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(cos Θ − cos Θ)^2 + (cos Θ + cos Θ)^2

Answer: [tex]\frac{1}{17576000}[/tex]

Step-by-step explanation:

Given: A state’s license plates consist of 3 letters followed by 3 numbers.

Since, there are 26 letters in English alphabet and 10 digits in set of numbers(0,1,....,9).

Then , the total number of license plates can be generated (if repetition is allowed)=

[tex]26\times26\times26\times10\times10\times10=17576000[/tex]

In AHW304, each alphabet and number occurs only once, the number of license plate with this = 1

Now, the probability of randomly generating a license plate that reads AHW 304=[tex]\frac{1}{17576000}[/tex]

Answer:

1/17,576,000

Step-by-step explanation:

Answer:

the input (x) values of the relation

Step-by-step explanation:

(a) No, The output (y) values of the relation are called Range. So it is the wrong option.

(b) Yes, the input (x) values of the relation are called Domain. Thus, it is the correct option.

(c) No, it is not a definition of Domain. Thus, this is an incorrect option.

(d) No, it is not a definition of Domain. It is called the cartesian point. Thus it is also an incorrect option.

Further,

The Domain is the all possible input values of a function that gives defined values.  

The Range is the all defined output values that we get from a function (or y).

20+0.15x = 35+0.10x

0.15x=15+0.10x

0.05x=15

x= 15/0.05

x= 300minutes

check:

300*.015 = 45+20=65

300*0.10 = 30 + 35 = 65

they equal

 so number of minutes would be 300

Answer:0

Step-by-step explanation:

A right triangle can have at most one obtuse angle since it already contains one right angle, and the sum of its angles must be 180 degrees according to geometrical axioms.

The question asks about the maximum number of obtuse angles that can be contained in a right triangle. In a right triangle, one angle is 90 degrees by definition, which is a right angle. According to Theorem 20, the sum of the angles of a triangle is two right angles, which equals 180 degrees. Having an obtuse angle, which is greater than 90 degrees, combined with a 90 degree angle, would exceed 180 degrees when the third angle is added, and this is not possible in a plane geometric figure. Therefore, a right triangle cannot have more than one right angle. As such, the option with the maximum number of obtuse angles a right triangle can contain is:

Answer: B) 1

Answer:

The correct answer to the following question will be Option B (Incenter).

Step-by-step explanation:

The middle of the circle which is carved in a triangle is the triangle incenter, the point where the triangle angle bisectors cross.

There are following steps to construct an inscribed circle in a triangle are as follows:

Step 1: Create the incenter.

Step 2: Construct a line that passes through incenter, perpendicular to one side of the triangle. The segment which connects the incenter with the triangle intersection point and the perpendicular line is the circle radius.

Step 3: Build a centered circle at the incenter with radius spotted in step 2.

Answer:

The correct option is 3.

Step-by-step explanation:

The given piecewise function is

[tex]f(x)=\begin{cases}3x^2+1 & \text{ if } -4<x<6 \\ 6 & \text{ if } 6\leq x<9 \end{cases}[/tex]

Range is the set of output or y values.

The given function for 6 ≤ x < 9 is

[tex]f(x)=6[/tex]

It is a constant function, the value of function is 6 for all values of x.

Range = 6

The given function for -4 < x < 6 is

[tex]f(x)=3x^2+1[/tex]          .... (1)

It is a quadratic function.

The vertex form of a quadratic function is

[tex]f(x)=a(x-h)^2+k[/tex]         ....(2)

Where (h,k) is vertex and a is constant.

From (1) and (2), we get a=3,h=0,k=1.

The vertex of this function is (0,1), it means the range of this function is greater than or equal to 1. But this function is only defined for -4 < x < 6.

[tex]f(-4)=3(-4)^2+1=49[/tex]

[tex]f(6)=3(6)^2+1=109[/tex]

The maximum value of the maximum value of the function is 109 at x=6. Since 6 is not included in the interval -4 < x < 6, therefore 109 is not included in the range.

Range = [1,109)

When we combined the range of both functions we get

Range = [1,109)

Therefore the correct option is 3.

Keywords:

Polynomial, classify, degree, greatest exponent

For this case we have the following polynomial: [tex]Q (x) = 3x ^ 2 + x-6[/tex], we must classify the polynomial according to its degree. For this, we must bear in mind, that by definition, a polynomial is of the form:

[tex]P (x) = ax ^ n + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f[/tex]

Where:

a, b, c, d, e, f: They are the coefficients of the polynomial

n, n-1,3,2,1,0: They are the exponents. This polynomial is of degree "n", because "n" is the largest exponent.

x: It is the variable

Thus, [tex]Q(x) = 3x ^ 2 + x-6[/tex]is of degree "2" because "2" is the largest exponent.

Answer:  

It is a quadratic polynomial

Option C

The correct classification for this polynomial is C. quadratic.

The polynomial 3x^2 + x - 6 is classified by its degree, a fundamental characteristic of polynomials determined by the highest power of the variable 'x.'

In this case, the highest power is 2, making it a quadratic polynomial. Quadratic polynomials represent a U-shaped graph when plotted, often described as a parabola.

They play a significant role in various areas of mathematics, science, and engineering, serving as fundamental models for various real-world phenomena.

Quadratic equations are commonly encountered in physics, engineering, economics, and other fields, making them essential for solving problems and making predictions. Thus, the correct classification for this polynomial is C. quadratic.

for such more question on polynomial

https://brainly.com/question/1496352

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The discriminant of the given polynomial is 0, indicating one real root.

The discriminant of a quadratic equation is a value that can be used to determine the nature of the solutions (roots) of the equation. It is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation.

In the given polynomial, the coefficients are a = 4, b = -20, and c = 25. Plugging these values into the formula, we get: (-20)^2 - 4(4)(25) = 400 - 400 = 0.

Since the discriminant is equal to zero, the polynomial has one real root.

2,4,7,12 for edgynuity. the way you can tell is because you look at the front.     12xy3 + 2x5y + 4x5y2 + 7x5y. the 12 1 4 7 are the coefficients.

Final answer:

The coefficients in the algebraic expression are 12, 2, 4, and 7, which are the numerical multipliers of the variable terms.

Explanation:

The coefficients in the expression 12xy^3 + 2x^5y + 4x^5y^2 + 7x^5y are the numerical factors that multiply the variables x and y in each term of the polynomial expression. The coefficients in this expression are 12, 2, 4, and 7. These are the numbers in front of the variable terms and not the exponents or the variables themselves.

V=1/3bh
324=1/3(9)* h
324=3h
h=324/3
h=108

height is 108cm

Answer: 12 cm

The other guy that answered didn't do it correctly, he didn't find the height. You have to do:

1/3 (9 • 9) (x) = 324

1/3 • 81x = 324

27x = 324

x = 12

Trust me, I just finished my quiz and got ths answer right.

Answer: Dilation is a transformation that proportionally reduces or enlarges a figure.

Step-by-step explanation:

It stretches or shrinks the actual figure. It produces similar figures.

Since the corresponding sides of similar figures are in proportion.

⇒ It proportionally reduces or enlarges a figure.

Hence, A dilation is a transformation that proportionally reduces or enlarges a figure.

Final answer:

A scale transformation or dilation is a linear transformation that proportionally enlarges or reduces a figure, maintaining the proportional size relationships within the figure.

Explanation:

A transformation that proportionally reduces or enlarges a figure is known as a scale transformation or dilation. In such a transformation, lines are transformed into lines, and parallel lines remain parallel, consistent with the requirement for a transformation to be linear. This is important because it maintains the proportionality of the figure, meaning the size relationship of the parts of a figure to each other and to the whole figure remains constant, even though the overall size changes. Dilation can be characterized by a scale factor, which dictates how much larger or smaller the figure will become. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure reduces in size.

Final answer:

To calculate the percent uncertainty in the volume of a spherical beach ball when the radius is uncertain, you multiply the square of the radius by four (surface area), by the uncertainty in the radius, and then compare this value to the total volume. The percent uncertainty is found to be approximately 2.62%.

Explanation:

To determine the percent uncertainty in the volume of a spherical beach ball with a radius of 2.86 1 0.09 meters, one must first calculate the volume's uncertainty, then relate this to the total volume, and finally convert this relationship into a percentage.

The formula for the volume of a sphere is [tex]V = (4/3)\pi(r^3)[/tex]. Since volume is proportional to the cube of the radius, any uncertainty in the radius dramatically affects the volume uncertainty. Using a function for the volume V(r) and applying the approximation for small changes in r, we have:

[tex]V = (4/3)\pi(r^2))(r)[/tex]

For a radius of 2.86 meters and an uncertainty of 0.09 meters, the uncertainty V in volume is 170 [tex]cm^3[/tex]. The volume is approximately V = [tex](4/3)(3.14)(2.86^3)[/tex] = 6538 [tex]cm^3[/tex]. Therefore, the volume expressed with its uncertainty is [tex]6500 \pm170[/tex] [tex]cm^3,[/tex] rounded to avoid false precision.

To find the percent uncertainty:

Convert the uncertainty to the same units as the ball's volume if needed (here both are in cm^3).

Divide the uncertainty by the volume: (170/6500) x 100%.

The percent uncertainty is approximately 2.62%.

To find the time it takes for the object to hit the ground, we can solve the quadratic equation -16t^2 + 1600 = 0 using the quadratic formula. The positive solution to this equation gives us the time in seconds. Therefore, the object will take √102400/32 seconds to hit the ground.

To find the time it takes for the object to hit the ground, we need to solve the equation -16t^2 + 1600 = 0. This is a quadratic equation, so we can use the quadratic formula. Plugging in the values, we get t = (-b ± √(b^2 - 4ac))/(2a). In this case, a = -16, b = 0, and c = 1600. Plugging in these values, we get t = (± √(0 - 4(-16)(1600)))/(2(-16)). Simplifying the equation further, we get t = (± √(0 + 102400))/(32). This gives us two possible values for t: t = √102400/32 and t = -√102400/32. Since time cannot be negative in this context, we can discard the negative solution. Therefore, the object will take √102400/32 seconds to hit the ground.

positive means add

 so it would be a deposit into the account

 so A is the correct answer

To find h(-12), substitute -12 into the function h(x)=2x²-2. The value of h(-12) is 286.

To find h(-12), we substitute -12 into the function h(x)=2x²-2:

h(-12) = 2(-12)² - 2

h(-12) = 2(144) - 2

h(-12) = 288 - 2

h(-12) = 286

Therefore, h(-12) is equal to 286.

Answer:

[tex]13.93ft^{2}[/tex]

Step-by-step explanation:

The area of the opening will be the sum of the area of the two shapes shown which are rectangle and half ellipse:

[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}[/tex]

The area of the rectangle is:

[tex]Area_{Rectangle}=a*b[/tex]

where:

[tex]a=4ft\\b=2\frac{1}{2}ft[/tex]

we replace values(we convert the mixed fraction to improper fraction by multiplying the whole number part by the fraction's denominator, then add that to the numerator  then write the result on top of the denominator.):

[tex]Area_{Rectangle}=4*2\frac{1}{2} =4*\frac{5}{2}=10[/tex]

The area of the ellipse is:

[tex]Area_{Ellipse}=a*b*\pi[/tex]

where:

[tex]a=Radius1=1\frac{1}{4}ft\\b=Radius2=2ft\\[/tex]

Radius2 will be half the side of the rectangle

[tex]Radius2=\frac{4}{2}=2[/tex]

we replace the values:

[tex]Area_{Ellipse}=1\frac{1}{4} *2*\pi=\frac{5}{4}*2*\pi=\frac{5}{2}\pi =7.85[/tex]

we calculate now the total area:

[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}\\Area=10+\frac{1}{2}(7.85)=10+3.93=13.93ft^{2}[/tex]

Answer: 3/5 is the probability that person's skin cleared up given that they used the medication.

Step-by-step explanation:

let S represents skin cleared and M represents medicine used.

According to the given Venn diagram,

P(S) = 40

P(M)= 50

[tex]P(M\cap S) = 30[/tex]

Thus by the definition of conditional probability,

If it is given that the skin is cleared then the probability that persons used the medicine,

P(M/S)=[tex]\frac{P(M\cap S)}{P(S)}[/tex]=30/50= 3/5.

P(M/S)=3/5.

The probability that the person's skin will clear up given that they used the medication is:

This refers to the likelihood of an event to occur based on certain conditions.

If we want to find the probability about whether the skin will clear up is:

We would assign S to represent the skin

M to represent medicine

Hence,

P(MnS) = 30

Using the conditional probability rule,

P9M/S)= P(MnS)/P(S) = 30/50

=3/5

Read more about probability here:
https://brainly.com/question/251701

Answer:

(-2, 18) and (8, 38)

Step-by-step explanation:

First, set the two equations equal to each other to get $2x^2-10x-10=x^2-4x+6$. Combine like terms to get $x^2-6x=16$. To complete the square, we need to add $\left(\dfrac{6}{2}\right)^2=9$ to both sides, giving $(x-3)^2=16+9=25$.

So we have $x-3=\pm5$. Solving for $x$ gives us $x=-2$ or $8$. Using these in our original parabolas, we find the points of intersection to be $\boxed{(-2,18)}$ and $\boxed{(8,38)}$.

Credit: AoPs