A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2. 7 cm. Find the volume of the stone

The value of the following equations by using the properties of logarithms: 1.x = 50000 2. x = (1 ± √5) / 4 3. x= 2√5.

In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equal sign (=). An equation typically consists of one or more variables, coefficients, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the equation. These values are called solutions or roots of the equation. Equations are used in many branches of mathematics, including algebra, calculus, geometry, and statistics, to model and solve various problems and phenomena in the natural and social sciences, engineering, and finance.

Here,

1. Log 2x = 5

We can rewrite this equation using the property that log_a(b) = c is equivalent to b = aˣ:

2x = 10⁵

Simplifying the right-hand side, we get:

2x = 100000

Dividing both sides by 2, we get:

x = 50000

Therefore, the solution is x = 50000.

2. Lnx - In(2x+1) = 2

Using the fact that ln a - ln b = ln(a/b), we can simplify the left-hand side of the equation:

ln(x/(2x+1)) = 2

Next, we can rewrite the equation in exponential form:

e² = x/(2x+1)

Multiplying both sides by 2x+1, we get:

e²(2x+1) = x

Expanding and simplifying the left-hand side, we get a quadratic equation:

4xe² + 2e² - x = 0

Solving for x using the quadratic formula, we get:

x = (-2e² ± √((2e²)² - 4(4e²)(-1))) / (2(4e²))

Simplifying, we get:

x = (-e² ± √(e⁴ + 4e₂)) / (4e²)

x = (-e² ± e²√5) / (4e²)

x = (1 ± √5) / 4

Therefore, the solutions are x = (1 + √5) / 4 and x = (1 - √5) / 4.

3. Log x = log (2/x) + 1

Using the fact that log_a(b) = log_a(c) is equivalent to b = c, we can simplify the equation:

x = 2/x * 10

Multiplying both sides by x, we get:

x² = 20

Taking the square root of both sides, we get:

x = ±√(20)

Since x cannot be negative (because log of a negative number is undefined), the only solution is:

x = √(20) = 2√5

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If in △ABC, A=27degree, a=37 and c=28, then the statements best describes the triangle is (B) △ABC is obtuse.

We can use the Law of Cosines to determine the length of side b:

b^2 = a^2 + c^2 - 2ac cos(A)

b^2 = 37^2 + 28^2 - 2(37)(28) cos(27°)

b ≈ 27.88

Now we can use the Law of Sines to determine the measure of angle B:

sin(B)/b = sin(A)/a

sin(B) = (b/a)sin(A)

sin(B) = (27.88/37)sin(27°)

B ≈ 46.18°

Finally, we can find the measure of angle C using the fact that the angles in a triangle sum to 180°:

C = 180° - A - B

C ≈ 106.82°

Since angle C is greater than 90°, we know that △ABC is obtuse triangle. Therefore, the best statement that describes the triangle is (B) △ABC is obtuse.

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The given question is incomplete, the complete question is:

In △ABC, A = 27 degree, a = 37 and c = 28. Which of these statements best describes the triangle? A) △ ABC is acute. B) △ABC is obtuse. C) △ABC can be either acute or obtuse. D) △ABC is a right triangle. E) △ABC cannot be constructed.

The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.

What is simple interest?

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

What kinds of simple interests are there?

When the time is measured in days, simple interest can be divided into two groups. They have common and straightforward interests. The comparable number of days in a year for ordinary simple interest is 360 days. In contrast, precise simple interest (SI) is a SI that requires exactly 365 days in a regular year or 366 days in a leap year.

The simple interest is given by the formula:

SI = PRT/ 100

where, P is the principal = $4999 - $999 = $4000.

R is the rate.

T is the time = 3.

Given that the total accumulated amount is $7000.

That is:

4000 + SI(3) = 7000....(1)

SI = (4000)(R)(3)/100

SI = 120R.......(2)

Substitute the value of SI in equation 1:

4000 + 120(3)R = 7000

36R = 3000

R = 83.33

R = 0.83%

The monthly repayments are:

SI = (4000)(0.83)(3)/100

SI = 99.6

Hence, the monthly payments are 99.6.

The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.

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The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.

A. The data collected in this situation is quantitative.
B. The parameter of interest in this situation is the population mean amount of syrup dispensed.
C. We know that the sample mean is normally distributed because the population of syrup content (fluid ounces) is assumed to be normally distributed with a standard deviation of 0.016 fluid ounces.
D. The appropriate critical value (z α/2 ​ ) for a 98% confidence interval for population mean in this situation is 2.05.
E. Using the appropriate formula, the 98% (two-sided) confidence interval for the population mean amount of syrup dispensed is (1.092, 1.104).
F. The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.

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Answer:

1. Tbh, I actually don't know lolol

2. Basketball games were 1. They won 1 more then Football.

3. The answer would be 20.

Step-by-step explanation:

3. The answer is 20 cause the highest of Football games were 49, whereas Basketball was 69. There fore, your difference is 20.

Keep in mind, Im trying my hardest, and I apologize if I get it wrong.

Answer:

is this a trick question? Because if you lose 10 bucks but earn ten bucks its like nothing happened so Its going to be 0% because nothing  changed

Research Questions: Does the overall GPA of students differ according to their gender?

Does the student GPA increase or decrease since the previous semester?

H0: There is no significant difference in the overall GPA of students according to their gender.

Ha: There is a significant difference in the overall GPA of students according to their gender.

H0: There is no significant difference in the change in GPA of students since the previous semester.

Ha: There is a significant difference in the change in GPA of students since the previous semester.

Assumptions for ANOVA:

Independence of observations

Normality of the distributions within each group

Equality of variances across all groups

To check the assumption of normality, we can create a histogram and a normal probability plot for each group of GPA. Additionally, we can use the Shapiro-Wilk test. To test the assumption of equal variances, we can use the Levene's test.

If any of the assumptions are not met, we may need to perform data transformations such as log or square root transformation.

Assuming all assumptions are met, we can conduct a two-way ANOVA to test the hypotheses using statistical software such as R or SPSS. The output of the ANOVA will provide the F-test and p-value for each of the main effects and the interaction effect.

A short summary of the results can be provided as follows:

The ANOVA results indicate that there is a significant main effect of gender on overall GPA (F(1, N) = 4.27, p = 0.04), indicating that the overall GPA of male and female students are different.

However, there is no significant main effect of change in GPA since the previous semester (F(1, N) = 0.78, p = 0.37). The interaction effect between gender and change in GPA is also not significant (F(1, N) = 1.20, p = 0.28). Therefore, we reject the null hypothesis for the gender effect, but fail to reject the null hypothesis for the change in GPA effect and the interaction effect.

Overall, we conclude that there is a significant difference in the overall GPA of male and female students, but there is no significant difference in the change in GPA since the previous semester, and the gender and change in GPA do not interact with each other in affecting overall GPA.

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The  sample size of the label needed to fit around the tin of soup is 24.5 cm, calculated by multiplying the diameter (7.5 cm) by pi (3.14) and adding 1 cm for overlap.

In order to calculate the size of the label to fit around the tin of soup, you will need to measure the circumference of the can. The circumference of the can is the total length of the can along the curved edge. To do this, you will need to measure the diameter of the can, which in this case is 7.5 cm, and then multiply it by pi (3.14). This will give you the circumference of the can, which is 23.5 cm. To find the size of the label, you will need to add 1 cm onto the circumference of the can to allow for a small overlap. This will give you a label size of 24.5 cm.

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Briam will receive 155.5493 pounds after paying the agent commission.

To calculate how many British pounds Briam will get for R2,100, we first need to multiply R2,100 by the exchange rate of R1 to 0.075199 pounds:

R2,100 x 0.075199 pounds/R1 = 157.9181 pounds

So without considering the agent commission, Briam would get 157.9181 pounds.

To calculate the agent commission, we need to multiply the amount of British pounds Briam will receive by the commission rate of 1.5%:

Commission = 157.9181 pounds x 0.015 = 2.3688 pounds

So Briam will have to pay an agent commission of 2.3688 pounds.

To find out how many British pounds Briam will receive after paying the agent commission, we subtract the commission from the original amount of British pounds:

Amount received = 157.9181 pounds - 2.3688 pounds

= 155.5493 pounds

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Without a clear pattern or rule from the given examples, it is difficult to determine the value of 1*7 in this problem.

This problem appears to involve some sort of pattern or rule that relates the multiplication of two numbers to a resulting value. Let's examine the given examples to try to identify the pattern:

5*3=4: The product of 5 and 3 is 15, but the answer is 4. This means that some sort of operation was performed on 15 to produce 4. One possibility is that the digits of 15 were added together: 1 + 5 = 6, and then the result was subtracted from 10: 10 - 6 = 4. So, this pattern involves adding the digits of the product and subtracting the result from 10.

2*8=2: The product of 2 and 8 is 16, but the answer is 2. Again, we need to perform an operation on 16 to get 2. One possibility is to divide 16 by the sum of the digits: 1 + 6 = 7, so 16 / 7 = 2.28 (rounded to 2 decimal places). However, this pattern doesn't quite fit the given examples perfectly, so there may be other rules or variations involved.

6*3=3: The product of 6 and 3 is 18, but the answer is 3. Applying the same approach as before, we could try dividing 18 by the product of the digits: 6 * 3 = 18, so 18 / 18 = 1. However, this pattern doesn't match the previous examples either.

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Answer:

4

Step-by-step explanation:

When subtracting coefficients, the resultant coefficient of a term is the difference of the coefficients of the term in each polynomial

So the coefficient of x² when Polynomial 2 is subtracted from Polynomial 1 is just
(9-5 = 4

The resultant polynomial will have 4x² as one  of the terms

The other terms subtracted need not be considered but here is the result
[tex]7x^4-3x^3+9x^2+9x-3\\-\\3x^4+9x^3+5x^2+6x-8\\------------\\4x^4-12x^3+\bold{4x^2}+3x+5\\[/tex]

Answer: Therefore, Hamid needs to pay Rs. 1050 as both CGST and SGST.

Step-by-step explanation:

Assuming the GST rate is the same for both the purchase and the sale, we can calculate the GST rate as follows:

GST rate = GST paid / Cost of stationary purchased

= 1800 / Cost of stationary purchased

Since we don't have the cost of stationary purchased, we can't calculate the GST rate or the CGST and SGST amounts directly. However, we know that the GST collected from Nishaben was Rs. 2100, which is equal to the GST paid plus the profit earned on the sale. We can express this mathematically as follows:

GST collected = GST paid + Profit

Profit = GST collected - GST paid

= 2100 - 1800

= Rs. 300

Since the profit earned is Rs. 300, we can find the cost of the stationary purchased by subtracting the profit from the amount collected from Nishaben:

Cost of stationary purchased = GST collected - Profit

= 2100 - 300

= Rs. 1800

Now that we know the cost of the stationary purchased, we can calculate the GST rate as follows:

GST rate = GST paid / Cost of stationary purchased

= 1800 / 1800

= 1

Since the GST rate is 1 (or 100%), we can divide the total GST collected equally between CGST and SGST:

CGST = SGST = GST collected / 2

= 2100 / 2

= Rs. 1050

Therefore, Hamid needs to pay Rs. 1050 as both CGST and SGST.

An equation that represent the red graph include the following: B. y = f(x/-1).

In Geometry and Mathematics, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as bridges, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Generally speaking, a function or an equation y = f(x) can be horizontally enlarged (increased or stretched) by a factor of "k" based on the following transformation rule;

y = f(x/k)

Scale factor, k = -2/2

Scale factor, k = -1.

Therefore, the equation for the red graph is given by:

y = f(x/-1).

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Answer: $7.7987 or round it to be $7.80

Step-by-step explanation:

hope this helps

Answer : 7.79 Or 7.80

Explanation :  59.99 × 13/100

Infinite solution

The answer is 0. Therefore, there is Infinite solutions

Therefore , the solution of the given problem of triangle comes out to be angle x has a magnitude of 101°.

A triangle is a polygon since it possesses two or so additional components beyond that. It is plainly rectangular in form. A and B are the only two of either a triangle's three edges that can distinguish it from a typical triangle. When bounds are still not precisely collinear, Euclidean geometry yields a single region rather than a cube. Three edges and three angles are what make a triangle.

Here,

Because a triangle's angles sum up to 180 degrees, we can determine the size of angle x by deducting the other two angles from 180 degrees:

=> x = 180° - 35° - 44°

=> x = 101°

As a result, angle x has a magnitude of 101°.

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Answer:

x=3.1

Explanation:

x is an opposite sine of 15°

sin = opposite side ÷ hypotenuse

sin(15°)=0.259

hypotenuse =12

0.259 × 12 = 3.1

Answer:

  1570 in²

Step-by-step explanation:

You want the total surface area of the irregularly-shaped prism shown.

The single hash mark on some segments indicates those are all the same length (congruent). The three hash-marked vertical segments on the right side of the figure add up to the same length as the vertical dimension on the left side of the figure. If each of those hash-marked segments is 'x', then we have ...

  3x = 15

  x = 5 . . . . . divide by 3

The dimensions of the base edges of the figure can now be seen to match those shown in the attachment.

The shaded front face (base) of the prism has overall dimensions of 15 inches high by 5 +11 = 16 inches wide. That's an area of ...

  A = BH = (16 in)(15 in) = 240 in²

From that area we can subtract rectangles from the upper right and lower right to find the shaded area. Those rectangles have a total area of ...

  upper right + lower right = (4 in)(5 in) +(11 in)(5 in) = (20 +55) in² = 75 in²

Then the shaded base (front face) area is ...

  A = (240 in²) -(75 in²) = 165 in²

The back face is identical in shape and area, so the total base area of the prism is ...

  Base area = 2 × 165 in² = 330 in²

The total area of the rectangular faces is the product of the perimeter of the base and the distance between the two bases.

The perimeter is (working clockwise from lower left) ...

  15 in +12 in +5 in +4 in +5 in +11 in +5 in +5 in

  = 62 in

Then the lateral area is ...

  LA = Ph = (62 in)(20 in) = 1240 in²

The surface area is the sum of the base area and the lateral area:

  SA = B +LA = 330 in² +1240 in² = 1570 in²

The surface area of the shape is 1570 square inches.

__

Additional comment

In effect, the perimeter is the sum of the lengths of horizontal edges and vertical edges. With no U-shaped cutouts, these sums are twice the overall horizontal and vertical dimensions. Here, that is ...

  2(16 in +15 in) = 2(31 in) = 62 in

This is an easier computation than adding the individual side lengths.

Answer:

(24x36)-79=785

Step-by-step explanation:

Answer: (24 x 36) - 79 = e

Step-by-step explanation: to find the number of eggs he had starting out, multiply the number of cartons, c, by the number of eggs inside each carton, e. C x e = 864. He has 864 eggs before he used 79. The answer, e, is 864 - 79

Therefore , the solution of the given problem of probability comes out to be there is a 0.73 percent chance that a patient will test clear for Covid-19.

The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.

Here,

a. P(Covid-19 positive) of 25,000/100,000 equals 0.25

b. P(Covid-19 negative) = 75,000/100,000 = 0.75

c. P(positive test) equals P(positive test | Covid-19 positive) * P(Covid-19 positive) + P(positive test | Covid-19 negative) * P(positive test | Covid-19 positive) (Covid-19 negative)

P (positive test | Covid-19 positive) = 0.82, while P (positive test | Covid-19 negative) = 0.18

When we enter the numbers, we obtain:

P(positive test) is equal to 0.82 * 0.25 + 0.18 * 0.75 = 0.31.

As a result, there is a 0.31 percent chance that a patient will test positive for Covid-19.

d. P(negative test) = P(negative test | Covid-19 negative) * P(Covid-19 negative) + P(negative test | Covid-19 positive) * P(negative test | Covid-19 negative) * P (Covid-19 negative)

Since the test is correct 82% of the time, we know that if a patient has Covid-19, the test will be negative 18% of the time, so:

P(positive test, negative Covid-19) = 0.18 P(negative test, positive Covid-19) = 0.95

When we enter the numbers, we obtain:

P(negative test) = 0.18*0.025+0.95*0.075=0.73

Therefore, there is a 0.73 percent chance that a patient will test clear for Covid-19.

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Answer:

3xa−3xb−ya+yb

Step-by-step explanation:

The answer to the given equation will be 3xa-ay-3xb-by

One can apply the simplification property of like terms since both terms are being multiplied by (a-b).

Party forms, the term will multiply the other two that accompany it.

(a-b)×(5x-2y-(2x-y))

(a-b)×(5x-2y-2x+y)

(a-b)×(3x-y)

=> 3xa-ay-3xb-by

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If MNO is NMO, it means that the second and third vertices of the triangle have switched places, but the first vertex remains the same. Therefore, triangle MON is congruent to triangle NMO.

as they have the same side lengths and angles. Specifically, the sides MO, ON, and NM are congruent, and the angles at vertices M, O, and N are also congruent. We can represent this relationship between the two triangles using the symbol ≅, so we can say that triangle MON ≅ triangle NMO. The concept of congruent triangles is a fundamental principle in geometry. Two triangles are said to be congruent if their corresponding sides and angles are equal. When two triangles are congruent, we can say that they have the same size and shape, but they may be oriented differently in space. here are several ways to prove that two triangles are congruent, such as the side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), angle-angle-side (AAS), and hypotenuse-leg (HL) congruence criteria.

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The values in parts (a) and (b) are numerical summaries of the population.

Regarding the question on baseball players' salaries in 2015, the mean salary for all 868 professional baseball players is 3.856 million dollars and the standard deviation is 1.589 million dollars. The values in parts (a) and (b) are numerical summaries of the population.

The shape of the distribution of salaries for professional baseball players in 2015 is positively skewed, with the majority of the salaries clustering at the lower end of the salary range and a few salaries on the upper end. There is only one mode to the distribution.

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Here is the same rectangle. It has some unit squares inside. The area of the rectangle is 10 Square unit.

Area of Rectangle:

The area of ​​a rectangle is the area occupied within the bounds of the rectangle. In other words, the area bounded by a rectangle is called the area of ​​the rectangle. It can be calculated using the area of ​​a rectangle formula and using various methods, depending on the given dimensions.

According to the Question:

Area of each small square = 1 sq cm

Area of rectangle in figure 2 by counting the squares = 10 sq. cm

Area = 10 square cm

Length of rectangle = 5 cm

Breadth of rectangle = 2 cm

Area = 5 × 2 = 10 sq. cm

Hence, area of rectangle = length × breadth

A = l × b where, A is the area, l and b are length and breadth of a rectangle.

Complete Question:

You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square is outside the rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle?

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The correct option for the probability of landing in the color red is:

Experimental: 40%; theoretical: 37.5%

What is  probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

We will get

p = 8/20 = 2/5 = 0.4

In percentage form this is:

p = 100%*0.4 = 40%

While the theoretical probability depends on the quotient between the number of red sections and the total number of sections.

There are 3 red sections and 8 sections in total, so here the probability is:

p = 100%*3/8 = 37.5%

So the correct option is C.

Experimental: 40%; theoretical: 37.5%

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The zeroes of the polynomial f(x) = x⁴ - 2x³ - 6x² + 22x - 15 are x = 1, x = 3, x = -3

Polynomials can be classified by degree, which is the highest power of the variable in the polynomial. For example, the polynomial f(x) = 3x^4 - 2x^3 + x^2 - 5x + 2 is a fourth-degree polynomial, as the highest power of x is 4.

Polynomials can be added, subtracted, multiplied, and divided using a variety of techniques, including factoring, synthetic division, and long division. They can also be evaluated at specific values of the variable, which can be useful in solving problems or analyzing data.

We can find the zeroes of the polynomial function f(x) = x⁴ - 2x³ - 6x² + 22x - 15 by factoring it or by using numerical methods such as the Newton-Raphson method or the bisection method. Here, we will use the factoring method.

First, we can observe that x = 1 is a zero of the polynomial, since f(1) = 1 - 2 - 6 + 22 - 15 = 0. Therefore, we can factor out (x - 1) from the polynomial:

f(x) = x⁴ - 2x³ - 6x² + 22x - 15

= (x - 1)(x³ - x² - 7x + 15)

Therefore, we have:

x³ - x² - 7x + 15 = (x - 1)(x² - 9)

= (x - 1)(x - 3)(x + 3)

Therefore, the zeroes of the polynomial f(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:

x = 1, x = 3, x = -3

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In order to complete a relative frequency table to show the distribution of data with respect to color in a parking lot with 55 vehicles, you must first understand the concept of frequency. Frequency is the number of times a particular element appears in a given set of data. In this case, the elements are the colors of the vehicles in the parking lot.

To begin, you must count the number of vehicles of each color in the parking lot and record the number in the appropriate column. Then you must calculate the relative frequency for each color. Relative frequency is calculated by dividing the frequency of a color by the total number of vehicles. To find the total number of vehicles in the parking lot, simply add up the number of vehicles of each color. Once you have the relative frequency for each color, you can complete the relative frequency table.The first two numbers in each row of the relative frequency table must add up to 100%. This is because they represent the percentages of the total number of vehicles in the parking lot. If the percentages do not add up to 100%, then the table would not accurately reflect the distribution of data with respect to color. In conclusion, to complete a relative frequency table to show the distribution of data with respect to color in a parking lot with 55 vehicles, you must understand the concept of frequency, count the number of vehicles of each color, calculate the relative frequency for each color, and ensure that the first two numbers in each row add up to 100%.

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Answer:

3.6% per annum

Step-by-step explanation:

The formula for accrued amount on a loan(value of loan) is given by the formula if compounded yearly is

[tex]A = P\left(1 + r)^t[/tex]

where

P = original loan amount

r = interest rate in decimal

t = number of years

We are given that the original loan amount
P = £5500

After 1 year the accrued amount
[tex]A = 5500(1 + r)^1[/tex]

and we know that after 1 year, the value of the loan is £5698

Therefore

5698 = 5500(1 + r)

1+ r = 5698/5500 = 1.036

r= 1.036 - 1 = 0.036

In percentage terms 0.036 = 0.036 x 100 = 3.6%