Which transformation maps △UVW to △EFG?

8. The depth of the water is solved to be = 2.9 cm (one decimal place).

9 The ratio r: s =√3 : 2.

The  depth of water is calculated by first using Pythagoras theorem to get the level between water level 7 cm and water level when completely full which is 10 cm

= √(10² - 7²)

= √(100 - 49)

= √51

The next step is to subtract from the radius

= 10 - √51

= 2.8586 cm

= 2.9 cm

9. The length of diagonal of a cube is given by the formula

= (√3)·s

The diameter of the sphere is equal to length of diagonal of a cube.

radius of a sphere = diameter / 2

r = (√3)*s / 2

r / s = √3 / 2

hence the ratio is

r : s = √3 : 2

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complete question is attached

The shape of the graph b will be linear with an immediate decrease in speed.

In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled by an object from its starting position with respect to the time when it is started moving.

Generally speaking, the position or distance traveled by a physical object in a position vs time graph is always plotted on the y-coordinate while time is always plotted on the x-coordinate (x-axis).

In this scenario, the rate of change of the shape's position can be calculated as follows:

Rate of change = (30 - 50)/(40 - 30)

Rate of change = -20/10

Rate of change = -2.

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you forgot to put the question

The expression that will give the distance between points is option D i.e. √(2 - 4)² + (3 + 3)². The solution has been obtained by using distance formula.

What is the distance formula?

The distance between two locations on a coordinate plane can be calculated using the distance formula. The distance equation is written as d = √(x₂ - x₁)² + (y₂ - y₁)².

We are given two points as (2,3) and (4,-3).

So, x₁ = 2, y₁ = 3, x₂ = 4, y₂ = -3

Now, substituting these values in the distance formula, we get

d = √(2 - 4)² + (3 + 3)²

Hence, the expression that will give the distance between points is option D.

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Full question has been attached below

what is even numbers and

Answer:

(x+y)(8a - 1)

Step-by-step explanation:

For the first expression:

(a-7) - y(a-7)

We can factor out (a-7) from both terms:

(a-7)(1 - y)

So, the factored expression is:

(a-7)(1 - y)

For the second expression:

8a(x+y) - (x+y)

We can factor out (x+y) from both terms:

(x+y)(8a - 1)

So, the factored expression is:

(x+y)(8a - 1)

Answer: (1-y)(a-7) and (8a-1)(x+y)

Step-by-step explanation:

When the values in the parentheses are the same twice, they reappear only once after grouping. In the first problem, the coefficients are 1 and -y, therefore, the answer becomes (1-y)(a-7).

Hope this helps

MM

The degrees of freedom for error in a two-way ANOVA experiment with 3 levels for factor a, 7 levels for factor b, and 100 replications is 2071.

The degrees of freedom (df) for error in a two-way ANOVA experiment depend on the sample size (n) and the number of parameters estimated in the model.

In a two-way ANOVA experiment, we are interested in modeling the response variable as a function of two factors, a and b, and their interaction. The model can be written as follows:

Yij = μ + αi + βj + (αβ)ij + εij

In general, the df for error can be calculated as follows:

df error = n - k

where k is the number of parameters estimated in the model.

In our case, we have 3 levels for factor a, 7 levels for factor b, and 100 replications. Therefore, the total sample size is n = 3 x 7 x 100 = 2100.

To estimate the parameters in the model, we need to calculate the following:

The overall mean μ

The effect of factor a, αi, for i = 1, 2, 3

The effect of factor b, βj, for j = 1, 2, ..., 7

The interaction effect between factors a and b, (αβ)ij, for i = 1, 2, 3 and j = 1, 2, ..., 7

Therefore, the total number of parameters estimated in the model is

=> k = 1 + 3 + 7 + 3 x 7 = 29.

Finally, we can calculate the df for error as:

df error = n - k = 2100 - 29 = 2071.

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The statement that " t-value changes depending on the number of data points collected" is (b) False because t-value is a statistic that is used in hypothesis testing to determine the difference between 2 sample means is significant or not.

The t-value does depend on the sample size (number of data points) as well as the sample mean and standard deviation, but it does not change "depending on" the number of data points in the sense that the same data set will always produce the same t-value for a given statistical test.  

So , it is important to note that the t-value is a fixed value for a given set of data, regardless of the number of data points collected.

Therefore, if the same data set is used to perform a t-test multiple times, the resulting t-value will always be the same.

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The frequency distribution table of the data is illustrated below.

The data we have been given represents the percentage of people who have completed 4 or more years of college education in different states. To create a frequency distribution, we need to first decide on the number of classes we want to use. In this case, we will use 7 classes.

Next, we need to determine the range of values for each class. To do this, we first find the minimum and maximum values in the data set, which are 18.9 and 37.9, respectively.

The range of values for each class will be (max value - min value) / number of classes, which in this case is (37.9 - 18.9) / 7 = 2.86.

We will start with the first class, which will include all values from 18.9 to 21.76 (the lower limit of the first class plus the range of values for each class). The next class will include values from 21.76 to 24.62, and so on, until we reach the final class which will include all values from 33.18 to 36.04 (the upper limit of the final class plus the range of values for each class).

To create the frequency distribution, we count the number of values in the data set that fall into each class. For example, the first class includes values between 18.9 and 21.76, and there are 2 values in the data set that fall into this range (21.4 and 20.0). We continue this process for each class until we have a table that shows the frequency of values in each class.

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Complete Question:

Percentage of People Who Completed 4 or More Years of College Listed by state are the percentages of the population who have completed 4 or more years of a college education. Construct a frequency distribution with 7 classes.

21.4,26.0,25.3,19.3,29.5,35.0,34.7,26.1,25.8,23.4,27.1,29.2,24.5,29.5,22.1,24,3,28.8,20,0,20.4,26.7,35.2,37.9,24.7,31.0,18.9,24.5,27.0

The one word that fits in each case will be slope, equal, decreasing, and increasing, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A steep line has a bigger slope than a flat line.

Equally steep lines have equal slopes.

Lines that go up from left to right have decreasing slopes.

Lines that go down from left to right have increasing slopes.

The one word that fits in each case will be slope, equal, decreasing, and increasing, respectively.

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If a set of grades have a large range and a small standard deviation, it means that there are few students with high marks and few with low marks. Most students falls in the average region.

Range is the difference between the maximum value and the minimum value. So for the range to be higher, there must be at least one very high grade and at least a very low grade. If the maximum mark scored by the highest scorer is 95 and 10 for the lowest, the range will be 95- 10 = 85.

If one scored 99 and the lowest scorer got 5, then the range is 99-5 = 94. So higher the range means there is great difference between the highest and lowest grade.

Standard deviation means how much the value deviates from average. If it is low, that means most of the students scored near to the average.

So high range and low standard deviation means, there are few high scorers and few low scores. But most students falls in the average category.

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The equation x(x - 3m) = -5m² is non-real as the discriminant of the quadratic equation will be negative.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

The equation for this problem is defined as follows:

x(x - 3m) = -5m²

x² - 3mx + 5m² = 0.

The parameters are given as follows:

a = 1, b = -3m, c = 5m².

Hence the discriminant is given as follows:

Δ = (-3m)² - 4(1)(5m²)

Δ = 9m² - 20m²

Δ = -11m².

-11m² is always negative, hence the discriminant is negative and the equation is non-real.

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To calculate the probability that the first heart it detects with muscle damage is the 8th image geometric distribution should be used.

According to the question medbiz develops and sells medical imaging devices. they are developing a computer program that reads heart images and detects heart muscle damage.

Machine has success rate of 90%

Number of images of hearts with muscle damage = 100

To calculate the probability that the first heart it detects with muscle damage is the 8th image, geometric distribution should be used because  

Geometric distribution is a type of discrete probability distribution that represents the probability of the number of successive failures before a success is obtained in a Bernoulli trial. A Bernoulli trial is an experiment that can have only two possible outcomes, ie., success or failure

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The question is incomplete, the following question is complete:

MedBiz develops and sells medical imaging devices. They are developing a computer program that reads heart images and detects heart muscle damage. Early studies show the machine has a 90% success rate. The programs is shown 100 images of hearts with muscle damage. What distribution should be used to calculate the probability that the first heart it detects with muscle damage is the 8th image?

binomial distribution

geometric distribution

hypergeometric distribution

none of the other choices

The least common denominator of the number 2, 3, 4, 7 is found to be 42.

Here, the least common denominator of the following numbers is asked,

2, 3, 4, 7

Now, first understand the meaning of least common denominator, it is basically meant that what is that least common value that will divide all of the four above mentioned numbers. So, it is actually ased about the least common multiple (LCM).

We can find the value which will be a multiple of all those numbers,

4 is multiple of 2 but 3 and 7 are not.

6 is a multiple of 2 and 3 but 7 is not.

42 is the number that is multiple of 6 as well as 7 and it also the smallest number doing so.

So, the least common denominator of 2, 3, 4, 7 is 42.

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Complete question - What is the least common denominator of 2, 3, 7, 4.

Let's call the original number of students in the group "n". Each student contributed $2.50, so the total amount the original group of students collected is $2.50 * n.

When 5 more students join the group, the new total number of students is n + 5, and each student contributes $2.50 - $0.50 = $2.00. So the total amount the new group collects is $2.00 * (n + 5) = $2.00n + $10.

Since the total amount collected remains the same, we can set the two expressions for the total amount equal to each other:

$2.50n = $2.00n + $10

Solving for n, we have:

$0.50n = $10

n = 20

So, there were originally 20 students in the group. To find out how much they plan to spend on the gift, we can multiply the original number of students by the original contribution amount:

$2.50 * 20 = $50.00

Therefore, the students plan to spend $50.00 on the gift.

Answer The formula df = (c – 1) (r – 1) is used to find the degree of freedom – The degree of freedom of the chi-square test is calculated by the formula df = (c – 1) (r – 1), where c represents the column number of cell and r represents the row number of the cell.

The information from the given set have the following solutions for:

a) X ∪ Y = {1, 3, 5, 6, 7, 9}

b) X ∩ Z = {1, 9}

c) X' = {2, 4, 6, 8}

In mathematics, a set is a collection of distinct objects, called elements or members, that share a common property or are grouped together for some reason. A set can be finite or infinite.

For the universal set S = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Z = {1, 2, 4, 6, 8, 9}

X = {1, 3, 5, 7, 9}

Y = {1, 5, 6, 7}

we shall evaluate for the following:

X ∪ Y = {1, 3, 5, 6, 7, 9} {all the elements in X and Y}

X ∩ Z = {1, 9} {the elements common to X and Z}

X' = {2, 4, 6, 8} {all the elements in the universal set not in X}

Therefore, the information from the given set have the following solutions for:

a) X ∪ Y = {1, 3, 5, 6, 7, 9}

b) X ∩ Z = {1, 9}

c) X' = {2, 4, 6, 8}

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Answer:

4/23

Step-by-step explanation:

I Did The Quiz :)

Tayjen's kite flew 5,860 centimeters in the air then Tayjen's kite flew 10.6 meters higher than Sara's kite.

What is BODMAS?

BODMAS is an acronym used to remember the order of operations in arithmetic. The acronym stands for:

B - Brackets (or Parentheses)

O - Orders (exponents and roots)

DM - Division and Multiplication (performed left to right)

AS - Addition and Subtraction (performed left to right)

BODMAS provides a set of rules that dictate the order in which mathematical operations should be performed in an expression that contains multiple operations. It is important to follow the order of operations to ensure that the expression is evaluated correctly and consistently. For example, in the expression 5 + 3 x 2, if we follow the BODMAS rule, we first perform the multiplication (3 x 2) and then the addition (5 + 6), giving us the answer of 11. If we were to perform the addition first, we would get a different answer (5 + 3 = 8, and 8 x 2 = 16), which would be incorrect.

To compare the height of Sara's kite, which is measured in meters, with the height of Tayjen's kite, which is measured in centimeters, we need to convert Tayjen's kite's height to meters.

To do that, we divide the height of Tayjen's kite by 100, since there are 100 centimeters in a meter:

5,860 centimeters ÷ 100 = 58.6 meters

Now we can compare the heights of the two kites:

58.6 meters - 48 meters = 10.6 meters

Therefore, Tayjen's kite flew 10.6 meters higher than Sara's kite.

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Answer: The equation of an ellipse with major axis of length 2, minor axis of length 5, center at (-1, -2), and major axis aligned with the vertical axis, can be given by:

((x + 1)/2)^2 + ((y + 2)/5)^2 = 1

The standard form of an ellipse is:

(x^2)/a^2 + (y^2)/b^2 = 1,

where a and b are the lengths of the major and minor axes, respectively. To convert the equation to this form, we can divide both the x and y terms by the corresponding axis lengths, and shift the center of the ellipse to the origin.

Step-by-step explanation:

Answer: If the transformation of the parent function f(x) = √x is a reflection over the x-axis, it means that the graph of the transformed function g(x) is obtained by reflecting the graph of f(x) over the x-axis.

The reflection of the function f(x) over the x-axis is obtained by negating its output, so the function g(x) can be written as:

g(x) = -√x

So the transformed function g(x) is a reflection of the parent function f(x) = √x over the x-axis.

Step-by-step explanation:

Answer:

Step-by-step explanation:

twelve triangles make 2 hexagons, which means there are 12 groups of in 2

The general equation of a circle is (x-h)² + (y-k)² = r²

Where,

Here we are given the equation (x+4)² + (y+5)² = 64 and given this we are asked to find the diameter as well as the coordinates of the center.

Finding the center

If (h,k) = center, then the coordinates of the center are the given values of h and k but negative. This is because the values are being subtracted from x and y. (x-h)² + (y-k)² = r²

This means that, (x+4)² + (y+5)² = 64 is the same as saying (x-(-4))² + (y-(-5))² = 64 based off of the general equation of a circle.

Notice how the plugged in values are negative rather than positive.

In conclusion, we can say that the center is at (-4,-5) (see attached image below to check answer)

In the equation, 64 takes the place of r²

So r² = 64

Taking the square root of both sides we get r = 8

So the radius is 8.

To convert to diameter we multiply by 2

So diameter = 8 * 2 = 16

In conclusion, a circle with the equation (x+4)² + (y + 5)² = 64, has a center  at (-4,-5) and a diameter of 16

Rounding to the nearest degree, the angle between the vector i + √5j and the positive direction of the x-axis is approximately 63 degrees.

The angle between a vector and the positive direction of the x-axis can be found using the inverse tangent function, also known as arctan. The formula for finding the angle θ between a vector (x, y) and the positive x-axis is given by:

θ = arctan(y/x)

In this case, the vector is i + √5j, so x = 1 and y = √5. Plugging these values into the formula, we get:

θ = arctan(√5/1) = arctan(√5)

The arctan function returns the angle in radians, so we'll need to convert it to degrees. To do this, we multiply by 180/π:

θ = arctan(√5) * (180/π) = 63.43 degrees (rounded to two decimal places)

So, Rounding to the nearest degree, the angle between the vector i + √5j and the positive direction of the x-axis is approximately 63 degrees.

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Answer: 54

Step-by-step explanation:

Answer:

260

Step-by-step explanation:

Substitute: (-2 · 7)² – 2 x (-2)⁵

Remove parenthesis: (2 · 7)² + 2 · 2⁵

Calculate the first two terms: 14ײ + 2 × 2⁵

Calculate the power: 196 + 2 × 32

Calculate the first two terms: 196 + 64

Calculate the first two terms: 260

Answer: 260

If the variance in the thickness of 20 textbooks is 0.0665 , then the random error in the mean value is  ±0.1207 inches and the confidence interval is (1.013 ± 0.1207) inches  .

The number of textbooks (number of observations) , n = 20 ;

So , v = n - 1 = 20 - 1 = 19 ;

For v = 19 and 95% confidence interval , we have t = 2.093  ;

The variance (σ²) is = 0.0665 ;

So , σ = √0.665 = 0.258 inches ;

We know that , Random Error (Δ) = tσ/√n = (2.093 × 0.258)/√20

= 0.1207 ;

The mean of the thickness of textbooks is ( [tex]\bar x[/tex] ) = 1.013 inches ;

So , the Random Error in the mean is = ±Δ = ±0.1207 inches ;

and the 95% confidence interval is = [tex]\bar x[/tex] ± Δ

⇒ (1.013 ± 0.1207) inches ;

Therefore , the Random Error is ±0.1207 inches , and the interval is (1.013 ± 0.1207) inches .

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substitute y

3x - 2(6 + 4x) = 3

3x - 12 -8x = 3

-5x - 12 = 3

- 5x = 15

x = -3