Solve the system of equations. 2x + 4y = 12 3x + y = 3 (0, 3) (1, 0) (2, 2) (2, −3)

Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation

v = √(16d)

a wave forms in water with a depth of 300 feet,

therefore d = 300 ft

so, we get,

velocity = √(16*300)

             = 4√300

             =4*17.32

             =69.28

Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

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Answer:

40 units^2

Step-by-step explanation:

The parallelogram shown is basically made of two triangles divided by the x-axis. The bases go from 3 to 13 on the axis, so they have a length of 10. The height of one triangle is from a 0 to 4, which is a height of 4.

The area of a triangle is [tex]\frac{bh}{2}[/tex], so plugging those numbers in gets:

[tex]\frac{4*10}{2}[/tex] = 20

Since there are two triangles it would be double the area: 40 units^2

The series 1/2 + 1/5 + 1/10 + 1/17 + 1/26 + ... converges

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

1/2 + 1/5 + 1/10 + 1/17 + 1/26.....

To apply the Integral test to given series, we can compare it to the area under the function 1/x.

As a general rule, the function 1/x is a decreasing function on the interval (1, ∞),

This means that the series converges.

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Answer: x/2

Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.

Answer: x/2 IS CORRECT

Step-by-step explanation:

I TRIED IT :)

The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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Answer:

30mg

Step-by-step explanation:

10 mg/mL x 3 mL

Answer:

$ 4.86

Step-by-step explanation:

Subtract 7.19 and 2.33

7.19-2.33=4.86

The solutions are given below:-

Part (a),

X₁ + X₂ have distribution Bi(n₁+n₂, p)

Part (b),

P(X ₁+ X₂ = 1 | X₂ = 0) =  np(1-p)ⁿ¹⁻¹

P(X₁+X₂ = 1| X₂ = 1) = (1-p)ⁿ¹

P(X₁ + X₂ = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹

Since both variables are independent but they have the same probability parameter, you can interpret that as if the experiment that models each try in both variables is the same.

When you sum both random variables together, what you obtain as a result is the total amount of success in n₁+n₂ tries of the same experiment, thus X₁+X₂have distribution Bi(n₁ + n₂, p).

b)

Note that, if X₂ = k, then X₁ +X₂ = 1 is equivalent to X₁ = 1-k. Since X1 and X₂ are independent, then P(X₁ +X₂ = 1| X₂ = K) = P(X1=1-k|X₂=k) = P(X₁ = 1-k).

If k = 0, then this probability is equal to P(X₁ = 1) = np(1-p)ⁿ¹⁻¹

If k = 1, then it is equal to P(X₁ = 0) = (1-p)ⁿ¹

Thus,

P(X₁+X₂ = 1) = P(X₁+X₂ = 1| X₂ = 1) * P(X₂=1) + P(X₁+X₂ = 1| X₂ = 0) * P(X₂ = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹.

The complete question is given below.

Let X1 and X2 be two random variables following Binomial distribution Bin(n1,p) and Bin(n2,p), respectively. Assume that X1 and X2 are independent.

(a) The mgf of binomial distribution Bin(n, p) is (1 − p + pet)n. Use this fact to obtain the distribution of X1 + X2.

(b) Find the probability P(X1 + X2 = 1|X2 = k) for k = 0 and 1. Then use the law of total probability to find P (X1 + X2 = 1)

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Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.

The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.

Estimated machine hours to be worked = 55,000 hours

Actual machine hours during the period = 54,000 hours

Total manufacturing overhead applied to production = $432,000

Estimated variable manufacturing overhead per machine hour = $2.70

Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)

Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)

Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.

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The standard form of the equation (x + 2)² = 4 (x + 5) + y is:

x² + y - 16 = 0

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

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

We have,

The standard form of an equation is Ax + By = c.

Now,

(x + 2)² = 4 (x + 5) + y

x² + 4x + 4 = 4x + 20 + y

x² + 4 = 20 + y

x² + y = 20 - 4

x² + y = 16

x² + y - 16 = 0

Thus,

x² + y - 16 = 0 is the standard form of an equation.

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The mathematical expression, for the given phrase is n / 8

A mathematical statement, containing variables and numbers related by a mathematical operator, is called an expression.

Given that, a mathematical phrase: The quotient of a number by eight, we are asked to convert it into a mathematical expression,

Let n be the unknown number,

The quotient shows a result of division of two numbers,

Therefore,

The quotient of a number, n by eight, can be written as,

n / 8

Hence, the mathematical expression, for the given phrase is n / 8

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The expression 0.8(−5w − 0.8) − 0.3(0.5w − 1) in the simplified form will be −4.15w + 0.36.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 0.8(−5w − 0.8) − 0.3(0.5w − 1)

Simplify the equation, then we have

⇒ 0.8(−5w − 0.8) − 0.3(0.5w − 1)

⇒ −4w − 0.64 − 0.15w + 0.30

⇒ −4.15w + 0.36

The expression 0.8(−5w − 0.8) − 0.3(0.5w − 1) in the simplified form will be −4.15w + 0.36.

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Answer: equal to the sum of the area of all of its faces

Step-by-step explanation:

The required 3/4 is 11/3 and 26/3 times in fractions 11/4 and 6 1/2 respectively.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Given ration 3/4

(1)
Fraction 3/4 in 11/4
= 11/4 / 3/4
= 11/3

Although, 3/4 is 11/3 times in the value 11/4

Similarly
(2)
Fraction 3/4 in  6 1/2
= 13 / 2 / [3/4]
= 26/3

Although, 3/4 is 26/3  times the value of 6 1/2.

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The probability that neither of them is chosen for inspection is given as follows:

a) 81 %

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

n = 2, p = 0.1.

The probability of neither is P(X = 0), hence:

P(X = 0) = (1 - 0.1)² = 0.81.

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Answer: 4.2

Multiply both sides by 10

0.42 (10) = 0.1 (10)

4.2 = 1

Answer:

4.2

Step-by-step explanation:

The values of {x} are given above upto 2³.

Given is that the graph with x - coordinate marks (-2, 0, and 2) and y -coordinate marks (-2, 0, and 2). There is a line which passes through the points (3, 3) and (2, 3.5).

The inequality line representing the shaded region as -

y ≥ - 13x + 4

Therefore, the inequality line representing the shaded region is y ≥ - 13x + 4.

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The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.

Simple interest is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for r.

I = P × r × t

r = I / Pt

r = 600 / ( 5,000 × 2 )

r = 600 / ( 10,000 )

r = 0.06

Interest rate = r × 100%

Interest rate = 0.06 × 100%

Interest rate = 6%

Therefore, the interest rate is 6%.

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The amount of oatmeal cookies with Mr. Ramirez is 18

The problem is dealing with multiplication of fractions

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split.

In the problem saying that 3 fourths were oatmeal means that 3/4 of the cookies where oatmeal hence

number of cookies = 3/4 * 24

number of cookies = 18

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The correct statements regarding the translation from function f(x) to function g(x) are given as follows:

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The translations for this problem are defined as follows:

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The expression to represent the given statement is:33 - (2 * 22 * ½x)

The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.

The given expression is "33 - (2 * 22 * ½x)".

To simplify it, let's break it down step by step:

The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.

Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.

Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.

Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".

In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.

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The sum of the measures of the exterior angles of the polygon is,  360°

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

A polygon,

Having 9 equal sides,

The sum of the measures of the exterior angles of the polygon = ?

The sum of each interior & exterior angles are 180°

Suppose, interior angles  are respectively

a, b, c, d, e, f, g, h, i,

Now, exterior angles are respectively

180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,

The sum of the measures of the exterior angles of the polygon =

180°-a  + 180°-b +180°-c +180°-d + 180°-e + 180°-f  + 180°-g +180°-h + 180°-i,

1620 - (a + b + c + d + e + f + g + h + i)

Sum of all the interior angles  = (9-2)x180°

                                                  =  1260°

The sum of  the exterior angles of the polygon =  1620 - 1260°

                                                                               =   360°

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The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.

Plates = 8 per pack

Cups = 12 per pack

the Lowest common multiple of 8 and 12

8 = 16, 24, 32, 40, 48, 56, 64, 72, 80

12 = 24, 36, 48, 60, 72

The Lowest common multiple of 8 and 12 is 24

The least number of plates and cups she can buy is 24

Packs of plates = 24 plates / 8 per pack

= 3 packs

She will buy 3 packs of plates

Packs of cups = 24 / 12 per pack

= 2 packs

She will buy 2 packs of cup

Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

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the equation of  line passes through points (0, -3) and (4, -1) is 4y  = 3x -12.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, an equation of a line in the graph.

Since the graph shows that the line passes through points (0, -3) and (4, -1).

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (value of y at x =0)

since

slope = (y - y')/(x -x')

In our case,

slope (m) = (-1 - (-3))/(4 -0)

m = 3/4

b = -3

Thus, the equation of the line:

y = 3/4x - 3

or, 4y  = 3x -12

therefore, the equation of the line will be 4y  = 3x -12.

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The general solution of the ODE is:

y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1

y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1

This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.

Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.

e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)

D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)

Integrating both sides, we get:

e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C

where C is an arbitrary constant of integration.

Using the initial condition y(0) = 1, we can find the value of the constant C.

y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C

So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx

For 0 ≤ x ≤ 1, we have f(x) = 1 and:

∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1

For x ≥ 1, we have f(x) = -1 and:

∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1

Therefore, the general solution of the ODE is:

y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1

y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1

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The number of victories that the team had this season is given as follows:

32.

The number of victories is obtained applying the proportions in the context of this problem.

A decrease of 48 represents a decrease of 60% of the amount, that is, 60% of the total amount is of 48, hence the amount x is obtained as follows:

0.6x = 48

x = 48/0.6

x = 80.

The amount x represents the number of victories in the previous season, hence the number of victories in the current season is given as follows:

80 - 48 = 32.

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Answer: 540°.

Step-by-step explanation:

by

Using simultaneous equations, during the dinner to raise money for a children's museum, 90 tickets were sold.

Simultaneous equations are two or more equations solved concurrently or at the same time.

Simultaneous equations are also called a system of equations.

The cost of one-person ticket = $200

The cost of two-people ticket = $350

The total number of attendees at the dinner = 130

The total ticket sales = $24,000

Let number of one-person ticket = x

Let number of two-people ticket = 2y

x + 2y = 130... Equation 1

200x + 250y = 24000... Equation 2

Multiply Equation 1 by 200:

200x + 400y = 26000... Equation 3

Subtract Equation 2 from Equation 3:

200x + 400y = 26000

-

200x + 350y = 24000

50y = 2000

y = 40

x = 130 - 2y

=  130 - 80

= 50

Thus, the number of tickets sold at the dinner was 90.

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Answer: 2x+10

same expression, just simplified