Let Events A and B be described as follows:• P(A) = buying popcorn• P(B) = watching a movieThe probability that you watch a movie this weekend is 48% The probability of watching amovie this weekend and buying popcorn is 38%. If the probability of buying popcorn is 42%,are watching a movie and buying popcorn independent?

Answer:

Step-by-step explanation:

It should be option D

The measure of the given polygon's angle is 2340°

Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.

In an n-sided polygon, there are n inner angles.

The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.

the formula is ;

Sₙ = ( n - 2 ) 180°

Here in question n is given as 15

Thus Sₙ = ( n - 2 ) 180° becomes

Sₙ = ( 15 - 2) 180

13 × 180

= 2340 °

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Answer:

it is really A 156 i took the test and got an 100%

Step-by-step explanation:

-5/4 can be shown as -1 1/4, and plotted on the number line as the first quarter tick past -1. Its opposite, 1 1/4, is the same way, the first quarter tick past 1.

Answer: On the plot line 5/4 is 5 tic marks passed 0 so -5/4 would be 6 tic marks before. Hope this helps

If this is wrong I am deeply sorry.

We will have the following:

Sphere solid is generated when the semicircle is rotated about the line.

Given,

The semi circle is rotated about the line.

To find the what solid is generated?

Now, According to the question:

We know that when a semicircle is rotated about any line then the three dimensional figure or a solid that is formed on this rotation transformation is Sphere.

Hence, Sphere solid is generated when the semicircle is rotated about the line.

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The solution for the given equivalent equation f(2x) is 10.

What is equation?

In mathematics, the term equation can be defined as the two algebraic expression which are equal to each other. This method is used to calculate the values of the parameters in the problems.

According to the question, the given equivalent equation is as follows:

Equivalent equation: f(2x) = 3x + 3 = x + 13

By using the addition-subtraction property, to generate the equivalent equations.

3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5

Now, f(2x) = 2x = 10

Hence, the solution for the given equivalent equation is 10.

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The correct equation is: f(2x) = 3x + 3 = x + 13

Answer:

Step-by-step explanation:

gee girls generation

The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]

Given,

Write the expression as a sum and/or difference of logarithms with all variables to the first degree.

[tex]In\sqrt{8t^4v^2}[/tex]

Convert to exponential form

= [tex]In(8t^4v^2)^\frac{1}{2}[/tex]

Simplify using exponent rule with same exponent [tex](ab)^n = a^n . b^n[/tex]

= [tex]In (8^\frac{1}{2} . (t^4)^\frac{1}{2}(v^2)^\frac{1}{2} )[/tex]

Apply laws of logarithms to simplify the expression.

= [tex]In 8^\frac{1}{2} + In(t^4)^\frac{1}{2} + In(v^2)^\frac{1}{2}[/tex]

Express the logarithm of a power of an expression as the power times the logarithm of the expression.

= [tex]\frac{1}{2} . In8 + In(t^4)^\frac{1}{2} + In(v^2)\frac{1}{2}[/tex]

=[tex]\frac{1}{2} . In8 + \frac{1}{2} . In(t^4) + \frac{1}{2} .In(v^2)[/tex]

Multiply the monomials

[tex]\frac{In8}{2} + \frac{1}{2} . 4 . In t + \frac{1}{2} . 2 . In v[/tex]

= [tex]\frac{In8}{2} + 2 . In t + \frac{1}{2} . 2 . In v[/tex]

= [tex]\frac{In8}{2} + 2 . In t + In v[/tex]

Hence, The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]

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The associative property of multiplication states that you can choose any pair of numbers to multiply first when there are more than two numbers being multiplied. This doesn't change the final result:

a . b . c = (a . b) . c = a . (b . c)

So, we see an example of such property in the first option:

7 . (3 . 5) = (7 . 3) . 5

Let's check this is indeed true:

7 . (3 . 5) = 7 . 15 = 105

(7 . 3) . 5 = 21 * 5 = 105

Therefore, the first option is correct.

Notice that the second option uses the distributive property of multiplication over addition:

a . (b + c) = a . b + a . c

The third uses the commutative property of multiplication:

a . b = b . a

The fourth is wrong since zero multiplied by any number is zero, not one:

0 . a = 0, for all values of a.

The two numbers whose sum is 50 and three times the first is 5 more than twice the second are 21 and 29.

What do you mean by sum?

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.

Let the two numbers be X and Y.

There are two condition given in the question through which we can form a system of equation containing two equations.

First condition: The sum of the numbers is 50.

Therefore,

X + Y = 50

Second Condition: Three times the first is 5 more than twice the second

Therefore,

3X = 2Y + 5

We get the system of equation:

X + Y = 50

3X = 2Y + 5

Solving this system of equation

3X - 5 = 2(50 - X)

3X - 5 = 100 - 2X

X = 105/5

X = 21

Putting the value of X in one of the equation:

Y = 50 - X

Y = 50 - 21

Y = 29

Therefore, two numbers are 21 and 29

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Answer:

  B: (3, 4, 5)

Step-by-step explanation:

You want to know which segment lengths could be used to form a triangle.

The triangle inequality requires the sum of the two short sides of a triangle exceed the length of the longest side.

A: 1+2 = 3 . . . not a triangle

B: 3+4 > 5 . . . forms a triangle

C: 1+10 < 100 . . . not a triangle

D: 1+2 < 5 . . . not a triangle

E: 1+3 = 4 . . . not a triangle

F: 1+20 < 100 . . . not a triangle

__

Additional comment

The above expression of the triangle inequality seems to be the one most commonly used in algebra and geometry courses.

The triangle inequality can also be seen to be expressed as ...

  a + b ≥ c . . . . . . where a, b, c are side lengths in any order

The "equal to" case allows triangles of zero height. (They look like a line segment.) Using that formulation, triples A and E in your answer list will also be considered to form a "triangle."

The range is the set of y-values of the points given.

The points given are:

{(3, 4), (7,-2), (11, -8)}

The range would be:

4, -2, and -8

Range = {4,-2,-8}

Option C

Answer: The line parallel to y = -2x + 5 that passes through the point(1,1)

Has the same slope, m but a different y intercept (0,b)

So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b

y = mx + b

m = -2

1 = -2(1) + b

1 = -2 + b

Add 2 to both sides of the equation to solve for b

1 + 2 = b

3 = b

The line is

y = -2x + 3

Step-by-step explanation:

Answer

ST = 14

According to the diagram

UV = VW

ST = UT

UT = VT - UV

UV = 14 and VT = 29

UT = 29 - 14

UT = 15

SInce UT = ST, Therefore, ST = 14

Answer:

Sue travels 8 miles per hour.

Step-by-step explanation:

The way that expresses the number of ways those textbooks could be distributed among the students is ⁵C₂.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr

Combination formula will be:

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

In this case, each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. This will be illustrated as ⁵C₂.

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There are ten ways (which are ⁵C₂ = 10) to distribute those textbooks could be among the students in this situation.

Combinations indicate the choosing of items from a predetermined list of items.

The combination is given by the relation, ⁿCₓ = n!/{x!(n-x)!}

The quantity is given by n. and x is equal to how many objects are taken at once.

Each of the five students in this situation wants to purchase a specific textbook, but there are only 2 books available.

The expression for the number of possible distributions of such textbooks among the students is

⇒ ⁵C₂

⇒ 10

Hence, there are ten ways to distribute those textbooks could be among the students.

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The weekly cost C of producing x units in a manufacturing process is given by

The number of units x produced in t hours is given by

(a) The composite function C(x(t)) is given by

The function C(x(t)) gives us the cost of production for t hours.

(b) The number of units produced in 4 hours is given by

200 units will be produced in 4 hours.

(c) Let us graph the function C(x(t)) = 3000t + 750 to find the value of t for which the cost increases to $15,000

As you can see, the value of t is 4.75 hours when the cost is $15,000.

Therefore, 4.75 hours must elapse until the cost increases to $15,000.

The average rate of change of the function at the interval x = -3 to x = 5 has a value of (b) 0

From the question, we have the following points

Parabola going through (-3, -1) and (5, -1).

Also from the question, the interval is given as

x = −3 to x = 5

This interval can also be represented as

(a, b) = (-3, 5)

The points in the question can be expressed as

f(a) = f(-3) = -1

f(b) = f(5) = -1

The value of the average rate of change of the graph at the interval is then calculated as

Rate = [f(b) - f(a)]/[b - a]

Substitute the known values in the above equation

So, we have the following equation

Rate = [f(5) - f(-3)]/[5 + 3]

So, we have the following equation

Rate = [-1 + 1]/[5 + 3]

Evaluate the above quotient

Rate = 0

Hence, the average rate of change of function f is (b) 0

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The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].

The given expression is [tex]-x^{2}-\frac{1}{6}[/tex].

We have to complete the given sentence;

The expression represents a ........... polynomial with ........terms. The constant term is .........., the leading term is..........., and the leading coefficient is ....................  .

we first complete the given sentence then we explain the sentence.

The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].

Firstly about Quadratic Polynomial

When the highest degree term in a second-degree polynomial equals to 2, the polynomial is said to be quadratic.

Now about Constant Term

A number that is constant and does not have any variables in an algebraic expression is a constant term.

Now about Leading Coefficient

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients.

Hence, the expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].

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Answer: (3,11)

Step-by-step explanation:

Answer: x<2 or (−∞,2)

Step-by-step explanation:

ANSWER

Amount = $3102.75

Interest = $1598.75

EXPLANATION

The annuity pays 6.6% compounded monthly.

The formula for an Amount compounded at a rate of r after t years is given as:

where P = principal (amount deposited) = $1,504

r = rate = 6.6% = 0.066

n = 12 (12 months in a year)

t = number of years = 11 years

Therefore, the amount in the account after 11 years is:

That's the amount in the account after 11 years.

This means that the amount of interest after 11 years is the amount after 11 years minus the amount that was there initially:

Interest = 3102.75 - 1504

Interest = $1598.75

Answer:

y= -7x-11

Step-by-step explanation:

m= -7 (gradient)

b= -11 (y-intercept)

write in the form of y=mx+b

y=-7x-11

The degree of the second term in the polynomial;

is 19

The inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car is 25y + 750 ≥ C.

If the car costs a total of $4500 number of yards you will have to mow is 150 yards at least.

In mathematics, a statement of an order relationship between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to) is called an Inequality.

Given:

Price of the car paid by your parents = $750

You have a summer job mowing yards for $25 per yard.

We have to determine an inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.

So, the required inequality is

25y + 750 ≥ C

Now, the Cost of the car given is $4500.

Substituting this in the inequality to find the number of yards,

25y + 750 ≥ 4500

Subtracting 750 from both sides

25y  ≥ 3750

Dividing both sides by 25,

y  ≥ 150

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The price of the lined jacket at discount heaven is 32.

To find the price of the lined jacket at the house of denim we use the rule of three.

Then the discount is:

Hence, the price of the lined jacket at house of denim is:

Therefore, the price of the lined jacket at house of denin is $31.73.

step 1

Find the slope

we need two points

take the points (0,3) and (1,0)

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

m=-3

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-3

b=3

substitute

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=-3

point (0,3)

y-3=-3(x-0)

step 4

standard form

AX+By=C

we have

y=-3x+3

The correct transformations are;

1. Reflection, then a translation

2. Rotation, then a reflection ​

3. Translation, then a rotation.

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Triangle XWY is transformed to produce triangle URL.

Now,

The images arise from transformation should remain the same with respect to the size or shape.

So, we get;

The correct transformations are;

1. Reflection, then a translation

2. Rotation, then a reflection ​

3. Translation, then a rotation.

Thus, The correct transformations are;

1. Reflection, then a translation

2. Rotation, then a reflection ​

3. Translation, then a rotation.

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