When Ruby bought her house, it cost £400,000. Each year the house increased in value by 1.05%. What was the value of her house after 6 years? Give your answer to 4 s.f.​

Answer:

949.2

Step-by-step explanation:

To solve this equation, you must use P.E.M.D.A.S...

First, solve 7x9 and 5x2...

7x9= 63  5x2 = 10

So...

1000+50-36+63+8÷10+1

Next, solve 8÷10 and get 0.8

So...

1000+50-36+63+0.8+1

Then, solve 1000 + 50, and 36+63, and that result with 0.8 and that with 1.

So...

1050-100.8

The Solve!

949.2

Hope this helps!

-kiniwih426

Answer:

-t+2>10

Step-by-step explanation:

Just ask.

Hope this helps! :D

Christopher's distance from his starting point is 3.6 km

Since Christopher initially walks South 5 km and then walks on a bearing of of 036º until he is due east of his starting point.

His distance South, his distance from his starting point and his distance from his 036º bearing, all form a right-angled triangle.

This right-angled triangle with opposite side to the angle 036º, as his distance from his starting point, x and the adjacent side to the angle 036º, as his distance 5 km south.

Since we have both the opposite and adjacent sides of a right-angled triangle,

From trigonometric ratios,

tanФ = opposite/adjacent

tanФ = x/5 km

Now Ф = 036º

So, tan36º = x/5km

x = 5 km(tan36º)

x = 5 km (0.7265)

x = 3.633 km

x ≅ 3.6 km to 1 decimal place.

So, Christopher's distance from his starting point is 3.6 km.

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Answer:

None of the above

Step-by-step explanation:

Step-by-step explanation:

Red=4

Blue=3

Yellow=3

Total=10

Pr(BY) without replacement= 3/10 *3/9

=6/90

=1/15

The average rate of change for d(t) = 40| t - 1.25| in interval 0.5 ≤ x ≤ 1.0 is -40.

Rate is a measurement to determine the change in one quantity with respect to another quantity.

The given function is,

d(t) = 40| t - 1.25|

And the given interval, is 0.5 ≤ x ≤ 1.0

To find the average rate of change for given function,

Use formula

Average rate of change = f(b) - f(a) / b - a

In the given question a = 0.5 and b= 1.0

d(0.5) = 40 | 0.5 - 1.25| = 40 |-0.75| = 40(1.20) = 30

d(1.0) = 40 |1 - 1.25| = 40 |-0.25| = 40(0.25) = 10

The average rate of change = 10 - 30 / 1 - 0.5 = -20 / 0.5 = -40

The average rate of change of the given function is -40.

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The solution to the algebraic simultaneous equations \(x^{2}\)- 3\(y^2\) = 13 and 2x + 3y = 4 is x = 2 and y = -1.

:To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method. From the second equation, we can express x in terms of y as x = (4 - 3y)/2. Substituting this value of x into the first equation, we get \(((4 - 3y)/2)^2\) - 3\(y^2\) = 13. Simplifying this equation gives (16 - 24y + 9\(y^2\)/4 - 3y^2 = 13. Rearranging terms and simplifying further leads to 13\(y^2\) + 24y - 51 = 0. Solving this quadratic equation, we find two possible values for y: y = -4 and y = 1. Substituting these values back into the second equation, we can find the corresponding values of x. For y = -4, x = 2; and for y = 1, x = 2/5. Therefore, the solution to the system of equations is x = 2 and y = -1.

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Answer:6-

Step-by-step explanation:

A value of 0.25 for p(1-p) in the sample size formula when the true value of p is unknown.

This is because the value of p(1-p) is maximum when p=0.5, and since we do not have any information about the true value of p, assuming p=0.5 is the most conservative approach. Therefore, to calculate the sample size required to estimate a proportion using a confidence interval with a margin of error e, we can use the formula:

\(n = [z^2 * p(1-p)] / e^2\)

where z is the z-score corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and e is the desired margin of error. We can use p=0.5 and solve for n to get a conservative estimate of the sample size required for the given confidence level and margin of error.

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If prior knowledge or data suggests that the proportion is significantly different from 0.5, then a more accurate estimate of p should be used in the formula.

To calculate the sample size formula for estimating a proportion using a confidence interval with a margin of error e, we

use the following formula:

\(n = (Z^2 × p × (1-p)) / e^2\)

where n is the required sample size, Z is the Z-score corresponding to the desired level of confidence,

p is the estimated proportion, and

e is the margin of error.

Since the product p(1-p) is not known, a conservative approach is to use p = 0.5, which is the value that maximizes the

product p(1-p) for any given proportion.

This approach ensures that the sample size will be large enough to obtain a reliable estimate of the proportion, even if

the true proportion is close to 0 or 1. However, if prior knowledge or data suggests that the proportion is significantly

different from 0.5, then a more accurate estimate of p should be used in the formula.

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Answer: 60%

Step-by-step explanation:

2,400/4,000 x 100/1

0.6 x 100 = 60%

Answer:

3.78%

Step-by-step explanation:

The formula for compound interest is given by:

A(t) = P(1 + r/n)^(nt), where

Thus, we can plug in 8500 for P, 11022 for A(t), 1 for n, and 7 for t to find r:

Step 1:  Plug in the values and simplify:

11022 = 8500 * ( 1 + r/1)^(7 * 1)

11022 = 8500 * (1 + r)^(7)

Step 2:  Divide both sides by 8500:

(11022 = 8500 * (1 + r)^(7)) / 8500

11022/8500 = (1 + r)^(7)

5511/4250 = (1 + r)^(7)

Step 3:  Raise both sides to the 1/7 power (this is the same as taking the 7th root of both sides):

(5511/4250 = (1 + r)^(7))^(1/7)

1.037815641 = 1 + r

Step 4:  Subtract 1 from both sides to find r:

(1.037815641 = 1 + r) - 1

0.0378154607 = r

Step 5:  Multiply 0.0378154607 by 100 to find the interest rate as a percentage:

0.0378154607 * 100

3.78156407 = %

Step 6:  Round to the nearest two decimal places:

3.78

Thus, the interest rate is about 3.78%

Number of phone calls the first evening: 17

Number of phone calls the second evening: 88

Number of phone calls on the third evening:​ 22

Given that Lena received a total of 127 phone calls at the call center.

On the third evening, she received 5 more calls than the first evening.

On the second evening, she received 4 times as many calls as on the third evening.

We have to calculate, How many phone calls did she receive each evening?

Let's say on the first day she received x calls

then the number of calls received on the third day = x + 5

number of calls received on second day = 4(x + 5)

Now, x + x + 5 + 4(x + 5) = 127 ( given )

6x + 25 = 127

6x = 102

x = 17

So the number of calls received on the first day = is 17

number of calls received on the second day = 88

number of calls received on the third day = 22

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Answer:

a. y = 3

b. x = 1

c. y-intercept = 5

d. x-intercept = -2.5

e. 2

f. y = 2x + 5

Step-by-step explanation:

Based on the graph, we can see the point where x is -1, y = 3.

Based on the graph, we can see the point where y = 7, x = 1.

Based on the graph, we can see the y-intercept is 5.

Based on the graph, we can see the x-intercept is -2.5.

To calculate the slope of the line, I will be using the points (-1, 3) and (0, 5).

Slope = \(\frac{rise}{run}\)

           = \(\frac{5-3}{0-(-1)}\)

           = \(\frac{2}{1}\)

           = 2

The equation of a line is: y = mx + c where m is the slope and c is the y-intercept. Thus, the equation of the line in this case is: y = 2x + 5

The number (up to isomorphism) of abelian groups of order n is different from the number (up to isomorphism) of abelian groups of order m, unless n and m are isomorphic.

To understand why, consider the fact that the number of abelian groups of a given order is determined by the prime factorization of that order. Specifically, the number of abelian groups of order p^n is equal to the number of partitions of n, where p is a prime number. Thus, the number of abelian groups of a given order is determined by the prime factorization of that order.

If two orders have different prime factorizations, then the numbers of abelian groups of those orders will be different. For example, the number of abelian groups of order 12 is different from the number of abelian groups of order 15, since 12 and 15 have different prime factorizations. On the other hand, if two orders have the same prime factorization, then the numbers of abelian groups of those orders will be the same (up to isomorphism), since the number of abelian groups of an order is determined solely by the prime factorization of that order.

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There are 10 numbers less than 100 but larger than 30 that, when divided by 5 and 6, yield the same remainder. This can be determined by finding the least common multiple (LCM) of 5 and 6, which is 30.

Then, we identify the numbers in the range (30, 100) that have the same remainder when divided by 30, which is 0.

To find the numbers that satisfy the given condition, we need to consider the common multiples of 5 and 6. The LCM of 5 and 6 is 30. Any number that leaves the same remainder when divided by 5 and 6 will also leave the same remainder when divided by their LCM, which is 30.

In the given range, (30, 100), we can find the numbers that yield a remainder of 0 when divided by 30. Starting from 30 itself, we can increment by multiples of 30 to find other such numbers. The numbers that satisfy the condition are: 30, 60, 90, and so on.

To determine the total count of these numbers, we need to consider how many multiples of 30 fall within the range of (30, 100). We can divide the range width, which is 100 - 30 = 70, by the increment, which is 30. The result is (70 ÷ 30 = 2 remainder 10), meaning there are two complete sets of multiples of 30, plus an additional 10 numbers.

Therefore, there are 2 sets of numbers (30, 60, 90) and an additional 10 numbers (40, 50, 70, 80, 100) that satisfy the condition. The total count is 2 + 10 = 12.

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Answer:

what do you need help with

If manny paid $114.03 for the items purchased , then he paid the correct amount .

The first step is to determine the total cost of all the items purchased.

Total cost = $32.65 + (3 x $14.89) + $39.99 = $117.02.

Now, determine the cost after the promotional sale: (100 - 10%) x $117.02 = $105.32

The last step is to determine the total cost after tax: (1.08) x 105.32 = $114.03

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Answer:c

Step-by-step explanation:

trust

Answer:

see below (I hope this helps!)

Step-by-step explanation:

We can split this into 2 cases:

3x + 2 > 9 or -(3x + 2) > 9

3x > 7 or 3x + 2 < -9

x > 7/3 or x < -11/3

The difference in mass between the bananas and the apples is 4 times the difference between the mass of one banana and the mass of one apple, which is represented by (b - a).

Let's say the mass of one banana is 'b' grams and the mass of one apple is 'a' grams. Since we have four bananas and four apples, the total mass of the bananas would be 4b grams, and the total mass of the apples would be 4a grams.

To find the difference in mass between the bananas and the apples, we need to subtract the mass of the apples from the mass of the bananas:

Difference in mass = Mass of bananas - Mass of apples

Mathematically, this can be represented as:

Difference in mass = (4b) - (4a)

We can simplify this further by factoring out the common factor of 4:

Difference in mass = 4(b - a)

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Answer:

X = 4

Step-by-step explanation:

17 -X = 1 +3X

NOTE: PUT X IN ONE SIDE AND THE NUMBER IN OTHER

so 17 -X = 1 +3X so it will be 3x + x = 4x

then 17 - 1 = 16

4 divide by 16 = 4

so X = 4

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Area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

The correct option is b.

The area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

What is Z score: The z-score (aka, standard score) is a dimensionless metric that represents the deviation of a score from the mean in units of the standard deviation.

The formula for computing z-scores is as follows:

Z = (X - μ) / σ

where X is the score,

μ is the mean,

and σ is the standard deviation.

Z-scores can be used to assess the relative position of a score in relation to the distribution's mean and standard deviation.

In this particular question, the Z score of two test scores is 1.2 and 1.5.

To obtain the area between these scores, we have to find the area between each score and the mean in the z-score table, and then subtract the smaller area from the larger area.

First, we need to find the area between 1.2 and 1.5.

We can see the area from the z-score table as P(z < 1.5) - P(z < 1.2).

The following z-score table can be used to find these probabilities:

z-score table

From the table, P(z < 1.5) is equal to 0.9332, and P(z < 1.2) is equal to 0.8849.

Thus, P(1.2 < z < 1.5) = 0.9332 - 0.8849 = 0.0483.

To find the answer to the question, we have to calculate the area between the scores, which is 0.0483 in this case, by finding the area between each score and the mean in the z-score table and then subtracting the smaller area from the larger area.

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The location of √ 7 on a number line between 2 and 3.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.

A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.

In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.

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Answer:

\(v=\frac{3\left(-z+5\right)}{5}\)

Step-by-step explanation:

im too good no ty

<3

Red

Answer:

I am not sure that there are 2 ways to evaluate that. Not that I know of. You just distribute the 32 to the 16 & 6 inside of the parentheses.

Step-by-step explanation:

(32*16)-(32*6)=

(512)-(192)=

320

To find all relative  extrema of the function f(x) = cos(x) - 8x on the interval [0, 4], we'll use the second derivative test where applicable.

Step 1: Find the first derivative of the function.
f'(x) = -sin(x) - 8

Step 2: Set the first derivative equal to zero to find critical points.
0 = -sin(x) - 8

Step 3: Solve for x.
sin(x) = -8 (Since the range of sin(x) is [-1,1], there are no solutions for this equation on the interval [0, 4].)

Step 4: Check endpoints of the interval.
f(0) = cos(0) - 8(0) = 1
f(4) = cos(4) - 8(4) ≈ -31.653

Step 5: Find the second derivative.
f''(x) = -cos(x)

Step 6: Apply the second derivative test.
Since there are no critical points, we don't need to use the second derivative test.

Conclusion: There are no relative extrema within the interval [0, 4] for the function f(x) = cos(x) - 8x. The extrema on the interval are the endpoints, with a maximum value of 1 at x = 0 and a minimum value of approximately -31.653 at x = 4.

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A relative maximum at x ≈ 2.301, a global minimum at x = 4, and no relative minimum.

To find all relative extrema of the function f(x) = cos(x) - 8x in the interval [0, 4], we will use the first and second derivative tests. Here's a step-by-step explanation:

1. Find the first derivative of the function:

f'(x) = -sin(x) - 8.

2. Find the critical points by setting f'(x) equal to 0:

-sin(x) - 8 = 0.

3. Solve for x to find the critical points within the interval [0, 4]. The equation is difficult to solve algebraically, so we can use a numerical method or graphing calculator to approximate the solution. We find one critical point x ≈ 2.301.

4. Find the second derivative of the function:

f''(x) = -cos(x).

5. Evaluate the second derivative at the critical point

x ≈ 2.301: f''(2.301) ≈ -cos(2.301) ≈ -0.74.

6. Since f''(2.301) < 0, the second derivative test tells us that there is a relative maximum at the critical point x ≈ 2.301.

7. Check the endpoints of the interval [0, 4].

For x = 0, f(0) = cos(0) - 8(0) = 1.

For x = 4, f(4) = cos(4) - 8(4) ≈ -31.653.

The relative extrema of the function f(x) = cos(x) - 8x in the interval [0, 4] are as follows:

a relative maximum at x ≈ 2.301,

a global minimum at x = 4,

and no relative minimum.

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Answer:

1. 24ft ^3

2. 64in^3

3. 500yd^3

4. 32.832cm^3

Step-by-step explanation:

1. 4 * 3 * 2

= 24ft

2. 4 *4 * 4

= 64in

3. 20*5*5

= 500yd

4. 1.9*3.2*5.4

= 32.832

Answer:

19

Step-by-step explanation:

The first thing is recognize that it is a rectangle and two triangles with given bases and heights.

So the first step is finding the area of both triangles, which you can do with the formula for the area of a triangle:

A = (BH)/2

Because the height is two, the area is going to be equal to the base.

The sum of the two triangles is 7.66.

Next you want to find the area of the rectangle, you can do so using the formula:

A = BH

A = 6(2)

The area of the rectangle is 13.

Find the sum of the areas of the three shapes.

3.30 + 4.36 + 12 = 19.66