What did Archimedes discover in the bath? Why was he so excited? Describe the discovery using geometric terms. What do you predict Archimedes did next with his new discoveries? Explain.

The total area of the shaded portion is (x² - 16)(x²- 1) square meters.

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.

The area of the outer square is (x² - 8)², and the area of the inner square is x². Therefore, the area of the shaded region can be found by subtracting the area of the inner square from the area of the outer square:

Area of shaded region = Area of outer square - Area of inner square

= (x² - 8)² - x²

Expanding the first term using the formula for the square of a binomial, we get:

Area of shaded region = (x⁴ - 16x² + 64) - x²

= x⁴ - 17x² + 64

Therefore, the expression that represents the total area of the shaded figure is x⁴ - 17x² + 64, which can be simplified by factoring:

x⁴ - 17x² + 64 = (x² - 16)(x² - 1)

So the simplified expression for the total area of the shaded figure is (x² - 16)(x²- 1).

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Nicky had $73 initially. Since Abby had the same amount, Abby also had $73 initially.

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

After Abby spent $37, she had A - 37 dollars left. After Nicky spent $61, she had N - 61 dollars left. We also know that after Abby spent $37, she had 3 times as much money as Nicky. So we can set up an equation:

A - 37 = 3(N - 61)

Substituting A = N from the earlier equation, we get:

N - 37 = 3(N - 61)

Expanding the brackets, we get:

N - 37 = 3N - 183

Simplifying and solving for N, we get:

2N = 146

N = 73

Therefore, Nicky had $73 initially. Since Abby had the same amount, Abby also had $73 initially.

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It will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.

Interest rate refers to the percentage of the principal amount charged by a lender to a borrower for the use of money over a certain period of time.

To calculate the time it takes for Allan to repay the loan, we can use the formula for the present value of an annuity:

PV = PMT x (1 - [tex](1 + r)^-n[/tex]) / r

where:

PV = present value

PMT = monthly payment

r = monthly interest rate (9.5% per year / 12 months = 0.00791667)

n = number of months

Plugging in the given values, we get:

3000 = 100 x (1 - (1 + 0.00791667)[tex]^-n[/tex]) / 0.00791667

Simplifying and solving for n, we get:

n = -ln(1 - (3000 x 0.00791667 / 100)) / ln(1 + 0.00791667)

n = 37.4 months

Therefore, it will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.

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The total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².

The shape described in the problem is a trapezoid. The formula to calculate the area of a trapezoid is:

[tex]Area = (base1 + base2) x height / 2[/tex]

We are given the following measurements:

Base1 = 21.3 yards

Height = 12.8 yards

A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards, which is a part of the base2.

A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards, which is the remaining part of the base2.

To calculate the missing part of base2, we subtract the known parts of base2 from the total length of the top, which is:

21.3 - 6.4 - 14.9 = 0

This means that the missing part of base2 is zero, and the trapezoid becomes a rectangle. Therefore, the area of the trapezoid is equal to the area of the rectangle, which is:

Area = base x height

Area = 21.3 x 12.8

Area = 272.64 square yards

Therefore, the total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².

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Answer:

B = 1/2

A = 1/3

D = 2/3

C = 5/6

Step-by-step explanation:

B = 3/6 = 1/2

A = 2/6 = 1/3

D = 4/6 = 2/3

C = 5/6

The x-intercept is 21/5 and the y-intercept is -7/2 of the given line.

What is the x and y-intercept of a line?

In a two-dimensional Cartesian coordinate system, the x-intercept of a line is the point where the line crosses the x-axis, which means the value of y is zero at that point. The x-intercept can be found by setting y = 0 in the equation of the line and solving for x.

Given that we have to find the y-intercept and x-intercept

The given equation is:

5x - 6y = 21

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero

Finding x-intercept:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

Substitute y = 0 in a given equation

5x - 6(0) = 21

x = 21/5

Thus x-intercept is 21/5.

Finding y-intercept:

To find the y-intercept, plug 0 in for 'x' and solve for 'y'

Substitute x = 0 in a given equation

5(0) - 6y = 21

-6y = 21

-2y = 7

y = -7/2

Thus y-intercept is   -7/2

hence, the x-intercept is 21/5 and the y-intercept is -7/2 of the given line.

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Complete question:

Find the y-intercept and x-intercept of the line. 5x-6y=21

Answer:

Step-by-step explanation:

Each die can show one of the five possible numbers. So, the number of possible outcomes for rolling one die is 5.

Since there are three dice being rolled, the total number of possible outcomes is the product of the number of possible outcomes for each die. That is:

Number of possible outcomes = 5 x 5 x 5 = 125

Therefore, there are 125 different outcomes possible when rolling three distinct, five-sided dice.

On an 8-question multiple-choice test, where each question has 2 answers,  the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]

Probability is a way to gauge how likely something is to happen1. It is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.

In an 8-item multiple-choice test with 2 possible answers for each, the likelihood of getting at least one question wrong can be computed as follows:

P(at least one mistake) = 1 - P (none wrong)

P(at least one wrong) [tex]=1-(\frac{1}{2})^{10[/tex]

P(at least one wrong) [tex]=1-\frac{1}{1024}\\\\=\frac{1023}{1024}[/tex]

On an 8-question multiple-choice test, where each question has 2 answers,  the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]

The complete question is-

On an 8-question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?

Give your answer as a fraction

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Answer:

Step-by-step explanation:

You want to know the monthly payment on a 30-year loan of $99,000 at 8%, and the total interest paid.

The monthly payment is given by the amortization formula ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where P is the loan amount, r is the annual interest rate, and t is the loan period in years

  A = $99000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 726.42692814058

The monthly payment is $726.43.

The total of monthly payments is about 360 times the "exact" value of the monthly payment. There is always a slight adjustment made in the last payment to account for the fact that the payment value is always rounded. We can approximate that adjustment by using the "exact" monthly payment amount: $726.42693

The interest paid is the difference between the total of payments and the original loan amount:

  I = 360×$726.42693 -99000 ≈ $162,513.69

The total interest paid is about $162,513.69.

__

Additional comment

If you use 360 times the monthly payment of $726.43, you will compute the interest paid as $162,514.80.

If you compute the future value of the loan after 360 payments of $726.43, you will find it is $4.58. This means the last payment will be $726.43 -4.58 = $721.85, and the total of payments will be $261,510.22, which includes $162,510.22 in interest.

If you make an amortization schedule, where interest is rounded every month (as in "real life"), the result will be different from any of these values. It is $162,510.63. (The last payment is $722.26.)

The upshot is that the amount you determine for total interest paid will depend on the method you use to determine it.

The estimated taxes for a taxable income of $63,700 using the 2020 Federal Tax Rates for Individuals is $9,804.00.

The estimated taxes for an individual with a taxable income of $63,700 for the fiscal year uses the progressive tax (graduated) system of the Federal Tax Rates for Individuals, as computed below.

Taxable Income for 2020 = $63,700

Tax rate  Taxable Income Bracket       Tax Payable

10%                $0 to $9875                       $987.50 ($9,875 x 10%)

12%                $9876 to $40,125           $3,630.00 ($30,250 x 12%)

22%               $40,126 to $85,525        $5,186.50 ($23,575 x 22%)

Estimated taxes                                   $9,804.00

Thus, an individual whose taxable income is $63,700 in 2020 is expected to pay taxes amounting to $9,804.00.

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The expression is equivalent  to -4x²-3x-5

An equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value of the variable that make the equation true. For example, in the equation 2x + 5 = 11, the variable x is being multiplied by 2, added to 5, and then compared to the number 11. To solve for x, one must isolate the variable on one side of the equation by performing the same operation on both sides of the equation until the variable is alone on one side. The resulting value of x will make the equation true.

Given expression is:

-4x²+2x-5(1+x)

Solving the expression

-4x²+2x-5-5x

-4x²-3x-5

Hence, the expression is equivalent  to -4x²-3x-5.

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Answer:

The function is shifted 1 unit to the right and then flipped over the x-axis. So the correct result is:

[tex]y = - f(x - 1)[/tex]

The values of the composite function are (f + g)(x) = 2x² + 3x - 2, (f - g)(x) = -2x² + 3x - 8, (f . g)(x) = 6x³ + 4x² - 15x - 15, (f o g)(x) = 6x² + 4, (g o f)(x) = 18x² - 60x + 53, (f o g)(3) = 58

To determine the values of the composite functions, we have to evaluate or simplify each as

7. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2

8. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8

9. (f . g)(x) = f(x) * g(x) = (3x - 5) * (2x² + 3) = 6x³ + 4x² - 15x - 15

10. (f o g)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4

11. (g o f)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53

12. (f o g)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58

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The container will be 7 meters high and 8 meters in diameter. Steel will be used to make the container (including its top and bottom). If a square meter of steel costs 29 dollars, the total cost of the steel will be $5,467.60.

The cylinder has a diameter of 8m and a height of 7m, which means the radius of the cylinder is 4m (half of the diameter).

The surface area of a cylinder is calculated as follows:

SA = 2πr² + 2πrh

where h is the cylinder's height and r is the radius.

Plugging in the values we get:

SA = 2 x 3.14 x 4² + 2 x 3.14 x 4 x 7

SA = 100.48 + 87.92

SA = 188.4 square meters

So, the surface area of the cylinder is 188.4 square meters.

If the steel costs $29 per square meter, then the cost of the steel for the cylinder would be:

Cost = 188.4 x $29

Cost = $5,467.60

Therefore, the cost of the steel for the cylinder would be $5,467.60.

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473,615 rounded to the nearest hundred is D. 473,600.

Number rounding or approximation is the adjustment of the digits (up or down) to make rough calculations easier.

The result of number rounding is an estimated value rather than a precise one.

Number rounding or approximation are useful when the precise information is not required for decision-making.

473,615 = 473,600

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We can use the multiplication principle of counting to find the total number of possible outcomes.

Since there are 5 options on the first spinner, 6 options on the second die, and 3 options on the third spinner, there are a total of:

5 x 6 x 3 = 90

different possible outcomes.

Therefore, there are 90 different possible outcomes if Madelyn spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.

Answer:

what is biology and types

Answer:

13 inches

Step-by-step explanation:

17=85

1=85/17

1=5

Now

For 65 cents,

65=nx5

65/5=n

n=13 inches

Answer: 13 inches

Step-by-step explanation:

To solve this problem you would need to make a ratio.

A Ratio can be the symbol, : , / or the word to.

In this case you would need to do the problem as shown:

17/85 = x/65

First you would need to cross multiply, then flip the equation. And should end up with something like this:

85x =1105

Then Divide both sides by 85.

85x/85 = 1105/85

Answer:

X= 13

part1)Rounding to four decimal places, the test statistic is z = -1.7918.  part2) Rounding to four decimal places, the p-value is p = 0.0728.

what is decimal places ?

Decimal places refer to the number of digits to the right of the decimal point in a decimal number. For example, in the decimal number 3.14159, there are 5 decimal places, with the digit 1 being in the first decimal place, the digit 4 being in the second decimal place, and so on.

In the given question,

Part 1:

To calculate the test statistic, we use the formula:

z = (p - P) / √[(P(1-P))/n]

where p is the sample proportion (71/341 = 0.2082), P is the hypothesized proportion (0.227), n is the sample size (341).

z = (0.2082 - 0.227) / √[(0.227 * 0.773)/341]

z = -1.7918

Rounding to four decimal places, the test statistic is z = -1.7918.

Part 2:

To calculate the p-value, we use a standard normal distribution table or a calculator. Since this is a two-tailed test, we calculate the area in both tails of the distribution.

Using a calculator or a standard normal distribution table, we find that the area to the left of z = -1.7918 is 0.0364. Therefore, the area in the right tail is also 0.0364.

Thus, the p-value is 2*0.0364 = 0.0728.

Rounding to four decimal places, the p-value is p = 0.0728.

Therefore, we would fail to reject the null hypothesis at the 0.05 significance level since the p-value is greater than the level of significance. We do not have enough evidence to suggest that the percentage of children who develop asthma by age two for expectant mothers who smoke 20 cigarettes per day during pregnancy is lower in this other country compared to the US.

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option D is correct answer  As we can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0

what is exponential curve?

An exponential curve is a mathematical curve that rises or falls at an increasing rate as its values get larger. The curve is defined by an exponential function

In the given question,

To graph this function, we can start by plotting the points for different values of x. Since the function behaves differently for x <= 0 and x > 0, we will plot the points separately for each region.

For x <= 0:

x     g(x)

-2     4

-1     1

0     0

For x > 0:

x          g(x)

0.5     e⁰⁵ = 1.65

1        e = 2.72

2       e²= 7.39

        x <= 0     x > 0

As you can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0 because the derivative from the left and the derivative from the right do not match.

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The point estimate for the proportion parameter for this population is A)0.305.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.

From the given information then,

Sample size n = 892

No of favorable outcomes (i.e successes) x=272

We know ,

The point estimate for the population parameter [tex]\hat P[/tex]=x/n.

Where n=sample size , x=number of success.

Here x = 272 ,n=892 then

The point estimate for the proportion parameter for this population then,

=> [tex]\hat p[/tex] = 272/892 = 0.305.

Hence  the point estimate for the proportion parameter for this population is A)0.305.

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Thus, the perimeter of the left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.

Given data:

Perimeter = sum of all sides:

The shaded portion in the figure shows the left over rectangle:

Perimeter of EFCD = EF + FC + CD + DE

ED = FC = 16 - 7.3 = 8.7

P = 8.7 + 13 + 8.7 + 13

P = 43.4 cm.

Thus, the perimeter of the  left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.

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complete question:

The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the left shape.

Step-by-step explanation:

Put both of the equations into   y = mx + b form to compare them

                   m = slope    if they have the same slope they are parallel and do not intersect

                    b = y axis intercept

                  if m and b are equal in each of the equations , they are the same line

2x+y = 0   ======>   y =  - 2x + 0

2y = -4x + 6  ====>   y =  - 2x + 3

The both have the same slope = -2   so they are parallel

   but they have different  b  values so they are not the same lines

No intersection means no solution :   parallel  lines do not intersect  

7) ∠1≅∠4 on the basis of opposite angles.

8) ∠1≅∠3 on the basis of opposite angles.

9) ∠5≅∠7 on the basis of opposite angles.

Opposite angles in geometry are equal in measure. This is known as the "vertical angles theorem." In other words, if two lines intersect, the opposite angles formed by those lines will have the same degree of measurement.

7) since ∠1 = ∠2

and ∠3 = ∠4, then by the rule of the congruence of opposite angles, ∠1≅∠4

8) In the above shape, we can see that ∠1 and ∠3 are a opposite angles, hence, they are both equal or congruent.

9) The logic is the same for ∠5 and ∠7. The are opposites hence they are equal.

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Answer:

B

Step-by-step explanation:

5280 yards does not equal one mile

Answer

B.5,280

Step-by-step explanation:

Im just smart like that

It might just be 536320

Answer:

[tex]-\frac{5}{2}[/tex] or -2.5

Step-by-step explanation:

1) [tex]2y + 5 = 0[/tex]

2) Move 5 over to the other side by subtracting

[tex]2y = -5[/tex]

3) Divide both sides by 2 so y is alone

[tex]y = -\frac{5}{2}[/tex]

Answer:

The two points (4, 5) and (-4, 5) have the same y-coordinate, which means they lie on a horizontal line. This horizontal line is the x-axis. So, the points are related in that they both lie on the x-axis, with a distance of 8 units between them.