find the area of the bermuda triangle if the sides of the triangle have the approximate lengths 846 miles, 926 miles, and 1315 miles.

Answer:

Maths is the subject which deals with numbers, calculations, areas, geometry etc

Various topics in maths are

trigonometry

geometry

airthmatic

etc

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

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Answer:

A.

Step-by-step explanation:

The probability that the student makes it to the second class before it starts is very close to 0.

To find the probability that the student makes it to the second class before it starts, we can use the concept of linear combinations of random variables and the properties of normal distributions.

Let's define the random variable X as the total time it takes for the student to transition from the end of the first class to the start of the second class. Since X is a linear combination of independent normally distributed random variables (X1, X2, X3), we can use their means and variances to calculate the mean and variance of X.

The mean of X is the sum of the means of X1, X2, and X3:

μX = μ1 + μ2 + μ3 = 9:02 + 9:15 + 10 = 28:17 minutes.

The variance of X is the sum of the variances of X1, X2, and X3:

σX^2 = σ1^2 + σ2^2 + σ3^2 = (2.5)^2 + (3)^2 + (2.5)^2 = 15.25 minutes^2.

Now, we need to calculate the probability that X is less than or equal to 0, meaning the student arrives before the second lecture starts. Since X follows a normal distribution, we can standardize the variable and calculate the probability using the standard normal distribution table.

Z = (0 - μX) / σX = (0 - 28:17) / √15.25 ≈ -9.43.

Using the standard normal distribution table or a calculator, we can find the probability corresponding to Z = -9.43. The probability is essentially 0, as the value is significantly far in the left tail of the standard normal distribution.

Therefore, the probability that the student makes it to the second class before it starts is very close to 0.

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The vertices of the ellipse are (-4,2) and (4,2), since these points lie on the major axis of the ellipse which is horizontal.

Two of the focuses given in the issue, (−4,2) and (4,2), are both situated on a similar even line. This implies that the significant hub of the oval should be level. Two different focuses given in the issue, (2,2) and (- 9,2), are likewise situated on this level line. Thusly, the focal point of the oval is the midpoint between the focuses (- 4,2) and (4,2), which is (0,2).

The other two focuses given in the issue, (−5,5) and (−5,−1), are situated on an upward line that goes through the focal point of the oval. This implies that the minor pivot of the oval should be vertical.

The vertices of the oval are the places where the significant hub meets the circle. Since the significant hub goes through the focuses (−4,2) and (4,2), the vertices of the oval are (- 4,2) and (4,2).

In this way, the vertices of the oval are (- 4,2) and (4,2).

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Answer: 1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

We know that 25% is equal to the decimal 0.25. So, we can convert the decimal into a fraction

To do so, we need to write the fraction 0.25 x 100 / 100.

Solving the top part (100 x 0.25), we get 25/100.

Next, we need to simplify this fraction. The GCF (greatest common factor) of both numbers is 25, so we divide 25 by 25 and 100 by 25.

This leaves us with 1/4, and our answer.

C) reflection over the x-axis

The statement is true. If y(t) solves the initial value problem (IVP) y'' = 3y' + 5y; y(0) = 8, then the function y(t-2) also solves the IVP y'' = 3y' + 5y; y(2) = 8.

To verify the statement, let's substitute t-2 into the original IVP and check if y(t-2) satisfies the given conditions.

Given that y(t) solves the IVP y'' = 3y' + 5y; y(0) = 8, we can substitute t-2 into the equation to obtain:

(y(t-2))'' = 3(y(t-2))' + 5(y(t-2)).

Differentiating y(t-2) twice with respect to t gives:

y''(t-2) = y'(t-2) = y(t-2).

Substituting these values back into the equation, we have:

y''(t-2) = 3y'(t-2) + 5y(t-2).

Now, let's consider the initial condition y(2) = 8 for the IVP y'' = 3y' + 5y. If we substitute t-2 into this initial condition, we get:

y(2-2) = y(0) = 8.

Therefore, the function y(t-2) satisfies the initial condition y(2) = 8 for the IVP y'' = 3y' + 5y.

In conclusion, the statement is true: if y(t) solves the IVP y'' = 3y' + 5y; y(0) = 8, then the function y(t-2) also solves the IVP y'' = 3y' + 5y; y(2) = 8.

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Using linear approximation, we estimate that sin(1.0) ≈ 1.0.

Linear approximation is a technique for approximating the value of a function near a given point by a linear function. It's also known as tangent line approximation, as the linear approximation is given by the equation of the tangent line at the given point. Using linear approximation, we can estimate

(a) ⁴√16.08 and (b) sin(1.0).(a) ⁴√16.08

To find the fourth root of 16.08, we'll use linear approximation centered at x = 16.

The function we're approximating is f(x) = x^(1/4), so the linear approximation is given by:

f(x) ≈ f(a) + f'(a)(x - a)where a = 16 and f'(x) = 1/4 x^(-3/4).

Therefore, we have:f(x) ≈ f(16) + f'(16)(x - 16)f(x) ≈ 2 + 1/(4 * 2^3/4)(x - 16)

Simplifying:f(x) ≈ 2 + (1/32)(x - 16)

Now, to estimate ⁴√16.08, we substitute x = 16.08 into the approximation equation:

f(16.08) ≈ 2 + (1/32)(16.08 - 16)f(16.08) ≈ 2.05

Therefore, using linear approximation, we estimate that ⁴√16.08 ≈ 2.05.(b) sin(1.0)

To estimate sin(1.0), we'll use linear approximation centered at x = 0.

The function we're approximating is f(x) = sin(x), so the linear approximation is given by:

f(x) ≈ f(a) + f'(a)(x - a)where a = 0 and f'(x) = cos(x).

Therefore, we have:f(x) ≈ f(0) + f'(0)(x - 0)f(x) ≈ 0 + cos(0)(x - 0)f(x) ≈ xNow, to estimate sin(1.0), we substitute x = 1.0 into the approximation equation:f(1.0) ≈ 1.0

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The answer of the question based on the linear approximation is , the approximate value of ⁴√16.08 is 2.005 and the approximate value of sin(1.0) is 1.0.

Linear approximation is an approach for approximating the value of a function near a particular point by considering the value and gradient of a tangent line to the graph at that point.

Linear approximation is also referred to as tangent line approximation.

We can use linear approximation to estimate the values of functions that cannot be easily computed.

Here is how to use linear approximation to estimate ⁴√16.08 and sin(1.0):

(a) Use linear approximation to estimate ⁴√16.08:

First, we'll choose the function to be approximated and a point near which we want to make the approximation.

In this case, the function is ⁴√x, and the point is 16.

The tangent line to the graph of ⁴√x at x = 16 is given by

y - ⁴√16 =

1/(4(16)³⁄⁴)(x - 16)

= 1/32(x - 16),

where m = 1/(4(16)³⁄⁴) and (x₁,y₁) = (16,⁴√16).

This simplifies to y = ⁴√16 + 1/32(x - 16).

To estimate ⁴√16.08, we substitute x = 16.08 into the equation and evaluate:

y = ⁴√16 + 1/32(16.08 - 16)

= 2 + 0.005= 2.005(approximately)

(b) Use linear approximation to estimate sin(1.0):

The function is sin(x), and we'll use x = 0 as the point near which we'll make the approximation.

The tangent line to the graph of sin(x) at x = 0 is given by

y - sin(0) = cos(0)(x - 0)

= x,

where m = cos(0) = 1 and (x₁,y₁) = (0,sin(0)).

This simplifies to y = x.

To estimate sin(1.0), we substitute x = 1.0 into the equation and evaluate:

y = 1.0(approximately)

Therefore, the approximate value of ⁴√16.08 is 2.005 and the approximate value of sin(1.0) is 1.0.

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Zero divided by any real number is equal to zero.

Lena's income tax is calculated by adding the tax on the first $7500 of her income, which is $1125, to the tax on the amount over $7500, which is $5400. Therefore, Lena must pay $6525 in income tax for last year.

To calculate Lena's income tax, we need to compute the tax on the first $7500 of her income and the tax on the amount over $7500, and then add them together.

Tax on the first $7500 = 0.15 * $7500 = $1125

Tax on the amount over $7500 = 0.18 * ($40000 - $7500) = $5400

Total tax = $1125 + $5400 = $6525

Therefore, Lena must pay $6525 in income tax for last year.

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Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.

ii. Tyler made no mistake.

Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.

To solve the question given to Tyler, we have:

\(\sqrt{x + 3}\) = -5

square both sides of the equation to have;

(x + 3) = \((-5)^{2}\)

x + 3 = 25

collect like terms to get;

x = 25 - 3

  = 22

x = 22

1. Thus the equation is true if x = 22.

2. Tyler did not make any mistake in solving for x.

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Answer:

Step-by-step explanation:

y=10

Answer:

(1,2)

Step-by-step explanation:

y = 2x. y = -x+3

Set the two equations equal

2x = -x+3

Add x to each side

2x+x = -x+x+3

3x = 3

Divide by 3

3x/3 = 3/3

x = 1

Now find y

y =2x = 2(1) = 2

(1,2)

Solve like how you solve the system of equations. System of Equations are to find the intercept of both graphs or to find which coordinate points are solution to both equations.

We are given the equations below:

\( \large{ \begin{cases} y = 2x \\ y = - x + 3 \end{cases}}\)

Since both equations are y-isolated and we want to find the coordinate point that both equations have or the coordinate point that is a part of two equations.

\( \large{2 x = - x + 3}\)

Isolate the x-term by adding both sides by x.

\( \large{2x + x = - x + 3 + x} \\ \large{3x = 3}\)

Divide both sides by 3 so we can finally get the x-isolated equation.

\( \large{ \frac{3x}{3} = \frac{3}{3} \longrightarrow x = 1 }\)

Next step is to find the value of y. x-term and y-term both have relations. That means when substituting x-term, we get y-term. Therefore, substitute x = 1 in any given equations. It is not necessary to substitute both, only one is fine. I will choose the first equation to solve for y-value.

\( \large{y = 2x}\)

Substitute x = 1:

\( \large{y = 2(1) \longrightarrow y = 2}\)

The value of y is 2 when x is 1. Since we want the answer to be in coordinate form or ordered pair. From (x,y) - we get (1,2).

Answer

I hope this helps! Let me know if you have any questions or doubts. Do not hestitate to ask if you've got a question. Good luck on your assignment and have a great day!

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer: A: substitution method

Step-by-step explanation:

The substitution method is one way of solving systems of equations. To use the substitution method, use one equation to find an expression for one of the variables in terms of the other variable. Then substitute that expression in place of that variable in the second equation.

The probability of a defect is 0.0013.

Given that the process standard deviation is 15, we can assume the process average is 9 (which is the mean of the given defect range).

Therefore, the defect range can be written as:

P(weight < 8.85) = P(X < 8.85 - 9) = P(X < -0.15)

and

P(weight > 9.15) = P(X > 9.15 - 9) = P(X > 0.15)

Since the standard deviation is 15, and the process control is at plus or minus 1 standard deviation, the range of values for defects can be written as:

P(-1×15 < X < 1×15) = P(-15 < X < 15)

Now, using the Normal distribution, we can calculate the probability of defects by finding the area under the distribution curve, outside of the process control. This is certainly outside the scope of this question, but the answer (to 4 decimals) is 0.0013.

Therefore, the probability of a defect is 0.0013.

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You can fold your paper on one, two, or more folds, but only on the folds we've already made. You can't make any new folds.

p=4n+2 equation describes the relationship between n and p

How to find a function?

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

Here the coordinates are (1,6),(2,10),(3,14),(4,18)

take two coordinates arbitrarily

ie. (1,6) and (3,14)

\(m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)

\(m=\frac{14-6}{3-1}\\ = \frac{8}{2}\)

=4

we know the equation

\(y-y_{0} = m(x-x_{0} )\)

where \((x_{0},y_{0})= (1,6)\)

y-6 = 4(x-1)

y-6 = 4x-4

y = 4x-4+6

y = 4x+2

here y is the profit and x is the number of shirts

∴p=4n+2

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Answer:

Alexander bought 2 peaches and 5 bananas.

Step-by-step explanation:

Since Alexander and his children went into a grocery store and he bought $ 6 worth of bananas and peaches, and each banana costs $ 0.60 and each peach costs $ 1.50, and he bought a total of 7 bananas and peaches altogether, in order to determine the number of bananas, x, and the number of peaches, y, that Alexander bought, the following calculation must be performed:

1.5 x 7 + 0.6 x 0 = 10.5

1.5 x 6 + 0.6 x 1 = 9.6

1.5 x 5 + 0.6 x 2 = 8.7

1.5 x 4 + 0.6 x 3 = 7.8

1.5 x 3 + 0.6 x 4 = 6.9

1.5 x 2 + 0.6 x 5 = 6

Therefore, Alexander bought 2 peaches and 5 bananas.

Answer: 3. supplementary 4. complementary 5.  supplementary 6. complimentary

Step-by-step explanation:

Answer:

whole numbers: 0

integers: -9

natural: 4 & 100

rational: 1.44 & 1/2

irrational: √17, √29, √60, & π (pie)

Answer:

$1h + $2

Step-by-step explanation:

\((2x^5)^3\implies \left(2^3x^{5\cdot 3} \right)\implies 8x^{15}\)

Brooklyn will read 1 1/3 books i.e one complete book and one-third of a book at the given rate.

By determining the number of books read in one day, we can use this as a unit rate to determine how many books she will read in 20 days.

Multiplying the unit rate by the number of days gives us the total amount of reading she will do in that time period.

Here we have

Brooklyn read 1/3 of a book in the series she was reading in 5 days

If Brooklyn read 1/3 of a book in 5 days,

The fraction of the book she reads in one day = 1/3 ÷ 5 = 1/15

This implies Brooklyn reads 1/15 of a book in one day.

To find out how many books Brooklyn will have read in 20 days at the same rate, we can multiply the fraction of a book she reads in one day by the number of days:

= (1/15) x 20 = 4/3 = 1 1/3

Therefore,

Brooklyn will read 1 1/3 books i.e one complete book and one-third of a book at the given rate.

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Using the Complex Conjugate Root Theorem, we know that if a complex number a+bi is a root of a complex polynomial with real coefficients, then a-bi, the complex conjugate of a+bi, is also a root.

Since -9 and 9-i are roots of f, and -9 is a real number, then the remaining zero of the function must be the complex conjugate of 9-i:

Answer:

degree: 4, leading coefficient: -1

Step-by-step explanation:

-v is -1 the 1 is invisible. The expression isn't in standard form, 4 is the degree of the expression because it's the highest exponent in the expression.

Answer:

A

Step-by-step explanation:

A run-on sentence occurs when independent clauses are not joined properly.