The diameter of a penny is 1 9/10 cm. Justin lined up 5 pennies next to each other. What is the length of the 5 pennies

Name all angles when there are two parallel lines cut by a transversal?

Alternate interior angles

Corresponding angles

Vertically opposite

From figure 1,

Since the angles marked with colour fulfil the vertically opposite angles properties ,so

(2x+35)° = (8x-49)°

⇒(2x-8x)=(-49-35)°

⇒-6x=-84

⇒x = 14°

Hence , x = 14°

From figure 2,

Since the angles marked are corresponding angles,therefore on equating both angles we get

(10x-18)°=(15x-48)°

⇒(10x-15x)=(-48+18)°

⇒-5x = -30°

⇒ x = 6°

From figure 3,

Since the given two angles are alternate interior angles ,so

(7x+5)°=(12x-75)°

⇒(7x-12x)=(-75-5)°

⇒-5x=-80°

⇒x = 16°

From figure 4 ,

Since the two angles lies in a straight line ,so sum is 180°

(27x-21)°+(10x-16)°=180°

⇒37x -37° = 0

⇒ x = 1°

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Answer:

m = \(\frac{2}{3}\) , b = - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

Given

2x - 3y = 6 ( subtract 2x from both sides )

- 3y = - 2x + 6 ( divide all terms by - 3 )

y = \(\frac{2}{3}\) x - 2 ← in slope- intercept form

with slope m = \(\frac{2}{3}\) and y- intercept b = - 2

Answer:

y- intercept is (0, -2)

slope is 2/3

Step-by-step explanation:

find 2 points on the line:

2x-3y=6

1/2*(6+3y) =x

if y is 2, x is 6 ((6,2))

if y is 4, x is 9 ((9, 4))

y-intercept is when x = 0.

0-3y=6

y=-2

slope is (y2-y1)/(x2-x1): choose y2 and the corresponding x-coordinate is x2. then the others are the 1's. let's use 4 as y2 which means:

x2 = 9

x1 = 6

y1 = 2

then plug in and solve.

(4-2)/(9-6)

= 2/3

m = 2/3

Hope this helps!

The percent increase in the flight increase is \(18.35\)%

Definition of percentages.

A percentage is a ratio of some value out of a hundred.

With this definition in mind, if \(20\)% of \(200\) students have a test tomorrow, then a total of \(40\) students have a test tomorrow.

Percentage Increase Calculation Example #1

For the first example, we find the percentage increase for the following scenario:

If your total savings of $\(60\) at the beginning of the week grew to $\(90\) by the end of the week, what is the percentage increase?

This is where our three-step process comes in:

Step 1: Find the difference in values ​​by subtracting the initial value from the final value.

In this case, the final value minus the initial value can be calculated as follows:

\(90 -60 = 30\)

So in this example, the difference between the two values ​​would be \(30\). Remember that when calculating the percentage increase, you will always subtract the smaller value from the larger value.

Step 2:Divide the difference by the initial number

The next step is to take the difference (\(30\) in this example) and divide it by the starting number (\(60\) in this example) like this:

\(30/60 = 0.50\)

Always express your answer as a decimal (this will make your life a lot easier when you get to step three).

Step 3: Multiply by \(100\)

The last step is to multiply the decimal result from step two by one hundred and express the final result as a percentage.

\(0.50 * 100 = 50\)

Final answer: 50% increase

That is all! Using three steps, you can conclude that there was a \(50\)% increase in the money you had from the beginning of the week to the end of the week.

Hence percent increase can be found as follows:

=$\((432-365)/365*100\)

=\(18.35\)%

Therefore, a percent increase in the flight increase is \(18.35\)%

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We apply the pythagorean theorem to find this answer.

a = 11 and b = 6 are the given legs

c = unknown hypotenuse

So,

a^2+b^2 = c^2

c = sqrt( a^2+b^2 )

c = sqrt( 11^2 + 6^2 )

c = sqrt( 121 + 36 )

c = sqrt( 157 )

c = 12.52996 approximately

c = 12.5

Side note: once you replace 'a' and b with 11 and 6, you can compute everything with a calculator in one single step more or less. The steps above are shown if you wanted to find the exact value sqrt(157).

The lines tangent and normal to the curve y = 2sin(πx - y) at the point (1, 0) are:

a) Tangent line: y = πx - π

b) Normal line: y = -x/π + 1/π

To find the lines that are tangent and normal to the curve y = 2sin(πx - y) at the point (1, 0), we need to determine the derivative of the curve at that point.

a) Tangent line:

The tangent line to a curve at a given point has the same slope as the derivative of the curve at that point.

Let's find the derivative of the curve y = 2sin(πx - y) with respect to x using the chain rule.

dy/dx = d/dx[2sin(πx - y)]

      = 2cos(πx - y) * d/dx(πx - y)

      = 2cos(πx - y) * (π - dy/dx)

Now, substitute the point (1, 0) into the derivative to find the slope at that point:

dy/dx = 2cos(π - 0) * (π - dy/dx)

      = 2cos(π) * (π - dy/dx)

      = -2π(π - dy/dx)

At the point (1, 0), the slope dy/dx can be found by substituting x = 1 and y = 0 into the derivative:

dy/dx = -2π(π - dy/dx)

0 = -2π(π - dy/dx)

0 = -2π² + 2π(dy/dx)

dy/dx = 2π² / 2π

dy/dx = π

Therefore, the slope of the tangent line at the point (1, 0) is π.

Using the point-slope form of a line, we can write the equation of the tangent line:

y - y₁ = m(x - x₁)

y - 0 = π(x - 1)

y = πx - π

The equation of the tangent line is y = πx - π.

b) Normal line:

The normal line to a curve at a given point is perpendicular to the tangent line and has a slope that is the negative reciprocal of the slope of the tangent line.

The slope of the normal line is -1/π, the negative reciprocal of the slope of the tangent line.

Using the point-slope form, the equation of the normal line can be written as:

y - y₁ = m(x - x₁)

y - 0 = (-1/π)(x - 1)

y = -x/π + 1/π

The equation of the normal line is y = -x/π + 1/π.

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Answer:

(-1, 9)

Step-by-step explanation:

given

\(y = - 3x + 6 \\ and \\ y = 9 \\ then \: we \: need \: to :\ find \: x \: so \: that \: when \: plugged \\ to \: - 3x + 6 \: the \: result \: is \: 9 \\ by \: transitive \: rule \\ y = 9 = - 3x + 6 \\ 9 = - 3x + 6 \: (substract \: both \: sides \: with \: 6) \\ 3 = - 3x \: (divides \: both \: sides \: with \: - 3) \\ - 1 = x\)

Answer:

the answer is c

Step-by-step explanation:

because i just took the test

Answer:

A

Step-by-step explanation:

18%=18/100=0.18

0.18*30.80=5.544 or about $5.50. Hope this helps!

Answer:

(x+4) (x^2−4 x+16)

Step-by-step explanation:

The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.

In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.

The Central Limit Theorem establishes that for a proportion p in a sample of size n:

The expected value is μ=р

The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)

In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.

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After 5 days, half of the sample would remain, which means 500g would be left. Therefore, the amount of radioactive Iodine-131 left would be (1/2)^6 of the original sample: (1/2)^6 x 1000g = 15.625g. So, the answer is 15.625g.

To solve this problem, we'll use the formula for radioactive decay:
Final Amount = Initial Amount * (1/2)^(time elapsed / half-life)

In this case, the Initial Amount is 1000g, the half-life is 5.0 days, and the time elapsed is 30 days. Now let's plug in these values into the formula:

Final Amount = 1000g * (1/2)^(30 / 5)

Final Amount = 1000g * (1/2)^6

Final Amount = 1000g * (1/64)

Final Amount = 15.625g

So, after 30 days, 15.625g of radioactive Iodine-131 is left. The correct answer is 15.625g.

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The length of one side of the box, in meters, is 0.138 meters.

The density of water is approximately 1000 kg/m^3 or 1 g/cm^3. If a cubic box is filled with 2650 g of water, we can find the volume of the box and then find one side length.

Volume = Mass / Density = 2650 g/(1 g/cm^3) = 2650 cm^3

Since the box is cubic, one side length is the cube root of the volume.

Side length = (Volume)^(1/3) = (2650 cm^3)^(1/3) = 13.8 cm

To convert cm to meters, divide by 100:

Side length = 13.8 cm/100 cm/m = 0.138 m

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Answer:

\(25x = 1250\)

\(\frac{1250}{25}\)

x=50

x has value 50

The value of the boxes, A , B and C are 22/4, 15/4 and 9 1/4 respectively

Note that from the information given, we have that the number in a box is the sum of the two numbers below it.

Then, we can deduce that;

A = The sum of the two mixed fractions, 3 1/4 and 2 1/4

B = The sum of the two mixed fractions, 2 1/4 and 1 1/2

Now, add the values

A = 3 1/4 + 2 1/4

convert to improper fractions

A = 13/4 + 9/4

Add the values

A = 22/4

B = 2 1/4 + 1 1/2

convert to improper fractions

B = 9/4 + 3/2

B =9 + 6 /4

B = 15/4

Then , the value of C = A + B

C = 22/4 + 15/4

C = 37/4

C = 9 1/4

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Answer:

(5,-3)

Step-by-step explanation:

You just find the middle #

(3,-1)  and   (7,-5)

the middle point of 3 and 7 is 5

the middle point of -1 and -5 is -3

so (5,-3)

Answer:

you can use desmos

Step-by-step explanation:

for example put x=88

and do the same with the rest

then put x+y+z and you will get your answer

A mathematical description of hexagon is given above.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is hexagon.

In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

Therefore, a mathematical description of hexagon is given above.

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If the area of the triangle is 120 cm^2, the value of x is equal to 6.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = 1/2 × b × h

Where:

According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]

Where:

s = (a + b + c)/2

s = (x + x + 1 + 2x - 1)/2

s = 4x/2

s = 2x

Substituting the parameters into Hero's Formula formula, we have the following;

x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]

x√10 = x√2(x − 1)

√10 = √2(x − 1)

Taking the square of both sides, we have:

10 = 2(x - 1)

10 = 2x - 2

2x = 12

x = 12/2

x = 6.

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\( {5}^{5} \)

is the answer.

The choice 1 and choice 4 indicate the correct advantage of using random forest versus a single decision tree.

Random forest refers to the machine learning algorithm using several decision trees formed by random data subset and it's features. While single decision tree as indicated by name is based on one decision tree.

Decision tree finds the application in regression and construction tasks, where the outcome is generated through decision made from tree like model.

The decision tree is easily readable and interpretable by humans. The disadvantage of decision tree includes sensitivity to minor data changes.

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The expected length of time spent writing email replies per day is 270 minutes. The correct answer is option e.

The expected length of time spent writing email replies per day can be calculated by multiplying the number of emails received per day by the probability of replying to each email and the time taken to write each reply. Since the number of emails received per day follows a Poisson distribution with variance 81, the average number of emails received per day is also 81.

The expected length of time spent on each reply is (2/3) * 5 minutes, as the professor replies with a probability of 2/3 and each reply takes five minutes to write.

Therefore, the expected length of time spent writing email replies per day is:

81 * (2/3) * 5 = 270 minutes.

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There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

Given,

The equations;

The value of k = -50

We have to solve the given equations using k as -50 and find the true ones;

Lets check;

1.5 - (-50/5) = 11.5

1.5 - (-10) = 11.5

1.5 + 10 = 11.5

11.5 = 11.5

This equation is true.

(-2 x -50) + 78 = -22

100 + 78 = -22

178 ≠ -22

This equation is false

(-4 x -50) + 80 = -120

200 + 80 = -120

280 ≠ -120

This equation is false

(6 x -50) - 150 = -150

-300 - 150 = -150

-450 ≠ -150

This equation is false

(-50/10) - 3 = -8

-5 - 3 = -8

-8 = -8

This equation is true.

That is,

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

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Answer:

15

Step-by-step explanation:

Answer:15

Step-by-step explanation:

At point P, ∂x f = e^(-4)*(-0.141) and ∂y f = 0.

To find ∂x f and ∂y f at point P, we need to differentiate f(x,y)=e^x*sin(y) with respect to x and y, respectively.

1. First, let's find ∂x f:
  - Differentiate e^x with respect to x: d(e^x)/dx = e^x
  - sin(y) is treated as a constant since we are differentiating with respect to x.
  - Therefore, ∂x f = e^x*sin(y)

2. Next, let's find ∂y f:
  - Differentiate e^x with respect to y: d(e^x)/dy = 0
  - sin(y) is treated as a constant since we are differentiating with respect to y.
  - Therefore, ∂y f = 0

At point P, which is (-4,-3), we substitute the values into our derivatives:

∂x f = e^(-4)*sin(-3) = e^(-4)*(-0.141)

∂y f = 0

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For the given perimeter and side length of the triangle , the equation and the measure of the longest side length of the triangle is given by :

Equation : x + 278 = 450 and side length = 172cm.

As given in the question,

The given measurements of the triangle are :

Perimeter of the triangle = 450cm

Measure of the two side length are :

Side length 1 = 128 cm

Side length 2 = 150 cm

let 'x' be the measure of the longest side length of the triangle we have,

Perimeter of the triangle = Side length 1 + Side length 2 + side length 3

⇒ 450 cm = 128 + 150 + x

⇒ 450 = 278 + x

Equation to represent the relation :

x + 278 = 450

Measure of the longest side of the triangle is :

⇒ x = 450 - 278

⇒ x = 172 cm

Therefore, the equation and the measure of the longest side length of the triangle with given perimeter and other side length is equal to

Equation : x + 278 = 450 and side length = 172cm.

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The p-value is 0.043, which is less than 0.05, then the null hypothesis should be rejected if the chosen level of significance is 0.05. Hence, the given statement is true.

When performing a hypothesis test, a significance level, also known as alpha, must be chosen ahead of time. A hypothesis test is used to determine if there is sufficient evidence to reject the null hypothesis. A p-value is a probability value that is calculated based on the test statistic in a hypothesis test. The significance level is compared to the p-value to determine if the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, which is typically 0.05, then the null hypothesis is rejected and the alternative hypothesis is supported. Since in this situation, the p-value is 0.043, which is less than 0.05, then the null hypothesis should be rejected if the chosen level of significance is 0.05. Hence, the given statement is true.

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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The area of the region bounded by the curve r = 9cos(θ) and the sector 0 ≤ θ ≤ π/6 is \($27\pi/8 - 81/8\times \sqrt{3}$\)

The curve r = 9cos(θ) is a polar curve that forms a half-circle with a radius of 9/2. To find the area of the region bounded by this curve and the sector 0 ≤ θ ≤ π/6, we can use the formula for the area of a polar region:

\($A = \frac{1}{2} \int_{a}^{b} r(\theta)^2 d\theta$\)

In this case, a = 0 and b = π/6, and the curve is given by r(θ) = 9cos(θ). Substituting these values into the formula, we get:

\($A = \frac{1}{2} \int_{0}^{\frac{\pi}{6}} (9\cos(\theta))^2 d\theta$\)

Simplifying and evaluating the integral gives:

\(A = \frac{1}{2} \int_{0}^{\frac{\pi}{6}} 81\cos^2(\theta) d\theta\\\\ = \frac{1}{2}\left(\frac{81}{2}\cdot\frac{\pi}{6}+\frac{81}{4}\cdot\sin\left(\frac{\pi}{6}\right)\right)\\ \\ = \frac{27\pi}{8} - \frac{81}{8}\sqrt{3}\)

Therefore, the area of the region bounded by the curve r = 9cos(θ) and the sector 0 ≤ θ ≤ π/6 is \($27\pi/8 - 81/8\times \sqrt{3}$\)

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Answer:

Step-by-step explanation:

3.50 x 400%

400% = 4

3.50 x 4 = 14.00

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.