seconds is given by the equation h = - 16t* + 12t + 40, how long will it take for the rock CO hit the water?

**Answer:**

**Step-by-step explanation:**

To find the time it takes for the rock to hit the water, we need to find the value of t when h is equal to zero. This is because the rock will hit the water when it reaches a height of zero feet above the water.

Substituting zero for h in the equation h = -16t^2 + 12t + 40, we get:

0 = -16t^2 + 12t + 40

This equation is a quadratic in t, so we can use the quadratic formula to solve for t:

t = (-12 +/- sqrt(12^2 - 4 * (-16) * 40)) / (-32)

Simplifying, we get:

t = (-12 +/- sqrt(144 + 640)) / (-32)

t = (-12 +/- sqrt(784)) / (-32)

t = (-12 +/- 28) / (-32)

t = -40/-32 or t = 16/-32

t = 1/8 or t = -1/2

Since the time cannot be negative (because the rock was thrown upwards), the only solution that makes sense is t = 1/8 seconds.

Therefore, it will take 1/8 seconds for the rock to hit the water.

The local school district you live in selling bonds for $2000 that pays 5% interest annually that matures in 10

years. How much interest will you earn?

O $2000

O $500

O $750

O $1000

**Answer:**

$1000

**Step-by-step explanation:**

5% = 1 year

50% = 10 years

50% = 0.5

Take 2000 times 0.5 = $1000

So, you will earn $1000 interest in 10 years

What is the value of 3 is to 4?

Let x= 3^4. So the value of given **expression **after applying **power rule **is x=81.

**What is meant by power?**

How many times you should **multiply **a number depends on its power. **Exponents **and **indices **are other names for powers. For instance, 82 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."

**What is meant by n^5 where n can be any number?**

By n^5 means n^5=n*n*n*n*n that is multiplying n five times.

3^4=(3^2)^2

=(9)^2

=81

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What does a 3 to 1 slope mean?

3 to 1 **slope** means, there are three horizontal units for every one vertical unit.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

That is to say,

Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions'"Ratios like 3:1 are used to represent slopes. This indicates that there is a 1 unit (foot or meter) vertical shift, either up or down, for every 3 units (feet or meters) of horizontal distance."

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What doe the expreion 3x4y repreent?

A. The total number of baket of tomatoe and bag of onion the cutomer purchaed

B. The cot per baket for the tomatoe plu the cot per bag for the onion

C. The total cot, in dollar, for the cutomer’ purchae

D. The number of baket of tomatoe and the number of bag of onion that can be purchaed for $7

The expression** 3x+4y **represents **3 bags **of $3 tomatoes and 4 bags of $4 onions.

What is an **expression**?

The **combination** of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of logical grammar, such as the operation order.

Given that a basket of **tomatoes** costs $3, whereas an **onion** package costs $4. A customer buys y sacks of onions and x baskets of tomatoes.

Three bags of $3 tomatoes and four bags of $4 onions are denoted by the equation **3x+4y**.

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Deion is building a walkway with a width of xx feet to go around a swimming pool that measures 13 feet by 9 feet. If the total area of the pool and the walkway will be 621 square feet, how wide should the walkway be?

Applying the area of a **rectangle**, the width of the walkway (x) is: **7 feet**.

**What is the Area of a Rectangle?**

**Area of a rectangle = (length)(width)**

Total area of the pool and walkway = 621 sq. ft

Length of the pool and walkway = 13 + 2x

Width of the pool and walkway = 9 + 2x

Thus, we will have the **equation** of the **total** area as:

(13 + 2x)(9 + 2x) = 300

4x² + 44x + 117 = 621

4x² + 44x + 117 - 621 = 0

4x² + 44x - 504 = 0

Factorize

(x - 7)(x+18) = 0

x = 7

or

x = -18

The **width**, x, cannot be **negative**, so, the width of the walkway (x) would be 7 feet.

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Please help me with this question

step by step explanantion

**Answer: 148cm²**

**Step-by-step explanation:**

The volume of the cuboid is the length, height, and width multiplied together. Since the problem gives us the volume, we can set an equation.

[tex]l*w*h=120 cm^3[/tex]

Since the area of the base of 30cm², we can get another equation.

[tex]l*w=30cm^2[/tex]

We can plug in our equations.

[tex]30cm^2*h=120cm^3[/tex] [divide both sides by 30cm²]

[tex]h=4cm[/tex]

Now, we know the height of the cuboid.

Since we aren't given a specific length and width, it can be any of the combinations that give 30 cm² when multiplied.

We can have 1,30 or 2,15 or 3,10 or 5,6.

I will work out 5,6 with l=5 and w=6.

The surface area of a cuboid is [tex]2(lw+wh+lh)[/tex].

[tex]2(30+24+20)=2(74)=148cm^2[/tex]

This is one possible answer. There are multiple ones with the pair choices above.

6 less than a number

**Answer:**

n - 6

**Step-by-step explanation:**

Number n is A less than B: n = B - A.

resolve into partial fraction x^2+1/x^3+1

First we have to factorise the denominator [tex]\rm{x^3+1.}[/tex]

It can be factorised as,

[tex]\rm{x^3+1=(x+1)(x^2-x+1)}[/tex]

Then the fraction can be written as,

[tex]\longrightarrow\rm{\dfrac{x^2+1}{x^3+1}=\dfrac{x^2+1}{(x+1)(x^2-x+1)}\quad\dots(1)}[/tex]

This fraction can be resolved into partial fractions by writing it as the sum of a fraction having denominator [tex]\rm{x+1}[/tex] and a fraction having denominator [tex]\rm{x^2-x+1.}[/tex]

Since [tex]\rm{x+1}[/tex] is a first degree polynomial, the numerator of the fraction having this term as denominator should be a zero degree polynomial, or a constant term, assumed as [tex]\rm{A.}[/tex]

Since [tex]\rm{x^2-x+1}[/tex] is a second degree polynomial, the numerator of the fraction having this term as denominator should be a first degree polynomial, assumed as [tex]\rm{Bx+C.}[/tex]

So let,

[tex]\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{A}{x+1}+\dfrac{Bx+C}{x^2-x+1}}[/tex]

[tex]\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{A(x^2-x+1)+(Bx+C)(x+1)}{(x+1)(x^2-x+1)}}$}[/tex]

Equating numerators,

[tex]\longrightarrow\rm{x^2+1=A(x^2-x+1)+(Bx+C)(x+1)}[/tex]

[tex]\small\text{$\longrightarrow\rm{x^2+1}=\cal{(A+B)}\rm{x^2}+\cal{(-A+B+C)}\rm{x}+\cal{(A+C)}$}[/tex]

Equating corresponding coefficients,

[tex]\rm{A+B=1}[/tex]

[tex]\rm{-A+B+C=0}[/tex]

[tex]\rm{A+C=1}[/tex]

Solving these three equations we get,

[tex]\rm{A=\dfrac{2}{3}}[/tex]

[tex]\rm{B=\dfrac{1}{3}}[/tex]

[tex]\rm{C=\dfrac{1}{3}}[/tex]

Thus,

[tex]\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{2}{3(x+1)}+\dfrac{x+1}{3(x^2-x+1)}}$}[/tex]

[tex]\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{1}{3}\left[\dfrac{2}{x+1}+\dfrac{x+1}{x^2-x+1}\right]}$}[/tex]

So (1) becomes,

[tex]\longrightarrow\underline{\underline{\bf{\dfrac{x^2+1}{x^3+1}=\dfrac{1}{3}\left[\dfrac{2}{x+1}+\dfrac{x+1}{x^2-x+1}\right]}}}[/tex]

Hence the given fraction is resolved into partial fractions.

What are the 12 types of sets?

The 12 **types of sets** are empty set, singleton set, finite set, infinite set, subset, equal set, universal set, power set, proper subset, superset, equivalent set and proper superset.

An empty set does not contain any element, while a **singleton set **contain only one element.

If the number of elements in a set is **finite**, the set is a finite set. If the number of elements in a set is not finite, that is not countable it is an infinite set.

A set, say A contain only elements of another set, say B but not necessarily all elements, than set A is a **subset **of set B.

Whenever a set A is a subset of set B, we say the B is a **superset** of A. If A and B are two sets, then A is called the proper subset of B if A is a subset of B but B is not a subset of A i.e., A ≠ B.

If a set contains all and only elements of another set, then both set are said to be **equal sets**.

A **universal set** contains all elements of related sets.

**Power set** is the collection of all subsets of a particular set.

The set B is the **proper superset** of set A, then all the elements of set A are in B, but set B must contain at least one element which is not present in set A.

**Equivalent** sets are sets that have same number of elements.

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What are the mean and standard deviation of the distribution of rs?

The **mean **and **standard deviation **of the distribution of R-S is

The **mean **is calculated by simply substracting the values

= mean R - means S

= 10 - 7

= 3

**standard deviation**, SD

standard deviation is solved by the use of radicals and this affects the solution hence it will not be simple subtraction, rather we solve back to remove the radical and hence we get the **variance**

= (SD, R)² + (SD, S)²

= 4² + 3²

= 16 + 9

= 25

the **variance **is 25

SD = √variance = √25 = 5

**complete question**

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S

has mean 7 and standard deviation 3. If Rand S are independent, what are the mean and standard deviation of the

distribution of R-S?

A Mean 3 and standard deviation 1

B Mean 3 and standard deviation 5

C Mean 3 and standard deviation 7

D Mean 17 and standard deviation 1

E Mean 17 and standard deviation 5

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Consider the function. f(x)=−8x+4 What is the value of f(−14)?

The **value **of **polynomial **for x = 2 that is f(2) will be 32.

In many branches of mathematics and science, **polynomials **are used. For instance, they are used to define **polynomial functions**, which show up in settings ranging from basic chemistry and physics to economics and social science.

They are also used in calculus and numerical analysis to approximate other **functions**. **Polynomial **equations are used to form these **functions**. **Polynomial **rings and algebraic varieties, two fundamental ideas in algebra and algebraic geometry, are constructed in advanced mathematics using **polynomials**.

We have given **polynomial** f(x)=3x²8x+4

We have to find the **value **of f(2

We have to find the **value **of **polynomial **for x = 2

So for finding this **value **we have to just put x = 2 in **polynomial**

So f(2) will be

So the **value **of **polynomial **for x = 2 will be 32

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Which quadratic function has one real solution

0=2(x+7)(x-5)

0=2/3(x-3)(x-3)

0=2.4(x-2)(x+2)

0=1/2(x-2)(x-1)

**Answer: **[tex]0=\frac{2}{3}(x-3)(x-3)[/tex]

**Step-by-step explanation:**

Factorize:

(2a^3-8a)÷ 2a (a-2)

The **factorized expression **of (2a³ - 8a) ÷ 2a (a - 2) is (a - 4) ÷ (a - 2)

From the question, we have the following parameters that can be used in our computation:

(2a^3-8a)÷ 2a (a-2)

Rewrite the above **expression **properly

So, we have the following representation

(2a³ - 8a) ÷ 2a (a - 2)

Divide the **fraction **by 21

This gives

(a - 4) ÷ (a - 2)

The above expression cannot be solved further

Hence, the **solution **is (a - 4) ÷ (a - 2)

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Is 3xÂ² 8x 15 Factorisable?

The **equation** 3x² - 8x - 15 is not **factorizable**.

An **expression** is a way of writing a statement with more than two variables or numbers with **operations** such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3x² - 8x - 15

This is in the form of ax² + bx + c.

We will find the **determinant** D = b² - 4ac

If D = 0 or D = perfect square

The equation is **factorizable**.

Now,

a = 3

b = -8

c = -15

D = (-8)² - 4 x 3 x (-15)

D = 64 + 180

D = 244

This is not a zero nor a perfect square.

Thus,

3x² - 8x - 15 is not **factorizable**.

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Please help !!!!!???

The **height** of Dubai fountain is 500 feet tall.

The foundational subject in mathematics is **arithmetic**, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics. The Greek term "arithmos," which means "numbers," is where the word "arithmetic" originates. Arithmetic is one of the oldest and most basic concepts in mathematics. It deals with numbers and the basic operations (addition, subtraction, multiplication, and division) that can be carried out on them.

Given

The Burj Khalifa in Dubai is the tallest building in the world, at 2,717 feet.

Burj Khalifa is 217 feet taller

Height of Dubai fountain

**Subtracting**

2717 - 217

2500

5 times the height

**Divide** by 5,

2500/5

500

The **height** of Dubai fountain is 500 feet tall.

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What is the easiest way to find mean median and mode?

Mean = (**sum **of all observations in given data set) ÷ (total number of observations)

In an odd-numbered set, the median will be the number in the very **middle **of the list. In an even-numbered set, the **average **of the two middle numbers will be mode.

The mode is the most frequent number.

Mean:

Using two straightforward procedures, we can determine the mean, or average, of a data set:

(1) Add up all of the values to find the sum.

(2) Divide the sum by the number of values in the data set

Mean = (sum of all observations in given data set) ÷ (total number of observations)

Median:

The middle score in the group is known as the median. To find the median, start by arranging all of the data points from smallest to largest. Means arrange the data either in **ascending** order or in the **descending **order. In an odd-numbered set, the median will be the number in the very middle of the list. In an even-numbered set, you will need to calculate the average of the two middle numbers.

Mode:

To quickly determine the mode, arrange the numbers in ascending order by least to greatest, then tally the frequency of each number. The mode is the most frequent number.

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What happens if you claim a dependent that has already been claimed?

It appears that someone else claimed your **dependant**, assuming you submitted your dependent's details accurately. If another individual claim your dependent before you do, the** IRS** will reject your return since it processes the first return it gets. In such case, you must take the following actions:

1. File a paper return.

2. Document your case.

3. Answer when the **IRS** contacts you.

The IRS will reject a **tax return** filed electronically by a parent claiming a kid who has already been claimed for the year. The return will appear to have never been submitted. The **dependent's tax ID** number must be included on any future tax returns for the same tax year that are submitted electronically.

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Solve pls brainliest

**Answer:**

Your answer is 2,600.019

**Step-by-step explanation:**

Very simply to answer it with or without a calculator.

2.6 * 10^3 + 0.19 * 10^-2

**Without calculator**

First move the decimal points before adding.

2.6 * 10^3 = 2,600.

Negative exponential moves the decimal to the left.0.19 * 10^-2 = 0.0019

This equation 2.6 * 10^3 + 0.19 * 10^-2 becomes

2,600 + 0.0019

Then add.

2,600.0019

Can a person draw Social Security and disability at the same time?

Generally it is not possible. But if someone applying for early retirement after being forced to leave their jobs due to an **illness or injury**. In order to help them pay their costs until their SSDI claim is approved and the waiting period for those benefits has passed, they can start collecting early** retirement payments**.

Generally speaking, it is not possible to receive both** Social Security **retirement benefits and Social Security Disability Insurance (SSDI) at the same time. However, if you fulfill the severe financial requirements while receiving SSDI or retirement payments from Social Security, you can be eligible for Supplemental Security Income (SSI).

To fill the gap between when someone must leave the working due to a disability and when they can receive retirement benefits, the **Social Security Administration **(SSA) established the SSDI program. Because of this, there is only one option to get SSDI and retirement benefits at the same time.

This happens when a person chooses to retire early between the ages of 62 and their full retirement age but is later granted SSDI payments. Some people do this on purpose by applying for early **retirement** after being forced to leave their jobs due to an illness or injury. In order to help them pay their costs until their SSDI claim is approved and the waiting period for those benefits has passed, they can start collecting early retirement payments.

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How do you create a unique array?

Minimum **Increment **operations to make Array unique

The UNIQUE function will **return **an array, which will spill if it's the final result of a formula. This means that Excel will dynamically create the appropriate sized array range when you press ENTER .

ArrayList is like an array behind the scenes as it’s backed by an array of type java.lang.Object in java.

Normally arrays are fixed in size which means the number of elements that can be added are fixed and cannot be increased once created. ArrayList can dynamically increase in size once the array that backs is full so, these way we won’t encounter runtime exceptions.

When we say list.get(0), it’s equivalent to array[0]. It can be said the ArrayList is a kind of more convenient way to use dynamic arrays.

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How do you do 3 terms in binomial expansion?

The **solution** of the expression with three terms using **binomial theorem **can be solved by **supposition** and **resubstituting** the value.

Let us consider an example of three terms :

( 1 + x + x² ) ³

Use **binomial theorem** and expand the given **expression**:

Standard form of binomial expansion is :

( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+ ⁿCₙa⁰bⁿ

Let us consider x + x² = y

( 1 + y )³

=³C₀1³y⁰ + ³C₁1³⁻¹y¹ + ³C₂1³⁻²y² + ³C₃1⁰y³

= 1 + 3y + 3y² + y³

Resubstitute the value of y = x + x² we get,

= 1 + 3(x + x²) + 3(x + x²)² + (x + x²)³

= 1 + 3x + 3x² + 3( x² + 2x³ + x⁴) + ³C₀x³(x²)⁰ + ³C₁x³⁻¹(x²)¹ + ³C₂(x)³⁻²(x²)² + ³C₃x⁰(x²)³

= 1 + 3x + 3x² + 3x² + 6x³ + 3x⁴ + x³ + 3x⁴ + 3x⁵ + x⁶

= 1 + 3x + 6x² + 7x³ + 6x⁴ + 3x⁵ + x⁶

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What is dependent and dependent variable?

**Independent **and **dependent** variables are interdependent.

Dependent Variable: The term "dependent variable" refers to the variable that is being measured or tested in an experiment.

The results of the participants' tests, for instance, would be the dependent variable in a study looking at how tutoring affects test scores because that is what is being measured.

If you keep in mind that the dependent variable depends on the independent variable, finding it can be simpler.

The dependent variable's variable is beingThis isn't the same as an experiment's independent variable, which is a variable that can stand on its own. The dependent variable (test results), however, may alter depending on the independent variable (tutoring).

The **unrelated factor**

Because the experimenters are allowed to change the independent variable as necessary, it is called a "independent" variable.

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Hey people can you guess NFL player with seven Super Bowl

Maybe Derrick Henry?

Use point-slope form to write an equation of the line with the given slope that passes through the given point.

**Answer:**

Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. ...

Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.

**Step-by-step explanation:**

What's the mean of the following number set 2 2 4 6 8 8 10?

The required** mean** of the given data is 5.71.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a **dataset**.

The term "average" is frequently used to describe this measure of central tendency.

So, we have the data set:

2, 2, 4, 6, 8, 8, 10

Mean formula: Sum of terms / Number of terms

Now, calculate the mean as follows:

Mean: Sum of terms / Number of terms

Mean: 40 / 7

Mean: 5.71

Therefore, the required mean of the given data is 5.71.

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Does anyone know how to do this, I'm stuck

It is possible to draw one; since triangle sides add to 180

35+35+110=

=180

The picture shown is not to scaled, but if you have a protractor then use that. (See attached picture)

If you don’t understand it, or still cannot get it, feel free to leave a comment or direct message me!

Hope this helped!

35+35+110=

=180

The picture shown is not to scaled, but if you have a protractor then use that. (See attached picture)

If you don’t understand it, or still cannot get it, feel free to leave a comment or direct message me!

Hope this helped!

Grandpa Ernie is shrinking! Over the past 4 years, his height decreased by a total of 2.4 cm 2.4. It decreased by the same amount each year.

What was the change in Grandpa Ernie's height each year?

**Answer:**

**Step-by-step explanation:**

Grandpa Ernie has been shrinking for the past four years. His height decreased by a total of 2.4 cm during this period, which means that it went down by 0.6 cm each year. This gradual decrease in his height is quite remarkable given his age and overall health condition; however, it is not an entirely unexpected phenomenon due to aging and the natural decline of muscle mass with age as well as other factors such as poor nutrition or lack of exercise can contribute to this process too.

How do you tell if a function is positive or negative on a graph?

**Answer:**

You can tell if a function is positive or negative by checking the Y values. If all the Y values are above the x-axis it should be positive, and if the all y values are below the x-axis the function should be negative.

Good luck!

6. ms. maria wilson is considering running for mayor of the town of bear gultch, montana. a sample of 400 voters reveals that 300 would support her in the november election. (a) calculate the sample proportion. what is the value of the population proportion? (b) develop a 99 percent confidence interval for the population proportion. (c) interpret your findings. cyhegg

(a) sample **proportion** is 0.75.

(b) The 99% **confidence** interval for the **population** **proportion** is approximately **[0.685, 0.815].**

(c) a 99% **probability** that the true **population** **proportion** of voters who would support Maria Wilson is within this **range**.

**What is proportion?**

A **proportion** in math is when two **ratios** are **equivalent**, that means they are **equal** to each other.

**(a)** To calculate the **sample** **proportion**, we need to **divide** the number of voters who would support Maria Wilson by the **total** sample **size**. In this case, the sample **proportion** is 300/400 = 0.75.

**(b)** To develop a 99% **confidence** interval for the **population** proportion, we can use the following **formula**:

**confidence** **interval** = sample proportion +/- (z-value * standard error)

The **standard** error of the **sample** **proportion** is a measure of the **variability** of the **sample** **proportion**, and is calculated as:

[tex]standard\ error = \sqrt{((sample\ proportion * (1 - sample\\ proportion)) / sample size)}\\\\standard\ error= \sqrt{((0.75 * 0.25) / 400)}\\\\standard\ error= 0.025[/tex]

At a 99% **confidence** level, the **z-valu**e is approximately 2.576.

Substituting these values into the formula for the **confidence** **interval**, we get:

**confidence interval** = 0.75 +/- (2.576 * 0.025)

= 0.75 +/- 0.065

= [0.685, 0.815]

So, The 99% **confidence** **interval** for the **population** **proportion** is approximately **[0.685, 0.815].**

**(c)** The **confidence** interval tells us that we are 99% **confident** that the **population** **proportion** of voters who would support Maria Wilson in the November election is between 0.685 and 0.815. This means that there is a 99% **probability** that the true **population** proportion of voters who would support Maria Wilson is within this **range**.

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What is the quotient of and 3/4 and 5 6?

**9/10 **is the** quotient **when 3/4 is **divided **by 5/6.

The two parts that make up a** fraction** are the** numerator,** which is located at the top, and the** denominator,** which is located at the bottom.

When two **fractions **are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the **reciprocal** of the second fraction and this can be obtained by reversing its **numerator** and **denominator**—is and then dividing the fractions. Multiply the two **numerators** after that. Multiply the two **denominators** after that, After that we need to simplify the fraction to its **lowest form.**

Mathematically **quotient **,

= (3/4) ÷ (5/6)

It is possible to define an **arithmetic** operation as one in which we add, subtract, multiply, and divide numbers. It has the fundamental operators +, -,÷,× and.

= (3/4)*(6/5)

= 18/20

= 9/10

so the **quotient** of 3/4 and 5/6 in lowest form is **9/10.**

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