jim tosses a fair coin to decide whether his next vacation will be in hawaii or alaska. if it is a head, jim visits hawaii, or else he decides to visit alaska. if in hawaii, jim surfs during the vacation with a probability of 0.9. if in alaska, jim is going to surf in the ocean with probability 0.1 only. given that we know that jim went on surf- ing during the vacation, what is the conditional probability that his vacation was in alaska?

The solution of the system using elimination method is x = 3 and y = 3

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem we must establish the equations according to the given data and solve the operations:

4x + 2y = 18       (1)

2x + 3y = 15      (2)

We have two equations with two unknowns, using the elimination method we have to multiply the (2) by -2 and we get:

-2*(2x + 3y) = 15

-4x - 6y = -30    

Now we solve the system:

4x  + 2y   = 18       (1)

-4x - 6y   = -30      (2)

0x   -4y   = -12

Clearing the variable:

-4y = -12

Multiply by (-1) we have:

4y = 12

y = 12/4

y = 3

Replacing the value of y in equation (1) we get the value of x:

4x + 2y = 18       (1)

4x +2*3 = 18

4x + 6 = 18

4x = 18-6

4x = 12

x = 12/4

x = 3

Both x and y are equal to 3 = (3 , 3)

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Correctly written question:

What is the solution of the system? Use the elimination method.

4x + 2y = 18

2x + 3y = 15

Answer:

-5m/2

Step-by-step explanation:

-m+ (-2m) +(-3m)+(-4m) +(-4m)+(-3m)+(-2m)+(-m)/8

-m-2m-3m-4m-4m-3m-2m-m/8

-20m/8

-5m/2

The equation represents the relationship between x and y is y = x + 5. The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The table represents a linear relationship between x and y, where y increases by 5 for every increase of 5 in x. This means that the slope of the line is 5/5 or 1, and the y-intercept is 5. Using this information, we can write the equation of the line in slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept. Substituting the values we found, we get:

y = 1x + 5

or

y = x + 5

Therefore, the equation that represents the relationship between x and y is y = x + 5.

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Given, p = D(Q) = 28 - 2.25q. We have to find the price at each level of demand.a. Find the price when the demand is 0 watches.As per the given information, the quantity demanded (q) is 0.

Therefore, we have to find the price when q = 0.Putting the value of q = 0 in the given equation, we getp = 28 - 2.25(0)p = 28 - 0p = $28Hence, the price when the demand is 0 watches is $28.b.

Find the price when the demand is 40 watches.As per the given information, the quantity demanded (q) is in hundreds.Therefore, we have to find the price when q = 40.Putting the value of q = 40 in the given equation, we getp = 28 - 2.25(40)p = 28 - 90p = -$62Therefore,

the price when the demand is 40 watches is -$62.c. Find the price when the demand is 80 watches.As per the given information, the quantity demanded (q) is in hundreds.Therefore, we have to find the price when q = 80.Putting the value of q = 80 in the given equation, we getp = 28 - 2.25(80)p = 28 - 180p = -$152Therefore, the price when the demand is 80 watches is -$152.d.

Find the price when the demand is 120 watches.As per the given information, the quantity demanded (q) is in hundreds.Therefore, we have to find the price when q = 120.Putting the value of q = 120 in the given equation, we getp = 28 - 2.25(120)p = 28 - 270p = -$242

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Answer: True

Step-by-step explanation:

Simple.

The projection of the point (4,4) onto the line passing through (3,1) is the point on the line that is closest to (4,4). To find this projection, we need to first find the direction vector of the line, which is (3-1, 1-0) = (2,1).

Next, we need to find the vector from the point (3,1) to the point (4,4), which is (4-3, 4-1) = (1,3).

Then, we can use the formula for projecting a vector onto another vector:

proj_v u = ((u · v) / (v · v)) v

where u is the vector we want to project, v is the vector we want to project onto, and · denotes the dot product.

Applying this formula, we get:

proj_v u = ((1,3) · (2,1)) / ((2,1) · (2,1)) (2,1)

= (5/5) (2,1)

= (2,1)

So the projection of (4,4) onto the line passing through (3,1) is the point (3,1) + (2,1) = (5,2).

To find the projection of vector (4, 4) onto vector (3, 1), you can follow these steps:

Step 1: Calculate the dot product of the two vectors.
Dot product = (4 * 3) + (4 * 1) = 12 + 4 = 16

Step 2: Calculate the magnitude squared of the vector you are projecting onto (3, 1).
Magnitude squared = (3 * 3) + (1 * 1) = 9 + 1 = 10

Step 3: Divide the dot product by the magnitude squared.
Scalar = 16 / 10 = 1.6

Step 4: Multiply the scalar by the vector you are projecting onto (3, 1) to find the projection.
Projection = 1.6 * (3, 1) = (4.8, 1.6)

So, the projection of (4, 4) onto (3, 1) is (4.8, 1.6).

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Answer:

a=4

Step-by-step explanation:

Hope this helps! Plz give brainliest!

Answer:

Subtract 6a6a from both sides.

12a-6a=24

12a−6a=24

2 Simplify 12a-6a12a−6a to 6a6a.

6a=24

6a=24

3 Divide both sides by 66.

a=\frac{24}{6}

a=

6

24

​

4 Simplify \frac{24}{6}

6

24

​

to 44.

a=4

a=4

Step-by-step explanation:

Answer:

y < 5/3x -3

Step-by-step explanation:

Used Desmos graphing calculator :)

Step-by-step explanation:

(-6x^3+8x^2+4x-4)

option D is correct answer

Answer:A

Step-by-step explanation:

The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.

To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:

\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:

\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)

        \(= [2(3) - (0)(3)] / (3)^2\)

        = 6/9

        = 2/3

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,  
y - 0 = (2/3)(x - 1)

y = (2/3)x - 2/3

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.

Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.

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The complete question is:

Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).

The equivalent expressiοn in the given οptiοns is -13/14t - 17/12.

In mathematics, an expressiοn that incοrpοrates variables, cοnstants, and algebraic οperatiοns is knοwn as an algebraic expressiοn (additiοn, subtractiοn, etc.). Terms cοmprise expressiοns.

The cοncept οf algebraic expressiοns is the use οf letters οr alphabets tο represent numbers withοut prοviding their precise values. We learned hοw tο express an unknοwn value using letters like x, y, and z in the fundamentals οf algebra. Here, we refer tο these letters as variables. Variables and cοnstants can bοth be used in an algebraic expressiοn. A cοefficient is any value that is added befοre a variable and then multiplied by it.

frοm the questiοn:

We can simplify the given expressiοn as fοllοws:

-8/7t + 4/12 - (-3/14t + 7/4)

= -8/7t + 1/3 - (-3/14t + 7/4) (4/12 = 1/3)

= -8/7t + 1/3 + 3/14t - 7/4 (dοuble negative becοmes pοsitive)

= (-16/14)t + (2/6) + (3/14)t - (49/14)

= (-24/14)t - (47/14) (cοmbining like terms)

= (-12/7)t - (47/14) (simplifying)

The equivalent expressiοn in the given οptiοns is -13/14t - 17/12.

Thus, the apprοpriate chοice is:

negative 13 οver 14 times t minus 17 οver 12

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To calculate a 15% tip, you can first find a 10% tip using a shortcut and then add half of that amount to get the 15% tip.

1. Calculate the 10% tip: To find a 10% tip, you can simply move the decimal point one place to the left. For example, if the total bill is $50, the 10% tip would be $5.

2. Determine the 15% tip: To find a 15% tip, you can add half of the 10% tip to the 10% tip amount. In the example above, the 10% tip is $5, so half of that is $2.50. Adding $2.50 to $5 gives a total of $7.50, which is the 15% tip.

Therefore, to calculate a 15% tip, you can first find the 10% tip using the shortcut by moving the decimal point one place to the left. Then, add half of the 10% tip amount to the 10% tip to get the 15% tip.

This method allows you to quickly calculate a 15% tip without needing to use complex calculations.

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Answer:

yes cause its in a form of y=mx+b

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

I got to K-12 and this was correct

Answer:

Step-by-step explanation:

28 kg + 750 g = 28*1000 + 750

                          28000 + 750

                       = 28750 g

Number of sack = Total quantity of sugar ÷ quantity of sugar in a sack

                           = 28750 ÷ 500

                           =  57 sacks

Answer:

57 sacks

Step-by-step explanation:

28750 ÷ 500 =

57 sacks

Glad to help! :)

Based on the accuracy of the stopwatch that measures time to tenths of a second, Lola would need approximately 507.8 seconds to sign all 96 invitations.

1. If it takes Lola 5.3 seconds to sign her full name, we can calculate the total time needed to sign all 96 invitations by multiplying the time per signature (5.3 seconds) by the number of invitations (96). However, since the stopwatch measures time to tenths of a second, it means we need to consider the additional time needed for each signature beyond the tenth of a second.

2. To calculate the additional time, we can subtract the whole number of seconds from the time per signature. In this case, 5 seconds can be subtracted, leaving us with 0.3 seconds. As Lola needs to sign 96 invitations, we can multiply the additional time (0.3 seconds) by the number of invitations (96). This gives us 28.8 seconds.

3. Adding the whole number of seconds (5 seconds) to the additional time (28.8 seconds), we get a total of 33.8 seconds per signature. To find the total time needed to sign all 96 invitations, we multiply the time per signature (33.8 seconds) by the number of invitations (96), resulting in approximately 507.8 seconds.

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Answer:

30 dólares es la ganancia neta.

Step-by-step explanation:

En la primera transacción, el hombre está perdiendo 50 dólares:

1. -50 dólares

En la segunda transacción, el hombre gana 70 dólares:

2. -50 + 70 = +20 dólares

En la tercera transacción pierde 80 dólares:

3. 20 - 80 dólares = -60 dólares

Y en la última transacción, la ganancia es de 90 dólares. Así, la ganancia neta es:

4. -60 dólares + 90 dólares =

Answer:

20,800

Step-by-step explanation:

10.00 per hour so 10x8=80

then 80x5=400

400x52=20,800

Answer:

y = \(\frac{1}{3}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = \(\frac{1}{3}\) , then

y = \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation

- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )

0 = c

y = \(\frac{1}{3}\) x + 0 , that is

y = \(\frac{1}{3}\) x

In a normal distribution, approximately 68% of scores lie within one standard deviation of the mean, approximately 95% lie within two standard deviations of the mean, and approximately 99.7% lie within three standard deviations of the mean.

Therefore, to find the percentage of scores that lie between the mean and 2 standard deviations above the mean, we can use the empirical rule and subtract the percentage of scores that lie above 2 standard deviations from the mean from the percentage of scores that lie within 2 standard deviations of the mean.

Since 95% of scores lie within two standard deviations of the mean, we can assume that 2.5% of scores lie above 2 standard deviations above the mean. Therefore, subtracting 2.5% from 95% gives us a percentage of 92.5% of scores that lie between the mean and 2 standard deviations above the mean.

Overall, this means that if a distribution is normal, approximately 92.5% of scores will fall between the mean and 2 standard deviations above the mean. It is important to note, however, that this rule only applies to normal distributions and may not be accurate for other types of distributions.

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Answer:

p + q + r is 12.

Step-by-step explanation:

Prime factors of a number is the expression of the number in terms of the product of its factors that are prime numbers only.

The prime factor of 686 = 2 x 7 x 7 x 7. Which can be expressed in the form;

p × \(q^{r}\) as 2 × \(7^{3}\).

So that, p = 2, q = 7 and r = 3.

p + q + r = 2 + 7  + 3

              = 12

Therefore, the sum of p, q, and r is 12.

Answer:

Y= 5

Step-by-step explanation:

\(3(0) + y = 5 \\ y = 5\)

The domain of the function is defined as 0 ≤  x ≤ 4.

option A is the correct answer.

A domain of a function refers to "all the values" that can go into a function without resulting in undefined values.

So the domain of a function is the set of x values, while the range of a function is the set of y values.

From the given statement, the range of the function is defined as;

y = vt

where;

y = 60 mph x 4 hr

y = 240 miles

From the given statement, the domain of the function is defined as;

0 ≤  x ≤ 4

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we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is

where we used the slope formula:

Then, our searched line has the form:

where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:

then, the searched line in slope-intercept form is

Therfore, the given area can be modeled as

because when a line is dashed it doesn't belong to the given area.

The number of books Henry read each number is 3 or 6/2 in a fraction.

A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

As given in the question,

The number of books read in 2 months is 4.

Henry read books at a constant rate.

The Number of books read by Henry in 1 month is ( 6/2 ) = 3 books.

Therefore, the number of books read by Henry as per the given condition of reading 6 books in 2 months at a constant rate is equal to 6/2.

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Answer:

B. 68°

Step-by-step explanation:

Since, opposite sides of the quadrilateral MNPQ are parallel.

Therefore, it is a parallelogram.

Measures of the opposite angles of a parallelogram are equal.

So,

(6x - 2)° = (4x + 36)°

6x - 2 = 4x + 36

6x - 4x = 36 + 2

2x = 38

x = 38/2

x = 19

\(m\angle M = (6x - 2)\degree \\ \\ m\angle M = (6 \times 19- 2)\degree \\ \\ m\angle M = (114- 2)\degree \\ \\ m\angle M =112\degree \\ \\ \because m\angle M + m\angle N = 180\degree \\ (adjacent \: angles) \\ \\ \therefore m\angle N = 180\degree - m\angle M \\ \\ \therefore m\angle N = 180\degree - 112 \degree \\ \\ \therefore m \angle N = 68\degree \)

The standard equation is 7x + y = 9

layoff Ax + By = C is the usual form for two-variable direct equations. A standard form direct equation is, for case, 2x + 3y = 5. When an equation is given in this format, chancing both intercepts is rather simple( x and y). When trying to break systems involving two direct equations, this form is also relatively helpful.

Given

7x + 3 = 5 and y - 1 = 6

Add the bottoms from the two given equations to produce a single standard-form equation.

By shifting the constant fromR.H.S. toL.H.S., the equations are reset to zero.

7x + 3 - 5 = 0

7x - 2 = 0----( 1)

y - 1 = 6

y - 1 - 6 = 0

y - 7 = 0-----( 2)

Equation 1 and equation 2 must be combined.

7x - 2 + y - 7 = 0

7x + y - 9 = 0

layoff Ax + By = C is the equation's conventional form.

A, B, and C are integers and x and y are variables in this type of equation.

Accordingly, the common equation is

7x + y - 9 = 0

7x + y = 9

therefore the standard equation is 7x + y = 9

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A city's citizens cast ballots on whether or not to increase property taxes. There were 8 yes votes and 5 nay votes, in that order. if there were 4955 no votes,The total number of votes was 6,940.

The ratio of yes votes to no votes was 8 to 5, meaning for every 8 yes votes there were 5 no votes.

This ratio can be expressed as a fraction: 8/5.

To calculate the total number of votes, we need to know only the number of no votes, which we know is 4955.

We can then multiply this number by the fraction 8/5. This gives us a total of 6,940 votes.

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Answer:

X²-8x+308

Step-by-step explanation:

two negative integers -x and -x= +x²

8units apart=-8x

all equals 308

X²-8x=308

bring everything to the LHS

X²-8x-308=0

Answer:

30.7

Step-by-step explanation: