Using trial and improvement, find the solution between 3 and 4 for the following equation: 2 x 3 − x 2 = 100 Give your answer rounded to 1 DP.

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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Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

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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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]

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

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 three consecutive multiples of 3 are 15, 18 and 21

First, let's determine three successive multiples of 3:

The subsequent two would be "x+3" and "x+6" if we call the initial number "x".

Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:

2/3(x + x+3) = (x+6) + 1

Simplifying this equation, we get:

2/3(2x+3) = x+7

Multiplying both sides by 3, we get:

2(2x+3) = 3(x+7)

Expanding and simplifying, we get:

4x + 6 = 3x + 21

Subtracting 3x and 6 from both sides, we get:

x = 15

Therefore, the three consecutive multiples of 3 are 15, 18 and 21

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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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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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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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Answer:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

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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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:

3√2 and 3 are the values of x and y respectively from the figure.

The given diagram is a right triangle with an acute angle of 45 degrees

We need to determine the values of variables x and y.

Applying the trigonometry identity, we will have:

sin 45 = opposite/hypotenuse
sin45 = 3/x

x = 3/sin45

x = 3/(1/√2)
x = 3√2

Similarly:

tan 45 = opposite/adjacent
tan 45 = 3/y

1 = 3/y

y = 3

Hence the values of x and y from the figure is 3√2 and 3 respectively

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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:

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°

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 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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The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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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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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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Answer: 6

Step-by-step explanation:

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

 \/ \/

 possitive 3 possitive 3

 3x3= 6

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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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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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 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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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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