Find the equation of the line.
Use exact numbers.

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.

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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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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Answer:

5 seconds

Step-by-step explanation:

20-15= 5 seconds

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]

Answer: 6

Step-by-step explanation:

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

 \/ \/

 possitive 3 possitive 3

 3x3= 6

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:

∠CDF = 48°

Step-by-step explanation:

∠CDE = ∠EDF + ∠CDF

Given that,

∠CDE = 114°

∠EDF = 66°

So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.

∠CDF = ∠CDE - ∠EDF

∠CDF = 114 - 66

∠CDF = 48°

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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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:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

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 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 input value which produces the same output values for the two functions in the graph is x=1

To determine which input value produces the same output value for two functions on a graph

we need to find the x-coordinate(s) where the two functions intersect or have the same y-coordinate.

x=1 is the input value which produces the same output values for the two functions in the graph

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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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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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Six over ten >_three over four__> one over two

D three over four.

To determine the fraction that goes in the blank, we need to compare the fractions six over ten and one over two.

To compare fractions, we can either find a common denominator or convert them into decimal form.

Let's go with the decimal approach.

To convert six over ten into a decimal, we divide 6 by 10, which equals 0.6. Similarly, for one over two, dividing 1 by 2 gives us 0.5.

Now, we can see that 0.6 is greater than 0.5.

Since six over ten is greater than one over two, we need to find a fraction that is greater than 0.6 but less than 0.5.

Among the given options, the only fraction that fits this criterion is three over four (option D).

To confirm this, let's convert three over four into a decimal.

Dividing 3 by 4 gives us 0.75, which is greater than 0.6 and less than 0.5.

Therefore, we can conclude that the correct fraction to fill in the blank is three over four (D).

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The value of x in the line intersection is 60.

When line intersect, angle relationships are formed such as linear angles, vertical angles etc.

Therefore, lets use the angle relationship to find the value of x in the line intersection.

Hence,

2x - 10 + 2x + 40 + 90 = 360(sum of angles in a point)

2x - 10 + 2x + 130 = 360

4x + 120 = 360

4x = 360 - 120

4x = 240

divide both sides by 4

x = 240 / 4

x = 60

Therefore,

x = 60

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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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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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√x+3 is an increasing function, the minimum value is L4 and the maximum value is R4.

Since we are given 4 subintervals, the width of each subinterval is:

Δx = (b - a) / n = (1 - (-1)) / 4 = 1/2

where a = -1 and b = 1 are the endpoints of the interval.

Now, L4 = f(-1)Δx + f(-1/2)Δx + f(0)Δx + f(1/2)Δx

= √2/Δx + √3/Δx + √3/Δx + √4/Δx

= (2√2 + 2√3 + 2√4) / Δx

= 10(2√2 + 2√3 + 2√4)

and, the right endpoint Riemann sum,

R4 = f(-1/2)Δx + f(0)Δx + f(1/2)Δx + f(1)Δx

= √3/Δx + √3/Δx + √4/Δx + √5/Δx

= (2√3 + 2√4 + 2√5) / Δx

= 4(√3 + 2√4 + √5)

Since √x+3 is an increasing function, the minimum value is L4 and the maximum value is R4.

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The statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

Given, two functions  y = -2f(x) = 1/x

To determine whether the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true or false, we need to find the value of Y for both functions when x = -2.

Substituting x = -2 in the functions we get:I would ask y = -2(-2) = 4f(-2) = 1/(-2) = -1/2Therefore, the Y value of the function I would ask is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2. Hence, the given statement is true.

Therefore, the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

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Answer:

The length of the third side is 1 unit.

Step-by-step explanation:

Because this is a right triangle, we can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean theorem: a² + b² = c², where variables a and b are the legs of the triangle and c is the hypotenuse

We are going to let a = (12/13) and b = (5/13), though the order does not particularly matter in this case. We are going to plug and play with the theorem, and then simplify as we go.

[tex](\frac{12}{13})^{2} + (\frac{5}{13})^{2} = c^{2}\\\\\frac{144}{169} + \frac{25}{169} = c^{2}\\\\\frac{144 + 25}{169} = c^{2}\\ \\ \frac{169}{169} = c^{2}\\\\1 = c^{2}\\\\\sqrt{1} = \sqrt{c^{2}} \\\\c = 1[/tex]

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 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 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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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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