Please help (algebra 1 question)

1. The chance that all 23 people have different birthdays is about 0.493 or 49.3%.

2. The chance that two people in the room have the same birthday is about 0.507 or 50.7%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

(1) The probability that all 23 people have different birthdays can be calculated as follows:

For the first person, there are 365 possible birthdays to choose from.

For the second person, there are 364 possible birthdays left to choose from (since one has already been taken).

For the third person, there are 363 possible birthdays left to choose from, and so on.

So the probability that all 23 people have different birthdays is:

P(all different) = 365/365 * 364/365 * 363/365 * ... * 344/365

                 = 0.493

Therefore, the chance that all 23 people have different birthdays is about 0.493 or 49.3%.

(2) The probability that two people in the room have the same birthday can be calculated as follows:

For the first person, there are 365 possible birthdays to choose from.

For the second person, there is a 1/365 chance that they have the same birthday as the first person.

For the third person, there is a 2/365 chance that they have the same birthday as one of the first two people, and so on.

So the probability that at least two people in the room have the same birthday is:

P(at least 2 people share a birthday) = 1 - P(all different)

                                     = 1 - 0.493

                                     = 0.507

Therefore, the chance that two people in the room have the same birthday is about 0.507 or 50.7%.

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Answer:

Step-by-step explanation:

1) Diagonal bisect the angles of Rhombus

∠CAB = ∠CAD

∠CAB = 71

2) ∠DAB = ∠CAB + ∠CAD

 ∠DAB = 71 + 71 = 142

In Rhombus, adjacent angles are supplementary

∠DAB + ∠ABC = 180

142 + ∠ABC = 180

           ∠ABC = 180 - 142

         ∠ABC = 38

3)  In rhombus, opposite angles are congruent

∠ADC = ∠ABC

∠ABC = 38

In rhombus, diagonal bisect angles

∠BDC = (1/2)*∠ADC

∠BDC= 38/2

∠BDC = 19

4) Diagonals bisect each other at 90

∠DEC = 90

5) Diagonals bisect each other

BE = DE

BE + DE = DB

7x -2 +7x -2 =24   {add like terms}

        14x - 4 =24

              14x = 24+4

              14x = 28

                 x = 28/14

                 x = 2 m

6) AB = 13m

BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m

In right angle ΔAEB,  {use Pythagorean theorem}

AE² + BE² = AB²

AE² + 12² = 13²

AE² + 144 = 169

         AE² = 169 - 144

         AE² = 25

         AE = √25

        AE = 5 m

Diagonals bisect each other

AE = EC

AC = 2*5

AC = 10 m

7)Side = 13 m

Perimeter = 4*side

                  = 4*13

 Perimeter = 52 m

8) d1 = AC = 10 m

   d2 = DB = 24 m

Area = \(\frac{d_{1}*d_{2}}{2}\)

         \(=\frac{10*24}{2}\\\)

          = 10 *12

          = 120 m²

No segments or lines are provided in the question, therefore it is not possible to determine which are parallel.

The values of x and y given in the question are not sufficient to determine which segments or lines are parallel. In order to determine whether two lines are parallel or not, we need to have their equations or coordinates. Without this information, it is impossible to determine which lines or segments are parallel.

Therefore, the answer to the question is that no segments or lines are parallel based on the information provided.

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The number of times to get a 3 will be 24 times.

It should be noted that the expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables

In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.

Therefore, when there are 64 tosses, the estimate will be:

= 3/8 × 64

= 3 × 8

= 24

The number of times is 24.

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Jimm tossed a die several times. He got the number "3" on 8 of the tosses. What is the best estimate of the total number of times he tossed the die 64 times?

Answer:

41

Step-by-step explanation:

Matrix Multiplication follows a row-column format. In order to compute this, you must be familiar with vector dot products.

With that in mind, lets get straight into it.

The order that matrix multiplication follows means that the terms in the result are filled in left to right, then top to bottom.

Therefore, a21 will be the 3 value that is computed. This is important becuase this allows to directly compute a21, instead of using up a lot of time computing all the values before.

As a21 is located in the bottom row 1st column, we take the dot product of the 2nd row in matrix 1 and the 1 column in matrix two.

So we have:

(7 2) dot (5 3) = 7*5 + 2*3 = 41

Answer:

35 inches

Step-by-step explanation:

Regular, means that all the sides of the pentagon are the same, so you can multiply 21 * 5/3 = 35

Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.

Answer:

b=-8

Step-by-step explanation:

9+1/4b=7

-2=1/4b

b=-8

Answer:

No solution.

Step-by-step explanation:

9.25 does not equal 7.

Answer:

z

Step-by-step explanation:

Answer:

B. 2x + $22 = $56 ; x = $17

Step-by-step explanation:

Assuming a pair of short is accounted for by the variable x.

Your total cost is $56. This means that your expression will equal 56:

________________ = 56

Next, you buy 1 shirt (denoted by s) for $22.

s = $22

You buy 2 pairs of pants. The cost is not given, so it can vary. Give it a variable. The answers denote it as x. As you are buying two pairs of pants, multiply 2 with x:

2 * x = 2x.

Combine the terms and plug it into the equation:

2x + 22 = 56

Next, solve for x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. Remember,  PEMDAS is the order of operation, &

PEMDAS =

Parenthesis

Exponents & Roots

Multiplication

Division

Addition

Subtraction

First subtract 22 from both sides:

2x + 22 (-22) = 56 (-22)

2x = 56 - 22

2x = 34

Next, divide 2 from both sides:

(2x)/2 = (34)/2

x = 34/2

x = $17

B. 2x + $22 = $56 ; x = $17 is your answer.

~

Answer:

B. 2x + $22 = $56 ; x = $17

Step-by-step explanation:

The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Answer:

288

Step-by-step explanation:

288 was the answer.

The total number of possible vacation packages 288.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.

The number of ways to choose a hotel or a cabin is 7 + 5 = 12, and the number of ways to choose one of each of the remaining options is 4 x 3 x 2 = 24, since there are 4 meal plans, 3 escape rooms, and 2 amusement parks to choose from.

To find the total number of possible vacation packages, we can multiply these numbers:

Total number of possible vacation packages = 12 x 24

Total number of possible vacation packages = 288

Therefore, there are 288 possible vacation packages.

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Answer:

I only

Step-by-step explanation:

7<=3x-2

9<= 3x

3<= x

The integral of the expression \(\int\limits^{\infty}_{-\infty} {x^2 - 2x + 5} \, dx\) is x³/3 - x² + 5x + c

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

\(\int\limits^{\infty}_{-\infty} {x^2 - 2x + 5} \, dx\)

The integral of the function can be calculated using the first principle which states that

if f'(x) = naxⁿ⁻¹, then f(x) = axⁿ

So, we have

\(\int\limits^{\infty}_{-\infty} {x^2 - 2x + 5} \, dx = \frac{x^3}{3} - x^2 + 5x\)

Introduce the constant variable

\(\int\limits^{\infty}_{-\infty} {x^2 - 2x + 5} \, dx = \frac{x^3}{3} - x^2 + 5x + c\)

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Question

Evaluate the integral \(\int\limits^{\infty}_{-\infty} {x^2 - 2x + 5} \, dx\)

Answer:

16, 64, 256

Step-by-step explanation:

Answer:

$11, $13, $14

Step-by-step explanation:

all of those answers are greater than $9 but less than or equal to $14.

There are 44 Democratic senators and no Independent senators based on ratio.

Since the ratio of Republicans to Democrats is 5:4, we can represent the number of Republican senators as 5x and the number of Democratic senators as 4x, where x is a positive integer. The total number of senators is given as 100, so we have:

5x + 4x + Independent = 100

Simplifying:

9x + Independent = 100

To find the values of x and Independent, we need to solve for these variables. We can start by subtracting Independent from both sides of the equation:

9x = 100 - Independent

Now, we need to find a value of x that makes the right-hand side of the equation divisible by 9. Since the sum of the digits of 100 is 1 + 0 + 0 = 1, which is not divisible by 9, we need to find a value of Independent that makes the sum of the digits of 100 - Independent divisible by 9. The only value that works is Independent = 1, which gives us:

9x = 99

x = 11

Now we can substitute this value of x back into the equation to find the number of Republican and Democratic senators:

Republican = 5x = 5(11) = 55

Democrat = 4x = 4(11) = 44

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The expected value of the sum of n dice is E[X] = 3.5n.

Indicator random variables are a probability theory tool. They are used to help evaluate probabilities for a given random variable.
Let X be the total number that results from n throws of a fair six-sided die.

By linearity of expectation,E[X] = E[X1 + X2 + ... + Xn] = E[X1] + E[X2] + ... + E[Xn]

Where Xj is the number obtained on the jth die roll.

Each Xi is a discrete random variable with a uniform distribution on the set {1, 2, 3, 4, 5, 6}.

To evaluate E[Xi], we define an indicator random variable Yi as follows: Yi = 1 if Xi = i and Yi = 0 otherwise.

Then, Xi = 1Y1 + 2Y2 + 3Y3 + 4Y4 + 5Y5 + 6Y6.

Thus,E[Xi] = E[1Y1 + 2Y2 + 3Y3 + 4Y4 + 5Y5 + 6Y6] = E[1Y1] + E[2Y2] + ... + E[6Y6] = 1P(Xi = 1) + 2P(Xi = 2) + ... + 6P(Xi = 6) = (1 + 2 + ... + 6) / 6 = 3.5.

Therefore, E[X] = E[X1] + E[X2] + ... + E[Xn] = 3.5n.

Thus, we have computed the expected value of the sum of n dice using indicator random variables. The expected value of the sum of n dice is E[X] = 3.5n.

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The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

x²

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

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The y-intercept of the sine function is -3

We know that the standard form of the sine function is, y = a sin(bx + c) + d

where, amplitude = |a|

period = 2π/b

phase shift = -c/b

and vertical shift = d

Here, a sine function has an amplitude of 3, a period of π, and a phase shift of π/4

a = 3,

So, 2π/b = π

⇒ b = 2

And phase shift -c/b = π/4

⇒ -c/2 = π/4

⇒ -c = π/2

⇒ c = -π/2

So, a sine function would be,

y = 3 sin(2x + -π/2) + 0

y = 3 sin(2x + -π/2)

When x = 0,

y = 3 sin(0+ -π/2)

y = 3 sin(-π/2)

y = 3 × (-1)

y = -3

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Answer:

23?

Step-by-step explanation:

unless its s trick question its really only one possible answer no?

Answer:

18 cm³

Step-by-step explanation:

To find the volume of a triangular prism, find the area of the cross-section (in this case, the triangle) and multiply it by the length.

The area of the triangle is 1/2 × 4 × 3 = 6 cm²

Now, multiply 6 by 3 to get 18 cm³

Hope this helps!

Answer:

1.25

Step-by-step explanation:

cause 5/4÷ 12/12 is 1/8 and 1/8 as a decimal is 1.25.

Answer:

502.40 inches

Step-by-step explanation:

First we need to find the circumference of the wheel, which is given by pi times the diameter:

C = (3.14)(20) = 62.8 inches

That's how far the unicycle will travel in 1 revolution, so from there just multiply by 8

D = (62.8)(8) = 502.40 inches

The unicycle travel 502 inches in 8 revolutions

The circumference is the perimeter of a circle. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment.

Given that, a unicycle wheel has a diameter of 20 inches.

To find that how many inches will the unicycle travel in 8 revolutions, we will multiply the circumference to the asked number of revolutions.

Circumference = π × diameter

= 3.14 × 20 = 62.8 inches

The unicycle travel in 8 revolutions = 62.8 × 8 = 502.4 inches

In nearest hundred = 502 inches

Hence, the unicycle travel 502 inches in 8 revolutions

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Answer:

D

Step-by-step explanation:

It would he D because if each shirt is $35 then 35 is the constant and if its a one time fee of 2.25 then it should only be added in. 6 shirts times $35=$210 + $2.25 shipping fee= $212.25

The z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

The determination of the z-coordinate of the mass center of the homogeneous paraboloid of revolution requires a long answer.

Firstly, we need to define the mass density of the paraboloid. Since it is a homogeneous object, its mass density is constant throughout its volume.

Let us denote this density as ρ.

Next, we need to find the volume of the paraboloid.

The volume of a paraboloid of revolution with a height h and a base radius r is given by V = (π/2) * r^2 * h/3.

In this case, the height of the paraboloid is 4 units and the radius of the base is 2 units. Thus, the volume of the paraboloid is:
V = (π/2) * (2)^2 * 4/3 = (8π/3) units^3

Now, we can find the mass of the paraboloid by multiplying its volume by its density:
M = ρ * V = ρ * (8π/3) units^3

The next step is to find the x and y coordinates of the mass center of the paraboloid.

We can do this by using double integrals:
x = (1/M) * ∬(paraboloid) x * ρ * dV
y = (1/M) * ∬(paraboloid) y * ρ * dV

Since the paraboloid is symmetric about the z-axis, we know that its mass center will lie on this axis, and thus, its x and y coordinates will be zero.

Finally, we need to find the z-coordinate of the mass center. We can do this by using the same double integral, but this time we integrate over the z-axis:
z = (1/M) * ∬(paraboloid) z * ρ * dV

To set up the double integral, we can use cylindrical coordinates, with ρ ranging from 0 to 2 and θ ranging from 0 to 2π.

The z-coordinate of any point on the paraboloid is given by z = (1/16) * (x^2 + y^2), so we can substitute this into the double integral:
z = (1/M) * ∫(0 to 2π) ∫(0 to 2) ∫(0 to (1/16)*(ρ^2)) ρ * z * ρ * ρ * dρ dθ dz

After evaluating this integral, we get:
z = (3/5) * h = (12/5) units

Therefore, the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

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Answer:

18.84

Step-by-step explanation:

The formula for circumference is 2(pi)r, I think. The radius is 3. 3 times 2 is 6. 6 times 3.14 is around 18, I think.

hope this helps

Answer:

A

Step-by-step explanation: