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GR.2.4 Homework February 6, 2023
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A tissue box is 9 inches (in.) long, 4 in. wide, and 7 in. tall. What is the surface area of the tissue box?
Answer:
f(x) in ²
Duration: 00:01:41
Pre

To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).

Divide the capital by the cost of borrowing, the length of time, and certain other considerations to arrive at simple interest. Simple return = principal + interest + hours is the commercial formula. This method allows it easiest to calculate interest. The most basic technique to figure the interest is as a portion of the outstanding amount. He will only pay his share of the 100% interest, for example, if he borrowed $100 from a partner and agrees to repay the loan th with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must lend money.

given

Future Value = Current Value x (Present Value + Interest Rate) (Years/frequency of payments per year)

FV = (-15,000 x [1+8%]^

[4/1])

PV is adverse because you are redistributing funds.

FV = $20,407

Calculator for Finances: Enter PV of -15,000 as

Make 4 N.

Set 8 as I/Y CPT FV and 0 as PMT

$20,407

To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).

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Information pertaining to the ownership of the business, such as changes in the number average of shares held by shareholders, dividend payments, and proceeds from stock issue, is included in the statement of changes in stockholder's equity.

Information about the ownership of the business and how it affects the financial statements of the business is captured in the statement of changes in stockholder's equity. This statement contains information on the number of shares issued and outstanding, ownership changes brought on by stock splits and dividends, issuance proceeds, and the impact of transactions involving treasury stock. As a result of net gains or losses and other adjustments, it also keeps track of changes in retained earnings. Because it gives a general picture of the company's equity and how it has changed over time, this statement is significant. It is also a helpful tool for investors since it enables them to assess the financial performance of the business and decide on their investments with knowledge.

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Answer:

m<1 = 119°

Step-by-step explanation:

The entire figure is an irregular hexagon, a 6-sided polygon.

The sum of the measures of the angles of a polygon with n sides is

(n - 2)180°

For a hexagon, n = 6.

(6 - 2)180° = 4(180°) = 720°

All angle measures of the polygon are known except for the measure of <1.

m<1 + (37° + 113°) + 90° + 147° + (80° + 44°) + 90° = 720°

m<1 + 601° = 720°

m<1 = 119°

Answer:

1st term(a)=0.25

2nd term(t2)=0.5

common difference (d)=0.25

nth term(tn)=a+(n-1)d

=0.25+(n-1)0.25

=0.25+0.25n-0.25

=0.25-0.25+0.25n

=0.25n

Answer: nth term of the geometric sequence = (n^-1)/2

Step-by-step explanation:  The nth term of a GP is Tn = arn^-1

where a is the first term 0.25  

r is the common ratio 0.5/0.25 or 1/0.5 or 2/1, which is 2

Therefore the nth term = 0.25 x 2 x n^-1

= 0.5n^-1

=(n^-1)/2

Answer:

[tex]\frac{61}{10}[/tex]

Step-by-step explanation:

14/5=28/10

By changing the denominator so that they are equal, you can now add the two fractions together.

(28/10)+(33/10)=61/10

Hope this helped! :)

Answer:

Step-by-step explanation:

I think it 5

Answer:

Step-by-step explanation:

The number that goes under the radical sign in 17.

The answer is [tex]\sqrt{17}[/tex]

use the distance formula to calculate the distance between to two points.

Distance (d) = √(3 - -1)² + (-1 - -2)²

= √(4)² + (1)²

= √17

Answer:

means that s = 10

Step-by-step explanation:

given P(s) = 60 and P(s) = 3s , then equating the right sides

3s = 60 ( divide both sides by 3 )

s = 10

an equilateral triangle with a perimeter of 60 has side length of 10

Answer:

d ≈ 5.1

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = L (3, 7 ) and (x₂, y₂ ) = M (- 2, 8 )

d = [tex]\sqrt{(-2-3)^2+(8-7)^2[/tex]

   = [tex]\sqrt{(-5)^2+1^2}[/tex]

   = [tex]\sqrt{25+1}[/tex]

    = [tex]\sqrt{26}[/tex]

    ≈ 5.1 ( to the nearest tenth )

The standard deviation for the cost is given as follows:

$12.

The total number of students is given as follows:

7 + 20 + 20 + 14 + 10 = 71.

Considering the midpoint of each interval, and dividing their absolute frequencies by 71, the discrete distribution modeling the situation is given as follows:

The expected value is given by the sum of each outcome multiplied by it's probability, hence:

E(X) = 15 x 0.0986 + 25 x 0.2817 + 35 x 0.2817 + 45 x 0.1972 + 55 x 0.1408

E(X) = 35.

The sum of the differences squared between each observation and the mean, multiplied by their respective probabilities, is given as follows:

V(X) = (15-35)² x 0.0986 + (25-35)² x 0.2817 + (35-35)² x 0.2817 + (45-35)² x 0.1972 + (55-35)² x 0.1408

V(X) = 143.65.

The standard deviation is obtained taking the square root of V(X), hence:

S(X) = sqrt(143.65)

S(X) = $12. (rounding).

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Therefore , the solution of the given problem of quadratic equation comes out to be quadratic equation., cubic equation and leading coefficient is 1.

For one-variable equations, the quadratic result x = ax2 + b + c=0 is used in regression modeling. The First Thesis basic Algebra asserts that there is just one solution because this equation has a second order. Both straightforward and complex solutions can be found. A "quadratic solution," as the name suggests, consists of four variables. This suggests that there might be a single squared word.

Here,

Given :

=> x² + 2x -5 its degree is 2

hence quadratic equation.

=> 4x³ -8 its degree is 3

hence cubic equation

=> 2x⁴ - 7x² -5x + 1 its degree is 4

hence its an degree 4 equation.

leading coefficient of:

=> x³ + 5x² + 28 -x

leading coeffcient is = 1

Therefore , the solution of the given problem of quadratic equation comes out to be quadratic equation., cubic equation and leading coefficient is 1.

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Answer: No. It is positive

Step-by-step explanation:

I am assuming 10.75 is the sum and you are not missing another additive. A positive sum holds a value equal to or over zero while a negative sum is less than zero on the number line.

Therefore, the probability of selecting a defective battery followed by another defective battery is 1/145.

Calculating the likelihood that a statement is true or that a particular event will take place is the centre of probability theory, a branch of mathematics. Any number between 0 and 1, where 1 is usually used to range confidence as well as 0 is routinely used it to convey possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

The probability of selecting a defective battery on the first draw is 3/30, or 1/10, since there are 3 defective batteries out of 30 total.

Since one battery has already been drawn, there are now 29 batteries left in the box, and 2 defective batteries remaining.

The probability of selecting another defective battery on the second draw, without replacement, is 2/29.

To find the probability of both events happening (selecting a defective battery followed by another defective battery), we multiply the probabilities of each event:

P(defective battery and then another defective battery) = P(defective battery on first draw) × P(defective battery on second draw)

= (1/10) × (2/29)

= 2/290

= 1/145

Therefore, the probability of selecting a defective battery followed by another defective battery is 1/145.

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The average rate of change of the function in the interval [5, 11] is -82.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The table of values is shown in the image.

The average rate of change of the function in the interval [5, 11],

= the slope of the function in the interval  [5, 11].

= (-623 + 131) / (11 - 5)

= -492/6

= -82

Therefore, -82 is the slope.

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Answer:

-3

Step-by-step explanation:

The slope of the line that passes through the points (-1, 4) and (1, -2) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the values, we get:

m = (-2 - 4) / (1 - (-1))

m = -6 / 2

m = -3

So, the slope of the line is -3.

The rate of change of the area of the triangle after two seconds have passed is 16 cm².

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Area of a right angled triangle = [tex]\frac{1}{2}[/tex] × base × height

Given that, the lengths of the right sides of a right triangle were 12 cm and 16 cm.

Initial area of the triangle = [tex]\frac{1}{2}[/tex] × 12 × 16

                                          = 96 cm²

The first side is increasing at a rate of 2 cm/sec and the second side is decreasing at a rate of 1 cm/sec.

After 2 seconds, length of base = 12 + (2 × 2) = 16 cm

After 2 seconds, length of height = 16 - (2 × 1) = 14 cm

Area of the triangle after 2 seconds = [tex]\frac{1}{2}[/tex] × 16 × 14

                                                            = 112 cm²

Rate of change of area = 112 cm² - 96 cm² = 16 cm²

Hence the rate of change of area is 16 cm².

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The quadrilateral exists not a parallelogram.

The formula to calculate the distance between two points is equal to

[tex]$$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$$[/tex]

We have Q(-10,-2), R(1,-1)

substitute the values in the above equation, we get

[tex]& d=\sqrt{(-1+2)^2+(1+10)^2} \\[/tex]

simplifying the equation, we get

[tex]& d=\sqrt{(1)^2+(11)^2} \\[/tex]

d = √122 units

Find the distance TS

the formula to calculate the distance between two points is equal to [tex]$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$[/tex]

we have

T(-11, -8), S(1, -7)

substitute the values in the above equation, we get

[tex]$d=\sqrt{(-7+8)^2+(1+11)^2}$[/tex]

simplifying the equation, we get

[tex]$d=\sqrt{(1)^2+(12)^2}$[/tex]

d = √145 units

We know that the opposite sides of QR and TS exist.

The opposing sides of a parallelogram are congruent, but in this case, QR TS.

√122 units ≠ √145 units

Therefore, the quadrilateral exists not a parallelogram.

The complete question is:

Determine whether the quadrilateral is a parallelogram using the indicated method Q(-10,-2), R(1,-1), S(1,-7), T(-11,-8) (Distance Formula)

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The only function that represents exponential decay is (A) f(x) = 2(1/3)ˣ.

What is exponential decay?

Exponential decay refers to a process in which a quantity decreases over time, with the rate of decrease becoming proportionally smaller as the quantity gets smaller.

Exponential decay occurs when a quantity decreases over time or space by a fixed percentage of the remaining amount per unit.

This is represented by an exponential function of the form [tex]f(x) = a \cdot b^x[/tex], where a is the initial value and b is the decay factor (a number between 0 and 1).

Among the given options, the only function that represents exponential decay is (A) f(x) = 2(1/3)ˣ.

To see why, note that as x increases, (1/3)ˣ gets smaller and smaller, approaching zero as x goes to infinity. This means that f(x) gets smaller and smaller over time or space, representing exponential decay.

Functions (B), (C), and (D) do not represent exponential decay because their exponential factors 3ˣ, -3ˣ, and 5/3ˣ are either greater than 1 or negative, meaning that the quantity being modeled increases over time or space instead of decreasing.

Hence,  the only function that represents exponential decay is (A) f(x) = 2(1/3)ˣ.

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Answer:

132

Step-by-step explanation:

The pattern is adding 18 napkins, so Friday would be 114 napkins and Saturday would be 132

The value of y in  [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex]  is y = 1.189 for the quadratic-like equation.

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

The equation [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex] is not a traditional quadratic equation, but it can be solved using numerical methods or by using a change of variables.

1) One possible method to solve the equation is to use the Newton-Raphson method, which is an iterative numerical method for finding the roots of a function. This method involves finding a first approximation for the root and then using that approximation to improve the estimate in each iteration until the root is found to a desired level of accuracy.

2) Another possible method is to change the variables to make the equation a traditional quadratic equation. For example, one could substitute  [tex]y\frac{1}{4} = x[/tex] and then solve for x. This would result in the equation [tex]x^{2} - 3x + 2 = 0[/tex], which can be solved using the quadratic formula.

Let us substitute [tex]y\frac{1}{4} = x[/tex]

Then we have x² - 3x + 2 = 0

On solving

⇒ x² -2x -  1x + 2

⇒ x² -2x -  1x + 2

⇒ x(x - 2) -1(x + 2)

⇒ (x - 2)(x - 1)

Thus, x = 1 and x = 2

Solving for y

[tex]y^{\frac{1}{4}} = 2[/tex]

y = [tex]\sqrt[4]{2}[/tex]

y = 1.189

[tex]1.189^{1/2} = 1.09[/tex]

Thus, the value of y in  [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex]  is y = 1.189 for the quadratic-like equation.

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Answer:

About $0.08 per an oz

Step-by-step explanation:

Without the cost of the electrical power, the cash cost of production would be $104,040 + $2460 = $106,500 per year.

What is the addition?

Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

The cost of raw materials can be calculated as follows:

Caprolactam: 1.02 tons per ton of product * 60 tons of product per year = 61.2 tons of caprolactam per year

Cost of caprolactam: 61.2 tons per year * $1700 per ton = $104,040 per year

The cost of utilities can be calculated as follows:

Fuel gas: 9 MMBtu per ton of product * 60 tons of product per year = 540 MMBtu per year

Cost of fuel gas: 540 MMBtu per year * $4.50 per MMBtu = $2460 per year

Cooling water: not a cost as it's a utility not charged

Electrical power: 130 kWh per ton of product * 60 tons of product per year = 7800 kWh per year

Cost of electrical power: Not specified, we need the cost per kWh to calculate it.

Hence, without the cost of the electrical power, the cash cost of production would be $104,040 + $2460 = $106,500 per year. If we had the cost of electrical power, we could add it to this amount to get the complete cash cost of production.

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The rectangular form of z1 is -4 + j3 and the polar form is 5∠153°. The rectangular form of z2 is 1 - j and the polar form is √2∠-45°. The other expressions have similar rectangular and polar forms.

The rectangular form of complex numbers is represented by two coordinates, one real, and one imaginary. The polar form of complex numbers is represented by the magnitude and angle of the number.

In the expression (a), z1 = -4 + j3; the rectangular form is -4 + j3, and the polar form is 5∠153°. In the expression (b), z2 = 1 - j; the rectangular form is 1 - j, and the polar form is √2∠-45°.

In the expression (c), z1 + z2 = -3 + 2j; the rectangular form is -3 + 2j, and the polar form is 2.82∠29.14°. In the expression (d), jz2 = j(1 - j); the rectangular form is j(1 - j) and the polar form is 1∠-135°.

In the expression (e), z1(-1) = 1/z1; the rectangular form is 1/z1, and the polar form is 0.25∠-33.7°. In the expression (f), z1/z2 = (-4+j3)/(1-j); the rectangular form is (-4+j3)/(1-j), and the polar form is 2.24∠-118.4°.

In the expression (g), ez2 = e(1 - j); the rectangular form is e(1 - j), and the polar form is 2.72∠-44.99°. In the expression (h), z1z1 = (-4+j3)(-4+j3); the rectangular form is (-4+j3)(-4+j3), and the polar form is 25∠306°.

In the expression (i), z1z2 = (-4+j3)(1-j); the rectangular form is (-4+j3)(1-j), and the polar form is 7∠-96.6°.

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The sum of two even integers or two odd integers is always even. However, the sum of an even and an odd integer is always odd.

The sum of two even integers or two odd integers is always even because an even integer is a multiple of two. Therefore, if two even integers are added together, the sum will also be a multiple of two (an even integer). Similarly, an odd integer is a multiple of two plus one, so when two odd integers are added together, the sum will be a multiple of two plus two (an even integer). On the other hand, the sum of an odd and an even integer is always odd because an even integer is a multiple of two and an odd integer is a multiple of two plus one. Therefore, when an even and an odd integer are added together, the sum will be a multiple of two plus one (an odd integer).

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The triangle is congruent by the Angle side Angle property.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.

The three parameters that are congruent are:-

BV ≅ BV ( common side)

∠1 ≅ ∠2  ( Bisector)

∠3 ≅ ∠4  ( Bisector)

Hence, the two triangles are congruent with each other.

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Answer:

x = -3

y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}6x-y=-14\\2x-3y=6\end{cases}[/tex]

Multiply the second equation by -3:

[tex]\implies 2x(-3)-3y(-3)=6(-3)[/tex]

[tex]\implies -6x+9y=-18[/tex]

Add this to the first equation to eliminate the term in x:

[tex]\begin{array}{crcrcl}\vphantom{\dfrac12}& 6x & - & y & = & -14\\\vphantom{\dfrac12}+ & (-6x & + & 9y & = & -18)\\\cline{2-6}\vphantom{\dfrac12}&&&8y&=&-32\\\cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies 8y=-32[/tex]

[tex]\implies y=-4[/tex]

Substitute the found value of y into one of the original equations and solve for x:

[tex]\implies 2x-3(-4)=6[/tex]

[tex]\implies 2x+12=6[/tex]

[tex]\implies 2x=-6[/tex]

[tex]\implies x=-3[/tex]

Therefore, the solution to the given system of equations is (-3, -4).

Answer:

Step-by-step explanation:

The given equations to us are ,

In elimination method we eliminate any variable and then find the find the value of second unknown variable. Using that value we can find the value of 1st variable.

Multiply equation 1 by 3 ,

3(6x-y)=-14*3

18x - 3y = -42 ..... (3)

Now subtract equation 2 and 3 to eliminate y as,

2x - 3y - (18x -3y) = 6 -(-42)

2x -3y -18x +3y = 6+42

-16x = 48

x = 48/-16 = -48/16

x = -3

Substitute this value in equation 2 ,

2*(-3) -3y = 6

-6-3y =6

-3y =6+6

-3y = 12

y = -4

And we are done!

Answer:

2A=B

Step-by-step explanation:

use ratio of axis to solve the scale. verify to second axis.

x axis: 4 A to 8 B

set Ratio A/4 = B/8 and solve

2A = B or A = (1/2)B

verify to sefond axis.

y axis: 3A to 6 B

A/3 = B/6

2A = B or A = (1/2)B

Number of outcomes are in R​,

⇒ n (R) = 8 / 19

And, Number of outcomes are not in R,

⇒ n (R') = 11 / 8

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

You take a random token from a bag that contains 8 red, 7 green, and 4 blue tokens.

Hence, Number of outcomes are in R​,

⇒ ⁸ C ₁ / ¹⁹C₁

⇒ 8 / 19

⇒ n (R) = 8 / 19

And, Number of outcomes are not in R,

⇒ 1 - 8/19

⇒ 11 / 8

⇒ n (R') = 11 / 8

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Answer:-5 -5

Step-by-step explanation: Look at the middle of 6 and 4 the middles 5 so the other one is 5 to because is one the same position and how is on the 3 quart is negative so don't forget to add that:)

Answer:2nd one

Step-by-step explanation: look carefully at the problem and you will see one thing that makes the only possible solution graph #2 I dont want to give you the answer just look carefully at the problem.

The amount of the required down payment is $532000.

The amount of the mortgage is $2710260/

The monthly payment for principal and interest is  $7528.5

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

The amount of the required down payment would be 19% of $2800000 which is, = (19/100)×2800000.

= $532000.

Felix obtains a 30​-year mortgage with an interest rate of ​%6.5 which is,

= [(2800000 - 532000)×6.5×30]/100.

= 2268×30×6.5.

= $442260 he has to pay in 30 years in addition to the principal of (2800000 - 532000) = 2268000.

P = $2710260

Now, 30 years has 30×12 = 360 months.

Therefore, His monthly downpayment would be,

= (2710260/360).

= $7528.5

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