In the figure, PQ is parallel to RS. (see picture)

Which of the following angles has a measure equal to 100°?

A) a

B) b

C) c

D) d

Answer:

29%

Step-by-step explanation:

Amount of girls in his class: 13/24

13/24 x 13/24 = 169/576 or 0.2934...

Basically, 29%

The value of y is multiplied by 6 when x is divided by 6

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

y = 3/x

Also, from the question we understand that

x is divied by 6

This means that the new equation is

y = 3/(x/6)

Evaluate

y = 6 * 3/x

This means that the new value of y is  multiplied by 6

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The ratio of the edge lengths of the large and small cubes is 6:1

The ratio that compares the edge lengths of the large and small cubes is the ratio of the length of the edge of the large cube to the length of the edge of the small cube.

The edge length of the large cube is 12 cm and the edge length of the small cube is 2 cm. To find the ratio, we divide the length of the large cube by the length of the small cube.

So the ratio of the edge length of the large cube to the small cube is:

12cm/2cm = 6

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Answer:

I think the answer would be C, I hope it helps! :) please mark me the brainiest

For any value of c, the equation holds true, meaning the function is continuous at x = -1 for all values of c. Any value of c will make the function continuous on the interval (−∞, 0) and (0, ∞).

To find the values of the constant c that make the function continuous on the interval (−∞, 0) and (0, ∞), we need to ensure that the left-hand limit and the right-hand limit of the function are equal at the point of discontinuity, which is x = -1.

First, let's find the left-hand limit of the function as x approaches -1. We substitute x = -1 into the function:

lim(x → -1-) f(x) = lim(x → -1-) (Ac^2 - cr)

Next, let's find the right-hand limit of the function as x approaches -1:

lim(x → -1+) f(x) = lim(x → -1+) (Ac^2 - cr)

To make the function continuous at x = -1, the left-hand limit and the right-hand limit must be equal:

lim(x → -1-) f(x) = lim(x → -1+) f(x)

Now, let's evaluate the left-hand and right-hand limits:

lim(x → -1-) (Ac^2 - cr) = lim(x → -1+) (Ac^2 - cr)

Simplifying the expressions:

(Ac^2 - c(-1)) = (Ac^2 - c(-1))

Ac^2 + c = Ac^2 + c

The c terms cancel out, leaving:

Ac^2 = Ac^2

We can see that for any value of c, the equation holds true, meaning the function is continuous at x = -1 for all values of c.

Therefore, any value of c will make the function continuous on the interval (−∞, 0) and (0, ∞).

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The approximate probability distribution of X - 10 is a constant distribution with a PDF of 1/2 for -10 ≤ y ≤ -8.

To find the probability distribution of X - 10, where X is a uniformly distributed random variable with a PDF equal to 1 for any positive x smaller than or equal to 2, we need to determine the PDF of X - 10.

Let Y = X - 10 be the random variable representing the difference between X and 10. We need to find the PDF of Y.

The transformation from X to Y can be obtained as follows:

Y = X - 10

X = Y + 10

To find the PDF of Y, we need to find the cumulative distribution function (CDF) of Y and differentiate it to obtain the PDF.

The CDF of Y can be obtained as follows:

\(F_Y(y)\) = P(Y ≤ y) = P(X - 10 ≤ y) = P(X ≤ y + 10)

Since X is uniformly distributed with a PDF of 1 for any positive x smaller than or equal to 2, the CDF of X is given by:

\(F_X(x)\) = P(X ≤ x) = x/2 for 0 ≤ x ≤ 2

Now, substituting y + 10 for x, we get:

\(F_Y(y)\) = P(X ≤ y + 10) = (y + 10)/2 for 0 ≤ y + 10 ≤ 2

Simplifying the inequality, we have:

0 ≤ y + 10 ≤ 2

-10 ≤ y ≤ -8

Since the interval for y is between -10 and -8, the CDF of Y is:

\(F_Y(y)\) = (y + 10)/2 for -10 ≤ y ≤ -8

To obtain the PDF of Y, we differentiate the CDF with respect to y:

\(f_Y(y)\) = d/dy [F_Y(y)] = 1/2 for -10 ≤ y ≤ -8

Therefore, the approximate probability distribution of X - 10 is a constant distribution with a PDF of 1/2 for -10 ≤ y ≤ -8.

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Answer:

54.1 inches (round to 1 dp)

Step-by-step explanation:

the formula to calculate the diagonal or a rectangle is

\(\sqrt{(w^{2} +l^{2})}\)

30^2+45^2 is 2925

and \(\sqrt{2925}\)

and the answer to that is 54.1 inches (to 1 dp)

Answer:

4

Step-by-step explanation:

Given scale factor of lengths k , then

scale factor of volumes = k³

Here scale factor of volume = 64 , then

scale factor of length = \(\sqrt[3]{64}\) = 4

The scale factor of length of the shape is calculated as: 4.

When two shapes are mathematically similar, it means that their corresponding sides are proportional, and the scale factor of length is the same as the scale factor of volume raised to the power of 1/3 (since volume is a three-dimensional concept).

Given that the scale factor of volume is 64, we can find the scale factor of length as follows:

Scale factor of length = Scale factor of volume^(1/3)

Scale factor of length = 64^(1/3)

Scale factor of length = ∛64 = 4

The scale factor of length is 4.

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The distance that he is from the home plate will be 245.37 feet.

From the diagram, look at the DACB. LACB is right angle and both the remaining We know that- two angles are equal (45°). So we know that in a in front of their are A two sides are equal then angles also equal and vice-versa.

AC = CB

So AC is also x.

Now by Pythagoras theorem

(AC)² + (BC)² - (AB)²

x² + x² = 347²

2x² = 347²

x = 347 / ✓2

= 245.37 ft.

l

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Answer:

The watermelon has fallen 15.53625m

Step-by-step explanation:

x=vi*t+.5*a*t^2

x=3*1.5+.5*9.81*1.5^2

x=15.53625m

Hello!

[ 50; 41; 30 ] = ?

50 | 2 × 5

5 | 5 => 50 = 2 × 5²

1 |

41 | 41 => 41 = 41

1 |

30 | 2 × 5

3 | 3 => 30 = 2 × 3 × 5

1 |

[ 50; 41; 30 ] = 2 × 3 × 5² × 41 = 2 × 3 × 25 × 41 = 6 × 25 × 41 = 150 × 41 = 6150

Good luck! :)

Answer:

8°

Step-by-step explanation:

The sum of the measures of the exterior angles of a any polygon = 360.

So,  x + 2x + 4x + 5x + 6x + 8x + 9x + 10x = 360

        45x = 360

            x = 8°

The measure of the smallest exterior angle would be equal to 8°

In geometry, a Octagon is a eight - sided polygon. For a [n] sided polygon -

According to the question, we have - A Octagon and the measures of the exterior angles of an octagon are x°, 2x°, 4x°, 5x°, 6x°, 8x°, 9x° and 10x°.

The sum of the exterior angles of the octagon will be 360°.

Therefore, we can write -

x + 2x + 4x + 5x + 6x + 8x + 9x + 10x = 360°

45x = 360°

x = 360/45

x = 8

The smallest exterior angle would be equal to [x]° = 8°

Therefore, the measure of the smallest exterior angle would be equal to 8°

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Answer:

c2

Step-by-step explanation:

(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))

To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:

dx / (10 - x) = 0.005 dt

Integrating both sides:

-ln|10 - x| = 0.005t + C

where C is the constant of integration. Solving for x:

|10 - x| = e^(-0.005t - C)

Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:

C = -ln(10)

Therefore, the solution to the differential equation is:

x(t) = 10 - e^(-0.005t - ln(10))

Simplifying:

x(t) = 10(1 - e^(-0.005t))

(b) New bills will make up 90% of the currency in circulation after approximately 461 days.

We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):

9 = 10(1 - e^(-0.005t))

Dividing both sides by 10 and taking the natural logarithm:

ln(0.1) = -0.005t

Solving for t:

t = 200 ln(10) = 460.51

Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.

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Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

The midpoint of the two points of P (-3,-7) and Q (3,-5) is (0, -6).

When you have the vertices of two points, you can find the midpoint by the formula :

= ( ( x 1 + x 2 ) / 2 , ( y 1 + y 2 ) / 2 )

Solving for the midpoint therefore gives:

= ( ( - 3 + 3 ) / 2 , ( - 7 + ( - 5 ) ) / 2 )

=  ( 0 / 2 , ( - 12 ) / 2 )

= (0, -6)

In conclusion, the midpoint is (0, -6).

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Answer:

The triangle is isosceles.

Step-by-step explanation:

This means that one angle's sine is the same as the other's cosine.

Answer:

Step-by-step explanation:

10/5x6=12

Freddy's group members probably find his interruptions to be distracting and frustrating, as they can tell Freddy thinks he knows more than they do. (chapter 6)

The scientific study of the shape and composition of living organisms is referred to as anatomy, which focuses on their anatomical structure and organization.

The skill of observing and analyzing the various components of a structured entity to unearth their placement, makeup, and workings is also known as science.

They find his behavior annoying because he is distracting them and not letting them focus.

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Answer:

C. 42

Step-by-step explanation:

Answer:

-2090

Step-by-step explanation:

1)  Remove parentheses.

-2 -8 -32 -2048

2) Simplify - 2 - 8 to -10.

-10 - 32 - 2048

3) Simplify -10-32 to -42.

-42 - 2048

4) Simplify.

-2090

The correct option is option (a) $3,992.50. Pavi currently has a $3,992.50 credit on her current card.

The calculation of the provided data, according to the question, is as follows:

$8000 is the credit limit on the card.

Paid in Full = $2,500

$1,500 has been credited to the account.

The value of recent purchases made by Pavi is $3,000

Applied finance charges equal $7.50

The card's current balance is equal to $4,007.50.

Using the formula below, we can now determine the amount of credit that is now available on the card:

The credit line on the card = Available Credit - New Balance

By entering values into the formula provided, we obtain

Credit available on the current card: $8,000 - $4,007.50= $3,992.50.

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Answer:

The perimeter is 24 units

Step-by-step explanation:

Given

\(A = (-9,2)\) --- \((x_1,y_1)\)

\(B = (-9,-6)\) --- \((x_2,y_2)\)

\(C = (-3,-6)\) --- \((x_3,y_3)\)

Required

Determine the perimeter

To do this, we calculate the distance AB, BC and AC.

Distance is calculated as:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2\)

So, we have:

\(AB = \sqrt{(-9 - -9)^2 + (2 - -6)^2\)

\(AB = \sqrt{64\)

\(AB = 8\)

\(BC = \sqrt{(-9 - -3)^2 + (-6 - -6)^2\)

\(BC = \sqrt{36\)

\(BC = 6\)

\(AC = \sqrt{(-9 --3)^2 + (2 --6)^2\)

\(AC = \sqrt{100\)

\(AC = 10\)

So, the perimeter (P) is:

\(P = AB + BC + AC\)

\(P =8 + 6 + 10\)

\(P =24\)

The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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Answer: The first answer choice

AKA: y = -1.74x + 46.6

Step-by-step explanation:

When dividing the period from 1993-2015 into three distinct periods based on the rate of growth of average student debt, one possible approach could be:

1. 1993-2003: Slow and steady growth
During this period, the rate of growth of average student debt was relatively stable and moderate. The increase in student debt was gradual, and the overall burden on students was not as pronounced as in later periods. For example, the average student debt may have increased by a few thousand dollars over these ten years.

2. 2003-2008: Accelerated growth
In this period, the rate of growth of average student debt started to accelerate. The increase in student debt became more significant, potentially due to factors such as rising tuition costs, increased borrowing, and changes in financial aid policies. For example, the average student debt may have doubled or tripled during this five-year period.

3. 2008-2015: Rapid and substantial growth
The period from 2008 to 2015 witnessed a sharp and substantial increase in the rate of growth of average student debt. This period corresponds with the aftermath of the 2008 financial crisis and its impact on the cost of education. The economic recession led to reduced financial support for higher education, resulting in higher borrowing rates for students. For example, the average student debt may have increased by tens of thousands of dollars or even more during this seven-year period.

It's important to note that the division of periods may vary based on the specific data and factors considered. The examples provided are meant to illustrate potential trends rather than represent precise figures. Additionally, it's crucial to consult reliable sources and data on average student debt to obtain accurate information for a comprehensive analysis of the topic.

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Answer: 9/4

Step-by-step explanation: Think of \((\frac{4}{9})^{-1}\)as \(\frac{4^{-1} }{9^{-1}}\).

Now, we can change 4⁻¹ to 4¹ by moving it to the denominator and

we can change 9⁻¹ to 9¹ by moving it to the numerator.

So we have 9¹/4¹ which simplifies to 9/4.

The global maximum occurs at x = 4 and the global minimum occurs at x = 12.

Method to find critical point:

The x-values at which the global maximum and global minimum occur with exactly one critical point can be calculated by the following criteria:

1. Identify the critical point.
2. Check the endpoints of the interval.
3. Determine the global maximum and global minimum based on the information given.

1. Identify the critical point
Since f'(4) = 0, we know that there is a critical point at x = 4. Moreover, since f''(4) = -1, which is negative, we can conclude that this critical point is a local maximum.

2. Check the endpoints of the interval
The interval is [4, 12), so the only endpoint we need to check is x = 12. We don't have information about f'(12), so we can't determine if there's a critical point at this endpoint.

3. Determine the global maximum and global minimum
Since there is only one critical point in the interval and it is a local maximum, the global maximum must occur at x = 4. Since the function is continuous, the global minimum must occur at the other endpoint of the interval, which is x = 12.

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