The amount of pizza left in the buffet line is given by the function A(t) = 50(0.8)t where t stands for the number of minutes the buffet is open and A(t) stands for the amount of pizza in any given time. How much pizza is there after five minutes?

For the function f (x) = 15x - 7, the value of f ⁻¹ (x) is,

⇒ f ⁻¹ (x) = (x + 7) / 15

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 15x - 7

Now, We can find the inverse of f (x) as;

⇒ f (x) = 15x - 7

Substitute y = f (x),

⇒ y = 15x - 7

Solve for x;

⇒ y + 7 = 15x

⇒ x = (y + 7) / 15

Hence, We get;

⇒ f ⁻¹ (x) = (x + 7) / 15

Thus, The inverse function is,

⇒ f ⁻¹ (x) = (x + 7) / 15

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1/2 x 80 x 60 = 2400 square feet was the area

Answer:

The tip of the minute hand moves approximately 37.7 inches in 15 minutes.

Explanation:

To find how far the tip of the minute hand moves in 15 minutes, we can use the formula for the circumference of a circle:

[tex]\[ \text{Circumference} = 2 \pi r \][/tex]

Where:

- [tex]\( r \)[/tex] is the length of the minute hand (radius of the circle).

Given:

- The length of the minute hand, [tex]\( r = 6 \)[/tex] inches.

Substitute the given value into the formula:

[tex]\[ \text{Circumference} = 2 \pi \times 6 \][/tex]

[tex]\[ \text{Circumference} = 12 \pi \][/tex]

So, the tip of the minute hand moves a distance of [tex]\( 12 \pi \)[/tex] inches in 15 minutes.

To approximate this value:

[tex]\[ 12 \pi \approx 37.7 \][/tex] inches (rounded to one decimal place).

12  x 10  = 120

12   X 100  = 1200

Take for instance in 6 x 2, 6 x 20 and 6 x 200. Find the factors and these are the computations. We can also say: 

6 x 20 = 6 x 2 x 10 = 12 x 10 = 120 
60 x 20 = 6 x 10 x 2 x 10 = 12 x 10 x 10 = 1200

It must be remembered that in the commutative and associative properties of multiplication, the order of the factors does not matter when solving this kind of problem

log(35) = 1.544

 rounded to nearest tenth = 1.5

Answer: The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5

Step-by-step explanation:

Given : The magnitude M of an earthquake is defined to be  [tex]M=\log \frac{I}{S}[/tex]---(1)

, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and

S is the intensity of a “standard” earthquake, which is barely detectable.

If  the magnitude of an earthquake that is 35 times more intense than a standard earthquake

⇒Intensity of earthquake I=35 S

Substitute the value of I in (1), we get [tex]M=\log(\frac{35S}{S})=\log(35)=\log(5\times7)=1.544068[/tex] [tex]\approx1.5[/tex]

∴ The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5

Answer:

A) Variables

A) Independent

A) X

Step-by-step explanation:

The base of the triangle is calculated to be 12 inches using the area and height. Then, through the Pythagorean theorem, the hypotenuse is found to be approximately 36.06 inches.

The subject of the question is related to the calculation of a triangle's hypotenuse using the area and height of a right triangle. Given that the area of a triangle is calculated by halving the product of the base and the height (Area = 1/2 * base * height), we can use the given area to find the base of the right triangle.

First, we call the base of the triangle 'x'. The area is 210 square inches and the height is 35 inches.

We rearrange the formula for the area of a triangle to find 'x' as follows:  base = (2*Area) / height.

Our calculation then becomes x = (2*210) / 35. This simplifies to x = 12 inches.  

Next, we use the Pythagorean Theorem, that states: a² + b² = c², where 'c' represents the hypotenuse. Here, 'a' is the base found (12 inches), 'b' is the height (35 inches), and 'c' is the hypotenuse we're seeking.

Plugging the values into the theorem, we get c = √(12² + 35²). Hence, the hypotenuse of the right triangle is approximately 36.06 inches.

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(5,-1) because it would turn the points to their opposite "charge" and turn the positive to a negative and a negative to a positive

The required number is 27.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Let x be the number,

Then

Twenty-four is subtracted from a number = x - 24

and number divided by nine = x/9

Now according to the question,

x - 24 = x/9

Multiplying whole equation by 9 we get,

9x - 216 = x

Adding 216 both the sides we get

9x  = x + 216

Substracting x both the side we get

8x = 216

Dividing whole equation by 8 we get

x = 27

which is the required number.

Hence,the required Number is 27.

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Answer:

the answer is c} 375

greg score = x

 kara score = 3/4x-1

x + 3/4x-1 = 153

1 3/4x -1 = 153

1 3/4x = 154

x = 154 / 1 3/4 = 88

gregs score was 88

 kara s score was 153 -88 = 65

Answer:50 percent

Step-by-step explanation:You need to subtract 2.25 and 1.50 and get 0.75 then divide it to 1.5 and 0.5 then convert it into decimal form and its 50%.

Answer:

Option C. [tex]BC=31.2\ units[/tex]

Step-by-step explanation:

step 1

In the right triangle ABD find the length side AB

Applying the Pythagoras Theorem

[tex]AB^{2}=5^{2}+12^{2}[/tex]

[tex]AB^{2}=169[/tex]

[tex]AB=13\ units[/tex]

step 2

In the right triangle ABD

we know that

[tex]m<ABD=m<BCD[/tex]

[tex]sin(<ABD)=\frac{5}{13}[/tex] -------> equation A

step 3

In the right triangle ABC

[tex]sin(<BCD)=\frac{13}{5+DC}[/tex] ------> equation B

Remember that

[tex]m<ABD=m<BCD[/tex]

so equate equation A and equation B solve for DC

[tex]\frac{5}{13}=\frac{13}{5+DC}[/tex]

[tex]5(5+DC)=13*13[/tex]

[tex]25+5DC=169[/tex]

[tex]5DC=169-25[/tex]

[tex]5DC=144[/tex]

[tex]DC=144/5=28.8\ units[/tex]

step 4

In the right triangle BDC find the length side BC

Applying the Pythagoras Theorem

[tex]BC^{2}=28.8^{2}+12^{2}[/tex]

[tex]BC^{2}=973.44[/tex]

[tex]BC=31.2\ units[/tex]

Final answer:

The student made an error in describing the expression 5/n as "the quotient of n and 5." The correct phrase to describe this expression would be "the quotient of 5 and n."

Explanation:

The student made an error in describing the expression 5/n as "the quotient of n and 5." The correct phrase to describe this expression would be "the quotient of 5 and n."

When describing division, it is important to remember that the dividend (the number being divided) comes before the divisor (the number dividing the dividend).