Which is the better buy?

2-gallon bucket of paint for $88.00

37-cup bucket of paint for $90.28

Answer:

Exponential Function

General form of an exponential function with base \(e\):

\(f(x)=Ae^{kx}\)

where:

The curve crosses the y-axis at y = 40.  Therefore, A = 40.  

Substitute the found value of A into the formula along with (1, 56) and solve for \(k\):

\(\begin{aligned}f(x) & =Ae^{kx}\\\implies 56 & =(40)e^{k}\\e^k & =\dfrac{56}{40}\\k & =\ln (1.4)\end{aligned}\)

\(\textsf{Equation}: \quad f(x)=40e^{x\ln 1.4}\)

To find the population in 10 years, substitute \(x = 10\) into the found equation:

\(\begin{aligned}\implies f(10)&=40e^{10\ln 1.4}\\ & =1157.01862\\ & =1157\end{aligned}\)

The curve crosses the y-axis at y = 10.  Therefore, A = 10.

Substitute the found value of A into the formula along with (1, 18) and solve for \(k\):

\(\begin{aligned}f(x) & =Ae^{kx}\\\implies 18 & =(10)e^{k}\\e^k & =\dfrac{18}{10}\\k & =\ln (1.8)\end{aligned}\)

\(\textsf{Equation}: \quad f(x)=10e^{x\ln 1.8}\)

To find the population in 8 years, substitute \(x = 8\) into the found equation:

\(\begin{aligned}\implies f(8)&=10e^{8\ln 1.8}\\ & =1101.996058\\ & =1102\end{aligned}\)

The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

Step-by-step explanation:

your doing the calculation wrong

The required unit rate for the nuts is $0.45/oz.(rounded to the nearest cent).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
The unit rate for the nuts can be found by dividing the total cost by the total weight,

Unit rate = total cost / total weight

Unit rate = $6.99 / 15.4 oz

Unit rate = $0.45/oz (rounded to the nearest cent)

Therefore, the unit rate for the nuts is $0.45/oz (rounded to the nearest cent).

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Answer: $0.45 is the correct answer

Step-by-step explanation: Answer verified correct on test

Answer:

Let y = the amount in Adrianna's savings account

Let x = the number of weeks passed

y = 5x + 20

Answer:(2,-3)

Step-by-step explanation:

Steps to solve:

5 - 8d = 16

~Subtract 5 to both sides

-8d = 11

~Divide -8 to both sides

d = -11/8

Best of Luck!

Answer:

Subtract 5 from both sides, then divide both sides by -8

Answer:

  150 ounces

Step-by-step explanation:

It is convenient to write an equation for the total amount of alcohol in the mix.

__

Let x represent the amount of pure alcohol added. Then the amount of alcohol in the mix is ...

  500(35%) +x(100%) = (500 +x)(50%)

  x = 500(15%) +x(50%) . . . . . . . subtract 500(35%)

  x(50%) = 500(15%) . . . . . . . . . . subtract x(50%)

  x = (500)(15%)/(50%) = 150 . . . . divide by the coefficient of x

150 ounces of pure alcohol should be added to produce the desired solution.

The system does not have a periodic solution in each of 10 and 11.

A solution of the period depends on the independent variable t is called Periodic Solution. For a periodic solution x(t)( in the case of a system, x is a vector), there is a number T≠0 such that

x(t+T)=x(t)  for t∈R.

The given equations are:

      \(\frac{dx}{dt} =-2x-3y-xy^2\\\\\frac{dx}{dt} =y+x^3+x^2y\)

F is the derivative of dx/dt and Gis the derivative of dy/dt:

\(F(x,y)=-2x-3y-xy^2\\G(x,y)=y+x^3+x^2y\)

When Fx+Gx has the same sign on the entire domain D, then there are no periodic solutions on the domain D.

Fx+Gx=-2-y^2+1-x^2

          =-1-y^2-x^2

             <for all real numbers x,y\(\neq\)0

Fx+Gx have the same sign  for all pairs of real numbers with x\(\neq\)0 and y\(\neq\)0

Thus, there are no periodic solutions in the system(excluding contact solutions)

Hence proved.

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Answer:

volume is 8 times larger and surface area is about 2.7 times larger

Step-by-step explanation:

a)24 in³ b) 76 in² c) volume is 8 times larger and surface area is about 2.7 times larger.

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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we have

25,078,746 people per year -------> given

so

Per month

Divide by 12

25,078,746/12=2,089,896 per month (rounded to a whole number)

Per day

1 year=365 days

so

25,078,746/365=68,709 per day

Per hour

1 day=24 hours

so

68,709/24=2,863 per hour

Per-minute

1 hour=60 minutes

2,863/60=48 per minute

Per second

1 minute =60 sec

48/60=0.8=1 per second

Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

Answer:

1.The  equation of best fit is ŷ = 2.69152X + 3.45818.

Step-by-step explanation:

Multiply her savings by the percent spent:

850 x 0.35 = 297.50

The tv cost $297.50

Answer:

the price of TV is = 297.5$

Step-by-step explanation:

all money= 850$

purchased money= 35% of all money ==> 850 ( 35%) = 297.5$

Answer:

Step-by-step explanation:

Answer:

150.8 I think

Step-by-step explanation:

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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Answer:

c. x =1.293

Explanation:

To solve the expression, we will apply the properties of the logarithms, so

Therefore, the value for x is

c. x =1.293

Answer:

(-1, 2)

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

it would be the same as it opposite side S because they are the same