How many times more powerful were the seismic waves of the Belair earthquake than standard seismic waves?

The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).

If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".

Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):

BD^2 = AB^2 - (AC/2)^2

BD^2 = 8^2 - (x/2)^2

BD^2 = 64 - x^2/4

To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:

BD < x

√(64 - x^2/4) < x

64 - x^2/4 < x^2

256 - x^2 < 4x^2

5x^2 > 256

x^2 > 51.2

x > √(51.2)

Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).

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Answer:

x < 5 because any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be less than 5.

Answer: (1/10, 9/10)

Step-by-step explanation:

Answer:

The total amount of capital invested is:

N2,000 + N4,000 + N1,500 = N7,500

The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:

N2,000 / N7,500 * N300 = N80

The second man gets:

N4,000 / N7,500 * N300 = N160

The third man gets:

N1,500 / N7,500 * N300 = N60

Therefore, each man gets N80, N160, and N60, respectively.

Step-by-step explanation:

Answer:

N80, N160, and N60

Step-by-step explanation:

The total amount of capital invested is:

N2,000 + N4,000 + N1,500 = N7,500

The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:

N2,000 / N7,500 * N300 = N80

The second man gets:

N4,000 / N7,500 * N300 = N160

The third man gets:

N1,500 / N7,500 * N300 = N60

Therefore, each man gets N80, N160, and N60, respectively.

Answer:

3m=24

m=8

12m=96

24m=192

48m=384

96m=768

The given quadratic equation is f(x) = x³ - 3x² + 2x-1. The two solutions to the equation are x = (3x + √(9x² + 4))/2x² and x = (3x - √(9x² + 4))/2x².

A quadratic equation is written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

To solve this equation, we will use the quadratic formula.

The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions are given by

x = [-b ± √(b² - 4ac)]/2a.

In this equation, a = x², b = -3x, and c = -1. Plugging these values into the formula, we get x = [3x ± √(9x² - 4(x²)(-1))]/2(x²). Simplifying this, we get

x = [3x ± √(9x² + 4)]/2x².

Now, we must solve for the two solutions. The first solution is x = (3x + √(9x² + 4))/2x². The second solution is

x = (3x - √(9x² + 4))/2x².

Therefore, the two solutions to the given equation are

x = (3x + √(9x² + 4))/2x² and

x = (3x - √(9x² + 4))/2x².

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The given function does not satisfy the condition for an odd function (f(-x) = -f(x)), we can conclude that -6.66 is not an odd function

Hi there! An odd function is a mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. In simpler terms, an odd function exhibits symmetry with respect to the origin in a coordinate plane.

Now, let's analyze the given function: -6.66. This function represents a constant function since it has no variables (e.g., x or y). Constant functions have a graph that appears as a horizontal line on the coordinate plane.

For constant functions, f(-x) will always equal f(x) because the function's value doesn't change regardless of the input.

In this specific case, the function value is -6.66,

so f(-x) = f(x) = -6.66 for all x.

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The linear regression line is:Y = 0.51X - 14.05

Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics, and is used in nearly every branch of the discipline. In everyday life, the notion of number is used to count objects, keep track of scores, measure amounts, and label objects.

City TV Commercials Car Sales
A 60 20
B 50 15
C 70 25
D 45 17
E 55 19

Calculating the linear regression line:

m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= (5(1475) - (325)(95)) / (5(5850) - (325)2)
= (7375 - 30875) / (29250 - 105625)
= -38500 / -75375
= 0.51

b = Intercept = (ΣY - m(ΣX)) / N
= (95 - 0.51(325)) / 5
= (95 - 165.25) / 5
= -70.25 / 5
= -14.05

Therefore, the linear regression line is:
Y = 0.51X - 14.05.

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Answer: Your welcome!

Step-by-step explanation:

The equivalent fractions for 3/10 and 1/7 using the least common denominator are 6/20 and 3/20. The least common denominator of 3/10 and 1/7 is 20, so the fractions must be multiplied by the same number to reach the denominator of 20. 3/10 multiplied by 2/2 is 6/20, and 1/7 multiplied by 3/3 is 3/20.

For the given situation the probability event can be denoted mathematically as P(V|W).

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The event we are interested in is "a randomly chosen person has varicose veins" (V), given that "the person drinks sixty-four ounces of water per day" (W).

So, we can write this as -

P(V|W)

which is the conditional probability of event V given event W.

Therefore, the event can be denoted as P(V|W).

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Answer:

Step-by-step explanation:

Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".

From the first sentence, we know that:

L = 2A - 25

From the second sentence, we know that:

A + L = 209

We can substitute the first equation into the second equation:

A + (2A - 25) = 209

Simplifying:

3A - 25 = 209

Adding 25 to both sides:

3A = 234

Dividing both sides by 3:

A = 78

Now we can use the first equation to find L:

L = 2A - 25 = 2(78) - 25 = 131

Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.

After addressing the issue at hand, we can state that Hence, x = 5.5 and rectangle m El H = 180.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. Alternately, it might be regarded as a hexagon with a fundamental rule or one with equal angles. Another option for the parallelogram is a straight angle. Four vertices in a square have equal lengths. Four 90° angle vertices and equal parallel sides make up a quadrilateral with a rectangular cross section. Because of this, it is occasionally referred to as a "equirectangular rectangle". A rectangle is occasionally referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

El = 3x + 5, EG = 5x + 16, and m IF G = 270 are all known values. We also understand that a rectangle's diagonals are of equal length. Hence, we can write:

El = HG

EG = IF

From the knowledge provided above, we can formulate two equations in terms of x:

3x + 5 = HG

5x + 16 = IF

90 m HG F and 90 m EFG

Since we know that GH is a straight line because m GHE = 0, m El G must be 180 degrees.

Now that the formulas for HG and IF are equivalent to one another, we may find x:

3x + 5 = 5x + 16

2x = 11\sx = 5.5

Hence, x = 5.5 and m El H = 180.

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1-Is the sum of two prime numbers always a prime number?

Solution:

No. Here is an example.

3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.

2-Is the product of two prime numbers also a prime number?

Solution:

Never because it will have 1 and itself as factors and also the two numbers involved in the product.

Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.

3-Which is the largest 3 digit prime number?

Solution:

Start with the largest three digit number 999.

4- Which is the smallest 2 digit prime number?

Solution

Start with the smallest 2 digit number 10.

10 is not a prime number

Answer: 11 is a prime number

Answer: W = 357.2

Step-by-step explanation:

x/38 * 940/100

100x * 35,720

x=357.2

Answer:

To find out which two students have the same median score, we need to find the median score for each student and compare them.

For James, the median score is 82 (the middle score when the scores are arranged in order).

For Rodney, the median score is 78 (the middle score when the scores are arranged in order).

For Traci, the median score is 82 (the middle score when the scores are arranged in order).

For Maddi, the median score is 67 (the middle score when the scores are arranged in order).

Therefore, the two students who have the same median score are James and Traci, as they both have a median score of 82.

Answer:

Step-by-step explanation:

To find the constant of proportionality, we can use the formula for a proportional relationship: y = kx, where y is the total cost, x is the number of songs, and k is the constant of proportionality.

Using the table, we can find two pairs of values for y and x:

When x = 6, y = $1.80

When x = 12, y = $3.60

We can set up a proportion:

y1 / x1 = y2 / x2

$1.80 / 6 = $3.60 / 12

Simplifying, we get:

$0.30 = $0.30

This tells us that the constant of proportionality is $0.30.

We can check this by using another pair of values:

When x = 20, y = $6

Using the formula y = kx, we get:

$6 = ($0.30)(20)

Simplifying, we get:

$6 = $6

This checks out, so we can be confident that the constant of proportionality is $0.30.

Answer:

7/9

Step-by-step explanation:

Find the reciprocal of the divisor

Reciprocal of 3/4 : 4/3

Now multiply it with the dividend..

so, 7/12 ÷ 3/4 = 7/12 × 4/3

=7/12×4/3 = 28/36

And after reducing the fraction, the answer is 7/9

Therefore , the solution of the given problem of volume comes out to be a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are these marks for cubic measurements. To compute an object's measurements, you must, however, comprehend its volume. Converting an object's weight into mass units including grams and kilograms is a common procedure.

Here,

The formula: can be used to determine the capacity of a hemisphere with a radius of 2 inches.

=> V = (2/3) * π * r³

where "π" is a mathematical constant that is roughly equivalent to 3.14159 and "r" is the hemisphere's radius.

When we substitute the radius's value, we obtain:

=> V = (2/3) * π * 2³

=> (2/3) * π* 8

=>  V = 16.755 cubic inches. (approx)

Therefore, a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.

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The y-intercept is (0, 9), and the parabola has no x-intercepts.

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.

X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.

To find the y-intercept of the parabola, we set x = 0 and solve for y:

y = 3x² - 9x + 9

y = 3(0)² - 9(0) + 9

y = 9

Therefore, the y-intercept is (0, 9).

To find the x-intercepts, we set y = 0 and solve for x:

0 = 3x² - 9x + 9

0 = x² - 3x + 3

Using the quadratic formula, we get:

x = [3 ± √((-3)² - 4(1)(3))]/(2(1))

x = [3 ± √(9 - 12)]/2

x = [3 ± √(-3)]/2

The square root of a negative number is not a real number.

The parabola does not intersect the x-axis, and therefore, there are no x-intercepts.

Therefore, the y-intercept is (0, 9), and the parabola has no x-intercepts.

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Answer:

10 2/3 kg

8 X 1 1/3 kg = 10 2/3 kg

Based on the given information, you would be giving $5 per month or $60 per year to charity.

Starting with a monthly gross income of $5,000, we can calculate the amount set aside for family activities as 10% of the gross income, which is:

= $5,000 x 0.10

= $500

Now, we will calculate the monthly allowance as 10% of the family activity money, which is:

= $500 x 0.10

= $50

Since you give 10% of your monthly allowance to support a charity organization, you will be giving:

= $50 x 0.10

= $5 per month

Now, in order to calculate how much you would give to charity in one year, we simply multiply the monthly amount by 12 which gives us:

= $5 x 12

= $60 per year

Therefore, the amount we would be giving to the charity is $5 per month or $60 per year.

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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}[/tex]

Answer:

3

Step-by-step explanation:

21 is 7 times the number three. You can get this answer by dividing 21 by 7 (answer is 3). You can check your work by multiplying 7 x 3 (you would get 21)

Answer:

$0.81

Step-by-step explanation:

We know

A grocery store sells a bag of 3 oranges for $2.43.

What is the unit cost?​

We take

2.43 / 3 = $0.81

So, the answer is $0.81

Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.

An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.

Here,

Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.

Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).

Since we know that A = B, we can substitute B for A in the last equation to get:

B² - B² = (2x - 9) - (B²)

Simplifying this equation, we get:

0 = 2x - 9 - B²

Now we can substitute the equation B² = 3x - 5 into the above equation to get:

0 = 2x - 9 - (3x - 5)

Simplifying this equation, we get:

0 = -x - 4

Solving for x, we get:

x = -4

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Answer:

10 small, 5 large

Step-by-step explanation:

if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l

students would need to rent 5 small cars and 8 large cars

The wrapping paper used by Aaron is 9 and 2/3 feet of paper

To solve this problem, use the given information about how much wrapping paper is needed for each game and gaming console, and then multiplied by the number of games and consoles that Aaron wraps in one hour. For simple calculation convert mixed fractions into an improper fraction and solve the problem.

Here we have

Aaron wraps present in a store. In one hour, he wraps 8 games and one console.

From the given figure,

Each game takes 2/3 foot of wrapping paper

Each gaming console takes 4 1/3 feet of wrapping paper

From the data

Aaron wraps 8 games in 1 hour

The wrap is used for 8 games = 8 × [ 2/3 foot ] = 16/3 foot

He wraps one console.

The wrap used for 1 console = 4 1/3

Here 4 1/3 = 13/3  [ Converting mixed fraction to improper fraction ]

Hence,

Total amount of wrap used = 16/3 + 13/3

= [ 16 + 13]/3 = 29/3 = 9 2/3  

Therefore,

The wrapping paper used by Aaron is 9 and 2/3 feet of paper

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Answer:

C: y=2x-4

Step-by-step explanation:

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