Work out the height of this triangle with base,
b
= 8.6mm and area,
A
= 256.28mm2.

The street can be represented in slope intercept form as follows:

y = x + 4

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Parallel lines have the same slope.

The street goes by the name y = x + 17.

The slope of the street is 1.

Therefore, the street parallel to that one should have the same slope.

The street can be represented in slope intercept form is as follows:

y = x + 4

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Answer:

Okie

Step-by-step explanation:

Answer:

K (2,-4)

L (4,-6)

J (2,-9)

Step-by-step explanation:

The required graph of the image of △JKL after a reflection over the line y=x has been attached below.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The triangle △JKL is given in the represented graph, which vertices are as follows :

J (-9, 2)

K (-4, 2)

L (-6, 4)

The image of △JKL after a reflection over the line y = x will be triangle △J'K'L' that vertices are as follows :

K' (2,-4)

L' (4,-6)

J' (2,-9)

Hence, the required graph of the image of △JKL after a reflection over the line y=x has been attached below.

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Answer:

It's 3

Step-by-step explanation:

Just divide the entire equation by 3 to isolate the y variable on the left side.

y = mx + b (m is the slope)

and in this equation, after you divide by 3, the value of m is 3.

The linear trend model is a commonly used technique in time series analysis, particularly when the data is expected to exhibit a consistent rate of growth or change over time.

First, Collect and organize your data, Before you can apply the linear trend model, you need to have a clear understanding of the data you're working with.

Then Plot your data on a graph, Once you have your data organized, the next step is to plot it on a graph. This will help you visualize any trends or patterns that may be present in the data.

Next, Calculate the slope of the line, To determine the rate of change in your data, you'll need to calculate the slope of the line. This is done using a formula called the least squares regression line.

And then determine the intercept of the line, by using the intercept of the line represents the starting point for the data. In other words, it's the value of the data at the beginning of the time series.

Finally, use the linear trend model to make predictions, Once you've calculated the slope and intercept of the line, you can use the linear trend model to make predictions about future values of the data.

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Answer:

J’ (-3,0)

Step-by-step explanation:

Right = x + 1 = -4 + 1 = -3

down = y-4 = 4-4 = 0

There are 205,768 ways to select four books from the shelf in such a way that exactly one pair of books are adjacent.

To solve this problem, we can break it down into two cases:

Case 1: The pair of books is at the beginning or end of the selection.

If the pair of books is at the beginning, there are 39 options for the third book, and 38 options for the fourth book. So, there are 39 * 38 = 1,482 ways to select the books in this case.

Similarly, if the pair of books is at the end, there are also 1,482 ways to select the books.

Case 2: The pair of books is not at the beginning or end of the selection.

In this case, we have 38 options for the first book, since it cannot be adjacent to the pair. Then, there are 37 options for the second book, as it also cannot be adjacent to the pair. For the third and fourth books, there are 38 and 37 options respectively.

So, there are 38 * 37 * 38 * 37 = 202,804 ways to select the books in this case.

Finally, we can add up the possibilities from both cases:

1,482 + 1,482 + 202,804 = 205,768

Therefore, there are 205,768 ways to select four books from the shelf in such a way that exactly one pair of books are adjacent.

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Answer:

(B) 7 x 10‐³

Step-by-step explanation:

A typical red blood cell in human blood has a diameter of approximately 0.007 mm.

In scientific form = 7 x 10-^3

(a) The conditions for inference are satisfied because the sample is random, the sample size is large enough (n=83), and the population of customers is much larger than the sample size.

(b) Null hypothesis (H0): The average savings for customers switching to the advertised car insurance is $435 (µ = $435).

(c) Alternative hypothesis (H1): The average savings for customers switching to the advertised car insurance is less than $435 (µ < $435).

(d) To calculate the p-value, first find the test statistic (z-score):
z = (sample mean - null hypothesis mean) / (standard deviation / √n)
z = ($399 - $435) / ($103 / √83) ≈ -3.46

Using a z-table, the p-value is approximately 0.0003.

(e) If the test was conducted at the 95% level (α = 0.05), the p-value (0.0003) is less than α, so we reject the null hypothesis.

(f) Based on the hypothesis test, I agree with the market researcher that the advertised savings of $435 is an overestimate since we rejected the null hypothesis in favor of the alternative hypothesis.

(g) To calculate a 90% confidence interval:
Margin of error = z * (standard deviation / √n)
Margin of error = 1.645 * ($103 / √83) ≈ $18.56

Confidence interval = (sample mean - margin of error, sample mean + margin of error)
Confidence interval = ($399 - $18.56, $399 + $18.56) ≈ ($380.44, $417.56)

(h) The results from the hypothesis test and confidence interval agree. The hypothesis test rejected the null hypothesis, suggesting the average savings is less than $435. The 90% confidence interval supports this, as the entire interval is below the advertised $435 savings.

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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The accumulated amount after 25 years is , $70,702.80.

Now, We can use the formula for compound interest to find the accumulated amount after 25 years:

A = P(1 + r/k)^(kt)

Where A is the accumulated amount, P is the principal , r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period.

In this case, we have:

P = $25,300

r = 0.045 (

k = 12 (monthly compounding)

t = 25

Substituting these values into the formula, we get:

A = $25,300(1 + 0.045/12)^(12 x 25)

A ≈ $70,702.80

Therefore, the accumulated amount after 25 years is ,

$70,702.80.

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Answer:

Just flip the points to the negative values in the 2nd quadrant

Answer:

y=8x+1

Step-by-step explanation:

y=mx+b

m=rise/run=(8)/(1)=8

y=8x+b

b is the y-intercept  

y=8x+1

7.051 can be written as the fraction 7051/1000.

To express 7.051 as a fraction in the form of p/q, we need to identify the decimal places and convert them to the corresponding fractional parts.

Since 7.051 has three decimal places, we multiply it by 1000 to move the decimal point three places to the right, which gives us 7051.

Now, the numerator (p) of the fraction will be 7051, and the denominator (q) will be the corresponding power of 10, which is 1000.

Therefore, 7.051 can be expressed as 7051/1000.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

In this case, the GCD of 7051 and 1000 is 1, so the fraction is already in its simplest form.

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Answer:

5

25/5=5

Step-by-step explanation:

To translate the given sentence into an inequality, we need to identify the key words and their mathematical symbols. The words "sum" and "is at most" indicate addition and less than or equal to, respectively.

Therefore, the inequality can be written as 9 + X ≤ 15. This means that the sum of nine and any number X cannot exceed 15, or in other words, X must be less than or equal to 6. To solve for X, we can subtract 9 from both sides of the inequality, giving us X ≤ 6. Therefore, any number less than or equal to 6 satisfies the given condition. This is an example of how to translate a sentence into an inequality and use it to find a solution for the variable.

To translate the given sentence into an inequality, we'll use the key terms provided. The sum of "nine" and "X" can be represented as 9 + X. The phrase "at most" signifies that the total is less than or equal to a certain value, in this case, 15. Now we can "translate" the sentence into an inequality:

9 + X ≤ 15

This inequality represents that the sum of nine and X is less than or equal to 15. To find the possible values of X, you can subtract 9 from both sides of the inequality:

X ≤ 15 - 9
X ≤ 6

So, X can be any value less than or equal to 6.

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To calculate the interval for a high degree of confidence that at least 95% of all UHPC specimens adhered to steel will have work of adhesion values between the limits of the interval, we need to use a confidence interval formula. Assuming a normal distribution, we can use the formula:

1. Obtain the mean (µ) and standard deviation (σ) of the work of adhesion values from the sample data.
2. Determine the desired confidence level (95% in this case), which corresponds to a Z-score of 1.96 (from a standard normal distribution table).
3. Calculate the standard error (SE) by dividing the standard deviation (σ) by the square root of the sample size (n): SE = σ / √n.
4. Calculate the margin of error (ME) by multiplying the Z-score by the standard error: ME = 1.96 * SE.
5. Find the confidence interval by subtracting and adding the margin of error from the mean: (µ - ME, µ + ME).

Round your answers to two decimal places. This interval provides a 95% confidence that the true work of adhesion values for at least 95% of all UHPC specimens adhered to steel lie between these limits.

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Answer:

Easy its 64

Step-by-step explanation:

Next time put the eqation in a calculator it will give you the answer trust me

In section 20 of the south half of the map, find the contour line that intersects the encircled area. The distance between that contour line and the ground surface represents the required well depth to access the water table.



To locate the point in question, refer to section 20 on the south half of the map where it is encircled. Next, examine the water table contours provided in Exercise 14A. Identify the contour line that intersects with the encircled area. This contour line represents the depth of the water table at that point.

To determine the depth a well would need to be drilled to access the water table, measure the vertical distance from the ground surface to the identified contour line. This measurement corresponds to the required depth for drilling the well.

Therefore, In section 20 of the south half of the map, find the contour line that intersects the encircled area. The distance between that contour line and the ground surface represents the required well depth to access the water table.

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For any positive real number ( M ), there exists a positive integer ( N ) such that for all ( n > N ), ( n^2 > M ). This proves that the limit of ( n^2 ) as ( n ) goes to infinity is infinity. Hence, the limit of the expression ( (n^2 + 1) - n ) as ( n ) approaches infinity is also infinity.

To find the limit of the expression ( \lim_{n \to \infty} (n^2 + 1) - n), we can simplify the expression and see how it behaves as ( n ) approaches infinity.

( (n^2 + 1) - n ) can be rewritten as ( n^2 - n + 1 ).

As ( n ) approaches infinity, the dominant term in the polynomial is ( n^2 ). The other terms become less significant compared to ( n^2 ).

So, when taking the limit as ( n ) goes to infinity, we can ignore the smaller terms ( -n ) and ( +1 ).

Therefore, the limit becomes: ( \lim_{n \to \infty} n^2 ).

The limit of ( n^2 ) as ( n ) goes to infinity is infinity. This can be proven formally using the definition of a limit:

For any positive real number ( M ), there exists a positive integer ( N ) such that for all ( n > N ), ( n^2 > M ).

Proof:

Let's assume ( M ) is a positive real number.

We need to find a positive integer ( N ) such that for all ( n > N ), ( n^2 > M ).

Let's choose ( N = \lceil \sqrt{M} \rceil ), where ( \lceil \cdot \rceil ) denotes the ceiling function.

Now, consider any ( n > N ).

Since ( N = \lceil \sqrt{M} \rceil ), we have ( N \geq \sqrt{M} ).

Squaring both sides, we get ( N^2 \geq M ).

Since ( n > N ), we also have ( n^2 > N^2 ).

Combining the above inequalities, we have ( n^2 > N^2 \geq M ).

Therefore, for any positive real number ( M ), there exists a positive integer ( N ) such that for all ( n > N ), ( n^2 > M ). This proves that the limit of ( n^2 ) as ( n ) goes to infinity is infinity.

Hence, the limit of the expression ( (n^2 + 1) - n ) as ( n ) approaches infinity is also infinity.

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Answer:

x=-2 and x = 5

Step-by-step explanation:

The solutions to the equation are where the graph crosses the x axis

We can see that the graph crosses at x=-2 and x = 5

Answer:

x = -2

x = 5

Step-by-step explanation:

The answer is found when the graph crosses the x-axis

Hope this helps :D

Answer: 2 pizzas

Step-by-step explanation: 4 times 4 times 2 is 32. 1/32 divided into 60 to get 2 pizzas

The Converse of the Angle Bisector Theorem states that if a point is in the same plane as an angle and divides the angle into two congruent angles, then it lies on the angle's bisector.

The fact that the converse states that the point must be in the same plane as the angle implies that if the point is not in the same plane as the angle, then it cannot divide the angle into two congruent angles, and thus cannot lie on the angle's bisector.

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. The converse of this theorem states that if a point on the interior of a triangle divides one side of the triangle into two segments that are proportional to the other two sides, then the point lies on the bisector of the angle opposite the divided side.

To understand why this implies that the point must be in the same plane as the angle, we need to consider the definition of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions.

It is determined by any three non-collinear points in space. In the context of a triangle, the three vertices of the triangle are non-collinear points that determine a plane.

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Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.

A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test  we can find the mean difference between pairs of measurements is zero or not. So  paired t-test is used, when data is in the form of matched pairs

Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

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Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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Work Shown:

4/10 = 10/x

4x = 10*10

4x = 100

x = 100/4

x = 25

The first equation set up shown above is valid because we have similar triangles. Having similar triangles means the corresponding sides form equal proportions. After the equation is set up, we cross multiply (step 2) and isolate x.

The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.

To find the confidence interval C.I,

It is given that,

Sample size n = 225

Sample mean μ = 11.6

Standard deviation σ = 4.1

Since 95% confidence interval, z-score is 1.96

So, the required confidence interval is calculated by,

C. I = μ ± z(σ/√n) or mean ± margin error

On substituting,

C. I = 11.6 ± 1.96(4.1/√225)

     = 11.6 ± 1.96 × 0.2733

     = 11.6 ± 0.5357

So, the lower bound = 11.6 - 0.5357 = 11.065 and

the upper bound = 11.6 + 0.5357 = 12.135.

Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.

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There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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Answer:

C. 135

Step-by-step explanation:

2x^2/x + x(100-15x)

When x=5

2(5)^2/5 + 5{100-15(5)}

2(25)/5 + 5(100-75)

=50/5 + 5(25)

=10+125

=135

Answer:

12

Step-by-step explanation:

the number of the available cases is :

3 × 4 = 12