The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles If the greater of the opposite interior angles exceeds the smaller by 30 degrees , find the measure of the interior angles of the triangle.​

Answer:

Deon drove 270 miles.

Let x be the number of miles driven.

The total cost is 20.95 + 0.74x = 221.49

Subtracting 20.95 from both sides gives 0.74x = 200.54

Dividing both sides by 0.74 gives x = 270 miles

So the answer is 270

Answer:

271 miles

Step-by-step explanation:

The equation to find the total cost is

C = 20.95 + .74 m  where m is the number of miles

221.49 = 20.95 +.74m

Subtract 20.95 from each side

221.49 -20.95 = 20.95-20.95 +.74m

200.54 = .74m

Divide each side by .74

200.74/.74 = m

271 = m

Answer:

point v at (3,-6)

point x at (1,-4)

other point that I can't see the letter lol is at (5,-3)

The actual measure of major arc JML is approximately 289.33°, which is closest to 287°.

We know that minor arc KL is supplementary to major arc JML. So,

m∠KL = 180° - m∠JML

Substituting the given values, we get:

8x - 6 = 180 - (25x - 13)

Solving for x, we get:

33x = 193

x = 193/33

Substituting this value of x in the expression for m∠JML, we get:

m∠JML = 25(193/33) - 13

m∠JML = 1468/3

m∠JML ≈ 489.33°

However, since lines KL and JM appear tangent, we know that minor arc KL and major arc JML share the same endpoint and thus are part of the same circle. So, the actual measure of major arc JML is:

m(arc JML) = 360° - m(arc KL)

We can find m(arc KL) by subtracting m∠KLM from 180°:

m(arc KL) = 180° - m∠KLM

m(arc KL) = 180° - (8(193/33) - 6)

m(arc KL) ≈ 70.67°

Substituting in the formula for m(arc JML), we get:

m(arc JML) = 360° - 70.67°

m(arc JML) ≈ 289.33°

Therefore, the actual measure of major arc JML is approximately 289.33°, which is closest to option (b) 287°.

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Answer:

y = 2x+4

Step-by-step explanation:

slope (m) = 2

point (-1,2)

so,

b = 2-2×(-1) = 4

y = mx+b

or, y = 2x+4

Answer: Choice D)

{(1, 4), (2, 3), (3, 2), (4, 1)}

========================================================

Explanation:

Let's go through the answer choices one at a time to see what is a function and what isn't.

In short, choices A,B,C are not functions because they have a repeated x coordinate; in contrast, choice D doesn't have any repeated x values so it is a function.

Side note: The y values are allowed to repeat themselves, but the function won't be one-to-one.

The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

The solution to the equations are given below.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1. System A          System B

−12x+9y=7           −12x+9y=7

9x−12y=6             −9x+5y=9

Solving system A

x= -46/21 and y= -15/7

and, solving system B

x= -46/21 and y= -15/7

We can say that

Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.

2. -7 should be multiply the second equation by so that the sum of the x-coefficients is zero.

3. x−y=3

2x−3y=−1

Solving the above equation gives

x= 10 and y= 7.

The equation yields the same solution as above is

2x−2y=6

2x−3y=−1

4. Equation A: 5x+9y=12

Equation B: 4x−3y=8

Now, solving both equations we can proceed as Multiply equation B by 3 and add the result to equation A.

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Answer:

To determine which system of equations would have the same solution, we evaluate each system of equations.

System 1 4x − 5y = 2, 3x − y = 8

x = 38/11

y = 26/11

System 2 4x − 5y = 2, 3x − 2y = 1

x = 1/7

y = -2/7

System 3 4x − 5y = 2, 3x − 8y = 4

x = -4/17

y = -10/17

System 4 4x − 5y = 2, 10x − 9y = 4

x = 1/7

y = -2/7

Therefore, the correct answer is option 3. System 2 and system 4 are equal, because the second equation in system 4 is obtained by adding the first equation in system 2 to two times the second equation in system 2.

    4x− 5y = 2 2( 3x − 2y = 1)

-----------------------    10x - 9y = 4

Step-by-step explanation:

Give me a brainilest please...

Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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Answer: D

Step-by-step explanation:

5x + 4x = 180°

Angles on a straight line add to 180°

The fraction that has been given illustrates that the person who ran further is Jane.

Your information isn't complete. Therefore, an overview of the fraction will given.

Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/4 of a mile. In order to know who ran more, you can convert the fraction to percentage.

This will be:

Lisa = 1/2 × 100 = 50%

Jane = 3/4 × 100 = 75%

Therefore, Jane ran more.

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Sample Mean: 3.25

Standard Deviation: 2.29

CI: 1.36 to 5.14

To compute the sample mean, add up all the values and divide the sum by the number of values in the data set. In this case, the data set is 3, 4, 6, 8, 2, 1, 0, 2.

Summing up the values: 3 + 4 + 6 + 8 + 2 + 1 + 0 + 2 = 26.

There are 8 values in the data set, so divide the sum by 8: 26 / 8 = 3.25.

Therefore, the sample mean is 3.25 cups of coffee per day.

To compute the sample standard deviation, we need to find the square root of the variance. The variance is the average of the squared differences from the mean.

First, calculate the squared differences from the mean for each value:
(3 - 3.25)^2 = 0.0625
(4 - 3.25)^2 = 0.5625
(6 - 3.25)^2 = 7.5625
(8 - 3.25)^2 = 20.0625
(2 - 3.25)^2 = 1.5625
(1 - 3.25)^2 = 5.0625
(0 - 3.25)^2 = 10.5625
(2 - 3.25)^2 = 1.5625

Next, find the average of these squared differences:
(0.0625 + 0.5625 + 7.5625 + 20.0625 + 1.5625 + 5.0625 + 10.5625 + 1.5625) / 8 = 5.25.

Finally, take the square root of the variance to find the sample standard deviation:
sqrt(5.25) ≈ 2.29.

Therefore, the sample standard deviation is approximately 2.29 cups.

To construct a 95% confidence interval for the mean number of cups of coffee consumed among all undergraduates, we can use the formula:

CI = sample mean ± (t * (sample standard deviation / sqrt(n))),

where t is the t-value for the desired confidence level, sample standard deviation is the calculated standard deviation, sqrt(n) is the square root of the sample size, and the sample mean is the calculated mean.

For a 95% confidence level, with a sample size of 8, we can find the t-value from a t-table. The t-value for a 95% confidence level with 8 degrees of freedom is approximately 2.306.

Plugging in the values, the confidence interval is:

CI = 3.25 ± (2.306 * (2.29 / sqrt(8))).

Calculating the lower limit:
3.25 - (2.306 * (2.29 / sqrt(8))) ≈ 1.36.

Calculating the upper limit:
3.25 + (2.306 * (2.29 / sqrt(8))) ≈ 5.14.

Therefore, the 95% confidence interval for the mean number of cups of coffee consumed among all undergraduates is approximately 1.36 to 5.14 cups per day.

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Mila will receive 68 EUROS of money after the exchange of 80 US dollar.

USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.

Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.

According to the given data in the question,

1 USD =0.85 EURO

80 USD = 0.85*80 EURO

80 USD= 68 EURO

Hence 80USD will be converted to 68 EUROS

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Answer:

6+15+21=42.

Step-by-step explanation:

21 is greater than 16

15 is less than 29

1*21=21

3*7=21

7*3=21

factors of 21 are 1, 3, 7 and 21

1*15=15

3*5=15

5*3=15

factors of 15 are 1, 3, 5 and 15

6+15+21=42

1*6=6

2*3=6

3*2=6

factors of 6 are 1, 2, 3 and 6

Answer:

-3.14530027393739338363829263839

-Step-by-step explanation:

Slope of y = 2x +80 is 2, y-intercept is 80, x-intercept is -40.

Slope is defined as how much the y-coordinate changes with respect to the x-coordinate. Slope remains constant anywhere on the line.

Given equation is y = 2x + 80, where y is total amount of spending by tourist in Florida, in billions of dollars and x represents the number of years since 2013.

Equation of a line in slope-intercept form is,

y = mx + c, where m is the slope of the line and c is the y-intercept.

Comparing the given equation with slope-intercept form, we get,

m = 2 and c = 80

Domain of the equation includes number of years from 2013 - 2017 and the range of the equation is the corresponding y values.

Since slope is positive, as x value increases, y value also increases.

x- intercept is the point where the line touches the x-axis. y-coordinate will be zero at that point.

0 = 2x + 80 ⇒ x = -40

For the equation y = 2x +80, slope = 2, y-intercept = 80, x-intercept = -40.

Domain is the set of all number of years from 2013 - 2017 and range is the corresponding amount spend by tourist in the years from 2013-2017. As x value increases, y value also increases.

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2. 0.5404 is the correct answer

Given that 5% of the chips fail, so 95% doesn't fail. P( a chip not failing) = 0.95. we can determine the probability that all the chips will not fail by multiplying the individual probabilities together. Since the chips are independent of each other, the probability that all the chips will not fail is calculated as:

P(all chips will not fail) = P(first chip will not fail) × P(second chip will not fail) × P(third chip will not fail) × ... × P(twelfth chip will not fail)

This can be simplified to:

P(all chips will not fail) = 0.95 × 0.95 × 0.95 × ... (12 factors)

Using the exponent notation, this can be written as:

P(all chips will not fail) = 0.95¹²

Calculating this expression, we find:

P(all chips will not fail) = 0.5404

Therefore, the required probability is 0.5404.

Answer: 0.5404

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Answer:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite so just move it over to the opposite side

Step-by-step explanation:

Answer:

12 cans were damaged

EXPLANATION:

Cause When You Divide 4 To Divide 40, It Gives You 100% Calculation, And Subtract 30% from 100% it gives you 70%, which is 28 cans of food

This is the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1).

The point-slope form is a method of writing the equation of a straight line, where the equation is written in the form:

y - y1 = m(x - x1)

where (x1, y1) is the coordinates of a point on the line, and m is the slope of the line.

To write the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1), we can use the point-slope formula:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points on the line, and m is the slope of the line.

First, we can find the slope of the line using the two points:

m = (y2 - y1) / (x2 - x1)

= (1 - 6) / (-6 - 6)

= -5 / (-12)

= 5/12

Next, we can choose one of the points, say (6, 6), to use in the formula:

y - y1 = m(x - x1)

y - 6 = (5/12)(x - 6)

This is the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1).

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Note that the depreciation for this vehicle using method 2 will be $340.

To calculate the depreciation using method 2, we need to multiply the cost of the car by the depreciation rate per mile, which is given in cents per mile.

First, we need to calculate the total depreciation for the car in cents by multiplying the miles driven by the depreciation rate per mile:

Total depreciation = Miles driven x Depreciation rate per mile

Total depreciation = 10,000 x 3.4 cents per mile

Total depreciation = 34,000 cents

Next, we need to convert the total depreciation from cents to dollars by dividing it by 100:

Total depreciation = 34,000 cents ÷ 100 cents/dollar

Total depreciation = $340

Therefore, the depreciation for this vehicle using method 2 will be $340.

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Answer:

Okay so your numbers are:

0, 2, 2, 4, 5, 1, 3, 4, 2, 4, 5, 0, 0, 1, 3, 4

You have to put them in order first:

0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5

Now that its all in order you have to pull out the middle number.

Since there are 16 numbers its an even pile so you have to get the 2 middle numbers:

2, 3

Add them both together:

2 + 3 = 5

Then divide by 2:

5 ÷ 2

= 2.5

Step-by-step explanation:

Hope this helps!

From your neighborhood sofite.

Answer: Median is 78

Step-by-step explanation: What you have to do in this stem and leaf plot is for example 6|0 is 60, 9|4 is 94, etc. To find the median height, ignore the stem (the number by itself) and do the median how you usually do it.  Sorry if its a bit complicated

Answer:

: = ÷

\(\frac{-2}{5}*\frac{6}{-1} : \frac{5}{-2} = \frac{-12}{-5} : \frac{5}{-2} = \frac{12}{5}*\frac{-2}{5}=\frac{-24}{25}\)

An equivalent fraction is -24 over 25.

The distance between their houses is (c) √80

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

Tim = (-3, 1)

Kim = (5, 5)

The distance between Tim and Kim houses can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute the known values in the above equation, so, we have the following representation

distance = √[(5 + 3)² + (5 - 1)²]

Evaluate

distance = √80

Hence, the distance is √80

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a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.

(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (500 - 694) / 112

z-score ≈ -1.732

Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.

So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (900 - 694) / 112

z-score ≈ 1.839

Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.

So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.

We use the z-score formula to find the z-score corresponding to the 99th percentile:

z-score = invNorm(0.99)

z-score ≈ 2.326

Now, we use the z-score to find the score corresponding to the 99th percentile:

X = mean + (z-score * standard deviation)

X = 694 + (2.326 * 112)

X ≈ 694 + 260.512

X ≈ 954.512

So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

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It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."

The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.

The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.

The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).

Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.

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