Mathematics High School

## Answers

**Answer 1**

The **mean** is 4.16 and the **standard deviation **is 1.648.

**What is probability distribution ?**

Probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take. It shows all possible values of a random variable and the likelihood, or probability, of each value occurring. A probability distribution can be discrete or continuous, depending on the type of variable it represents. Discrete probability distributions are used when the random variable can only take on a finite number of values, while continuous probability distributions are used when the random variable can take on any value within a certain range. Probability distributions are used in various fields such as statistics, finance, physics, and engineering, among others.

**According to given conditions :**

To find the mean and standard deviation of the probability distribution, we need to input the given data into our TI-83, TI-83 Plus or TI-84 graphing calculator.

Here are the steps to find the mean and standard deviation using a TI-83, TI-83 Plus or TI-84 graphing calculator:

Press the "STAT" button.

Use the arrow keys to highlight "Edit" and press "ENTER."

Enter the values of X in L1 and the probabilities in L2.

Press the "STAT" button again.

Use the arrow keys to highlight "Calc" and press "ENTER."

Select "1-Var Stats" and press "ENTER."

In the "List:" field, enter "L1."

In the "Freq:" field, enter "L2."

Press "ENTER" to calculate the mean and standard deviation.

Using the calculator, we get:

Mean = 4.16 (rounded to two decimal places)

Standard deviation = 1.648 (rounded to three decimal places)

Therefore, the **mean** is 4.16 and the **standard deviation** is 1.648.

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## Related Questions

PLEASE HELP MEE LOOOK AT IMAGE

### Answers

The **perimeter **of the **shape **is, 72 inches.

**What is Addition?**

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The **shape** of figure is shown.

We know that, **perimeter **of any **shape **is sum of all the sides.

Hence, The perimeter of the shape is,

⇒ Perimeter = 12 + 5 + 6 + 13 + 12 + 5 + 6 + 13

= 72 inches

Thus, The **perimeter **of the shape is, 72 inches.

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Daria ell televiion. She earn a fixed amount for each televiion and an additional $20 if the buyer get an extended warranty. If Daria ell 16 televiion with extended warrantie, he earn $1,120. How much i the fixed amount Daria earn for each televiion?

### Answers

The fixed **amount** Daria earns for each television is $50.

Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations.

A** linear equation** in one variable is defined as an equation with a hom*ogeneous variable of degree 1 (i.e. only one variable).

A linear equation can include several variables. If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on. 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3 are some instances of linear equations.

Let's call the **fixed amount **Daria earns for each television x.

If she **sells **16 televisions with extended warranties,

She earns 16x + 16 * $20 = $1,120.

Expanding the right side of the** equation**, we have:

16x + $320 = $1,120

**Subtracting** $320 from both sides:

16x = $800

Dividing both sides by 16:

x = $50

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When Stephane plays chess against his favorite computer program he wins with probability 0.60 loses with probability 0.10 and 30% of the games result in a draw. Assume independence.

O Find the probability that Stephane wins 7 games if he plays 10 games.

### Answers

The** probability **that Stephane wins 7 games out of 10 is 0.215 or about 21.5%.

We can model the number of games **Stephane** wins out of 10 as a binomial distribution with parameters n = 10 (number of trials) and p = 0.6 (probability of winning). The probability** mass function **of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!) is the** binomial coefficient**.

To find the **probability** that Stephane wins 7 games out of 10, we can plug in k=7, n=10, and p=0.6 into the formula:

P(X=7) = (10 choose 7) * 0.6^7 * 0.4^3

= 120 * 0.0279936 * 0.064

= 0.215

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In Montreal, a taxi ride costs $2.00 plus

a certain amount for each kilometre

travelled. Serge paid $18.00 for a 20 km

ride. How much would Marie–Claude pay

for a 5 km ride?

### Answers

Based on the **total cost equation**, if Serge paid $18.00 for a 20 km ride in Montreal that charges $2.00 plus x for each kilometer, the total amount Marie-Claude paid for a 5 km ride is $6.00.

What is the total cost equation?

The **total cost equation** is like a linear function in the form of y = mx + b.

The **total cost equation** includes the fixed element (b or **y-intercept**), the **variable cost** per unit (m or the **slope**), and the variable x (number of units).

The fixed cost per taxi ride in Montreal = $2.00

The variable cost per kilometer traveled = x

The total amount paid by Serge for a 20 km ride = $18.00

The **equation **of the total cost paid by Serge is 2 + 20x = 18

Solving the **equation** for x:

20x = 18 - 2

20x = 16

x = 0.8

= $0.80

For a 5 km ride, Marie-Claude would pay = (2 + 0.8x)

= $6.00 (2 + 0.8(5))

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Subtracting a polynomial from itself always results in another polynomial because 0 is a constant monomial. question 3 options: true false

### Answers

**True**. Deducting a polynomial from itself generally brings about another polynomial since 0 is a steady **monomial** is true.

A polynomial is a numerical articulation comprising of factors and **coefficients**, which are consolidated utilizing just the tasks of expansion, deduction, and duplication. On the off chance that we deduct a polynomial from itself, the outcome will be one more polynomial articulation since deduction of two **polynomials** is characterized as adding the main polynomial to the nullification of the subsequent polynomial. The **refutation** of a polynomial is likewise a polynomial. The deduction of a polynomial from itself brings about a polynomial articulation equivalent to nothing, which is a steady monomial. Consequently, the **deduction** of a polynomial from itself generally brings about another polynomial since 0 is a steady monomial.

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4(g-h)+10 when g=12,h=7

### Answers

It's like you multiply the 4 when variables are in parentheses.

So basically 12 - 7 = 5

And then you multiply 4 by 5 which is 20

and then you add 10 to 20 which makes 30.

4 (12 - 7) + 10 = 30

**Answer:**

=4(12-7) + 10

=4×5 + 10

=20 + 10

=30

stressed help me please

Two boats were 400 miles apart at midnight and were both sailing to the same port on Honolulu. One boat was heading west and the other was heading east. If they both arrived at 8:00am, find the speed of each boat if one was 20MPH faster than the othe

### Answers

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What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?A.9 milesB.16 milesC.38 milesD.48 miles

### Answers

The **shortest distance** Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home is; 16 miles

How to find the shortest distance?

The **shortest distance** is the distance that is shortest of all the distances between two points lying on both lines.

Now, we want to find the **shortest distance** Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home.

The shortest distance from her home to city hall = 21 cm

The shortest distance from the city hall to the post office = 24 cm

Then returning back home = 3 cm

**Total distance** = 21 + 24 + 3 = 48 cm

**Conversion to miles** is;

3 cm = 1 mile

Thus, 48 cm = 16 miles

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VA council review the number of bedroom in 40 houe located in the ame area. The table how the information gathered. A) Find the modal average number of bedroom. B) Work out the mean number of bedroom. Number of bedroom

Frequency

5

1

10

2

15

3

4

7

5

3

### Answers

The **modal average** number of bedrooms is 3, and the mean number of bedrooms is also 3.

a) The modal average number of bedrooms is found by finding the most frequent number of bedrooms in the data. According to the table, the most frequent number of bedrooms is 3, with a **frequency **of 15. Thus, the modal average numbers of bedrooms are 3.

b) The **mean** number of bedrooms can be found by adding up all the number of bedrooms and dividing by the total number of houses.

The total number of bedrooms can be calculated by multiplying each number of bedrooms by its frequency and then adding them all up:

(1 x 5) + (2 x 10) + (3 x 15) + (4 x 7) + (5 x 3) = 5 + 20 + 45 + 28 + 15 = 113

The mean number of **bedrooms** is then:

113 ÷ 40 = 2.825

Therefore, the mean number of bedrooms is 2.835 ≈ 3.

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--The given question is incomplete; the complete question is

"A council reviews the number of bedrooms in 40 houses located in the same area.

The table shows the information gathered.

a) Find the modal average number of bedrooms.

b) Work out the mean number of bedrooms."--

What is the decimal of 1/8?

### Answers

To convert 1/8 to a decimal, divide the denominator into the numerator. 1 divided by 8 = . 125

Guest Check #6

2 Dozen Donuts 24.00

1 Donut Holes 4.89

4 Iced Coffees 8.76

Subtotal 37.65

8% Tax

18% Tip

Total

### Answers

**Answer:**

don't know 7273772+$+4;2+7272+2+;3;$;;3

Subtotal = 37.65

Tax = 37.65 * 0.08 = 3.01

Tip = 37.65 * 0.18 = 6.79

Final Total = 37.65 + 3.01 + 6.79 = 47.45

robin was given a $40 monthly allowance. she wants to go to the movies as many times as possible and have at least %12.50 left at the end of the month to go to a concert. a movie ticket costs $5. write and solve an inequality to determine how many times robin can go to the movies this month. then interpret the solution.

### Answers

**Answer: ≤7 tickets.**

**Step-by-step explanation:**

Robin can go to the movies less than or equal to 7 times this month.

Robin was given a $40 monthly allowance. She wanted to save 12.50% of that $40. 12.50% of 40 is 5. (X/40 = 12.50/100. Cross multiply. X=5)

Each movie ticket is $5. In order to save $5 or 12.50%, Robin can only buy $35 dollars worth of tickets (or 7 tickets).

So, the inequality is ≤7.

2. Let S(x,y) be the statement "x has sent an email to y," where the domain of x and y consists of all people. Write the following sentence as a logical expression (i.e., using predicates, quantifiers, and logical operators). "There is exactly one person who has been sent an email by everyone."

### Answers

The sentence "There is exactly one person who has been sent an email by everyone" can be written as a **logical expression** as follows:

∃x ∀y (S(y,x) → (∀z (S(y,z) → z = x)))

This expression uses the **existential quantifier **∃x, which states that there exists at least one x such that the statement inside the quantifier is true. The **universal quantifier **∀y states that the statement inside the quantifier is true for all y.

The statement S(y,x) says that y has sent an email to x, and the implication (→) says that if y has sent an email to x, then the statement inside the implication is true.

The statement ∀z (S(y,z) → z = x) states that for all z, if y has sent an email to z, then z must equal x. This **expression** states that there is exactly one person who has been sent an email by everyone, meaning that there is one person who is the recipient of all emails sent.

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there are only a few roller coasters in the world whose path takes them underground. Suppose a portion of the rollercoaster can be modeled by the function f(t)=(t^2-13t+40)(t^2-2t+3), where t represents the time elapsed in seconds since passing point A on the roller coaster and f(t) represents the height in feet above the ground. find the zeros of the function. what do these zeros represent in the context of the problem?

### Answers

The challenge requires you to change the **equation **from f(t)=a(x-h)2 + k to the parabola function f(t)=a(x-h)2 + k.

What is the roller coaster mathematical formula?

The centripetal **acceleration **is therefore given by the equation ac= v2/r = 2gh/r at every point along the frictionless roller coaster, where h is the **distance **from the highest point and r is the local radius of curvature.

If f(t) = 4t2 -8t + 7 then

= (4t2 - 8t + 4) + 7 - 4

=4 (t2 - 2t + 1) + 3

= 4 (t-1) 2 +3

As a result, options C and D are no longer possible.

recognising the f (t),

The maximum/minimum value is at f'(t) = 0 and f'(t) = 8t - 8.

0 = 8t – 8

t = 1

figuring out whether f"(t) > 0 or if minimum, f"(t) 0 maximum

Since f"(t) = 8 > 0, the minimal

f(1) =4(1)^2 – 8(1) +7= 3

Consequently, the minimal height is 3.

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Answer: t=5 t=8

Step-by-step explanation:

The function f is defined by f (x) = sin(x2). What are the first four nonzero terms of the Taylor series for f', the derivative of f, about x = 0 ?

### Answers

**Taylor** **series** for f(x) = sin x² is:

Sin x² = x² - [tex]x^6[/tex]/3! + [tex]x^{10}[/tex]/5! - [tex]x^{14}[/tex]/7! + .....

The first four nonzero **terms** are x², - [tex]x^6[/tex]/3!, [tex]x^{10}[/tex]/5!, and [tex]x^{14}[/tex]/7!.

What is a function?

A**function** isa relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The **Taylor** **series** of **sin x**.

Sin x = x - x³/3! + [tex]x^5[/tex]/5! - [tex]x^7[/tex]/7! + .....

Now,

**Replace** x = x².

We get,

Sin x² = x² - [tex]x^6[/tex]/3! + [tex]x^{10}[/tex]/5! - [tex]x^{14}[/tex]/7! + .....

Thus,

The first four nonzero **terms** are x², - [tex]x^6[/tex]/3!, [tex]x^{10}[/tex]/5!, and [tex]x^{14}[/tex]/7!.

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4. Vic bikes to the soccer field from his school at a constant speed of 10 miles per hour.

Vic's coach leaves the school of 1/3 an hour later. He drives at a constant speed of 30 miles per

Vic and his coach arrive at the soccer field at the same time. How long did it take Vic to get from

his school to the soccer field?

### Answers

It took Vic (1/2) **hour **to get from his school to the soccer field.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown **variables**. We can form numerical expressions from statements.

We know, Distance = Speed×Time or **d = rt**.

Given, Let, The distance between the soccer field from his school be '**d**'.

Therefore, From the given information,

**10t = 30(t - 1/3)**.

10t = 30t - 10.

- 20t = - 10.

t = 1/2.

So, The distance is 10×(1/2) miles = 5 miles or 30[(1/2) - (1/3) miles = 30×(1/6) = 5 miles.

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Compare these fractions with < and > and = 4/12 and 1/6

### Answers

**Answer:**

**Step-by-step explanation:**

How to compare fractions?

Verify whether the denominators are the same or different when comparing fractions. The fraction with the larger numerators is the larger fraction if the denominators are equal. If the fractions' numerators and denominators are the same, the fractions are considered to be equal.

**Answer:**

Compare: 4/12 and 1/6

**Using the given inputs:**

4/12 and 1/6

**The least common denominator (LCD) is: 12.**

**Rewriting as equivalent fractions with the LCD:**

4/12 and 2/12

**Comparing the numerators of the equivalent fractions we have:**

4/12 > 2/12

**Therefore, comparison shows:**

**4/12 > 1/6**

**(Hope this helped!)**

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A 8 cm cube i built from mall cube, each 2 cm on an edge. Write a ratio that compare the edge length of the large and mall cube

### Answers

The ratio of the** edge length** of the large **cube** (8 cm) to the small cube (2 cm) can be written as 8:2 or 4:1.

Comparing two or more related quantities using a **ratio** typically involves using a fraction or decimal. Ratios are used to evaluate relationships between two or more things or to compare values.

To calculate this ratio, we divide the length of the large cube (8 cm) by the length of the **small** cube (2 cm). The result is 4, which is the first **number** in the ratio. The second number in the ratio is the number we divided by, which is 1. Therefore, the ratio of the edge length of the large cube to the small cube is 4:1.

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A carpenter is cutting pieces of wood that are 4.65 meters long. The wood must be within 0.09 meters of the required length.

### Answers

An **absolute **value **inequality **that represents the situation is,

I x - 0.09 I ≤ 4.65.

The **solution **is -4.56 ≤ x ≤ 4.74.

What is an inequality?

In mathematics, "**inequality**" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the **inequality **sign if you multiply or divide either side by a negative number.

Given:

A **carpenter **is **cutting **pieces of wood that are 4.65 meters **long**.

The **wood **must be within 0.09 meters of the required **length**.

That means,

I x - 0.09 I ≤ 4.65

**Solving **further,

-4.65 ≤ (x - 0.09) ≤ 4.65

-4.56 ≤ x ≤ 4.74

Therefore, the **solution **is -4.56 ≤ x ≤ 4.74.

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A line ha a lope of 10/7 and include the point (7,d) and (0,–3). What i the value of d?

### Answers

The value of **d **is:

**7**

A line can be represented by the **equation** y = mx + b, where **m** is the slope and **b** is the y-intercept. In this case, the slope **m** is given as **10/7**.

Using the point **(7,d)**, we can find the value of b:

d = m * 7 + bd = 10/7 * 7 + bd = 10 + bb = d - 10

So the **equation** of the line is:

y = 10/7 x + (d - 10)

Using the point (0, -3), we can find the value of d:

-3 = 10/7 * 0 + (d - 10)-3 = d - 10d = -3 + 10d = 7

So the value of **d** is **7**.

**Complete Question**:

"A line has a slope of 10/7 and includes the point (7,d) and (0,–3). What is the value of d?"

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How long does it take for $10,000 to become $17,500 if your money is placed in a CD that draws 4.5% compounded quarterly? Get answer in years and months (newest month).

### Answers

If $10,000 is placed in a CD that draws 4.5% **compounded quarterly**, it would take approximately 4 years and 6 months for it to reach $17,500.

To calculate this, you need to use the **compound interest **formula: [tex]A = P (1 + r/n)^{nt}[/tex]

A = Final amount of the investment

P = Principal amount (initial investment)

r = Annual interest rate

n = Number of times the interest is compounded per year

t = Number of years

Plugging in the values for this example, you get: [tex]17,500 = 10,000 (1 + 0.045/4)^{4t}[/tex]

Solving for t, you get: t = 4.5 years

Therefore, it would take 4 years and 6 months for the** initial investment** of $10,000 to become $17,500 in a CD that draws 4.5% **compounded quarterly.**

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Convert the following equation into standard form

y= 4x-7

### Answers

As a result, the **standard** version of the **equation** is 4x - 1y = -7.

What is equation?

An **equation** is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two **expressions** separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an **equal** sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B are not both zero. In this case, A=4, B=-1, and C=-7.

So, the **equation** can be **written** as 4x - 1y = -7 in the standard **form**.

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When a variable x is normally distributed, the sampling distribution of the sample mean xbar

O is uniformly distributed. O is also normally distributed. O is correct.

### Answers

The correct statement is "When a variable x is normally distributed, the **sampling distribution **of the sample mean **xbar **is also normally distributed." **(B)**

This is known as the **Central Limit Theorem**, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the original distribution.

The mean and **standard deviation** of the sample mean can be calculated using the mean and standard deviation of the original distribution and the sample size.

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when do you use a bionomial random variable to model a statistical experiment? when do you rather use a hypergeometric random variable?

### Answers

**Binomial and hypergeometric random variables** are two different statistical tools used to model different types of experiments. **Binomial random variables** are used to model experiments that have two possible outcomes and **hypergeometric random variables** are used to model experiments where the number of successes and failures is fixed and the outcome of one trial affects the probability of success in subsequent trials.

In statistics, **random variables** are used to model the outcomes of a statistical experiment. **Binomial and hypergeometric random variables** are two such variables that are used to model different types of experiments. Understanding the difference between these two variables and when to use them is essential for statistical analysis.

**Binomial random variables** are used to model experiments that have two possible outcomes, typically referred to as success and failure. For example, flipping a coin, rolling a dice and getting a certain number, or observing if a person is male or female. In these types of experiments, the outcome of one trial does not affect the outcome of another trial, and the probability of success remains constant for all trials.

On the other hand, **hypergeometric random variables** are used to model experiments where the number of successes and failures is fixed and the outcome of one trial affects the probability of success in subsequent trials. For example, suppose you have a deck of cards with 52 cards, 13 of which are spades. You draw 5 cards without replacement from the deck. The number of spades you draw depends on the cards you have already drawn, and the probability of drawing a spade changes from trial to trial.

To determine which **random variable** to use, you need to consider the specific details of the experiment. If the experiment involves a fixed number of trials with only two possible outcomes and a constant probability of success, then you would use a binomial random variable. If the experiment involves a fixed population size and a variable number of successes, with the outcome of one trial affecting the probability of success in subsequent trials, then you would use a hypergeometric random variable.

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A we orginized your cloet you counted 20 hirt and 12 pair of pant what wa the pant to the hirt ratio

### Answers

The pant to **shirt** ratio is 12 pants to 20 shirts, which **simplifies** to a ratio of 3 pants to 5 shirts or 3:5. It's **important **to keep in mind that the** ratio **of 3:5 is just a** representation** of the current **number** of pants and shirts in your closet and may not **reflect** the ideal proportion for your needs or **preferences.**

This ratio of 3 pants to 5 shirts can be used to** compare** the relative **quantities **of pants and shirts in the closet. For **example**, if you have 15 shirts, you would have 9 pants **(**15 shirts * 3 pants / 5 shirts = 9 pants**)**. This ratio can also be useful when **determining** the proportion of pants to shirts to** purchase** or keep in your closet.

The ratio of pants to shirts is 12 pants to 20 shirts, which can be **expressed** as 3 pants to 5 shirts.

It's crucial to** remember** that the 3:5 ratio only **represents** the amount of shirts and pants you currently have in your **wardrobe** and may not be the **optimal **ratio for your needs or **tastes.**

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A coin is tossed. Find the theoretical probability of the coin landing on heads. Write your answer as a fraction in simplest form.

Question 1 options:

3/4

1/2

1

1/4

### Answers

**Answer:**

Option 2 or B, 1/2

**Step-by-step explanation:**

Technically, Coins only have **two **sides since they only have two sides we can put it in a form such as the following:

Coins have 2 sides: 50/50

Fractions have only 1 half: 1/2

Since there is only a 50/50 chance lets make it a percentage:

Percentage goes to 100%:

50%...

Since there is 50% chance to land on heads, now lets make it in fraction form:

1/2.

And there is your final answer:

1/2 or B

if the grass is wet, then the grass is dry true or false?

### Answers

The answer is FALSE because if the grass is wet why would it be dry.

Toby bought 192 kg of coconuts.

The ratio of the mass of the large coconuts to the mass of the medium-sized coconuts to the mass of the small coconuts is 3:5:2. There are 3/4 as many small coconuts as medium-sized coconuts. The number of large coconuts is 1/3 that of the small coconuts. If the total mass of 3 medium-sized coconuts is about 3 kg,

a) How many medium-sized coconuts did he buy?

b) How many large coconuts did he buy?

### Answers

The 196 kg **mass **of the coconuts and the 3:5:2 **ratio **of the mass of the **coconuts **indicates that we get;

a) There are 96 medium-sized coconuts

b) There are 24 large coconuts

What are ratios?

A **ratio **indicates the **quantitative relationship **between two quantities, which specifies the number of times a quantity can be obtained from or contains another quantity.

a) The **mass **of the cococniuts = 192 kg

The specified ratio of the coconuts = 3:5:2

The **number **of small coconuts = (3/4) × The number of medium sized coconuts

Number of large coconuts = (1/3) × The number of small coconuts

The mass of 3 medium-sized coconuts = 3 kg

The mass of 1 medium-sized coconut = 3 kg/3 = 1 kg

The ratio of the mass of the coconuts indicates that we get;

The mass of the large coconuts = (3/(3+5+2)) × 192 = 57.6 kg

Mass of the medium-sized coconut = (5/(3+5+2)) × 192 kg = 96 kg

The number of medium-sized coconuts = 96 kg/(1 kg/coconut) = 96 coconuts

The number of medium-sized coconuts = 96 coconuts

b) Number of number small coconuts = (3/4) × The number of medium sized coconuts

Therefore; The number of small coconuts = (3/4) × 96 coconuts = 72 coconuts

Number of large coconuts = (1/3) × The number of small coconuts

Therefore; Number of large coconuts = (1/3) × 72 coconuts = 24 coconuts

The number of large coconuts = 24 coconuts

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Beth and Kristin leave their homes at the same time to visit a water park. They both drive at the same rate. The

equation b = k + 2 models Beth's distance in miles, b,

from the park in terms of Kristin's distance in miles, k, from the park.

a. Determine the independent and dependent variables in the situation.

b. Use the equation to complete the table.

c. How does Beth's distance change when Kristin's distance decreases by 5 miles? Show your work.

### Answers

Beth's distance drops by 3 miles if Kristin's **distance **drops by 5 miles.

What is the difference between independent variable and dependent variable?

The variable that is altered or managed in a scientific experiment is known as an independent variable. It stands for the rationale or cause behind an outcome. The experimenter modifies the independent factors to test the dependent variable.

The dependent variable is impacted by the independent variable. For instance, your exam results are influenced by how much sleep you get (an independent variable) (dependent variable). This is understandable, but Eg. How much sleep you get depends on your test results.

a. **Independent Variable** = Kristin's distance (K)

Dependent Variable = Beth's distance (b)

c. b = k + 2

If Kristin's decreases by 5 miles, we represent new distance as (k - 5)

b = (k + 5) + 2

simplifying the above equation, we get

b = k - 3

Kristin and Beth are now **equally **separated from the park and the pork.

Beth's distance drops by 3 miles if Kristin's distance drops by 5 miles.

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Evaluate the expression when d=2

20 divided by d

A.1

B.10

C.40

D.2

### Answers

**Answer: B. 10**

**Step-by-step explanation:**