A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 25 books and each large box can hold 50 books. There were 3 more large boxes sent than small boxes, which altogether can hold 450 books. Determine the number of small boxes sent and the number of large boxes sent.
There were ____ small boxes sent and ____ large boxes sent.

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

for such more question on inverses

https://brainly.com/question/15066392

#SPJ8

The Romberg array is a table of values that is used to estimate the value of a definite integral. To compute the Romberg array, we use the Richardson extrapolation method, which is a process of successive approximation.

To compute the eight rows and columns of the Romberg array, we begin by splitting the integration interval into two equal-length subintervals. The trapezoidal method is then applied to each subinterval to produce two estimates of the integral. The Richardson extrapolation method is then used to get a better estimate of the integral based on these two estimations. This operation is continued, splitting the subintervals into smaller and smaller subintervals, until the Romberg array has the necessary number of rows and columns.

The Romberg array's general formula is as follows:

R(m,n) = (4^n R(m,n-1) - R(m-1,n-1)) / (4^n - 1)

where R(m,n) is the value of the integral estimate at row m and column n in the Romberg array.

The first column of the Romberg array contains the estimates obtained by the trapezoidal rule, while the subsequent columns are obtained by applying the Richardson extrapolation method using the values in the previous column.

To learn more about Arrays, visit:

https://brainly.com/question/24275089

#SPJ11

Answer:

The slope is 4.

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=16-12/4-3

m=4/1

m=4

Answer:

I think its m = 1/4

Step-by-step explanation:

subtract 4 from 3 and 16 from 12 and you will get the answer

Answer:

Looks right to me! Great work!

Answer:

Could you please provide more information so I can help you with your problem?

The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

To know more about function check the below link:

https://brainly.com/question/22340031

#SPJ1

Answer:

the first one equals 4. the second one equals 2

Step-by-step explanation:

mark me brainliest pls

Answer:

simplified expression for √x^2+6x+9 if x≥3

is x+3

Step-by-step explanation:

\(\sqrt{x^2+6x+9} \\=>\sqrt{x^2+3x+3x+9} \\=>\sqrt{x(x+3)+3(x+3)} \\=>\sqrt{(x+3)(x+3)} \\=>\sqrt{(x+3)^2}\\=>(x+3) \ or -(x+3)\)

but given that x≥3

then we have to negate solution -(x+3)\

Then simplified expression for √x^2+6x+9 if x≥3

is x+3

Answer:

7x^2 - 16x + 5

Step-by-step explanation:

find the area of the unshaded box

(3x + 1) (x + 1) =

3x^2 + 3x + x +1 or 3x^2 + 4x + 1

whole shaded ares

(2x - 3) (5x - 2) =

10x^2 - 4x - 8x +6 or 10x^2 - 12x + 6

whole shaded area minus the unshaded area

10x^2 - 12x + 6

- 3x^2 + 4x + 1

7x^2 - 16x + 5

Answer:Cell content

Started at 20° and dropped 4° each minute                      -4

Cell content

Started at −20° and rose 1° each minute                              1

Cell content

Started at 20° and dropped 1° each minute                       -1

Cell content

Started at −20° and rose 4° each minute                             1

Step-by-step explanation:

Answer:

Cell content

Started at 20° and dropped 4° each minute                      -4

Cell content

Started at −20° and rose 1° each minute                              1

Cell content

Started at 20° and dropped 1° each minute                       -1

Cell content

Started at −20° and rose 4° each minute                             1

Step-by-step explanation:

The absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5

The given parameters are:

Minimum = 70 mg/dL

Maximum = 99 mg/dL

Calculate the mean using:

Mean = (Minimum + Maximum)/2

This gives

Mean = (70 + 99)/2

Evaluate

Mean = 84.5

Calculate the range using

Range = Maximum -Minimum

This gives

Range = 99 - 70

Evaluate

Range = 29

The absolute value equation that represents the minimum and maximum normal glucose levels is

|x - Mean| = Range/2

So, we have:

|x - 84.5| = 29/2

Evaluate

|x - 84.5| = 14.5

Hence, the absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5

Read more about absolute value equation at

https://brainly.com/question/17795998

#SPJ1

I totally typed the right answer for the wrong question sorry

The correct that refers Facts, statistics, numerical data, quotations, specific examples, and expert opinions that support a claim are called evidence.

The term numerical data refers the data which is in the form of numbers, and not in any language or descriptive form.

Here we have to find the suitable term for the statement "Facts, statistics, numerical data, quotations, specific examples, and expert opinions that support a claim are called".

While we have looking into the given statement, we have identified the following from it,

When we look into the meaning of each one we have identified that each of them are acted as the proof to prove the thing is liable.

So, all these things are collectively called as evidence.

To know more about numerical data here.

https://brainly.com/question/28541113

#SPJ4

a) There are 4368 strings of hexadecimal digits consisting of one through three digits.

b) There are 17909080 strings of hexadecimal digits consisting of two through six digits.

(a) To determine the number of strings of hexadecimal digits consisting of one through three digits, we can calculate the total number of possibilities for each case and then sum them up.

For one-digit strings, there are 16 options (0 through F).

For two-digit strings, each digit can be one of the 16 options independently. So, there are 16 options for the first digit and 16 options for the second digit, resulting in a total of 16 * 16 = 256 possibilities.

For three-digit strings, we apply the same logic as for two-digit strings. Each digit can be one of the 16 options independently, so there are 16 * 16 * 16 = 4096 possibilities.

By summing up the possibilities for each case, we have 16 + 256 + 4096 = 4368 strings of hexadecimal digits consisting of one through three digits.

(b) To calculate the number of strings of hexadecimal digits consisting of two through six digits, we need to consider the possibilities for each case.

For two-digit strings, we already determined that there are 256 possibilities.

For three-digit strings, we have 4096 possibilities.

For four-digit strings, the logic is the same as for two-digit strings, so there are 16 * 16 * 16 * 16 = 65536 possibilities.

For five-digit strings, we have 16 * 16 * 16 * 16 * 16 = 1048576 possibilities.

For six-digit strings, we have 16 * 16 * 16 * 16 * 16 * 16 = 16777216 possibilities.

By summing up the possibilities for each case, we have 256 + 4096 + 65536 + 1048576 + 16777216 = 17909080 strings of hexadecimal digits consisting of two through six digits.

To learn more about strings click on,

https://brainly.com/question/31682438

#SPJ4

Answer:

The elevation when the boiling point of water is \(190\) °\(F\) is 12790.70 feet

Step-by-step explanation:

Let every 1,000 feet of elevation be \(x\). Hence, we can write

\(T = 212\) \(- 1.72x\)

Where \(T\) is the boiling temperature of water at different elevations

Now, to the determine the elevation when the boiling point of water is \(190\) °\(F\).

We will determine \(x\) by putting \(T = 190\) °\(F\).

Hence,

\(T = 212\) \(- 1.72x\)

\(190\)  \(= 212\)  \(- 1.72x\)

\(190 - 212\)    \(= - 1.72x\)

\(- 22\)  \(= - 1.72x\)

\(22 = 1.72x\\x = \frac{22}{1.72} \\x = 12.79070\)

Since \(x\) represents every 1,000 feet of elevation, then the elevation when the boiling point of water is \(190\) °\(F\)

\(12.79070\) × \(1000\\\) \(= 12790.70\) feet

Hence,  the elevation when the boiling point of water is \(190\) °\(F\) is 12790.70 feet

The height of Ernies shadow is 4 feet when his height is 6 feet.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the length of his shadow. Given that the ratio of ernie's height to his shadow's height is 1.5 to 1. Hence:

(1/2.5) * 10 = x

x = 4 feet

The height of Ernies shadow is 4 feet when his height is 6 feet.

Find out more on equation at: https://brainly.com/question/13763238

t equals u minus v minus w (t = u - v - w.). The equation can be used to calculate t given values of u, v, and w.

The equation u = t + v + w expresses a relationship between u, t, v, and w. To solve for t in terms of u, v, and w, we need to isolate t on one side of the equation. We can do this by subtracting v and w from both sides of the equation, which gives us u - v - w = t. Therefore, t is equal to u minus v minus w. This means that if we know the values of u, v, and w, we can calculate the value of t using this equation.

Learn more about solving equation here: brainly.com/question/19297665

#SPJ9

To determine whether a slope is increasing or decreasing, you can look at the direction of the line on a graph. If the line is sloping upwards from left to right, the slope is increasing. If the line is sloping downwards from left to right, the slope is decreasing.

In math, what is a slope?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

For example, consider the following two graphs:

[Graph of a line with a positive slope]

[Graph of a line with a negative slope]

In the first graph, the line is sloping upwards from left to right, so the slope is increasing. In the second graph, the line is sloping downwards from left to right, so the slope is decreasing.

You can also determine whether a slope is increasing or decreasing by calculating the slope of the line using the formula:

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

If the value of the slope is positive, the slope is increasing. If the value of the slope is negative, the slope is decreasing. If the value of the slope is zero, the line is horizontal and has no slope.

For example, consider the line with equation y = 2x + 1. The slope of this line is 2, which is positive. This means that the line is sloping upwards from left to right, and the slope is increasing.

On the other hand, consider the line with equation y = -2x + 1. The slope of this line is -2, which is negative. This means that the line is sloping downwards from left to right, and the slope is decreasing.

Learn more about Slope

https://brainly.com/question/3493733

#SPJ4

1. The area of the base, B, of the prism is: B = 12 ft².

2. The volume, V, of the prism is: V = 72 ft²

A prism is a transparent object with flat, polished surfaces that refract or bend light as it passes through. The most common type of prism is a triangular prism, which has two triangular faces and three rectangular faces. When light enters the prism at an angle, it is refracted or bent as it passes through the first surface of the prism.

Area of the base, B:

As given in the question, we can see that the prism is a rectangular prism. Thus, the shape of the base is rectangle.

∴ Length of the base of a rectangular prism = 4 ft

   Width of the base of a rectangular prism = 3ft

⇒ Area of the base of a rectangular prism is  = ( length of the base ) × ( Width of the base)

= ( 4 × 3 ) ft²

= 12 ft²

∴ B = 12 ft²

Volume of a prism: V = BH

Where B = Base of the prism =  12 ft²

H = Height of the prism = 6 ft²

∴ 12 × 6 = 72 ft²

Thus, V = 72 ft²

Learn more about prism on https://brainly.com/question/23963432

#SPJ1

Simple analysis of variance is used in designs having a single independent variable (factor) that has two or more levels or categories. It is a statistical technique that can be used to compare means and determine if there are significant differences between them.

Analysis of Variance (ANOVA) is a statistical technique that is used to analyze the differences among group means. This approach is beneficial when comparing two or more groups. This statistical technique has several variations, each of which is intended to handle a specific experimental design.

The two main types of ANOVA are one-way ANOVA and two-way ANOVA.

One-way ANOVA is used when there is just one independent variable, while two-way ANOVA is used when there are two independent variables, each with two or more levels.

In conclusion, simple analysis of variance is used in designs having a single independent variable that has two or more levels or categories.

The purpose of ANOVA is to compare group means and identify significant differences between them.

Learn more about ANOVA at

https://brainly.com/question/23638404

#SPJ11

Answer:

20%

Step-by-step explanation:

Answer:

I believe the answer is 5.

The articulation (C₁fᵢ + C₂fz) is Riemann-Stieltjes integrable as for g, and the necessary of (C₁fᵢ + C₂fz) dg is equivalent to C₁ ∫ fᵢ dg + C₂ ∫ fz dg.

To exhibit that the articulation (C₁fᵢ + C₂fz) is Riemann-Stieltjes integrable as for g and figure its necessary, we really want to show that the integrator capability g is of limited minor departure from the span [a, b].

On the off chance that g is of limited variety, both fi and fz are Riemann-Stieltjes integrable concerning g. Since Riemann-Stieltjes integrability is shut under direct mixes, (C₁fᵢ + C₂fz) is likewise Riemann-Stieltjes integrable regarding g.

To ascertain the basic, we can utilize the linearity property of the Riemann-Stieltjes necessary. The integral of (C₁fᵢ + C₂fz) dg can be expressed as the sum of the integrals C₁  fi dg and C₂  fz dg by applying this property.

Learn more about Riemann-Stieltjes integrable

brainly.com/question/30601826

#SPJ11

Answer:

x=12

Step-by-step explanation:

just combine them so they equal the 64 then solve from there and you get 12.

Answer:

the answer is yes

Step-by-step explanation:

Answer:84/5

Step-by-step explanation:dd

Answer:

  -8

Step-by-step explanation:

Put the given values where the corresponding variables are, and do the arithmetic.

__

  f(x) = 12 -3x

  f(5) = 12 -3(5) = -3

__

  j(x) = x² +4x -1 = (x +4)x -1

  j(-2) = (-2 +4)(-2) -1 = 2(-2) -1 = -5

__

  f(5) +j(-2) = -3 +(-5) = -8

The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

For more questions on Linear .

https://brainly.com/question/2030026

#SPJ8