At the book store, you purchased some $3 clearance mystery books and $8 regular-priced science fiction books. How many of each did you buy if you spent a total of $77?

The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.

To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:

The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.

The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.

Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.

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Answer:

b is not a part of that equation

The distribution 14,13,13. 5,16,14,15.5,14.5 has plotted using the box plot

To visualize the distribution of this dataset, you can create a box plot

A box plot, also known as a box-and-whisker plot, is a type of graph used to display the distribution of a dataset.  A box plot summarizes the distribution of a dataset by displaying the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers.

In this box plot, the box represents the middle 50% of the data (the interquartile range), the line inside the box represents the median, and the whiskers represent the range of the data excluding outliers. The circles represent the outliers in the data.

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The given question is incomplete, the complete question is:

Plot the distribution 14,13,13. 5,16,14,15. 5,14. 5 in box plot

The probability that all 4 members are teachers from a committee of 4 being formed randomly from the employees at a school which includes 6 administrators, 37 teachers, and 5 staff is 0.0147.

The probability that all 4 members are teachers from a committee of 4 being formed randomly from the employees at a school which includes 6 administrators, 37 teachers, and 5 staff is:

Probability of selecting 1 teacher out of 37 teachers, P(teacher) = 37/482)

Probability of selecting 2 teachers out of 37 teachers, P(teacher and teacher) = 37/48 * 36/473)

Probability of selecting 3 teachers out of 37 teachers, P(teacher and teacher and teacher) = 37/48 * 36/47 * 35/464)

Probability of selecting 4 teachers out of 37 teachers, P(teacher and teacher and teacher and teacher) = 37/48 * 36/47 * 35/46 * 34/45

Now, the probability that all 4 members are teachers,P(all teachers) = P(teacher and teacher and teacher and teacher)= 37/48 * 36/47 * 35/46 * 34/45= 0.0147

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If AE = DE, then ∠A = ∠D. This follows from the Side-Angle-Side (SAS) Congruence Theorem.

An angle is a measure of the amount of turn between two lines or planes. It is usually measured in degrees or radians, with a full turn being equal to 360 degrees or 2π radians. Angles can be used to describe the orientation of objects in two-dimensional and three-dimensional space. They can also be used to describe the size of an opening or formed between two intersecting lines or planes.

.4. If AB = EB, then ∠B = ∠E. This follows from the Side-Angle-Side (SAS) Congruence Theorem.
5. If D = CED, then ∠DCB = ∠ECB. This follows from the Angle-Side-Angle (ASA) Congruence Theorem.
6. If EBC = ECB, then ∠BCE = ∠BCE. This follows from the Reflexive Property of Congruent Angles.

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If AE = DE, then ∠A = ∠D. This follows from the Side-Angle-Side (SAS) Congruence Theorem.

An angle is a measure of the amount of turn between two lines or planes. It is usually measured in degrees or radians, with a full turn being equal to 360 degrees or 2π radians. Angles can be used to describe the orientation of objects in two-dimensional and three-dimensional space. They can also be used to describe the size of an opening or formed between two intersecting lines or planes.

.4. If AB = EB, then ∠B = ∠E. This follows from the Side-Angle-Side (SAS) Congruence Theorem.
5. If D = CED, then ∠DCB = ∠ECB. This follows from the Angle-Side-Angle (ASA) Congruence Theorem.
6. If EBC = ECB, then ∠BCE = ∠BCE. This follows from the Reflexive Property of Congruent Angles.

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Answer:

30cm

Step-by-step explanation:

Perimeter of an equilateral triangle = 3L

Mathematically we have;

P = 3L

Where P = perimeter of the triangle

L = Length

Therefore;

90 = 3L

Divide both side by 3

L = 30cm

Therefore, the length of each side of the triangle is 30cm.

Answer:

Step-by-step explanation:

so their is probably about 20 or 10 marbles in each bag so if they take them just kinda subtract the amount each kid got to see how many were left for emila to get I think that’s how you do if not then I was happy to help and I hope you get better help

The line [tex]12x + 6y = 432[/tex] is represented by the red line, and the line equation [tex]9x + 3y = 270[/tex]is represented by the blue line. The point where these two lines intersect is (36,0).

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex]states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" [tex]x^2 + 2x - 3 = 0[/tex]," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.

To plot these lines on a graph, we first need to solve for y in terms of x for each equation.

can plot these lines

[tex]12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90[/tex]

[tex]|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300[/tex]

The line[tex]12x + 6y = 432[/tex]is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).

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a) The expression of volume(V) of a cube whose side length is a is, [tex]V=a^3[/tex]

b) The volume of a cube whose edge length is 2 cm, is 8 [tex]cm^3[/tex].

The volume of a cube is calculated by multiplying the length of any one side of the cube by itself twice (i.e., cubing it). In mathematical terms, the formula for the volume of a cube is:

Volume of a cube = (side length)³

The cube's volume formula is provided by: Volume equals [tex]a^3[/tex].

Where a represents how long its sides or edges are.

The fact that each of these dimensions measures exactly the same is good news for cubes. As a result, you can multiply any side's length by three. Volume is calculated as follows: volume = side * side * side. It is frequently expressed as:

[tex]V = a^3[/tex]

If the edge is 2 cm

then

the volume of cube is

[tex]2^3 = 8[/tex] cubic cm

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A relative efficiency greater than 1 means that the estimator is less efficient than the most efficient estimator. A relative efficiency less than 1 means that the estimator is more efficient than the most efficient estimator.

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The utilization of the machines is the processing time for the machines divided by the cycle time: 14 / 20 = 0.7 or 70%.

The bottleneck resource in this process is the hand-dry step, as it is the only step that is performed manually and thus has limited capacity. The processing time for the hand-dry step is 6 minutes per car, which is longer than any of the other steps.

To calculate the flow rate of the process, we need to determine the cycle time, which is the time it takes to process one car through all the steps. The cycle time is the sum of the processing times for all the steps, which is 2 + 7 + 1 + 4 + 6 = 20 minutes per car.

To convert this to customers per hour, we divide the number of minutes per hour (60) by the cycle time: 60 / 20 = 3 customers per hour.

Therefore, the flow rate of the process is 14 cars per hour x 3 customers per hour = 42 customers per hour.

To calculate the utilization of the machines, we need to calculate the total time that the machines are processing cars. Since all the steps except for the hand-dry step are performed by dedicated machines, the total processing time for the machines is 2 + 7 + 1 + 4 = 14 minutes per car.

Therefore, the utilization of the machines is the processing time for the machines divided by the cycle time: 14 / 20 = 0.7 or 70%.

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120 is 30 percent of 400

The derivative of the implicit function x · cos y = 1 at point (2, π / 3) is equal to y' = √3 / 6.

In this problem we find the case of a implicit function of the form f(x, y), whose derivative must be found. This can be done by implicite differentiation, whose procedure is shown:

Step 1 - Derive the expression by derivative rules:

cos y - x · sin y · y' = 0

Step 2 - Clear y' within the expression:

y' = cos y / (x · sin y)

Step 3 - Clear x and y in the resulting expression:

y' = cos (π / 3) / [2 · sin (π / 3)]

y' = 1 / [2 · tan (π / 3)]

y' = √3 / 6

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First of all, perfect squares do not end in 2.

The exponent has to be an even number when 2 is the base. For example 2^8 = 64. 8 is an even number. So 64 is a square number.

The trip would be shorter by $\frac{1}{4}-\frac{15}{16} = \frac{1}{16}$ of a mile  as per pythagorean theorem.

The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. A right triangle is a triangle that has one angle that measures exactly 90 degrees, which is also known as a right angle.

In the given question, to find out how much shorter your trip would be if you could fly like a bird, we first need to find out the total distance of your current trip.

You go 1 block south, which is $\frac{1}{16}$ of a mile.

You then go 1 block east, which is also $\frac{1}{16}$ of a mile.

You then go 5 blocks north, which is $5\cdot\frac{1}{16} = \frac{5}{16}$ of a mile.

Finally, you go 2 blocks east, which is $2\cdot\frac{1}{16} = \frac{1}{8}$ of a mile.

So the total distance of your trip is $\frac{1}{16}+\frac{1}{16}+\frac{5}{16}+\frac{1}{8}=\frac{1}{4}$ of a mile.

If you could fly like a bird, you could go directly from your house to the grocery store, which we can assume is a straight line. Let's call the distance between your house and the grocery store "x".

Using the Pythagorean theorem, we can see that $x² = (\frac{1}{16})²+ (\frac{1}{8}+5\cdot\frac{1}{16})²$, which simplifies to $x² \frac{225}{256}$.

So the distance you would have to travel if you could fly like a bird is $\sqrt{\frac{225}{256}} = \frac{15}{16}$ of a mile.

Therefore, your trip would be shorter by

$\frac{1}{4}-\frac{15}{16} = \frac{1}{16}$ of a mile if you could fly like a bird.

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Answer:

  (a, b) alternate interior angles at M and N, and at A and B are congruent

  (c) the triangles are congruent by SAS and by ASA (and MX = NX)

  (d) angles are no longer congruent, so the triangles are not congruent. The radii are given as congruent, but the chords cannot be shown congruent.

Step-by-step explanation:

Given same-size circles A and B, externally tangent to each other at X, each with chords MX and NX, you want to know what can be concluded if AM║BN, and what is unprovable if those segments are not parallel.

The circles being the same size means all the radii are congruent. This is shown by the single hash marks in the attached diagram.

Alternate interior angles where a transversal crosses parallel lines are congruent. If AM║BN, this means the angles marked with a single arc are congruent, and the angles marked with a double arc are congruent. These are the alternate interior angles at transversal MN and at transversal AB.

If AM║BN, in addition to the given congruences, we also know ...

∆AMX ≅ ∆BNX by SAS or ASA (take your pick).

If AM and BN are not parallel, MN is not a straight line through X, the angles at A and B are not congruent, and the angles at M and N are not congruent. (We assume segment AB still goes through X.)

__

Additional comment

Triangles MAX and NBX are isosceles, so their base angles are congruent. If X lies on MN, then AM and BN must be parallel, since the vertical angles at X will be congruent along with the other base angles at M and N. If AM and BN are not parallel, point X cannot lie on segment AB.

The distance between car A and the airplane is changing at a rate of 148.38 km/hr.

To better understand this answer, we can draw a sketch of the scenario and label the variables accordingly.

Let x represent the horizontal distance from P to the airplane, y the vertical distance from P to car A, and z the altitude of the airplane. The equation that relates the distance from car A to the plane can be written as:

[tex]d^2 = (x^2 + y^2 + z^2)[/tex]

We can use implicit differentiation to solve for the derivative of this equation with respect to time, which answers the “how fast” question. The derivative of the equation is:

x = 185t (horizontal distance from P to airplane)

y = 15 - 55t (vertical distance from P to car)

z = 2 (altitude of airplane)

Now we can substitute these expressions into our equation for the distance between the car and the airplane, and take the derivative with respect to time:

distance between car and airplane = sqrt((185t)^2 + (15 - 55t)^2 + 2^2)

d/dt(distance between car and airplane) = d/dt(sqrt((185t)^2 + (15 - 55t)^2 + 2^2))

= 1/2 * (185^2 * 2t + (15 - 55t)(-55)) / sqrt((185t)^2 + (15 - 55t)^2 + 2^2)

Evaluating this expression at t = 0 (the time when the car is at its closest point to the airplane), we get:

d/dt(distance between car and airplane) = 1/2 * (185^2 * 2(0) + (15 - 55(0))(-55)) / sqrt((185(0))^2 + (15 - 55(0))^2 + 2^2)

= 1/2 * (-825) / sqrt(15^2 + 2^2)

= -412.5 / sqrt (229)

The negative sign indicates that the distance between the car and the airplane is decreasing, as expected. Finally, we can take the absolute value of this expression to get the speed at which the distance is changing:

d/dt (distance between car and airplane)| = 412.5 / sqrt (229) ≈ 148.38 km/hr.

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If 4.2712 moles of Fe(OH)3 are produced, 12.8136 moles of NH4Cl will be produced as well.

An equation is a mathematical statement that expresses two expressions as equal. It is typically written using an equals sign (=) and consists of two expressions separated by an equals sign. The expressions in the equation represent a relationship between the two terms, and the equation can be used to solve for an unknown value. Equations can involve numbers, variables, and constants.

To determine the number of moles of NH4Cl that will be produced, we can use the mole ratio from the balanced chemical equation. According to the equation, for every 1 mole of Fe(OH)3 that is produced, 3 moles of NH4Cl will also be produced. Therefore, if 4.2712 moles of Fe(OH)3 are produced, 12.8136 moles of NH4Cl will be produced as well.

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For every 4 moles of Fe(OH)3 produced, 3 moles of NH4Cl are also produced. Since 4.2712 moles of Fe(OH)3 are produced, then 3 x 4.2712 = 12.8136 moles of NH4Cl will also be produced

An equation is a mathematical statement that expresses two expressions as equal. It is typically written using an equals sign (=) and consists of two expressions separated by an equals sign. The expressions in the equation represent a relationship between the two terms, and the equation can be used to solve for an unknown value. Equations can involve numbers, variables, and constants.


The reaction of FeCl3 with 3 moles of NH4OH produces 4.2712 moles of Fe(OH)3 and 3 moles of NH4Cl. This can be determined by using the balanced chemical equation for the reaction:

FeCl3 + 3 NH4OH → Fe(OH)3 + 3 NH4Cl

Since the reaction produces 4.2712 moles of Fe(OH)3, then the amount of NH4Cl produced can be calculated using the mole ratio. The mole ratio of NH4Cl to Fe(OH)3 is 3:4.2712, which can be simplified to 3:4. Therefore, for every 4 moles of Fe(OH)3 produced, 3 moles of NH4Cl are also produced. Since 4.2712 moles of Fe(OH)3 are produced, then 3 x 4.2712 = 12.8136 moles of NH4Cl will also be produced.

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The company should sell their phones for $250 each to get the maximum revenue.

What do you mean by maximum revenue?

Maximum revenue refers to the highest possible amount of income that can be generated from a particular product or service. In the context of the given problem, it means finding the price at which the company can sell its cell phones to earn the highest amount of revenue.

Finding the price at which the company should sell their phones to get the maximum revenue:

We need to find the vertex of the parabolic function [tex]r(x)=x(1,000-2x)[/tex], which represents the revenue as a function of the selling price.

To find the vertex of the function r(x), we need to first rewrite it in standard form by expanding the product:

[tex]r(x) = 1000x - 2x^2[/tex]

Now we can see that the function is a quadratic polynomial in standard form, with [tex]a=-2, b=1000[/tex], and [tex]c=0[/tex]. To find the x-coordinate of the vertex, we can use the formula:

[tex]x = -b / (2a)[/tex]

Substituting the values of a and b, we get:

[tex]x = -1000 / (2\times(-2)) = 250[/tex]

Therefore, the company should sell their phones for $250 each to get the maximum revenue. To find the maximum revenue, we can substitute this value of x into the function r(x):

[tex]r(250) = 250\times(1000-2\times250) = $125,000[/tex]

So the maximum revenue the company can expect to earn is $125,000 if they sell their phones for $250 each.

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The height of the storage unit needs to be 5 feet according to mentioned length, width and volume.

The volume is calculated using the formula -

Volume = length × width × height. We have all the values except height. Thus, it can be easily calculated from the formula.

Rewriting the formula -

Height = Volume/ (length × width)

Height = 400/ (10 × 8)

Performing multiplication in denominator

Height = 400/80

Performing division and cancelling zero on Right Hand Side of the equation

Height = 5 feet

Hence, the height of the unit needs to be 5 feet.

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The intensity of the beam 10 feet below the surface can be calculated using Beer-Lambert's law, which states that the rate of decrease in intensity of light through a transparent medium is proportional to the thickness of the medium. This means that the intensity i of the beam at a depth t below the surface is given by the equation i = i0 * e^(-kt), where i0 is the initial intensity of the incident beam, k is a constant, and e is Euler's number.
For the given scenario, we know that the intensity at a depth of 3 feet is 25% of the initial intensity i0. Substituting the known values into the equation, we can calculate the value of k:
i = i0 * e^(-3k)
0.25i0 = i0 * e^(-3k)
0.25 = e^(-3k)
ln(0.25) = -3k
k = ln(0.25) / -3
k = 0.0451
Therefore, the intensity of the beam 10 feet below the surface can be calculated as follows:
i = i0 * e^(-0.0451 * 10)
i = i0 * e^(-0.451)
i = 0.6139i0

Rounding any constants or coefficients to five decimal places, the intensity of the beam 10 feet below the surface is 0.6139i0.

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The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).

So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:

3x + 4(x+15) = 900

7x + 60 = 900

7x = 840

x = 120

The figure has three angles of 120 degrees, and four angles of 135 degrees.

Refer to pic...........

Answer:

g(x)= x²-3

Step-by-step explanation:

C. g(x)=x²-3

There are no values of x that satisfy the equation f(x) = 0.

what is a function?

A function is a mathematical concept that relates a set of inputs (known as the domain) to a set of outputs (known as the range), such that every input corresponds to exactly one output.

In other words, a function is a rule that assigns each element of the domain to a unique element of the range.

We are given that the mapping f(x) = x² + 1, and that the range of f is R - {2, 5, 10}.

To determine the domain of f, we need to consider what values of x will result in a valid output for f(x). Since f(x) is defined as x² + 1, we know that f(x) will always be greater than or equal to 1. Therefore, the domain of f is all real numbers, or D = R.

To find f⁻¹(5), we need to solve for x when f(x) = 5. That is, we need to solve the equation x² + 1 = 5. Rearranging, we get x² = 4, so x = ±2. Therefore, f⁻¹(5) = {-2, 2}.

Finally, to find the values of x when f(x) = 0, we need to solve the equation x² + 1 = 0. However, this equation has no real solutions, since the square of a real number is always non-negative.

Therefore, there are no values of x that satisfy the equation f(x) = 0.

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Answer:

The value of t is 16

For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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Answer: The answer is A) Players on the basketball team are generally taller than players on the baseball team. This is the most likely conclusion we can draw based on the information given.

Step-by-step explanation:

We know that the interquartile range (IQR) is the range of the middle 50% of the data. So for the basketball team, the heights of 50% of the players lie within the range of 73 ± 2.5 (since the IQR is 5). Similarly, for the baseball team, the heights of 50% of the players lie within the range of 72 ± 3 (since the IQR is 6).

Comparing the medians, we see that the basketball team has a median height of 73, while the baseball team has a median height of 72.

Based on this information, we can conclude that:

A) Players on the basketball team are generally taller than players on the baseball team - this is the most likely answer, as the median height of the basketball team is higher.

B) Players on the baseball team are generally taller than players on the basketball team - this is not supported by the given information.

D) There is less variation in heights on the baseball team than on the basketball team - we cannot determine this based on the given information.

C) Players on the baseball team are generally the same height as players on the basketball team - this is not supported by the given information.