Roll two fair dice. find p(a |b) where a stands from sum of the two faces is 10 and b stands for two dice are showing different faces. [a] (reduced fraction)

It is recommended that when an ambulance arrives at an accident scene, it should park a safe distance away from the scene, at least 500 feet away.

This is to ensure the safety of the paramedics and other emergency responders, as well as to ensure that the ambulance does not impede the movement of other emergency vehicles. Additionally, it is also to protect the privacy of the individuals involved in the accident and ensure that the scene is not tampered with.

It is also important to follow any additional instructions given by the police or fire department at the scene, as they may have specific parking instructions based on the situation.

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Answer:

The diagonals bisect each other.

Step-by-step explanation:

Given

Rhombus ABCD

Required

Which property proves AEB ≅ DEC by SAS

From the question, we understand that the property is to be proved by SAS; SAS implies that Side-Angle-Side

We can assume that point E is where the diagonals meet.

So, we have:

Equal sides: AE = DE and BE = CD

Equal angle: <E = <E

The above implies that the diagonals bisect one another.

Answer:

its both the Diagonal answers

Step-by-step explanation:

Answer:

Answer:x=−1+126or x=−1+−126

Step-by-step explanation:

In the image

Answer:

\(x=\dfrac{-2 +\sqrt{6}}{2}, \quad x=\dfrac{-2 -\sqrt{6}}{2}\)

Step-by-step explanation:

Given quadratic equation:

\(2x^2+4x-1=0\)

Solve by completing the square

Move the constant to the right side of the equation:

\(\implies 2x^2+4x-1+1=0+1\)

\(\implies 2x^2+4x=1\)

Factor out the common factor of 2 from the left side:

\(\implies 2(x^2+2x)=1\)

\(\implies x^2+2x=\dfrac{1}{2}\)

Add the square of half the coefficient of the term in x to both sides of the equation:

\(\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=\dfrac{1}{2}+\left(\dfrac{2}{2}\right)^2\)

\(\implies x^2+2x+(1)^2=\dfrac{1}{2}+(1)^2\)

\(\implies x^2+2x+1=\dfrac{1}{2}+1\)

\(\implies x^2+2x+1=\dfrac{3}{2}\)

Factor the perfect square trinomial on the left side of the equation:

\(\implies (x+1)^2=\dfrac{3}{2}\)

Square root both sides:

\(\implies \sqrt{(x+1)^2}=\sqrt{\dfrac{3}{2}}\)

\(\implies x+1=\pm\dfrac{\sqrt{3}}{\sqrt{2}}\)

\(\implies x+1=\pm\dfrac{\sqrt{3}}{\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}}\)

\(\implies x+1=\pm\dfrac{\sqrt{6}}{2}\)

Subtract one from both sides:

\(\implies x+1-1=\pm\dfrac{\sqrt{6}}{2}-1\)

\(\implies x=-1\pm\dfrac{\sqrt{6}}{2}\)

\(\implies x=-\dfrac{2}{2}\pm\dfrac{\sqrt{6}}{2}\)

\(\implies x=\dfrac{-2 \pm \sqrt{6}}{2}\)

Answer: x=2, y=-8

Step-by-step explanation: there are a couple of different methods you can use, my favourite is substitution

to do this, find a value of x or y from one equation and plug it into the other. let's use x in this case

so we have 13x-6y=22 and x=y+6

for the x value of the first equation, plug in x=y+6 from the second equation to get:

13(y+6)-6y=22

then you solve for y,

13y+78-6y=22

7y=-56

y=-8

then to solve for x, plug in your y value to either of the first 2 equations. lets use x=y+6

so you'd have x=(-8)+6 to give you x=2

hope this helps!

Constructing a 98% confidence interval with a larger sample size would result in a wider, yet more precise interval compared to a 95% confidence interval with a smaller sample size.

If you construct a 98% confidence interval for the population mean instead of a 95% confidence interval and the sample size is larger for the 98% interval, with everything else being the same, the confidence interval would:

1. Be wider than the 95% confidence interval:

A higher confidence level (98% vs. 95%) requires a wider interval to capture the true population mean with greater certainty.

2. Be more precise due to the larger sample size:

A larger sample size provides more information about the population, which generally leads to a more precise estimate of the population mean.

To summarize, constructing a 98% confidence interval with a larger sample size would result in a wider, yet more precise interval compared to a 95% confidence interval with a smaller sample size.

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Therefore, the solution to the given system of linear equations is (x, y) = (3, -6).

To solve the given system of linear equations using matrix inversion, we can represent the system in matrix form as AX = B, where A is the coefficient matrix, X is the column vector of variables (x and y), and B is the column vector of the constants on the right-hand side. By finding the inverse of matrix A, we can solve for X using the equation \(X = A^{(-1)} * B:\).

The given system of linear equations is:

x/2 + y/3 = 0

x/3 + y = -7

We can rewrite the equations as:

2x + 3y = 0

3x + y = -21

In matrix form, the system becomes:

| 2 3 | | x | | 0 |

| 3 1 | * | y | = |-21 |

The coefficient matrix A is:

| 2 3 |

| 3 1 |

To solve for X, we need to find the inverse of matrix A. The inverse of A is:

| -1/7 3/7 |

| 3/7 -2/7 |

Now, we can solve for X using the equation \(X = A^{(-1)} * B:\)

| x | | -1/7 3/7 | | 0 |

| y | = | 3/7 -2/7 | * |-21 |

Multiplying the matrices, we get:

| x | | -1/70 + 3/7(-21) |

| y | = | 3/70 + (-2/7)(-21) |

Simplifying the expressions, we find:

x = 3

y = -6

Therefore, the solution to the given system of linear equations is (x, y) = (3, -6).

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The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.

A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.

Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.

It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.

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The divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

To find the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k, you need to take the divergence operator (∇ · F).

The divergence of a vector field in Cartesian coordinates is given by the following formula:

∇ · F = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z),

where Fx, Fy, and Fz are the x, y, and z components of the vector field F, respectively.

In this case, we have:

Fx = (5x^2 + 7 - sin(xz)),

Fy = 0, and

Fz = (5x^2 + 7 - sin(xz)).

Taking the partial derivatives, we get:

∂Fx/∂x = 10x - zcos(xz),

∂Fy/∂y = 0, and

∂Fz/∂z = 10x - zcos(xz).

Now, substituting these derivatives into the divergence formula, we have:

∇ · F = (10x - zcos(xz)) + 0 + (10x - zcos(xz)).

Simplifying further, we get:

∇ · F = 20x - 2zcos(xz).

Therefore, the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

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Answer:

The coordinates of b are (3, -5)

Step-by-step explanation:

\(c(1,-1)\)

\(a(-1,3)\)

\(1=\frac{-1+x}{2}\)

\(2=-1+x\)

\(x=2+1\)

\(x=3\)

\(-1=\frac{3+y}{2}\)

\(-2=3+y\)

\(y=-2-3\)

\(y=-5\)

Answer:

149 is the 47th term in the given sequence.

Step-by-step explanation:

An = A1 + (n-1)d

In this problem, An is represented as A47, or the term we are looking to find,

A1 is the first number in the sequence, so in this case, it would be 11,

n is the term that is attached to An, in this case, it would be 47,

d is the common difference, or what number can I add or subtract to get the other number and all other numbers in the sequence, for this case it would be 3. (11+3=14, 14+3=17, 17+3=20)

Now, we plug in all numbers, and it would look like

11+(47-1)3

11+(46)3

11+138=149

The expected number of boys who make good score is found to be 188 by using random sample method.

To get the projected number of boys who get good grades, multiply the total number of boys by the proportion of boys who answered they would like to get good grades the most.

According to the table, the total number of boys surveyed is:

188 +64 +192 = 444

And the percentage of guys who indicated they

would like to get good grades is:

188/444 0.423

As a result, the projected number of guys with good grades is:

Expected number of boys = total number of boys

x percentage of boys who get high grades

444 x 0.423 = 444 boys expected

Number of boys expected = 187.812

When we round to the nearest full number, we get: The expected number of males with good grades

is 188.

So, as a result there are 188 boys who say they

would like to score more good grades.

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Complete question - A study examines the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achievement of personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Results are presented in the following table by the sex of the child.

Boys Girls

Be good in sports 188 590

Be popular 64 80

Make good grades 192 90

Answer:

0.27 expressed in ratio form is 27:100

Step-by-step explanation:

Before we give Tommy the estimate of 0.27 probability in ratio form, we shall need to turn 0.27 to fraction

Mathematically, that would be 27/100

Now expressing this in ratio form, we will have 27:100

The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.

Here, the two boundaries are 1692 and 1842.

Mean = (1692+1842) /2 = 1767

Here the degree of freedom, df = (n-1) = 25-1 =24

Margin of error = (1842-1692)/2 = 75

Confidence level = 99%

From the t table, value of T with confidence level 99% and df= 24 is 2.80

The equation for margin of error is M = Ts/√n

            M= 75 , T= 2.80, n =25

75 = (2.80 × s) / √25

75 = 2.80s/ 5

s = (75×5)/2.80 = 133.928 = 133.93

So the sample mean is 1767 and the standard deviation is 133.93.

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From the statement, we know that to win the lottery we must choose 5 numbers from the numbers 1 through 172.

a) Assuming that order is unimportant.

To win, we must pick correctly 5 numbers from 1,...,172.

0. For the first number, we have 5 possibilities from 172, so the probability is 5/172,

1. for the second number, we have 4 possibilities from 171, so the probability is 4/171,

2. for the third number, we have 3 possibilities from 170, so the probability is 3/170,

3. for the fourth number, we have 2 possibilities from 169, so the probability is 2/169,

4. for the fifth number, we have 1 possibility from 168, so the probability is 1/168,

To figure out the odds of winning, we multiply together all of the fractional odds of picking each number. Multiplying all the probabilities we get:

So the probability is 1 in 1183009464.

b) Assuming that the order matters.

To win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to multiply. So, to figure out the odds of winning, we multiply together all of the fractional odds of picking a given number correctly. The probability of selecting correctly:

• the first number is 1/172,

• the second number is 1/171,

• the third number is 1/170,

• the fourth number is 1/169,

• the fifth number is 1/168,

Multiplying all the probabilities we get:

So the probability is 1 in 141961135680.

Answer

1) The probability of winning the lottery by choosing 5 numbers from 1,...,172 if the order is unimportant, is 1 in 1183009464. or:

2) The probability of winning the lottery by choosing 5 numbers from 1,...,172 if the order matters, is 1 in 141961135680, or:

64.77% of a given amount remains after 900 years.

To determine the percentage of radioactive radium remaining after 900 years, we'll use the half-life formula:

Final Amount = Initial Amount * \(1/2^{(time elapsed / half-life)}\)

In this case, the half-life is 1599 years and the time elapsed is 900 years. We want to find the percentage remaining, so let's assume the initial amount is 100%.

Final Amount = 100 * \((1/2)^{(900 / 1599)}\)

Now, we'll calculate the exponent:

Exponent = 900 / 1599 ≈ 0.5635

Then, we'll compute the final amount:

Final Amount ≈ 100 * \((1/2)^{0.5635}\) ≈ 100 * 0.6477 ≈ 64.77%

After 900 years, approximately 64.77% of the initial radioactive radium remains. This percentage was found using the half-life formula, which accounts for the exponential decay of radioactive substances over time.

The formula shows how the remaining amount of a substance decreases as time progresses based on its half-life, which is the time it takes for half of the substance to decay. In this scenario, radium's half-life of 1599 years and the 900-year time frame were used to determine that roughly 64.77% of the initial radium remains.

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Answer:

A

Step-by-step explanation:

For every 4 cups of flour, there is one cup of milk, therefore, the first equation describes the relationship.

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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The margin of error at a 95% confidence level will be approximately 0.107.

To calculate the margin of error at a 95% confidence level, we will use the formula:

Margin of Error = z  (√((p-hat (1 - p-hat)) / n))

Where we have z is the z-score associated with the desired confidence level (95% confidence level corresponds to a z-score of approximately 1.96).

- p-hat is the sample proportion (in this case, -0.75).

- n is the sample size (in this case, 240 ).

To calculate the margin of error:

Margin of Error = 1.96  (√((0.75(1 - (0.75))) / 240 ))

Margin of Error ≈ 0.107

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Answer:

A, B, E

Step-by-step explanation:

Answer:

sometimes

Step-by-step explanation:when a >b?

ax+y=8

bx + y = 5

always

sometimes

O

never

The equivalent system of equations that would guarantee a solution of (3,-1) are

The system of equations is given as:

px +qy =r

fx + gy = h

Add both equations

(p + f)x + (q + g)y = r + h

Multiply the second equation by a constant (say 5)

5fx + 5gy = 5h

Multiply the first equation by a constant (say 2)

2px + 2qy = 2r

The combination of any of the above equations to the given equation would guarantee a solution of (3,-1)

Hence, the equivalent system of equations are (a), (d) and (e)

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Answer:

c=-18 d=2

Step-by-step explanation:

[ 6 8 -11 15 ]-[c+2 3 -5 d-4 ]=[ 22 5 -6 17]

The equation tells that when the two matrices are subtracted we get the resultant matrix.

Each element of the first matrix corresponds to each element of the second matrix

From above

6- (c+2)= 22

6- c-2= 22

4-c= 22

-c= 22-4

-c= 18

c= -18

And

15-( d-4)= 17

15- d+4= 17

19-d= 17

-d= 17-19

-d= -2

d= 2

Answer:

D

Step-by-step explanation:

c= -18

d= 2

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

Answer:?

The following list shows how many brothers and sisters some students have:

2, 4, 3, 3, 4, 2, 4, 3, 3, 2, 3, 4

State the mode.

Step-by-step explanation:

In an isosceles triangle with legs of length 18 and a base of 14, the angles can be determined using trigonometric properties and the Pythagorean theorem.

Let's denote the two congruent legs of the isosceles triangle as 'a' and the base as 'b'. In this case, 'a' would be 18 and 'b' would be 14. Since the triangle is isosceles, the two congruent angles opposite the congruent legs are equal.

To find the angles, we can use the law of cosines, which states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

Plugging in the values, we have:

18^2 = 14^2 + 14^2 - 2 * 14 * 14 * cos(C)

Simplifying the equation:

324 = 196 + 196 - 392 * cos(C)

324 = 392 - 392 * cos(C)

392 * cos(C) = 392 - 324

cos(C) = (392 - 324) / 392

cos(C) = 68 / 392

cos(C) = 17 / 98

Now, we can find the angle C by taking the inverse cosine (arccos) of (17/98).

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A quadrilateral can be classified as a parallelogram if and only if it has a pair of opposite sides that are both parallel and congruent (equal in length).

To determine whether a quadrilateral is a parallelogram or not, we need to check if its opposite sides are equal and parallel. If they are, then the quadrilateral is a parallelogram.

If we are given the measurements of all four sides and the angles, we can use the properties of parallelograms to determine if it is a parallelogram or not. The opposite angles of a parallelogram are equal, and the adjacent angles are supplementary (add up to 180 degrees).

If we are given only the coordinates of the vertices, we can calculate the slopes of the four sides using the slope formula. If a pair of opposite sides have the same slope, then they are parallel. If the opposite sides also have the same length, then the quadrilateral is a parallelogram.

In short, to determine whether a quadrilateral is a parallelogram, we need to check if its opposite sides are equal and parallel, either by measuring or by calculating the slopes and lengths of the sides.

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Full Question: A quadrilateral is a parallelogram if a pair of opposite sides are equal and parallel.

Answer:

20 ÷ 2 = 10

Each of them will get 10 doars each.

Answer:

-3, -2.5, -3/4, 0.8, 2.5, 6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 = 0.5

6 = 6

6 + 0.5 = 6.5

----------------------------------------------------------------------------------------------------------------

1/4 = 0.25

-1/4 = -0.25

-3/4 = -0.75

----------------------------------------------------------------------------------------------------------------

Hope this helps! <3