the graph below describes the journey of a train between two cities

The measure of angle 5 is 32 degrees, which is calculated by subtracting 136 degrees (the measure of angle 4) from 168 degrees (the measure of angle 6).

Angles 1 and 6 have been given as 56 degrees and 168 degrees respectively. To find the measure of angle 5, we must first calculate the measure of angles 2, 3 and 4.The sum of the measures of the angles at a point is always 360 degrees. Therefore, by subtracting the measure of angles 1 and 6 from 360, we can find the measure of the other four angles.

360 - 56 - 168 = 136

Therefore the measure of angles 2, 3 and 4 is 136 degrees each. To find the measure of angle 5, we must subtract the measure of angle 4 (136 degrees) from the measure of angle 6 (168 degrees).

168 - 136 = 32

Therefore the measure of angle 5 is 32 degrees.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:

The equation for the speed of the train is: 162 = 3x

I think the speed of the train is 54 miles per hour

Step-by-step explanation:

We know that:

y = distance in miles

x = speed of train (miles/hour)

t = time traveled from the departing station (hours)

The equation: y = xt is given, we can therefore substitute the give values:

y = xt or tx

162 = 3x (This would be the equation)

Now we can find x by diving 3 on both sides of "="

162/3 = x

54 = x (This would be the speed of train)

Hope this helps!

The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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Hence,  when \(n=10\) the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.

So,

\(2(n + 2) < 5(n-1)\)

When

\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)

Hence,  when \(n=10\) the given inequality is true.

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Answer:

\(k=-28\)

Step-by-step explanation:

\(k+1=-27\)

Subtract 1 from both sides:

\(k+1-1=-27-1\)

\(k=-28\)

The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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Answer:

horizontal line: y=-4

vertical line: x=-3

Step-by-step explanation:

This one is simple. all you need to do is look at the x and y in the ordered pair.

Horizontal goes left and right so it's for y

Vertical goes up and down so it's for x

let me know if you need more explaining :)

Answer:

1140 in.

Step-by-step explanation:

Multiply the length value by 12, so 95*12=1140

Have a beautiful day! v(⌒o⌒)v♪

Answer:

y=2/3x - 6

Step-by-step explanation:

use the formula y=mx+b. the m of this equation is equal to the slope and you know that the slope is 2/3. the b of the equation is equal to the y-intercept so, to find b you simply look at the points given. the points are written in (x,y) form so if -14 is x, -6 must be y. remember to KEEP CHANGE CHANGE your signs so that plus sign becomes negative 6. Hope this helps!

Answer:

  (b)  56.5 ft

Step-by-step explanation:

The circumference of a circle of diameter d is given by ...

  C = πd

For the given diameter, the circumference of the frame is ...

  C = (3.14)(18 ft) ≈ 56.52 ft

The length of the outside edge of the frame is about 56.5 feet.

Answer:

To find the new width of the photograph, we need to multiply the original width by the scale factor of 2.6:

New width = Original width x Scale factor

New width = 3.6 in x 2.6

New width = 9.36 in (rounded to two decimal places)

Therefore, the new width of the photograph will be approximately 9.36 inches when both dimensions are enlarged by a factor of 2.6.

Answer:

r7

Step-by-step explanation:

Answer:

where is the options? or is any given.

Step-by-step explanation:

b. The system has a unique solution when k is not equal to -2 or 10.

c. The system has infinitely many solutions when k = 10.

d. The system has no solution when k = -2.

The augmented system for the system is:

[1 0 2 -2]

[1 1 k  2]

[3 k  -2 2]

The system to have a unique solution, the rank of the coefficient matrix must be equal to the rank of the augmented matrix.

Using row reduction to reduce the augmented matrix to echelon form, we get:

[1 0 2 -2]

[0 1 k+2 4]

[0 0 (k-10)/(k+2) 10]

So, the system has a unique solution when k is not equal to -2 or 10.

The system to have infinitely many solutions, the rank of the coefficient matrix must be less than the rank of the augmented matrix, and the last row of the echelon form of the augmented matrix must be all zeros.

This occurs when:

(k-10)/(k+2) = 0

which happens when k = 10.

So, the system has infinitely many solutions when k = 10.

The system to have no solution, the last row of the echelon form of the augmented matrix must have a non-zero constant on the right-hand side.

This occurs when:

(k-10)/(k+2) ≠ 0

True for all values of k except k = -2. So, the system has no solution when k = -2.

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(a) The augmented matrix for the system is: [1   0   2  |  -2] [1   1   k  |  2] [3   k   -2 |  2] (b) The system has a unique solution when the determinant of the coefficient matrix is nonzero.

In this case, the determinant is 2k + 3. Therefore, the system has a unique solution for any value of k except k = -3/2. (c) The system has infinitely many solutions when the determinant of the coefficient matrix is zero, and the system is consistent (i.e., the right-hand side of each equation is consistent with the others).

In this case, when k = -3/2, the determinant becomes zero, and the system has infinitely many solutions.

(d) The system has no solution when the determinant of the coefficient matrix is zero, and the system is inconsistent (i.e., the right-hand side of at least one equation is inconsistent with the others). In this case, there are no specific values of k that make the system inconsistent.

To determine the unique solution, infinitely many solutions, or no solution for the system, we analyze the determinant of the coefficient matrix. If the determinant is nonzero, there is a unique solution. If the determinant is zero and the system is consistent, there are infinitely many solutions. If the determinant is zero and the system is inconsistent, there is no solution.

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Answer: 38.465 feet

Step-by-step explanation: The diameter (7 feet) divided by 2, equals 3.5. multiply 3.5 squared (12.25 feet) by pi (3.14) equals your answer of 38.465 feet.

Answer:

d

Step-by-step explanation:

is d cause it is so yh ot is d

Answer:

-6 (A)

Step-by-step explanation:

It would be A because the absolute value means we're counting on how far away the number is from 0

to make it easier for you, just forget about the negatives in general and pretend they are regular numbers, then compare the numbers, since its asking for a number greater than 5 you would choose 6 or in this case -6.

Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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The center and radius of a circle given by the equation x² - 10x + y² + 6y - 30 = 0  is (5,-3) and√64 = 8 units.

When finding the center and radius of a circle given by the equation x² - 10x + y² + 6y - 30 = 0, one can use the following steps:

The first step is to rearrange the equation into the standard form, (x - a)² + (y - b)² = r². This is done by completing the square for both the x and y terms in the equation.

x² - 10x + y² + 6y - 30 = 0x² - 10x + 25 + y² + 6y + 9 - 30 = 25 + 9(x - 5)² + (y + 3)² = 64 Therefore, the center of the circle is (5,-3), and the radius is √64 = 8 units.

Explanation:  Given the equation x² - 10x + y² + 6y - 30 = 0, we want to find the center and radius of the circle. The standard form of the equation of a circle with center (a,b) and radius r is (x - a)² + (y - b)² = r². We will begin by completing the square for the x terms and the y terms separately: For the x terms: x² - 10x= x² - 10x + 25 - 25= (x - 5)² - 25 For the y terms: y² + 6y= y² + 6y + 9 - 9= (y + 3)² - 9 Now we can substitute these expressions back into the original equation and simplify: x² - 10x + y² + 6y - 30 = 0(x - 5)² - 25 + (y + 3)² - 9 - 30 = 0(x - 5)² + (y + 3)² = 64 The equation is now in standard form,

which means that the center of the circle is (5,-3) and the radius is √64 = 8 units.

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The function that best model the given data is linear function with an equation: y = -19x + 120.

Based on the data provided, it appears that the number of frogs in the local wetlands is decreasing each year. To determine the best function to model the data, we'll analyze the changes in the number of frogs:

Year 0 to 1: 120 - 101 = 19

Year 1 to 2: 101 - 86 = 15

Year 2 to 3: 86 - 72 = 14

Year 3 to 4: 72 - 60 = 12

The decrease in the number of frogs is not constant, but it is close. Therefore, a linear function would be a reasonable choice to model the data. To write the equation, we can use the data points (0, 120) and (1, 101) to find the slope:

Slope (m) = (101 - 120) / (1 - 0) = -19

Now, we can use the slope and one of the points (let's use (0, 120)) to write the linear equation in the form y = mx + b:

120 = -19(0) + b

b = 120

So the linear equation that best models the data is:

y = -19x + 120

This equation shows that the number of frogs decreases by 19 each year, approximately. Keep in mind that this is a simplified model and may not precisely predict the number of frogs in future years.

Note: The question is incomplete. The complete question probably is: A conservation organization collected the data on the number of frogs in a local wetlands. Which kind of function best models the data? Write an equation to model the data.

Year     Number of Frogs

0            120

1            101

2            86

3            72

4            60

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Answer:

\(\cos \theta=-\dfrac{8}{17}\)

Step-by-step explanation:

Coordinates of Point b\(=(-8,15)\)

b lies on the circle whose equation is \(x^2+y^2=289\)

\(x^2+y^2=17^2\)

Comparing with the general form a circle with center at the origin: \(x^2+y^2=r^2\)

The radius of the circle =17 which is the length of the hypotenuse of the terminal ray through point b.

For an angle drawn in standard position through point b,

x=-8 which is negative

y=15 which is positive

Therefore, the angle is in Quadrant II.

\(\cos \theta=\dfrac{Adjacent}{Hypotenuse} \\$Adjacent=-8\\Hypotenuse=17\\\cos \theta=\dfrac{-8}{17} \\\cos \theta=-\dfrac{8}{17}\)

Answer:

acute angle

Step-by-step explanation:

The acute angle is the angle that has an amplitude of less than 90°. The obtuse angle, on the other hand, has a width greater than 90°. The right angle measures 90° and its sides are orthogonal.

Answer:

an angle less than 90° is an acute angle

Step-by-step explanation:

an angle less than 90° is an acute angle

an angle equal to 90° is a right angle

an angle greater than 90° but less than 180° is an obtuse angle

an angle greater than 180° is a reflex angle

The frequency table for wins and losses is given at the end of the table.

The frequencies are as follows:

The relative frequency of an event in an experiment is calculated as the number of trials in which the event happened divided by the total number of trials of the experiment.

In the context of this problem, the team played 20 games, and the numbers used to construct the frequency table are as follows:

These absolute frequencies are used to construct the frequency table.

Hence the relative frequencies are calculated as follows:

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The maximum possible area is 36 square units.

Answer:

36sq Units at max? i think

Step-by-step explanation:

Have a good day!

#ViolentJax~

Answer:

just do the other answer you know-you know-you dont know- oh well i dont know

Step-by-step explanation:

Answer:

108°

Step-by-step explanation:

since m<ETA is 36° its congruent angle m<TEA is also 36°. add the 2 together to get 72°. all triangles come out to 180° so subtract the 72 from 180 to get 108

If we look at the tree diagram, we can see that we have 12 numbers, they are:

{12, 13, 16, 21, 23, 26, 31, 32, 36, 61, 62, 63}

That's our sample space, if we look at each tree we can count how many numbers has 1 or 6, on the first tree we have 2 numbers: 21 and 26. On the second tree we have three numbers: 12, 13 and 16, that's expected because the first digit is 1. For the second tree we have just two, 31 and 36. For the last tree we have three again because of the digit 6.

Therefore the probability will be how many numbers that has 1 or 6 divided by the sample space, then

The probability is

The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

Answer: 263.088

Step-by-step explanation:

Multiply the equation

¨What does Multiply mean?¨

To compute a product; to perform a multiplication.

(8.1) x (8.12) x 4

Answer    c

Step-by-step explanation: I did the test i hope this help unlike that girl who just wrote random numbers anyways have a good day