10 Points ..........................................................................................

The speed of the bullet is 1000 m/s when A 10 kg gun recoils with a speed of 0.1 m/s after it fires a 0.001 kg bullet.

As we know that here gun + bullet system is isolated from all other external force systems

so here the momentum of the system is always conserved

so we will say

m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f

here we know that

v₁i = v₂i = 0

m₁ = 10kg

m₂ = 0.001kg

v₁f = 0.1m/s

now we will have

0+0  = 10(0.1) + 0.001v₂f

by solving the above equation we will have

v₂f = 1000m/s.

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The correct question is:

A 10 kg gun recoils with a speed of 0.1 m/s after it fires a 0.001 kg bullet. What is the speed of the bullet?

(1) if the loan is paid off after 6 years, the interest paid on the loan is $10,800. (2) $5,400 in interest will be conserved if the debt is repaid in 3 years as opposed to 6 years.

Simple Interest (S.I.) is a technique for figuring out how much interest will accrue on a specific initial sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a cost of ten p.a. for 2 years, they will pay S.I. on the loaned money for those two years.

(a) Using the straightforward interest calculation, we can determine the amount of interest paid on the debt if it is repaid after six years:

I = Prt

where P represents the loan's capital, r represents the interest rate, and t represents the quantity of time (in years).

P is $30 000, r is 6%, and t is 6 years in this example. With these numbers entered into the algorithm, we obtain:

I = 30,000 * 0.06 * 6 = $10,800

Therefore, if the loan is paid off after 6 years, the interest paid on the loan is $10,800.

(b) To calculate the interest saved by paying off the loan after 3 years instead of 6 years, we can calculate the interest paid in both scenarios and then subtract the interest paid at 3 years from the interest paid at 6 years.

If the loan is paid off after 3 years, the total interest paid can be calculated using the same formula as before:

I = 30,000 * 0.06 * 3 = $5,400

By deducting the interest costs at 3 years from of the interest charged at 6 years, we can determine the amount of interest that would have been paid had the debt been repaid after 3 years:

Interest saved = Interest paid at 6 years - Interest paid at 3 years

= 10,800 - 5,400

= $5,400

Therefore, $5,400 in interest will be conserved if the debt is repaid in 3 years as opposed to 6 years.

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High temp ≥ Low temp + difference

High temp ≥ -8°F + 35°F

High temp ≥ 27°F

An inequality is a relationship between two different quantities or expressions.

An inequality may be expressed by a mathematical sentence that uses the following symbols:

< is less than

> is greater than

≤ is less than or equal to

≥ is greater than or equal to

≠ is not equal to

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The conditional of the given statement is;

Option B: Conditional: If an angle is a right angle, then it is not an obtuse angle. True.

Option C: Conditional: If an angle is obtuse, then it is not a right angle. True.

A conditional statement is represented in the form of “if…then”. Let p and q are the two statements, then statements p and q can be written as per different conditions, such as;

p implies q

p is sufficient for q

q is necessary for p

p ⇒ q

By definition, obtuse angles are angles that are greater than 90 degrees.

Right angles are defined as angles that are equal to 90 degrees.

Thus, If an angle is a right angle, then it is not an obtuse angle.

Similarly, If an angle is obtuse, then it is not a right angle.

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Radians are multiplied by 180° radians to convert to degrees.

A unit of measurement for angles that is about 57.3°, or the angle covered in the center of a circle by an arc that has the same length as the radius.

Conversion factor between radians and degrees

One radian, or degree, equals 0.01745329252:

1° = π/180°

0.005555556π = 0.01745329252 rad

There are 57.295779513 radians in a degree.

1 rad = 180°/π \s= 57.295779513°

The angle in degrees is equal to the angle in radians times 180 degrees divided by the constant pi: degrees = radians 180° /

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The percentage increase in the area of Server A to get the area of the Net Area is 460%.

What is area ?

Area is a measure of the amount of surface a two-dimensional shape or figure occupies. It is usually measured in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

a. To find the actual length of the court, we can use the given scale of 1 inch representing 8 feet. From the drawing, the length of the court is approximately 10.5 inches. Therefore, the actual length of the court is:

Actual length = 10.5 inches x 8 feet/inch = 84 feet

b. Receiver A has a length of approximately 2.5 inches and a width of approximately 1 inch. Therefore, the actual dimensions of Receiver A are:

Actual length = 2.5 inches x 8 feet/inch = 20 feet

Actual width = 1 inch x 8 feet/inch = 8 feet

c. The Net Area has a length of approximately 3.5 inches and a width of approximately 2 inches. Therefore, the actual dimensions of the Net Area are:

Actual length = 3.5 inches x 8 feet/inch = 28 feet

Actual width = 2 inches x 8 feet/inch = 16 feet

d. To find the percentage of the area of Server B to the area of Server A, we need to calculate the area of each server. From the drawing, Server A has an area of approximately 2.5 inches x 0.5 inches = 1.25 square inches, and Server B has an area of approximately 1 inch x 1 inch = 1 square inch. Therefore, the percentage of the area of Server B to the area of Server A is:

(Area of Server B / Area of Server A) x 100%

= (1 square inch / 1.25 square inches) x 100%

= 80%

e. The perimeter of Receiver B is approximately (1 inch + 2.5 inches + 1 inch + 2.5 inches) = 7 inches, and the perimeter of the Net Area is approximately (3.5 inches + 2 inches + 3.5 inches + 2 inches) = 11 inches. Therefore, the ratio of the perimeter of Receiver B to the perimeter of Net Area is:

Perimeter of Receiver B / Perimeter of Net Area

= 7 inches / 11 inches

= 7/11

f. The area of Receiver B is approximately 2.5 inches x 2.5 inches = 6.25 square inches, and the area of the Net Area is approximately 3.5 inches x 2 inches = 7 square inches. Therefore, the ratio of the area of Receiver B to the area of Net Area is:

Area of Receiver B / Area of Net Area

= 6.25 square inches / 7 square inches

= 0.893

g. Receiver B and Net Area are not similar rectangles, as they have different dimensions.

h. To find the percentage increase in the area of Server A to get the area of the Net Area, we can calculate the area of Server A and the Net Area, and then find the percentage increase. From the drawing, Server A has an area of approximately 1.25 square inches, and the Net Area has an area of approximately 7 square inches. Therefore, the percentage increase in the area of Server A to get the area of the Net Area is:

[(Area of Net Area - Area of Server A) / Area of Server A] x 100%

= [(7 square inches - 1.25 square inches) / 1.25 square inches] x 100%

= 460%

Therefore, The percentage increase in the area of Server A to get the area of the Net Area is 460%.

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Answer:

Step-by-step explanation:

To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.

To use this formula, we first need to find the slope of the line that passes through the two given points (-4, -2) and (-6, -5). The slope, denoted by m, is given by the formula:

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

where (x1, y1) = (-4, -2) and (x2, y2) = (-6, -5). Substituting these values, we get:

m = (-5 - (-2)) / (-6 - (-4))

= (-5 + 2) / (-6 + 4)

= -3 / -2

= 3/2

So, the slope of the line is 3/2.

Now, we can choose either of the two given points and use it with the slope to write the equation of the line. Let's use the first point, (-4, -2). Substituting the values of x1, y1, and m in the point-slope formula, we get:

y - (-2) = (3/2)(x - (-4))

Simplifying the right side of the equation, we get:

y + 2 = (3/2)(x + 4)

Expanding the right side, we get:

y + 2 = (3/2)x + 6

Subtracting 2 from both sides, we get:

y = (3/2)x + 4

So, the equation of the line that passes through the points (-4, -2) and (-6, -5) is:

y = (3/2)x + 4

Answer: 13

Step-by-step explanation:

the Price of each rose will be $6.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  Masha buys three roses she will have 7 dollars left.

Let's assume the cost of one rose is "x" dollars.

From the first piece of information, we know that if Masha buys three roses, she will have 7 dollars left.

This can be expressed as:

3x + 7 = Masha's initial amount of money

From the second piece of information, we know that Masha needs to borrow 11 dollars to buy nine roses.

This means that the cost of nine roses is:

9x - 11 = Masha's initial amount of money

Since we know that both expressions represent Masha's initial amount of money, we can set them equal to each other:

3x + 7 = 9x - 11

Subtracting 3x from both sides, we get:

7 = 6x - 11

6x = 18

x =3

Therefore, the Price of each rose will be $6.

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Answer:

The correct answer is B. 60 and 64. When y is directly proportional to x, it means that the ratio of y to x remains constant. In this case, when x=6, y=36, which means that the ratio of y to x is 36/6. Since the ratio is constant, we can use that ratio to find the values of y when x=8 and x=10. When x=8, y = (36/6)x8 = 60 and when x=10, y = (36/6)x10 = 64.

Population growth is usually an exponential equation. By forming and solving an exponential equation the population in 2009 will be 11,373,300.08

The exponential equation for population growth is,

P = P₀ ( 1+r)ⁿ

P₀ is the initial population, r is the rate and n is the time.

Here r = 1.5% = 1.5/100 = 0.015

n is 10 years and P₀ is 9800000

Substituting the values in equation,

P = 9800000 ( 1+0.015)¹⁰

     = 9800000 × 1.160 = 11,373,300.08

So with the growth rate of 1.5% over 10 years, the population will grow and reach 11,373,300.08.

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By the concept of a segment parallel to one side of a triangle divides the other two sides in the same ratio FC is equal 36 in.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to one side of a triangle divides the other side in the same ratio.

Therefore, From the given information BE/CE = DF/FC.

3/27 = 4/(x - 2).

3(x - 2) = 108.

x - 2 = 36.

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The statement that would be true from what we have here would be that opposite angles of a parallelogram are congruent. Option C

A special kind of quadrilateral known as a parallelogram is one in which both sets of its opposite sides are parallel and equal.

PQRS is a parallelogram, therefore.

PQ ≅ RS

QR ≅ PS

Using the SSS criterion, PQR and PQS both equal RSP and RQS.

As a result, since the corresponding angles of congruent triangles are congruent, ∠QPS ≅ SRQ and ∠PQR ≅ ∠RSP.

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Answer:

86.1825503

Step-by-step explanation:

190lbs to kg is 86.1825503

On January 31st, the money invested would have amounted to $10,737,418.

What is meant by investment?

An asset or object acquired with the intention of creating income or recognition is referred to as an investment. The purchase of products that are not consumed right away but will be utilised to create wealth down the road is referred to as an investment in an economic outlook. An investment in finance is a financial asset that is purchased with the expectation that it will either continue to generate income or be sold at a profit at a later date.

Given,

 A penny is invested on January 1.

It doubles each day.

We should find the amount on January 31.

First day = 1

Second day = 2

Third day = 4

Fourth day = 8

So basically if it is the xth day of January, then the amount on that day is 2ˣ⁻¹

Therefore on the January 31st, the money invested would have amounted to

2³¹⁻¹ = 2³⁰ = 1,073,741,824 pennies = $10,737,418.24 = $10,737,418

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The conversion of the physical quantities 183cm in length to equivalent mass in pounds is 5.435* 10²⁷ lbs.

What is a physical quantity?

A physical quantity is a property of a substance or system that can be measured and quantified. A value, created by multiplying a numerical value by a unit in algebra, can be used to express a physical amount. Every physical characteristic of a substance or system that can be quantified, or measured in numerical terms, is referred to as a physical quantity in physics. Time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity are the seven base quantities that make up the current SI.

Centimetres(cm) is the unit of length and pounds(lbs) is the unit of mass.

They are physical quantities of a substance.

Both mass and length are not equal to each other but these physical quantities are proportional to each other.

Here we are asked to convert 183cm to lbs.

We know the force between two bodies M and M' is

The ratio of gravitational constant G and the speed of light c can be used as a conversion factor for length to mass.

G/c² = 7.424 * 10⁻²⁸  m/kg

183 cm = 1.83m = 1.83 m / 7.424 * 10⁻²⁸  m/kg = 2.465 * 10²⁷kg

1kg = 2.205 lbs

2.465 * 10²⁷kg * 2.205 = 5.435* 10²⁷ lbs

Therefore the conversion of the physical quantities 183cm in length to equivalent mass in pounds is 5.435* 10²⁷ lbs.

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Answer:

NM=5, NL=4.3

Step-by-step explanation:

Using Poisson distribution, the probability mass function is approximately 4.2%

To solve the problem, we can use the Poisson distribution since we are interested in the probability of a certain number of events (in this case, cars with 4 occupants) occurring in a given time period (morning commute).

The Poisson probability mass function is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable (number of cars with 4 occupants), λ is the mean (average) number of occurrences in the given time period (morning commute), and k is the number of occurrences we are interested in (k = 4 in this case).

Since the average number of non-driver passengers per car is 0.52, we can assume that the average number of total occupants (including the driver) is 1.52. Therefore, the mean (average) number of cars with 4 occupants in a given time period can be calculated as:

λ = (1.52)^4 * e^(-1.52) / 4!

Using a calculator, we get λ ≈ 0.0331.

Now we can plug in the values of λ and k into the Poisson probability mass function:

P(X = 4) = (e^(-0.0331) * (0.0331)^4) / 4!

Using a calculator, we get P(X = 4) ≈ 0.042

Therefore, the probability that a randomly selected car passing through the toll booth during the morning commute has 4 occupants (the driver and 3 passengers) is approximately 0.042 or 4.2%.

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Answer:

Step-by-step explanation: Yes, but ONLY when you are multiplying or dividing.

The equation is given by 5n + 100n = 210

Peggy has 8 quarters and 2 nickels

Let's call q the number of quarters and n the number of nickels.

If Peggy has four times as many quarters as nickels, we can write the following equation:

q = 4n

Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so

0.25q + 0.05n = 2.10

Because she had $2.10. Now, we can replace the first equation on the second one

0.25(4n) + 0.05n = 2.10

1n + 0.05n = 2.10

Finally, we can multiply both sides by 100, so

100n + 0.05(100)n + 2.10(100)

100n + 5n = 210

Therefore, the equation that can be used to solve the problem is

5n + 100n = 210

Now, we can solve the equation for n

105n = 210

105n/105 = 210/105

n = 2

Then, q is equal to

q = 4n

q = 4(2)

q = 8

It means that Peggy has 8 quarters and 2 nickels.

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complete question is listed below:

Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?

Which of the following equations could be used to solve the problem?

On+4 n=210

5 n+100 n=210

n+4 n=2.10

5n+100 n=2.10.

The set of all shows for the overall group would be well-defined because it would include all seven shows from the Friday night line-up, ordered from most watched to least watched among all viewers.

A set is well-defined if it is clear which elements belong to the set and which do not. In this case, each set (the set of sitcoms, the set of dramas, and the set of all shows) is well-defined because each show is clearly identified as either a sitcom or a drama and is ordered from most watched to least watched within its respective group (women, men, and overall).

Therefore, each set is well-defined.

For example, the set of sitcoms for the women's group would be well-defined because it would include the four sitcoms from the Friday night line-up, ordered from most watched to least watched among women. Similarly, the set of dramas for the men's group would be well-defined because it would include the three dramas from the Friday night line-up, ordered from most watched to least watched among men.

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The distance the submarine needs to travel to get to the destination is 15 feet.

Distance is a numerical measurement of how far apart two points or objects are in space. In mathematics, distance is typically measured using the Euclidean distance formula, which applies to points in two- or three-dimensional space.

The Euclidean distance between two points, (x1, y1) and (x2, y2), in a two-dimensional plane is given by the formula:

d = √[tex][(x2 - x1)^2 + (y2 - y1)^2][/tex]

where the symbol √ represents the square root function.

Similarly, the Euclidean distance between two points, (x1, y1, z1) and (x2, y2, z2), in a three-dimensional space is given by the formula:

d = √[[tex](x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2][/tex]

The distance between two points can be positive or zero, but it cannot be negative. Distance is an important concept in many areas of mathematics and science, such as geometry, physics, and engineering. It is also used in real-life applications, such as navigation, transportation, and sports.

There are other measures of distance used in different contexts, such as Manhattan distance or taxicab distance, which measure the distance between two points by the sum of the absolute differences of their coordinates, rather than the square of the differences as in Euclidean distance. Additionally, distance can be defined in different ways for objects other than points, such as for the distance between two lines or two planes in geometry.

To determine the distance the submarine needs to travel to get to the destination, we need to calculate the vertical distance between the submarine and the destination point.

The vertical distance is the difference between the destination point and the submarine's current position:

Distance = Destination Point - Submarine's Position

Distance = (-10.5 ft) - (4.5 ft)

Distance = -15 ft

Therefore, the distance the submarine needs to travel to get to the destination is 15 feet.

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The speed of sound in seawater is around 4.46 times faster than speed of sound in air.

Unit conversion is the process of converting the measurement of a given quantity between different units, often by multiplicative conversion factors that modify the value of the measured quantity without altering

its effects.

Speed of sound, the rate at which sound waves move through various substances. Modern estimates of the speed of sound, specifically for dry air at a temperature of 0 °C (32 °F), are 331.29 metres (1,086.9 feet) per second.

Now in the given question ,

speed of sound in air is 1225 km/hr.

speed of sound in sea water = 1520 m/s.

To compare the speed of sound we have to make them in same unit form.

So , we will change speed of sound in air in m/s.

speed of sound in air = 1225 km/hr

                                     [tex]=\frac{1225*1000}{60*60} m/s\\\\=\frac{12250}{36} m/s\\\\=340.28m/s[/tex]

So , it can be clearly seen that speed of sound in air is less than speed of sound in  seawater.

Also , the speed of sound in seawater is around 4.46 times faster than speed of sound in air.

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The man has to pay Rs 9,000 as Ushr for 80 tons of apples

Multiplication is a basic arithmetic operation that involves combining equal groups or adding the same number repeatedly. It is represented using the multiplication symbol × or the asterisk *.

To calculate the Ushr, we first need to convert the weight of the apples from tons to kilograms, since the price is given in rupees per 40 kg:

80 tons = 80,000 kg

Next, we need to find out how many 40-kg units are in 80,000 kg:

80,000 kg / 40 kg = 2,000 units

Therefore, the man sold his apples in 2,000 units of 40 kg each. To find the total revenue frm the sale, we need to multiply the price per unit by the number of units:

2,000 units x Rs 1800/40kg = Rs 90,000

The Ushr is typically calculated as one-tenth of the total revenue, so in this case:

Ushr = 1/10 x Rs 90,000 = Rs 9,000

Therefore, the man has to pay Rs 9,000 as Ushr.

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The two x-intercepts of the quadratic function are:

x = 8.69

x =  -0.69

Here we want to find the x-intercepts of the function:

f(x) = -x^2 + 8x + 6

Then we need to solve:

0 =  -x^2 + 8x + 6

Using the quadratic formula we will get the solutions:

[tex]x = \frac{-8 \pm \sqrt{8^2 - 4*(-1)*6} }{2*-1} \\\\x = \frac{-8 \pm 9.38 }{-2}[/tex]

Then the two solutions are:

x = (-8 - 9.38)/-2 = 8.69

x = (-8 + 9.38)/-2 = -0.69

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C is the correct answer. If there is a total of 399 pages, adding the pages she has left to the pages she has already read (266 pages) it would equal the total, that she has to read 133 pages still.

By using the current exchange rate for converting "Japanese Yen" to "US Dollar" , 500000 Yen is = 3729.12 USD .

To convert the amount of 500000 YEN to USD, we use the current exchange rate between the currencies  "Japanese Yen" and the "US Dollar" .

The exchange rate varies constantly due to fluctuations in the global financial markets ,

The current exchange rate of 1 US Dollar = 134.08 Japanese Yen  ,

We have to convert the amount 500000 yen to USD by dividing 500000 by 134.08  ;

⇒ 500000/134.08 = 3729.1169 USD ;

≈ 3729.12 USD .

Therefore, 500000 Japanese yen is approximately equal to 3792.12 US Dollars .

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Answer:

30√5 + 7√2

Step-by-step explanation:

To simplify this expression, we can first use the fact that the square root of a product is equal to the product of the square roots. We can also simplify any perfect squares under the square root sign.

5√180 + 4√18 - √50

= 5√(36 × 5) + 4√(9 × 2) - √(25 × 2)

= 5√36 × √5 + 4√9 × √2 - √25 × √2

= 5 × 6√5 + 4 × 3√2 - 5√2

= 30√5 + 12√2 - 5√2

= 30√5 + 7√2

Therefore, the simplified form of the expression is [30√5 + 7√2.]

Answer:

y^2 - 5y = 750

Step-by-step explanation:

If length = y

then width = y - 5

Area = length x width

= y(y-5) = 750

Or, y^2 - 5y = 750

This equation can be further solved as follows:

y^2 - 5y - 750 = 0

Or, y^2 - 30y + 25y - 750 = 0

Or, y(y - 30) + 25(y - 30) = 0

Or, (y + 25)(y-30) = 0

So, there are two possibilities:

If (y + 25) = 0

then y = -25

but value of length cannot be negative,

Let us look at second possibility

If (y - 30) = 0

then y = 30

So, length = 30 feet

Check Answer:

Length = 30 feet

so, width = 30 - 5 = 25 feet

so, area  = 30 x 25 = 750 square feet

Henry had deposited approximately $8,000.32 if he received $13,299.23 after 5 years. Rounded to the nearest dollar, the answer is $8,000.To solve this problem, we can use the formula for compound interest:

[tex]$$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$[/tex]

where A is the amount after t years, P is the principal (the amount deposited), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have:

A = $13,299.23

r = 0.08 (8%)

n = 4 (quarterly compounding)

t = 5 years

We can rearrange the formula to solve for P:

[tex]P = \frac{A}{(1 + \frac{r}{n})^(nt) }[/tex]

Plugging in the values, we get:

[tex]P = \frac{ $13,299.23}{(1 + \frac{0.08}{4} ) ^ {(4*5)} }[/tex]

P ≈ $8,000.32

Therefore, Henry had deposited approximately $8,000.32 if he received $13,299.23 after 5 years. Rounded to the nearest dollar, the answer is $8,000.

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Answer:

x = 12

x = 9

Step-by-step explanation:

See picture below :)