-4)/5 = x

=(5b-10)/5

=b–2

The average, x=b – 2 (where b = a-5)

Ultimately, the value of the required average is; = a+5-2 = a+3.

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Answer: — By replacing x with -9, we have f(-9)=(-9)^2+2=81+2=83 I hope that this was helpful.

Step-by-step explanation:

Answer:

Measure of angle b is 42 degrees

Step-by-step explanation:

Since angle b is part of a right angle, we can see that part of the right and blue is 48 degrees, and the other part is b. So, we can do 90-48 to get 42 degrees.

Answer:

42

Step-by-step explanation:

since one of the lines for angle b makes a 90° angle all you have to do is subtract 48 from 90 and that is your answer

Answer: Here you go! Any questions?

Step-by-step explanation:

Sorry if this is not right...I tried forgive me

The required graph has been attached below that represents the function f(x) = 5 cos (2x).

The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.

Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.

The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).

Thus, the graph has been attached below that represents the given function.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

C  5

Step-by-step explanation:

The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5

Please have this at the back of your mind that two coats of special rust prevention paints is needed.

Each covering is the same as finding the total surface area of the propane tank with the shape of a cylinder with 2 hemispheres ends

The total surface of a Propane Tank (PT) is given as:

Note that radius(r)=2.7ft

The surface area of the propane tank will give

Answer:

4.75 = 475/100 = 19/4 = 4 3/4

Approximate value(s):

4.75 =~ 4 (error = -15.789473%)

\( - 4.74\)

\( = - 4 + 0.74\)

\( = - 4 + \frac{74}{100} \)

\( = - 4 + \frac{37}{50} \)

\( - 4 \frac{37}{50} \)

In this case the answer is very simple . .

Step 01:

Data

rent a golf club = $4

bucket of balls = $2.75

Step 02:

x 1 = 0 bucket y1 = $4

x2 = 1 bucket y2 = 4 + 2.75 = $6.75

Slope formula

Point-slope form of the line

(y - y1) = m (x - x1)

(y - 4) = 2.75 (x - 0)

y = 2.75 x + 4

x = 3 bucket of golf balls

y = 2.75 (3) + 4 = $12.25

The answer is:

Lana must pay $12.25

Slope: m = 2.75

y intercept = 4

equation of the line: y = 2.75 x + 4

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

104°

This is because there are two lines, each line is 180°, so both is equal to 360°. Angle y and the one with 76° are the same, so that should mean angle z and x are the same. So you subtract 152° from 360° (76° doubled) and you get 208° leftover. Now to get the last two angles, you divide 208° by 2, so each angle should be 104°. :))

\(\text{Given that,}\\\\\dfrac{dy}{dx} = x^2 y^2\\\\ \implies \dfrac{d^2 y}{dx^2} = x^2\cdot 2y \dfrac{dy}{dx}+ y^2 \cdot 2x\\\\\implies \dfrac{d^2 y}{dx^2} = x^2 \cdot 2y \cdot x^2 y^2 +2xy^2\\\\\implies \dfrac{d^2 y}{dx^2} =2x^4y^3 + 2xy^2 = 2xy^2(x^3y+1)\)

Part A: Grocery Store: unit price = $1.65 (Tomatoes)

Farmer's Market: unit price  = $1.75

Part B: Grocery Store offers a better deal because the unit price is less.

Unit price is defined as the price for one of something. For example, if 10 oranges cost $50, the unit price will be $50/10 = $5 i.e.  $5 for one orange.

PART A:

Let's choose tomatoes

Grocery Store

8 tomatoes for $13.20

Unit price = $13.20/8 = $1.65

10 tomatoes for $17.50

Unit price = $17.50/10 = $1.75

Part B:

The location that offers a better deal is Grocery Store. This is because the unit price is less.

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Answer:

\(x=12\times \text{tan}(20^0)\)

Step-by-step explanation:

From the figure attached,

Measure of an angle = 20°

Measure of the opposite side = x

Measure of the adjacent side = 12

By applying tangent rule in the given right triangle,

tan(20°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

\(\text{tan}(20^0)=\frac{x}{12}\)

\(x=12\times \text{tan}(20^0)\)

Therefore, equation to get the value of 'x' will be,

\(x=12\times \text{tan}(20^0)\)

The AR(1) model was used to create an updated forecast for Amazon sales that account for trend, seasonality, and serial correlation is 97.6510

Accounting and revenue

Given that:

Equation of regression

Revenue = 22.67 + 2.538*t - 10.44*Q1 + 11.156*Q2- 8.77*Q3

t = 1 for the third quarter of 2013.

t = 33 for the third quarter of 2021

Revenue = 22.67 + 2.538*33 - 8.77 = 97.6510 billion dollars.

Therefore, Revenue = 97.6510 billion dollars

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The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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It should be noted that the correct matching of the expressions illustrated will be:

a. (2^3)(2^2) = 32

b. 2^(-2) x 2^(-3) = 1/32

C. (2^3) x (2^-3) = 1

d. (2^2)^3 = 64

e. 2^2/2^3 = 1/2

f. 2^3/2^2 = 2

It should be noted that (2^3)(2^2) will be:

= 2³ × 2²

= 8 × 4

= 32

b. 2^(-2) x 2^(-3) will be illustrated as:

= 1/4 × 1/8

= 1/32

C. (2^3) x (2^-3)

= 8 × 1/8

= 1

d. (2^2)^3

= 4³

= 64

e. 2^2/2^3

= 4 / 8

= 1/2

f. 2^3/2^2

= 2³ / 2²

= 8 / 4

= 2

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Answer:

20 months

Turn sentences into equation:

She deposits $225 every month after initial deposit of $2500 in first month

Equation: y = 2500 + (x - 1)225

where y represents total amount, x represents months

Use this equation to find at which month her account will have $6,775

2500 + (x - 1)225 = 6,775

(x - 1)225 = 6,775 - 2,500

(x - 1)225 = 4275

x - 1 = 19

x = 20

Thus, it will take 20 months when she have a total of $6,775.

Answer:

$10.12

Step-by-step explanation:

Step one:

given data

we are told that the cost of binoculars is $155.75

and also the sales tax is 7%

Step two:

We want to first solve for the sales tax which is 7% of  $155.75

=7/100* 155.75

=0.070*155.75

=10.12

Cassie will pay a tax of $10.12

Also Cassie will pay a total amount of

= 155.75+10.12

=$165.87

I hope this helped you

Answer:

a = 3

Step-by-step explanation:

24 x 2ªx 3

8= 2ª

a= 3

\(\huge\text{Hey there!}\)

\(\mathsf{24 = 2a \times 3}\\\mathsf{\rightarrow 2a \times 3 = 24}\\\mathsf{\rightarrow 2(3)(a) = 24}\\\mathsf{\rightarrow 6(a) = 24}\\\mathsf{\rightarrow 6a = 24}\\\\\text{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\rightarrow\dfrac{6a}{6} = \dfrac{24}{6}}\\\\\text{SIMPLIFY it}\\\\\mathsf{\rightarrow a = \dfrac{24}{6}}\\\\\mathsf{\rightarrow a = 4}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{a = 4}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

7(1+2)

Step-by-step explanation:

So find the Greatest common factor first which is7 in this case

now we divide each number by 7

1+2 now

now we put that around parthesis and multiply it by 7

7(1+2)

Thats how you factpr

Check:

using distributive property

7+14, same answer.

Answer:

7(1+2)

Step-by-step explanation:

Find the factors of each number

7 has factors of 1,7

14 has factors of 1,2,7,14

The greatest common factor is 7

7*1 + 2*7

Factor out the 7

7(1+2)

Answer:

Step-by-step explanation: