how many paths from $a$ to $b$ consist of exactly six line segments (vertical, horizontal or inclined)?

Answer:

the awnser is:30° yup it is

Answer:

30°

Step-by-step explanation:

We Know

(4x - 2) + (20x - 10) = 180°

4x - 2 + 20x - 10 = 180

24x - 12 = 180

24x = 192

x = 8

Find m∠EBD

∠ABC is a vertical angle to ∠EBD, meaning they will equal it.

4(8) - 2

32 - 2

30°

So, m∠EBD is 30°

Answer: 212998.58

Step-by-step explanation:

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if the price increases 6% every year for 7 years you would have to multiply 7 by 6 which is 42 so you have to add 42% to 149,999 which is 212998.58.

Answer:

$212998.58

How I Found The Answer:

6% Would Be $8999.94

$8999.94 × 7 = $62999.58

$149999 + $62999.58 = $212998.58

We have found two quadratic functions with x-intercepts (-5,0) and (5,0): f(x) =\(x^2 - 25\), which opens upward, and g(x) = \(-x^2 + 25\), which opens downward.

For the quadratic function that opens upward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

f(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens upward, then a must be positive. Expanding the equation, we get:

f(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open upward, we need the coefficient of x^2 to be positive, so we can set a = 1:

f(x) = x^2 - 25

For the quadratic function that opens downward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

g(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens downward, then a must be negative. Expanding the equation, we get:

g(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open downward, we need the coefficient of x^2 to be negative, so we can set a = -1:

g(x) = -x^2 + 25

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Given data:

The given amount of equipment purchased by the Sandra is A=$1,200.

9514 1404 393

Answer:

  45 feet

Step-by-step explanation:

Each link is 3/12 foot or 1/4 foot. Then 180 links will total ...

  180(1/4 ft) = 45 ft

The paper chain is 45 feet long the first day of school.

Answer:

37 students in each bus so 111 students went on the bus

Step-by-step explanation:

6 students went on the bus so 117 - 6 = 111 there are 3 buses so 111 / 3 = 37 so 37 students per bus

20x + 1 = 720

20x = 719

x = 35.95

Your answer: 35.95

Proof:

(5(35.95))+(35.95-10)+(3(35.95)+5)+(2(35.95)-2)+(5(35.95)+6)+(4(35.95)+2) = 720

The correct option is C. 3.52/(22 - n) = 24/100.

The equation which can be used to find n, the number of gallons of water he should remove is 3.52/(22 - n) = 24/100.

Mathematical symbols can represent numbers (constants), variables, functions, operations, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.

Now, as per the given question.

22 gallons of water is evaporated from the grant plans which is 16% ammonia solution to make a 24% ammonia solution.

First, we determine how much ammonia is in 22 gallons of 16% ammonia solution.

16%  x 22 gal  =  3.52 gal

That after water evaporates, the quantity of ammonia remains constant, however the total quantity of solution is diminished by the quantity of water that evaporates.

Amount of ammonia: 3.52 gal

Amount of water that sustained: 22 - n

Requires concentration of ammonia is  24% = 24/100

The measurement will be formatted as follows:

(3.52)/(22 - n) = 24/100

Therefore, the equation which is used for the formation of the  number of gallons of water he should remove ammonia is (3.52)/(22 - n) = 24/100.

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The complete question is -

Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. which equation can he use to find n, the number of gallons of water he should remove?

The options are-

A. 3.52(22 - n) = 0.24

B. (22 - n)/3.52 = 24/100

C. 3.52/(22 - n) = 24/100

D. 3.52 + (22 - n)  = 0.24

a) A scatterplot of strength (y) versus diameter (x) is illustrated below.

b) The Model Equation is 30.71429X - 76.19048

c) The strength for a diameter of 5.5 mm through the equation is 92.73

d) The diameter would you predict a strength of 95kN/mm is 5.8

Spot welding is a popular method of joining metals, and it is crucial to understand the relationship between weld diameter and strength. In this scenario, we have a table that presents shear strengths (in kN/mm) and weld diameters (in mm) for a sample of spot welds. Our objective is to create a scatterplot of strength (y) versus diameter (x), report the model equation, and predict the strength for a diameter of 5.5 mm.

To create a scatterplot, we will plot the strength values on the y-axis and the diameter values on the x-axis. Each point on the graph represents a particular spot weld. We can use the scatterplot to observe the general pattern of the data, identify potential outliers, and assess the strength-diameter relationship.

After creating the scatterplot, we will fit a regression line to the data points.

Regression Equation = y = bX + a

b = SP/SSX = 21.5/0.7 = 30.71429

a = MY - bMX = 68.17 - (30.71 x 4.7) = -76.19048

y = 30.71429X - 76.19048

To predict the strength for a diameter of 5.5 mm, we will use the model equation. We will substitute the value of 5.5 for x in the equation and solve for y.

y = 30.7142(5.5) - 76.19048 = 92.73

In conclusion, understanding the relationship between weld diameter and strength is essential in spot welding. By constructing a scatterplot, reporting the model equation, and predicting strength for a specific diameter, we can gain valuable insights into the performance of spot welds.

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Complete Question:

The following Table presents shear strengths (in kN/mm) and weld diameters (in mm) for a sample of spot welds.

a. Construct a scatterplot of strength (y) versus diameter (x).

b. Report the Model Equation.

c. Predict the strength for a diameter of 5.5 mm.

Diameter                Strength

4.2                                      51

4.4                                      54

4.6                                       69

4.8                                        81

5.0                                        75

5.2                                     79

Answer:

The angle swept by the swing is 120 degrees

Step-by-step explanation:

Here, we are given the radius of the circle that makes the arc, and the length of the arc

Mathematically, we are to find the central angle

That would be;

The length of an arc is;

theta/360 * 2 * pi * r

theta is the central angle we are looking for and r in this case is 2.1 m

Thus, we have it that;

theta/360 * 2 * 22/7 * 2.1 = 4.4

theta = (360 * 4.4 * 7)/(2 * 22 * 2.1)

theta = 120 degrees

Answer:

the answer is -109  

:)

Answer:

-109

Step-by-step explanation:

Answer:

Option (C)

Step-by-step explanation:

Given formula of a line passing through \((x_1, y_1)\) and slope 'm' is,

\(y-y_1=m(x-x_1)\)

Further solving this equation,

\(y-y_1=mx-mx_1\) [By distributive property]

\(y-y_1+mx_1=(mx-mx_1)+mx_1\) [By adding \(mx_1\) on both the sides]

\(y-y_1+mx_1=mx\)

\(\frac{y-y_1-mx_1}{m}=\frac{mx}{m}\) [Divide the equation by m]

\(\frac{y-y_1}{m}-x_1=x\)

Therefore, Option (C) will be the answer.

a) The maximum error in the calculated area of the disk =  23.87 cm²

b) The relative error is: 0.0211 and the percentage error is 2.11%

Let us assume that r represents the radius of the circular disk and A represents the area.

Here, the radius of a circular disk is given as 19 cm

So, r = 19 cm

and the radius has a maximum error in measurement of 0.2 cm.

So, dr = 0.2

The area of the circular disk would be,

A = πr²            ..........(1)

A = π × 19²

A = 361π cm²

Differentiating equation (1) with respect to r,

dA = 2πr × dr

dA = 2 × π × 19 × 0.2

dA = 7.6π

dA = 23.87 cm²

So, the maximum error in the calculated area is: 23.87 cm²

Now we find the relative error.

R = dA/A

R = 7.6π / 361π

R = 0.0211

And the percentage error would be:

P = relative error × 100

P = 0.0211 × 100

P = 2.11%

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Answer:

b

Step-by-step explanation:

The solution to the initial value problem x' = [1 -5; 1 -3]x, x(0) = [H], can be expressed as -tcos(t)-2sin(t), \(sin(t)e^(^-^t^)\), [cos(t) + 4sin(t)]sin(t) -tcos(t) + 2sin(t), -2tcos(t) + 2sin(t)sin(t), -2t[cos(t) + sin(t)].

The solution to the given initial value problem is a vector function consisting of five components. The first component is -tcos(t)-2sin(t), the second component is\(sin(t)e^(^-^t^)\), the third component is [cos(t) + 4sin(t)]sin(t), the fourth component is -tcos(t) + 2sin(t), and the fifth component is -2t[cos(t) + sin(t)]. These components represent the values of the function x at different points in time, starting from the initial time t = 0. The solution is derived by solving the system of differential equations represented by the matrix [1 -5; 1 -3] and applying the initial condition x(0) = [H].

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The validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.

The validity of the Universal Modus Tollens can be derived from the validity of Universal Instantiation and Modus Tollens. Let's examine the logic behind each of these rules and how they lead to the validity of Universal Modus Tollens.

Universal Instantiation (UI): This rule allows us to infer a specific instance of a universally quantified statement. For example, if we have the universal statement "For all x, if P(x) then Q(x)," we can instantiate it to a particular instance by replacing the variable x with a specific element, resulting in "If P(a) then Q(a)." This rule is valid and widely accepted in formal logic.

Modus Tollens (MT): Modus Tollens is a deductive rule of inference used to infer the negation of the consequent of a conditional statement. It states that if we have a conditional statement "If P, then Q," and we know the negation of Q (¬Q), we can conclude the negation of P (¬P). This rule is also valid and widely accepted.

Now, let's demonstrate how the validity of Universal Instantiation and Modus Tollens leads to the validity of Universal Modus Tollens:

Universal Modus Tollens (UMT): If we have the universally quantified statement "For all x, if P(x) then Q(x)," and we know the negation of Q for a specific instance, ¬Q(a), then we can conclude the negation of P for that same instance, ¬P(a).

To derive UMT, we can apply the following steps:

Apply Universal Instantiation (UI) to the universally quantified statement, replacing x with a specific element, let's say a. This gives us "If P(a) then Q(a)."

Assume the negation of Q for that specific instance, ¬Q(a).

Apply Modus Tollens (MT) to the conditional statement "If P(a) then Q(a)" and the negation of Q, which allows us to conclude the negation of P, ¬P(a).

Thus, by using Universal Instantiation to instantiate a universally quantified statement, and then applying Modus Tollens to the instantiated conditional statement and the negation of the consequent, we can derive Universal Modus Tollens.

It's important to note that the validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.

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The value of  \(cos^{-1}(\frac{2}{3})\) is 0.84 radian or 48.18°

Given,

\(cos^{-1}(\frac{2}{3})\)

It is an inverse trigonometric function.

Inverse trigonometric functions are also known as "Arc Functions" because they produce the length of arc required to obtain a given value of trigonometric functions. Inverse trigonometric functions are the inverse of trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are particularly useful for right angle triangles. When two sides of a right triangle are known, these six important functions are used to find the angle measure.

Thus, the value of \(cos^{-1}(\frac{2}{3})\)  using a calculator is 0.84 radian or 48.18°

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Answer:

m<B=74°

Step-by-step explanation:

3x-23+2x-12=180

5x-35=180

5x=180+35

5x=215

x=215÷5

x=43

m<B=2x-12=2(43)-12=86-12=74

answer:

b= 10x i pretty sure

Step-by-step explanation:

When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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The required answer is "The function has a local maximum at x = 15 with value 2 and a local minimum at x = -9 with value -2."

Given the function f(x) = 3 + 3x + 12x⁻¹, which has one local minimum and one local maximum.

The function has a local maximum at x = 15 with value 2 and a local minimum at x = -9 with value -2.

Therefore, the required answer is "The function has a local maximum at x = 15 with value 2 and a local minimum at x = -9 with value -2."

Therefore, the local maximum and minimum of the given function f(x) = 3 + 3x + 12x⁻¹ are as follows:

Local Maximum: The value of f(x) is 2 and occurs at x = 15

Local Minimum: The value of f(x) is -2 and occurs at x = -9.

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the focal length of these glasses is approximately 57.14 centimeters.

The focal length (f) of a lens in centimeters is given by the formula:

1/f = (n-1)(1/r1 - 1/r2)

For reading glasses, we can assume that the lens is thin and has a uniform thickness, so we can use the simplified formula:

1/f = (n-1)/r

D = 1/f (in meters)

So we can convert the diopter power (P) of the reading glasses to the focal length (f) in centimeters using the formula:

P = 1/f (in meters)

f = 1/P (in meters)

f = 100/P (in centimeters)

For 1.75 diopter reading glasses, we have:

f = 100/1.75

f = 57.14 centimeters

Therefore, the focal length of these glasses is approximately 57.14 centimeters.

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Answer:

A

y=-19/12x+17/12

Step-by-step explanation:

Write in slope-intercept form,y=mx+b

The equation i.e. 19x + 12y = 17 equivalent to the  \(y = \frac{19}{12}x + \frac{17}{12}\).

Given that,

Based on the above information, the calculation is as follows:

19x + 12y = 17

Here we need to solve it for y

\(y = \frac{19}{12}x + \frac{17}{12}\)

Therefore, we can conclude that the first option is correct.

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Answer:

47.975, 50.975

Step-by-step explanation:

hypotenuse = 70

x = 1st leg

x + 3 = 2nd leg

70² = x² + (x + 3)² = x² + x² + 6x + 9 = 2x² + 6x + 9

2x² + 6x + 9 = 4900

2x² + 6x² - 4891 = 0

use quadratic equation to solve for x:

a=2, b=6, c=-4891

x = 47.975, -50.975

Throw out the negative solution

Therefore, the 2 legs are:

47.975 and 47.975 + 3 = 50.975

Test the answers for correctness:  47.975² + 50.975² = 4900

√4900 = 70 = the hypotenuse

Answer:

it's the account number for the fun of the bird and the first one is a good one is a

Step-by-step explanation:

how to download a game on give me a call when we get home and get a

Answer:

82.758620689655

Step-by-step explanation:

48/0.58=82.758620689655

Michael will need 54 yards of fencing.

Dimensions of Michael's rectangular yard =  22 yards, 16 yards

Length of Michael's rectangular yard = 22 yards

Breadth of Michael's rectangular yard = 16 yards

Perimeter of Michael's yard = 2 [l+b] = 2 [22+16]   = 2×38 = 76 yards                            

As Michael nee

ds to fence only 3 sides leaving a long side, so he needs to fence = perimeter - length = 76-22 = 54 yards

Hence, Michael will need 54 yards of fencing.

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Answer:

1). x = 14

2). y = 2.4 cm

Step-by-step explanation:

In the diagram ΔNPQ ~ ΔNLM and NL = 3,

1). ∠P ≅ ∠L [All angles of similar triangle are equal in measure]

   (3x + 18)° = 60°

   3x = 60 - 18

   x = 14

2). Since, both the triangles are similar, corresponding sides will be proportional.

   \(\frac{PN}{NL}=\frac{NQ}{NM}\)

   \(\frac{y}{3}=\frac{3.2}{4}\)

   y \(=\frac{3.2\times 3}{4}\)

   y = 2.4 cm

Answer:

29,36,43

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

the numbers are being added by 7

1 + 7 = 8

8 + 7 = 15

and so on

Answer:

200% = 2.00    150% = 1.50    15% = 0.15

Step-by-step explanation: