Brian says the graph shows the circle with a center (-3, 2) and a radius of 2. Mia says the graph shows all possible centers for a circle that passes through (-3, -2) with a radius of 2. Which student is correct? Explain.

The transformation of Δ ABC  to ΔADE is a dilation by a scale factor of 1/2 and then 180 degrees rotation about the origin.

We have,

In ΔABC,

The coordinates of each point are:

A = (0, 0)

B = (0, -6)

C = (8, -6)

And,

ΔADE,

A = (0, 0)

D = (0, 3)

E = (4, 3)

Now,

We can see that,

If we use a scale factor 1/2 on each the coordinates of A, B, and C and rotated to 180 degrees about the origin.

We get,

A = (0, 0) = (0, 0)

B = (0, - 6) = (0, -3) = (0, 3)

C = (8, -6) = (4, -3) = (4, 3)

Thus,

The transformation of Δ ABC  to ΔADE is a dilation by a scale factor of 1/2 and then 180 degrees rotation about the origin.

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Answer: 6

Step-by-step explanation:

(-4 + 7) x (-4 - 7)

 \/ \/

 possitive 3 possitive 3

 3x3= 6

The required measure of point P above the sea level is 6717.22 feet.

Given that,

A is known to be 6,500 feet above sea level; AB = 230 feet.

And, The angle at A looking up at P is 20°.

The angle at B looking up at P is 35°.

Since, These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,

Let the horizontal distance between A and Q be x and the vertical distance between P and Q be h.

Now,

tan20 = h / x

034x = h

Now,

tan35 = [230 + h]/x

0.7x = 230 + 0.34x

x = 636.89

Now,

h = 0.34 x 636.89

h = 217.2

Now,

The measure of peak P above sea level = 217.2 + 6500 = 6717.22

Thus, the required measure of point P above the sea level is 6717.22 feet.

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Zero:

x = 0,

Multiplicity:

1,

Effect:

Intersects x-axis at x = 0

Zero:

x = 1,

Multiplicity:

1,

Effect:

Intersects x-axis at x = 1

Zero:

x = -2/5,

Multiplicity:

3,

Effect:

Intersects x-axis at x = -2/5 =0 with a steep curve

The zeros, multiplicity, and effect of the function f(x) = 3x(x - 1)˚ (5x + 2)³, we need to factor the expression.

First, let's identify the zeros by setting the expression equal to zero and solving for x:

3x(x - 1)˚ (5x + 2)³ = 0

Setting each factor equal to zero:

3x = 0 --> Zero: x = 0

x - 1 = 0 --> Zero: x = 1

(5x + 2)³ = 0 --> Zero: x = -2/5

Now, let's determine the multiplicity and effect of each zero:

Zero:

x = 0

To determine the multiplicity, we look at the exponent of the factor (x) in the expression.

The factor x has a multiplicity of 1 since it appears once.

The effect of this zero is that it is a root of the function and causes the graph to intersect the x-axis at x = 0.

Zero:

x = 1

Similar to the previous case, the factor (x - 1) has a multiplicity of 1 since it appears once.

The effect of this zero is that it is a root of the function and causes the graph to intersect the x-axis at x = 1.

Zero:

x = -2/5

The factor (5x + 2) has a multiplicity of 3 because it appears cubed (exponent of 3).

The effect of this zero is that it is a root of the function and causes the graph to intersect the x-axis at x = -2/5 with a steep curve, as it is raised to the power of 3.

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1. The tax rate is 5%.

2. The discounted rate is 24.9%.

Let x be the tax rate as a decimal.

The discounted price = Original price * The discount rate (1 - discount percentage). The discounted price is:

26.63 = 35.50 * (1 - discount percentage)

Solving discount percentage

Discount percentage = 1 - (26.63 / 35.50)

Discount percentage = 0.249

Discount percentage = 24.9%.

To get tax rate, we will: Total price = discounted price + (discounted price * tax rate).

27.96 = 26.63 + (26.63 * x).

Solving for x

x = (27.96 - 26.63) / 26.63

x = 0.04994

x = 0.05

x =  5%.

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The statements that is missing is " 2x -6 +10x = 15 + 5x and this step is justified by the distributive property.

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

For example, (2x+6) ( 5x +4) is thesame as

2x( 5x+4) 6( 5x +4)

This law is called distributive property.

Similarly, Julian solving should go like this;

2( x -3) + 10x = 5( 3+x)

2x -6 +10x = 15 +5x

collecting like terms

2x -5x +10x = 15 +6

= 7x = 21

x = 3

Therefore the statement that shows the Missing step is 2x -3 +10x = 15+ x and it is justified by distributive property.

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The length of the other leg of the right triangle is 13.9 cm.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of the right triangle can be named according to it angle position as hypotenuse side, adjacent side and opposite side.

Therefore, let's find the other leg of a right triangle with hypotenuse as 19 cm and one leg as 13 cm using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore,

b = √19² - 13²

b = √361 - 169

b = √192

b = 13.8564064606

Therefore,

length of the other leg = 13.9 cm

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The shapes matched to the correct answers are given as follows.

A  = 3  - SAS

B = 1  Not Similar

C = 4 - SSS

D = 2 - AA

SAS stands for "side, angle, side," and it denotes that we have two triangles with two sides and an included angle that are equal.

The triangles are congruent if two sides and the included angle of one triangle are equivalent to the corresponding sides and angle of another triangle.

From A, we can see that ΔFEQ is similar to ΔRSQ because the ration of their sides are similar. That is

EQ/FQ = SQ/RQ

⇒ 36/18 = 48/24

⇒ 2 = 2

Also since they share the same angle EQF and SQR (congruence of opposite angles)

then A  = 3  - SAS

B)  B = 1 - that is both triangles are not similar. If the above principles are applied, we would find that none of the sides have similar ratio.

For example,

48/28 ≠ 36/20

Thus, B =  1  Not Similar

C  = 4 - SSS

this is because all side are similar.

BC: TU = 9:1
BD : SU = 9:1

DC : TS = 9:1

Hence, Side - Side - Side postulate applied.

D. In tis case we are given triangles with two similar angles each so Angle - Angle postulate applies. That is D =  2 - AA

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Answer:

Step-by-step explanation:

Find the square of 25/9. Thought the answer was 5/3 but the test prep answer key has 7 58/81

[tex](\frac{25}{9} )^2\\=(\frac{5}{3} )^4\\= \frac{625}{81}[/tex]Answer:

Step-by-step explanation:

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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The equation of the circle with center (-4, 4) and passing through (-2, 4) is [tex](x + 4)^2 + (y - 4)^2 = 4.[/tex]

We have,

To determine the equation of a circle, we need the center coordinates and the radius. The center coordinates are given as (-4, 4), and we have a point on the circle as (-2, 4).

The distance between the center (-4, 4) and the point on the circle (-2, 4) represents the radius of the circle.

Using the distance formula.

[tex]radius = √[(x_2 - x_1)^2 + (y_2 - y_1)^2]\\= \sqrt{(-2 - (-4))^2 + (4 - 4)^2}\\= \sqrt{2^2 + 0^2}\\= \sqrt{4}\\= 2[/tex]

Now that we have the center coordinates (-4, 4) and the radius 2, we can write the equation of the circle in standard form:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Substituting the values:

[tex](x - (-4))^2 + (y - 4)^2 = 2^2\\(x + 4)^2 + (y - 4)^2 = 4[/tex]

Therefore,

The equation of the circle with center (-4, 4) and passing through (-2, 4) is [tex](x + 4)^2 + (y - 4)^2 = 4.[/tex]

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The estimated number of collisions in 1998 is 4,262.

The n-intercept of 8.06 represents the estimated number of collisions at highway-railroad crossings in the year 1980

We have,

n = -0.211t + 8.06

a. To estimate the number of collisions in 1998, we need to find the value of n when t = 1998 - 1980 = 18. Substitute this value into the equation:

n = -0.211(18) + 8.06

n ≈ -3.798 + 8.06

n ≈ 4.262

Therefore, the estimated number of collisions in 1998 is 4,262.

b. The n-intercept of the linear model represents the value of n when t = 0. Let's substitute t = 0 into the equation and solve for n:

n = -0.211(0) + 8.06

n ≈ 8.06

In this situation, the n-intercept of 8.06 represents the estimated number of collisions at highway-railroad crossings in the year 1980, which is the starting point of the time frame under consideration.

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Sure, here is a diagram of a plane flying on a bearing of 140 degrees for 90km:

[Image of a plane flying on a bearing of 140 degrees for 90km]

The distance traveled south is 60km and the distance traveled east is 53.5km.

To calculate the distance traveled south, we can use the following formula:

distance = (90km * sin(140 degrees)) / 180 degrees

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This gives us a distance of 60km.

To calculate the distance traveled east, we can use the following formula:

distance = (90km * cos(140 degrees)) / 180 degrees

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This gives us a distance of 53.5km.

The measurement that is closest to the volume of the sphere is given as follows:

1,767.1 in³.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:

r = 0.5 x 15

r = 7.5 units.

Then the volume of the sphere is given as follows:

V = 4/3 x π x 7.5³

V = 1,767.1 in³.

The sphere is given by the image presented at the end of the answer.

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The statement is not true because random sampling does not eliminate all potential sources of bias and variability in the sample selection process.

Other factors and variables that influence study outcomes include sampling bias, sample size, sampling frame, selection methods, population heterogeneity, and study design and execution.

The statement that random sampling guarantees a representative sample of the population is not entirely true.

While random sampling is a valuable method to increase the likelihood of obtaining a representative sample, it does not provide an absolute guarantee.

There are several factors and variables that can influence the outcomes of studies, even with random sampling.

Sampling Bias: Despite random sampling, certain biases can still occur. For example, non-response bias can arise if selected individuals choose not to participate or are unavailable, which can lead to a non-representative sample.

Sample Size: The size of the sample plays a crucial role in its representativeness.

If the sample size is too small, it may not accurately reflect the diversity and characteristics of the population, leading to biased results.

Sampling Frame: The sampling frame refers to the list or method used to identify potential participants.

If the sampling frame is incomplete or inaccurate, the resulting sample may not be representative of the entire population.

Selection Methods: Random sampling is just one method of selecting a sample. Other sampling methods, such as stratified sampling or convenience sampling, may introduce additional biases and affect the representativeness of the sample.

Population Heterogeneity: The variability and diversity within the population can impact the representativeness of the sample.

If the population is highly heterogeneous, it may be challenging to capture all its characteristics accurately.

Study Design and Execution:

The design and execution of the study, including survey questions, data collection methods, and potential confounding variables, can influence the outcomes and introduce biases.

While random sampling is a valuable tool, researchers must consider and address these factors and variables to enhance the representativeness and reliability of their study results. It is essential to employ rigorous methodologies and employ statistical techniques to account for potential biases and limitations.

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Kelvin and Fiona had a total of 200 + 200 = 400 postcards left together. Let's assume that Kelvin had x postcards initially. Fiona would then have (600 - x) postcards since they had a total of 600 numbers postcards altogether.

After Kelvin donated 2/7 of his postcards, he would have (1 - 2/7)x = (5/7)x postcards left.

Fiona gave away 120 postcards, so she would have (600 - x - 120) = (480 - x) postcards left.

According to the problem, both Kelvin and Fiona had the same number of postcards left. Therefore, we can set up an equation:

(5/7)x = 480 - x

Multiplying both sides of the equation by 7 to eliminate the fraction, we get:

5x = 3360 - 7x

Combining like terms, we have:

12x = 3360

Dividing both sides by 12, we find:

x = 280

So, Kelvin initially had 280 postcards, and Fiona had (600 - 280) = 320 postcards.

After Kelvin donated 2/7 of his postcards, he had (5/7) * 280 = 200 postcards left.

After Fiona gave away 120 postcards, she had (320 - 120) = 200 postcards left.

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Answer:

Step-by-step explanation:

[tex]\frac{1}{cosx} . \frac{1}{sinx} =\frac{2}{sinx}\\ \frac{1}{cosx} . \frac{1}{sinx} - \frac{2}{sinx} = 0\\\frac{1}{sinx}(\frac{1}{cosx} - 2) = 0\\\frac{1}{cosx} = 2\\cosx = \frac{1}{2} \\x = 60[/tex]

1. Triangles ABC and DEF are not similar

2. Triangle JMN and JKL are similar

3. Triangle ABC and XYZ are similar

4. Triangle PQR is not similar to RST

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two angles to similar, the corresponding angles must be equal and the ratio of corresponding sides are equal.

1. 30/24 is not equal to 24/18, therefore the two triangles are not similar.

2. Since MN is parallel to KL then

M = K ( corresponding angles) , therefore the two triangles are similar.

3. 22/33 = 30/45

= 2/3 = 2/3

therefore the two triangles are similar.

4. 10/4.5 is not equal to 9/5

therefore the two triangles are not similar.

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Answer:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

Using the least-squares regression method, the line of best fit is line d.

According to the graph, we can see that the sum of distance to line d is smallest ( least-square).

Least-squares regression is a statistical technique employed to ascertain the optimal line of best fit within a dataset. This line is determined by minimizing the total sum of squared discrepancies between the observed y-values and the predicted y-values that lie on the line.

In this method, we aim to find the line that best captures the relationship between the variables by minimizing the squared differences. By doing so, we strive to minimize the overall error and maximize the accuracy of the line in representing the data.

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The total mass of the packages is 37.67 kg

From the question, we have the following parameters that can be used in our computation:

Packages    Mass (kg)

1                         3.94

2                      14.81

3                          11.27

4                           7.65

The total mass of the packages is the sum of each mass

using the above as a guide, we have the following:

Total mass = 3.94 + 14.81 + 11.27 + 7.65

Evaluate the sum

So, we have

Total mass = 37.67

Hence, the total mass of the packages is 37.67 kg

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The statement about the function is: "The function is decreasing for all real values of x where x < -4." D.

The given information tells us that the graph represents a downward-opening parabola.

The vertex of the parabola is located at (-4, 4) indicates that this point is the highest point on the graph.

As we move to the left of the vertex, the function values decrease, indicating a decreasing trend.

Moreover, the graph passes through the point (-6, 0), which lies to the left of the vertex.

This confirms that the function is decreasing for all real values of x less than -4, including x < -6.

On the other hand, the graph also passes through the point (-2, 0), which lies to the right of the vertex.

This does not impact the conclusion that the function is decreasing for x < -4, as the graph's behavior to the right of the vertex is not relevant to this particular statement.

Based on the given information and the properties of the downward-opening parabola, we can conclude that the function is decreasing for all real values of x where x < -4.

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5. The probability that the sample mean weight is greater than 3.55 kilograms is about 0.1230.

6. The probability that less than 20% of the sample is from poverty-level households is about 0.2119.

The probability that the sample mean weight is greater than 3.55 kilograms is determined as follows;

The standard error of the mean is determined using the formula:

where;

Substituting the given values:

SE = 0.5/√15

SE ≈ 0.1291

The z-score corresponding to this value will be:

z = (3.55 - 3.4) / 0.1291

z ≈ 1.16

Using a calculator, the probability of a z-score being greater than 1.16 is about 0.1230.

6. The standard error of a proportion is determined using the formula:

where;

Substituting the given values:

SE = √[0.22(1-0.22)/300]

SE ≈ 0.0251

The z-score corresponding to this value will be:

z = (0.20 - 0.22) / 0.0251

z ≈ -0.80

Using a calculator, the probability of a z-score being less than -0.80 is about 0.2119.

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Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

Answer:

Step-by-step explanation:

A = 10 cm - 4cm = 6cm

B =

[tex]\sqrt{4^2+7^2}\\ = \sqrt{16+49}\\ = \sqrt{65}[/tex]

C  =  [tex]\sqrt{10^2+3^2}\\ = \sqrt{109}[/tex]

D = [tex]\sqrt{10^2+6^2}\\ = \sqrt{136}[/tex]

The graph of the piecewise function g(x) is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The definitions to the function in this problem are given as follows:

Hence the graph of the piecewise function g(x) is given by the image presented at the end of the answer.

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5. The probability that exactly four adults out of 19 say cashews are their favorite nut is approximately 0.252.

6. The probability that 12 or more stolen bikes will be returned out of 335 is approximately 0.181.

a. Probability of exactly four adults saying cashews are their favorite nut:

n = 19 (number of trials)

k = 4 (number of successes)

p = 0.49 (probability of success)

Using the formula, we have:

P(X = 4) = (¹⁹C₄) * 0.49⁴ * (1 - 0.49)¹⁵

Calculating the binomial coefficient:

((¹⁹C₄) = 19! / (4! * (19 - 4)!) = 3876

Calculating the probability:

P(X = 4) = 3876 * 0.49⁴ * (1 - 0.49)¹⁵ ≈ 0.252

b. Probability that 12 or more stolen bikes will be returned:

n = 335 (number of trials)

k = 12, 13, ..., 335 (number of successes, from 12 to 335)

p = 0.03 (probability of success)

We want to find the sum of probabilities for k = 12 to 335.

P(X ≥ 12) = P(X = 12) + P(X = 13) + ... + P(X = 335)

Calculating each probability:

P(X = k) = (³³⁵C k) * [tex]0.03^{k}[/tex] * (1 - 0.03) [tex]^{335 - k}[/tex]

Calculating the binomial coefficients for each k:

(³³⁵ C ₁₂) = 335! / (12! * (335 - 12)!) ≈ 7.27587e+22

(³³⁵ C ₁₃) = 335! / (13! * (335 - 13)!) ≈ 2.21733e+23

...

(³³⁵ C ₃₃₅) = 335! / (335! * (335 - 335)!) = 1

Calculating the probabilities and summing them up:

P(X ≥ 12) ≈ P(X = 12) + P(X = 13) + ... + P(X = 335) ≈ 0.181

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The standard deviation of the population function x is 2.

We have,

To find the standard deviation of the population function x, we need the mean M(x) and the mean of the squared values M(x²).

So,

Standard Deviation = √[M(x²) - (M(x))²]

Given that M(x) = 2 and M(x²) = 8, we can substitute these values into the formula:

Standard Deviation = √[8 - (2)²]

Standard Deviation = √[8 - 4]

Standard Deviation = √4

Standard Deviation = 2

Therefore,

The standard deviation of the population function x is 2.

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