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On a coordinate plane, 2 triangles are shown. Triangle D E F has points (6, 4), (5, 8) and (1, 2). Triangle R S U has points (negative 2, 4), (negative 3, 0), and (2, negative 2).

Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?

ΔDEF ≅ ΔSUR
ΔDEF ≅ ΔSRU
ΔDEF ≅ ΔRSU
ΔDEF ≅ ΔRUS

Answer: I think it’s (2x+y)•(4x2-2xy+y2)•(2x-y)•(4x2+2xy+y2)

The table showing the exponential function is completed and presented below  

x      y

0    96

1    192

2   384

3   768

The expression for the table is given as

y = a * b^x,

Point (0, 96) is on the table.

a = 96,

when b = 2, we have that

for x = 1

y = 96 x 2^x = 96 x 2^1 = 192

for x = 2

y = 96 x 2^x = 96 x 2^2 = 384

for x = 3

y = 96 x 2^x = 96 x 2^3 = 768

Therefore, The required exponential function will be  

x      y

0    96

1    192

2   384

3   768

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1. The probability that the number picked is divisible by either 4 or 5 or both is 0.4. 2. The probability that the number picked is divisible by 4 and not 3 is 0.167.

1. Using the principle of inclusion-exclusion. There are 250 integers between 1 and 1000 that are divisible by 4, and 200 integers that are divisible by 5.

However, some integers are divisible by both 4 and 5 (i.e., by 20), and we have counted them twice. There are 50 integers in the range [1, 1000] that are divisible by 20.

So, the number of integers between 1 and 1000 that are divisible by either 4 or 5 or both is:

250 + 200 - 50 = 400

Therefore, the probability that the integer picked is divisible by either 4 or 5 or both is:

400/1000 = 0.4

2. Using the principle of inclusion-exclusion again, there are 250 integers between 1 and 1000 that are divisible by 4, and 333 integers that are not divisible by 3.

There are 250 integers in the range [1, 1000] that are divisible by 4, and 83 integers that are divisible by 12.

So, the number of integers between 1 and 1000 that are divisible by 4 but not 3 is:

250 - 83 = 167

Therefore, the probability that the integer picked is divisible by 4 and not 3 is:

167/1000 = 0.167

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Answer:

First, let's find the equation of the circle with a centre at (-4,5). the standard form of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the centre of the circle and r is the radius.

So, substituting the center point (-4,5) into the equation, we get:

(x - (-4))^2 + (y - 5)^2 = r^2

(x + 4)^2 + (y - 5)^2 = r^2

Now, let's find the slope of the line 2x + 3y = -19 by putting it into slope-intercept form:

2x + 3y = -19

3y = -2x - 19

y = (-2/3)x - (19/3)

The slope of this line is -2/3.

At a given location, the tangent to a circle is perpendicular to the radius. As a result, we must calculate the radius of the circle with centre (-4,5) that passes through the line's point of tangency (x,y).

The radius of the circle is equal to the length of the perpendicular line segment from the centre to the tangent line (-4,5). This perpendicular line segment will be denoted by the letter d.

We may use the formula for the distance between a point and a line to get d. The distance d between the point (x,y) and the line 2x + 3y = -19 is calculated as follows:

d = |2x + 3y + 19| / sqrt(2^2 + 3^2)

To be tangent to the circle, the radius should be equal to d. Let's call this radius r.

So, we have two equations:

(x + 4)^2 + (y - 5)^2 = r^2 (equation of circle)

d = |2x + 3y + 19| / sqrt(13) (equation of distance between point and line)

Substituting d = r into the second equation, we get:

r = |2x + 3y + 19| / sqrt(13)

We can now substitute this expression for r into the equation of the circle:

(x + 4)^2 + (y - 5)^2 = (|2x + 3y + 19| / sqrt(13))^2

Since the point of tangency lies on the line 2x + 3y = -19, we can substitute (-19 - 3y)/2 for x in the above equation and solve for y:

((-19 - 3y)/2 + 4)^2 + (y - 5)^2 = (|2((-19 - 3y)/2) + 3y + 19| / sqrt(13))^2

Simplifying and solving for y, we get:

y = -5 ± 2√13

Therefore, the two tangent points are (-19/2, -5 + 2√13) and (-19/2, -5 - 2√13).

Answer:48 yd2

Step-by-step explanation:

The area of the yard that William would have to mow would be C. 112 yards ²

To find the area to be mowed, find the area of the entire yard including the porch, and then the area of the porch, and then subtract the area of the porch.

Area of yard :

= 12 x 12

= 144 yard ²

The area of the porch is:

= ( 12 - 8 ) x ( 12 - 4 )

= 4 x 8

= 32 yards ²

The area to be mowed is:

= 144 - 32

= 112 yards ²

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The range of Box A is 31 grams which is smaller.

Given that, Jaxon bought two boxes of eggs at a market and recorded the mass of each egg in the stem-and-leaf diagram,

So, the ranges are ;

Box A = 76 - 45 = 31 grams

Box B = 78 - 43 = 35 grams

Therefore, we see that the range of the box A is smaller than the range of the box B.

Hence, the range of Box A is 31 grams which is smaller.

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Answer:

$78.7092

Step-by-step explanation:

He wants to buy a skateboard. The percentage value of the skateboard before any changes is 100%. So $73.56 = 100%. Now when you add a sales tax to it, the price will increase by 7% so it'll now be 107% right? You just have to find how much the 107% is equal to.

100% = 73.56

1% = 73.56÷100 = 0.7356

107 % = 0.7356 × 107 = 78.7092

The point that could be the location of the other end of the wall will be (0, 5).

By using one or more elements or coordinates, a reference frame can properly pinpoint location alongside other mathematical components on such space, including Euclidean space.

A point or object in a two-dimensional plane can be found by utilizing its coordinates, which appear to be sets of integers. The y and x vectors can be used to identify the position of a point on a double surface. a group of photos used to identify certain areas.

In conclusion, the point that could be the location of the other end of the wall will be (0, 5).

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

Stem | Leaf

1| 9

2| 5 9

3| 0 3 3 8

4| 0 7 9

5| 4 5

6| 1 5

7| 2 7

8| 1

Step-by-step explanation:

Minimum: 19

Maximum: 81

Range: 62

Count: 17

Sum: 808

Mean: 47.53

Median: 47

Mode: 33

Standard Deviation: 18.9

Variance: 357.3

1. The quadratic regression model is [tex]Y = b0 + b1X + b2X^2[/tex] . The regression coefficient b2 represents the rate of change in muscle mass with respect to age squared. 2. The quadratic term can not be dropped from the regression model, since the calculated F-value is less than the critical value. 3. The fitted regression function in terms of the original variable X is [tex]Y = 87.017 + 0.241X - 0.002X^2[/tex].

To determine the quadratic regression model follow these steps:

1. Using R program, the quadratic regression model:

[tex]Y = b0 + b1X + b2X^2[/tex]

where Y is the muscle mass, X is the age.

The regression coefficients are:

b0 = 283.962

b1 = -14.501

b2 = 0.162

The regression coefficient b2 (quadratic term) represents the rate of change in muscle mass with respect to age squared. It measures the acceleration or deceleration of the change in muscle mass as the age increases.

2. Using the F-test.

[tex]F = [SSR(x,x^2) - SSR(x)] / [(k - 1) * MSE][/tex]

where k = number of coefficients = 3 (b0, b1, b2).

MSE = Mean Squared Error = 47.086

[tex]SSR(x,x^2), SSR(x) =[/tex] Sum of Squares due to Regression with both X and [tex]X^2[/tex]  as predictors = 230.74, due to Regression with only X as predictor = 135.03

Therefore,

[tex]F = [230.74 - 135.03] / [(3 - 1) * 47.086] = 2.214[/tex]

Using a significance level the critical value for F-test is 5.143.

Since the calculated F-value (2.214) is less than the critical value (5.143), we fail to reject the null hypothesis. Therefore, there is not enough evidence that quadratic term can be dropped from regression model.

3. The fitted regression function in terms of the original variables:

[tex]Y = 87.017 + 0.241X - 0.002X^2[/tex]

where X is the age and Y is the measure of muscle mass.

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It should be noted that to obtain measurements for the Prism or Pyramid:

- Identify prism or pyramid as 3-D shape

- Measure length, width, and height

- Calculate base area. For a prism: find the base's dimension (i.e., rectangle or triangle) and multiply it by height. For a pyramid: halve the calculation of the base and then multiply it by height.

- To calculate volume, obtain the product of the base area and height

- Compute surface area via summation of each face, including the base.

Also, to determine measurements for Cone or Cylinder:

- Recognize cone or cylinder as 3-D shape

- Take note of dimensions through measuring the radius and the height

- Compute for Area of Base. For a cone, use the formula πr^2; while for a cylinder, make use of 2πr^2 instead  

- In order to measure volume of a cone, get the result of multiplying base area by height and dividing by 3. Meanwhile, the cylinder requires solely multiplying the base area by height.

- Tabulate surface area for cone after applying Pythagorean theorem to solve slant height divided by curved surface area with formula πrl. Do not neglect inclusion of base area in computation.

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The number of pods of peas would be 38. So there are 38.038 pods of peas for Gregor Mendel to examine.

To find out how many pods of peas there are, you simply need to divide the total number of peas by the number of peas per pod. In this case, Gregor Mendel has 228 peas, and each pod contains 6 peas.

Step 1: Divide the total number of peas by the number of peas per pod.
228 peas ÷ 6 peas/pod = 38 pods
Number of peas = 22.8228
Peas per pod = 6

Therefore, the number of pods of peas would be:
22.8228/6 = 38.038
So, there are 38 pods of peas for Gregor Mendel to examine in his study of traits passed from parents to offspring.

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Which sends 1 to 2, and then apply the permutation (1,3) to the result, which sends 2 to 3. So (1,3)(1,2) = (1,2,3), not (1,3,2).

(a) To write f as a product of transpositions, we can track the movement of each number in the permutation. Starting from 1, we see that it goes to 4, which means we can write the transposition (1,4). Next, we look at where 4 goes, which is to 6, so we can write the transposition (4,6). Continuing this process, we get:

f = (1,4)(4,6)(6,9)(9,8)(8,5)(5,2)(2,1)(7,3)

So f can be written as the product of the transpositions (1,4), (4,6), (6,9), (9,8), (8,5), (5,2), (2,1), and (7,3).

(b) To find f-1, we need to reverse the order of the transpositions in f and also reverse each transposition. For example, the transposition (1,4) becomes (4,1). Applying this process to all the transpositions in f, we get:

f-1 = (3,7)(1,2)(2,5)(5,8)(8,9)(9,6)(6,4)(4,1)

So f-1 can be written as the product of the transpositions (3,7), (1,2), (2,5), (5,8), (8,9), (9,6), (6,4), and (4,1).

(c) The rule for multiplication of permutations (fg)(x) = f(g(x)) means that we apply the permutation g to x first, and then apply the permutation f to the result. For example, if we have the permutations f = (1,2,3) and g = (1,3), then (fg)(1) = f(g(1)) = f(3) = 2. To see why this is true, note that g sends 1 to 3, and then f sends 3 to 2.

Using this rule, we can see that (1,3)(1,2) means that we apply the permutation (1,2) first, which sends 1 to 2, and then apply the permutation (1,3) to the result, which sends 2 to 3. So (1,3)(1,2) = (1,2,3), not (1,3,2).

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Answer:

Step-by-step explanation:

Tam's initial amount of money = $74

Tam spends $5 on lunch, so she has $74 - $5 = $69 left.

Tam's parents double the money she has left, so she now has $69 x 2 = $138.

Tam adds all the money to the $148 in her savings account, so her total amount of money becomes $138 + $148 = $286.Expression that models this series of events: 148 + 2(74-5)For Sarah:

Sarah starts with $18.

Sarah doubles her money, so she now has $18 x 2 = $36.

Sarah subtracts $9 from her current amount, so she now has $36 - $9 = $27.

Sarah adds $50 to her current amount, so she now has $27 + $50 = $77.A possible series of events that led to Sarah's current amount of money: Starts with $18, doubles it to $36, subtracts $9, and then adds $50.

The value of cos X is approximately given as .80000.

The correct answer choice is option C.

Hypotenuse = 50

Adjacent = 30

Opposite = 40

cos X = adjacent / hypotenuse

= 30/50

= 0.6

Cos 0.6 = 0.825335614

Approximately,

.80000

Hence, cos X is .8000

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ANSWER:    ln(x) is indeed continuous on [1,4] and differentiable on (1,4) therefore it satisfies the hypothesis of the mean value theorem.

WHY:

The mean value theorem states that the slope of the secant line connecting the points (x1, f(x1)), (x2, f(x2)) equals the slope of the tangent line at some c in the open interval (x1, x2)

The slope of the secant line, say m = ln(4) - ln(1) / (4-1) = ln(4) / 3

f'(x) = 1/x

Setting the derivative equal to the slope of the secant and solving for x:

1/x = ln(4) / 3

x = 3 / ln(4)

Since 3 / ln(4) ~ 2.16, this value of x does indeed fall in the open interval (1,4) and so satisfies the conclusion of the mean value theorem. Therefore the function satisfies the conclusion of the mean value theorem on [1, 4] with c = 3 / ln 4

The mean value theorem states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in the open interval (a, b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

In other words, there exists a point c in the interval where the instantaneous rate of change (slope of the tangent line) is equal to the average rate of change (slope of the secant line) between the endpoints of the interval.

For the given function f(x) = sqrt(x) on the interval [0, 4], we can first find the average rate of change using the endpoints:

(f(4) - f(0)) / (4 - 0) = (2 - 0) / 4 = 1/2

To find the point c where the instantaneous rate of change is equal to 1/2, we can take the derivative of f(x):

f'(x) = 1 / (2sqrt(x))

Setting f'(c) equal to 1/2 and solving for c, we get:

1 / (2sqrt(c)) = 1/2
sqrt(c) = 2
c = 4

Therefore, the number c that satisfies the conclusion of the mean value theorem on the interval [0, 4] is 4.

To determine if the secant line and the tangent line are parallel, we need to compare their slopes. The slope of the secant line between the endpoints [0, 4] is 1/2, as we found earlier. The slope of the tangent line at x = 4 is:

f'(4) = 1 / (2sqrt(4)) = 1/4

Since the slopes are not equal, the secant line and the tangent line are not parallel. Therefore, the statement "2. False" is correct.

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The area of each shaded sector of a circle with radius 6 units and measure of central angle 36 degrees is approximately equals to the 11.31 square units.

The area of a sector is defined as the space inside a section of the circle made by two radius and an arc. The area of a circular sector is written by the following formula [tex]Area = \frac{θ}{360°}\pi \: r^2[/tex], where, r represents the radius

See the above figure, we have a circle with radius of circle, r = 6 units

Measure of central angle, θ = 36°

Area of circle = πr²

Substitute all known values, so, Area = π× 6² = 36π

Using the formula for the area of a sector, Area of sector of circle with radius 6

[tex] = \frac{36°}{360°}π(6)²[/tex]

[tex]= \frac{1}{10} \times 36 × 3.14[/tex]

= 11.304 ~ 11.31

Hence, the required area of the shaded sector is approximately 11.31 square unit.

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Complete question:

The above figure complete the question.

Find the area of each shaded sector. Round to the hundredths place

Answer: Partitioning a Segment in a Given Ratio ; Find the coordinates of the point that divides the directed line segment · with the coordinates of endpoints at M(−4,0) ...

Step-by-step explanation:

The probability of selecting two families, neither of which had their taxes prepared by H&R Block is (7/10) * (6/9) = 42/90, which simplifies to 7/15.

a. There are a total of 10 families. 7 had taxes prepared by a local professional, and 3 by H&R Block. This means 0 families prepared their own taxes. The probability of selecting a family that prepared their own taxes is 0/10 = 0.

b. Since no families prepared their own taxes, the probability of selecting two families, both of which prepared their own taxes is 0.

c. Similarly, the probability of selecting three families, all of which prepared their own taxes is 0.

d. If we want to select two families, neither of which had their taxes prepared by H&R Block, we are looking for families that had their taxes prepared by a local professional. There are 7 such families. The probability of selecting the first family is 7/10. After selecting the first family, there are now 9 families left, 6 of which had their taxes prepared by a local professional. The probability of selecting the second family is 6/9. Therefore, the probability of selecting two families, neither of which had their taxes prepared by H&R Block is (7/10) * (6/9) = 42/90, which simplifies to 7/15.

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This statement is generally true.

When hydrogen is added to the structure of an oil through a process called hydrogenation, the oil becomes more saturated with hydrogen atoms, which reduces the amount of double bonds in the oil's molecules. This can cause the melting point of the oil to decrease and the oil to become more liquid and easier to pour. Additionally, hydrogenated oils tend to have a longer shelf life and are more stable at high temperatures, making them useful in many food processing applications.

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The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is given as follows:

(1.9, 2.3).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 18 - 1 = 17 df, is t = 1.33.

The parameters are given as follows:

[tex]\overline{x} = 2.1, s = 0.74, n = 18[/tex]

The lower bound of the interval is given as follows:

2.1 - 1.33 x 0.74/sqrt(18) = 1.9.

The upper bound of the interval is given as follows:

2.1 + 1.33 x 0.74/sqrt(18) = 2.3.

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The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.

c. Responsible, Accountable, Consult & Inform matrix

The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.

The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.

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The total amount she earned $945.75.

We have,

P= 900

bank A deposition= 550

R= 2.25%

So, the interest from Bank A

= 550/100 x 2.25

= 12.375

and, Interest from Bank B

= (900 - 550)/100 x 3

= 350/100 x 3

= 10.5

So, total she earned

= 10.5 + 12.375 = 22.875

In 2 years she will earned

= 22.875 x 2

= 45.75

Thus, the total amount she earned

= 900 + 45.75 = 945.75

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Answer:

83

Step-by-step explanation:

78 + 4= 83

Answer:

Please mark me the brainliest

Step-by-step explanation:

To solve the equation (6 – 2x)(3 – 2x)x = 40, we can start by simplifying the left-hand side:

(6 – 2x)(3 – 2x)x = 40

(18x – 12x^2 – 6x + 4x^2)x = 40

(2x^3 – 8x^2 + 18x)x = 40

2x^4 – 8x^3 + 18x^2 = 40

2x^4 – 8x^3 + 18x^2 – 40 = 0

We can try to factor this equation by grouping terms:

2x^4 – 8x^3 + 18x^2 – 40 = 0

2(x^4 – 4x^3 + 9x^2 – 20) = 0

2((x^2 – 2x + 1)(x^2 – 2x – 20)) = 0

2(x – 1)^2(x – 5)(x + 4) = 0

Therefore, the real solutions of the equation are x = 1 (with multiplicity 2), x = 5, and x = -4.

Now, to answer the question, we need to determine whether it is possible to cut squares with sides of 3/2 in. to make a box. We can use the value of x = 3/2 to find the dimensions of the box:

length = 6 – 2x = 6 – 2(3/2) = 3 in.

width = 3 – 2x = 3 – 2(3/2) = 0 in.

height = x = 3/2 in.

Since the width is 0, it is not possible to cut squares with sides of 3/2 in. to make a box. Therefore, the correct answer is:

No. It is not possible to cut squares of this size.

Answer:(2, 3)

Step-by-step explanation:

Because we are reflecting the point across the y axis, we know that we are changing the X coordinate. Reflecting across in this case, since there is no other given rule means we are changing the current X coordinate to be the negative version of itself, since it is already negative, this makes the new point a positive one.

This can be explained as moving the point across the given axis at the same distance as the original point from the axis, but in the opposite direction. If it is on the left of the axis, we move it the same distance from the axis to the right, and vice-versa.

We do not change the y coordinate, because we are reflecting the point across the Y axis, which is the vertical line that has an x origin of 0.

All of this means that the new coordinate for our point will be (2, 3).

The given parabola has its vertex at the origin and the directrix as a horizontal line passing through the point (0,-7), and the equation is y^2 = 28x, which opens to the right. So, the correct answer is A) The student's answer is correct.

To determine if the student's answer is correct, we need to check if the equation of the parabola and the direction of its opening match the given conditions.

The given parabola has its vertex at the origin and the directrix as a horizontal line passing through the point (0,-7). Therefore, the axis of symmetry is the y-axis, and the focus is located at (0,7).

The standard equation of a parabola with the vertex at the origin and the directrix as a horizontal line passing through the point (0,-p) is y² = 4px, where p is the distance from the vertex to the directrix. In this case, p = 7, so the equation of the parabola is y² = 28x.

The coefficient of x in the equation is positive, indicating that the parabola opens to the right. Therefore, the student correctly determined the direction of the parabola as well.

Hence, the answer is A. The student's answer is correct.

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