Mathematics High School

## Answers

**Answer 1**

The next **consecutive **even **integer **represented by the statement is a + b + 3.5

How to determine the next consecutive integers?

The **statement **in the question is represented as

a+b+1.5 is an even integer

As a general rule of numbering;

Consecutive integers are integers that have a **difference **of 1These numbers can be negative or **positive**

In this case, the integers have a **difference **of 2

This is so because, they are **even integers **and even integers have a difference of 2

Solving further, we can represent the **integer** with x

So, we have

Current integer = a+b+1.5

Rewrite properly

This gives

Current integer = a + b + 1.5

Recall that:

even integers have a difference of 2

This means that

Next consecutive integer = Current integer + 2

Substitute the known values in the above equation, so, we have the following representation

Next consecutive integer = a + b + 1.5 + 2

Evaluate the **sum **in the above equation

Next consecutive integer = a + b + 3.5

Hence, the **next **integer is a + b + 3.5

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## Related Questions

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books. Determine the number of small boxes sent and the number of large boxes sent

### Answers

The **number **of **small boxes** sent is** 6** and the number of **large boxes** sent is **3**.

Given:

Each small box can hold 20** books** and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books.

Let x be the number of small boxes and y be the number of large boxes.

20x + 35y = 225

x = 2y

20(2y) + 35y = 225

40y + 35y = 225

75y = 225

divide by 75 on both sides

75y/75 = 225/75

y = 225/75

y =** 3 large boxes.**

x = 2y

= 2*3

x= **6 small boxes.**

Therefore the number of small boxes sent is **6** and the number of large boxes sent is** 3**.

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Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long. How long is the remaining piece of rope?

### Answers

In a case whereby **Carmen** has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters **long **the lenght of the remaining piece of rope is 9.84 metres.

What is distance?

Distance can be described as the space that exist between two or more point, the concept that willbe used in the question is the** concept **of **distance**.

The total distance of the rope is **18 meters long** , ** **and she cut 8.16 meters long awya which implies that the remaining lenght of the rope will be ( 18 - 8.16)= 9.84 metres

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Read the description of a proportional relationship. Ever since Brian was a small child, his favorite food has always been carrots. He likes them so much he wants to plant a garden in his backyard just to grow carrots. There is a proportional relationship between the size of Brian's garden (in square feet), x, and the number of carrots he can grow at a time, y. The equation that models this relationship is y=4x. What size garden does Brian need to grow 20 carrots at a time?

### Answers

**The size of the garden** That Brian need to grow** 20 carrots **at a time is 5 square feet

The size of the Brian's garden in square feet = x

**The number of carrots **that he can grow at a time = y

**The equation** that models the relationship is

y = 4x

The means the number of carrots that he can grow at a time is **directly proportional** to the size of the Brian's garden,

The number of carrots that he need to grow = 20 carrots

**Substitute the values** in the equation and find the value of x

20 = 4x

The size of the garden x = 20/4

= 5 square feet

Hence, the size of the garden That Brian need to grow 20 carrots at a time is 5 square feet

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the line y = mx + 7 passes through the point ( -2, 5). find m.

the line y = 2x + c passes through the point ( 1 , 4). find c

### Answers

Question 1

y = mx+7

5 = m*(-2)+7

5 = -2m+7

-2m+7 = 5

-2m = 5-7

-2m = -2

m = -2/(-2)

m = 1 is the final answer

===============================================

Question 2

y = 2x+c

4 = 2(1)+c

4 = 2+c

4-2 = c

2 = c

c = 2 is the final answer

consolidated builders has bid on two large construction projects. the company president believes that the probability of winning the first contract (event a) is 0.6, that the probability of winning the second (event b) is 0.5, and that the joint probability of winning both jobs (event {a and b}) is 0.4. what is the probability of the event {a or b} that consolidated will win at least one of the jobs?

### Answers

The **probability** of an event {a or b} is 0.7

**Probability: **It is the branch of mathematics concerning **numerical**, descriptions of how likely an** event** is to occur or how likely it is that a proposition is true. the **probability** of an event is a number between

0 and 1.

if the two events a and b are **mutually exclusive** then the addition rule of probability is:

P( a or b) = P(a) + P(b) - P(a∩ b)

Given that,

P(a) = 0.6 P(b) = 0.5

P(a ∩ b)= 0.4

According to **probability **methods, if two events are mutually exclusive, then the probability of either occurring is denoted as P (a ∪ b).

Now, we know that,

P( a ∪ b) = P(a) + P(b) - P( a ∩ b)

= 0.6 + 0.5 - 0.4

= 0.7

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Using technology, determine the present value given that you make quarterly payments of $1,635 at 4.2% compouded quarterly over a 3 year period. Round your answer to the nearest cent. a. $15,168.06 c. $19,180.84 b. $19,188.94 d. $18,344.05

### Answers

**Present value** of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year **period **is $18,344

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

The present value of the** quarterly **payments of $1,635 at 4.2% compounded quarterly over a 3 year period is calculated as follows:

Present Value = $1,635 × PVIFA ( 4.2%/4 ,3 Years)

**Present Value** = $1,635 × PVIFA (1.05% ,12)

= $1,635 × 11.21960

= $18,344

The present value of the **quarterly payments** of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344

Hence, **present value** of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year **period **is $18,344

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a group contains 6 men and 5 women. find the number of ways to select a committee with 3 men and 3 women.

### Answers

The **number** of ways to select a **committee** with 3 men and 3 women is **200**.

We have a group. The number of men in the group is 6. The number of women in the group is 5. We need to find out the number of ways to select a committee with 3 men and 3 women.

We will use the concepts of **permutations** and **combinations**. The number of ways to select 3 men out of 6 men is 6C3 = 20. The number of ways to select 3 women out of 5 women is 5C3 = 10. The total number of ways to form the committee that consists of 3 men and 3 women is the **product** of the above-mentioned calculation.

N = 20*10

N = 200

Hence, the number of ways to select a committee with 3 men and 3 women is 200.

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Find the value of x.

Round to the nearest tenth.

A

63

B

142°

X

61

C

X

x = [?]

Law of Cosines: c² = a² + b² - 2ab cos C

Enter

### Answers

**Answer: **117.2

**Step-by-step explanation:**

c² = a² + b² - 2ab cos C

b²= a² + c² - 2ac cosB

x² = 61² + 63² - 2(61)(63) cos142

x²= 13746.65065

x ≈ 117.2

Terry deposits a principal amount of $500 in a savings account that earns an annual rate of simple interest. If he makes no deposits or withdrawals, he will earn $40 in simple interest in 4 years. What is the annual rate of simple interest?

### Answers

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r[/tex]

Solve for x. Help me and I will do anything for you.

### Answers

x = 8

**Step-by-step** -e-x-p-l-a-n-a-t-i-o-n- *below*

The angles shown are vertical angles

Vertical angles are congruent (equal to each other)

This means that 8x + 36 = 5x + 60

Using this equation we can solve for x

8x + 36 = 5x + 60

==> subtract 36 from both sides

8x = 5x + 24

==> subtract 5x from both sides

3x = 24

==> divide both sides by 3

x = 8

**Answer:**

[tex]\huge\boxed{\sf x = 8}[/tex]

**Step-by-step explanation:**

From the diagram,

8x + 36 = 5x + 60 (**Vertically opposite angles** are equal)

Subtract 5x to both sides

8x - 5x + 36 = 60

3x + 36 = 60

**Subtract** 36 to both sides

3x = 60 - 36

3x = 24

**Divide** 3 to both sides

x = 24/3

x = 8

[tex]\rule[225]{225}{2}[/tex]

Each month working in a sales job, you earn $4300 plus $250 for every big client, c, you sign. However, there is a $400 penalty for every client, x , whose business you lose for the company. Write an expression to represent your monthly earnings

### Answers

The **expression** to represent your **monthly** **earnings** would be 4550x - 400y.

**What are the linear equations in two variables?**

A **linear** **equation** in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable **linear** **equations**.

Let the number of **clients** **signed** be 'x' and the number of **clients** whose business **lose** for the company be 'y'.

For each **client** **signed** company will earn = $4300 + $250

and for every client, y, whose business you **lose** for the company the penalty would be = $400

So we can prepare the equation for total **monthly earning** as

** Monthly earning **= (4300 + 250)x - (400)y

= 4550x - 400y.

Hence, the **expression** to represent your **monthly** **earnings** would be

4550x - 400y.

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What warning did the Monroe Doctrine give Europe?

A) not to import any more slaves to America

B) to stop building Indian reservations in America

C) not to get involved in America’s politics

D) to stop using the Atlantic Ocean for trade

### Answers

**Answer: President James Monroe's 1823 annual message to Congress contained the Monroe Doctrine, which warned European powers not to interfere in the affairs of the Western Hemisphere. Understandably, the United States has always taken a particular interest in its closest neighbors – the nations of the Western Hemisphere**

**Step-by-step explanation:**

thats time4learning

Camilla feed each of her dog 1/8 of a can of food each day. She ue a total of 1/2 of a can of food each day. How many dog doe Camilla have?

### Answers

Camilla have **total **of 7 dogs.

What is unitary method?The **unitary **technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be **computed **on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

acc to our question-

0.35 + 0.350.7*107

hence,Camilla have **total **of 7 dogs.

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David bought 5 of the ame ize pumpkin at the pumpkin patch for $33. 75. How much money would it be for David to buy 2 more of the ame pumpkin?

### Answers

David requires $13.5 to buy 2 more **pumpkins**.

Firstly calculating the cost of one pumpkin and then calculating the desired answer.

Cost of one pumpkin = total cost ÷ number of pumpkins

**Keep the values** in formula to find the cost of one pumpkin

Cost of one pumpkin = 33.75 ÷ 5

Performing **division** on Right Hand Side of the equation

Cost of one pumpkin = $6.75

Now, the amount required to buy 2 more pumpkins = 2 × 6.75

Performing **multiplication** on Right Hand Side of the equation

The **amount** required = $13.5

Thus, the amount required by **David** is $13.5.

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11.) Renee has a checking balance of -$18 in her bank account. She makes a deposit of $25, then spend

$8. What is Renee's new checking balance?

### Answers

**Answer:**

-1

**Step-by-step explanation:**

How do I solve this problem 4i)(-8i)(5 + 5i)

### Answers

**Answer:**

**Step-by-step explanation:**

(4i)·(-8i)·(5+5i) = 160+ 160i

We take into account that (i)² = -1

1)

(4i)·(-8i) = (-32)·i² = (-32)·(-1) = 32

2)

32·(5 + 5i) = 32·5 + 32·(5i) = 160 + 160 i

find the product (x+2)(3x+1)(x-3)

### Answers

(x+2)(3x+1)

x(3x+1)+2(3x+1)

3x²+x+6x+2

3x²+7x+2

(3x²+7x+2)(x-3)

x(3x²+7x+2)-3(3x²+7x+2)

3x³+7x²+2x-9x²-21x-6

3x³+7x²-9x²+2x-21x-6

3x³-2x²-19x-6

A closed top box with a square base is to have a volume of 4000 cubic inches. What are the dimensions that will minimize the amount of material used to build the box?.

### Answers

The **minimum dimensions** to minimize the amount of material is **15.87 x 15.87 x 15.87 inch**.

We need to know about the minimum function to solve this problem. The minimum function can be defined as the **minimum value of the variable**. It can be calculated by the derivative of the function. The minimum function can be written as

f'(s) = 0

where f'(s) is the derivative function

From the question above, the given parameter is

V = 4000 inch³

The cubic volume can be written as

s² x h = 4000

where s is the length of the base area and h is the height of the box.

the minimum value of the box refer to its surface area, hence

f(s) = 4sh + 2s²

f'(s) = 4h + 4s

4h + 4s = 0

h = s

It means that the length of the base area and the height must have the same dimension. The minimum volume should have a cube shape

V = s³

s³ = 4000

s = 15.87 inch

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What is the solution to the linear equation?.

### Answers

The solution of a linear equation is defined as the **points**, in which the lines represent the** intersection** of two linear equations.

What is a linear equation ?

**Linear equations **are equations of the **first order**. The linear equations are defined for lines in the coordinate system. When the equation has a hom*ogeneous variable of **degree 1** (i.e. only one variable), then it is known as a **linear equation** in **one **variable.

The** intersection **or **meeting** points of the **lines** or **planes** used to illustrate the linear equations are known as the **solutions.** The set of values for **each variable **in a **system of linear equations** is referred to as the solution set. For instance, while resolving linear equations, one can construct two linear graphs and locate the point at which they cross to see how the system of **simultaneous linear equations** is resolved.

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A tank ha 120 gallon of water and i being drained at a rate of 1/2 gallon each econd. Another tank ha 100 gallon of water and i being drained at a rate of 1/4 gallon each econd. Which equation could be ued to determine x, the number of econd, when the two tank have the ame amount of water?

### Answers

The **equation **that could be used to determine x, the number of seconds, when the two tanks have the same amount of water is 120 - 1/2(x) = 100 - 1/4(x) or x = 80.

An **algebraic expression** is the combination of numbers and variables in expressing and solving a particular mathematical question. An **equation **is the equality of expressions.

Let x be the number of seconds at the moment that the two tanks have the same amount of water.

If a tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second, the the amount of water left after time = x is "120 - 1/2(x)".

If another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second, the the amount of water left after time = x is "100 - 1/4(x)".

Equate the two expressions to determine the time, x , at which the two tanks have the same amount of water left.

120 - 1/2(x) = 100 - 1/4(x)

20 = 1/4 x

x = 80

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For a concert event there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800. The promoter must take in at least 63,000 in ticket sales?

### Answers

The system of **inequalities** is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

What is inequality?

A **relationship** between two **expressions** or values that are not equal to each other is called '**inequality**'.

Given that, for a concert event, there are 30 **reserved** seat tickets and 20 general admission tickets. There are 1,900 **reserved **seats available, and fire regulations limit the number of** paid** ticket holders to 2,800.

The system of **inequalities** can be explained as follows:

30x + 20y ≥ 63,000 → Indicating a take in of at least $63,000 in ticket sales.

x ≤ 1900 → Indicating that 500 **reserved** seats are available.

x + y ≤ 2800 → Indicating limits of the **paid** ticket holders to 2800.

x ≥ 0 → Indicating ticket x must be equal or greater than 0.

y ≥ 0 → Indicating ticket y must be equal or greater than 0.

Hence, The system of **inequalities** is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

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i don't understand, can someone explain? ¡ 20 pointsss!!!!!

### Answers

The **volume** of cone is 324cubic inch, **volume** of Cuboid **volume** is equal to 4,080 cubic meter and cylinder **Volume** is 550 cubic cm

**How would you define rounding?**

Making a number simpler while maintaining a value that is close to what it was is known as **rounding**. Although less **accurate**, the outcome is simpler to utilize. Example: Since 73 is closer to 70 than to 80, 73, when rounded to the closest ten, equals 70. However, 76 rises to 80.

Given: A **variety **of solid shapes

To determine the **volume** and surface area of each solid

Solution:

Cone radius = 9 inch.

H height equals 12 inch

15 feet is the slant height.

**Volume** equals (1/3)πr²h = 324cubic inch.

Round to nearest tenth = 320 sq inch

Surface area equals πr² + πrl = π(81 + 135) sq inch = 679 sq inch

Round to nearest tenth = 680 sq inch

Cuboid **volume** is equal to 16 x 15 x 17 = 4,080 cubic meter.

Round to nearest tenth = 4,080 cubic meter

Surface area is equal to 2 (15 * 17 + 15 * 16 + 17 * 16) = 1,474 square meter.

Round to nearest tenth = 1,470 square meter

cylinder **Volume** = πr²h = π(5)² * 7 = π 175 cubic cm = 550 cubic cm

Round to nearest tenth = 550 sq cm

cylinder Surface area is equal to 2πr(r + h ) = 10π (5+7) = 377 sq cm.

Round to nearest tenth = 380 sq cm

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suppose that the number of asbestos particles in a sample of 1 squared centimeter of dust is a poisson randomv ariable with a mean of 1000. what is the probaiblity taht 10 squared centimeters of dust contains more than 10140 particles? use normal approximation without continuity correction

### Answers

The** probability **that** **10 squared centimeters of dust contains more than 10140 particles is 0.1841

What is probability ?

Probability turned into added into arithmetic to are expecting the possibility of an** occasion occurring**. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental** principle of possibility **and is likewise utilized in possibility distributions to examine feasible** **consequences of random experiments.

Calculation

The mean asbestos particles in 1 cm2 is given as 1000, therefore in 10 cm2 of dust, the mean number of particles is given as: 1000*10 = 10,000

The number of particles here is given as:

X ~ Poisson(y = 10000)

Therefore the normal approximation here is given as:

X Nu = 10000,02 = 10000)

The probability here is computed as:

P(X > 10090)

Converting it to a standard normal variable, we get here:

10090 – 10000 P(Z > V10000

P(Z > 0.9)

Getting it from the standard normal tables, we get here:

P(Z > 0.9) = 0.1841

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Aright circular cylinder, its volume is 343 π cm3 .if its height

Equals its base radius length, then its height equals

### Answers

Alright it’s height equals 7 cm because 7•7=49 and 49•7=343

ade's gem shop is having its annual spring sale, when every item in the store gets marked down. during the sale, charm bracelets sell for $4 less than full price. kristen purchases 5 identical charm bracelets: one for each of her friends. she pays a total of $45. which equation can kristen use to find how much money, c, each charm bracelet costs at full price?

### Answers

Based on the information provided, the **equation** that can be used to find how much money, c, each charm **bracelet cost** at full price is 5(c – 4) = 45.

An **equation** is its simplest form in algebra, refers to a **mathematical statement** that represents that two mathematical expressions are equal. For example, 2x + 6 = 14 is an equation, where 2x + 6 and 14 are two expressions that are separated by an **equal sign**. In the given case, as each bracelet cost is reduced by $4 from the full price, and the total cost of 5 identical charm bracelets is $45, the equation that can be used is given by:

5(c – 4) = 45

Solving the equation,

5(c – 4) = 45

c – 4 = 9

c = 9 + 4 = $13

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9 ÷ 2 = ?

show solution, ty!

### Answers

**Answer:**

4.5

**Step-by-step explanation:**

4.5 + 4.5 = 9

OR

4.5 x 2 = 9

If h(x)=6x+8 then h-'(x) = ?

### Answers

The **inverse** of the given **function** is, **h^(-1)(x) = (x - 8)/6.**

**What is inverse of function?**

What a function's **inverse function** is F is a** function** that reverses what F did. The inverse of f is represented by f-1 if it exists and only if f is a bijective **function**.

Consider, the given function

h(x) = 6x + 8

Let,

y = 6x + 8

Replace x with y,

x = 6y + 8

Solving the equation for y,

x - 8 = 6y

y = (x - 8)/6

Replace y with h^(-1)(x),

So,

h^(-1)(x) = (x - 8)/6.

Hence the **inverse** of the given **function** is, **h^(-1)(x) = (x - 8)/6.**

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What is the 41st term of the sequence 8, 10, 12, 14,... ?

88

41

322

90

### Answers

**Answer:**

**Step-by-step explanation:**

We will find the 41st term of the given arithmetic sequence is equal to 88.

In a 30 60 90 triangle where the long side is equal to 4, what are the values of the hypotenuse and short side ?

### Answers

For given** 30 60 90 triangle**, the values of the **hypotenuse **= 4 units and** short side **= 2 units

We know that, a **30 60 90 triangle** is right triangle.

In** right triangle **the longest side is **hypotenuse**.

Here, hypotenuse = 4 units

The short side of triangle is the opposite to the side of smallest angle.

So, we need to find the **length **of the side opposite to angle 30.

Consider **sin(30)** = short side/hypotenuse

1/2 = short side/4

short side = 4/2

short side = 2 units

Therefore, for given** 30 60 90 triangle**, the values of the **hypotenuse **= 4 units and** short side **= 2 units

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In regression analysis, the error term ε is a random variable with a mean or expected value of.

### Answers

In **regression analysis** , the error term ε is a random variable with expected value of 0.

**What is regression analysis?**

A set of statistical procedures known as **regression analysis** is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer to error term is 0.

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