Kolton is working through a setup for his new video that he wants to shoot and send to his friends. He's obsessed with trains and has so many of the "mini" trains that he thought it would be fun to set the trains up as if they were in seats at a stadium watching the big trains. (think theater seating) He knows that he wants to set it up so that there are 5 more trains in the next row for each of the next rows that he sets up and that the very first row in the front can only have 12 trains to start. Kolton asked me to help him come up with an equation to figure out how many mini trains he would need in each of the rows. Tell me what this equation would be describing the individual parts and then show all steps from start to finish for using that equation to solve for how many trains will be in row 15.

SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!

We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

area of a rectangle

Area = length x width

To do this, we can factor the expression for the area, which gives us:

x² + 9x + 14 = (x + 2)(x + 7)

Area = length x width

(x + 2)(x + 7) = (x + 7) x width

x + 2 = width

Therefore, the expression for the width of the porch is x + 2 feet.

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Theoretical probability of drawing the letter "o" is 1/4, or 0.25 as a decimal.

The probability of drawing the letter "o" from the bag of tiles depends on the number of tiles with the letter "o" and the total number of tiles in the bag.

Since the word "Colorado" has two "o's", there are two "o" tiles in the bag. The total number of tiles in the bag is the number of letters in the word "Colorado", which is 8.

Therefore, the theoretical probability of drawing the letter "o" is:

P("o") = number of "o" tiles / total number of tiles

= 2/8

= 1/4

So the theoretical probability of drawing the letter "o" is 1/4, or 0.25 as a decimal.

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The only number between 18 and 30 that is a multiple of 5 and satisfies this condition is 20, Therefore, the mystery number is 20

The GCF of 18, 36, and the mystery number is 2.

This means that the mystery number is divisible by 2.

The mystery number is also a multiple of 5, so it must end in either 0 or 5.

The mystery number is greater than 18 and less than 30, so it can only be 20 or 25.

Let's check if the GCF of 18, 36, and 20 is 2.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

The only factor that 18, 36, and 20 have in common is 2, so the mystery number is 20.

Therefore, the mystery number is 20.

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According to the exponential growth formula , there will be 38400 bacteria present after 3 days.

The given formula for the bacteria population, f(x) = 75 - 8², seems to be incorrect. Since the bacteria reproduce by dividing in half every 8 hours, we should use an exponential growth formula.

Let's denote the number of bacteria present after z days as f(z). Since there are 24 hours in a day, there are 3 reproduction cycles in a day (24 hours / 8 hours per cycle = 3 cycles). Therefore, the total number of reproduction cycles after z days is 3z.

The formula for the bacteria population after z days is: f(z) = 75 * 2^(3z)

Now, let's find the total number present after 1, 2, and 3 days.

1 day: f(1) = 75 * 2^(3 * 1) = 75 * 2^3 = 75 * 8 = 600
There will be 600 bacteria present after 1 day.

2 days: f(2) = 75 * 2^(3 * 2) = 75 * 2^6 = 75 * 64 = 4800
There will be 4800 bacteria present after 2 days.

3 days: f(3) = 75 * 2^(3 * 3) = 75 * 2^9 = 75 * 512 = 38400
There will be 38400 bacteria present after 3 days.

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Thus, the value of x found by Chord Arcs Theorem for the given Arc AD and arc CD is found as: x = 11.

The chords of such a circle are covered by a number of theorems. The chord arcs theorem is one such example. The intercepted arcs with congruent chords also were congruent according to this theorem.

Now,

chord AB  = chord DC

Thus,

m AB = m DC = 13x - 21

For the complete circle: angle = 360.

AB + DC + AD + BC = 360

(13x - 21) + (13x - 21) + 85 + 31 = 360

(36x - 42) + 116 = 360

26x - 42 = 244

26x = 244 + 42

x = 286/26

x = 11

Thus, the value of x found by Chord Arcs Theorem for the given Arc AD and arc CD is found as: x = 11.

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Complete question:

if m AD = 85 and m BC =31 find the value of x.

The diagram is attached.

The total area of the composite figure is 114.25 square feet.

The area of a circle of diameter D is:

A = 3.14*(D/2)²

And the area of a triangle of base B and height H is:

A = B*H/2

We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:

A = 10ft*15ft/2 = 75ft²

And half of a circle of diameter of 10ft, whose area is:

A = 0.5*3.14*(10ft/2)² = 39.25 ft²

Then the total area of the figure is:

area =  75ft² + 39.25 ft² = 114.25 ft²

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Answer:

1. irrational

2. irrational

3. rational

4. rational

5. irrational

6. rational

Step-by-step explanation:

A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.

1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL

2.) the line above the 46 means that it is repeating, making it IRRATIONAL

3.) the square root of 100 is 10, making it RATIONAL

4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL

5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL

6.) 10 is a whole number, making it RATIONAL

The height of the arch at a distance of 1.5 meters from the center is approximately D. 1.73 meters

The shape of a semi-elliptical arch can be described by the equation:

y = c * sqrt(1 - (x/a)^2)

where "a" is half the span of the arch, "c" is the central height of the arch, and (x,y) are the coordinates of a point on the arch, measured relative to the center of the arch.

In this case, we have a span of 6 meters, so a = 3 meters. The central height of the arch is 2 meters, so c = 2 meters. We want to find the height of the arch at a distance of 1.5 meters from the center, so x = 1.5 meters.

Substituting these values into the equation, we get:

y = 2 * sqrt(1 - (1.5/3)^2)

y = 2 * sqrt(1 - 0.25)

y = 2 * sqrt(0.75)

y = 2 * 0.866

y = 1.732

Therefore, the height of the arch at a distance of 1.5 meters from the center is approximately 1.73 meters. Answer D

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Your question is incomplete, but probably the complete question is :

A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.

A.   1.41 m C.   1.56 m

B.   1.63 m D.   1.73 m

the simplified expression is: (X*(2x - 1) - 1)/(2x*(x+1))

The given expression is:

X/(x+1) - 1/(1-1+2x) = X/(x+1) - 1/(2x)

To simplify this expression, we need to find a common denominator. The denominator of the first term is (x+1) and the denominator of the second term is 2x. To get a common denominator, we can multiply the first term by 2x and the second term by (x+1).

So, the expression becomes:

(2xX)/[(x+1)2x] - (1(x+1))/[(1-1+2x)(x+1)]

Simplifying further, we get:

(2xX - (x+1))/(2x(x+1))

Now, we can simplify the numerator by distributing the X term and combining like terms:

(2xX - x - 1)/(2x(x+1))

We can factor out an X from the numerator:

(X*(2x - 1) - 1)/(2x*(x+1))

Therefore, the simplified expression is:

(X*(2x - 1) - 1)/(2x*(x+1))

In summary, the given expression is simplified by finding a common denominator and then simplifying the resulting expression by distributing and factoring. The final expression is the simplified form of the given expression.

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Answer:

The correct answer is OD.

Step-by-step explanation:

To find how many classes each instructor teaches per week, you need to set up and solve a system of equations based on the given information. In other words,

Let x be the number of classes Bo teaches per week and y be the number of classes Erica teaches per week.

The first equation is based on the total number of classes they teach

x + y = 37

The second equation is based on the relationship between their numbers of classes

y = 2x - 14

To solve this system, you can use substitution or elimination methods. For example, using substitution, you can plug in y = 2x - 14 into the first equation and get

x + (2x - 14) = 37

Simplify and solve for x

3x - 14 = 37

So, Bo teaches 17 classes per week and Erica teaches 20 classes per week.

Answer:

A. 19 Bo; 18 Erica

Step-by-step explanation:

im good like that hehe

This shows that they read less frequently than 95.7% of their classmates in the same grade level.

In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.

given

We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.

z = (x - μ) / σ

where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.

Inputting the values provided yields:

z = (46.2 - 85) / 22

z = -1.727

We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.

As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).

This shows that they read less frequently than 95.7% of their classmates in the same grade level.

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The extreme values of the function f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27 are minimum = 0 and maximum = 18

Given that

f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27

To find the extreme values of the function f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.

Defining the Lagrangian function L as follows:

L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))

where g(x, y, z) is the constraint function and λ is the Lagrange multiplier.

In our case, we have:

f(x, y, z) = x^2 + y^2 + z^2

g(x, y, z) = x^2 + y^2 + z^2 + xy - 27

So, our Lagrangian function becomes:

L(x, y, z, λ) = x^2 + y^2 + z^2 - λ(x^2 + y^2 + z^2 + xy - 27)

To find the extreme values of f(x, y, z) subject to the constraint g(x, y, z) = 0, we need to solve the following system of equations:

∂L/∂x = 0

∂L/∂y = 0

∂L/∂z = 0

∂L/∂λ = 0

g(x, y, z) = 0

Taking the partial derivatives of L with respect to x, y, z, and λ, we get:

∂L/∂x = 2x - λ(2x + y) = 0

∂L/∂y = 2y - λ(2y + x) = 0

∂L/∂z = 2z - λz = 0

∂L/∂λ = x^2 + y^2 + z^2 + xy - 27 = 0

From the third equation, we get:

2z - λz = 0

z(2 - λ) = 0

So, either z = 0 or λ = 2.

If z = 0, then from the first two equations, we get:

2x - λy = 0

2y - λx = 0

Multiplying the first equation by y and the second equation by x, we get:

2xy - λy^2 = 0

2xy - λx^2 = 0

Subtracting the second equation from the first, we get:

λ(x^2 - y^2) = 0

Since λ cannot be zero, we have x^2 = y^2 and x = y

Similarly, if λ = 2, then from the first two equations, we get:

2x - 2y = 0

x = y

Substituting x = y into the constraint equation, we get:

2x^2 + x^2 = 27

x^2 = 9

x = ±3

So, the possible critical points are:

(3, 3, 0)

(-3, -3, 0)

(0, 0, 0)

Recall that

f(x, y, z) = x^2 + y^2 + z^2

So, we have

f(3, 3, 0) = 3^2 + 3^2 + 0^2 = 18

f(-3, -3, 0) = -3^2 + -3^2 + 0^2 = 18

f(0, 0, 0) = 0^2 + 0^2 + 0^2 = 0

Hence, the minimum is 0 and the maximum is 18

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Answer:

2

Step-by-step explanation:

Answer:  3

Step-by-ste3p explanation:

The probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.

The given problem can be solved using the Poisson distribution. Let [tex]$\lambda$[/tex] be the average rate of cars passing through the section per hour. Then, since the probability of no cars passing in one hour is 0.4, we have:

Solving for [tex]$\lambda$[/tex], we get [tex]$\lambda= -ln(0.4) \approx 0.916$[/tex]. Therefore, the probability of no cars passing in three hours (two hours have already passed) is:

The probability of waiting at least 1 more hour for the next car is the same as the probability of having no cars pass in the next hour, given that no cars have passed in the last 2 hours. This can be calculated using the conditional Poisson distribution:

[tex]$= \frac{\frac{(0.916\cdot1)^0e^{-0.916\cdot1}}{0!}\cdot \frac{(0.916\cdot2)^0e^{-0.916\cdot2}}{0!}}{0.148} \approx 0.631$[/tex]

Therefore, the probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.

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The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:

d = √((x₂- x₁)²+ (y₂ - y₁)²)

The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.

The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:

Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)

= (-4/3) - (11/3)

= -15/3

= -5

Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.

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The measure of angle J, m∠J = 41.2°.

angle mwasurement:

We can use trigonometry to find the measure of ∠J. Since we know the lengths of the two sides adjacent to ∠J (GH and GJ), we can use the tangent function, which is defined as the opposite side divided by the adjacent side:

tan(J) = opposite/adjacent = GH/GJ

We can solve for J by taking the inverse tangent (or arctan) of both sides:

J = [tex]tan^{-1}[/tex](GH/GJ)

Substituting the given values, we get:

J = [tex]tan^{-1}[/tex](14/16)

Using a calculator, we find:

J ≈ 41.186

Rounded to the nearest tenth, the measure of angle J is 41.2°.

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The goal of calculating an acceptance interval is to find the probability that the true mean lies between two values, hence the correct answer is option a.

The acceptance interval is a method for developing a tolerance interval for a specified percentage of future measurements in a distribution. The tolerance interval specifies the interval into which a specified percentage of future measurements will fall.

An acceptance interval is a quality control tool for assessing whether the characteristics of a production lot meet predetermined quality criteria. These predetermined criteria are usually in the form of upper and lower limits for the interval.

The acceptance interval is utilized to detect whether a production lot's results are within the tolerances or specifications of the quality criteria.

The purpose of calculating an acceptance interval is to locate the probability that the true mean falls between two values. In conclusion, the goal of calculating an acceptance interval is to find the probability that the true mean lies between two values.

Therefore, option a is the correct answer.

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Answer:

To find the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures, we first need to convert both temperatures to Celsius or Fahrenheit. Since Oklahoma's temperature is given in Fahrenheit and New Jersey's temperature is given in Celsius, we'll convert Oklahoma's temperature to Celsius.

Using the formula F = 1.8C + 32, we can solve for C:

-31°F = -35°C

(To see how we arrived at this conversion: first, we use the formula to convert Fahrenheit to Celsius: F = 1.8C + 32. Rearranging the equation, we can solve for C: (F - 32) / 1.8 = C. Plugging in -31°F for F, we get (-31 - 32) / 1.8 = -35°C)

Now we can find the difference in Celsius between the two temperatures:

|-35°C| - |-37°C| = |-2| = 2°C

So the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures is 2°C.

The garden would require 84 plants, which is the same number of plants as the garden's surface area.

The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.

Area of the garden = (1/2) x Base x Height

Area of the garden = (1/2) x 7 x 24

Area of the garden = 84 square yards

Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.

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The length of the long diagonal of the cube is 3sqrt(3) inches.

Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).

Using the given equation, we can write

a^3 + 3(12a) = 2(6a^2)

Simplifying this equation, we get

a^3 + 36a = 12a^2

a^3 - 12a^2 + 36a = 0

a(a^2 - 12a + 36) = 0

a(a - 6)^2 = 0

The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.

To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".

Using the Pythagorean theorem, we can write

d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2

d^2 = 3(6^2)/4

d = (sqrt(3)×6)/2

d = 3sqrt(3) inches

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Johnny has 1258 more pineapples than Bobby.

Bobby has 37 pineapples, Johnny has 35 times more pineapples than Bobby. To find how many more pineapples does Johnny have than Bobby, we can use the below formula,

More pineapples = Johnny's pineapples - Bobby's pineapples

Let x be the number of pineapples that Bobby has. Therefore, the number of pineapples owned by Johnny is 35x.

It is given that Bobby originally has 37 pineapples, thus x = 37. The number of pineapples Johnny has = 35*37 = 1295

Thus, difference in number of pineapples between Johnny and Bobby:

=1295-37 = 1258

Therefore, Johnny has 1258 more pineapples than Bobby.

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Answer:

a two-dimension surface formed by two number lines.

Hence, the correct match of probabilities with their corresponding situations is given by option 4.

To match the probabilities with their corresponding situations, we can utilize the formulas given below:

[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]

P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663

Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)

4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663

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The probability that an ugly splice is weak is 2/3.

This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).

In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).

The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.

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The probability that an even number or a number greater than 3 is rolled on a 12-sided die is 0.833.

A 12-sided die has 12 equally likely outcomes, numbered from 1 to 12. To find the probability of rolling an even number or a number greater than 3, we need to count the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.

There are 6 even numbers on a 12-sided die, namely 2, 4, 6, 8, 10, and 12, and there are 9 numbers greater than 3, namely 4, 5, 6, 7, 8, 9, 10, 11, and 12. However, we need to be careful not to count the numbers that satisfy both conditions twice, namely 4, 6, 8, 10, and 12.

Therefore, the number of outcomes that satisfy the condition is 6 + 9 - 5 = 10. The probability of rolling an even number or a number greater than 3 is therefore 10/12, which simplifies to 5/6 or approximately 0.833.

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The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

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Answer:

12x - 6

Step-by-step explanation:

[tex] \rm \: 4 + 5(3x - 2) - 3x[/tex]

[tex] \rm \: = 4 + 15x - 10 - 3x \: \sf (distribute \: the \: 5)[/tex]

[tex] \rm= 12x - 6 \: \sf (combine \: like \: terms)[/tex]

[tex] \rm= 6(2x - 1) \: \sf (factor \: out \: a \: 6)[/tex]

[tex] \rm \: = 6(2x) - 6(1) \: \sf (distribute \: the \: 6)[/tex]

[tex] \rm \:= 12x - 6 \: \sf (simplify)[/tex]

Answer:

bar chart

Step-by-step explanation:

you are right box plot, histogram and a circle graph aren't the right ones

The total number of t-shirts principal ordered in $1520 for the school store is given 214.

Let us consider the number of t-shirts the principal ordered be equal to 'x'.

The cost of each t-shirt is equal to $7.

⇒ The total cost of 'x' t-shirts =  7x dollars.

Shipping cost is a flat rate for any order, regardless of the number of t-shirts =  $22

Total cost of the order (including shipping) =  $1520.

Required equation is equal to,

7x + 22 = 1520

Subtract 22 from both sides of the equation we get,

⇒ 7x = 1498

Divide both sides of the equation by 7 we get,

⇒ x = 214

Therefore, the number of t-shirts ordered by  principal for the school store is equal to  214.

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