What to work this problem

Answer:

x=$3059.00

Step-by-step explanation:

To solve this equation, we need to use the properties of exponential functions and perform some algebraic manipulations. First, we can simplify the right-hand side of the equation by combining the constant terms and the exponent on the x:

$4001.035 = $105 + x(1.03)3 + x(1.032)

Next, we can combine the x terms on the left-hand side by multiplying them out and combining the exponents:

x(1.03)3 + x(1.032) = x(1.03)3 + x(1.03)(1.03) = x(1.03)4

Now we have:

$4001.035 = $105 + x(1.03)4

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 105 from both sides:

$3900.035 = x(1.03)4

Next, we divide both sides by 1.03^4

x = $3900.035 / (1.03)^4

x = $3,059.00

x= $3059.00 (rounded to the nearest cent)

The length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

Now, According to the question:

The area of a rectangular page can be calculated using the area of a rectangle which is just the product of the length and the width of the page.

                                                         A = lw

Here, l represents the length of the page and w represents the width of the page.

Determine the dimensions of a page given that the printed area is [tex]30in^2[/tex]

and the page has margins on each side, each having a width of 1in.

We will first set up an equation using the details that we know. We know that the printed area is  [tex]30in^2[/tex] We can let x be the length of the printed area and y be the width of the printed area. Assuming that the printed area is rectangular, the area is

[tex]A_p=xy[/tex]

30 = xy

[tex]y = \frac{30}{x}[/tex]

Now, we want to minimize the amount of paper used. The length of the entire page would be x + 2 since we have to consider the 1-in margins at the top and the bottom. Similarly, the width would be y+ 2  since we have to consider the margins at the sides. The area of the page is as follows.

A = (x+2)(y + 2)

We can substitute the value of y in terms of x.

A(x) = (x + 2)([tex]\frac{30}{x} +2[/tex])

A(x) = x ([tex]\frac{30}{x}[/tex]) + 2x + 2[tex](\frac{30}{x} )[/tex] + 4

A(x) = 30 + 2x + [tex]\frac{60}{x}[/tex] + 4

A(x) = 34 + 2x + [tex]\frac{60}{x}[/tex]

We want to minimize this area, so we will apply differentiation to this function. By finding its derivative and equating it to zero, we can find the value/s of x that will minimize the area.

A'(x) = [tex]2-\frac{60}{x^2}[/tex]

0  = [tex]2-\frac{60}{x^2}[/tex]

[tex]2 =\frac{60}{x^2}[/tex]

[tex]2x^2=60\\\\x^{2} =\frac{60}{2}\\ \\x^{2} =30\\\\x =[/tex]±[tex]\sqrt{30}[/tex]

Since we are dealing with dimensions, we can only choose the positive value, x =√30. Now, to determine if this would really minimize the area of the page, we can substitute it into the second derivative of the function. If the result is positive, the value of x would give the minimum area.

A"(x) = [tex]\frac{120}{x^3}[/tex]

[tex]A"(\sqrt{30} )=\frac{120}{(\sqrt{30})^3 }[/tex]

[tex]A"(\sqrt{30} )=0.73[/tex]

We can now use the value of x to find the dimensions of the page. Take note that the dimensions of the page are x + 2 and y + 2

x + 2 = √30 + 2

y + 2 = [tex]\frac{30}{x}[/tex] + 2

y +2  = [tex]\frac{30}{\sqrt{30} }[/tex] + 2

y + 2 = [tex]\sqrt{30}+2[/tex]

Therefore, the length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

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Answer:

5 cookies and 4 brownies

Step-by-step explanation:

First, let's assign variable for cookies and brownies:

x= cookies

y= brownies

Now, let's create an equation with the information given to us:

[Note: "#of brownies + 8" equals the number of cookies because, in the question, we are told He bought 8 more cookies than brownies ]

cost of a brownie * #of brownies +  cost of a cookie * (#of brownies + 8 ) = $7.50

1.25y + 0.5x = 7.5

Since we want to solve the problem graphically, let's solve our equation for y, so it can be graphed:

1.25y + 0.5x = 7.5   [Subtract 0.5x from both sides]

1.25y = -0.5x + 7.5   [Divide both sides by 1.25 so we just get y]

y = -0.4x + 6

This equation will be used to determine what we can buy at the bakery with $7.50.

Now, we will graph the equation (see attached image). What we will see is that as x increases, y decreases. This makes sence, since the number of brownies (y) you can buy with your budget decreases as the number of cookies (x) you buy increases. Lastly, since we can't buy a fraction of a cookie, we want to find a coordinate on the line that has both a natural [see definition if confused] x and y value. To do this, we will look at the graph and see if a x value of 1 gives us a natural y value. If not, we go on to 2 and see if it gives us a natural y value. This continues until you find both a natural x and y value. This will happen at x=5 and y=4. This answer tells us that, with $7.50, Qasim and his children bought 5 cookies and 4 brownies.

*Natural number: Positive, whole numbers

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10.44 Percent of increase in the price of a basketball .

A percentage is a number or ratio that is expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to denote it. A percentage is a dimensionless number; there is no specific unit of measurement for it.

By divided the number by the entire value and multiplying the outcome by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

The price of basketball increased = $18.50 -$16.75 = 1.75$

Now the percent of increase in the price= 1.75/16.75×100

= 10.44%

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Using mathematical operations, since 1/3 of the sundaes Lisa is making are mint, and 1/2 of the remaining (or 1/3) are chocolate, the number of vanilla sundaes is 10.

The basic mathematical operations are addition, subtraction, division, and multiplication.

Mathematical operations can be applied to any mathematical problem to find their solutions.

The total number of Sundaes Lisa is making = 30

The proportion of the sundaes that are mint ice cream = 1/3

The proportion of the sundaes that are = 1/3 (1/2 of 2/3)

The vanilla proportion = 1/3 (1 - 1/3 - 1/3)

The number of sundaes that will be vanilla = 10 (30 x 1/3)

Thus, determining the fractional values using mathematical operations, Lisa is making an equal number of mint, chocolate, and vanilla ice cream.

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The role of the media in a democracy is essential for a free and informed society.

Democracy is a form of government in which power is held by the people through their elected representatives. It is based on the principle of political equality and rule of law, where all citizens have an equal say in the decisions that affect their lives. It is a system of government in which citizens have the right to vote, stand for office, and participate in decision-making processes that shape their communities and the nation as a whole.

The media acts as a watchdog for the government, keeping them accountable and ensuring that the people are aware of the decisions being made. It also provides a platform for citizens to express their opinions and to discuss important issues. Additionally, the media can help to educate the public on important topics, such as politics, economics, and social issues. This helps to ensure that citizens are well informed and can make informed decisions when voting or engaging in other forms of political participation.

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Answer:

below

Step-by-step explanation:

This is isosceles because you have TWO equal sides

Equilateral has THREE equal sides

The solution is Option B.

The scale factor of the translated triangle is S = 16

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the perimeter of the first triangle be P

The value of P = 3 m

Now , the triangle is translated by a scale factor of S

And , the perimeter of the translated triangle = 48 m

So , the scale factor = perimeter of the translated triangle / perimeter of the first triangle

Substituting the values in the equation , we get

The scale factor of the translation S = 48/3

The scale factor of the translation S = 16

Hence , the scale factor is 16

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The scale factor of the triangles will be 16:1. The correct option is B.

A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size.

It aids in altering the figure's size but not its shape. The scale factor is defined as the proportion of the new image's size to that of the previous image.

Given that a triangle with a perimeter of 48 meters was created from a triangle with a perimeter of 3 meters using a scale factor.

The scale factor will be calculated as:-

Scale factor = 48 / 3

Scale factor = 16: 1

Therefore, the scale factor of the triangles will be 16:1. The correct option is B.

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Answer:

80 months

Step-by-step explanation:

If the present monthly heating costs average $300, but the insulation is expected to reduce heating costs by 10%, then there will be a monthly saving of 10%:

[tex]\implies \rm Monthly\;saving=10\%\;of\;\$300 =\dfrac{10}{100} \times \$300=\$30[/tex]

To calculate how many months it will take to recover the cost of the insulation, divide the cost of installing the insulation by the monthly saving:

[tex]\implies \rm Number\;of\;months=\dfrac{\$2400}{\$30}=80[/tex]

Therefore, it will take 80 months to recover the cost of the insulation.

Answer:

80 months

Step-by-step explanation:

The expected monthly savings from the insulation are: $300 × 10% = $30.

So, the number of months required to recover the cost of the insulation, $2400, is $2400/$30 = 80 months.

Given: f(x)=  4x 2 +1 / x

​When we differentiate both sides in relation to x, we obtain

f ′ (x)=  x(8x)−(4x² +1)/x² = 4x² −1 / x²

​(a) To improve function.

f  (x)≥0

⇒ 4x²-1/ ≥0

⇒ 4x²- 1 ≥ 0

⇒ (2x-1) (2x+1) ≥0

⇒ x ≥ 1/2 or x≤ -1/2

So, f(x) is increasing function on (-∞, -1/2] ∪ [1/2,∞)

(b) for decreasing function,

⇒ 4x²-1/x² ≤0

⇒ 4x²-1 ≤0

⇒(2x - 1) (2x+1)≤0

⇒ x ≤ 1/2 or x≥ -1/2

so, f(x) is decreasing on [-1/2, 1/2]

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​

Between the ages of 14 and 16, g(x) increases by a factor of 64/56 = 1.1429.

A defined range of values inside a piece of data is known as an interval. It measures the spread of the data and is defined as the difference between the maximum and minimum values of the data set. Intervals can be applied in many different contexts, from tracking the evolution of data distribution to spotting trends. Additionally, outliers and unusually high or low values in a data collection can be found using intervals. In statistics, interval data are frequently used to quantify data variability.

Divide the value of g(16) by the value of g to find the factor by which g(x) increases across the range of 14 to 16. (14).

G(14) has a value of 56, and G(16) has a value of 64.

Therefore, 64/56 = 1.1429 is the factor by which g(x) increases between 14 and 16.

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Answer:

The future value of the annuity is $14,170.

The total amount invested is $39,000.

The interest earned is $14,170 - $39,000 = -$24,830

Step-by-step explanation:

The future value of the annuity can be calculated using the formula:

FV = P * (1 + r)^n

where FV is the future value, P is the annual payment, r is the annual interest rate, and n is the number of years.

In this case, the annual payment is $13,000, the annual interest rate is 3%, and the number of years is 3. So, the calculation is:

FV = $13,000 * (1 + 0.03)^3

FV = $13,000 * 1.09

FV = $14,170

So, the future value of the annuity is $14,170.

How much was invested?

The annual payment is $13,000. We multiply that by the number of years of the investment, 3 years. The total amount invested is $39,000.

How much interest was earned?

We can calculate the interest earned by subtracting the total amount invested from the future value.

The interest earned is $14,170 - $39,000 = -$24,830

So, the future value of the annuity is $14,170, the total amount invested is $39,000 and the interest earned is -$24,830.

Due to length restriction, we kindly invite to check the explanation for further details on profit and risk minimization.

In this problem we find the case of a person that invests a lot of money, distributed in two investments. We need to determine how much money must be invested in each plan to earn a desired return:

R = (C - c) · (r₁ / 100) + c · (r₂ / 100)

Where:

Part A - If we know that R = 9300, C = 91000, r₁ = 10 and r₂ = 11, then the amount invested in the most risky investment:

9300 = (91000 - c) · (10 / 100) + c · (11 / 100)

930000 = (91000 - c) · 10 + c · 11

930000 = 910000 - 10 · c + 11 · c

c = 20000

The person must invest $ 20000 in the least risky investment and $ 71000 in the most risky investment.

Part B - The use of two accounts gives a reasonable equilibrium between profit and risk minimization.

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The number of number plates assigned is 40,219,200.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, a seven-digit license plate with the following pattern: L L N – L N N N.

There are 3 letters with the restriction of no vowels and 4 numbers between 0-9.

With no vowels, we have 21.

= 21!/3!(21-3)! + 10!/(10-4)!

= 7980×5040

= 40,219,200

Therefore, the number of number plates assigned is 40,219,200.

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16.25 percent the total number of students on the honor roll decreased.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, last year at a certain high school, there were 140 boys on the honor roll and 100 girls on the honor roll.

This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 6%.

So, the number of boys = 140 - 25% of 140

= 140 - 0.25×140

= 140 - 35

= 105

The number of girls = 100 - 6% of 100

= 96

Total number of students last year = 140+100

= 240

Total number of students this year = 105+96

= 201

Difference = 240-201

= 39

Now, percentage decrease = 39/240 ×100

= 0.1625×100

= 16.25%

Hence, 16.25 percent the total number of students on the honor roll decreased.

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$120.00 increased by 20% is $144.00

Answer:

see below

Step-by-step explanation:

2x+5y=50.25

3x+4y=53.50

use 2nd equation minus first equation to get

x-y=3.25

so x = 3.25+y

substitute x with above equation

2*(3.25+y) +5y =50.25

so 6.5+2y+5y = 50.25

7y = 43.75

y=6.25

x=3.25+y =9.5

Answer:

The dimensions of the garden are not provided in the question, so it is not possible to determine the area for which Jane needs to buy mulch. Without knowing the dimensions, there is not enough information to answer the question.

Step-by-step explanation:

The quadratic regression in this case is y = 126.01x2 - 312.04x + 888.88.

An analysis tool called quadratic regression is implemented to identify the parabola equation that perfectly matches a given collection of data. Finding the equation of the straight line that most closely matches a collection of data is the goal of this sort of regression, which is an expansion of simple linear regression.

Step 1:  Input the data sets into the graphing calculator.

Step 2: Choose "Scatter Plot" from the graphing calculator's interface.

Step 3: Choose "Quadratic Regression" from the graphing calculator's toolbar.

Step 4: The calculator will create the equation y=ax2+bx+c, where a, b, and c are constants.

Step 5: Round the constants to the hundredths place, and the best-suited quadratic model's equation will be: y = 0.06x2 - 3.12x + 4.00.

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Applying the exterior angle theorem, m<JKL = 22 degrees.

According to the exterior angle theorem, the following equation is created to find the value of x:

5x - 3 = x - 1 + 2x + 8

Combine like terms:

5x - 3 = 3x + 7

5x - 3 - 3x = 3x + 7 - 3x

2x - 3 = 7

Add 3 to both sides

2x = 10

x = 5

Find the measure of m<JKL (exterior angle):

m<JKL = 5x - 3

Plug in the value of x:

m<JKL = 5(5) - 3 = 22 degrees.

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Answer: The answer is 6.75

Step-by-step explanation:

I did the math :b

Answer:

B

Step-by-step explanation:

9x² - y² = 1

use the power rule to differentiate

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = an[tex]x^{n-1}[/tex]

[tex]\frac{d}{dx}[/tex] (y² ) = 2y [tex]\frac{dy}{dx}[/tex]

[tex]\frac{d}{dx}[/tex] ( constant ) = 0

differentiate both sides with respect to x

9 × 2x - 2y [tex]\frac{dy}{dx}[/tex] = 0 , that is

18x - 2y[tex]\frac{dy}{dx}[/tex] = 0

Answer:The missing length can be found using the formula for the area of a triangle, which is:

Area = (base * height) / 2.

We know the base is 18.7 inches and the area of the shaded region is 152.405 in^2.

So, the height can be found using the formula:

152.405 = (18.7 * height) / 2

Solving for height:

height = 2 * 152.405 / 18.7

height = approximately 12.67 inches.

Answer:

  No

Step-by-step explanation:

You want to know if -8 is irrational.

A number is irrational if it has a decimal fraction part that does not terminate and does not repeat.

If you can describe all of the digits of the number explicitly without resort to functions or symbols, the number is not irrational.

  -8 is not irrational

Answer:

4x - 7

Step-by-step explanation:

The x represents Bob's age since, we don't know what it is, I put it as a variable.

2x      This represents Jeff who is 2 times Bob's age.

x - 7    Peter is younger than Bob by 7 years so we need to take away 7                    from Bob's age

2x + x - 7 + x    This would be the expression

4x - 7                Now just combine the like terms. We don't have Bob's age so the expression will stay like this.

By the synthetic division method, the polynomial x³ - 2x - 8 dividing by x - 2 will get a remainder -4.

Given the polynomial,

x³ - 2x - 8

dividing a polynomial by x - 2

Solution will be :

Coefficients are required for Synthetic Division.

As a result, the coefficients are :

1, 0, -2, -8

as well as we have x-2

2   1   0  -2   8

          2   4    4              

------------------------

      1    2   2   -4

By synthetic division, the remainder is now -4.

Substituting  the polynomial in x = 2 the Remainder theorem yields the required remainder.

  = 2³ -2 x 2 - 8

  = 8 -4 -8

  = -4

Which is equivalent to synthetic division. Therefore the correct division is option B.

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Gina Wilson is an Australian intersex human rights activist. She was the founding president of Intersex Human Rights Australia

Define parallel lines?

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Following are the different sides of the triangles -

The line segment that divides a triangle in half and connects one vertex to the middle of the other side is known as the median in geometry. There are an equal number of medians at each vertex of a triangle, and they all intersect at the triangle's centroid.

The triangle's three medians are the line segments with endpoints at the triangle's vertices and the midpoint of the opposite side. The point where all medians converge is known as the centroid.

1. The sides are in same ratio,

[tex]\frac{24}{9} = \frac{32}{x}\\[/tex]

⇒ [tex]x = \frac{32 \times 9}{24}[/tex]

⇒ [tex]x = 12[/tex]

2. [tex]\frac{20}{14} = \frac{33}{x}[/tex]

⇒ [tex]x = \frac{33 \times 14}{20}[/tex]

⇒ x = 23.1

3. [tex]\frac{x+ 5}{30} = \frac{16}{20}[/tex]

⇒ [tex]x = \frac{16 \times 30 }{20} - 5\\x = 19[/tex]

4. [tex]\frac{x+8}{2x - 5} = \frac{20}{22.5}[/tex]

⇒ [tex]22.5x + 180 = 40x - 100\\[/tex]

⇒ [tex]17.5 x = 280[/tex]

⇒ [tex]x = 16[/tex]

8. [tex]\frac{33}{41.8} \neq \frac{45}{57}[/tex]

∴ ST is not parallel to PR.

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From the given triangle, the value of sin Θ is 3/√34.

To find the value of sin Θ, we have to know the definition of sin Θ first. Sin Θ can be calculated using formula of:

sin Θ = the front side : the hypotenuse

Based on the given triangle, we need to find the lenght of hypotenuse first to be able to find the value of sin Θ. The hypotenuse of the given triangle is:

h = √(5² + 3²)

h = √(25 + 9)

h = √34

The exact value of sin Θ is:

sin Θ = 3 / √34

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According to the information, 11 boxes and 2 units are required to complete the order.

To find the number of boxes and units required to complete the order we must perform the following procedure:

If we know that each box can hold 8 units and the order is for 90 units, then we divide the total number of units by the number of units per box.

So we know that we are going to need 11 boxes to complete part of the order. Now, to know how many units we have left without storing we must multiply 8 * 11 and subtract the result from 90:

According to the above, the number of boxes would be 11 and the number of units would be 2.

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Answer:

Step-by-step explanation:

The quantity of cells that will be in the culture on the 8 day assuming the number of cells is growing at an exponential rate would be = 128,000 cells.

An exponential rate of growth is defined as the increase in the population of an object under study over a period of time.

The number of cells the scientist started with = 1,000 cells

The number of cells in 4th day = 64,000

Therefore the rate of growth of cells per day;

= 64000/4

= 16,000

Therefore on the 8th day, the number of cells would be = 8×16000 = 128,000 cells.

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