how many people have to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least assume that all possible monthly outcomes are equally likely.

The equation of the parabola is x^2 = 8(y + 3)

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

Focus = (4, -3)

Directrix, y = 1

Since the directrix is a horizontal line, the parabola opens downward or upward.

The focus is located 4 units to the right of the vertex

So, we have

Vertex = (0, -3).

The equation is of the form:

(x - h)^2 = 4p(y - k),

where (h, k) is the vertex, and p is the distance from the vertex to the focus (and to the directrix).

In this case, h = 0, k = -3, and p = 2.

Substituting these values, we get:

(x - 0)^2 = 8(y + 3)

x^2 = 8(y + 3)

So the equation is x^2 = 8(y + 3)

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By the property of SAS criterion,

ΔKMN is similar to ΔKJL.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are proportionate, and the corresponding angles are equal.

Given:

In ΔJKL,

MN is parallel to JL.

That means MN and JL are equally spaced.

So,

JM/MK = LN/NK

∠KMN ≅ ∠KJL {By corresponding angles}

ΔKMN is similar to ΔKJL. {By the SAS criterion}

Therefore, ΔKMN is similar to ΔKJL.

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The equivalent expression is -0.45t - 0. 05. Option D

Equivalent expressions are those expressions having the same solution.

From the information given, we have the expression as;

(0.35t -0.4) - (0.8t - 0.35)

Now, to simply the expression, take the steps;

expand the bracket;

0.35t - 0.4 - 0.8t+ 0.35

Now, collect the like terms

0.35t  - 0.8t - 0.4 + 0.35

Add or subtract the like terms

-0.45t - 0. 05

Hence, the expression is -0.45t - 0. 05

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By completing the square, the equation. x2 + 20x + 82 = 7. The solutions are x = -15 and x = -5, going from least to largest.

The square of half the x-coefficient must equal the constant on the left:

 (20/2)^2 = 100

To get it to that value, we can add 18 to both sides of the equation:

 x^2 + 20x + 100 = 25 . . . add 18 to both sides of the equation

 (x + 10)^2 = 25 . . . . . . .  . write the left side as a square

 x + 10 = ±√25 = ±5 . . . . . take the square root

 x = - 10 ± 5 = {-15, -5}

The solutions are x = -15 and x = -5.

The attached graph shows the solutions to ...

 x^2 + 20x + 82 -7 = 0 . . . . . the result of subtracting 7 from both sides

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The value of 33.4 meters to centimeters is 3340 centimeters

Conversion of units is described as the  conversion between different units of measurement for the same quantity, and it is done mostly through multiplicative conversion factors.

It also involves multiple steps of multiplication or division by a numerical factor or, a conversion factor.

From the information given, we have to convert meters to centimeters

Note that;

100 centimeter = 1 meter

Then x centimeters = 33.4 meters

cross multiply

x = 100(33.4)

multiply the values

x = 3340 centimeters

Hence, the value is 3340 centimeters

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Using substitution method, the value of x and y are -13/3 and 2/3 respectively

A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the set of values for the variables that satisfies all of the equations simultaneously. The variables represent unknown values that we are trying to solve for, and each equation provides a constraint on those variables.

To find the value of x and y, we can use substitution method.

4x + 8y = 12 ...eq(i)

x + 2y = -3 ...eq(ii)

From eq(ii)

x = -3 + 2y ...eq(iii)

Put eq(iii) into eq(i)

4(-3 + 2y) + 8y = 12

-12 + 8y + 8y = 12

-12 + 16y = 12

16y = 24

y = 2/3

Put y = 2/3 in eq(ii)

x + 2(2/3) = - 3

x + 4/3 = -3

x = -13/3

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Answer:

The length of the unknown side of the triangle is

[tex]5 \sqrt{5} [/tex]

The mean difference between the skier's practice times and the qualifying time is given as follows:

-2.01 seconds.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

The observations for this problem are given as follows:

1.25, -5.38, -0.92, 2.19, -6.74, -2.46.

The sum of these six observations is of:

1.25 - 5.38 - 0.92 + 2.19 - 6.74 - 2.46 = -12.06.

Hence the mean is of:

Mean = -12.06/6

Mean = -2.01 seconds.

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The transformations map polygon ABCD to polygon A'B'C'D' shows dilation and then reflection.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. In geometry, object transformations constitute the foundation for the majority of proofs.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

From the figure we observe that the figure is compressed or dilated using a negative scale factor, and then the figure is reflected on the y -axis.

Hence, the transformations map polygon ABCD to polygon A'B'C'D' shows dilation and then reflection.

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Tyler drove 138miles, and brittney drove 116miles, the ratio of tyler's miles to brittney's miles is 69/58.

The ratio of Tyler's miles to Brittney's miles can be found by dividing Tyler's miles by Brittney's miles.

Ratio of Tyler's miles to Brittney's miles = Tyler's miles / Brittney's miles

Ratio of Tyler's miles to Brittney's miles = 138 miles / 116 miles

Simplifying the ratio by dividing both numbers by their greatest common factor, which is 2, we get:

Hence,

Ratio of Tyler's miles to Brittney's miles = 69/58

This means that for every 69 miles Tyler drove, Brittney drove 58 miles.

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$2627625 much should you expect to pay in interest over the life of the loan if your interest rate is 10.50%.

The amount of interest payable each period expressed as a percentage of the amount lent, deposited, or borrowed is known as the interest rate. The total amount of interest on a loaned or borrowed sum is determined by the principle amount, the interest rate, the frequency of compounding, and the period of time during which it is lent, deposited, or borrowed.

Simple interest rate = P × R × T

where,

P = Principal = $19,250

R = Rate of Interest in % per annum = 10.50%

T = Time, usually calculated as the number of years = 13 years

Thus,

simple interest =  19250 × 10.50  × 13

simple interest = 2627625

$2627625 much should you expect to pay in interest over the life of the loan if your interest rate is 10.50%

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Answer:

A Y=10

Step-by-step explanation:

Answer:

Option B is the right answer.

Step-by-step explanation:

See Attachment

The average velocity from 4 to 8 seconds is given as follows:

v = [position at 8 seconds - position at 4 seconds]/4.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The change in the distance from 4 to 8 seconds is given as follows:

position at 8 seconds - position at 4 seconds

The change in the time from 4 to 8 seconds is given as follows:

8 - 4 = 4 seconds.

Hence the velocity is of:

v = [position at 8 seconds - position at 4 seconds]/4.

The problem is incomplete, hence the general procedure to obtain the average velocity was presented.

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The width of the rectangle is 4*m⁷*n³

Remember that for a rectangle of length L and width W the area is given by the formula:

A = W*L

Here we know that:

A = 20*m¹⁰*n⁴

L = 5*m³*n

Then we can write:

20*m¹⁰*n⁴ = (5*m³*n)*W

Now we can solve that for W.

(20/5)*(m¹⁰/m³)*(n⁴/n) = W

4*m¹⁰⁻³*n⁴⁻¹ = W

4*m⁷*n³ = W

That is the width.

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The recursive rule for the geometric sequence 10, -80, 640, -5120, is a(1) = 10 (the first term) For n > 1, a(n) = -8*a(n-1) (each term is -8 times the previous term).

Recursive definitions of objects are those in which they are defined in terms of other objects of the same kind. The whole class of objects can then be built from a small set of initial values and a few of rules by utilising a recurrence relation of some sort. The most typical way to define the Fibonacci numbers is recursively.

geometric sequence 10, -80, 640, -5120

a(1) = 10 (the first term)

For n > 1, a(n) = -8*a(n-1) (each term is -8 times the previous term).

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The expressions, in terms of t, for each vehicle so that the vehicles start separated and meet at 10 seconds is:

Tractor's position = Vt * t

Scooter's position = Vs * t

Let's assume that the starting point for both the tractor and the scooter is at "0". We can then write the expressions for their positions in terms of time "t" as follows:

For the tractor:

Tractor's speed = Vt

Tractor's position = Vt * t

For the scooter:

Scooter's speed = Vs

Scooter's position = Vs * t

Now, as both the vehicles meet at 10 seconds, we can write the equation:

Vt * 10 = Vs * 10

The above equation represents the position of both the vehicles at 10 seconds. If we assume the speed of the tractor and the scooter to be constant, then the equation gives us the relationship between their speeds.

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Answer: -5r+8r+5=3r+5

Step-by-step explanation:

First add like terms, so -5r and 8r. For a second lets pretend the r doesn't exist. So, what is -5 + 8, 3, so 3r. Since 3r and 5 cannot be combined, the equivalent expression is 3r+5.

We can use the sine ratio to solve this problem and the value of x would be 8.604.

What are trigonometric ratios?

Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.

Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we have given the hypotenuse of the triangle, and  an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x

sin35°= x/15

To solve for x, we can use the following steps:

Multiply both sides of the equation by 15 to isolate x:

sin 35° = x/15

15 * sin 35° = x

Use a calculator to approximate sin 35°:

sin 35° ≈ 0.5736

Substitute the approximation into the equation and solve for x:

x = 15 * 0.5736

x ≈ 8.604

Therefore, x is approximately equal to 8.604.

Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.

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A graph of the system of linear equations y = -2x + 2 and y = -2x + 1 is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines have the same slope and are parallel.

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Step-by-step explanation:

h represents the number of hours

15 represents the initial price for bike rentals

0.75h represents that for every hour, the price of bike rentals increases by 0.75

The total amount y collected from x students is y = 10x.

The graph is given below.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The club is charging $10 per student that attends.

This means,

Number of students = x

The total amount y collected from x students.

y = 10x

The graph is given below.

Thus,

y = 10x is the total amount y collected from x students is

The graph is given below.

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Answer:

Step-by-step explanation:

Part A:

The actual length of the dining room is 120 inches and the percent error is -5%, which means that Rihana's measurement was too short. To find the length she measured, we need to add 5% to the actual length:

120 inches * (1 + (-5%)/100) = 120 inches * (1 - 0.05) = 120 inches * 0.95 = 114 inches

So Rihana measured the length of her dining room as 114 inches.

Part B:

To find the length that Rihana measured, we used the formula for calculating percent error:

measured length = actual length * (1 + (percent error)/100)

Since the percent error was negative (-5%), this means that Rihana's measurement was too short, so we subtracted the percent error from 100%. To do this, we added the negative percent error to 100%:

100% + (-5%) = 100% - 5% = 95%

So the measured length was 120 inches * 95% = 114 inches.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The length of the dining room measured by Rihana with a -5%  percent error  is 114 inches.

What is a percent error?

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.

A) Given the percent error as -5%.

The actual length = 120inches

Now error in measurement = 5% of 120 inches = 6 inches.

Since there is a negative sign in percent error, the measured value is 6 inches less than actual value.

Therefore the measured value = 120 - 6 = 114 inches.

B) We are given the actual length as 120 inches.

There is a -5% error in the measured value.

This means that the measured value is (5% of 120) inches less than actual value. It is identified as less because of the negative sign.

So the measured value is = 120 - 0.05*120 = 114 inches.

Therefore the length of the dining room measured by Rihana with a -5%  percent error is 114 inches.

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The number of elements in the sample space for this experiment are 969 by combination formula.

In an experiment where a person eating at a cafeteria choose 3 out of the 19 vegetables on offer, the number of elements in the sample space is 969.

A sample space of an experiment is the set of all possible outcomes of a random experiment. So the number of elements in a sample space is the total number of possible outcomes of  the experiment.

Here the experiment is choosing 3 vegetables from a set of 19 vegetables offered. The total number of ways to choose 3 out of 19 distinct vegetables = [tex]^{19}C_{3}[/tex]

= [tex]\frac{19!}{3!\times16!}[/tex]

= 969

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By using the unitary method to find out that Priya practiced the violin for 45 minutes, which is 75% of the time Han spent practicing the piano.

Unitary method is a method that involves finding the value of one unit and then using that value to find the value of multiple units. This method is particularly useful in solving problems that involve proportions, ratios, and rates.

Now let's apply the unitary method to the given problem. We know that Han practiced the piano for 60 minutes over the weekend. We also know that Priya practiced the violin for 75% as much time as Han practiced the piano. To find out how long Priya practiced, we need to first find out how long 75% of Han's practice time is.

To do this, we can use the following equation:

75% of Han's practice time = 75/100 x 60 minutes

= 45 minutes

So Priya practiced the violin for 45 minutes over the weekend.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Answer:

Step-by-step explanation:

How many pattern block trapezoids would create for hexagons?

2 trapezoids compose a hexagon using equal-size shapes: 2 trapezoids, 6 triangles, or 3 blue rhombuses. compose hexagons using different shapes. So 2 trapezoids create 1 hexagon. This means 6 trapezoids make 3 hexagons.

The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons.

However, in general, you would need at least 18 trapezoids.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.

If you are looking to create larger hexagons you will need more trapezoids.

Depending on the size and shape, you could need as many as 24 or more trapezoids.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.

Hence, To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids.

Therefore, to create 5 hexagons.

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The boat travels a distance of [tex](1/2k) ln(61/42)^2[/tex] in the first 2 minutes after its motor quits.

We can solve this problem using separation of variables. The differential equation that models the velocity of the boat is:

[tex]dv/dt = -kv^2[/tex]

To do this, we first need to separate the variables and integrate both sides:

[tex]1/v^2 dv = -k dt[/tex]

Integrating both sides, we get:

-1/v = kt + C

where C is the constant of integration. To find C, we can use the initial condition that the boat is moving at 83 ft/s when the motor quits:

-1/83 = k(1) + C

C = -1/83 + k

Now we can substitute C back into our equation:

-1/v = kt - 1/83 + k

Solving for v, we get:

v = 1 / (k(t - 1/83 + 1))

Now we can integrate v over the time interval [1, 121] to find the distance traveled by the boat:

d = ∫[1,121] v dt

Substituting v into the integral, we get:

d = ∫[1,121] 1 / (k(t - 1/83 + 1)) dt

We can simplify the integral by using the substitution u = t - 1/83 + 1:

d = ∫[84/83, 122/83] 1 / (ku) du

Now we can integrate this expression to get:

d = ln(u) / k |[84/83, 122/83]

d = ln(122/83) / k - ln(84/83) / k

d = (1/k) ln(122/83) - (1/k) ln(84/83)

We can simplify this expression using the fact that C = -1/83 + k:

d = (1/k) ln(122/83 / 84/83)

d = (1/k) ln(61/42)

Finally, we can plug in the initial condition k > 0 to get the distance traveled by the boat:

d = [tex](1/k) ln(61/42) = (1/2k) ln(61/42)^2[/tex]

d = [tex](1/2k) ln(61/42)^2[/tex]

Since we are not given the value of k, we cannot compute the exact numerical value of the distance traveled.

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According to the given information Congruent diagonals is not a property of parallelogram.

A kite's opposing forces aren't always parallel, just like not every kite is just a parallelogram. Trapezoids are quadrilaterals having a single pair of parallel sides. The parallel sides make up the bases. If somehow the foundation angles are equal, the trapezoid is said to be an isosceles trapezoid.

Since a diamond has four slanted, equal-length sides, it is an example of a rhombus. They are also both parallelograms since a parallelogram is indeed a rhombus and a diamond is one as well.

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Answer:

SX = 20

Step-by-step explanation:

the midsegment of a trapezoid is half the sum of the parallel bases, then

[tex]\frac{UV+SX}{2}[/tex] = TW , that is

[tex]\frac{40+SX}{2}[/tex] = 30 ( multiply both sides by 2 to clear the fraction )

40 + SX = 60  ( subtract 40 from both sides )

SX = 20