If it costs 1.85 dollars to rent 3 books at the library, how much would cost to rent 51
books?

Answer:

(2, -4)

Step-by-step explanation:

\({ \sf{f(x) = {x}^{3} - {3x}^{2} }} \\ { \sf{ {f}^{l}(x) = {3x}^{2} - 6x }} \\ \\ { \sf{0 = x(3x - 6)}} \\ { \sf{0 = 3x - 6}} \: \: \: \: \: \\ { \sf{3x = 6}} \\ { \sf{x = 2}}\)

For x = 2

\({ \sf{f(2) = {2}^{3} - 3 {(2)}^{2} }} \\ { \sf{f(2) = 8 - 12}} \\ { \sf{f(2) = - 4}}\)

Point is (2, -4)

Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Answer:

The number 49/4 should be added on both sides of \(x^2 + 7x = 4\)  to complete the square.

Step-by-step explanation:

\(x^{2} + 7x +\frac{49}{4} = 4 + \frac{49}{4}\)

\({4x^{2} + 28x + \frac{49}{4} = {16 + \frac{49}{4}\)

\({4x^{2} + 28x + 49} = 16 + 49\)

\((2x + 7)2 = 65\)  [since \(a^{2} + 2ab + b^{2} = (a + b)^{2}\)]

\((2x + 7)^{2}\) \(=\) \((\sqrt65)^2\)

Answer:

See below

Step-by-step explanation:

x^2 + 7x - 4 = 0      take 1/2 of the 'x ' coefficient (this is 7/2)  and do this:

(x + 7/2)^2    -4       now when you expand this (see botom line) you will see you have added  49/4  to the equation....you will need to subtract this               for the equation to be the same :

(x+7/2)^2  - 49/4 - 4  = 0     then simplify to:

(x+7/2)^2  - 65/4 = 0     you can re-arrange if needed to this:

(x+7/2)^2 = 65/4

(x+7/2)^2 = x^2 + 7x + 49/4    <====== this needs to be subtracted

If you are standing 45 feet away from a school and the angle of elevation is 66 degrees than the building is 101.07 ft tall.

To find this, we can use the tangent function to find out how tall is the buiding:-

Let the height of building be x

Distance from building = 45 ft

tan 66° = x/45

x = 45 tan 66°

x = 45 (2.246)

x = 101.07 ft

Therefore, If you are standing 45 feet away from a school and the angle of elevation is 66 degrees than the building is 101.07 ft tall.

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Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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As an operations manager for a plant that manufactures batteries, I can use both descriptive statistics and inferential statistics to make better managerial decisions

Descriptive statistics help me to summarize and describe the data collected from the manufacturing process.

For instance, I can use measures such as mean, median, mode, range, and standard deviation to summarize the data on the production output of batteries over a specific period.

Inferential statistics allow me to draw conclusions and make predictions based on the data collected from a sample of batteries produced.

For example, I can use inferential statistics to determine the probability of the battery meeting the required specifications. I can also use inferential statistics to make predictions about future production output, based on the historical data.

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Answer:

The practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.

Step-by-step explanation:

The practical domain of the function is limited by the given constraints: Joe can purchase up to 8 boxes of hot dogs, and he cannot purchase partial boxes. Therefore, the number of boxes he can purchase is a whole number between 0 and 8, inclusive.

Substituting the values from 0 to 8 into the function, we get:

f(0) = 48(0) + 20 = 20

f(1) = 48(1) + 20 = 68

f(2) = 48(2) + 20 = 116

f(3) = 48(3) + 20 = 164

f(4) = 48(4) + 20 = 212

f(5) = 48(5) + 20 = 260

f(6) = 48(6) + 20 = 308

f(7) = 48(7) + 20 = 356

f(8) = 48(8) + 20 = 404

Therefore, the practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

Part A: \(T(t)=79e^{-0.015t}+19\)

Part B: \(76.4^\circ \text{C}\)

Step-by-step explanation:

Newton's law of cooling can be modeled with the general equation \(\displaystyle \frac{dT}{dt}=-k(T-T_a)\) with solution \(\displaystyle T(t)=(T_o-T_a)e^{-kt}+T_a\) for cooling. \(T(t)\) represents the temperature of the coffee after \(t=45\) minutes given the initial temperature \(T_o=98^\circ \text{C}\) and room/air temperature of \(T_a=19^\circ \text{C}\) with constant \(k\).

Part A: Temperature of coffee after "t" minutes

\(T(t)=(T_o-T_a)e^{-kt}+T_a\\T(45)=(98-19)e^{-45k}+19\\60=79e^{-45k}+19\\41=79e^{-45k}\\\frac{41}{79}=e^{-45k}\\\ln(\frac{41}{79}) =-45k\\k\approx0.015\\T(t)=79e^{-0.015t}+19\)

Part B: Average temperature of coffee after 45 minutes

\(\displaystyle T_{avg}=\frac{1}{b-a} \int\limits^b_a {T(t)} \, dt\\\\=\frac{1}{45-0}\int\limits^{45}_0 {(79e^{-0.015t}+19)} \, dt\\\\=\frac{1}{45}\biggr(\frac{79}{-0.015}e^{-0.015t}+19t\biggr)\biggr|_0^{45}\\ \\=\frac{1}{45}\biggr(\biggr(\frac{79}{-0.015}e^{-0.015(45)}+19(45)\biggr)+\frac{79}{0.015}\biggr)\\ \\\approx 76.4^\circ \text{C}\)

Answer:

1

Step-by-step explanation:

a fourth is 1/4 meaning Fourth = 1/4

Answer:

abigail

Step-by-step explanation:

abigail is correct because she has 30 dimes a dime is worth 30 cents and if 30 times ten equals 300 it would be 3 dollars so all together they have 6 dollars so now all they need is 3 dollars

I hope that made it easier for you good luck

Joan delivered more than twice as many large loads of firewood as small loads on 2 of the last 10 days, which is option B.

In mathematics, a graph is a collection of vertices or nodes, along with edges or arcs, that connect pairs of these nodes. A graph can be used to represent a variety of mathematical and real-world phenomena, including social networks, transportation networks, and the structure of molecules.

To find the number of days Joan delivered more than twice as many large loads of firewood as small loads, we need to check each coordinate in the given set of points and see if the y-coordinate (large loads) is greater than twice the x-coordinate (small loads) multiplied by 2. Mathematically, we can write this as y > 2x.

Checking each coordinate, we have:

(1,4): y = 4, 2x = 2, y is not greater than 2x

(1,6): y = 6, 2x = 2, y is greater than 2x

(2,6): y = 6, 2x = 4, y is not greater than 2x

(3,5): y = 5, 2x = 6, y is not greater than 2x

(3,6): y = 6, 2x = 6, y is not greater than 2x

(3,8): y = 8, 2x = 6, y is greater than 2x

(4,4): y = 4, 2x = 8, y is not greater than 2x

(5,2): y = 2, 2x = 10, y is not greater than 2x

(6,3): y = 3, 2x = 12, y is not greater than 2x

(7,5): y = 5, 2x = 14, y is not greater than 2x

Thus, Joan delivered more than twice as many large loads of firewood as small loads on 2 of the last 10 days, which is option B.

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Complete Question:

Yanay gets a lot of spam calls. An area code is defined to be a three digit number from 200-999 inclusive. In reality, many of these area codes are not in use, but for this question we'll simplify things and assume they all are.

Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804?

Answer:

1/6400 or 0.0000015625

Step-by-step explanation:

Given

Area Codes = 200 to 999 (inclusive)

Required

Determine the probability that back to back calls have area code 804

[First, we need to calculate the totality of area codes]

Total Area Codes = 999 - 200 + 1

Total Area Codes = 800

The probability of each code is 1/800

So, the probability of having back to back code of 804 is:

Probability = 1/800 * 1/800

Probability = (1/800)²

Probability = 1/640000

Hence, the required probability is 1/640000 or 0.0000015625

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.

Part A:

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5.

Part C:

Simply, the domain is constrained by x=0.

We are obliged at x=6 .

This is because we have to avoid a negative profit.

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Answer:

-2x^2+8x-9+4x+7x^2+2 = 5x²+12x-7

Step-by-step explanation:

The area of the right triangle is 18.02 cm².

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's find the area of the right angle triangle as follows;

let's find the height and base of the triangle.

using trigonometric ratios,

cos 75 = adjacent / hypotenuse

cos 75 = base / 12

base = 3.10582854123

Therefore,

sin 75 = opposite / hypotenuse

sin 75 = h / 12

height = 11.5911099155

height = 11.59

Therefore,

area of the triangle = 1 / 2 × 3.11 × 11.59

area of the triangle = 36.0483518371 / 2

area of the triangle = 18.0241759186

area of the triangle = 18.02 cm²

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Answer:

Step-by-step explanation:4.4

Answer:

1:4

Step-by-step explanation:

Ratio of 40 to 10 = 40:10 = 4:1 (after reducing 40:10 to lowest form). Hence, ratio of 40 to 10 is 4:1.

Answer:

d. 0%

Step-by-step explanation:

Based on the given information, the fair conclusion would be:

C. The current stock price is up for the day by 0.38%.

The statement mentions that the stock price is up for the day, which is indicated by the positive change of 0.27 (+0.38%).

Answer:

1020

Step-by-step explanation:

20+500= 520

520+500= 1020

The half-life of the given exponential function is of 346.57 years.

It is the value of t when A(t) = 0.5A(0).

In this problem, the equation is:

\(A(t) = A(0)e^{-0.002t}\).

In which t is measured in years.

Hence the half-life is found as follows:

\(0.5A(0) = A(0)e^{-0.002t}\)

\(e^{-0.002t} = 0.5\)

\(\ln{e^{-0.002t}} = \ln{0.5}\)

\(0.002t = -\ln{0.5}\)

\(t = -\frac{\ln{0.5}}{0.002}\)

t = 346.57 years.

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Answer:

a is correct

Step-by-step explanation:

sides get reduced by a half

angles don't change

Answer:

The Answer is A)

Step-by-step explanation:

sides get reduced by a half

angles don't change AND CAN YOU MAKE ME THE BRAININIEST.

Answer:

6^3

Step-by-step explanation:

3 × 3 × 3 × 3 × 3 × 3=729

6^3=216

3 × 3 × 3 × 3 × 3 × 3=729

3^6=729

Hope this helps :)

3 × 3 × 3 × 3 × 3 × 3

63

9 × 9 × 9

36

Using the equation of the line, the slope of the line is -2.  

The slope of a line is the change in y with respect to the change in x.

In other words, slope is rise over run.

Therefore, the equation of a line can be represented as follows:

y = mx + b

where

Hence, we will rearrange the equation of the line to get the slope of the line.

y + 3 = - 2x

y = -2x - 3

Therefore, the slope is -2.

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