AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle. 6.5 C Provide your answer below: یز چز لئے A 12 B

Answer: 16 cups per second.

Step-by-step 5.5 minutes into seconds 320.

620 gallons into cups 9920.

9920 divided by 320 seconds.

16 cups per second

Answer:

\(f(x) = 2000 * 1.05^x\)

Step-by-step explanation:

The key to this question is interpreting the graph and then modelling it into an exponential function.

You are given 2 key characteristics of this graph. 1 characteristic being that it intercepts the y-axis at (0,2000), and another characteristic being that it goes through the point (1,2100)

Now refer to the standard form of an exponential function.

\(y = a * b^x\)

Since you know that when x = 0, y = 2000, a must be 2000. Because \(b^0 = 1\), 2000 * 1 = 2000

So you got your a value. Sub it into the equation and now you got.

\(y = 2000 * b^x\)

You still need to solve for b, so this is where you do some algebra. Pick your key point, (1,2100), sub in those values for x and y, and solve for b.

\(2100 = 2000 * b^1\\\frac{2100}{2000} = b\\ 1.05 = b\)

Now you have your a and b values. Now you can express using a function:

\(f(x) = 2000 * 1.05^x\)

Answer:

V≈5.23×10-7m³

Step-by-step explanation:

V=π(d

2)2h=π·(0.014

2)2·3.4×10-3≈5.23389×10-7m³

Answer: 523.1 mm^2

You first want to find the radius for the volume of cylinder formula. You first do 14 divided by 2 to get the radius. You should get 7. Then after you find the radius you then put it into the formula which is v=3.14 x radius^2 x height. The equation with all the numbers from the problem is 3.14 x 7^2 x 3.4. After you put the equation into your calculator you should get 523.1 mm^2.

The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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Answer:

See below for answers and explanations

Step-by-step explanation:

10) The domain is (-∞,+∞) because no matter what x is, it is defined for all real numbers. The range is (-∞,3] because if y is greater than 3, then no x-value can be defined for that.

11) The domain would be (−∞,3)∪(3,∞) because of the vertical asymptote located at x=3 which means x can be any real number other than 3. The range is (-∞,0)∪(0,∞) because of the horizontal asymptote located at y=0, which means y can be any real number other than 0.

The correct statements about the set X of all sets of exactly three integers are:

c. X is countably infinite

e. X is infinite

To determine the nature of the set X, we can analyze its cardinality and structure. By investigating whether X is countable or uncountable, finite or infinite, we can gain insights into the properties and size of the set.

Therefore, the correct statements about the set X of all sets of exactly three integers are:

c. X is countably infinite

e. X is infinite

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GIVEN:

We are given the following equation;

Required;

Solve the equation for y.

Step-by-step solution;

To solve, we simply collect like terms as follows;

We now have;

Observe that -2x and +2x cancel out each other on the right hand side.

Next step, we divide both sides by 9, that is the coefficient of y.

Note that we can split up the left hand side. We do this by taking both numbers in the numerator and writing each as a fraction with 9 as the denominator. This is because 9 is the LCM of both fractions as it is expressed above.

We now have;

Now we divide both fractions by any common factors;

Therefore,

ANSWER:

Answer:

D

Step-by-step explanation:

its D trust

All of these statements are correct.

When describing categorical data, several methods can be used to provide meaningful insights and summarize the data.

Counts and proportions: Counting the number of observations in each category can provide information about the distribution and frequency of different categories. Proportions, also known as percentages, can be calculated by dividing the count in each category by the total count, allowing for a comparison of the relative frequencies of different categories.

Measures of center, spread, and shape: Although measures of center, spread, and shape are commonly associated with numerical data, they can also be used to describe certain aspects of categorical data. For example, the mode represents the most frequent category, which can be considered a measure of center. Measures of spread, such as the range or interquartile range, may not be applicable to categorical data. However, bar graphs and pie charts can visually depict the distribution and shape of categorical variables.

Box plots: Box plots are graphical representations primarily used for numerical data. They display the median, quartiles, and any potential outliers. While box plots are not commonly used for categorical data, they can be adapted by representing the frequency or proportion of categories instead of numerical values.

In summary, when describing categorical data, counts and proportions are commonly used to present the frequency and relative frequency of categories. Measures of center, such as the mode, can provide insights into the most frequent category. Measures of spread and shape may not be applicable, but graphical representations like bar graphs and pie charts can be used to visualize the distribution and shape of the categorical data. Box plots are not typically used for categorical data, as they are more suitable for numerical variables.

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a) Different outcomes possible when a pair of dice are rolled two successive times is 36. (b) The probability that each die shows the same value on the second roll as on the first roll is 1/36. (c) The probability that the sum of the two dice is the same on both rolls is 1/6. (d) The probability that the sum of the two dice is greater on the second roll is 5/12.

a) There are 36 different outcomes possible when a pair of dice, one red and one white, are rolled two successive times. This is because there are 6 possible outcomes for each die, and there are two dice, so 6 x 6 = 36 different outcomes.

b) The probability that each die shows the same value on the second roll as on the first roll is 1/36. This is because there is only one outcome out of the 36 possible outcomes that will result in both dice showing the same value on both rolls.

c) The probability that the sum of the two dice is the same on both rolls is 6/36, or 1/6. This is because there are 6 possible sums (2, 3, 4, 5, 6, 7) that can be rolled on both dice, and each of these sums has a 1/6 chance of occurring on both rolls.

d) The probability that the sum of the two dice is greater on the second roll is 15/36, or 5/12. This is because there are 15 possible outcomes where the sum of the two dice is greater on the second roll (3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17), and each of these outcomes has a 1/36 chance of occurring, so 15 x 1/36 = 15/36, or 5/12.

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Answer:

the answer would be 25

Step-by-step explanation:

10 goes in to 250 25 times

The correct answer for the value of  division of 250 by 10 is 25.

What is Division?

Division involves splitting a number or quantity into equal parts or groups. it  is a mathematical operation.

When  the division of  one number (the dividend) by another number (the divisor) is performed, the results determined  how many times the divisor can fit into the dividend.

quotient is the result of division.

Signs that used to indicate division are ÷  and /.

In the given question \(250\) is divided by \(10\) , which is expressed as \(250\) ÷ \(10\)

or \(\dfrac{250}{10}\).

\(\dfrac{250}{10} = 25\).

The Quotient for the division of 250 divide by 10 is 25.

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Answer: -3/4 and 4/3

Step-by-step explanation:

A bisector splits an angle into two equal angles.

The answer is the last one: it splits the angle into two congruent angles.

Answer: 22/25

Step-by-step explanation:

54x+6x-30=7(x+2)+3x

60x-30=7(x+2)+3x

60x-30=7x+14+3x

60x-30=10x+14

60x-10x-30=14

60x-10x=14+30

50x=14+30

50x=44

x=22/25

An inequality depicts the relationship between two values in an algebraic statement that are not equal.

Inequality, a declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions.

An inequality is a claim that demonstrates the connection between two (or more) expressions that have one of the following five signs:,, >,,. Similar to an equation, an inequality can be true or untrue. A true statement is: 34 - 12 > 5 + 2. An incorrect statement is 1 + 3 6 - 2.

When two values in an algebraic expression are not equal, an inequality illustrates their relationship. One of the two variables on the two sides of the inequality can be represented by an inequality sign as greater than, greater than or equal to, less than, or equal to another value.

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The probability that a patient, randomly selected and not allergic to pollen, tested negative is 0.90.

To find the probability that a patient tested negative given that they are not allergic to pollen, we can use Bayes' theorem:

P(N|A complement) = [P(N complement|A complement) × P(A complement)] / P(N complement)

We know that P(A complement) = 1 - P(A) = 1 - 0.10 = 0.90. Additionally, P(N complement) can be calculated as:

P(N complement) = P(N complement|A) × P(A) + P(N complement|A complement) × P(A complement)

= 0.10 × 0.10 + 0.20 × 0.90

= 0.01 + 0.18

= 0.19

Substituting these values into the formula, we have:

P(N|A complement) = (0.20 × 0.90) / 0.19 = 0.90

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Answer:

  34 square units

Step-by-step explanation:

You want the area of the triangle with vertices X(6, 8), Y(3, 3), and Z(13, -3).

There are several ways the area of a triangle can be calculated from the coordinates of the vertices. One relatively easy method is to find half the absolute value of the sum of the determinants of adjacent pairs of points.

This calculation is shown in the second attachment.

The area of ∆XYZ is 34 square units.

A slope calculation will tell you side XY is perpendicular to side YZ. This means you can find the area from the lengths of these two sides. The distance formula can tell you the lengths.

  XY = √((3 -6)² +(3 -8)²) = √(9 +25) = √34

  YZ = √((13 -3)² +(-3 -3)²) = √(100 +36) = 2√34

 Area = 1/2bh = (1/2)(√34)(2√34) = 34 . . . . square units

Pick's theorem tells you the area of a polygon with vertices on grid points can be found by counting the grid points on the boundary and interior to the boundary.

  A = i + (b/2) -1

This triangle has the three given vertices on grid points, along with point (8, 0), which is the midpoint of YZ. There are 33 interior points, so the area is ...

  A  = 33 +(4/2) -1 = 34 . . . . square units

The length of XZ is ...

  XZ = √((13 -6)² +(-3 -8)²) = √(49 +121) = √170

Heron's formula tells you the area is given by ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

The third attachment shows this calculation gives an area of 34 square units.

__

Additional comments

The slope calculation tells you the slope of XY is ...

  m = (y2 -y1)/(x2 -x1) = -5/-3 = 5/3

and the slope of YZ is ...

  m = -6/10 = -3/5 . . . . . . . . the opposite reciprocal of the slope of XY

Hence these sides are perpendicular, as we noted above.

We like Pick's theorem for finding the areas of small figures with irrational side lengths (such as this one). It just involves counting, which is often easier than using a bunch of different formulas for slope or length.

The determinant formula is easy to compute, but tedious to enter on a calculator. It is much easier to program a spreadsheet for this. As with Pick's theorem, the method applies to a polygon with any number of vertices.

  \(\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc\)

In these 2×2 matrices, the coordinates can be listed in rows or in columns. It makes no difference to the calculation. The key is to work in one direction around the figure. (Here, we went CCW.)

The triangle is drawn in the first attachment. The geometry program that drew it also calculated its area to be 34 square units.

You may have noticed that the "determinant" method and Pick's theorem guarantee that the area of any polygon with integer coordinates will be an integer multiple of 1/2 square unit. That is, it will never be irrational. (You might not see that using Heron's formula.)

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Answer:

Step-by-step explanation:

The answer is D because all you need to do is multiply everything by 0.5, or one half.

The relationship between chocolate sales and student happiness can be tested using the mean difference.

Specifically, a statistical test such as a correlation analysis or regression analysis can be used to examine the relationship between the amount of chocolate sales and the level of student happiness.

The mean difference refers to the difference in the average level of student happiness between two groups, such as those who consume more chocolate and those who consume less chocolate. This can help determine if there is a significant association between chocolate consumption and student happiness.

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The phone is worth $128 after 2 years, which is option C.

What is exponential decay ?

Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.

Calculating the worth of the phone :

The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.

Let's use the formula for exponential decay: \(A = A_0(1 - r)^t\), where A is the final amount, \(A_0\) is the initial amount, r is the decay rate, and t is the time elapsed.

In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:

\(A = 800(1 - 3/5)^2\)

\(A = 800(2/5)^2\)

\(A = 800(4/25)\)

\(A = 128\)

Therefore, the phone is worth $128 after 2 years, which is option C.

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Answer:

Step-by-step explanation:

it's this one

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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According to the question, Let us assume the total number of students is \(100\). In which \(43\) students own a CD player. And \(28\) students own both CD player as well as MP3 Player.

Now, to calculate the probability that a student owns an MP3 player and also they own a CD player. It is clear from the given data, the percentage is higher than \(28\) percent.

Using conditional probability rule:

\(P(MP3|CD) = \frac{P(MP3 and CD)}{P(CD)} = \frac{0.28}{0.43} = 0.65\)

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Answer:

9x-5=546

Step-by-step explanation:

9x-5=546

9x=551

x=61.22222222

Answer:

We conclude that the sequence 2, -4, -16, -36,... is not a geometric sequence.

Step-by-step explanation:

Given the sequence

2, -4, -16, -36,...

Let us compute the ratio of all the adjacent terms

\(\frac{-4}{2}=-2,\:\quad \frac{-16}{-4}=4,\:\quad \frac{-36}{-16}=2.25\)

It is clear that the ratio is not constant.

Thus, the given sequence is not a geometric sequence.

Therefore, we conclude that the sequence 2, -4, -16, -36,... is not a geometric sequence.

Answer:

450 employees work at this company.

Step-by-step explanation:

300 = 2/3 of x
300 × 3 = 2x
900 = 2x
450 = x

Answer:

11

Step-by-step explanation:

3 times 11 gives you 33 which would be the product

3 x 11 = 33

subtract the 12(twelve) from the 33(product)

33 - 12 = 21

Answer:

102in2

Step-by-step explanation:

The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.

Given equations are (5.1) z 4 +16=0 and z 3 −27=0.(5.1) z 4 +16=0z⁴ = -16z = 2 * √2 * i, 2 * (-√2 * i), -2 * √2 * i, -2 * (-√2 * i)Therefore, the roots of the equation are z = 2^(3/4) * i, 2^(1/4) * i, -2^(3/4) * i, -2^(1/4) * i.(5.2) z 8 −16i=0z⁸ = 16i z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i

Therefore, the roots of the equation are:

z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i. z 8 +16i=0z⁸ = -16i z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i

Therefore, the roots of the equation are:

z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i.

First of all, we need to know that a polynomial equation of degree n has n roots and they may be real or imaginary. Roots are also known as zeros or solutions of the equation.If the degree of the polynomial is n, then it can be written as an nth degree product of the linear factors, z-a, where a is the zero of the polynomial equation, and z is any complex number. Therefore, the nth degree polynomial can be factored into the product of n such linear factors, which are known as the roots or zeros of the polynomial.In the given equations, we need to find the roots of each equation. In the first equation (5.1), we have z⁴ = -16 and z³ = 27. Therefore, the roots of the equation:

z⁴ + 16 = 0 are:

z = 2^(3/4) * i, 2^(1/4) * i, -2^(3/4) * i, -2^(1/4) * i.

The roots of the equation z³ - 27 = 0 are:

z = 3, -1.5 + (3^(1/2))/2 * i, -1.5 - (3^(1/2))/2 * i.

In the second equation (5.2), we need to find the roots of the equation z⁸ = 16i and z⁸ = -16i. Therefore, the roots of the equation z⁸ - 16i = 0 are:

z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i.

The roots of the equation z⁸ + 16i = 0 are also the same.

Thus, we can find the roots of polynomial equations by factoring them into linear factors. The roots may be real or imaginary, and they can be found by solving the polynomial equation.

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