2. At the beginning of a storm, a pond was 16 cm deep. During the storm, the depth increased by 1.5 cm every hour, for 8 hours.

Drag each tile to the correct box. Not all tiles will be used.

vodomira [7]

If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.

<h3>What is inverse of a function?</h3>

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = √(7x – 21)

Then the inverse function will be

x = √[7{f⁻¹(x)} – 21]

x² = 7f⁻¹(x) – 21

7f⁻¹(x) = x² + 21

f⁻¹(x) = (1/7) x² + 3

Learn more about inverse function here:

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3 0

2 years ago

Log(x - 3) + log(x + 4) – log x = log 5

Rzqust [24]

Answer:

lol

Step-by-step explanation:

5 0

3 years ago

1. A luge race is very dangerous, and a crash can cause serious injuries. The league requires anyone who has a crash to have a t

antiseptic1488 [7]

Answer:

0.7061 = 70.61% probability she will have her first crash within the first 30 races she runs this season

Step-by-step explanation:

For each race, there are only two possible outcomes. Either the person has a crash, or the person does not. The probability of having a crash during a race is independent of whether there was a crash in any other race. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A certain performer has an independent .04 probability of a crash in each race.

This means that $p = 0.04$

a) What is the probability she will have her first crash within the first 30 races she runs this season

This is:

$P(X \geq 1) = 1 - P(X = 0)$

When $n = 30$

We have that:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{30,0}.(0.04)^{0}.(0.96)^{30} = 0.2939$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2939 = 0.7061$

0.7061 = 70.61% probability she will have her first crash within the first 30 races she runs this season

7 0

3 years ago

A movie theater charges $4.50 for children and $8.00 for adults. On a certain day, 1200 people enter the theater and $8375 is co

Lady bird [3.3K]

Answer:

The number of adults who attended=850

The number of children who attended=350

Step-by-step explanation:

a). Determine first expression

Let the number of each group be as follows;

adults=a

children=c

total number of people=1200

This can be expressed as;

number of people=number of children+number of adults

replacing;

a+c=1200...equation 1

b). Determine the second expression

Let the total cost be expressed as shown;

total cost=(cost per child×number of children)+(cost per adult×number of adults)

where;

total cost=$8,375

cost per child=$4.5

number of children=c

cost per adult=$8

number of adults=a

replacing;

(8×a)+(4.5×c)=1,200

8 a+4.5 c=8,375...equation 2

c). Combine equation 1 and 2 and solve simultaneously

1(8 a+4.5 c=8,375)

4.5(a+c=1,200)=4.5 a+4.5 c=5,400

(8 a-4.5 a)+(4.5 c-4.5 c)=(8,375-5,400)=2,975

3.5 a=2,975

a=2,975/3.5

a=850

replacing the value for a in equation 1

850+c=1200

c=1200-850=350

The number of adults who attended=850

The number of children who attended=350

4 0

3 years ago

Work out the mean for the data set below:<br> 4.7, 4.2, 8.2, 9.5, 3.1

lubasha [3.4K]

Answer:

5.94?

Step-by-step explanation:

8 0

3 years ago

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