Suppose a and b are independent events if P(A) =0.4 and P(B) =0.45 what is P(A*B)?

Answer:1 3/7

Step-by-step explanation: A mathematical equation

Answer:

x=15

Step-by-step explanation:

To get the answer I thought, what times 2 equals 22 and i got 11. 15-4=11. so i figured x=15.

Titus had half a can of paint and used two-thirds of it, which means he used (1/2) * (2/3) = 2/6, which simplifies to 1/3 of a full can of paint.

The student is asking about how to calculate the fraction of a full can of paint Titus used given that he had half a can and used two-thirds of it. To find out what fraction of the full can he used, you need to perform a multiplication of the two fractions.

Here is the step-by-step calculation:

Therefore, Titus used 1/3 of a full can of paint.

The function h(x, y) is given by the composition of the functions g(t) and f(x, y). With the given expressions for f and g, the function h(x, y) = g(f(x, y)) equals to (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).

The question asks to find the function h(x, y) from the functions g(t) and f(x, y), where g(t) = t + ln(t), and f(x, y) = 4 − xy^2+ x^2y^2. To begin with, it is necessary to substitute f(x, y) in place of 't' in function g which is g(f(x, y)), since we have h(x, y) = g(f(x, y)).

Performing the substitution, we obtain:

h(x, y) = g(f(x, y)) = (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).

This is your final function h in terms of x and y.

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0.75 degrees centigrade is a positive temperature.

Integers come in three types:

Given:

Temperature= 0.75 Centigrade

Now, As, the temperature 0.75 lies between whole number 0 and 1.

also, 0.75 is greater than 0.

Any number greater than is a positive number.

Hence, 0.75 is Integer integer.

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Final answer:

The solution x=12 is correct for the problem 34+x=46, as substituting x=12 into the original equation results in 46, matching the right side. Verification by substitution is a common practice to confirm the accuracy of solutions, particularly in the case of equations with two solutions.

Explanation:

The problem provided is 34+x=46; you have also provided that x=12 is the solution. To verify if x=12 is the correct solution, we substitute x=12 into the original equation: 34+12=46. Upon calculating, 34+12 equals 46, which is indeed the right side of the equation, confirming that the solution x=12 is correct.

Moreover, in general mathematical practice, checking solutions by substituting them back into the original equation is a reliable method for verification. If a problem has two solutions, as some quadratic equations do, both solutions should be checked in this way to ensure that each solution satisfies the original equation, indicating that both are correct. For example, if we have a quadratic equation like 2x²-8=0, solving it would give us two possible values for x that can be substituted back into the equation to verify if the identity holds true for both solutions.

Final answer:

The given solution x=12 for the equation 34+x=46 is correct because when substituted back into the original equation, it results in an identity, confirming the solution's validity.

Explanation:

In mathematics, particularly in algebra, when we have an equation such as 34 + x = 46, and we are given a solution, in this case x=12, we can verify its correctness by substituting the value back into the original equation. If the equation simplifies to an identity, which is an equation that always holds true like 6 = 6, then the given solution is correct. To check if x=12 is a solution for the original problem, we perform the substitution:

34 + 12 = 46

After the substitution, the equation simplifies to:

46 = 46

This results in an identity, confirming that the given solution x=12 is indeed correct.

This process is similar to checking solutions for other types of equations, such as linear, quadratic, or higher-degree polynomials. Whether a problem has a single solution like in this case, or multiple solutions such as x=3, x=-7, each potential solution must be verified individually by substituting them back into the original equation to ensure they lead to an identity.

Answer:

A) [tex]25x^2y^{22}[/tex]

Step-by-step explanation:

The given expression is [tex](5xy^{5})^2 . (y^3)^4[/tex]

Here we have to use exponent rules and simplify the expression.

Power rule : [tex](a^m)^n = a^{mn}[/tex]

Using the above rule, we can write

[tex](5xy^{5} )^2 = 5^2.x^2.y^{5*2}[/tex]

= [tex]25.x^2.y^10[/tex]

Again using the power rule

[tex](y^{3} )^4 = y^12[/tex]

Now we have to put together this expression, we get

= [tex]25.x^2.y^{10} .y^{12}[/tex]

Now we have to use product rule.

Product rule: [tex]a^m . a^n = a^{m + n}[/tex]

Using this rule, we can simplify further

= [tex]25..x^2.y^{10 +12}[/tex]

= [tex]25x^2y^{22}[/tex]

Answer:

Option A) 25x^2y^22

Step-by-step explanation:

The equation for the nth term of the given arithmetic sequence is an = -17 + 5(n - 1), which matches answer choice C.

The given sequence is an arithmetic sequence, where each term increases by a common difference. To find the equation for the nth term (an), you start with the first term (a1 = -17) and add the common difference (d = 5) multiplied by (n - 1), since the first term is already in place.

A correct formula for an arithmetic sequence is an = a1 + (n - 1)d. Applying this to the given sequence, we have an = -17 + (n - 1)5. Simplifying this expression gives us an = -17 + 5n - 5, which further simplifies to an = 5n - 22. Thus, the correct answer is an = -17 + 5(n - 1), which corresponds to answer choice C.

Length of the segment AC is 14 feet

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given,

Length of the hypotenuse = 17 feet

Angle of C =35 degrees

We know that,

Cos θ = Adjacent side / Hypotenuse

cos 35 = [tex]\frac{x}{17}[/tex]

x= [tex]17(cos 35)[/tex]

x= 13.9 ≅ 14 feet

Hence, the length of the segment AC is 14 feet

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The perimeter of a square measuring 5.35 cm on a side is 21.4 cm

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Length of Side = 5.35 cm

Unknown:

Perimeter = ?

Solution:

Perimeter of Square = 4 × ( Length of Side )

Perimeter of Square = 4 × ( 5.35 )

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width

Final answer:

To find the orbital period of an asteroid at 5 AU, apply Kepler's Third Law, resulting in approximately 11.18 years.

Explanation:

The question asks to find the orbital period of an asteroid with an average distance of 5 astronomical units (AU) from the Sun. We can use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period (T, in years) is proportional to the cube of the average distance from the Sun (a, in astronomical units) for any object orbiting the Sun, expressed as-

[tex]T^2 = a^3[/tex]

Applying the formula for the asteroid in question:

Therefore, the orbital period of the asteroid is approximately 11.18 years.

Number of Electoral votes for Florida is 29.

The question: North Carolina has 12 less electoral votes than Florida. To find the number of electoral votes for Florida, we can set up a subtraction equation.

Let x be the number of electoral votes for Florida.

Since North Carolina has 12 less electoral votes, the equation would be x = x + 12.

Solving for x, Florida has 29 electoral votes.