In the figure, OAPB is a quadrant of a circle and OAP is a sector. If | AOP = 30° and the area of the shaded region is 462 cm2, then find the length of the arc PB. A P B​

Answer:

50

Step-by-step explanation:

To determine the total number of kilograms from 15 boxes, we need to know the weight of one box. Let's assume that one box contains 50 sachets (this is just an assumption, the actual number may vary). Then the weight of one sachet is 4 grams or 0.004 kilograms.

the weight of one box is:

50 sachets x 0.004 kg/sachet = 0.2 kg

the total weight of 15 boxes is:

15 boxes x 0.2 kg/box = 3 kg

the total weight of 15 boxes is 3 kilograms.

to determine whether the 15 boxes will be enough to last for a year, we need to know how many sachets a person uses in a day. Let's assume that a person uses one sachet per day.

then the total number of sachets used in a year is:

1 sachet/day x 365 days = 365 sachets

the total number of sachets in 15 boxes is:

15 boxes x 50 sachets/box = 750 sachets

since 750 sachets is greater than 365 sachets, 15 boxes will be enough to last for a year.

to determine the number of sachets that will make one box, we need to know the weight of one box and the weight of one sachet. Let's assume that one box weighs 0.2 kg and one sachet weighs 4 grams or 0.004 kg.

then the number of sachets in one box is:

number of sachets = weight of box / weight of one sachet

number of sachets = 0.2 kg / 0.004 kg

number of sachets = 50 sachets

therefore, one box contains 50 sachets.

The value of each investment scenario based on the given interest compounded will be:

Let's discuss each scenario we have.

The value of Rod's annuity after 20 years will be $30,904.95. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.88%), n is the number of times compounded per year (quarterly, or 4), and t is the number of years (20).

The value of Bubba's investment after 25 years will be $41,438.55. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.26%), n is the number of times compounded per year (monthly, or 12), and t is the number of years (25).

The equivalent APY for the account at Crab Key Bank with an annual interest rate of 5.15% compounded quarterly is 5.25%. This is calculated by using the formula APY = (1+r/n)^n - 1, where r is the annual interest rate (5.15%), and n is the number of times compounded per year (quarterly, or 4).

The difference between an investment earning 8.75% annual interest compounded quarterly and one earning 8.7% compounded monthly is the number of times the interest is compounded each year. An investment earning 8.75% compounded quarterly has an interest rate of 8.75% that is compounded four times per year, while an investment earning 8.7% compounded monthly has an interest rate of 8.7% that is compounded twelve times per year.

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It can be concluded that 3¹⁵⁰ is the greater among them.

This question can be solved if we use the numerical factorization concepts

First, we do the factorization, looking for a number that is common between divisors 3 and 5

[tex]\begin{array}{r|l}\sf 100,150 & \sf 2\\\sf 50,75 & \sf 2\\\sf 25,75 & \sf 3\\\sf 25,25 & \sf 5\\\sf 5,5 & \sf 5\\\sf 1,1&\sf 1\end{array}[/tex]

With this, we can see that the number 25 is common between divisors 3 and 5.
It will be our main exponent, when factoring the exponents 100 and 150.

[tex]\begin{array}{cc}\sf 5^{100}&\sf 3^{150}\\\raisebox{5pt}{$\sf \Big(\big[5^{2}\big]^{2}\Big)^{25}$}&\raisebox{5pt}{$\sf \Big(\big[3^{2}\big]^{3}\Big)^{25}$}\\\raisebox{5pt}{$\sf \big(5^{4}\big)^{25}$}&\raisebox{5pt}{$\sf \big(3^{6}\big)^{25}$}\\\raisebox{5pt}{$\sf 625^{25}$}&\raisebox{5pt}{$\boxed{\bf729^{25}}$}\end{array}[/tex]

Since 729²⁵ > 625²⁵, it follows that 3¹⁵⁰ is the greater of the two

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If you have any question about this solution, you can ask me in the comments :)

Answer: Approximately 2 * AC = 737.2 meters. Rounded to the nearest tenth, the answer is 737.2 meters.

Step-by-step explanation: To solve the problem, we can draw a diagram:

              A

             /|

            / |

           /  |  x

          /   |

         /    |

        /θ    |

       /      |

      /       |

     /        |

    /         |

   /          |

  B-----------C

          y

where A and B are the entrances of the tunnel, C is the point in the middle of the tunnel that we want to find, and θ, x, and y are the angles and distances given in the problem. We want to find the length of AC.

Using trigonometry, we can find the distances BC and AB: tan(57°) = x / y  =>  x = y * tan(57°)

tan(14°) = x / (y + 212)  =>  x = (y + 212) * tan(14°)

Setting these two expressions for x equal, we get: y * tan(57°) = (y + 212) * tan(14°)

Solving for y, we get: y = 212 / (tan(57°) / tan(14°) - 1) ≈ 286.5 meters

Now we can use the law of sines to find the length of AC: sin(θ) / AC = sin(14°) / BC = sin(57°) / AB

Solving for AC, we get: AC = AB * sin(θ) / sin(57°) ≈ 368.6 meters

Therefore, the length of the entire tunnel is approximately 2 * AC = 737.2 meters. Rounded to the nearest tenth, the answer is 737.2 meters.

Answer:

n ≤ -48

Step-by-step explanation:

The correct answer is D. The value of a in the equation of the second function is greater than 1.

A quadratic function is a type of function in algebra that can be written in the form f(x) = ax² + bx + c, where a, b, and c are constants (coefficients) and x is the independent variable. The graph of a quadratic function is a parabola, which is a U-shaped curve.

The coefficient a determines whether the parabola opens upwards (if a > 0) or downwards (if a < 0). The point where the parabola changes direction is called the vertex, which is located at the point (-b/2a, f(-b/2a)).

The coefficient b determines the horizontal position of the vertex, and c determines the vertical position of the vertex.

We know that the parent quadratic function f(x) = x² is a U-shaped curve with its vertex at the origin (0,0).

If the graph of a second function g(x) = ax² intersects the graph of f(x) at exactly one point, then this point must be the vertex of g(x), since the vertex of f(x) is already fixed at the origin.

In order for g(x) to intersect f(x) at exactly one point, the vertex of g(x) must lie on the x-axis (since it cannot be above the x-axis, or else there would be two points of intersection). Therefore, the y-coordinate of the vertex of g(x) is 0.

The vertex of a quadratic function of the form ax² + bx + c has x-coordinate -b/2a and y-coordinate c - b²/4a. Since the y-coordinate must be 0 in this case, we have:

0 = c - b²/4a

Solving for c, we get:

c = b²/4a

Therefore, the vertex of g(x) is (0, b²/4a).

We can see from the graph that the vertex of g(x) is to the right of the origin, so its x-coordinate is positive. This means that the coefficient a must be positive, since otherwise the parabola would open downwards and the vertex would be below the x-axis.

We also know that the vertex of g(x) is above the x-axis, so its y-coordinate (which is b²/4a) must be positive. This means that b^2 and a have the same sign.

Putting this information together, we can conclude that:

If a > 0, then b²/4a > 0, which means that b² and a have the same sign. This means that the parabola opens upwards, and the vertex is above the x-axis. From the graph, we can see that this is the case, so we can eliminate options B and C.

If a < 1, then the parabola is narrower than the parent function f(x) = x², and the vertex is closer to the y-axis. This is not the case from the graph, so we can eliminate option A.

Therefore, the correct answer is D. The value of a in the equation of the second function is greater than 1.

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The complete question is:

Answer:

150 isnt a thing but I will gladly take 5 :)

(2x+3)(2x−9)

Step-by-step explanation:

Hope this helps^^

Answer:

4x

Step-by-step explanation:

mark me hope it is a good answer

Answer:

The factors of 2x^2 are 2, x, and 2x.

Therefore , the solution of the given problem of percentage comes out to be this amount to the closest dollar, we get $1,042.

A number or measure that is represented as a proportion of 100 is known as a "a%" in statistics. Additionally, the terms "pct," "pct," and "pc" are not commonly used. However, it is commonly denoted by the symbol "%". There are no dimensions; the percentage total is flat. Since a percentage's numerator is almost always 100, percentages are actually integers. To indicate that a number is a percentage, either the percentage symbol (%).

Here,

a. The formula: can be used to calculate the weekly payment.

=> P = (Ar(1+r)ⁿ) / ((1+r)^n - 1)

A = 9900, r = 0.06/12, and n = 48 in this instance (since there are 4 years or 48 months in total).

Substituting these numbers into the formula, we get:

=> P = (99000.005(1+0.005)⁴⁸) / ((1+0.005)⁴⁸ - 1) ≈ $227.88

Therefore, the monthly payment is roughly $227.88.

=> Overall = P*n = $227.88 * 48 = $10,942.24

We arrive at $10,942 by rounding this sum to the closest dollar.

c. The total interest paid over the course of the loan's four-year term is equivalent to the total amount repaid less the loan balance:

Total interest equals the total sum less A, or $10,942 minus $9,900, or $1,042.

Rounding this amount to the closest dollar, we get $1,042.

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The conditional probabilities are are (a) P(A/B) = 0.69   b) P(A/B) = 31/100

You should recall that Probability is the chance that a given event will occur; the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes;

The conditional probability P(A|B) is calculated using:

P(A/B)

P(A/B) = P( A and B) / P(B)

P(A/B) = (18/26 * 8/26)/ 8/26

P(A/B) = (0.69 * 0.31)/ 0.31

P(A/B) = 0.69

P(A/B) = 69/100

b)  Using the same formula

P(B/A) = P( B and A) / P(A)

P(A/B) = (8/26 * 18/26) / 18/26

P(A/B) = (0.31 * 0.69)/0.69

P(A/B) = 0.31

P(A/B) = 31/100

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Jon's parents invested $300 for his college tuition in a savings account when he was born. The account pays 5% simple interest every year. Consequently, if no additional money was invested, the account would be worth $570 after 18 years.

To answer the problem, we must employ the basic interest formula:

Principle x Interest Rate x Time = Simple Interest

where:

Principal = the initial amount invested

Interest Rate = the yearly interest rate expressed in decimal form.

Time = the amount of years the money has been invested for.

The principal in this scenario is $300, the interest rate is 5% (0.05 as a decimal), and the term is 18 years. Thus we may enter the following values into the formula:

Simple Interest = $300 x 0.05 x 18 = $270

As a result, after 18 years, the total money in the account would be:

Total amount = Principal + Simple Interest

=$300 + $270 = $570

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The numeric value of the composite function at x = 1 is given as follows:

(h ∘ k)(1) = 28.

The composite function of f(x) and g(x) is given by the rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, in this example g(x), serves as the input of the outer function, in this case f(x).

Hence the numeric value at x = 1 for the function in this problem is:

h(k(1)).

The numeric value of k at x = 1 is:

k(1) = 3.

Then, as the numeric value of h at x = 3 is of 28, the composite function is:

(h ∘ k)(1) = 28.

The problem is given by the image presented at the end of the answer.

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The probability of selecting all four bulbs of the same color is approximately 0.0061.

To calculate the probability that all four bulbs are of the same color, we need to consider the following cases,

1) The probability of selecting the first blue bulb is 3/12 (since there are 3 blue bulbs out of 12 total bulbs). After one blue bulb has been selected, there are 2 blue bulbs left out of 11 total bulbs, so the probability of selecting a second blue bulb is 2/11. Similarly, the probability of selecting the third blue bulb is 1/10, and the probability of selecting the fourth blue bulb is 0/9 (since there are no more blue bulbs left). Therefore, the probability of selecting all four blue bulbs is:

(3/12) × (2/11) × (1/10) × (0/9) = 0

2) Using the same logic as in Case 1, the probability of selecting all four green bulbs is:

(4/12) × (3/11) × (2/10) × (1/9) = 1/495

3) The probability of selecting all four red bulbs is:

(5/12) × (4/11) × (3/10) × (2/9) = 2/495

Therefore, the total probability of selecting all four bulbs of the same color is the sum of the probabilities from Cases 2 and 3

1/495 + 2/495 = 3/495

Simplifying this fraction, we get:

3/495 = 1/165

= 0.0061

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Answer:

y=-21/10

Step-by-step explanation:

20y=-42

20y/20=-42/20

y=-42/20

y=-21/10

The volume of the pyramid is found to be approximately 18.046 cubic units.

To find the volume (V) of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3) × Base Area × Height.

In this case, the base is a square, so we can find the area of the base by squaring one of the sides: Base Area = AB² = 4.5² = 20.25.

To find the height of the pyramid, we need to use the Pythagorean theorem to find the slant height, and then use that to find the height. Let h be the height of the pyramid and s be the slant height. We have:

s² = AB² + (1/2) DC² (Pythagorean theorem for triangle ABC)

s² = 4.5² + (1/2) DC²

Since all edges of the pyramid are congruent, we have DC = AB = 4.5. Substituting this into the equation above, we get:

s² = 4.5² + (1/2) × 4.5²

s² = 30.375

s ≈ 5.509

To find the height h, we can use the Pythagorean theorem again for triangle ABD:

h² = AB² - (1/4) s²

h² = 4.5² - (1/4) × 30.375

h² ≈ 7.875

h ≈ 2.807

Now that we have found the base area and the height, we can use the formula for the volume of a pyramid to find V:

V = (1/3) × Base Area × Height

V = (1/3) × 20.25 × 2.807

V ≈ 18.046

Therefore, the volume of the pyramid is approximately 18.046 cubic units.

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The missing measures of the pentagon are a = 18.4, c = 61.2, d = 75, and x = 22.08.

Let's label the sides of the first pentagon as a, 20, c, 30, and x, and the sides of the second pentagon as 46, 50, d, 102, and 24.

Since both pentagons have the same shape, we know that the corresponding sides are proportional. This means we can set up the following equations:

a/46 = 20/50 = c/d = 30/102 = x/24

Solving for the missing variables:

a = 46(20)/50 = 18.4

c = 30(102)/50 = 61.2

d = 50(30)/20 = 75

x = 24(46)/50 = 22.08

Therefore, the missing measures are a = 18.4, c = 61.2, d = 75, and x = 22.08.

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Step-by-step explanation:

area of rectangle= 9×4=36m^2

9-3=6 which is the base of the triangle

6×3=18

18÷2=9m^2

36+9=45m^2

answer: 45m^2

According to the means, the average typical daily sales for Farmer's equation Market A are higher than the average typical daily sales for Farmer's Market B.

A mathematical statement which thus proves the equality of two factors linked by an equal sign '=' is known as an equation. For example, 2x - 5 = 13. Two examples of phrases are 2x-5 and 13. The character '=' is used to connect the two expressions. A mathematical formula with two algebraic expressions on either side of a =) (=) is called an equation. It depicts the relationship of equivalence between left and right equations. In any formula, L.H.S. = R.H.S. (left side = right side).

[tex]$30 + $31 + $32 + $33 + $35 + 36 + $38 + $40 + $41 + $42 + $43 + $45 + $47 + $49 + $50 = $575 for Farmer's Market A[/tex]

Because there are 15 days, we divide the total sales by 15 to find the mean:

Farmer's Market A Mean [tex]= $575/15 = $38.33[/tex]

Farmers' Market B:

[tex]$20 + $22 + $24 + $26 + $28 + $31 + $32 + $34 + $36 + $39 + $40 + $42 + $44 + $46 + $49 = $524[/tex]

Farmer's Market A has a mean of $38.33, while Farmer's Market B has a mean of $34.93. According to the means, the average typical daily sales for Farmer's Market A are higher than the average typical daily sales for Farmer's Market B.

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It should be noted that the value on the blank on the equation will be -2.

The equation given is:

2(4x+1) + 8 = 4(2x+1) + 8 - x

Simplifying the left-hand side:

8x + 2 + 8 = 8x + 4 + 8 - x

Simplifying the right-hand side:

8x + 4 + 8 - _ = 8x + 12 - x

Combining like terms on both sides:

8x + 10 = 8x + 12 - x

Subtracting 8x from both sides:

10 = 12 - x

x = 10 - 12

x = -2

The value will be -2 to make the equations equal.

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Cοllege wοmen whο play have had mοre success than οthers with using sοcial media tο benefit frοm their name, image, and likeness. (False)

Female cοllege athletes and their success in using sοcial media tο mοnetize their name, image, and likeness which is false.

This statement means that female cοllege athletes whο participate in spοrts have been mοre successful in leveraging their name, image, and likeness fοr financial gain thrοugh sοcial media platfοrms than their nοn-athlete peers.

In οther wοrds, female athletes whο engage in spοrts don't have an advantage in mοnetizing their sοcial media presence and using it tο prοmοte their persοnal brand, cοmpared tο female cοllege students whο dο nοt participate in spοrts.

Therefore, it is false that college women who play have had more success than others with using social media to benefit from their name, image, and likeness

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Complete question:

True or False:

11. College women who play have had more success than others with using social media to benefit from their name, image, and likeness (___).

The area of the blue region is 28.93 cm²

To find the area of the blue region, we need to subtract the area of the four circle from the area of the rectangle.

Since the diameter of the circle is 3cm. The radius (r) = 3/2 = 1.5 cm.

Length of the rectangle (L) = 4 * diameter of circle (we have 4 circles)

Length of the rectangle = 4 * 3 = 12 cm

Width of the rectangle (W) = diameter of circle = 3 cm

Area of rectangle = L * W

Area of rectangle = 12 * 3 = 36 cm²  

Area of circle = πr²

Area of circle = π * 1.5² = 2.25π cm²  

Area of the blue region = Area of rectangle - Area of circle

Area of the blue region = 36 - 2.25π

Area of the blue region = 36 - (2.25* 22/7)

Area of the blue region = 28.93 cm²

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Complete Question

Check the attached image

Answer:

System A: C)infinite answers

System B: B)special answer (x,y)=(3,1)

Step-by-step explanation:

System A:

if we find sum of same variables, we get 5x-5x-y+y=-2+2, it means 0=0 so, this system has infinite answers.

System B:

same thing applied here,

x-x+4y+4y=7+1

8y=8

y=1

so,

x+4*1=x+4=7

x=3

If a rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters, the perimeter of the door in the scale drawing is 70 centimeters.

To find the perimeter of the door in the scale drawing, we first need to determine the dimensions of the door in the scale drawing. To do this, we need to multiply the actual dimensions of the door by the scale factor of 3.5.

The height of the door in the scale drawing would be 7 cm x 3.5 = 24.5 cm, and the width would be 3 cm x 3.5 = 10.5 cm.

The perimeter of the door in the scale drawing can be calculated by adding up the lengths of all four sides. The two vertical sides have a length of 24.5 cm, and the two horizontal sides have a length of 10.5 cm. Therefore, the perimeter of the door in the scale drawing is:

P = 2(24.5 cm) + 2(10.5 cm) = 49 cm + 21 cm = 70 cm

Note that the scale drawing is a proportional representation of the actual door, where all corresponding dimensions are multiplied by the same factor of 3.5.

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The answer of the given question based on the Voltage drop the answer is , the voltage dropped across R3 is 277.11 V.

Ohm's law is  fundamental principle in electrical engineering and physics that describes  relationship between voltage, current, and resistance in  electrical circuit. It states that current through conductor between two points is directly proportional to voltage across  two points, and inversely proportional to resistance between them.

To determine the voltage dropped across R3, we need to use Ohm's law and Kirchhoff's circuit laws. First, we can calculate the total resistance in the circuit:

Rtotal = R1 + R2 || R3

R2 || R3 = (R2 * R3) / (R2 + R3) (parallel resistance formula)

Rtotal = R1 + (R2 || R3)

Rtotal = 152 + ((18 * 362) / (18 + 362))

Rtotal = 149.89 Ω (rounded to 2 decimal places)

Next, we can use Ohm's law to calculate the current flowing through the circuit:

I = ET / Rtotal

I = 120 / 149.89

I = 0.8004 A (rounded to 4 decimal places)

Finally, we can use Kirchhoff's voltage law to determine the voltage dropped across R3:

ET = IR1 + IR2 || IR3 + IR3

ET = I(R1 + R2 || R3) + IR3

ET - I(R1 + R2 || R3) = IR3

R3 = (ET - I(R1 + R2 || R3)) / I

R3 = (120 - (0.8004 * (152 + ((18 * 362) / (18 + 362))))) / 0.8004

R3 = 277.11 V (rounded to 2 decimal places)

Therefore, the voltage dropped across R3 is 277.11 V.

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Answer: A,

Step-by-step explanation:

it will be -170 feet after 8 min

Answer:

16 - 25z²

Step-by-step explanation:

(4 - 5z)(4 + 5z)

each term in the second factor is multiplied by each term in the first factor, that is

4(4 + 5z) - 5z(4 + 5z) ← distribute parenthesis

= 16 + 20z - 20z - 25z² ← collect like terms

= 16 - 25z²

Answer:

16-25z

Step-by-step explanation:

you will use the first term 4 to multiply the first which is (4+5z) then after that you will use the second term which is -5z to multiply the same (4+5z) to give you 16+20z-20z-25z then you will also simplify to give you 16-25z

Set A and Set B have 2 numbers in common: 3 and 7. The intersection of both sets is the set of numbers that appear in both sets.

Set A consists of all odd integers between 0 and 10, which are 1, 3, 5, 7, and 9. Set B consists of all prime numbers less than 16, which are 2, 3, 5, 7, 11, and 13. There are two numbers that Set A and Set B have in common: 3 and 7.

Sets A and B are both subsets of the set of all integers between 0 and 16. Set A is a subset of the set of all odd integers between 0 and 16, while Set B is a subset of the set of all prime numbers between 0 and 16. While Set A and Set B have 2 numbers in common, they are not the same set. Set A includes the numbers 1, 3, 5, 7, and 9, while Set B includes the numbers 2, 3, 5, 7, 11, and 13.

Each set includes a unique set of numbers, and the intersection of Set A and Set B is the set of numbers that appear in both Set A and Set B. In this case, the intersection of Set A and Set B is the set of 2 numbers that both sets have in common: 3 and 7.

In conclusion, Set A and Set B have 2 numbers in common: 3 and 7. While both sets include a unique set of numbers, the intersection of Set A and Set B is the set of numbers that appear in both sets.

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Answer:

ANSWER: -5,2.55

Step-by-step explanation:

I got it right

Rounding to the nearest hundredth, the density of the candle is 22.46 grams per cubic inch.

The density of the candle can be found by dividing the mass by the volume of the candle.

The volume of a cylindrical candle can be found using the formula V = πr^2h,

where V is the volume, r is the radius, and h is the height.

First, we need to find the radius of the candle.

The diameter is 3 inches, so the radius is 1.5 inches.

Next, we can plug in the values for r and h into the formula for the volume of a cylinder:

V = π(1.5)^2(4) = 9π

Now, we can divide the mass of the candle by the volume to find the density:

Density = 200 grams / 9π

Density= 22.46 grams per cubic inch

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Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar when compounded daily.

The interest that is accrued on both the principle and any prior interest is known as compound interest. This implies that the interest received in succeeding periods rises as the interest is added to the principle. Compound interest is a crucial idea in personal finance that may be utilised in calculations for both savings and loans.

The compound interest is given by the formula:

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

For Elijah substituting the values we have:

[tex]A = $94,000(1 + 0.04125/4)^{(4*7)} = $129,852.94[/tex]

For Kayden substituting the values we have:

[tex]A = $94,000(1 + 0.0425/365)^{(365*7)} = $130,963.39[/tex]

The difference between the two amounts is:

$130,963.39 - $129,852.94 = $1,110.45

Therefore, Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar.

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Answer:$1286 when rounded. Got it right

Step-by-step explanation: