the amount of bacteria present in a medium after t hours is given by a (t )equals 16 e to the power of 0.32 t end exponent. at what rate is the amount of bacteria changing after 12 hours?

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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Answer:

g(x)= x²-3

Step-by-step explanation:

C. g(x)=x²-3

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 system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y

Let's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,

Let S represent the total cost of purchasing a pool membership from the Swimming Hole.

Then we can write the following system of inequalities:

A = 75 + 20x (total cost of Aquatics Club membership)

S = 15 + 65x (total cost of Swimming Hole membership)

Alfonso has no more than y dollars to spend

So, we have

75 + 20x ≤ y

15 + 65x ≤ y

Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y

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Answer:

b is not a part of that equation

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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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 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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The induced emf in a region of the brain when a conducting loop is held near a person's head and the current in the loop is changed rapidly, is equal to -525 V.

The induced emf can be calculated using Faraday's law of electromagnetic induction, which states that the emf induced in a loop of wire is equal to the rate of change of magnetic flux through the loop.

The magnetic flux (Φ) is equal to the product of the magnetic field (B) and the area (A) through which it passes. Therefore, the induced emf (ε) is given by:

ε = -dΦ/dt ⇒ -B dA/dt.

Where the negative sign indicates that the emf is induced in a direction that opposes the change in magnetic flux.

In this problem, the magnetic field changes at a rate of 3.00 × 10^4 T/s over an area of 1.75 × 10^-2 m^2. Therefore, the induced emf is:
Plugging in our values, we get:
E = (-3.00 10^4 T/s)(1.75 10^(-2) m^2)/(1 s)
E = -525 V

Therefore, the induced emf, in this case, is -525 V. Here, the negative sign shows that the emf is induced in a direction that opposes the change in magnetic flux

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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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Answer:

The value of t is 16

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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When one of the coin is flipped it lands on heads with probability 0.6 and when the other is flipped, it lands on heads with probability 0.3, then the probability that the coin lands on heads is 0.45 and the coin lands on heads but the probability that the chosen coin was the one that lands on heads with probability 0.6 is 0.67.

a) The probability of getting heads, we can use the law of total probability.

There are two coins, and each has a probability of landing on heads. So we can calculate the probability of getting heads by weighting each coin's probability by its probability of being chosen.

Therefore,

P(heads) = P(heads from coin 1) * P(choose coin 1) + P(heads from coin 2) * P(choose coin 2)

Plugging in the values, we have:

P(heads) = 0.6 * 0.5 + 0.3 * 0.5 = 0.45

Therefore, the probability of getting heads is 0.45.

b) The probability that the chosen coin was the one that lands on heads with probability 0.6, given that the coin lands on heads, we need to use Bayes' theorem. Specifically, we have:

P(choose coin 1 | heads) = P(heads from coin 1 | choose coin 1) * P(choose coin 1) / P(heads)

Plugging in the values, we have:

P(choose coin 1 | heads) = 0.6 * 0.5 / 0.45 = 0.67

Therefore, the probability that the chosen coin was the one that lands on heads with probability 0.6, given that the coin lands on heads, is 0.67.

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To answer the question, this equation has only one solution, which is x = 4.

An equation is a mathematical statement that shows the equality between two expressions. It usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).

The expressions on both sides can contain variables, constants, and mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and others. The goal of an equation is to find the values of the variables that make both sides equal.

by the question.

Let's start by setting up the equation:

[tex]1/2x + 8 = 14 - x[/tex]

where x is the number, we're trying to find.

Now let's simplify the equation by combining like terms:

[tex]3/2x + 8 = 14[/tex]

Subtracting 8 from both sides:

[tex]3/2x = 6[/tex]

Multiplying both sides by 2/3:

[tex]x = 4[/tex]

So, the solution to the equation is x = 4.

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The purchaser rejects 26.01% of the lots that contain five or more defective components, and the conditional probability of having four defective components given that the lot was rejected is 0.1653.

The percentage of defective lots that the purchaser rejects can be found by using the given formula. We can also calculate the conditional probability of having four defective components, given that the lot was rejected. Here's how to do it.

Let p be the probability that any component is defective. Then the probability that any component is non-defective is 1-p.

According to the given data, a lot is rejected if and only if there are at least five defective components in it. Let q be the probability that a lot is defective, i.e. the probability that there are five or more defective components in a lot.

Then, q = P(X ≥ 5), where X is the number of defective components in the lot. We can find the probability of rejecting a lot by subtracting the probability of accepting the lot from 1. So, we have:

P(reject) = 1 - P(accept)

P(accept) = P(X ≤ 4)

Now, we need to find q. We can do this by using the binomial distribution:

[tex]P(X = k) = C(n, k) * pk * (1-p)n-k[/tex]

where C(n, k) is the number of ways to choose k items out of n items. Here, n = 20 (the number of components in a lot). So,

[tex]q = P(X \geq  5) = 1 - P(X\leq  4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)][/tex]

[tex]q = 1 - [C(20, 0) * p0 * (1-p)20-0 + C(20, 1) * p1 * (1-p)20-1 + C(20, 2) * p2 * (1-p)20-2 + C(20, 3) * p3 * (1-p)20-3 + C(20, 4) * p4 * (1-p)20-4][/tex]

[tex]q = 1 - [1 * p0.2 * (1-0.2)20-0 + 20 * p0.2 * (1-0.2)20-1 + 190 * p0.2 * (1-0.2)20-2 + 1140 * p0.2 * (1-0.2)20-3 + 4845 * p0.2 * (1-0.2)20-4][/tex]

[tex]q = 0.2601[/tex] (rounded to four decimal places)

So, the purchaser rejects 26.01% of the lots that contain five or more defective components.

Now, we need to find the conditional probability that a lot contained four defective components given that it was rejected. Let R be the event that a lot is rejected, and let F be the event that a lot contains four defective components.

Then, we have to find P(F | R), the conditional probability of F given R. We can use Bayes' theorem to find this:

P(F | R) = P(R | F) * P(F) / P(R)

where P(R | F) is the probability of rejecting a lot given that it contained four defective components, P(F) is the prior probability of a lot containing four defective components, and P(R) is the overall probability of rejecting a lot.

[tex]P(F) = C(20, 4) * p4 * (1-p)20-4 = 0.186[/tex]

[tex][tex]P(R) = P(X \geq  5) = q = 0.2601[/tex][/tex]

[tex]P(R | F) = P(X \geq  5 | X = 4) = P(X = 5) / P(X = 4) = C(20, 5) * p5 * (1-p)20-5 / C(20, 4) * p4 * (1-p)20-4[/tex]

[tex]P(R | F) = 0.2308[/tex]

So, we have:

[tex]P(F | R) = P(R | F) * P(F) / P(R)[/tex]

[tex]P(F | R) = 0.2308 * 0.186 / 0.2601[/tex]

[tex]P(F | R) = 0.1653[/tex] (rounded to four decimal places)

Therefore, the conditional probability of having four defective components given that the lot was rejected is 0.1653.

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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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The approximate probability that the mean credit card debt for a sample of 50 US households will exceed $7,500 is , based on a normal distribution with a mean of $7,115 and a standard deviation of $2,160.

What is the z-score formula?

The z-score formula is a statistical method used to calculate the standard deviation of a raw score or data point relative to the mean of the group of raw scores or data points. It is given as:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

where z is the z-score, x is raw score, μ is the mean, and σ is the standard deviation.

The approximate probability can be calculated as follows:

First, find the standard error of the mean: [tex]SE = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]SE = \frac{2,160}{\sqrt{50}}\\\\SE = 305.39[/tex]

Secondly, find the z-score: [tex]z = \frac{\overline{x} - \mu}{SE}[/tex]

[tex]z = \frac{7,500 - 7,115}{305.39}\\\\z = 1.263[/tex]

The probability that a z-score will be greater than 1.263 is 0.1038 from the standard normal table or calculator.

Therefore, the approximate probability is 0.1038 or 10.38%.

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

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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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 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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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

In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines  by  co-exterior angles property.

Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.  

∠ZHIK and ∠ZEFI are equal by alternative angles property.

∠ZGFD and ∠ZEFD are equal by co-interior angles property.

∠ZGFD and ∠ZEFI are equal by interior alt. angles property.

∠ZEFI and ∠ZJIK are equal by  co-exterior angles property.

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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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In a 5x5x5 cube, 125-unit cubes are formed by assembling. According to the pattern shown, nine-unit squares are painted on each of the six faces of the cube.  So the number of unit cubes that have no paint on them is 71.

     To calculate the total number of unit cubes, multiply the number of unit cubes in each dimension.

                  Thus, 5 × 5 × 5 = 125 cubic units.

      Since there are 6 faces to be painted, and each face has nine painted unit cubes, the total number of painted cubes is

                  6 × 9 = 54.

         Each painted cube has three faces painted since the cube has three faces of the same size.

          There are eight cubes on each of the edges that have three faces painted, so there are

                 8 × 12 = 96 of them that have three faces painted.

           There are 12 edge cubes in total, all of which have two painted faces, for a total of

                 12 × 2 = 24 cubes that have two painted faces.

            There are 6 center cubes in the cube, all of which have one painted face, for a total of 6 cubes with one painted face.

            Each painted cube contributes one face to the total. As a result, the number of unpainted cubes is

                 125 - 54 = 71.

       The number of unit cubes that have no paint on them is 71.

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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:

  (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.)

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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.

We divide the number of boys by the total number of students (1200) and multiply by 100. Percentage of boys = (420/1200) x 100% = 35%.

To find the percentage of boys in the school, we need to subtract the number of girls from the total number of students, then divide by the total number of students and multiply by 100 to get the percentage.

Number of boys = total number of students - number of girls

Number of boys = 1200 - 780

Number of boys = 420

Percentage of boys = (number of boys / total number of students) x 100

Percentage of boys = (420 / 1200) x 100

Percentage of boys = 35

Therefore, the percentage of boys in the school is 35%.

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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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