-An antique diamond engagement ring was purchased many years ago for $500. If the
ring has grown in value 8.7% annually and has a current value of $28,262, how old is the
ring?

In mathematics, a ratio is a comparison of two quantities or numbers expressed in terms of division. The order in which the quantities are expressed in a ratio is also important.

Ratios are used in various mathematical applications such as in finance, geometry, and physics. The units or quantities being compared in a ratio are crucial in determining the meaning and significance of the ratio.

For example, if the ratio is expressed as 2:1, it could mean that the first quantity is twice the size of the second quantity, or it could mean that the second quantity is half the size of the first quantity. Therefore, it is important to clearly define the units or quantities being compared to avoid any ambiguity or misunderstanding.

In the example above, if the ratio was expressed as 1:2 instead of 2:1, the meaning of the ratio would be reversed. Therefore, the order of the quantities in a ratio should be consistent with the context in which it is being used. In summary, the units and the order in which the quantities are expressed in a ratio are important in conveying accurate and meaningful information.

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Complete question:

In mathematics, the units or quantities being compared and the order in which they are expressed in a ratio are both important. The _____ in which ratio is expressed is important  

the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature.

How to find middle angle?

In a right triangle, the middle angle is the angle opposite the hypotenuse. To find this angle using trigonometry, you can use either the sine, cosine, or tangent ratio. Let's say that the two legs of the right triangle are a and b, and the hypotenuse is c. Then, you can use the following trig ratios to find the middle angle:

Sine ratio: sin(theta) = a/c

Cosine ratio: cos(theta) = b/c

Tangent ratio: tan(theta) = a/b

To find the middle angle, you would use the inverse sine, cosine, or tangent function, depending on which ratio you used. For example, if you used the sine ratio, you would take the inverse sine of a/c to find the angle: theta = sin²-1(a/c).

What is the relationship between the sine and cosine of the two non-right angles in a right triangle, and how do they define the ratios sine, cosine, and tangent?

In a right triangle, the two non-right angles are complementary, which means that their sum is 90 degrees. Let's call these angles alpha and beta. The sine and cosine of these angles are defined as follows:

Sine of alpha: sin(alpha) = opposite leg / hypotenuse

Cosine of alpha: cos(alpha) = adjacent leg / hypotenuse

Sine of beta: sin(beta) = adjacent leg / hypotenuse

Cosine of beta: cos(beta) = opposite leg / hypotenuse

Note that the opposite and adjacent legs are relative to the angle being considered. The ratios sine, cosine, and tangent are defined in terms of these ratios:

Sine ratio: sin(theta) = opposite leg / hypotenuse

Cosine ratio: cos(theta) = adjacent leg / hypotenuse

Tangent ratio: tan(theta) = opposite leg / adjacent leg

Therefore, the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature. If you know the value of one of these ratios, you can use it to find the value of the other using the fact that sin(alpha) = cos(beta) and cos(alpha) = sin(beta). This relationship is known as the complementary angle identities.

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Option (D) is correct because we can not determine whether the given pair of angles are complementary, supplementary, or neither

The given pair of angles can be either complementary or supplementary, depending on the value of x.

Complementary Angles: Two angles whose sum is 90 degrees are called complementary angles. In other words, if the sum of two angles is 90 degrees, then they are called complementary angles.

Supplementary Angles: Two angles whose sum is 180 degrees are called supplementary angles. In other words, if the sum of two angles is 180 degrees, then they are called supplementary angles.

Neither: If the sum of two angles is neither 90 degrees nor 180 degrees, then they are called neither complementary nor supplementary angles.

Not Enough Information (It depends on the value of x): If the measure of x is not given, then we cannot determine whether the given pair of angles are complementary, supplementary, or neither.

Hence, it depends on the value of x. Therefore, option D is the correct answer.

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Therefore, Thabo will get R18, Patrick will get R24, and Lucas will get R30.

In mathematics, a ratio is a comparison between two quantities or numbers, indicating how many times one quantity is contained within another. Ratios are often expressed in the form of a fraction, with the first quantity as the numerator and the second quantity as the denominator. Ratios can also be simplified by dividing both the numerator and denominator by their greatest common factor. Ratios are used in many areas of mathematics, science, and everyday life, such as in finance, cooking, and sports. They are particularly useful for comparing two quantities of different units or scales, as they provide a standardized way to express the relationship between them.

Here,

To determine how much each person will get, we first need to find the total of the ratios which is:

3 + 4 + 5 = 12

This means that the total amount of money is divided into 12 equal parts.

To find out how much each person gets, we need to multiply their share of the ratio by the total amount of money:

Thabo's share = 3/12 x R72 = R18

Patrick's share = 4/12 x R72 = R24

Lucas's share = 5/12 x R72 = R30

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Answer:

To find the perimeter, we need to add up the lengths of all the sides. In this case, we have four sides with lengths given by the expressions 2v-5, 4v+5, 2v-5, and 8v-7.

So the perimeter P is:

P = (2v-5) + (4v+5) + (2v-5) + (8v-7)

Simplifying and combining like terms, we get:

P = 16v - 12

Therefore, the perimeter is 16v - 12.

We can reduce the width of the confidence interval by increasing the sample size, reducing the confidence level and decreasing the mean (A, D, and F)

A confidence interval is an estimate of the interval that has a specified probability of including an unknown population parameter.

The purpose of a confidence interval is to estimate the true value of the population parameter being measured, such as a mean, a standard deviation, or a proportion.

In general, a wider confidence interval indicates more uncertainty about the estimate, while a narrower confidence interval suggests more precision in the estimate.

We want narrower confidence intervals to demonstrate more precision, as this allows us to draw more reliable conclusions about population parameters.

We cannot reduce the width of the confidence interval by increasing the sample size, increasing the confidence level or increasing the mean.

Thus, the correct options are a, d, and f.

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Answer:

Step-by-step explanation:

First find BC:

      [tex]BC^2=BD^2+DC^2[/tex]       (Pythagoras Theorem)

  [tex]\rightarrow BC^2=4^2+4^2[/tex]

  [tex]\rightarrow BC^2=32[/tex]

    [tex]\rightarrow BC=\sqrt{32} cm[/tex]

Now find AB:

    [tex]AB^2=AC^2+BC^2[/tex]          (Pythagoras Theorem)

  [tex]\rightarrow AB^2=4^2+(\sqrt{32}) ^2[/tex]

  [tex]\rightarrow AB^2=16+32[/tex]

  [tex]\rightarrow AB^2=48[/tex]

  [tex]\rightarrow AB=\sqrt{48}=6.9cm[/tex]

Diagonal AB = 6.9cm

The temperature in Buffalo when it is 23 degrees Fahrenheit is equivalent to -5 degrees Celsius.

Fahrenheit is a temperature scale that was created by Gabriel Fahrenheit in 1724. Fahrenheit is used primarily in the United States and a few other countries. The boiling point of water on this scale is 212 degrees Fahrenheit, while the freezing point is 32 degrees Fahrenheit.

The Celsius scale, on the other hand, is a temperature scale that is used throughout the world. It was created in 1742 by Swedish astronomer Anders Celsius. On this scale, the boiling point of water is 100 degrees Celsius, and the freezing point is 0 degrees Celsius.

The formula for converting degrees Fahrenheit to degrees Celsius is: C=5/9(F-32). C is the equivalent Celsius temperature, while F is the equivalent Fahrenheit temperature.

Let's put the formula into practice to answer the question, "If the temperature in Buffalo is 23 degrees Fahrenheit,

We can simply plug in the given value for Fahrenheit temperature, which is 23 degrees Fahrenheit.

C = (5/9) (23 - 32)C = (5/9) (-9)C = -5

Therefore, -5 degrees Celsius is equivalent to 23 degrees Fahrenheit when the temperature is in Buffalo.

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The value of y when x=36 is 31/3.

According to the question,

x varies directly with 3y+5

Thus,

[tex]x = k(3y+5)[/tex]

where K is any positive integer.

Now, from the question,

y=5/3 when x=10

Thus,

[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]

Now we can use k to find the value of y when x=36:

[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]

In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.

Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.

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Complete Question:

If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36

The missing value to find the length of BC is 9x.

The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.

The distance formula is given as:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values of the coordinates of B and C we have:

distance = √((7x - (-2x))² + (-1y - (-4y))²)

distance = √((9x)² + (3y)²)

distance = √(81x² + 9y²)

distance = 3√(9x² + y²)

Hence, the missing value to find the length of BC is 9x.

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The 90% confident sample of size 191 with 23 successes that the true population proportion falls between 0.077 and 0.163 based on the sample data.

To find the 90% confidence interval for a sample proportion, we can use the following formula:

Confidence Interval = sample proportion ± margin of error

where the margin of error is:

Margin of Error = z* (\sqrt{(p*(1-p)/n))}

where z is the z-score corresponding to the level of confidence,

p is the sample proportion, and n is the sample size.

In this case, we have a sample size of n = 191 and 23 successes,

which gives a sample proportion of p = 23/191 ≈ 0.120.

To find the z-score corresponding to a 90% confidence level,

The z-score for a 90% confidence level is approximately 1.645.

Plugging in the values into the formula, we get:

Margin of Error = 1.645 * (\sqrt{(0.120*(1-0.120)/191)}) ≈ 0.043

Therefore, the 90% confidence interval for the population proportion is:

0.120 ± 0.043

which can be expressed as (0.077, 0.163) rounded to three decimal places.

So we are 90% confident that the true population proportion falls between 0.077 and 0.163.

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Answer:

Starting with the left side of the equation:

cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)

= cosθ + sinθ

Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.

Answer:f(-2)=6+10

So f(-2) =16

Step-by-step explanation:

To estimate the distance traveled  we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.

A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.

The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.

Using the trapezium rule, the estimated area of each strip is:

Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s

Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s

Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s

Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s

The total estimated area is the sum of the areas of the 4 strips:

Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s

Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:

Estimated distance traveled is = |-4000| = 4000 meters

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Answer:

x² - 49

Step-by-step explanation:

(x - 7)² =

(x - 7) * (x - 7) =

x * x - 7 * 7 =

x² - 49

The successfullly completed the proof of the cancellation property of vector addition.

Complete proof of the cancellation property of vector addition:Let u, v, and w be vectors in a vector space V such that u + w = v + w. We have to show that u = v.  We know that the cancellation property of vector addition states that for all vectors u, v, and w in a vector space V, if u + w = v + w, then u = v.So, u + w = v + w can be written as, u + w - w = v + w - w, applying subtraction on both sides.u + 0 = v + 0 (as - w + w = 0)0 is an additive identity, so it can be dropped off.u = v, which is the desired result.The statement "u + w = v + w" was given, and we have shown that it implies that "u = v". Hence, we have successfully completed the proof of the cancellation property of vector addition.

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A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.

A p-value is a statistical indicator that, under the null hypothesis, shows the likelihood of receiving a test statistic that is as extreme to or more extreme than the one seen in the sample data. Depending on the degree of statistical significance the researcher selects, it is employed in hypothesis testing to determine whether to reject or fail to reject the null hypothesis. The null hypothesis is rejected in favour of the alternative hypothesis if the p-value is less than or equal to the selected level of significance (typically 0.05). The null hypothesis is not rejected if the p-value is higher than the selected level of significance.

A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.

B. The alternative hypothesis may be that the additional exercise has no impact on the frequency of heart attacks.

C. Depending on the study's specific design and the outcome measure used to gauge the prevalence of heart attacks, the comparison distribution would vary.

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Answer: The weight of the Apples is 160g

Step-by-step explanation:

If the apples were priced at $3.50/kg, then the cost of 1 kg of apples would be $3.50.

To find out the weight of 12 apples, we can divide the total cost of $6.72 by the cost of 1 kg of apples:

$6.72 ÷ $3.50/kg = 1.92 kg

So, the weight of 12 apples is 1.92 kg.

To find the average weight of 1 apple, we can divide the total weight of the 12 apples by the number of apples:

1.92 kg ÷ 12 = 0.16 kg

Finally, we need to convert the weight of 1 apple from kilograms to grams:

0.16 kg x 1000 g/kg = 160 g

Therefore, the average weight of an apple in grams is 160 g.

Answer:

No, Jamel is not correct. While the 9 in 129,082 is indeed two places to the left of the 9 in 127,694, it is not two times greater.

In fact, the value of a digit in a number is determined by its place value. Each place value to the left represents a value that is ten times greater than the previous place value. So, the 9 in the ten thousands place of 129,082 represents a value of 9 x 10,000 = 90,000.

Similarly, the 9 in the ten thousands place of 127,694 represents a value of 9 x 10,000 = 90,000 as well. Therefore, both 9s have the same value and are not different by a factor of two.

In summary, Jamel's reasoning is flawed and not correct. The value of a digit in a number is based on its place value, and not its position relative to other digits.

the possible dimensions of the rectangular prism are:

1 unit by 12 units by 10 units

2 units by 6 units by 10 units

3 units by 4 units by 10 units

Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:

V = l × w × 10

We are also given that the prism requires 120 unit cubes to fill completely, which means:

V = l × w × 10 = 120

Dividing both sides by 10, we get:

l × w = 12

Now we need to find pairs of positive integers l and w that multiply to 12. These are:

1 × 12

2 × 6

3 × 4

Therefore, the possible dimensions of the rectangular prism are:

1 unit by 12 units by 10 units

2 units by 6 units by 10 units

3 units by 4 units by 10 units

Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.

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Answer:

Step-by-step explanation:

xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc

First, we need to find the value of g(pi/2):

g(pi/2) = cos(pi/2) = 0

Now we can substitute this value into f(x):

f(g(pi/2)) = f(0) = sin(0) = 0

Therefore, f(g(pi/2)) = 0.

Solution:

we have been asked to graph [tex]f(x)=2^x+1[/tex] and [tex]g(x)=-x+7[/tex] on the same coordinate plane.

Then we have been asked to find the solution to the equation ?

So we will plot the graph and look for their point of intersection, the x-coordinate of the point of intersection will give the value of x.

So from the graph its clear that the point of intersection is (2,5)

Hence the value of x=2.

A. deposit $735.03 one year from now. B. $210.48 for each of the four years. C. choose the lump sum of $750 from your father. D. Interest rate of 7.4% compounded annually. E. Interest rate of 12%.

a. To have a balance of $1,000 four years from now, you need to calculate the present value of this amount. Using the compound interest formula, we can calculate that you need to deposit $735.03 one year from now to have a balance of $1,000 four years from now.

b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, you can use the annuity formula to calculate the required payments. The formula gives us a payment of $210.48 for each of the four years.

c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 one year from now, you can compare the present value of both options. The present value of the four payments of $210.48 each, using an 8% annual interest rate, is $682.96. Therefore, you would choose the lump sum of $750 from your father.

d. If you have only $750 one year from now, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 7.4% compounded annually.

e. If you can only deposit $186.29 each at Years 1 through 4, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 12% compounded annually.

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Complete question:

Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.

a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?

b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?

c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?

d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now? 7.4%

e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?

Answer:

Step-by-step explanation:

To factor the left side of the equation, we can first factor out the common factor of (n+8):

n7(n + 8) - 4(n + 8) = (n + 8)(n7 - 4)

So the complete factored form of the expression is (n + 8)(n7 - 4).

The distance between the third traffic light from the second traffic light is 35 yards.

Three traffic lights on a street span 120 yards.

If the second traffic light is 85 yards away from the first.

Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.

This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.

Thus, the distance between the third traffic light from the second traffic light is 35 yards.

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There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.

It is calculated by adding up all the values in the set and then dividing the sum by the total number of values. The mean is often used as a measure of central tendency, which describes the typical or representative value in a set of data.

This is a two-sample independent means t-test problem.

The null hypothesis is that there is no difference between the mean times needed to access flight information for the two major airlines, and the alternative hypothesis is that there is a difference.

Assuming the conditions for inference are met (random sampling, normality of the population, and independence between the two samples), we can calculate the t-value and the p-value for the test.

The formula for the t-value in a two-sample independent means t-test is:

t = (x1 - x2) / √[ (s1²/n1) + (s2²/n2) ]

Plugging in the given values, we get:

t = (2.5 - 2.1) / √[ (0.8²/20) + (1.1²/20) ]

t = 1.21

Using a t-table with 38 degrees of freedom (df = n1 + n2 - 2), we find that the p-value is between 0.10 and 0.05.

Therefore, the correct answer is c:

There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.

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Answer:

  11/168  

Step-by-step explanation:

You want the decimal value 0.06547619047 represented as a fraction.

The obvious choice is ...

  [tex]\dfrac{6547619047}{100000000000}[/tex]

However, we see that this might be a truncation of the repeating decimal fraction ...

  [tex]0.065\overline{476190}[/tex]

This value can be represented  by the fraction 11/168.

  [tex]0.065\overline{476190}=\boxed{\dfrac{11}{168}}[/tex]

__

Additional comment

You can arrive at this several ways. The attached calculator display shows one way.

Another is to write it as the sum 0.065 +(1/1000)(476190/999999). Reducing the fraction here may require a bit of trial and error.

You can also write it as a continued fraction and then evaluate the result.

  0.06547619047 = 1/(15 +1/(3 +1/(1 +1/2))) = 11/168

where the last 2 is a rounding of 1.999999825...

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Answer:

11 weeks

Step-by-step explanation:

42 + 15 * x = 207

42 + 15x = 207

15x = 207 - 42

15x = 165

x = 11

Hope this helps <3

If the parametric equations for x and y are both non-constant linear functions of t, then curve must be a line.

A curve (sometimes known as a curved line in ancient texts) is a mathematical entity that is similar to a line but does not have to be straight.

A curve may be conceived of intuitively as the trace left by a moving point. "The [curved] line[a] is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width," Euclid wrote more than 2000 years ago.

Let x = at+b and y = ct+d

Then,

[tex]\frac{x-b}{a}=\frac{y-d}{c}=t xc-bc=ay-adxc-ay+ad-bc=0[/tex]

Which is linear equation in x and y.

Therefore, curve is always a line.

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