Select the correct answer.
In the given diagram, line segment BD
bisects angle ABC
. Segment BD
is extended to E, where line segment EC
is parallel to line segment AB
. Write a two-column proof to show that AB/AD = BC/DC
.

1. The probability that the point is on the triangle is 2/15

2. The probability that the point is in the circle is 1/15

3. The probability that the point is in the circle or triangle is 3/15

4. The probability that the point is not triangle is 13/15

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it is equivalent to 100% in percentage.

Probability = sample space / Total outcome

sample space is the area of the shapes

Area of triangle = 1/2 bh

= 1/2 × 3 × 4

= 3 × 2 = 6cm²

area of circle = πr²

= 3.14 × 1² = 3.14

= 3( to whole number)

Total outcome is the area of rectangle

= l× w = 9 × 5 = 45 cm²

1. The probability that the point is on the triangle is 6/45 = 2/15

2. The probability that the point is in the circle is

= 3/45 = 1/15

3. The probability that the point is in the circle or triangle = 1/15 +2/15 = 3/15 = 1/5

4. The probability that the point is not triangle is

= 1-2/15 = 13/15

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Answer:

Try A

Step-by-step explanation:

By checking to see if there is correlation, Sam is evaluating the criterion validity of the metric.

From the question, we understand that Sam tests the metric to check for the presence or absence of correlation in the metric.

This, in other words means that Sam is checking the criterion validity of the metric.

Hence, the true statement is that Sam is evaluating the criterion validity of the metric.

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The measure of the angle m∠ZYX of the trapezoid is equal to 139°

A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.

3x + 19 + x + 1 = 180°

4x + 20 = 180°

4x = 180 - 20 {collect like terms}

4x = 160

x = 160/4 {divide through by 4}

x = 40

m∠ZYX = 3(40) + 19 = 139°.

WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.

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9514 1404 393

Answer:

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

The equation of the parabolic arc that accomplishes this task is:

y = (-k/256)(x - 16)² + k.

In which k is the maximum height of the arc.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the arc has these following characteristics:

The road under the arc is 20 feet wide with a 6-foot sidewalk on both sides of the road, hence it's total length is of 20 + 2 x 6 = 32 feet, and the peak of the arc will be at h = 16.

Hence:

y = a(x - 16)² + k.

The height is of 0 at x = 0 and x = 32, hence:

0 = 256a + k.

a = -k/256

y = (-k/256)(x - 16)² + k.

In which k is the maximum height of the arc.

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Answer:

A. Margin of error=0.0346

B. Confidence interval=0.4854 to 0.5546

Step-by-step explanation:

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let plug in the formula

Confidence level= 1-0.95

Confidence level= 0.05

Second step is to find Z using this formula

Zα/2

Let plug in the formula

Z= 0.05/2

Z=0.025

Third step is to find the Z score of Z=0.025

Zα/2=1.96

Now let calculate the margin of error using this formula

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Computation for the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009

Computation for the boundaries of confidence interval

Using this formula

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

Therefore the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009 is 0.4854 to 0.5546

P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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Answer: 450000, 160

Step-by-step explanation:

4.5 ⋅ 10^5 =

4.5*100000=

4*100000+0.5*100000=

400000+50000=450000

1.6 ⋅ 10^2=

1.6*100=

1*100+0.6*100=

100+60=160

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

The value of x is 17° due to the pair of angles being complementary.

The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles. There are two types of supplementary angles.

Adjacent angles: Adjacent angles are the type of supplementary angles. Adjacent angles have a common side and vertex, for example, a corner point. Their points do not overlap in any way. In other terms, adjacent angles are pairs of two angles next to each other.

We have been given that the pair of angles as

(3x + 1)° and (4 + 2x)°

Here, the pairing of angles sums up to 90° then they are called complementary angles.

So 3x + 1 + 4 + 2x = 90°

⇒ 5x + 5 = 90°

⇒ 5x = 85°

⇒ x = 17°

Therefore, the value of x is 17°.

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Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Answer:

\(\sqrt{y^2 + 10y + 25} = r\)

Step-by-step explanation:

So we're given that the volume of a cone can be defined as:

\(V=\frac{1}{3}\pi r^2h\)

We're also given that:

\(h=9 \text{ (since height = 9 inches)}\)

So let's substitute in that nine in to the equation:

\(V=\frac{1}{3}\pi r^2 * 9\)

Let's simplify a bit by multiplying the 9 by 1/3 (same as dividing by 3)

\(V=\frac{9}{3}\pi r^2\\\\V=3\pi r^2\)

We're finally given that:

\(V = 3\pi y^2 + 30\pi y + 75\pi\)

so let's use this definition and substitute it in for our volume to get:

\(3\pi y^2 + 30\pi y + 75\pi = 3\pi r^2\)

From here we want to solve for r, since we want the radius in terms of y.

So let's first divide by \(3\pi\) on both sides to get rid of the coefficient.

\(\frac{3\pi y^2 + 30\pi y + 75\pi}{3\pi} = \frac{3\pi r^2}{3\pi}\)

from here we can distribute the division across the terms (and simplify on the right) to get:

\(\frac{3\pi y^2}{3\pi} + \frac{30\pi y}{3\pi} + \frac{75\pi}{3\pi} = r^2\)

from here we can simplify the terms to get:

\(y^2+10y+25=r^2\)

Now the only thing that we need to remove is that square, which we can do by applying the square root to both sides of the function:

\(\sqrt{y^2 + 10y + 25} = \sqrt{r^2}\\\\\sqrt{y^2 + 10y + 25} = r\)

and now we're done isolating "r" and it's expressed in terms of y

The three statements that are true include:

Amy's age is a factor of the age of her grandmother.

The age of Amy's grandmother is a composite number.

The number 6 is a factor if the age of Amy's grandmother.

A factor simply means a number that can be multiplied by another number to get the original number.

Let's say Amy is 10 years. The grandmother will be 69 years. In this case, 10 is a factor of 60. Therefore, Amy's age is a factor of the age of her grandmother.

The complete options are given below.

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Which three statements below must be true?

1.The age of Amy’s grandmother is a prime number.

2.Amy’s age is a factor of the age of her grandmother.

3.The age of Amy’s grandmother has exactly two factors.

4.The age of Amy’s grandmother is a composite number.

5.The number 6 is a factor of the age of Amy’s grandmother.

6.The age of Amy’s grandmother has exactly four factors.

Answer:

That is incorrect because ten you are multiplying the two sets then the exponents just add but but when you put the brackets around it then the exponents are being multiplied not added

Step-by-step explanation:

(xy)^3 * (xy)^4

x^3y^3*x^4y^4

x^7y^7

The rest of the explanation is in the picture

Answer:

y=3x+5

0 hours is $5

1 hour is $8

2 hours is $11

3 hours is $14

Step-by-step explanation:

y=mx+b

m = slope and b = y intercept

in this case 3 dollars an hour (x) would be m

and 5 rental fee would be B

Answer:

She will find 1054 viruses.

Step-by-step explanation:

The number of viruses after t hours is given by the following equation:

\(N(t) = N(0)(1+r)^{t}\)

In which N(0) is the initial number of viruses and r is the growth rate, as a decimal.

100 viruses that grow at a rate of 17% per hour.

This means that \(N(0) = 100, r = 0.17\)

So

\(N(t) = N(0)(1+r)^{t}\)

\(N(t) = 100(1+0.17)^{t}\)

\(N(t) = 100(1.17)^{t}\)

She will check on the viruses in 15 hours. How many viruses will she find?

This is N(15).

\(N(15) = 100(1.17)^{15} = 1053.87\)

Rounding to the nearest whole number:

She will find 1054 viruses.

Answer:

21%

Step-by-step explanation:

210 is 10.5% of the amount that is for 6 months doubling it will make it 420 that is 21% of the total amount of 2000.

Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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Answer:

12y=m

Explaination:

because there's 12 months in a year

I hope this is right

The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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Answer:

-2

Step-by-step explanation:

Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).

Answer:

A. Compare the sum 12.50 + 15.67 + 9.32 = 37.49 to the sum 14.333 + 12.100 + 10.780 = 37.213; he spent more time practicing the backstroke than the butterfly.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i took the qiuz

Answer:

25/28

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

8 is the digit after 7  and previous to 9

Answer:

1) the connection between 2 or more meausures

2) when the r value is closer to 1 or -1 it is a stronger correlation

3) positive correlation would be height and weight. Taller people tend to be heavier. A negative correlation is a relationship between two variables in which an increase in one variable is associated with a decrease in the other

Step-by-step explanation:

choose me as brainlyest:)