Question 2 While watching a game of Champions League football in a cafe, you observe someone who is clearly supporting Real Madrid in the game. What is the probability that they were actually born wit

Answer:

C

Step-by-step explanation:

Answer:

Tienes que dividir las fracciones en el dibujo por las fracciones de los números y luego obtendrás las respuestas correctas.

Answer:

40°, 60° and 80°

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 + 4 = 9 parts

Divide 180° ( sum of angles in a triangle) by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio , then

2 parts = 2 × 20° = 40°

3 parts = 3 × 20° = 60°

4 parts = 4 × 20° = 80°

The angles in the triangle are 40°, 60°, 80°

Based on the given information, the theorem the paragraph proof offers proof for is: A. Alternate Interior Angles Theorem

The Alternate Interior Angles Theorem states that when two parallel lines are intersected by a transversal (a line that intersects two or more other lines), the pairs of alternate interior angles formed are congruent.

In other words, if you have two parallel lines and a transversal intersecting them, and you draw a line segment connecting two nonadjacent interior angles on opposite sides of the transversal, then those two angles will be congruent. This is because they are alternate (they are on opposite sides of the transversal and between the parallel lines) and interior (they are inside the parallel lines).

Therefore, the theorem the paragraph proof offers is: Alternate Interior Angles Theorem.

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Answer: (A) Alternate Interior Angles Theorem

Step-by-step explanation: cyberia

Answer:

0 solutions / no solutions

Step-by-step explanation:

If two lines have the same slope but different y-intercepts, it means that they are parallel.

For example, we have two lines:  

y = x

y = x + 1

Both lines have the same slope of 1, but different y - intercepts. Because each equation increases the x and y at the same right (slope) but started at different points, the two equations will never touch.

It's similar to two runner who run at the same pace. If one runner started 50 meters ahead, that runner will always be ahead 50 meters (y-intercept) because they both run at the same rate.

9514 1404 393

Answer:

Step-by-step explanation:

It can work well to factor the leading coefficient from the x-terms.

  5(x² -8x) +60

Now, add the square of half the x-coefficient inside parentheses, and subtract the same amount outside parentheses.

  5(x² -8x +16) +60 -(5)(16)

  5(x -4)² -20 . . . . write as a square, simplify the added constant

The vertex form is ...

  5(x -4)² -20

It shows you the vertex is (4, -20). This is the turning point.

_____

Vertex form is a(x -h)² +k, where (h, k) is the vertex.

Step-by-step explanation:

35 × 14 = 476

476 × 4 = 1904 yd

14 × 14 = 196

196 × 2 = 392 yd

now,

392 yd + 1904 yd = 2296 yd². ans.

hope this helps you !

Answer:

$1,407.10

Step-by-step explanation:

1000(1.05)^7 = 1.05^7 ≈ 1.40710 * 1000 = $1,407.10

Answer:

35

Step-by-step explanation:

Answer:

The angle between the diagonal of the rectangle is \(\frac{\pi }{2}\).

Given:

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4), and d = (4, 1)

To find:

The objective is to find the angle between the diagonals.

Step 1 of 3

Consider the diagram attached.

Step 2 of3

The position vector of diagonal AC is-

=(3-1)î+(4-0)j=2î+4j

And the position vector of diagonal BD is-

=(4-0)î+(1-3)j=4î-2j

Step 3 of 3

cosθ=\(\frac{AC.BD}{|AC|.|BD|}\)

cosθ=\(\frac{(2i-4j)(4i-2j)}{\sqrt{2^2+4^2} \sqrt{4^2+(-2)^2\\} }\)

=\(\frac{8-8}{\sqrt{20}.\sqrt{20} }\)

=0

θ=\(cos^{-1}\)(0)

θ=\(\frac{\pi }{2}\)

Therefore the angle between the diagonal of the rectangle is \(\frac{\pi }{2}\)

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The angle between the diagonals of a rectangle is π/2

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4),  d = (4, 1)

The diagonal position vector AC  

=(3-1)î+(4-0)j=2î+4j

And the diagonal position vector BD  

=(4-0)î+(1-3)j=4î-2j

cos Ф = (AC.BD) / (|AC| . |BD|)

cos Ф = (8-8) / (root20 -roo20)

= 0

Ф = π/2

Therefore the angle between the diagonals of the rectangle is π/2

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The minimum number of terms required for the sum sn to have an error less than 0.0399, assuming K = 1 and b-a = 1.

To determine the minimum number of terms n required for the sum sn to have an error less than 0.0399, we need to use the formula for the error term of a finite series:

|En| ≤ ((M * (b-a)^n)/(n!))

where En is the error term, M is the maximum value of the (n+1)th derivative of the function, a and b are the limits of integration, and n is the number of terms in the series.

Since we do not have a specific function or limits of integration, we cannot determine the exact value of M. However, we can use an upper bound for M, which is the maximum value of the (n+1)th derivative of the function over the entire interval [a,b]. Let's assume that M = K, where K is some constant.

Then we have:

|En| ≤ ((K * (b-a)^n)/(n!))

We want the error to be less than 0.0399, so we can set up the following inequality:

((K * (b-a)^n)/(n!)) < 0.0399

To solve for n, we need to use a numerical method such as trial and error, or a graphing calculator. We can also use a table of values for n! and (b-a)^n to simplify the inequality.

For example, if we assume that K = 1 (which is a reasonable assumption for many functions), and let b-a = 1 (i.e. we are integrating over the interval [0,1]), we can create a table of values for n! and (b-a)^n:

n | n! | (b-a)^n
--|----|---------
1 | 1  | 1
2 | 2  | 1
3 | 6  | 1
4 | 24 | 1
5 | 120| 1
6 | 720| 1

Using these values, we can rewrite the inequality as:

(K/n!) < (0.0399/(b-a)^n)

Plugging in our values, we get:

1/n! < 0.0399

Solving for n using trial and error or a graphing calculator, we find that n = 4 is the minimum number of terms required for the sum sn to have an error less than 0.0399, assuming K = 1 and b-a = 1. However, keep in mind that this value may change depending on the specific function and limits of integration.

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Answer: b

Step-by-step : not needed

Answer:

angles 1 & 3: 63 angle 4: 117

Step-by-step explanation:

fo this all you'd do, is look at the diagram in front of you (assuming you have one), and you'll soon figure out that two of the components are the same size.

2 is parrallel to 4, which means 4 is 117.

now, the whole circle is equal to 360 degrees.

this mean that your equation should look like:

x + x + 117(2) = 360

2x + 117(2)  = 360

2x + 234 = 360

     -234      -234

2x =  126

x = 63

now since we've already figured out 2 & 4, since we found the number 63 with the variable "2x", that means there are 2 angles. therefore angles 1 & 3 would be equal to 63.

lets check!

63 (2) + 117(2) = 360 or not?

126 + 234 = 360

so theres your answer. : D

-7th grade math-

The measure of angle 1 and angle 2 is 63 degrees and the measure of angle 4 is 117 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

The missing figure is attached in the picture.

From the figure

Angle 2 = 117 degrees

As we know,

From the definition of the vertically opposite angles:

Agle 1 = Angle 3

Angle 2 = Angle 4

Angle 2 = Angle 4 = 117

Let

Angle 1 = Angle 3 = x

x + x + 117(2) = 360

2x + 234  = 360

2x + 234 = 360

2x = 360 - 234

2x = 126

x = 126/2

x = 63 degrees

Angle 1 = Angle 3 = 63

Thus, the measure of angle 1 and angle 2 is 63 degrees and the measure of angle 4 is 117 degrees.

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Period of the functions: The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ). The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.

We know that cos (t) is periodic and has a period of 2π.∴ b = 2π∴ The period of the function f(t) =

(7 cos t)² = 2π/b = 2π/2π = 1.

The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ) Hence, the period of the function f(t) =

cos (2φt²/m) is √(4πm/φ).

The function f(t) = (7 cos t)² is a trigonometric function and it is periodic. The period of the function is given by 2π/b where b is the period of cos t. As cos (t) is periodic and has a period of 2π, the period of the function f(t) = (7 cos t)² is 2π/2π = 1. Hence, the period of the function f(t) = (7 cos t)² is 1.The function f(t) = cos (2φt²/m) is also a trigonometric function and is periodic. The period of this function is given by T = √(4πm/φ). Therefore, the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

The period of the function f(t) = (7 cos t)² is 1, and the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

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Option C is correct, , the expression 6.1+7.7-5.4 can be used to find  find the value of the expression.

The given expression is 6.1 - 5.4 - (-7.7).

We have to find the expression which is used to find the value of the given expression.

Which means we have to simplify the given expression.

When negative sign is multiplied with negative sign we get positive.

6.1 - 5.4 +7.7

We get 8.4.

Hence, the expression 6.1+7.7-5.4 can be used to find  find the value of the expression.

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The IRA (individual retirement account) of a 22-year-old college student, who deposits $55 into the account each month, will have a total balance at retirement. To calculate this, we need to consider the time period, the monthly deposit, and the annual percentage rate (APR).

The student plans on retiring at age 65, which means the IRA will have 65 - 22 = 43 years to grow. Since the student deposits $55 each month, we can calculate the total number of deposits over the 43-year period: 43 years * 12 months/year = 516 deposits.

To calculate the total balance at retirement, we need to consider the growth of the account due to the APR. The annual growth rate is 6%, which can be expressed as 0.06 in decimal form. To calculate the monthly growth rate, we divide the annual growth rate by 12: 0.06/12 = 0.005.

Using the formula for the future value of an ordinary annuity, we can calculate the total balance at retirement:
FV = PMT * [(1 + r)^n - 1] / r

Where:
FV = future value (total balance at retirement)
PMT = monthly deposit ($55)
r = monthly interest rate (0.005)
n = number of deposits (516)

Plugging in these values into the formula:
FV = 55 * [(1 + 0.005)^516 - 1] / 0.005

Calculating this equation, the IRA will contain $287,740.73 at retirement.

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The required value of the given function is (f ⋅ g)(4) = 130.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x)=3x+1 and g(x)=x²-6

(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).

(f ⋅ g)(x) = f(x) × g(x)

So, substituting x = 4:

(f ⋅ g)(4) = f(4) × g(4)

= (3 × 4 + 1)×(4² - 6)

= 13 × 10

= 130

So, (f ⋅ g)(4) = 130.

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The probability of drawing a white marble on the first draw and another white marble on the second draw is 1/3.

Probability theory is an area of mathematics that examines random events. A random event's outcome cannot be predicted before it happens, although it could take any of several different forms. The final result is thought to have been determined by chance.

In everyday speech, the word "probability" has numerous meanings. For the growth and applicability of the mathematical theory of probability, two of these are particularly crucial. One is the representation of probabilities as relative frequencies, which is illustrated by examples from basic teams playing coins, cards, dice, and roulette wheels.

Given that, a bag contains 6 white marbles and 4 black marbles. a marble is drawn from the bag and then a second marble is drawn without replacing the first one.

The total number of balls = 10 marbles.

The probability of drawing a white marble on first draw = 6/10.

The probability of drawing a white marble on the second draw = 5/9.

The probability of drawing a white marble on the first draw and another white marble on the second draw is:

6/10 × 5/9 = 30/90 = 1/3

Hence, the probability of drawing a white marble on the first draw and another white marble on the second draw is 1/3.

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A sample that does not represent the entire group of interest is called a biased sample.

A biased sample is a sample that doesn't reflect the real-world population it is supposed to represent. It happens when the sample is chosen in such a way that some members of the population are less likely to be included than others.

Therefore, a biased sample may not be an accurate representation of the entire population.

For example, if a researcher wants to know how many people in a given area have access to the internet and chooses a sample of people from a high-income neighborhood, the results may be biased because people from low-income areas may have lower rates of internet access.

A biased sample can lead to inaccurate conclusions, and therefore, it's important to ensure that the sample is representative of the population. A random sample, on the other hand, ensures that all members of the population have an equal chance of being included in the sample.

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The probability of getting 1 on two of the dice, given that the sum of the numbers on the three dice is 7, is:

P(A|B) = P(A and B) / P(B) = 3/3 = 1

To solve this problem, we need to use conditional probability.

We are given that the sum of the numbers on the three dice is 7, so let's first find the number of ways that we can obtain a sum of 7.

There are six possible outcomes when rolling a single die, so the total number of outcomes when rolling three dice is 6 x 6 x 6 = 216.

To get a sum of 7, we can have the following combinations:

- 1, 2, 4
- 1, 3, 3
- 2, 2, 3

So there are three possible outcomes that give us a sum of 7.

Now let's find the number of ways that we can obtain 1 on two of the dice.

There are three ways that this can happen:
- 1, 1, x
- 1, x, 1
- x, 1, 1

where x represents any number other than 1.

We need to find the probability of getting 1 on two of the dice, given that the sum of the numbers on the three dice is 7. This is a conditional probability, which is given by:
P(A|B) = P(A and B) / P(B)

where A is the event of getting 1 on two of the dice, and B is the event of getting a sum of 7.

The probability of getting 1 on two of the dice and a sum of 7 is the number of outcomes that satisfy both conditions divided by the total number of outcomes:

- 1, 1, 5
- 1, 5, 1
- 5, 1, 1

So there are three outcomes that satisfy both conditions.

Therefore, the probability of getting 1 on two of the dice, given that the sum of the numbers on the three dice is 7, is:
P(A|B) = P(A and B) / P(B) = 3/3 = 1

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if the "d"iameter of the pie is 30, then its radius must be half that, or 15.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}\)

Answer:

(-1,-2, -3, -4)

Step-by-step explanation:

-15 < 3n <6

-15 < 3 (-1,-2, -3, -4) <6

3 • -1 = -3

3 • -2 = -6

3 • -3= - 9

3 • -4 = -12

so all these answer still make -15 the lowest value and 6 the highest value.

Answer:

60

Step-by-step explanation:

You would just plug everything in so you get -5(-2-(-5)(-2)) which can be reduced so -5(-12) which is 60

The value of expression x(y-xy) at x=-5 and y=-2 is -40.

An expression is a combination of numbers, symbols ,fraction, indeterminants, coefficients. It is not usually found in equal to form and it is equated to find the value of the expression by putting the value of variables.

We have been given the expression x(y-xy) and we have to find the value at x=-5 and y=-2 and for that we have to just put the value of x and y.

x(y-xy)=-5{-2-(-5*-2)

=-5(-2+10)

=-5*8

=-40

Hence the value of expression x(y-xy) at x=-5 ,y=-2 is -40.

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Answer:

£9

Step-by-step explanation:

3 x 4 = 12

3 x 3 = 9

Answer:

£9

Step-by-step explanation:

£3   ->   €4

            x3

£?    ->  €12

so three times three

3 x 3 = 9  

Another way

3 divided by 4 is .75

so multiply .75 by 12

Answer:

Trinominal

Step-by-step explanation:

By definition, Trinominals are those expressions having 3 values, in this case, x^2, x, and the constant 6 are the values.

hope it helps.

Let a,b∈Z and m∈N. Prove that if a≡b(modm), then a 3≡b 3(modm).Solution:

We have to prove that if a≡b(modm), then a3≡b3(modm).Let us assume that a ≡ b (mod m)Then there exists a k ∈ Z such that, a = b + mk

We need to prove that, a3 ≡ b3 (mod m)or a3 - b3 ≡ 0 (mod m)

On factorizing, we get;a3 - b3 ≡ (a - b) (a2 + ab + b2) ≡ (mk) (a2 + ab + b2) ≡ m (k(a2 + ab + b2))

Hence, we can write it as, a3 ≡ b3 (mod m)Thus, if a ≡ b (mod m), then a3 ≡ b3 (mod m)

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Answer:

By translating the graph of f(x) two units to the left

Answer:

down 2 units I think

Step-by-step explanation: