Margaret is saving $20 every week so that she can have enough money to buy a bracelet she wants. The bracelet costs $525. What is the minimum number of weeks she will have to save to be able to buy the bracelet.?

Hello There!

To simplify fractions, divide both the numerator "top number" and the denominator "bottom number" until you can't go any lower.

EXAMPLE

[tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]

You divide the numerator and the denominator both by 4 which gives you the fraction [tex]\frac{1}{2}[/tex]

The diameter is 80 mm, the volume of the sphere is increasing at a rate of approximately 40211.2 mm³/s.

To find how fast the volume of the sphere is increasing, we can use the formula for the volume of a sphere:

[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]

Where V is the volume of the sphere and r is the radius.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\[ \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt} \][/tex]

Given:

- [tex]\( \frac{dr}{dt} = 2 \)[/tex] mm/s (rate at which the radius is increasing)

- [tex]\( r = \frac{d}{2} = \frac{80}{2} = 40 \)[/tex] mm (radius when the diameter is 80 mm)

Substitute these values into the formula:

[tex]\[ \frac{dV}{dt} = 4\pi (40)^2 (2) \][/tex]

[tex]\[ \frac{dV}{dt} = 4\pi (1600) (2) \][/tex]

[tex]\[ \frac{dV}{dt} = 12800\pi \][/tex]

Now, let's evaluate this numerically:

[tex]\[ \frac{dV}{dt} ≈ 12800 \times 3.14 \][/tex]

[tex]\[ \frac{dV}{dt} ≈ 40211.2 \text{ mm}^3/\text{s} \][/tex]

Therefore, when the diameter is 80 mm, the volume of the sphere is increasing at a rate of approximately 40211.2 mm³/s.

To ship 3,456 chairs with each box holding 9 chairs, you will need a total of 385 boxes.

To find the number of shipping boxes needed, we need to divide the total number of chairs by the number of chairs that can fit in one box. So, with 3,456 chairs and the capacity of each box being 9 chairs, we use the formula:

Number of boxes = Total chairs / Chairs per box

This gives us:

Number of boxes = 3,456 / 9

This division results in 384 with a remainder of 0. Since you can't ship a fraction of a box, but you need a whole box even for a single chair, this means that you will need 385 boxes to ship all the chairs.

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The length of the wall is : 26 ft.

 and width of the wall is: 9 ft.

What is area of a rectangle?

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

The area of a rectangle is: Area= length × width

Solution:

area = 234

length = ?

width = ?

Given, length is 8 ft greater than twice the width.

Now, l = 2w ₊ 8

        l × w = 234 (given)

Substitute for l

(2w ₊ 8)w = 234

multiply

2w² ₊ 8w = 234

2w² ₊ 8w ₋ 234 = 0

Now divide by 2 to eliminate the coefficients of w.

w² ₊ 4w ₋ 117=0

get the factors for the above equation.

We get the factors as: 9 and ₋13,( ₋13 is not applicable as width cannot be negative)

Hence we get the width as 9, now substitute it in:

l = 2w ₊ 8

l = 2(9) ₊ 8

l = 26 ft,

Hence the length and width of the rectangle is 26 ft and 9 ft respectively.

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To calculate the price using the constant dividend growth model, we can use the formula: Price = Dividend / (Market Capitalization Rate - Dividend Growth Rate). Given the expected dividend per share, market capitalization rate, ROE, and plowback ratio, we can calculate the price per share.

To calculate the price using the constant dividend growth model, we can use the formula:

Price = Dividend / (Market Capitalization Rate - Dividend Growth Rate)

Given that the expected dividend per share is $5 and the market capitalization rate is 10%, we can calculate the dividend growth rate using the ROE and plowback ratio. The plowback ratio is the portion of earnings retained by the company to finance growth. It is calculated as (1 - Dividend Payout Ratio). The dividend payout ratio is the portion of earnings paid out as dividends, which is the complement of the plowback ratio.

Using the formula for the dividend growth rate:

Dividend Growth Rate = ROE * Plowback Ratio

Given that the ROE is 14% and the plowback ratio is 60%, the dividend growth rate is:

Dividend Growth Rate = 14% * 60% = 8.4%

Now we can calculate the price:

Price = $5 / (10% - 8.4%) = $5 / 1.6% = $312.50 per share

To test the claim that whether a subject lies is independent of the polygraph test indication, a chi-square test of independence is conducted. The results, with a chi-square value of 34.774, suggest that polygraphs are effective in distinguishing between truths and lies.

To test the claim that whether a subject lies is independent of the polygraph test indication, we will conduct a chi-square test of independence. Using a significance level of 0.05, we will compare the observed frequencies in the table to the expected frequencies assuming independence. If the test statistic is significant, it would suggest that polygraphs are effective in distinguishing between truths and lies.

First, let's calculate the expected frequencies assuming independence. The total number of subjects who lied is 42+15=57, and the total number of subjects who did not lie is 15+129=144. The proportion who lied is 57/(57+144)=0.283. Multiplying this proportion by the number of subjects who were indicated as lying (57), we would expect (0.283)(57)=16.131 subjects to be accurate. Similarly, multiplying the proportion who did not lie by the number of subjects who were indicated as not lying, we would expect (0.717)(144)=103.488 subjects to be accurate.

Now, let's calculate the chi-square test statistic. Using the formula: chi-square = Σ (observed frequency - expected frequency)^2 / expected frequency, we calculate the chi-square value to be 34.774. Comparing this value to the critical chi-square value at a significance level of 0.05, with (2-1)(2-1) = 1 degree of freedom, the critical chi-square value is 3.841. Since the calculated chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the results suggest that polygraphs are effective in distinguishing between truths and lies.

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To calculate the cost of a circular property with a diameter of 50', determine the area using the formula π * r^2, and then multiply by the cost per square foot. The total cost of the property comes to $235,619.40.

The question asks us to calculate the cost of a property with a circular shape having a diameter of 50'. To begin with, we will find the area of the circular property by using the formula for the area of a circle, A = π * r2, where π (pi) is approximately 3.14159, and r is the radius of the circle. Since the diameter is given as 50', the radius (r) would be half of that, which is 25'. Therefore, the area (A) of the property is 3.14159 * (25')2 = 3.14159 * 625 = 1963.495 square feet.

Now, if the cost is $120 per square foot, we multiply the area by this cost to find the total price of the property. So, the total cost is 1963.495 square feet * $120/square foot = $235,619.40.

Therefore, the cost of the property is $235,619.40.

The combined rate of the small and large pumps is 16/63 pools per hour, and it will take them approximately 3.94 hours to drain the pool when working together.

To figure out how long it would take for both pumps to drain the pool simultaneously, we will use the concept of rates. Since the small pump can drain the pool in 9 hours, it has a rate of 1/9 pools per hour. Similarly, the large pump can drain the pool in 7 hours, so it has a rate of 1/7 pools per hour.

When we use both pumps together, we add their rates. So, the combined rate of the small and large pumps is (1/9 + 1/7) = 16/63 pools per hour.

To find the time it will take them to drain the pool together, we divide the size of the pool (1 pool) by their combined rate (16/63 pools per hour). Therefore, it will take the two pumps approximately 3.94 hours to drain the pool when working together.

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Answer:

Option A) P > 18 is the correct option.

Step-by-step explanation:

Louisa and Jill scored jointly in basketball = Score of Louisa + score of Jill

Joint score is greater than 30 points

So Score of Louisa P + score of Jill > 30

If Jill scored 12 points then inequality becomes as

score of Louisa P + 12 > 30

Now by subtracting 12 from both side

score of Louisa P + 12 - 12 > 30 - 12

score of Louisa P > 18

To calculate the compound interest, use the formula A = P(1 + r/n)^(n*t), where A is the future amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Beatrice could have earned $419.38 more over a 4-year period with compounded interest.

To calculate the compound interest, we can use the formula: A = P(1 + r/n)^(n*t), where A is the future amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Beatrice invests $1,440 at an interest rate of 3% for 4 years.

Using the formula, the future amount with compound interest would be: A = 1440 * (1 + 0.03/1)^(1*4) = $1576.18.

To find the difference in earnings, we subtract the future amount with simple interest from the future amount with compound interest: $1576.18 - $1156.80 = $419.38. Therefore, Beatrice could have earned $419.38 more over a 4-year period with compounded interest.

The small business owner made $44,486 during his fourth year of business. His total earnings during the first four years equal $173,168.

The small business owner made $44,486 during his fourth year of business.

To calculate this, we find that he made $40,000 in the first year, then 7% more each year.

So, in the fourth year:

[tex]$40,000 + ( 0.07 * 40,000) + (0.07^2 * 40,000) + (0.07^3 * 40,000) = 44,486[/tex]

His total earnings during the first four years equal $173,168.

This total is found by summing his earnings from each year:

[tex]$40,000 + 42,800 + 45,796 + 44,486 = 173,168.[/tex]

Answer:

f(x)=1sin(1/2x)+5

Step-by-step explanation:

The required numbers that can be constructed are given as 1440 words.

Given that,
Using the digits 3, 4, 5, 6, 7, 8, and 9, how many 7-digit numbers can be constructed if the number must begin with an odd digit and digits may not be repeated is to be determined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,

Because, there are four odd digits, there are only four options for the initial digit.

It has six digits from which to choose 4, 6C4 = 15. And there are 4! = 24 different ways to arrange those four digits.

The total number of choices is 4 × 15 × 24 = 1440

Thus, the required numbers that can be constructed are given as 1440 words.

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The total height of the climbing tower is found by dividing 42 feet by 0.60, as 42 feet represents 60% of the total height. The calculation gives us 70 feet, which is the height of the tower.

The student has asked a question related to artificial wall climbing and its connection to mathematics, specifically regarding percentages and solving for an unknown total given a part and its percentage of the whole. The question asks to find out the total height of a climbing tower given that 42 feet is 60% of its total height.

To solve this, we would set up a proportion where 42 feet equals 60% of the total height. Using the formula part = percent × whole, we can represent the total height of the tower by the variable x. Therefore, the equation is:

42 = 0.60x

To find x, we divide both sides of the equation by 0.60:

x = 42 / 0.60
x = 70 feet

Thus, the height of the tower is 70 feet.

Using the properties of normally distributed random variables and Chebyshev's inequality, we can find the upper and lower bounds for the probability of next week's automobile sales, given the expected value and variance. These calculations involve finding the 'k' value, which is derived from subtracting the expected value from the target sales value, and then using this in the inequality.

The subject of this question is Probability in Mathematics, and this question is likely for a College level course. To bound the probability of a normally distributed random variable exceeding a given value, we can use Chebyshev's inequality: Pr(|X - μ| ≥ kσ) ≤ 1 / k2. Here, X represents the random variable (automobile sales), μ is its expected value (16 sales), and σ is its standard deviation (the square root of the variance).

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Final answer:

The sum of the series of powers of 2 from 1 to 65,536 is a geometric series, which can be calculated using the geometric series sum formula to find that the sum is 131,071.

Explanation:

The student is asking about the sum of a series of powers of 2, starting from 2⁰ (which is 1) up to 2¹⁶ (which is 65,536). This is a geometric series where each term is a power of 2, and the common ratio is 2. The sum of a geometric series can be found using the formula:

S = a₁(1 - rⁿ) / (1 - r), where S is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a₁ = 1 (first term), r = 2 (common ratio), and n = 17 (since the series starts at 2⁰ and ends at 2¹⁶, giving us 17 terms).

Plugging these values into the formula gives us:

S = 1(1 - 2¹⁷) / (1 - 2)

S = 1(1 - 131,072) / (-1)

S = 131,071

Therefore, the sum of the series is 131,071.

The t-statistic for a repeated-measures study with a sample of n = 20 participants would have df=19.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, For determine the degrees of freedom (df) for a repeated-measures study with a sample size of n = 20, we can use the formula:

⇒ df = n - 1

However, in a repeated-measures study, we are comparing two sets of measurements from the same participants.

This means that the difference scores between the two sets of measurements will be used to compute the t-statistic.

Now, For a paired t-test with a sample size of n=20, we would have;

⇒ n - 1 = 19

⇒ n = 20 degrees of freedom.

Therefore, the t-statistic for a repeated-measures study with a sample of n = 20 participants would have df=19.

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He made 1,350,000 in sales.

A percentage is a number that tells us how much out of 100.

Given that, A real estate agent makes an annual salary of $30,000 plus a 4% commission on sales, and a realtor's salary is $84,000,

84000 - 30000=54000

54000 is his sales

100/4 = 25

54000*25 = 1350000

1,350,000

Hence, He made 1,350,000 in sales.

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