Mathematics High School

## Answers

**Answer 1**

The converse of the following **conditional** is B. If **Jason** is not buying a roll of duct tape, then he is not at the hardware store

What is a conditional statement?

A **conditional statement** is a type of compound statement which satisfies “if...then” condition.

It should be noted that **conditional** **sentences** in everyday speech indicate that one thing depends on another, as in "The picnic will be canceled if it rains." They are so named because the dependent clause's influence on the sentence's main clause is **dependent**.

In conclusion, the correct option is B.

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## Related Questions

What are 5 ways to study a test?

### Answers

Start your **schoolwork**, **Schedule **study time Study according to the exam, Defy **procrastination**, and Study in groups these are the 5 ways to study for a test.

5 ways to study a test can be in the following manner.

1. start your **schoolwork**

Actually, you should begin preparing for exams and quizzes well before you are aware that a test is coming up. As you take notes in class, you can start **developing** good study habits. Taking notes helps you to recall what you've read or been taught.

2. **Schedule **Study Time

Consider how much time you want to spend on **each topic** before starting to study. By doing this, you'll avoid feeling overloaded.

Determine how much time you will need to study between now and your three tests on Friday if it is Monday and you have three tests on Friday. Then **calculate **how much time each subject will require

3. Study according to the kind of exam you're taking

A lot of teachers prepare their pupils for exams by **explaining the format** in advance. You can adjust your study **methods **as a result. For instance, if you know there will be **multiple-choice questions** about World War II, you can concentrate on learning facts and specifics. However, if the test will include essay questions, you should consider the subjects that are most likely to be addressed.

4. **Defy** the urge to put **off things.**

5. **Organize **a study group.

Going through the material with others who are preparing for the** same test** can **occasionally **be **beneficial **for ensuring that your notes are accurate and that you **comprehend **the material. Study groups are beneficial since you may brainstorm strategies to make topics stick in your minds while also testing one another.

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Factor the following quadratic function to reveal the roots. Then find the vertex of the quadratic function. f(x) = x² + 6x - 16

The roots are

The vertex is

### Answers

**Answer:**

To factor the quadratic function f(x) = x² + 6x - 16, we need to find two integers whose product is -16 and whose sum is 6. The pair of integers that satisfies these conditions is -8 and 2.

We can then factor the quadratic as follows:

f(x) = x² + 6x - 16

f(x) = (x - 8)(x + 2)

The roots of the quadratic are the values of x that make the quadratic equal to 0. In this case, the roots are x = 8 and x = -2.

The vertex of a quadratic function is the point on the graph where the function reaches its minimum or maximum value. The vertex of a quadratic of the form f(x) = ax² + bx + c is given by the coordinates (-b/2a, f(-b/2a)).

In this case, the coefficient of the x² term is 1, and the coefficient of the x term is 6. Therefore, the vertex of the quadratic is (-6/21, f(-6/21)) = (-3, f(-3)).

To find the value of f(-3), we can substitute -3 for x in the quadratic:

f(-3) = (-3)² + 6(-3) - 16 = 9 - 18 - 16 = -25

Therefore, the vertex of the quadratic is (-3, -25).

A sphere of radius 10 cm has the same surface area as a circle. What is the radius of the circle?

A) r=20

B) r=36

C) r=16

D) r=24

E) r= 48

### Answers

The **radius** of circle is **20 cm** so that **cirlcle** have same **surface area** as that of sphere.

The **surface area** of a sphere with **radius **r is given by:

4 * π * [tex]r^2[/tex]

The **surface area** of a** circle **with radius R is given by:

π * [tex]R^2[/tex]

We are given that the **surface area** of a sphere with radius 10 cm is equal to the **surface area** of a circle. Setting the two expressions for** surface area** equal to each other and solving for R gives:

4 * π * [tex]r^2[/tex] = π * [tex]R^2[/tex]

=> 4 [tex]r^2[/tex] = [tex]R^2[/tex]

=> R =2r

as given that r = 10cm

so R = **20 cm**

Thus, the **radius** of the **circle** is **20 cm.**

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Analia wants to know which school has the higher sat average relative to the resources invested per

student.

1) analia thought of two different ways to define this quantity. identify these two definitions among the

following options.

choose 2 answers:

sat average divided by number of sports medals won

b

sat average divided by number of students

sat average divided by budget per student

sat average divided by teachers per student

### Answers

Option B is the correct option of the given statement.

sat **average** divided by number of students.

sat average divided by budget per student.

How average is math?

The **average **value in a set of numbers in mathematics is the middle value, which is calculated by dividing the total number of values by the sum of all the values. When determining the **average** for a set of data, we add up all the values and divide that total by the number of values.

The average calculation is how.

**Average** The arithmetic mean is computed by summing the outcomes of adding a group of** integers**, dividing them by their count, then adding the answers back together. For instance, 30 divided by 6 equals 5, as the total of 2, 3, 4, 5, 7, and 10 is 5.

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A right cylinder shaped water tank is used to supply water to a reservoir. if the cylinder has a diameter of 16 feet and a height of 22 feet, what is a reasonable estimate of the maximum amount of water the tank can hold?

### Answers

**Answer:**

The amount of water the tank can hold is about 4421.12 cubic feet.

**Step-by-step explanation:**

Given,

Cylinder has a diameter of 16 feet. height of 22 feet.

**To Find**: The Volume of the cylindrical Tank

The volume of the cylinder is given by the formula,

[tex]V=\pi r^{2} h[/tex]

where r is the radius (half the diameter), and h is the height.

So first we need to find the radius by the formula

[tex]r=\frac{d}{2}[/tex]

[tex]r=\frac{16}{2}[/tex]

[tex]r=8[/tex]

Now we can find the volume by,

[tex]V=( 3.14)(8)^{2} (22)\\V=4421.12ft^{3}[/tex]

The maximum amount of water the tank can hold is about 4421.12 cubic feet.

Ada recorded the thickness a of a set of books. this line plot shows her results.

jada stacked the books that were 1/12 inches thick on top of the books that were 2/14 inches thick.

how thick was her pile of books?

### Answers

Ada pile of books as a **result** of stacking 1/12 inches thick on top of the books that were 1 inches thick = 0.933 inches

From the** line plot**, if Ada stacked the books that were 1/12 inches thick on top of the books that were 1/7 inches **thick**, the result would be as follows.

A line plot shows the **frequency of data** using a number line.

As seen from the line plot, 5 books are 1/12 inches thick and 4 books are 1/7 inches thick. If the 1 /7 inches thick books was **stacked** on the 1/12 inches thick book, the resulting thickness would be:

= (1/12)* books that were 1/12 inches thick + (1/7)*books that were 1/7 inches thick

= (1/12)*5 + (1/7)*4

= 5/12 + 4/7

= 0.416 + 0.517

= 0.933

Therefore Ada pile of books as a **result** of stacking 1/12 inches thick on top of the books that were 1 inches thick = 0.933 inches

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Gwendolyn has $725,000 she wants to save. if the fdic insurance limit per depositor, per bank, is $250,000, which of these ways of distributing her money between three banks will guarantee that all of her money is insured?

### Answers

In **three ways **of distributing her money between three banks will guarantee that all of her money is insured .

Given :

Gwendolyn has $725,000 she wants to save.

fdic **insurance** limit per depositor, per bank, is $250,000

The three ways of distributing her money between three banks will guarantee that all of her **money** is insured are :

**first way** if $250,000 deposit in one bank, $250,000 deposit in second bank and remaining money $225,000 in third bank .**second way** if Gwendolyn deposite $200,000 in one bank , $250,000 deposite in second bank ,$275,000 deposite in third bank.**third way** if Gwendolyn deposit $225,000 in one bank ,$225,000 deposite in second bank and $ 275,000 in third bank .

Hence , In **three ways** of distributing her money between three banks will guarantee that all of her money is insured .

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Joe works 18 hours at $13/hour. His tax rate is 12 percent. What is Joe's gross pay?

### Answers

**Answer:**

$ 234

**Step-by-step explanation:**

GROSS pay is pay before taxes are taken = 18 hr * $ 13/hr = $ 234

LCM for 20 and 44, (division method)

### Answers

The LCM for 20 and 44 is 220.

What is least common multiple (LCM)?

The least or smallest common **multiple** of any two or more given natural numbers are termed as LCM.

For example, LCM of 10, 15 and 20 is 60.

According to the question,

LCM for 20 and 44,

Step 1 : Divide the given numbers by the least **prime number**.

Here, 2 is the least number which will divide both 20 and 44.

we get, 10 and 22.

Step 2 : Divide the given numbers by the least **prime number**.

Here, 2 is the least number which will divide both 10 and 22.

we get, 5 and 11.

Then, the** LCM** for 20 and 44 is 2×2×5×11.

= 220.

Hence** LCM** for 20 and 44 s 220.

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How can you identify and plot points on a coordinate grid?

### Answers

**Answer:**

There are two axes, the y coordinate (vertical, or up and down), and the x coordinate (horizontal, or side to side. There are four quadrants, the top left in which y is positive and x is negative, the top right in which both y and x are positive, the bottom left in which both y and x are negative, and the bottom right in which x is positive and y is negative. To plot a point on a coordinate grid, look at the ordered pair which should be in parenthases. It should look like this - (x,y). So, for example, if the ordered pair was (6,4), you would go six places to the right on the x-axis (if it were negative you would go left) and 4 places up on the y-axis (if it were negative you would go down).

How to do missing digits in division?

### Answers

With the help of **formula, **Dividend = Quotient (Divisor)+ Remainder, we can calculate missing digits in **division**.

What is division?

Divide means to **divide **into two or more equally sized parts, areas, **classes**, groups, or **divisions**. Divide, in layman's terms, means to **divide **something into **equal **portions or distribute the entire thing to a **group**. Let's say that a diagonal cuts a **square **into two equal-area triangles. A division **operation **may or may not **produce **an integer as its output. Occasionally, the outcome will be in **decimal **form.

Given to find the **missing **digit in division,

let us take an example a number is divided by 8 gives 94 as quotient and 4 as **reminder **find the **number**,

we know ** Dividend **= Quotient(Divisor) + **Remainder**

where The dividend is the number, which is being **divided**

The divisor is the **number**, which divides the number,

The **quotient **is the result of the division,

and left digit is **reminder**

substitute the **values**

** **Dividend = Quotient( Divisor) + Remainder

Dividend = 94(8) + 4

**Dividend **= 752 + 4

Dividend = 756

Hence using the **formula **of division ** **Dividend = Quotient( Divisor) + Remainder, missing digits in **division **can be found.

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The boys had 5 4 6 gallons of water to share throughout the day. james drank 1 1 3 5 6 1 2 gallons and simon drank 2 3 gallon. how much water did the boys have left at the end of the day?

### Answers

At the end of the day, the boys had **average ** 2 gallons of water left to share since James drank 5 **gallons **and Simon drank 2 gallons.

At the end of the day, the boys had 2 gallons of water left to **share**. This was because James had **initially **drank 5 gallons of the water and Simon had drank 2 gallons. They had started the day with 5 4 6 gallons, which they were supposed to share. James had drank 1 1 3 5 6 1 2 gallons and Simon had drank 2 3 gallons, leaving them with only 2 gallons left at the end of the day. This meant that they had **consumed **8 gallons of their **allocated **water in total, leaving only 2 gallons of the water to share between them. This shows how important it is to manage the water that we have, as it can easily be wasted if not used correctly.

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Two times a number is the result when 7 times a number is taken away from 99. Find the number.

### Answers

11 is the **whole ** **number**.

**What in mathematics is a whole number?**

**Whole numbers** those figures that contain zero and **natural integers**. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.

Simply put, a whole number is any positive number without a decimal or fractional component. This implies that, for instance, all whole numbers are 0 and 1, 2, 3, 4, 5, and 6. All natural numbers, including 0, are considered whole numbers. 5 is therefore a whole number.

2x=99-7x

9x=99

x = 11

2x11 = 22

99-&7*11) = 22

so the number is 11

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Solve the triangle. round decimal answers to the nearest tenth. a triangle a b c with base a c is drawn. the length of side a b is 26 units. the measure of angle a c b is 81 degrees and the measure of angle b a c is 33 degrees.

### Answers

Angles in a triangle add to [tex]180^{\circ}[/tex], so [tex]\boxed{\angle ABC=66^{\circ}}[/tex].

We can solve for the two side lengths using the law of sines.

[tex]\frac{BC}{\sin 33^{\circ}}=\frac{26}{\sin 81^{\circ}}\\\\BC =\frac{26 \sin 33^{\circ}}{\sin 81^{\circ}}\\\\\boxed{BC \approx 14.3}\\\\\\\frac{AC}{\sin 66^{\circ}}=\frac{26}{\sin 81^{\circ}}\\\\AC=\frac{26 \sin 66^{\circ}}{\sin 81^{\circ}}\\\\\boxed{AC \approx 24.0}[/tex]

What were the causes of civil disobedience movement?

### Answers

The main causes were the creation of the **Simon Commission**, the rejection of the petition for Dominion Status, and demonstrations against the detention of social revolutionaries.

**Civil disobedience movement;**

Civil disobedience, also known as passive resistance, is the act of refusing to comply with the requests or orders of a government or **occupying power **without using force or other aggressive forms of resistance. Its typical goal is to pressure the government or occupying power into making concessions

The** **Civil Disobedience Movement's goal was to encourage people to defy **government demands**, laws, decrees, and mandates.

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1. according to a large university, 32% of their graduating class will have full time employment within

one month after graduation. the admissions office wants to investigate this claim. they contact

an srs of 300 of the previous semester's graduates. let p = the proportion of graduates in this

sample who had full time employment within one month of graduation.

(a) what is the shape of the sampling distribution ofp ? justify.

(b) what are the mean and standard

deviation of the sampling distribution ofp?

(c) interpret the standard deviation of the sampling distribution of

### Answers

(a) The shape of the sampling distribution of p is **0.32**

(b) The mean of the sampling distribution of p is **937.5**

(c) The **standard deviation **of the sampling distribution is **96**

Here we have given that according to a large university, 32% of their graduating class will have full time employment within one month after graduation.

And here we also know that they contact an SRS of 300 of the previous semester's graduates.

Let us consider that p refers the proportion of graduates in this **sample **who had full time employment within one month of graduation.

While we looking into the given question, we have identified that this is a question for one population proportion.

Here we have to use the normal **distribution **if the conditions are satisfied.

Here we have given that sample **proportion **of students having full time employment within a month p = true proportion and n = total sample size

Then the value p = 0.32 and n = 300.

Then the **standard deviation** is calculated as,

=> 0.32 x 300

=> 96

Similarly, the **mean **is calculated as,

=> 300/0.32

=> 937.5

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A person is 90 miles away from islamabad and cars fuel guage shows that cars tank is one quater full the cars tank can hold 12 litres of petrol and the car can travel 25 miles per litre does the person need to stop for petrol

### Answers

Yes, the** person needs to stop for petrol.** The **car can travel distance **25 miles per litre, so it has 4 litres left in the tank. 90 miles divided by 25 miles per litre is 3.6, so the person needs approximately 4 litres of petrol in order to complete the journey.

1. Calculate how many litres the car can hold - 12 litres

2. Calculate how many miles the car can travel with **one litre of petrol - **25 miles

3. Calculate how many litres of petrol left in the tank - 1/4 of 12 litres = 3 litres

4. Calculate how many miles the car can travel with 3 litres of petrol - 3 x 25 miles = 75 miles

5. Calculate how many miles the** person is away from Islamabad **- 90 miles distance

6. Calculate how many **litres of petrol** the person needs to complete the journey - **90 miles divided by 25 miles** per litre = 3.6 litres

7. The person needs to stop for petrol – Yes

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Brad chose a representative sample of 5 random numbers from 1 to 31 and recorded the high temperature in his town for that day of the month in may and october.

select the three true statements based on the sample.

### Answers

The first, third, and fifth statements are accurate since the averages for May and October are 79 and 62 degrees, respectively, with a **mean **difference of 17 degrees.

What is mean?

The sum of all values divided by the **total number** of values determines the mean (also known as the arithmetic mean, as opposed to the geometric mean) of a dataset. The "mean" is frequently used to refer to this central tendency **measurement**. This is calculated by just dividing the total number of values in the dataset by the sum of all values in the dataset. Calculations may be made using either raw data or data that has been compiled into frequency tables. Typical - Usually, when someone uses the word "average," they mean average. The average may be calculated by adding together all the data's numbers and dividing by the total amount of numbers. For instance, put the 12 numbers together, then divide by 12.

The following were the average high temperatures for the chosen May days:

= (total of May's temperatures) / total observations

[tex]= 395/5 = 79 F[/tex]

The following were the mean high temperatures for the chosen days in October:

= (total of October's temperatures)/the number of observations

[tex]310/5= 62 F[/tex]

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**Answer: Look at the attachment (Option A, Option C, and Option E)**

**Step-by-step explanation: **

**There u go have a amazing day. **

The table shows the total numbers y of people who reported an earthquake x minutes after it ended. a. Use a graphing calculator to find an equation of the line of best fit. Then plot the data and graph the equation in the same viewing window. b. Identify and interpret the correlation coefficient. c. Interpret the slope and y-intercept of the line of best fit.

### Answers

The required **equation** is y=90x-80 and slope is 90 and y intercept is -80.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the **steepness **of line in the coordinate plane.

The** slope intercept form** of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the table we can observe that y represents the number of **people **abs x represents the number of **minutes**.

Let us find the equation by taking two points

(1,10) and (2, 100)

m=100-10/2-1=90

Now let us find the **y intercept**

10=90(1)+b

10=90+b

-80=b

The equation is y=90x-80

The **slope **is 90 and y intercept is -80.

Hence, equation is y=90x-80 and slope is 90 and **y intercept **is -80.

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The number of bacteria in a culture is given by the function

0.3t

n(t) = 920e

where t is measured in hours.

(a) what is the relative rate of growth of this bacterium population?

your answer is

percent

(b) what is the initial population of the culture (at t=0)?

your answer is

(c) how many bacteria will the culture contain at time t=5?

your answer is

### Answers

Therefore , the solution to the given problem of **function **comes out to be a) 45 %. , b) 950. and c) 9013 bacteria.

Define Function.

A function is made up of three parts: a set of inputs, a set of outputs, and a rule that links the** components** of the input set to the components of the output **set **so that each input is paired with exactly one output.

Here,

A exponential function is modeled by:

n(t) = n(0)[tex]e^{kt}[/tex]

In which:

The initial value is n(0).

The constant growth rate is k.

The model in this issue is:

n(t) = 950[tex]e^{0.45t}[/tex]

Therefore, k = 0.45, n(0) = 950, and:

A) 45 %

B) 950.

C)

Assuming t = 5, we get that:

n(5) = 950[tex]e^{0.45*5}[/tex] = 9013

So 9013 bacteria.

Therefore , the solution to the given problem of function comes out to be

a) 45 percent. , b) 950. and c) 9013 bacteria.

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Translate to a system of equations: the sum of two numbers is fifteen. One number is three less than the other. Determine the system of equations. Call the first number m and the second number n.

### Answers

The system of **equation **is m = 15 - n and the numbers m and n are 9 and 6 respectively.

What are **equations**?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the value of the **variable **x is 7.

So, according to the given statements the equations will be:

1st number = m

2nd number = n

m - 3 = n

Now,

m + n = 15 ..... (1)

m - 3 = n ...... (2)

Obtain from equation (1):

m + n = 15

m = 15 - n ...... (3)

Fill in the equation with the value of m from equations (3) and (2):

m - 3 = n

Now, calculate:

15 - n - 3 = n

15 - 3 = n + n

12 = 2n

n = 12/2

∴ n = 6

Enter the value of n into equation (3) for m:

m = 15 - n

m = 15 - 6

m = 9

∴ m = 9 and n = 6

Therefore, the system of equation is m = 15 - n, and the numbers m and n are 9 and 6 respectively.

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using a green number cube and blur number cube find the folloeing probability. P(blue less than 7 and green less than 3)

### Answers

The probability that a blue number cube will show a number less than 7 is 6/6, or 1. The probability that a green number cube will show a number less than 3 is 2/6, or 1/3. To find the probability that both events will occur, we multiply the probabilities together:

P(blue less than 7 and green less than 3) = 1 * (1/3) = 1/3

Therefore, the probability that a blue number cube will show a number less than 7 and a green number cube will show a number less than 3 is 1/3.

A researcher counted the number of saturday calls to emergency dispatch for a year. the data set is normally distributed with a mean of 64 and a standard deviation of 6.

what percentage of saturdays had at least 72 calls to emergency dispatch?

91%

9%

### Answers

Therefore , the solution to the given problem of **mean** comes out to be the of saturdays had at least 72 calls to emergency dispatch is 9%.

Define mean.

The "mean" is the "average" to finding by adding together all the numbers and dividing by the total. The value "in the middle" of the range of numbers is the **median**. Before you can discover the median, you may need to modify your list since your numbers must be placed in number order from largest to smallest. The value that happens most frequently is considered the "**mode**." There really is no mode again for list if there are no repeated numbers.

Here,

A bell-shaped curve with a symmetrical shape around the distribution's mean characterizes the normal distribution.

Standard normal distribution (SND) is a type of normal distribution with mean 0, and standard deviation 1.

The normal random variable can be converted into standard normal score using the method z = I".

An interval's area under the curve is equal to the percentage of data that falls within it.

Then it is asked to determine the ratio that is greater than 72, which will equal the region to the right of a = 72. First, change this x value into a z-score by replacing 64 and σ = 6 in the

=>z = u - x/ σ

z=72-64/6 ≈1.33

Therefore , the solution to the given problem of mean comes out to be the of saturdays had at least 72 calls to emergency dispatch is 9%.

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Ruby has to climb 36 steps to reach her apartment, on the third floor of the residential complex. She climbs 18 steps and reaches the second floor. How many more steps should she climb to reach her apartment? Provide an equation and explanation of how you arrived at your answer

### Answers

She should **climb** 18 more **steps** to **reach** her **apartment**. The result is obtained by subtracting 18 from the total steps to reach her apartment.

How to count the steps to reach a place?

When we walk from one place to another, we can count our **steps** as the **distance**. If one place to another is on the difference floor, one step up the stairs would be count as one step.

The distance from** first floor** to Ruby's apartment on the **third floor** is 36 steps. The distance from the first floor to the **second floor** is 18 steps. Find how many more steps to reach her apartment!

Let's say

x = distance from second floor to third floor.

The **sum** of steps from the first to the second floor plus steps from the second to the third floor is the total steps to reach her apartment.

18 + x = 36

x = 36 - 18

x = 18 steps

Hence, **Ruby** has to **climb** 18 more steps to **reach** her **apartment** on the **third floor**.

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find the value of each

### Answers

sin45=perpendicular/Hypotenuse 5/y = 1/√2

**y=5√2**

cos45= Base/Hypotenuse=x/5/√2 = 1/√2

=√2x/5 = 1/√2

=**x=5/2**

It seems these days that college graduates who are employed full-time work more than 40 hour weeks. Data are available that can help us decide if this is true. A survey was recently sent to a group of adults selected at random. There were 14 respondents who were college graduates employed full-time. The mean number of hours worked per week by these 14 respondents was 43 hours, with a standard deviation of 10 hours. Assume that the population of hours worked per week by college graduates employed full-time is normally distributed with mean Î¼. Can we conclude that Î¼ is greater than 40 hours? Use the 0.05 level of significance.

### Answers

Yes, we conclude that Î¼ is **greater **than 40 hours after performing t-test.

Define t-test.

A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in **hypothesis **testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

When -test be used?

When you want to compare the mean from your sample to another value, you should apply a t test after taking a small, random sample from some statistical "population." The comparison value could be the mean of a second sample or a set value, like 10, for example.

H0: μ ≤ 40

H1: μ > 40

t- test statistic

(47-40) / 10/sqrt(9) = 2.1000

t(8,0.9) = 1.3968

since the test statistic is larger than the critical value.

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isabella's house has bedrooms. each bedroom is feet long, feet wide, and feet high. isabella must paint the walls of all the bedrooms. doorways and windows, which will not be painted, occupy square feet in each bedroom. how many square feet of walls must be painted?

### Answers

**Isabella **must paint **1410 **square feet of walls in all the bedrooms.

To calculate the** total square feet** of walls that must be painted in all the bedrooms, we will first calculate the total area of each bedroom.

The area of each bedroom can be calculated using the formula for the area of a **rectangular** room:

Area = Length x Width

Therefore, the area of each bedroom is:

**Area **= 20 ft × 12 ft = 240 ft2

Now we will calculate the total square feet of walls that must be painted by subtracting the area of the doorways and windows from the total area of each bedroom.

The area of the doorways and windows is 5 ft2 in each bedroom.

Therefore, the total square feet of walls that must be painted in each bedroom is:

Area of walls = 240 ft2 - 5 ft2 = 235 ft2

Since Isabella has bedrooms, the total square feet of walls that must be painted in all the bedrooms is:

Total Area of Walls = 235 ft2 x = 1410 ft2

**Therefore**, Isabella must paint 1410 square feet of walls in all the bedrooms.

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A particular baseball diamond is actually a square with 71-foot sides. what is the distance from home plate to second base? express the answer in simplified

radical form. then find a decimal approximation

### Answers

When a baseball diamond is a **square** with 71-foot sides, the **distance** from home plate to second base is 71√2 feet.

What is Pythagoras theorem?

The **Pythagorean** theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the **hypotenuse** square is equal to the sum of the areas of the squares on the other two sides.

Here,

We have been that a particular baseball diamond is actually a square with 71-foot sides.

We can see that distance from home plate to second base would be equal to hypotenuse with each leg of 71-ft.

We will use Pythagoras theorem to find the distance x as:

x²=71²+71²

x=71√2 ft

The **distance** from home plate to second base when particular baseball diamond is actually a **square **with 71-foot sides is 71√2 feet.

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Two functions are defined by these equations: f(x) = 5. 1 + 0. 8x g(x) = 3. 4 + 1. 2x Which function has a greater value when x is 3. 9? How much greater?

### Answers

f(x) is 0.14** units** more than g(x).

In mathematics, a function from a set X to a set Y assigns to each **element** of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the **codomain** of the function. A function has special rules:

1) It must work for every possible input value

2) And it has only one relationship for each input value

The set of values of x is called the** domain **of the function, and the set of values of f(x) generated by the values in the domain is called the **range** of the function.

The two **functions** are defined by these equations:

f(x) = 5.1 + 0.8x

g(x) = 3.4 + 1.2x

Put x = 3.9 in f(x).

f(x) = 5.1 + 0.8(3.9) = 8.22

Put x = 3.9 in g(x).

g(x) = 3.4 + 1.2(3.9) = 8.08

Here, f(x) is greater than g(x).

Now,

f(x)-g(x) = 8.22 - 8.08 = 0.14

Thus, f(x) is 0.14** units **more than g(x).

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Two trains are driving toward each other. The first

train leaves Town A at 5 am, traveling at 60 miles per

hour. The second train leaves Town B at 7am

traveling at 70 miles per hour. The distance between

Town A and Town B is 455 miles,

What is the EXACT time that the collision will occur?

### Answers

**Answer:**

To find the exact time that the collision will occur, we need to use the formula:

time = distance / (rate of first train + rate of second train)

Plugging in the values from the problem, we get:

time = 455 miles / (60 miles/hour + 70 miles/hour) = 455 miles / 130 miles/hour = 3.5 hours

Since the first train leaves Town A at 5 am and the collision occurs 3.5 hours later, the exact time of the collision is 5 am + 3.5 hours = 8:30 am.

Final answer:

To find the exact time of the collision between the two trains, calculate the time it takes for the trains to meet by using the distance between the towns and the sum of their speeds. Then, convert the time into hours and minutes to determine the exact time of the **collision**.

Explanation:

To find the exact time that the collision will occur, we need to determine how long it will take for the two **trains** to meet. The first train leaves at 5 am and the second train leaves at 7 am, so the second train has a head start of 2 hours. Let's calculate the time it takes for the two trains to meet.

The first train is traveling at a speed of 60 miles per hour, and the second train is traveling at a **speed **of 70 miles per hour. When two objects are traveling towards each other, their relative speed is the sum of their individual speeds. So, the relative speed of the two trains is 60 mph + 70 mph = 130 mph.

Now, we can use the formula distance = speed x time to find the time it takes for the two trains to meet. The distance between Town A and Town B is 455 miles. Let's substitute the values into the formula: 455 miles = 130 mph x time. Solving for **time**, we get: time = 455 miles / 130 mph.

Using a calculator, we find that the time it takes for the two trains to meet is approximately 3.5 hours. Therefore, the collision will occur at 5 am + 3.5 hours = 8:30 am.

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