Which of these planes is NOT in the {100} family for a tetragonal crystal? (A tetragonal unit cell drawn to proportion is included below for reference.)(A) (010)(B) (001)(C) (110)(D) Both B & C(E) All of these planes are in the {100} family.

To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.

An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.

If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:

P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e

= a(x⁴) - b(x³) + c(x²) - d(x) + e

Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:

a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e

Simplifying this equation, we get:

2b(x³) + 2d(x) = 0

Since this equation holds for all values of x, we can set x = 0 to get:

2d(0) = 0

which implies that d = 0. Similarly, setting x = 1, we get:

2b(1³) + 2d(1) = 0

2b = 0

b = 0

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After solving the given equations we know that the value of x and y are -4 and -7 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

This form is also highly useful when solving systems involving two linear equations.

So, we have the equations:

y=2x+1 ...(1)

-4x+y=9 ...(2)

Now, substitute y=2x+1 in equation (2):

-4x+y=9

-4x+2x+1=9

-2x=8

x=-4

Now, insert x=-4 in equation (1):

y=2x+1

y=2(-4)+1

y=-8+1

y=-7

Therefore, after solving the given equations we know that the value of x and y are -4 and -7 respectively.

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Answer:

The equation of a line perpendicular to y=3 that goes through the point (-5, 3) is: x = -5.

Step-by-step explanation:

To find the equation of a line perpendicular to y=3 that goes through the point (-5, 3), we need to remember that the slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The equation y=3 is a horizontal line that goes through the point (0,3), and its slope is zero. The negative reciprocal of zero is undefined, which means that the line perpendicular to y=3 is a vertical line.

To find the equation of this vertical line that goes through the point (-5, 3), we can start with the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line. Since the line we want is vertical, its slope is undefined, so we can't use the point-slope form directly. However, we can still write the equation of the line using the point (x1, y1) that it passes through. In this case, (x1, y1) = (-5, 3).

The equation of the vertical line passing through the point (-5, 3) is:

x = -5

This equation tells us that the line is vertical (since it doesn't have any y term) and that it goes through the point (-5, 3) (since it has x=-5).

So, the equation of a line perpendicular to y=3 that goes through the point (-5, 3) is x = -5.

Answer:

x= -5

Step-by-step explanation:

The perpendicular line is anything with x= __.

x= -5 however, will go through the point (-5, 3) and that is our answer.

If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:

The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.

Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).

As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.

The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:

∬Rf(x,y)dydx

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.

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This principle is validated by the data shown in the table.

Tests and measurements is an essential aspect of the education process as it enables educators to gauge the level of knowledge and skills their students have acquired. The principle that longer tests tend to be more reliable than shorter ones has some merit because it allows educators to assess a broader range of skills and knowledge, which increases the validity of their assessments.In my opinion, the principle that longer tests tend to be more reliable than shorter ones is illustrated in the reliability coefficients shown in the table. This is because the data shows that the reliability coefficients for longer tests are consistently higher than those for shorter tests. Additionally, the results for the 10-item test indicate a higher reliability coefficient compared to the 5-item test, which supports the notion that longer tests are more reliable than shorter ones.The table displays that the longer tests have higher reliability coefficients compared to the shorter tests. For example, in the 5-item test, the reliability coefficient is .45, while the 10-item test's reliability coefficient is .73. This shows that the 10-item test is more reliable than the 5-item test, as the higher reliability coefficient indicates that the assessment is consistent in measuring the skill or knowledge it is intended to measure. As a result, this principle is validated by the data shown in the table.

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Answer:

h = 15 cm

Step-by-step explanation:

Area of triangle equals the area of rectangle. As the dimensions of the rectangle is given, we can first find the area of the rectangle.

      [tex]\boxed{\bf Area \ of \ the \ rectangle = length * width}[/tex]

                                               = 10 * 9

                                               = 90 cm²

Area of triangle = area of rectangle

                          = 90 cm²

base of the triangle = b = 12 cm

 [tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex]  where h is the altitude and b is the base.

         [tex]\bf \dfrac{1}{2} b* h = 90 \\\\\dfrac{1}{2}*12* h = 90[/tex]

                      [tex]\bf h = \dfrac{90*2}{12}\\\\\boxed{\bf h = 15 \ cm}[/tex]

Answer:

Step-by-step explanation:

44

Answer:

The perimeter of a rectangle is given by:

P = 2(L + W)

where P is the perimeter, L is the length, and W is the width.

In this case, we know that P = 270 cm and L = 90 cm, so we can solve for W as follows:

270 = 2(90 + w)

Divide both sides by 2:

135 = 90 + w

Subtract 90 from both sides:

w = 45

Therefore, the width of the map is 45 cm.

Step-by-step explanation:

The probability mass function of X( -3, -1, 1 ,3)  is P(X) 1/8 3/8 3/8 1/8.

A fair coin is flipped 3 times and the random variable X is defined as follows:

   X = 3 times the number of heads - 2 times the number of tails

To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.

The Possible outcomes are as shown:

   3 heads (X = 3)

   2 heads, 1 tail (X = 1)

   1 head, 2 tails (X = -1)

   3 tails (X = -3)

And the Probabilities are:

   P(X = 3) = 1/8

   P(X = 1) = 3/8

   P(X = -1) = 3/8

   P(X = -3) = 1/8

Therefore, the probability mass function of X is:

X( -3, -1, 1 ,3)  is  P(X) 1/8 3/8 3/8 1/8

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In the given system of equations one taco costs $0.80 and one burrito costs $0.72.

An equation system is a finite collection of equations for which we searched for the common solutions. It is sometimes referred to as a set of simultaneous equations or an equation set. The classification of a system of equations is similar to that of a single equation. In modelling issues where the unknown values may be expressed in the form of variables, a system of equations finds use in everyday life.

Let us suppose the cost of one taco = x.

Let us suppose the cost of one burrito = y.

Then, for Emma we have:

3x + y = 3.65

For Cooper we have:

x + 2y = 3.30

Using elimination, multiply the first equation by 2 and subtract it from the second equation:

(2)(3x + y = 3.65)

6x + 2y = 7.30

x + 2y = 3.30

-5x = -4

x = 4/5

Substituting this value of x into either equation:

3(4/5) + y = 3.65

y = 2.15/3 ≈ 0.72

Therefore, one taco costs $0.80 and one burrito costs $0.72.

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Answer:

a. Jason's equation in y = mx + b form is y = 15x + 1.

b. Scott's equation in y = mx + b form is y = 15x.

Since both are moving at the same speed, they will meet at the point where their distances from the starting point are the same. Let d be the distance from Scott's starting point to the store. Then, the distance from Jason's starting point to the store is d + 1. Using the formula distance = rate × time, we can set up an equation:

15t = d

15t - 1 = d + 1

Solving for t in both equations, we get t = d/15 and t = (d+2)/15, respectively. Equating these expressions for t, we get d/15 = (d+2)/15, which simplifies to d = -2. This means that they will not meet before reaching the store, as Jason is already 1 mile ahead of Scott and will stay ahead throughout the trip.

If we were to graph both lines on the same coordinate plane, we would have two parallel lines with a slope of 15, where Jason's line would intersect the y-axis at 1.

Answer: 4 batches of fudge brownies and 1 batch of peanut butter brownies were made.

Step-by-step explanation:

Let x be the number of batches of fudge brownies made, and y be the number of batches of peanut butter brownies made.

From the problem, we can write two equations based on the information given:

   Each batch of fudge brownies makes 1 pan: x = number of pans of fudge brownies.

   Each batch of peanut butter brownies makes 9 pans: 9y = number of pans of peanut butter brownies.

We also know that the class made 5 batches in total, and ended up with 29 pans:

x + 9y = 29 (total number of pans)

We can now solve for x and y by using a system of two equations:

x + 9y = 29 (equation 1)

x + y = 5 (equation 2)

Solving for x in equation 2 and substituting into equation 1, we get:

(5 - y) + 9y = 29

Simplifying and solving for y:

8y = 24

y = 3

Substituting y = 3 into equation 2, we get:

x + 3 = 5

x = 2

Therefore, the class made 2 batches of fudge brownies (2 pans) and 1 batch of peanut butter brownies (9 pans), for a total of 29 pans. Alternatively, we can say that the class made 4 batches of fudge brownies (4 pans) and 1 batch of peanut butter brownies (9 pans) for a total of 29 pans.

Answer:

[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]

Answer:

A- 2

B- 4,100

C- 82

D- 4,182

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

Give a short note on Median?

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

The smallest number in the data set that is not an outlier: 15

The median of the first half of the data set: 17

The median of the entire data set: 20.5

The median of the second half of the data set: 22

The largest number in the data set that is not an outlier: 35

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

The smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

To determine the smallest value of n for which S_n has an element of order greater than or equal to 100, we can use the formula

S_n = n!/r!(n - r)!,

where n is the number of elements in the set, and r is the number of elements being chosen at a time.

Given, S_n has an element of order greater than or equal to 100. The smallest value of n should be determined.

The formula for the number of permutations in a set with n elements is given by, `S_n = n!/r!(n - r)!`

where `n` is the number of elements in the set and `r` is the number of elements being chosen at a time.

The element of order `n` in `S_n` is an `n` cycle. For `n = 100`, we have an element of order 100.

This element can be expressed as `(1 2 3 ... 99 100)`. Thus, `r = 100`.

Substituting these values in the formula of S_n we get, S_n = n!/r!(n - r)! => n!/(100!(n - 100)!)

Now, we have to find the smallest value of n for which S_n has an element of order greater than or equal to 100. If we substitute `n = 100`, then we will have an element of order 100. But the question asks for the smallest value of n. So, if we substitute `n = 101`, we will have an element of order `101`. Hence, the smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

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The statement that is correct is (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.

The binomial distribution can be used to calculate the probability of a certain number of successes in a given number of trials, where each trial has a fixed probability of success.

The probability of a flight being delayed is 0.24, and the probability of a flight not being delayed is 0.76. Therefore, the probability of exactly 10 flights out of 100 being delayed can be calculated using the binomial distribution with n = 100, k = 10, and p = 0.24.

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It would cost €27 to buy a sheet of area 4 meters by 75 centimeters.

We solve this problem easily by employing the unitary method. To answer this question, we need to first calculate the area of the metal sheet being sold and the area of the metal sheet being purchased.

The area of the metal sheet being sold is:

5 meters × 2 meters = 10 square meters

The area of the metal sheet being purchased is:

4 meters × 0.75 meters = 3 square meters

Now we can calculate the price per square meter of the metal sheet being sold:

€90 ÷ 10 square meters = €9 per square meter

Finally, we can calculate the cost of the metal sheet being purchased:

3 square meters × €9 per square meter = €27. Therefore, the cost to buy a sheet of area 4 meters by 75 centimeters which costs €90 to a metal of area 5 meters by 2 meters would be €27.

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In the equation A’ = 364V relating the surface area A and the volume V of a spherical balloon. We are also given that the volume is increasing at a rate of 18 cubic inches per second.so the rate at which the surface area of the balloon is increasing is 6552 square inches per second

We want to find the rate at which the surface area is increasing when A = 153.24 square inches and V = 178.37 cubic inches.

To find the rate of change of A with respect to time, we can use the chain rule of differentiation:

dA/dt = dA/dV × dV/dt

We know that dV/dt = 18 cubic inches per second, so we just need to find dA/dV and then we can find dA/dt.

To find dA/dV, we differentiate the equation A’ = 364V with respect to volume V:

dA/dV = 364

Now we can find dA/dt:

dA/dt = dA/dV × dV/dt ⇒ 364 × 18 ⇒ 6552 square inches per second

So the rate at which the surface area of the balloon is increasing is 6552 square inches per second when A = 153.24 square inches and V = 178.37 cubic inches.

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Each pair of children gets to bat for 7.5 minutes.

To find out how much time each pair gets to bat, we need to divide the total session time by the number of pairs of children who bat.

Number of pairs of children who bat = 6 groups x 1 pair/group = 6 pairs

Total time for the session = 45 minutes

Time per pair of children who bat = Total time / Number of pairs of children who bat

= 45 minutes / 6 pairs

= 7.5 minutes per pair

Therefore, each pair of children gets to bat for 7.5 minutes.

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Answer:

Step-by-step explanation:

The given line is y = 5x + 2. We know that any line perpendicular to this line will have a slope that is negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Line A is perpendicular to y = 5x + 2, so it has a slope of -1/5. We also know that the y-intercept of line A is 3. Therefore, the equation of line A can be written as:

y = (-1/5)x + 3

or in the form y = mx + c, where m = -1/5 and c = 3.

Therefore , the solution of the given problem of unitary method comes out to be it weighs 0.01 times as much as the first nugget.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

We can divide the weight of the second nugget by the weight of the first nugget to determine how many times as much the second nugget weights the first:

=> 0.8 oz / 0.008 oz = 100

The second piece is therefore 100 times heavier than the first.

We can divide the first nugget's weight by the second nugget's weight to determine how much the first nugget weights in relation to the second nugget:

=> 0.008 oz /0.8 oz = 0.01

In other terms, the second nugget weighs 100 times as much as the first nugget, or it weighs 0.01 times as much as the first nugget.

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Answer: $3.64

Step-by-step explanation:

At the store, you buy four toys for $1.5, which means you pay $1.5 * 4, or $6.

Then, you calculate the sales tax, which is 6%, which means you multiply $6 by (100% + 6%), or $6*(1.06) which is $6.36.

Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.

To create opposite x terms, we need to multiply the first equation by -5.

How to choose what term to multiply the first equation?

To choose what term to multiply the first equation, we need to consider the coefficients of the variable that we want to eliminate (in this case, the x variable) in both equations. Our goal is to create opposite terms for that variable in the two equations, so that when we add or subtract the equations, that variable will be eliminated.

Determining the number to multiply the first equation by to form opposite terms for the x-variable :

In this case, the coefficient of x in the first equation is 2/5, and the coefficient of x in the second equation is -2.

To create opposite terms for x, we need to find a constant that, when multiplied by the first equation, will result in a coefficient of x that is the negative of the coefficient of x in the second equation (i.e., -2).

To do this, we can divide the coefficient of x in the second equation by the coefficient of x in the first equation, and then multiply the entire first equation by the resulting constant.

In this case, we have:

[tex](-2)/(2/5) = -5[/tex]

Multiplying the first equation by -5 gives:

[tex]-5(2/5)x + (-5)6y = -5(-10)[/tex]

which simplifies to:

[tex]-2x - 30y = 50[/tex]

Now we have two equations with opposite x terms:

[tex]-2x - 4y = 40[/tex]

[tex]-2x - 30y = 50[/tex]

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According to the circle theorem, we can find the length of the cord, x = 4 units.

Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.

A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.

Here in the given circle,

As per the intersecting chords theorem,

AB × CB= BE × BD

⇒ 6 × 6 = 9× x

⇒ x = 36/9=4

Therefore, the length of the chord, x = 4 units.

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Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

The rounding of the number to 1 significant figure is-

216 × 876 = 180000

216 × 876

This number can be written in form of rounding to 1 significant figure as;

200 × 900 = 180000

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Answer: Associative property

Step-by-step explanation:

The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!

120 middle schοοl students prefer the dοcumentaries televisiοn genre.

A percentage in mathematics is a number οr ratiο that can be expressed as a fractiοn οf 100. If we need tο calculate a percentage οf a number, we shοuld divide it by 100 and multiply the result. Therefοre, the percentage refers tο a part per hundred. Per 100 is what the wοrd percentage means. The symbοl "%" is used tο represent it.

The tοtal is 100%.  Subtract the οther parts οf the circle tο find the percent fοr spοrts.

100 - 14 -22-20 -20

24

Spοrts is 24%

Multiply the number οf students by the percentage οf students that prefer spοrts

500 *24%

500 *.24

120

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Answer:

4.25 x + 7 = 24

Second choice

Step-by-step explanation:

Plug in x = 4 into each equation and see which one is consistent

The correct answer is 4.25x + 7 = 24

Left side = 4.25(4)  + 7

= 17 + 7

=24

which matches the right side 24

The required percentage of values that should fall in the interval 56-88 is approximately 74.37%.

Chebyshev’s Theorem:Chebyshev's Theorem states that, for any given data set, the proportion (or percentage) of data points that lie within k standard deviations of the mean must be at least (1 - 1/k2), where k is a positive constant greater than 1.Calculation:Given,Mean (μ) = 72N (Total number of values) = 387Interval (x) = 64-80 and 56-88Minimum values (n) = 344Minimum percentage (p) = (344 / 387) x 100 = 88.85%From the given data we have,1. Calculate the variance of the distribution,Variance = σ2 = [(n × s2 ) / (n-1)]σ2 = [(344 × 42) / 386]σ2 = 18.732. Calculate the standard deviation of the distribution,σ = √(18.73)σ = 4.33. Calculate k = (|x - μ|) / σ for the given interval 56-88,Here, x1 = 56, x2 = 88, k1 = |56-72| / 4.33 = 3.7, k2 = |88-72| / 4.33 = 3.7Thus, k = 3.74. Calculate the minimum percentage of values within the interval 56-88 using Chebyshev's Theorem,p = [1 - (1/k2)] x 100p = [1 - (1/3.7)2] x 100p = 74.37% (approximately)Therefore, the required percentage of values that should fall in the interval 56-88 is approximately 74.37%.

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