Mathematics High School

## Answers

**Answer 1**

Using **proportions**, he should put **3 yellow blocks** on each tower.

What is a proportion?

A proportion is a **fraction **of a total amount, and the measures are related using a **rule of three**. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The **proportion **between the number of **yellow **blocks and the number of **red **blocks is given by:

21/7 = 3.

Since each tower will have **one red block**, considering the proportion, he should put **3 yellow blocks** on each tower.

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## Related Questions

What is the slope of the line shown below? A.–4 B. 1/4 C.4 D.– 1/4

### Answers

you're given two points here, which is just enough info to figure out the slope.

the equation for slope is as follows.

the two points you have can be notated as (x1, y1) and (x2, y2).

(y2-y1) divided by (x2-x1) will give you the slope.

let's use that and plug the points in.

(8-(-4))/(-1-2)

= 12/-3 = **-4**

so your answer will be **A!**

hope i helped! good luck.

The distance traveled by Earth in one orbit around

the Sun is about 580,000,000 miles. Earth makes

one complete orbit around the Sun in one year. Of

the following, which is closest to the average speed of

Earth, in miles per hour, as it orbits the Sun?

A) 66,000

B) 93,000

C) 210,000

D) 420,000

### Answers

The** average speed** of Earth as it orbits the Sun = 66000 miles/hour (option A).

What is average speed?

The** average speed** is the total distance traveled by the object in a particular time interval.

It is given by the formula:

**Average speed **= [tex]\frac{Total Distance Covered}{Total Time Taken To Cover The Distance}[/tex]

Now, given:

Distance travelled by Earth in 1 orbit = [tex]58 \times 10^{7} miles[/tex]Time taken by Earth to complete 1 orbit = 1 year = 365 days = 8760 hours

To find: **Average Speed** of Earth as it orbits the Sun

Now, we know that **average speed**= [tex]\frac{Distance}{Time}[/tex]

Thus, **average speed** of Earth as it orbits the Sun = [tex]\frac{Distance Travelled By Earth In 1 Orbit}{Time Taken By Earth To Complete 1 Orbit}[/tex]

=> **Average speed **of Earth = [tex]\frac{58 \times 10^{7} miles}{8760 hours}[/tex] = 66210 miles/hour ≈ 66000 miles/hour

Hence, The **average speed** of Earth as it orbits the Sun = 66000 miles/hour (option A).

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Tory has a scarf that is 72 inches long. How long is the scarf in yards?

### Answers

**Answer:**

6 yd

**Step-by-step explanation:**

72 ÷ 12 = 6

A forest fire covers twice the amount of forest as it did 3 days ago. 3 days ago, this fire covered 300 square miles and it continues to grow at the same rate. how many square miles will it cover 9 days from now?

### Answers

It will cover 900 Miles

Which property

x²+2x=2x+x²

closure property

commutative property

### Answers

The equation x²+2x=2x+x² is a **commutative property,** which means the sum of x²+2x will exactly equal x²+2x.

The **commutative property** says that changing the order of two numbers (4 + 2; 2 + 4) does not change the sum of the numbers (6 = 6).

The **closure property **states that the sum of two whole numbers (say a, b) will always be a whole number (a+b).

For example, putting the value of x = 1, in x²+2x=2x+x²

1²+2(1)=2(1)+ 1²

3 = 3

Therefore, the equation x²+2x=2x+x² shows **a commutative property, **that is by changing the order of numbers, their sum remains the same.

The **commutative property** says that changing the order of two numbers (4 + 2; 2 + 4) does not change the sum of the numbers (6 = 6).

The **closure property **states that the sum of two whole numbers (say a, b) will always be a whole number (a+b).

Therefore, the equation x²+2x=2x+x² shows **a commutative property, **that is by changing the order of numbers, their sum remains the same.

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What is the end behavior of this function?

For algebra 2

### Answers

As x approaches both infinity and negative infinity, y approaches 4.

A hexagonal pyramid is located ontop of a hexagonal prism. how many edges are there? a. 13 b. 6 c. 15 d. 24

### Answers

Number of **edges **of the final figure = 24.

**What is an edge?**

**Edge** refers to the lines, drawing and connecting which, we may obtain various shapes and figures.

Given: A hexagonal pyramid which pyramid on the top of a hexagonal prism (refer to the image attached).

Number of **edges** = 24

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10) Alicia, an employee of Dunkin' Donuts, receives 23+ days per year of vacation time. So far

this year she has taken 3 days in January, 5 days in May, 6 days in July, and 4+ days in

September. How many more days of vacation does Alicia have left?

Alicia has

more days of vacation left.

### Answers

**Answer:**

Alicia has 5 days of vacation left

**Step-by-step explanation:**

add the number of days she has used and subtract that from her 23 days of vacation time

The following expression gives an approximate value of the total average credit card debt in a U.S. household

(in dollars) t years after 1995.

405t + 5850

Use this expression to predict what the total average credit card debt was or will be in the year 2011.

Answer: In the year 2011, the total average credit card debt for a U.S. household will be (or was)

### Answers

The **calculation** below shows that the total average credit card debt was or will be **12,330** in the year 2011.

How can we calculate the total average?

From the question, we have the following:

t = 2011 - 1995

t = 16

Therefore, the total **average** credit card debt in 2011 can be calculated as follows:

Total average credit card debt = 405t + 5850 ..................... (1)

**Substituting** t = 16 into equation (1), we have:

Total average credit card debt = (405 * 16) + 5850

Total average credit card debt = 6480 + 5850

Total average credit card debt = 12,330

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The author initially responded to Herd’s request "with

condescension" (lines 13-14) because the author

(A) knew that Herd had not been to graduate school

(B) believed that historians should avoid controversial

projects

(C) had too many other projects requiring her

attention

(D) rejected Herd’s contention that such a history

would address the Black struggle for social

justice

(E) viewed Herd’s request as irrelevant and

presumptuous

### Answers

The author initially responded to Herd’s request "with condescension" (lines 13-14) because the author viewed Herd’s request as irrelevant and **presumptuous**.

What is presumptuous?

Going past what is legitimate It would be **pretentious** to pose individual **inquiries**. It's not ideal to be** pompous**. Truth be told, when somebody considers you that, they are saying that you're carrying on of line such that is **substantially** more inconsiderate than **abnormal**. They could likewise be saying that you're careless, that you take such a large number of **freedoms**, or that you're acting in a strong and outlandish manner. **Pretentious** sins are purposeful. They are committed with the full information that they are sins and in full light of what God has said, **Arrogant** sins are planned.

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Question 4(Multiple Choice Worth 10 points) (04.05 LC) Based on your research, how many individual battles occurred at the Battle of Philippi

### Answers

The only 2 individual battles were between, Mark Antony and Octavian, and Brutus and Cassius at the **Battle of Philippi.**

With up to 200,000 soldiers, the **Battle of Philippi **was one of the largest Roman civil wars, consisting of two skirmishes on the plains west of the ancient city of Philippi. The first he occurred in the first week of October. Brutus confronted Octavian while Antony's army fought Cassius' army.

**Battle of Philippi** (October 3 and 23, 42 BC). In 300 BC, Philippi witnessed the final extermination of those who supported the old Roman republic, the culmination of the wars that followed the assassination of Julius Caesar in 44 BC.

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Evaluate a + 4 when a=7

### Answers

The answer is 11

Because:

(7) + 4 = 11

Select the statement that is known to be true.

a) the brute force algorithm to factor numbers is not efficient, but there is a different algorithm that can efficiently factor numbers.

b) most of the integers in the range from 2 to 1,000,000 are prime

c) there is an efficient algorithm to test whether an integer is prime

d) the brute force factoring algorithm is considered to be an efficient algorithm for factoring large numbers.

### Answers

**Answer:**

c) there is an efficient algorithm to test whether an integer is prime

**Step-by-step explanation:**

The basis of modern cryptography is the fact that **factoring** large numbers is **computationally difficult**. No algorithm is efficient for that purpose.

Choicesa)

False - there is no known efficient algorithm for factoring large numbers

b)

False - there are 78,498 prime numbers less than 1,000,000. That is about 8% of them--far from being "most of the integers."

c)

**True** - a variety of algorithms exist for testing primality. In 2002, a test was published that runs in time roughly proportional to the 7.5 power of the logarithm of the number being tested.

d)

False - there is no known efficient algorithm for factoring large numbers

hank is thinking of a number. if he multiplies his number by seven and then adds 10, he gets 59. what is hank's number?

### Answers

**Answer:**

x = 7

**Step-by-step explanation:**

hank is thinking of a number. if he multiplies his number by seven and then adds 10, he gets 59. what is hank's number?

'hank is thinking of a number' means x

x. if he multiplies his number by seven and then adds 10, he gets 59. what is hank's number?

'if he multiplies his number by seven' means 7x

'and then adds 10' means 7x + 10

'he gets 59' means 7x + 10 = 59

'what is hank's number?' means 'what is x?'

7x + 10 = 59

7x = 49

x = 7

The following summarizes the number of fiction books read last summer by a sample of 29 students at a certain college.

### Answers

Using the given information, the **mean number **of books read is 3.41

Calculating mean

From the question, we are to calculate the** mean number **of **books **read

From the given **information**, we have the table

**Number of students Number of books **

2 1

11 3

16 4

Then,

Mean number of books read = [(2×1) +(11×3) + (16×4)]/(2+ 11+ 16)

Mean number of books read = (2 + 33+ 64)/29

Mean number of books read = 99/29

Mean number of books read = 3.41

Hence, the **mean number **of books read is 3.41

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Please help me with this question ( 20 points )

### Answers

**Answer:**

4 / 12

? = 12

**Step-by-step explanation:**

(16 / 48 ) / 4 = 4 / 12 = 1 / 3

**Answer:**

the missing number is 12

**Step-by-step explanation:**

16/4 =4

48/4=12

=

4

?

the unknown number is 12

A frog moves in a sequence of unit steps. Each step is N, S, E or W with equal probability. It starts at the origin. Find the probability that it reaches (2, 2) in less than 7 steps.

### Answers

The answer is **067.**

It takes an even number of steps for the object to reach (2,2), so the number of steps the object may have taken is either 4 or 6 .

If the object took 4 steps, then it must have gone two steps [tex]$\mathrm{N}$[/tex] and two steps E, in some permutation. There are [tex]$\frac{4 !}{2 ! 2 !}=6$[/tex] ways for these four steps of occuring, and the **probability **is [tex]$\frac{6}{4^{4}}$[/tex].

If the object took 6 steps, then it must have gone two steps N and two steps E, and an additional pair of moves that would cancel out, either N / S or W/E. The sequences N, N, N, E, E, S can be permuted in [tex]$\frac{6 !}{3 ! 2 ! 1 !}=60$[/tex] ways. However, if the first four steps of the sequence are N, N, E, E in some permutation, it would have already reached the point (2,2) in four moves. There are [tex]$\frac{4 !}{2 ! 2 !}$[/tex] ways to order those four steps and [tex]$2 !$[/tex] ways to determine the order of the remaining two steps, for a total of 12 sequences that we have to exclude. This gives [tex]$60-12=48$[/tex] sequences of steps. There are the same number of sequences for the steps N, N, E, E, E, W, so the **probability** here is [tex]$\frac{2 \times 48}{4^{6}}$[/tex].

The total **probability** is [tex]$\frac{6}{4^{4}}+\frac{96}{4^{6}}=\frac{3}{64}$[/tex], and [tex]$m+n=067$[/tex].

What is **probability?**

**Probability **is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. **Probability **has been introduced in mathematics to predict the likelihood of occurrences occurring.** Probability** is defined as the degree to which something is likely to occur. This is the fundamental **probability** theory, which is also utilized in **probability** distribution, in which you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

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Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. select all that apply. (4.5, -1.5) (2.6, 0.4) (-2.6, 0.4) (-3.6, 0.6) (3.6, 0.6)

### Answers

Use technology to approximate the solution(s) to the system of **equations **to the nearest tenth of a unit.

Select all that apply.

f(x) = logx and

g(x) = {x-3}

(3.6,0.6)

(-2.6,0.4)

(-3.6,0.6)

(2.6,0.4)

(4.5,-1.5)

Option A : (3.6, 0.6) is the solution to the system of equations.

Option D: ( 2.6, 0.4) is the solution to the system of equations.

The two **equations **are and f(x) = logx and 9 (x) = {x-3}

To determine the solution of the system of equations using technology, let us plot the equations in the graphing calculator.

The solution of the system of equations is the intersection of the two lines.

Thus, from the graph, we can see that the two lines f(x) and g(x) intersect at the points and (2.587, 0.413) and (3.6, 0.6)

Thus, the solution to the system of **equations **is (2.587, 0.413) and (3.6, 0.6).

Hence, Option A and Option D are the correct answers.

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The sequence negative one fourth comma two fifths comma negative three sixths comma four sevenths and so on is given. Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points) Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points) Part C: Is the sign of f (59) positive or negative

### Answers

The next four terms in the** sequence** = [tex]\frac{-5}{8} , \frac{6}{9} ,\frac{-7}{10}[/tex][tex], \frac{8}{11}[/tex]The** explicit equation** for f (n) to represent the **sequence**, [tex]f(n)=(-1)^{n} \frac{n}{n+3}[/tex]The sign of f(59) is negative

Given,

The** sequence**: [tex]\frac{-1}{4} ,\frac{2}{5} ,\frac{-3}{6} ,\frac{4}{7} ...[/tex]

Part A: We have to find the next four terms in the **sequence**.

We can use the equation [tex]f(n)=(-1)^{n} \frac{n}{n+3}[/tex]

Where, n is the number of term.

For first term [tex]f(1)=(-1)^{1} \frac{1}{1+3} =(-1)\frac{1}{4} =\frac{-1}{4}[/tex]

Now, we can determine the next four terms in the **sequence**.

[tex]f(5)=(-1)^{5} \frac{5}{5+3} =(-1)\frac{5}{8} =\frac{-5}{8}[/tex]

[tex]f(6)=(-1)^{6} \frac{6}{6+3} =(1)\frac{6}{9} =\frac{6}{9}[/tex]

[tex]f(7)=(-1)^{7} \frac{7}{7+3} =(-1)\frac{7}{10} =\frac{-7}{10}[/tex]

[tex]f(8)=(-1)^{8} \frac{8}{8+3} =(1)\frac{8}{11} =\frac{8}{11}[/tex]

Part B: The** explicit equation **for f (n) to represent the **sequence**.

[tex]f(n)=(-1)^{n} \frac{n}{n+3}[/tex]

Where n is the number of term

Part C: The sign of f(59)

[tex]f(59)=(-1)^{59} \frac{59}{59+3} =(-1)\frac{59}{62} =\frac{-59}{62}[/tex]

From the above calculation it is clear that the sign of f(59) is negative.

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Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 units. The base of cylinder B

has an area of 9л units.

The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

### Answers

**Answer:**

[tex]\frac{3}{2}[/tex] ( the third choice)

**Step-by-step explanation:**

Let [tex]r_a[/tex] be the radius of cylinder A and let [tex]r_b[/tex] be the radius of cylinder B. We assume the heights of both cylinders are the same

Base circumference of cylinder A = [tex]2\pi r_a = 4\pi == > r_a = 2[/tex]

Base area of cylinder B = [tex]\pi (r_b)^2 = 9\pi == > r_b = \sqrt{9} = 3[/tex]

In order to have [tex]r_a[/tex] (2) have the same value as [tex]r_b[/tex] (3) we must multiply by a factor of [tex]\frac{3}{2}[/tex]

Calculate the surface area of this truncated square pyramid.

### Answers

**Answer:**

I think it's 81

**Step-by-step explanation:**

since the bottom is a square, I do think you multiply Side × side that is 9 × 9 which gives us 81cm²

Pls, help...

Find the equation of the line.

Use exact numbers

y=__x+__

### Answers

[tex]m = \frac{5 - 4}{0 - 3} = \frac{ - 1}{3} [/tex]

[tex]b = 5 \: \: \: \: (y \: intercept)[/tex]

[tex]y = \frac{ - 1}{3} x + 5[/tex]

( 3b - 4b ) ²

with explanation

### Answers

Answer: b^2

explanation:

**Answer:**

b^2

**Step-by-step explanation:**

(3b-4b)^2

=(-b)^2

we know that,

- * - =+

minus(-) * minus(-) = +

By using formula to the f

given equation is;

( 3b - 4b ) ²

We know that,

(a-b)^2 =a^2-2ab+b^2

Soo,

=9b^2 - 2*3b*4b +16b^2

=9b^2-2*3*4b^2+16b^2

=9b^2+16b^2-24b^2

=25b^2-24b^2

=b^2

Darryl wants to add enough water to 8 gallons of a 10% bleach solution to make a 5% bleach solution. which equation can he use to find x, the number of gallons of water he should add? original (gallons) added (gallons) new (gallons) amount of bleach 0.8 0 0.8 amount of solution 8 x 8 x startfraction 0.8 over 8 x endfraction times startfraction 5 over 100 endfraction = 1 startfraction 0.8 over 8 x endfraction times = startfraction 5 over 100 endfraction startfraction 0.8 over 8 x endfraction = startfraction 100 over 5 endfraction startfraction 0.8 over 8 x endfraction divided by startfraction 5 over 100 endfraction = 1

### Answers

0.80 = (x + 8)(0.05) is the **equation **used to find x.

Given,

Darryl has a solution of bleach with the **concentration **of 10%.

10% bleach solution means in 100 ml solution amount of bleach is 10 gm

Here,

Darryl wants to change the **concentration **of this solution to 5%, means he wants to add water so that amount of liquid will change but amount of bleach in grams will remain the same.

Amount of bleach in 8 gallons of 10% solution of bleach will be = (Volume)×(**concentration)** = 8(.10) gm

Let Darryl adds x gallons of water in 10% solution of bleach to make it 5% solution of bleach.

Amount of bleach in 5% solution of bleach = (x + 8)(0.05) gm

Now in both the **concentrations** of bleach solution amount of bleach will remain same.

So, 0.8 = (x + 8)(0.05) will be the equation from which he can find the value of x.

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Justify each step. x/3-7=11

### Answers

**Answer:** x = 54

**Step-by-step explanation:**

We will **solve **for x by **isolating **the x **variable**.

Given:

x/3-7=11

**Add **7 to both sides of the **equation**:

x/3 = 18

**Multiply **both sides of the **equation** by 3:

x = 54

**Answer:**

x=-44

**Step-by-step explanation:**

calculate the difference of 3-7

then multiply both sides by -4/1

11x-4=-44

Find the mean and standard deviation for the set of data.

(16,22,8,5,20, 18, 14, 17, 24)

A mean: 16; standard deviation: 5.87

B. mean: 17; standard deviation: 5.95

C. mean: 16; standard deviation: 5.95

D. mean: 17; standard deviation: 5.87

### Answers

The **mean **and **standard deviation **for the set of **data **will be 16 and 5.87. Then the **correct **option is **A**.

What is a standard deviation?

It is the **measure **of the dispersion of statistical **data**. Dispersion is the extent to which the value is in a **variation**.

The **set **of **data **is given below.

16, 22, 8, 5, 20, 18, 14, 17, 24

The **mean **of the **data **set will be

μ = (16 + 22 + 8 + 5 + 20 + 18 + 14 + 17 + 24) / 9

μ = 144 / 9

μ = 16

Then the **standard **deviation of the **data **set will be

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}} \\\sigma = \sqrt{\dfrac{(16 - 16)^2 +(22 - 16)^2 + (8-16)^2 + ......+(24-16)^2 }{9}} \\\sigma = \sqrt{\dfrac{310}{9}}\\[/tex]

Simplify the expression further, then we have

σ = √34.44

σ = 5.87

The **mean **and **standard deviation **for the set of **data **will be 16 and 5.87.

Then the **correct **option is **A**.

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A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The

100

function (x)--

-5 represents the remaining time in minutes needed to fill the tank. How is the graph of the parent

X

function f(x)-

X

100

transformed to create the graph of the function f(x)=-

X

-57

### Answers

- Stretching the parent function f(x) = 1/x vertically .

- Shifting the parent function f(x) = 1/x 5 units right.

The complete exercise is: " A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function **f(x) = 100/(x-5)** represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function f(x) = 1/x transformed to create the graph of f(x) = 100/(x-5) ?"

Below are some transformations for a function :

1. If f(x) +k, the function is shifted "k" units up.

2. If f(x) -k, the function is shifted "k" units down.

3. If f(x) -k , the function is shifted "k" units right.

4. If f(x) +k , the function is shifted "k" units left.

5. If bf(x) and b>1 the function is stretched vertically by a factor of "b".

6. If bf(x) and 0<b<1 the function is compressed vertically by a factor of "b".

The exercise gives the following parent function:

f(x) = 1/x

And you know that the transformed function which represents the remaining time in minutes needed to fill the tank, is:

f(x) = 100/(x-5)

Therefore, based on the transformations explained before you can identify that the graph of the transformed function is created by:

- Stretching the parent function f(x) = 1/x vertically.

- Shifting the parent function f(x) = 1/x 5 units right.

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There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?.

### Answers

The correct option is** C**

Containing both **apples** and **oranges**.

What exactly are permutations and combinations?

Two techniques for dividing a **set** of objects into smaller groups are **combination** and **permutation**. Combining the components of the subset allows for any **configuration**. A permutation with the components of the subset listed in a **specific order**.

Brief explanation of the stated fact:

The briefing states that the "**apples and oranges**" box needs to be opened. The fruit that is within the box is the only type of fruit there is, so to speak. Imagine you **discovered** one apple in the container that was labeled with the words "apples" and "oranges" as well. You conclude that since all the boxes have allegedly been** improperly labeled**, the box **labelled** "apples" must logically contain only apples, and the box marked "oranges" cannot contain only oranges. In contrast to the box marked "apples," which may only include apples, the box marked "oranges" must contain both apples and oranges.

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I understand that the question you are looking for is:

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, you can immediately label all of the boxes correctly. Which box did you open?

A. Containing apple

B. Containing oranges

C. Containing both apples and oranges

D. Cannot be determined

The computed chi-square value is positive because the difference between the observed and expected frequencies is Group of answer choices A. squared. B. linear. C. uniform. D. always positive.

### Answers

The computed chi-square value is **positive **because the difference between the observed and expected frequencies is squared.

**Positive **people focus on the good things in their lives, find joy in the simple things, and although they don't have direct control over many things, what they focus on, what they do, and what they do in life. Adopt a general attitude that you can control what you tend to do. Optimistic. When we are positive, we engage in positive thoughts, have positive emotions, and engage in positive actions such as **kindness **and generosity. It means being optimistic about situations, interactions, and yourself. People with a positive attitude stay hopeful and do their best in difficult situations.

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Alicia rides her bike 4 miles due north and 3 miles due west to a playground. what is the shortest distance to alicia's home from the playground? 5 mi 5 mi 7 mi 7 mi 12 mi 12 mi 25 mi

### Answers

**Answer:**

5 mi

**Step-by-step explanation:**

See attached figure for graphical view

Since Alicia travels 4 mi north and then 3 miles west, the corners of her home and playground can be viewed as points on a right triangle.

The shortest distance (as the crow flies) is the hypotenuse of the right triangle

This can be calculated using the Pythagorean formula

[tex]d = \sqrt{4^2 + 3^2} = \sqrt{16+9} = \sqrt{25} = 5 \text{ mi}[/tex]