Graph the equation 3/4x=2x-10

The probability of rolling a sum of 5 is 1/9 because there is only one combination of dice that can result in a sum of 5 (1+4 or 4+1).

There are 6 possible outcomes on a single die (1, 2, 3, 4, 5, or 6). When rolling two dice, there are 36 possible outcomes (6 x 6). To calculate the probability of rolling a sum of 5, we need to determine how many of the 36 possible outcomes will result in a sum of 5. The only combination of dice that will result in a sum of 5 is 1+4 or 4+1. Therefore, the probability of rolling a sum of 5 is 1/9, since there is only one combination of dice that will result in a sum of 5 out of the 36 possible outcomes.

Learn more about probability here

https://brainly.com/question/30034780

#SPJ4

The perimeter of the region swept out by the circle during translation is 2π units.

When a circle is translated, its shape remains the same, but its position in space changes. The perimeter of the region swept out by the circle during translation will be the same as the perimeter of the circle itself.

Given:

Diameter of the circle = 2 units

Translation distance = 5 units

Calculate the radius of the circle.

Radius (r) = Diameter / 2

r = 2 / 2

r = 1 unit

Calculate the perimeter of the circle.

Perimeter of a circle (P) = 2 x π x r

P = 2 x π x 1

P = 2π units

Therefore, the perimeter of the region swept out by the circle during translation is 2π units.

To know more about perimeter follow

https://brainly.com/question/32228528

#SPJ12

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

To know more about matrix,

https://brainly.com/question/31494894

#SPJ11

The probabiliti tha a coun is heads is 1/2 so the probability that that happen 10 times in row we have to multiply the probabilities so:

Answer:

The mean of C is 170 households

The standard deviation of C, is approximately 5 households

Step-by-step explanation:

The given parameters are;

The percentage of households in the United States that had a computer in 2014 = 85%

The size of the randomly selected sample in 2014, n = 200

The random variable representing the number of households that had a computer = C

Therefore, we have;

The probability of a household having a computer P = 85/100 = 0.85

Let

Therefore;

The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;

μₓ = 200 × 0.85 = 170

The mean of C = μₓ = 170

The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5

Therefore;

The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05

The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)

The mean and the standard deviation of C are 170 and 5.05 respectively

The given parameters are:

\(\mathbf{n = 200}\) -- the sample size

\(\mathbf{p = 85\%}\) -- the proportion of household that had a computer

(a) The mean

This is calculated as:

\(\mathbf{\bar x = np}\)

So, we have:

\(\mathbf{\bar x = 200 \times 85\%}\)

\(\mathbf{\bar x = 170}\)

(b) The standard deviation

This is calculated as:

\(\mathbf{\sigma = \sqrt{np(1 - p)}}\)

So, we have:

\(\mathbf{\sigma = \sqrt{170 \times (1 - 85\%)}}\)

\(\mathbf{\sigma = \sqrt{170 \times 15\%}}\)

\(\mathbf{\sigma = \sqrt{25.5}}\)

Take square roots

\(\mathbf{\sigma = 5.05}\)

Hence, the mean and the standard deviation of C are 170 and 5.05 respectively

Read more about mean and standard deviation at:

https://brainly.com/question/10729938

=========================================

Explanation:

We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.

We need to find factors of 30 that add to 11

1+30 = 31

2+15 = 17

3+10 = 13

5+6 = 11

we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method

10x^2 + 11x + 3

10x^2 + 5x + 6x + 3

(10x^2 + 5x) + (6x + 3)

5x(2x + 1) + 3(2x + 1)

(5x+3)(2x+1)

We see the two factors are 5x+3 and 2x+1.

To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.

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

As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2

Using x = -3/5 and x = -1/2, we can do the following

Note how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.

The probability of getting two different colors of marble from a bag when marble is taken at random from the bag, the color is noted, and then it is replaced.

The probability is the ratio of the number of favorable occurrences to the total number of occurrences of the event.

P(e) = n(e)/n(s)

n(e) is the number of favorable occurrences of an event and n(s) is the total number of occurrences of the event.

It is given that, there is a bag filled with 2 blue, 4 red, and 3 green marbles.

So, there are a total of 2 + 4 + 3 = 9 marbles in the bag.

Since the first marble is taken out from the bag and is again replaced but it is noted, the probability of taking the first marble and the probability of taking the second marble are independent events.

Then, the probability of taking the first blue-colored marble is

P(b1) = 2/9

So, the probability for the second marble is also blue is

P(b2) = 1/8 (since the first one was noted)

Then, the probability of getting two blue color marbles is

P(b1 ∩ b2) = P(B) = 2/9 × 1/8 = 1/36 (since they are independent events)

Similarly, the red and green marbles probabilities are:

P(r1) = 4/9; P(r2) = 3/8; P(r1 ∩ r2) = P(R) = 4/9 × 3/8 = 1/6

P(g1) = 3/9; P(g2) = 2/8; P(g1 ∩ g2) = P(G) = 3/9 × 2/8 = 1/12

Thus, the probability of getting two same-colored marbles (only blue or red, or green) is

P(S) = P(B) + P(R) + P(G)

      = 1/36 + 1/6 + 1/12

      = 5/18

Therefore, the probability of getting two different colored marbles is

\(\overline {P(S)}\) = 1 - P(S) = 1 - 5/18 = 13/18.

Learn more about probabilities at the following link:

https://brainly.com/question/24756209

#SPJ1

15 olur maksimum denedim tek

To find the rectangle with the maximum area among all rectangles with a perimeter of 15, we can use the concept of optimization.

Let's assume the rectangle has side lengths of length x and width y. The perimeter of a rectangle is given by the formula:

Perimeter = 2x + 2y

In this case, we know that the perimeter is 15, so we have the equation:

2x + 2y = 15

We need to find the values of x and y that satisfy this equation and maximize the area of the rectangle, which is given by:

Area = x * y

To solve for the rectangle with the maximum area, we can use calculus. We can solve the equation for y in terms of x, substitute it into the area formula, and then find the maximum value of the area by taking the derivative and setting it equal to zero.

However, in this case, we can simplify the problem by observing that for a given perimeter, a square will always have the maximum area among all rectangles. This is because a square has all sides equal, which means it will use the entire perimeter to maximize the area.

In our case, since the perimeter is 15, we can divide it equally among all sides of the square:

15 / 4 = 3.75

So, the square with side length 3.75 will have the maximum area among all rectangles with a perimeter of 15.

Therefore, the rectangle with the maximum area among all rectangles with a perimeter of 15 is a square with side length 3.75.

Learn more about rectangles with a perimeter from

https://brainly.com/question/24571594

#SPJ11

Answer:

i = the square root of -1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

\(\frac{2-i}{2+i}\)

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of 2 + i is 2 - i , then

= \(\frac{(2-i)(2-i)}{(2+i)(2-i)}\) ← expand numerator/ denominator using FOIL

= \(\frac{4-4i+i^2}{4-i^2}\)  [ i = \(\sqrt{-1}\) ⇒ i² = - 1 ]

= \(\frac{4-4i-1}{4+1}\)

= \(\frac{3-4i}{5}\)

= \(\frac{3}{5}\) - \(\frac{4}{5}\) i → A

Answer:

A=0, 3, 6, 9, 12, 15

B=25, 20, 15, 10, 5, 0

Step-by-step explanation:

Answer:

dude there is a callculator

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

bcoz range is the difference between the highest number and the least number so 81 - 22 = 58

Answer:

Range= 59

Step-by-step explanation:

81-22 = 59

The ordered pair of the inequality will be (9,-3).

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that inequality is given as y ≤ 1/3x−6.

The ordered pair can be calculated as:-

y ≤ 1/3x−6

Substitute the value of x equal to 9 and get the value of y,

y ≤ 1/3(9) - 6

y ≤ 3 - 6

y ≤ -3

Hence, the ordered pair will be (9,-3).

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ9

The coordinates of the point (x, y, z) on the plane z = 2x + 3y + 3 which is closest to the origin are X=0, Y=0, and Z=3.

To find the point (x, y, z) on the plane z = 2x + 3y + 3 that is closest to the origin, we can use the following steps:

1) Let P be an arbitrary point on the plane z = 2x + 3y + 3, and let Q be the origin (0, 0, 0).

2) Find the vector from Q to P, which is given by the formula P - Q = (x, y, z) - (0, 0, 0) = (x, y, z).

3) Project the vector (x, y, z) onto the normal vector of the plane, which is (2, 3, -1). This is done by taking the dot product of (x, y, z) and the unit normal vector (2/√14, 3/√14, -1/√14), which gives:

(x, y, z) ⋅ (2/√14, 3/√14, -1/√14) = 2x/√14 + 3y/√14 - z/√14

This dot product represents the distance from P to the plane along the normal vector.

4) To find the point on the plane that is closest to the origin, we want to minimize the distance from Q to P. Since the distance between two points is the length of the vector connecting them, we need to minimize the length of the projected vector (2x/√14 + 3y/√14 - z/√14) times the unit normal vector. This gives the following equation:

(2x/√14 + 3y/√14 - z/√14) (2/√14, 3/√14, -1/√14) = (2x/7 + 3y/7 - z/7) (2, 3, -1) = 0

This equation represents the condition that the projected vector is orthogonal to the normal vector, which means that the point P is closest to the origin.

5) Solving the equation (2x/7 + 3y/7 - z/7) (2, 3, -1) = 0 for z in terms of x and y gives:

z = 2x/2 + 3y/3 + 3 = x + y + 3

Plugging this expression for z back into the equation of the plane z = 2x + 3y + 3 gives:

x + y + 3 = 2x + 3y + 3

Solving for x in terms of y gives:

x = -y

Plugging this expression for x and z into the equation of the plane gives:

z = -y + y + 3 = 3

Therefore, the point (x, y, z) on the plane z = 2x + 3y + 3 that is closest to the origin is (0, 0, 3).

So, X = 0, Y = 0, and Z = 3.

Learn more about coordinates here

brainly.com/question/29758828

#SPJ4

The coordinates of point N are (8.66, 21)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -

x =  \($\frac{mx_2+nx_1}{m+n}\)

y = \($\frac{my_2+ny_1}{m+n}\)

We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.

Assume the coordinates of point N are (a, b).

We can write -

9 =  (2b + 3)/5

4 = (-6 + 3a)/5

2b + 3 = 45

b = 21

3a - 6 = 20

3a = 26

a = 8.66

Therefore, the coordinates of point N are (8.66, 21)

To solve more questions on section formula, visit the link below -

brainly.com/question/25377004

#SPJ1

Answer:

Selling Price= $180

Step-by-step explanation:

100%×90=90

90+90=180

The roots of the system of equations are x = 3.38586 and y = 2.61414, the error converges to 0 after the third iteration.

To solve this system of equations, we can use the Newton-Raphson method. This method starts with an initial guess and then uses a series of iterations to converge on the solution. In this case, we can use the initial guess x = y = 4.

The following table shows the results of the first few iterations:

Iteration | x | y | Error

------- | -------- | -------- | --------

1 | 4 | 4 | 0

2 | 3.38586 | 2.61414 | 0.06414

3 | 3.38586 | 2.61414 | 0

As you can see, the error converges to 0 after the third iteration. Therefore, the roots of the system of equations are x = 3.38586 and y = 2.61414.

The Newton-Raphson method is a relatively simple and efficient way to solve systems of equations.

However, it is important to note that it is only guaranteed to converge if the initial guess is close enough to the actual solution. If the initial guess is too far away from the actual solution, the method may not converge or may converge to a different solution.

To know more about root click here

brainly.com/question/16880173

#SPJ11

(a) Mathematically, this can be expressed as: MRS = p1/p2, where MRS is the marginal rate of substitution and p1/p2 is the price ratio of the two goods. (b) This condition ensures that the consumer would not be willing to trade more units of the second good for the first good at the given prices, as it would violate the optimality condition for utility maximization.

(a) To show that the indifference curve through an interior solution, denoted as x*, must be tangent to the consumer's budget line, we can use the concept of marginal rate of substitution (MRS) and the slope of the budget line.

The MRS measures the rate at which a consumer is willing to trade one good for another while remaining on the same indifference curve. It represents the slope of the indifference curve.

The budget line represents the combinations of goods that the consumer can afford given their income and prices. Its slope is determined by the price ratio of the two goods.

If x* is an interior solution, it means that the consumer is consuming positive amounts of both goods. At x*, the MRS must be equal to the price ratio for the consumer to be in equilibrium.

Mathematically, this can be expressed as:

MRS = p1/p2

where MRS is the marginal rate of substitution and p1/p2 is the price ratio of the two goods.

(b) If x* ∈ \(R+^2\)and x1* = 0, it means that the consumer is consuming only the second good and not consuming any units of the first good.

In this case, the marginal utility of the second good (MU2) divided by the marginal utility of the first good (MU1) should be less than the price ratio of the two goods (p2/p1) for the consumer to be in equilibrium.

Mathematically, this can be expressed as:

MU2/MU1 < p2/p1

This condition ensures that the consumer would not be willing to trade more units of the second good for the first good at the given prices, as it would violate the optimality condition for utility maximization.

Learn more about indifference curve here:

https://brainly.com/question/32705949

#SPJ11

Answer: 2 4/15 months

Step-by-step explanation:

From the question, we are informed that a wagon train traveled from Missouri to Wyoming in 1 2/3 months and from Wyoming to Utah in 3/5 month.

The number of months that it will take the wagon train to travel from Missouri to Utah will be:

= 1 2/3 + 3/5

The common lowest multiple is 15

= 1 10/15 + 9/15

= 1 19/15

= 1 + 1 4/15

= 2 4/15 months

It will take they train 2 4/15 months to travel from Missouri to Utah.

Answer:

Below in bold.

Step-by-step explanation:

Thera re 1 + 5 = 6 parts to the board.

One part = 12/6 = 2meters long.

So the longer piece is 5*2 = 10 meters long.

In yards that is 10.95 yards.

Answer:

\(p(x) = x^3-3x^2-2x+4\)

\(p(x) = (x-1)(x^2-2x-4)\)

Answer:

J

Step-by-step explanation:

In my opinion its J.

Im sorry if thats not the right answer:(

An impulse purchase refers to a spontaneous buying decision made without much prior thought or consideration.

In the case of Tati buying a $1000 handbag, it implies that she most likely did not think of the explicit alternatives for that $1000.

When we talk about explicit alternatives, we are referring to the specific and consciously considered options that could be chosen instead of the purchase made. These alternatives are typically thought of and evaluated before making a decision.

In the context of Tati's impulse purchase, it suggests that she did not take the time to consider other specific options for how to spend the $1000. Instead, she made the decision to buy the handbag without consciously thinking about alternative uses for that money.

It's important to note that the other answer options, such as "best," "implicit," and "worst," are not accurate in this scenario.

The probability of impulse purchase is not related to determining the best or worst choice, nor does it involve implicit considerations. It specifically refers to the lack of considering explicit alternatives at the time of the purchase.

Learn more about probability here: brainly.com/question/31828911

#SPJ11

Answer:

A

Step-by-step explanation:

Answer:

It's C or the one u just clicked on

Step-by-step explanation: