Two events e and f are​ __________ if the occurrence of event e in a probability experiment does not affect the probability of event f.

he hiked 4 km east in 45 minutes

45 minutes = 3/4 of an hour

4 /.75 = 5.33

 so the answer would be D. 5.3 km per hour east

Answer:

g(x)= (1/5x) ^2

Step-by-step explanation:

Just did the test got a 100.

The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]² so none of the given option are correct.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

If we streatch a function f(x) horizontally by factor of c then the value of new function g(x) become f(x/c)

By stretching f(x) by 5 it will  be

g(x) = f(x/5)

So replace x → x/5

Since,f(x) = x²

So,

g(x) = (x/5)²

Hence "The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]²".

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Step 1: (ab-9)(ab+8)

Step 2: ab x ab +8 x ab -9 x ab -9 x 8

Step 3:  ab2  +8ab-9ab-72=

Step 4: ab2 -ab-72

solved!!! that how you would solve it everything will continue as normal

Answer:

75°

Step-by-step explanation:

The numbers cannot be uniquely determined with the given information.

Let's solve this problem step by step.

Let's assume the second number is 'x'. Since the first number is 10 more than the second number, then the first number can be represented as 'x + 10'.

Since the first number is also twice the third number, the first number can be represented as '2y', where 'y' is the third number.

Now, we can form an equation using the given information: x + (x + 10) + 2y = 45

Simplifying the equation, we get: 2x + 2y + 10 = 45

Further simplifying, we get: 2x + 2y = 35

Dividing both sides of the equation by 2, we get: x + y = 17.5

Now, we have two variables and one equation, which means we have an infinite number of possible solutions. We need more information to determine the actual values of x and y.

Therefore, the numbers cannot be uniquely determined with the given information.

each little square = 1 square inch

the design takes up 21 squares so area is 21 square inches

 the perimeter = 6 +2+3+3+3+5 = 22 inches

Answer:

C

Step-by-step explanation:

The answer is b, not c. I just completed the quiz and got the question wrong by answering c. :/

Final answer:

To create a box with a volume of 9075 in3, a 61 in. by 61 in. piece of cardboard is needed after cutting out 3 in. squares from each corner and folding up the sides.

Explanation:

To determine the size of the cardboard needed to construct a box with a volume of 9075 in3 when 3 in. squares are cut from each corner and the sides are folded up, we first need to express the volume of the box in terms of the dimensions of the cardboard. Let x represent the length of one side of the original square piece of cardboard. After cutting out 3 in. squares from each corner, the length and width of the base of the box will be x - 6 inches (since 3 inches are removed from each side), and the height will be 3 inches (the size of the squares cut from the corners).

The volume V of the box can be expressed as V = (x - 6)(x - 6)(3). Given that V = 9075 in3, we can set up the equation 9075 = (x - 6)2 × 3. Solving for x will give us the size of the original cardboard piece.

To solve the equation, divide both sides by 3 to isolate (x - 6)2, which gives 3025 = (x - 6)2. Taking the square root of both sides gives x - 6 = 55, so x = 61. Therefore, a 61 in. by 61 in. piece of cardboard is needed to construct the box.

The side of the square having an area of 121 yards² is 11 yards

What is the area of a square?

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the area of the square be Y = 121 yards²

Now , let the side of the square be = a

And the equation for the area of the square is

Area of the square = a²

where a is the side of the square

So , substituting the values in the equation , we get

a² = 121 yards²

Taking square root on both sides , we get

a = 11 yards

Therefore , the value of a is 11 yards

Hence , The side of the square having an area of 121 yards² is 11 yards

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CR = CP = 17

PQ = QR = 15

CQ = x^2 +15^2 = 17^2 = x^2 + 225 = 289

x^2 = 289-225 = 64, sqrt(64) = 8, CQ = 8

Final answer:

The division Property of Equality is used to transform Equation 1 (35 = 5x) into Equation 2 (7 = x) by dividing both sides of the equation by 5.

Explanation:

The property of equality used to transform Equation 1 (35 = 5x) to Equation 2 (7 = x) is the division Property of Equality.

This property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. To get from Equation 1 to Equation 2, both sides of Equation 1 are divided by 5.

Division is similar to multiplication in that it follows the same rules for signs and equality. When dividing both sides by the same number, the numerator and denominator cancel out if they are the same, leaving a value of 1.

For instance, dividing 5x by 5 will lead to x, and dividing 35 by 5 will give 7, hence 7 = x, which is Equation 2.

Answer:

B

Step-by-step explanation:

If you divide x so only x and a number remains, you will get B.

[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex] has multiple zero = 4; multiplicity = 2.

" A multiple zero has the multiplicity which represents the number of times linear factor of multiple zero occur in the polynomial .Zero of the polynomial is associated with multiple zero."

According to the question,

Given,

[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex]

Simplify the given polynomial to get the multiple zero and multiplicity,

[tex]f(x) = x^{3} - 4x^{2}- 4x^{2} + 16x[/tex]

       [tex]\implies x^{2} (x-4) -4x(x-4)=0\\\\\implies (x^{2} -4x)(x-4) =0\\\\\\\implies (x) (x-4)(x-4)=0\\\\\implies x(x-4)^{2} =0[/tex]

Zero is associated with x =4.

(x-4) occur twice.

Hence, multiple zero = 4 and multiplicity = 2 of the given function.

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