pls solve this question for me

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=8 \end{cases}\implies V=\cfrac{\pi (3)^2(8)}{3}\implies V=24\pi ~cm^3[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7700\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 7700\left(1+\frac{0.039}{12}\right)^{12\cdot 4}\implies A=7700(1.00325)^{48} \implies A \approx 8997.69[/tex]

The x-intercept of (-2, 0) has both functions. The behavior of the function g(x) for x ⇒ -∞ then g(x) → ∞. The y-intercept of the function f(x)  is (0, 6). And both functions have real roots.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = x³ - 2x² - 5x + 6

g(x) = - x³ + 4x

The factor of the function f(x) is given as,

f(x) = 0

x³ - 2x² - 5x + 6 = 0

(x + 2)(x - 1)(x - 3) = 0

x = -2, 1, 3

The factor of the function g(x) is given as,

g(x) = 0

- x³ + 4x = 0

x = 0, 2, -2

The y-intercept of the function f(x) is given as,

f(0) = (0)³ - 2(0)² - 5(0) + 6

f(0) = 6

The y-intercept of the function g(x) is given as,

g(0) = - (0)³ + 4(0)

g(0) = 0

The graph of the function is given below.

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The long division problem can be used to prove the formula for factoring the difference of two perfect cubes (a-b)(a²+ab+b²).

The difference of two perfect cubes: a³-b³  = (a-b)(a²+ab+b²)

let the two perfect cubes be a³ and b³. Factoring the  difference between these two perfect cubes we have: a³ - b³

First, we need to factorize (a-b)³:

(a-b)³ = (a-b) (a-b)²

(a-b)³ = (a-b)(a²-2ab+b²)

(a-b)³ = a³-2a²b+ab²-a²b+2ab²-b³

(a-b)³ = a³-b³-2a²b-a²b+ab²+2ab²

(a-b)³ = a³-b³ - 3a²b+3ab²

(a-b)³  = (a³-b³) -3ab(a-b)

Then we will make a³-b³ the subject of the formula from the result equation;

a³-b³ =  (a-b)³+ 3ab(a-b)

a³-b³  = a-b{(a-b)²+3ab}

a³-b³  = a-b{a²+b²-2ab+3ab}

a³-b³  = (a-b)(a²+b²+ab)

a³-b³  = (a-b)(a²+ab+b²)

The long division problem that can be used is (a-b)(a²+ab+b²).

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Step-by-step explanation:

1. MN || LO - ( PARALLEL LINES ) .

2. <NMO = <LOM - ( GIVEN ) .

3. <MLO = <ONM - ( REFLEXIVE PROPERTY ) .

4. ..... - ( AAA S-C ) .

Jessica gets more rocks to skip across the surface of the pond than Henry.

To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.

For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.

For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.

Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.

We will multiply the numerator and denominator of Henry's ratio by 12 to get -

5/9 x 12/12 = 60/108

Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -

7/12 x 9/9 = 63/108

Comparing the numerators we get 60<63.

This implies that 60/108 < 63/108.

Therefore, Jessica gets more rocks to skip across the surface of the pond.

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The complete question is -

Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks

Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond​?

If the rate of walking is 1. 4 meters per second, then 357.14 sec would take you to walk 500 meters.

We can calculate speed, distance or time using the formula s = d/t, distance equals speed times time. The Speed Distance Time formula can solve for the unknown sdt value given two known values.

Time can be entered or solved in units of seconds (s), minutes (min), hours (hr), or hours and minutes and seconds (hh: mm: ss).

We have,

The rate of walking is 1. 4 meters per second.

The distance to cover is 500 meters.

Now, we know the formula

Speed = Distance/Time

⇒Time = Distance/Speed

⇒Time = 500/1.4

⇒Time = 357.14 sec

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The packages of paintbrushes, p, that Mr. Grant needs to buy in order to have at least 55 paintbrushes will be at least 5 packages.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

In this case, Grant has 25 paintbrushes already and will buy more paintbrushes in packages of 6.

The inequality to illustrate this will be:

25 + 6p ≥ 55

where P = packages of paintbrushes

Collect the like terms

6p ≥ 55 - 25

6p ≥ 30.

Divide

p ≥ 30 / 6

p ≥ 5

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Answer: The graph of f(x) = 2^x and g(x) = 2^x +2 are the same.

Explanation: The functions f(x) = 2^x and g(x) = 2^x + 2 are identical. The only difference between them is the constant term in the second function. This constant term does not change the shape, direction or the relative position of the graph of the function, it only shifts the graph along the y-axis. Because both functions have the same base, the graphs will have the same shape, direction and relative position, regardless of the constant term.

Answer: 54% of youths surveyed prefer reading electronic books.

Step-by-step explanation: 74 divided by 100 = 0.74. Divide 40 by 0.74 and you get 54.05%. Round that to 54% and you have your answer.

Answer: $3.22 tax

Step-by-step explanation:

7/100 x 46 = $3.22

Answer:3.22$

Step-by-step explanation:3.22$ in the USA

According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).

To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.

We must add all the values of the group that wears glasses

According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.

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As per the given mortgage, the remaining balance be after the first 5 years is $678125

Here Kathy and Jake are purchasing a house and are financing $465,000. The mortgage is a 20-years 5/1 ARM at 3. 5% with a 2/7 cap structure.

As we know that the formula for the calculation is written as

=> (Mortgage X Rate)/ 12 months

And then we have to subtract the Monthly PI payment from monthly interest on payment.

When we apply the value on it, then we get,

($465,000 x 3.5)/12

= $135625

Then the amount after 5 years is calculated as,

⇒ $135625 x 5

= $678125

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[tex]4y-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies 4\stackrel{y}{\left( -\cfrac{1}{2} \right)}-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies -2-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( -2-\cfrac{1}{2} \right)=6\left( \cfrac{x}{3}-\cfrac{5}{2} \right)}\implies -12-3=2x-15 \\\\\\ -12-3+15=2x\implies 0=2x\implies \cfrac{0}{2}=x\implies \boxed{0=x}[/tex]

Paul's pig pen has a width of 2 feet and an area of 16 square feet is the true statement.

The area of Rectangle is length times of width.

This is a simple calculus problem but it can be solved without calculus, as follows:

let L=length of the pen and W = width

2(L + W) = 20  

L + W = 10

L = 10 - W

Let A = area of the pen

A = Length × Width = 10W - W²

Sketch this parabola which has a positive maximum which occurs at W = 10/2

This means the area is maximum when w = 2, in other words the maximum area occurs when the rectangle is a square.

Hence,  Paul's pig pen has a width of 2 feet and an area of 16 square feet.

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This statement is False.

The formula provided in the statement is used to calculate the variance of the sample mean difference between two independent samples, but it is not necessarily true that the sample variances, and , are independent of one another.

The sample variances are calculated based on the data from their respective samples, and thus their relationship will depend on the specific data and the underlying population distributions.

For example, let's consider two samples of size n = 25, one from a normal population with mean 100 and variance 10, and another one from a normal population with mean 110 and variance 20. The sample variances for each sample are:

S1² = 9.6 and S2² = 20.8

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I bought 30 gifts costing $2 each and 10 gifts costing $4 each for my family.

An equation is an expression showing the relationship between numbers and variables.

Let x represent the number of gifts costing $2 and y represent those costing $4

You spend $100 on gifts for your family and friends. Hence:

2x + 4y = 100    (1)

You buy 40 gifts altogether, hence:

x + y = 40     (2)

From both equations:

x = 30, y = 10

A total of 40 gifts was bought

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OC (x+1)(x-8)(4)=56 indicates that the volume of the box is 56 in³ because it takes into account the length of the sides after the four corners were cut off, and the height of the box which is 4 in. The equation can be written as (length of sides)(width of sides)(height) = volume.

A volume is a three-dimensional space that contains a specific amount of material, which is commonly measured in liters, cubic meters, or gallons. It is frequently used to calculate the capacity of containers like tanks, bottles, and barrels. Volume may also refer to the quantity of space occupied by an item, such as the volume of a room or the volume of a sphere.

In the given question, OC is the correct answer: (x+1)(x-8)(4)=56. This equation reveals that the volume of the box is 56 [tex]in^{3}[/tex] because it considers the length of the sides after the four corners were taken off, which are (x+1) and (x-8), as well as the height of the box, which is 4 in. The formula is (length of sides)(width of sides)(height) Equals volume. As a result, the equation (x+1)(x-8)(4) = 56 reveals that the box's volume is 56 [tex]in^{3}[/tex].

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The range of the function is (d) [150, 275]

The graph that completes the question is added as an attachment

From the graph, we have the following properties:

The range is simply the amount of values between the y axis

In this case represented by the graph, we have:

Minimum y value = 150

Maximum y values = 275

Sinfe both values are inclusive, the range would be [150, 275]

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The answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a. The solution has been obtained by using the concept of exponents.

What is an exponent?

The exponent of a number shows that how many times a particular number has been multiplied by itself. For instance, the number 2^4 means that we are multiplying the number 2 itself by four times. It is enlarged to 2*2*2*2. An exponent is also known as a number's power. One may use a whole number, fraction, negative number, or decimal.

We are given [tex]\sqrt[4]{125a^{4} }[/tex]

This can be also written as (125a^4)^1/4

Splitting the power, we get

⇒[tex]a^{4^{1/4} } 125^{1/4}[/tex]

⇒a 125^0.25

⇒a 3.34

⇒3.34a

Hence, the answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a.

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Since there are multiple questions so, the question answered above is

[tex]\sqrt[4]{125a^{4} }[/tex]

The slope and the intercept of the function f(x) = -x + 5 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The function for this problem is defined as follows:

f(x) = -x + 5.

Comparing to the standard definition of a linear function, we have that:

The problem asks for the slope and the intercept of the function f(x) = -x + 5.

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The number of hamsters as a function of the cycle number, c, can be represented by the equation:

f(c) = 5 * 3^c

This equation was determined by the fact that the population triples every cycle and the starting number of hamsters is 5. The function notation is f(c) which represents the number of hamsters as a function of the cycle number. The base of the equation is 3, which represents the rate at which the population triples. The exponent is c, which represents the cycle number. The coefficient is 5, which represents the starting number of hamsters.

Answer:

w = 11 , x = 25

Step-by-step explanation:

for Δ ABC ≅ Δ TUV, then corresponding sides must be congruent, that is

AB = TU and BC = UV ( using these to create 2 equations )

- 9x + 20w + 89 = 4w + x + 15 ( subtract 4w + x + 15 from both sides )

- 10x + 16w + 74 = 0 → (1)

and

x + w + 41 = - 18w + 11x ( subtract - 18w + 11x from both sides )

- 10x + 19w + 41 = 0 → (2)

multiplying (2) by - 1 and adding to (1) will eliminate x

10x - 19w - 41 = 0 → (3)

add (1) and (3) term by term to eliminate x

0 - 3w + 33 = 0 ( subtract 33 from both sides )

- 3w = - 33 ( divide both sides by - 3 )

w = 11

substitute w = 11 into either of the 2 equations and solve for x

substituting into (1)

- 10x + 16(11) + 74 = 0

- 10x + 176 + 74 = 0

- 10x + 250 = 0 ( subtract 250 from both sides )

- 10x = - 250 ( divide both sides by - 10 )

x = 25

thus the values x = 25 and w = 11 will make the triangles congruent

Parallelograms are quadrilaterals with two sets of parallel sides

Slope Formula: y2-y1/x2-x1

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

KL: 12-7/6-2 = 5/4

LM; 13-12/13-6 = 1/7

MN: 8-13/9-13 = 5/4

KN: 7-8/9-2 = 1/7

We can identify this as a parallelogram since it has congruent angles and sides, which are found on a parallelogram.

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The monthly payment during the initial period is  about $1,682.94

The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM

The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.

Let us assume that m represents the initial monthly payment.

[tex]M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}[/tex]

where, M is the monthly payment during the initial period

P is the amount on loan

r is the interest rate = 5% = 0.05

n is period = 30 × 12 = 360

Here, P = $313,500

r = 5%

r = 0.05

n =  30 × 12

n = 360

Substituting these values in the above formula we get,

[tex]M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}[/tex]

M  ≈ 1,682.94

Therefore, the monthly payment is about $1,682.94

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The statement in algebraic terms is given by 8z-89/8

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The statement " 11¹/₈less than the product of 8 and the number z"

The translation of the statement in the form of an algebraic expression is given by

8z - 11¹/₈

8z-89/8

Hence, The statement in algebraic terms is given by 8z-89/8

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The quotient for the given expression is 8x^2-8x+14 and the remainder is -19.  The solution has been obtained using the method of long division of polynomial.

What is polynomial long division?

A formula for dividing one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

Using Polynomial Long Division,

Dividing :  8x^3 + 6x - 5 ("Dividend")

By         :    x+1   ("Divisor")

Dividend              8x^3  +  0x^2  +  6x  -  5

- divisor  * 8x^2   8x^3  +  8x^2        

Remainder                     -  8x^2   +  6x  -  5

- divisor  * (-8x)               -  8x^2   -  8x    

Remainder                                       14x  -  5

- divisor  * 14                                     14x +  14

Remainder                                               - 19

Quotient :  8x^2-8x+14

Remainder:  -19

Hence, the quotient for the given expression is 8x^2-8x+14 and the remainder is -19.

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The bar representing her 7-day vacation will have a class width of 16 - 22 and a height of 1.

The frequency distribution of a collection of data reveals how frequently each unique value appears.

The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.

In the given histogram class width(horizontal width)  represents the number of days and frequency(vertical height) represents the number of vacations taken.

Therefore, The 7-day vacation yet she took this summer will be represented by a bar having a class width 16 - 22 and a height of 1.

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The equation of the circle with center (-7, -15) and area π is

(x + 7)² + (y + 15)² = 1.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Centre of the circle = (-7, -15)

The equation of a circle is r² = (x - h)² + (y - k)²

Where (h, k) is the center of the circle.

Now,

h = -7

k = -15

The equation of a circle.

r² = (x + 7)² + (y + 15)² _____(1)

Now,

Area = πr²

πr² = π

r² = 1 _____(2)

Now,

From (1) and (2),

(x + 7)² + (y + 15)² = 1

Thus,

The equation of the circle is (x + 7)² + (y + 15)² = 1.

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Answer: An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. We can call this constant difference "d".

In this sequence, we can see that the difference between consecutive terms is -6x - 5.

The 9th term of an arithmetic sequence can be found by using the formula:

a_n = a_1 + (n-1)d

Where a_n is the nth term of the sequence, a_1 is the first term of the sequence and d is the common difference.

Given the sequence -5x + 2, -11x - 3, -17x -8, ...

The 9th term is:

-5x + 2 + (9-1) (-6x-5) = -5x + 2 - 48x - 40 = -53x -38

Therefore the 9th term of the arithmetic sequence is -53x -38.

Step-by-step explanation: