4. VPQRS is a rectangular pyramid where PQ = 10 cm and QR=6 cm. Given that the volume of the pyramid is 100 cm³, find its height VO. P S V 0 10 cm 0 R 6 cm​

Using the half ten fact for rounding and distributive property helped us efficiently solve the multiplication problem of 47 x 550.

Let's take the 2-digit number 47 and multiply it by the 3-digit number 550:

To use the half ten fact, we can first round the 3-digit number to the nearest half ten, which in this case would be 550 rounded to 550 + 50 = 600.

Then, we can split the 2-digit number into its tens and ones digits: 47 = 40 + 7.

Next, we can use the distributive property of multiplication to simplify the problem:

47 x 600 = (40 + 7) x 600 = 40 x 600 + 7 x 600

Now, we can use the half ten fact for the first term: 40 x 600 = (20 x 10) x 600 = 20 x (10 x 600) = 20 x 6000 = 120,000.

For the second term, we can use the fact that 7 x 6 = 42:

7 x 600 = 7 x (10 x 60) = (7 x 10) x 60 = 70 x 60 = 4,200.

Finally, we can add the two terms to get the final answer:

47 x 550 = 47 x 600 - 47 x 50 = 120,000 + 4,200 - 2,350 = 121,850.

Therefore, using the half ten fact for rounding and distributive property helped us efficiently solve the multiplication problem of 47 x 550.

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The equation for modeling its exponential decay is N(t) = 16 * e^(-0.0578t) where N(t) is the amount of radioactive element remaining after t hours.

We can use the formula for exponential decay to model the decay of the radioactive element. The formula is:

N(t) = N0 * e^(-kt)

where N(t) is the amount of the radioactive element remaining after t hours, N0 is the initial amount of the element, e is the mathematical constant approximately equal to 2.71828, and k is a constant that represents the rate of decay.

We are given that half of the initial 16-gram sample remains after 12 hours. That means the initial amount N0 is 16 grams and the amount remaining after 12 hours is 8 grams. We can use these values to solve for k.

8 = 16 * e^(-k*12)

Dividing both sides by 16, we get:

0.5 = e^(-12k)

Taking the natural logarithm of both sides, we get:

ln(0.5) = -12k

Solving for k, we get:

k = -ln(0.5)/12

k ≈ 0.0578

Therefore, the constant k for this radioactive element is approximately 0.0578. The equation of modeling its exponential decay is

N(t) = 16 * e^(-0.0578t)

where N(t) is the amount of radioactive element.

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Answer:

To find the percent sales tax, we can use the following formula:

Percent tax = (Tax amount ÷ Base price) × 100%

Where "Base price" is the original price of the item before tax is added.

In this case, the base price of the sneakers is $22, and the total price with tax is $23.98. The tax amount is:

Tax amount = Total price - Base price

Tax amount = $23.98 - $22

Tax amount = $1.98

Now we can calculate the percent sales tax:

Percent tax = (Tax amount ÷ Base price) × 100%

Percent tax = ($1.98 ÷ $22) × 100%

Percent tax = 0.09 × 100%

Percent tax = 9%

Therefore, the percent sales tax is 9%.

The fare that would maximize revenue is $70.

To prove this, we must first calculate the number of passengers who will use the train at different fares. This is because the revenue formula for this is:

Revenue = Fares x Passengers

where revenue is a function of both the fare and the number of passengers using the train. From the given data, we have:

Initial Fare = $50

Initial Passengers = 10,000

Assuming X = Increase in fare (in dollars) and Y = Decrease in passengers, we can derive the following table:

Fare ($)|Passengers|Revenue ($)
--|--|--
50|10,000|500,000
60|9,000|540,000
70|8,000|560,000
80|7,000|560,000
90|6,000|540,000

Here's how we computed it:

Starting at the $50 fare, every additional $10 fare increase decreases the number of passengers by 1000 (see the problem statement). So, at $60, the number of passengers is 10,000 – 1,000 = 9,000. Similarly, at $70, the number of passengers is 10,000 – 2,000 = 8,000. Continuing this way, we can fill in the table. Then, we can plug in the values of fares and passengers into the revenue formula to obtain the revenue values in the last column.

Note that the revenue maximizes at a fare of $70 because at that point, the revenue is the highest ($560,000) compared to any other fare in the table. Therefore, the fare that maximizes revenue is $70.

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The side length of dilated cubes is 10.08 units. Then the surface area of the dilated cube is 609.6384 square units.

What is dilation?

Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

A solid has a volume of 2 cubic units and a surface area of 10 square units.

The solid is dilated, and the image has a volume of 128 cubic units.

Let the original side length of the cube be a and dilated length of the cube be b.

MsReid CTEA

The loan rate assumptions are:

1) Assumption that the family has good credit

2) Assumption that the family is borrowing for a large purchase

3) Assumption that the loan is secured

Savings Plan Rate Assumptions are:

1) Assumption that the family has a significant amount of disposable income

2) Assumption that the family has a long investment horizon

3) Assumption that the family has a high tolerance for risk

There are a few assumptions that may not necessarily be valid for a typical family regarding both the loan rate and savings plan rate. Some of these assumptions include:

a. Assumption that the family has good credit: Most loan rate calculators assume that the borrower has good credit.

b. Assumption that the family is borrowing for a large purchase: Many loan rate calculators assume that the family is borrowing for a large purchase, such as a house or a car.

c. Assumption that the loan is secured: Many loan rate calculators assume that the loan is secured by collateral, such as a house or a car.

a. Assumption that the family has a significant amount of disposable income: Many savings plan calculators assume that the family has a significant amount of disposable income to invest in a savings plan.

b. Assumption that the family has a long investment horizon: Many savings plan calculators assume that the family has a long investment horizon, such as 10 or 20 years.

c. Assumption that the family has a high tolerance for risk: Many savings plan calculators assume that the family has a high tolerance for risk and can invest in high-risk investments that offer a higher rate of return.

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The required value of AC is 10 inches.

Let's use the fact that the perimeter of a triangle is the sum of the lengths of its sides. We are given that the perimeter of triangle ABC is 40 in:

AB + BC + AC = 40

We are also given the lengths of AB, AC, and BC in terms of x:

AB = 2x

AC = x + 1

BC = x + 3

Substituting these values into the equation for the perimeter, we get:

2x + (x + 3) + (x + 1) = 40

Simplifying and solving for x, we get:

4x + 4 = 40

4x = 36

x = 9

Now that we know the value of x, we can find the length of AC:

AC = x + 1 = 9 + 1 = 10

Therefore, The required value of AC is 10 inches.

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trust me its 10 i just did it

Step-by-step explanation:

The probability of a randomly selected timber stand having more than 92 trees is 0.0744 or 7.44%.

Managed timber stands average 150 trees per acre with a standard deviation of 40. Assume acres are normally distributed.To find the probability of a randomly selected timber stand having more than 92 trees.We have to calculate the Z-Score using the formula,Z= (X-μ)/ σWhere X= 92 treesμ = 150 treesσ= 40Using the formulaZ= (X-μ)/ σZ= (92-150)/40= -1.45We know that the area under the normal distribution curve is 1. To find the probability of a random variable that falls between two points, we need to find the area between those points.A normal distribution curve is shown below:To find the probability of a randomly selected timber stand having more than 92 trees, we need to find the area to the right of Z= -1.45 using a normal distribution table. The probability is 0.0744 or 7.44%.Therefore, the probability of a randomly selected timber stand having more than 92 trees is 0.0744 or 7.44%.

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Answer:

your question is unclear

i assume the answer would be

x= -(b+1)/(a-d)

The 3/4  is questionable figure in the statement because it is based on a limited and potentially unrepresentative sample.

The statement "We know that 3/4 of Australians work force are happily with their jobs" is based on the survey results of only 100 government employees aged 25-30. While this may provide an indication of job satisfaction among this particular group, it is not necessarily representative of the entire Australian workforce.

The sample size of 100 employees is relatively small, and the sample may not be representative of the larger population. Additionally, the sample only includes government employees aged 25-30, which further limits its generalizability. There may be significant differences in job satisfaction levels among different age groups or in different industries.

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The value of x is 13.

A line segment is a straight line formed by a continuous arrangement of series of points. As such, it can be divided into parts.

Considering the given question, it can be deduced that; MP is a line segment which has been divided into two parts MN and NP.

Thus we have;

MP = MN + NP

But we are given that; MN = x - 1, NP = 9x - 68, and MP = 5x - 4.

Then we can say that;

MP = MN + NP

5x - 4 = (x-1) + (9x - 68)

          = 10x - 69

collect like terms

69 - 4 = 10x - 5x

65 = 5x

x = 65/ 5

  = 13

The value of x is 13.

MP = 5x - 4

     = 5(13) - 4

     = 65 - 4

MP = 61

MN = x - 1

      = 13 - 1

MN = 12

NP = 9x - 68

     = 9(13) - 68

     = 117 - 68

NP = 49

Therefore, the appropriate value of x is 13.

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The correct question is:

Range of x-values: 6. MN = x - 1, NP = 9x - 68, MP = 5x - 4.

we divide both sides by 7, giving us x < -6, which is the answer.We can do this by using the distributive property and combining like terms on the left side of the inequality.

To solve this inequality, we must first isolate the variable x on one side of the inequality. We can do this by using the distributive property and combining like terms on the left side of the inequality. We start by multiplying 4 and 3x, which gives us 12x. We then add two to both sides, giving us 12x + 2 < 5(3x - 2). We then distribute 5 over the parentheses on the right side, giving us 12x + 2 < 15x - 10. We then combine like terms on the left side, giving us 7x < -8. Finally, we divide both sides by 7, giving us x < -6, which is the answer.

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The amount of pineapple juice that was left in the batch after a quantity was removed for testing would be = 77,000cm³

The total volume of juice that was produced in the batch = 0.08m³

To convert 0.08m³ to cm the following is carried out;

1 m³ = 1,000,000

0.08m³ = X

make X the subject of formula;

X = 0.08×1,000,000

X = 80000 cm³

The quantity of pineapple juice that was removed = 3000 cm³

The quantity left = 80000-3000 = 77,000cm³

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If the volume of a cylinder is given, the dimensions of cylinder can be written and r = √(V/(πh)) and h = V/(πr²)

The volume of a cylinder is given, find dimensions of cylinder. To find the dimensions of a cylinder given its volume, we need to know either the radius or height. The formula for the volume of a cylinder is:

V = πr²h

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

If we are given the volume V, we can solve for either r or h as follows:

If we solve for the radius r:

V = πr²h

r² = V/(πh)

r = √(V/(πh))

If we solve for the height h:

V = πr²h

h = V/(πr²)

So, to find the dimensions of the cylinder, we need to know the volume V and either the radius r or height h. Once we have one of these values, we can use the equations above to find the other value and determine the dimensions of the cylinder.

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The average rate of change is $22.50 per class

The table of values represent the given parameter

The average rate of change is calculated as

Rate = Change in T(c)/Corresponding change in c

So, we have

Rate = (50 - 27.50)/(2 - 1)

Rate = 22.50

We start by calculating the function from

T(c) = mc + b

Where

m = Rate = 22.50

So, we have

T(c) = 22.5c + b

Using the points, we have

22.5 * 1 + b = 27.50

So, we have

b = 5

So, we have

T(c) = 22.5c + 5

For 5 classes, we have

T(5) = 22.5 * 5 + 5

T(5) = 117.5

The first class is 27.50 because the studio charges a registration fee of $5

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The fraction of the square represented by a figure constructed with pieces of a tangram can be calculated by dividing the area of the figure by the area of the square.

The fraction of the square that a figure constructed with the pieces of a tangram represents can be calculated by dividing the area of the figure with the area of the square. The area of a square can be determined using the formula A = s2, where s is the side length of the square. The area of the figure can be calculated by adding together the area of the individual pieces of the tangram. For example, if the figure is composed of two triangles with base lengths of b1 and b2 and heights h1 and h2, then the area of the figure can be calculated using the formula A = b1h1 + b2h2. The fraction of the square represented by the figure is calculated by dividing the area of the figure by the area of the square.

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The given statement is false. A pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.

A pooled model is a method that entails the estimation of regression coefficients over different groups or periods by pooling the data from those groups or periods. When a pooled model is used, the dataset is combined from different groups and treated as one group, making it a more significant dataset. It is a statistical approach that includes data from two or more groups to examine variables in a wider context.

A pooled model is used when all groups have the same coefficient estimates and the same variance. It is a helpful technique for identifying variables that influence an outcome over time, as it examines changes that occur over different periods.

The assumptions of a pooled model are:

Hence, the given statement is false.

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Ramona's mistake was in substituting the value of 8.5 for the wrong variable, which led her to obtain a nonsensical answer of -17.52 inches for the man's height.

Based on the given information, Ramona made a mistake in substituting the wrong variable. It is unclear what the original equation was, but it seems that Ramona was trying to solve for the height of a man based on some given variables.

Ramona's mistake was in substituting the value of 8.5 for the wrong variable, which led her to obtain a nonsensical answer of -17.52 inches for the man's height. Additionally, the solution of -17.52 should not represent the man's height, but rather some other variable in the equation.

The correct approach would have been to carefully substitute the given values for the correct variables and then solve for the unknown variable. In this case, it appears that Ramona should have added 0.444 and 8.5, rather than substituting 8.5 for the wrong variable. It is also worth noting that the resulting value for y should be positive, since negative shoe sizes do not make sense.

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The difference in the distance of the route of the two mountaineers to reach the meeting point is approximately 311.67m.

To solve this problem, we need to find the total distance each mountaineer traveled to reach the meeting point. Then we can compare the two distances to find the difference.

Let's start with José's route. We can use the Pythagorean theorem to find the total distance he traveled:

total distance = √(365² + 584²) ≈ 694.36m

Now let's find the total distance for Damián's route. Again, we can use the Pythagorean theorem to find the distance he walked on the ground:

distance on the ground = √208² + (584 - 465)² = √208² + 119² ≈ 236.98m

And we can add the distance he ascended:

total distance = 236.98m + 465m = 701.98m

Finally, we can find the difference in distance between the two routes:

difference = 701.98m - 694.36m ≈ 7.62m

Therefore, there is a difference of approximately 7.62 meters between the route of the two mountaineers to reach the meeting point.

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The question is -

José and Damián are mountaineers, each of them has taken a different path to climb a mountain. José walks straight for 365m and climbs 584m, while Damián climbs 465m and walks straight for 208m to reach the meeting point. How many meters of difference are there in the path taken by the two mountaineers to reach the meeting point?

The tank contains only pure water, so the amount of sugar in the tank is zero: S(0) = 0 kg. Therefore, the amount of sugar in the tank initially is 0 kg.

The concentration of sugar in the incoming solution is 0.04 kg/l. Therefore, the amount of sugar entering the tank per minute is:

0.04 kg/l × 3 l/min = 0.12 kg/min

Since the solution is mixed thoroughly with the water in the tank, the concentration of sugar in the tank is uniform at all times. Let's assume that after t minutes, the amount of sugar in the tank is S(t) kg.

During each minute, 0.12 kg of sugar enters the tank and 3 l of solution (which contains 0.04 kg of sugar per liter) leaves the tank. Therefore, the rate of change of the amount of sugar in the tank is:

dS/dt = 0.12 kg/min - (0.04 kg/l × 3 l/min) = 0.00 kg/min

This differential equation has a constant solution: S(t) = S(0). That is, the amount of sugar in the tank is constant over time, as long as the rate of inflow and outflow of solution remains constant.

Initially, the tank contains only pure water, so the amount of sugar in the tank is zero:

S(0) = 0 kg

Therefore, the amount of sugar in the tank initially is 0 kg.

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Therefore , the solution of the given problem of arithmetic comes out to be 32 is the 9th term in the series.

The values of a list are added up to obtain its average values, also referred to as the company's values, which are then scaled by the number of list elements in the highest population. In math, similar growth trends can be observed. The mean of the real numbers 5, 7, as well as 9, is 4, and also the number 21 enhanced by three (there are presently several three numbers) equals seven.

Here,

The following formula can be used to describe the nth term of an arithmetic sequence:

=> a = a1 + (n-1)d

where the term number is n, d is the common difference, and a1 is the first term.

A1 = 28 in this instance, and d = 1/2. By adding n = 9 to the calculation and simplifying, we can determine the ninth term:

=> a9 = a1 + (9-1)d

=> a9 = 28 + 8(1/2)

=> a9 = 28 + 4

=> a9 = 32

Consequently, 32 is the 9th term in the series.

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the nth term of the sequence is (16n²2 - 29n + 15)/(90n).

How to find?

To find the nth term of this sequence, we can use the formula:

an = a1 + (n-1)d

where a1 is the first term, d is the common difference, and n is the term number.

In this sequence, we can see that the common difference is not constant. However, we can still find a pattern:

a1 = 1/3

a2 - a1 = 2/5 - 1/3 = 1/15

a3 - a2 = 3/7 - 2/5 = 1/35

a4 - a3 = 4/9 - 3/7 = 1/63

We can see that the common difference is decreasing by a factor of 5 with each term. So the next difference would be 1/63× 1/5 = 1/315.

Using this pattern, we can find the nth term as:

an = 1/3 + (n-1)(1/15 - (n-2)(1/315))

Simplifying this expression, we get:

an = (16n²2 - 29n + 15)/(90n)

So the nth term of the sequence is (16n²2 - 29n + 15)/(90n).

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Answer: x=24

Step-by-step explanation:

When you get this type of problem you do the opposite of the equation

so for this one you 4x6=24 because it x divided by 4 so we times.

Therefοre, the sοlutiοn οf the given prοblem οf trigοnοmetry cοmes οut tο be cοt²(135-b) = 3.

Relatiοnships between cubic splines and maths variable astrοphysics is believed tο have been created when the variοus fields came tοgether. Many metric prοblems can be sοlved triangle οr the results οf their calculatiοn can indeed be determined with the help οf precise mathematical methοds. Trigοnοmetry is the study οf six basic trigοnοmetric calculatiοns. They gο by a variety οf titles and acrοnyms, including sine, deviatiοn, angle, and sο fοrth (csc).

Here,

First, we need tο find the value οf cοs(b) using the given infοrmatiοn that sin(2b) = -1/5:

=> sin(2b) = 2sin(b)cοs(b)

=> -1/5 = 2sin(b)cοs(b)

We knοw that sin^2(b) + cοs^2(b) = 1, sο we can rearrange this equatiοn tο sοlve fοr cοs(b):

=> cοs²(b) = (1 - sin²(b))

Substituting this intο the equatiοn we fοund abοve:

=> -1/5 = 2sin(b)cοs(b)

=> -1/5 = 2sin(b)√(1 - sin²(b))

Squaring bοth sides and simplifying:

=> 1/25 = 4sin²(b)(1 - sin²(b))

=> 1/25 = 4sin²(b) - 4sin²(b)

=> 4sin²(b) - 4sin²(b) + 1/25 = 0

We can sοlve fοr sin^2(b) using the quadratic fοrmula:

sin²(b) = [4 ± √(16 - 4(4)(1/25))] / (2(4))

sin²(b) = [4 ± 2/5] / 8

sin²(b) = 3/10 οr 1/20

Since sin(2b) is negative, we knοw that sin(b) is negative as well, sο sin²(b) = 3/10. Therefοre:

cοs²(b) = 1 - sin²(b) = 1 - 3/10 = 7/10

Nοw we can use the identity

=> cοt²(θ) = 1 / [tan²(θ)] tο find cοt²(135-b):

1 / [tan(135-b)] = cοt(135-b)

By applying the fοrmula tan(x) = sin(x) / cοs(x):

=> tan(135-b) Equals cοs(135-b) / sin(135-b) (135-b)

The identities sin( + 90) = cοs() and cοs( + 90) = -sin() are used tο illustrate:

=> Cοs(90-b) = sin(135-b) = sin(45 + (90-b)) = sin (b)

=> Sin(90-b) = cοs(135-b) = cοs(45 + (90-b)) = cοs (b)

Using these numbers in place οf:

=> 1/tan(135-b) = sin(b) / cοs(b) (3)

=> 1 / [tan(135-b)] = cοt(135-b) = 1 / [(-1/√(3))²] = 3

Cοnsequently, cοt2(135-b) = 3.

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Complete question:

Solve for b in cot²(135-b) if sin²b = -1/5

Answer:

2

Step-by-step explanation:

We use complex conjugates. A complex number multiplied by its conjugate creates a difference of squares pattern. In this scenario, 3-2i’s conjugate is 3+2i, because (3-2i)(3+2i)=9-(-4)=13. So how do we use conjugates to simplify this expression? We first multiply by [tex]\frac{3+2i}{3+2i}[/tex] to make the denominator real, while keeping the fraction the same, because the fraction we multiplied is 1.
our new fraction is (8-i)(3+2i)/13.

Expand the numerator: (26+13i)/13 = 2+i, so a is 2

 It is possible that the observed proportion of 0.46 is due to chance, and the true proportion is actually 0.5.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

which the penny stack will land on its edge.

To test the hypotheses, the student can use a two-sided z-test for proportions. The test statistic is calculated as:

z = (p' - p) / sqrt(p * (1 - p) / n),

where p' is the sample proportion (46/100), p is the hypothesized proportion (0.5), and n is the sample size (100).

Substituting the values, we get:

z = (0.46 - 0.5) / sqrt(0.5 * 0.5 / 100) = -0.8

Using a significance level of 0.05 (i.e., a 95% confidence level), the critical values for a two-sided test are -1.96 and 1.96.

Since the calculated z-score (-0.8) falls between the critical values, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

In other words, the data does not provide convincing evidence that the student's claim is true.

Therefore,  It is possible that the observed proportion of 0.46 is due to chance, and the true proportion is actually 0.5.

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The expressions (3x+19) and (5x-9) when set equal gives the solution x = 14

Equivalent equation is an assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign from which one is to determine a particular quantity.

(3x + 19) = (5x - 9)

open parenthesis

3x + 19 = 5x - 9

combine like terms

3x - 5x = -9 - 19

-2x = -28

divide both sides by -2

x = -28/-2

x = 14

Therefore, x = 14 is the solution to the expressions when set equal.

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The owners need to deposit in an account paying 0. 65% compounded quarterly so that they will have $120,000 in 270 days is $119,262.94

To calculate the amount the owners need to deposit today, we can use the formula for compound interest:

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

where:

A is the future value of the investment

P is the principal amount (the amount to be deposited)

r is the annual interest rate (0.65%)

n is the number of times the interest is compounded per year (4 for quarterly)

t is the time in years (270 days/365 = 0.7397 years)

Substituting the values given into the formula, we get:

$120,000 = [tex]P(1 + 0.0065/4)^{4\times0.7397}[/tex]

$120,000 = [tex]P(1.001625)^{2.9588}[/tex]

$120,000 = P(1.004845)

P = $120,000/1.004845

P = $119,262.94

Therefore, the owners need to deposit $119,262.94 in an account paying 0.65% compounded quarterly so that they will have $120,000 in 270 days.

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Answer: The tiger eats 13.875 pounds more food per day than the large dog.

Step-by-step explanation: A tiger eats approximately 15 pounds of food per day, while a large dog eats about 18 ounces of food per day. To determine how many more pounds of food a tiger eats per day than a large dog, we need to convert the weight of the dog's food into pounds. Since there are 16 ounces in a pound, 18 ounces is equivalent to 18/16 = 1.125 pounds. Therefore, the tiger eats 15 - 1.125 = 13.875 pounds more food per day than the large dog.

Answer:

Answer below

Step-by-step explanation:

2 1/4, 2 3/4, 3 1/4, 3 3/4

Answer:[tex]2\frac{1}{4} , 2\frac{3}{4} , 3\frac{1}{4} , 3\frac{3}{4}[/tex]

Step-by-step explanation:

This series is in arithmetic progression, where all the elements in this series increase progressively. They have a common difference. You can find the common difference by substracting any term by its preceding term as:

d = t(n+1) - t(n)

In this case:

[tex]\frac{3}{4} - \frac{1}{4} = \frac{1}{2}[/tex]

You can use the cd. to find the remaining elements by adding the difference to the 4th term to find the 5th term, and adding it to 5th term to get the 6th term and so on.