Find the determinant of the triangular matrix.​−37−6​057​00−3​​

The approximate probability that the total aggregate cost of fighting

The approximate probability that less than 1801800 citizens will get vaccinated can be calculated using the de Moivre-Laplace theorem. This theorem states that the probability distribution of the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is whether or not a citizen gets vaccinated, and the sum is the total number of citizens who get vaccinated.

To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of getting vaccinated, which is 9.10^6 * (1/5) = 1820000. The standard deviation is equal to the square root of the number of citizens times the probability of getting vaccinated times the probability of not getting vaccinated, which is sqrt(9.10^6 * (1/5) * (4/5)) = 1200.

Using the de Moivre-Laplace theorem, we can approximate the probability that less than 1801800 citizens will get vaccinated as the probability that a normal random variable with mean 1820000 and standard deviation 1200 is less than 1801800. This can be calculated using the standard normal distribution:

P(Z < (1801800 - 1820000)/1200) = P(Z < -1.52) = 0.064

Therefore, the approximate probability that less than 1801800 citizens will get vaccinated is 0.064.

The approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars can be calculated using the Central Limit Theorem (CLT). The CLT states that the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is the cost of treating a single non-vaccinated individual, and the sum is the total cost of treating all non-vaccinated individuals.

To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of not getting vaccinated times the expected value of the cost of treating a single non-vaccinated individual, which is 9.10^6 * (4/5) * (2000/2) = 7207200000. The standard deviation is equal to the square root of the number of citizens times the probability of not getting vaccinated times the variance of the cost of treating a single non-vaccinated individual, which is sqrt(9.10^6 * (4/5) * (2000^2/12)) = 1633333.33.

Using the CLT, we can approximate the probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars as the probability that a normal random variable with mean 7207200000 and standard deviation 1633333.33 is greater than 7207200000. This can be calculated using the standard normal distribution:

P(Z > (7207200000 - 7207200000)/1633333.33) = P(Z > 0) = 0.5

Therefore, the approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars is 0.5.

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Step-by-step explanation:

So, let's say that we have 5/20. 5 and 20 can divide by a similar number (5) so you divide each variable by 5. in the end, you get 1/4.

The coordinates of N can be estimated as: (-8, -12)

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

If point N is dilated with a scale factor of 5/4 centered at the origin, the coordinates of the image point, let's call it N', can be found by multiplying the coordinates of N by the scale factor:

N' = (5/4)N

We also know that the image point N' is located at (-10, -15), so we can substitute these values into the equation:

(-10, -15) = (5/4)N

Solving for N, we can multiply both sides by the reciprocal of 5/4, which is 4/5:

N = (4/5)(-10, -15)

N = (-8, -12)

Therefore, the coordinates of point N are (-8, -12).

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Answer:

= -4

Step-by-step explanation:

To solve this expression, we need to perform the division in the correct order, following the rules of mathematical operations. We can simplify the expression as follows:

(-168) ÷ (-14) ÷ (-3) = (-168) ÷ [(-14) x (-3)] [dividing by a negative number is the same as multiplying by its reciprocal]

= (-168) ÷ 42

= -4

Therefore, the quotient of (-168) ÷ (-14) ÷ (-3) is -4.

The maximum height reached by the baII is 9 meters.

In mathematics, a functiοn is a relatiοn between twο sets, typically called the dοmain and range, that assigns tο each element οf the dοmain a unique element οf the range. In οther wοrds, a functiοn is a rule οr a set οf rules that assοciates each input value with exactly οne οutput value.

Tο find the maximum height reached by the ball, we need to find the vertex of the parabolic functiοn [tex]h = -t^2 + 6t[/tex]. The vertex of a parabola in the form[tex]y = ax^2 + bx + c[/tex] is located at the point [tex](-b/2a, c - b^2/4a)[/tex].

In this case, the functiοn is[tex]h = -t^2 + 6t[/tex]t, which has a=-1, b=6, and c=0. Therefοre, the vertex οf the parabοla is located at:

t = -b/2a = -6/(-2) = 3

Tο find the maximum height, we substitute t = 3 into the functiοn:

[tex]h = -t^2 + 6t = -3^2 + 6(3) = 9 meters[/tex]

Therefοre, the maximum height reached by the baIl is 9 meters.

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The given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.

As per the given data:

The function is [tex]f(x) = \frac{2}{x^2 + 1}[/tex]

To determine the function: [tex]f(\frac{1}{x}) - x^2f(-1)[/tex]

Substituting (1/x) and (-1) respectively:

[tex]= \frac{2}{\frac{1}{x}^2 + 1} - x^2\frac{2}{(-1)^2 + 1}[/tex]

[tex]= \frac{2x^2}{x^2 + 1} - x^2\frac{2}{2}[/tex]

[tex]= \frac{2x^2}{x^2 + 1} - x^2[/tex]

Taking the LCM:

[tex]= \frac{2x^2 - x^3 - x^2}{x^2 + 1}[/tex]

[tex]= \frac{x^2 - x^3}{x^2 + 1}\\= \frac{x^2(1-x)}{x^2 + 1}[/tex]

Hence, the given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex]

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The simplified fraction is given as follows:

(2x - a)/(2x + a).

At the numerator, the fraction is simplified applying the least common factor as follows:

2 - (a/x) = (2x - a)/x.

At the denominator, the fraction is also simplified applying the common factor as follows:

2 + (a/x) = (2x + a)/x.

x is a common denominator to both of the fractions, hence it can be simplified, and then the simplified fraction is given as follows:

(2x - a)/(2x + a).

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The mentioned relationship is an additive relationship as the total cost is not proportional to the number of games played.

To represent the relationship between the total cost, y, and the number of games played, x, we can create a table, graph, and equation as follows:

Number of games played (x) Total cost (y)

0                                                          10

1                                                          11

2                                                          12

3                                                          13

4                                                          14

5                                                          15

The equation that represents this relationship is: y = 1x + 10

Where 10 is the fixed cost to enter the arcade and 1 is the cost per game played.

To represent this relationship graphically, we can plot the points from the table on a graph. Refer to the image attached with this answer.

This graph shows that the relationship between the total cost and the number of games played is a straight line with a positive slope.

This relationship is an additive relationship because the total cost is not proportional to the number of games played. If the relationship was proportional, the cost per game played would remain constant regardless of the number of games played. In this case, the cost per game played is always $1, but the total cost increases by $1 for each additional game played.

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The complete question is :  

Sam went to play video games in Video Game Central arcade. Video Game Central charges $10 to get into the arcade and then $1 per game played. Represent the relationship between total cost, y, and number of games played, x using a table, graph and equation. Is this relationship a proportional or additive relationship? Explain.

Answer:

56.14

Step-by-step explanation:

673.36/12

Answer: six hundred nine thousandths

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

They both are added by 4

The rectangle has a length of y + 2xy + x meters and a width of (y + 7x) / (2y + x) meters.

What is a formula of area of rectangle?

Formula for rectangle's area

When calculating a rectangle's area, we multiply the length by the width of the rectangle.

The area of a rectangle is given by the formula:

A = L × W

where A is the area, L is the length, and W is the width.

In this case, we are given that the area is:

[tex]A = y^2 + 8xy + 7x^2[/tex]

and the length is:

L = y + xy + xy + x = y + 2xy + x

To find the width, we can rearrange the formula for the area:

W = A/L

Substituting the given values, we get:

[tex]W = (y^2 + 8xy + 7x^2)/(y + 2xy + x)[/tex]

Now, we can simplify this expression by factoring the numerator:

W = [(y + 7x)(y + x)] / [(y + x)(2y + x)]

Canceling out the common factor of (y + x), we get:

W = (y + 7x) / (2y + x)

Therefore, the width of the rectangle is:

W = (y + 7x) / (2y + x)

So the rectangle has a length of y + 2xy + x meters and a width of (y + 7x) / (2y + x) meters.

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The total miles that all eight vehicles drove is 375 miles, and the correct answer is A. 375.

To calculate the total miles that all eight vehicles drove, we need to add up the miles driven by the seven vehicles that completed the trip and the miles driven by the eighth vehicle that only completed 50% of the journey.

The seven vehicles that completed the trip each drove 50 miles, so their total mileage is 7 x 50 = 350 miles.

The eighth vehicle only completed 50% of the journey, so it drove 50 x 0.50 = 25 miles.

To find the total miles driven by all eight vehicles, we add the miles driven by the seven vehicles and the miles driven by the eighth vehicle:
350 + 25 = 375 miles

Therefore, the total miles that all eight vehicles drove is 375 miles, and the correct answer is A. 375.

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The  answer is b^((-3)/(8))*a^(-1)

The expression (b^((3)/(2))*a^(4))^(-(1)/(4)) can be simplified by using the properties of exponents. First, we can distribute the exponent -(1/4) to each of the terms inside the parenthesis:

b^((3)/(2))^(-(1)/(4))*a^(4)^(-(1)/(4))

Next, we can simplify the exponents by multiplying them:

b^((-3)/(8))*a^((-4)/(4))

Finally, we can simplify the exponents further:

b^((-3)/(8))*a^(-1)

So, the final answer is b^((-3)/(8))*a^(-1). This is the simplified form of the expression without any assumptions about the values of the variables.

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Answer:

B. 6

Step-by-step explanation:

3/4 can be added to itsef to be 6/8

6/8

----      6/1   = 6

1/8

Answer:

Step-by-step explanation:

tbh i don't know how to explain it but i feel like its D i multiply and add

Answer:-12&-8

Step-by-step explanation:

since 3x is negative the -12 and -8 become positive to combine with 5 to either become 41 or 37

The correct answer is option C. Only Table 1 and Table 3 represent a function.

Each input value should be paired with only one output value, as stated in the definition of a function. Therefore, we must verify that each input value is paired with only one output value in order to determine which tables represent a function.

For each input value, Table 1 contains unique output values and unique input values. As a result, a function is represented by Table 1.

For the same input value (input 1), there are two distinct output values in Table 2. As a result, there is no function represented in Table 2.

For each input value, Table 3 contains unique output values and unique input values. As a result, a function is represented by Table 3.

For the same input value (input -2) in Table 4, there are two distinct output values. Subsequently, Table 4 doesn't address a capability.

Consequently, c is the correct response because Tables 1 and 3 only depict functions.

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Complete Question:

Which table(s) represent(s) a function? A. Table 1 only B. Table 2 only C. Tables 1 and 3 only D. Tables 1, 3, and 4 only

a. The standard error of the mean would be 9.49.

b. The probability that the sample mean will be less than $125 is 0.1539.

c. The probability that the sample mean will be more than $145 is 0.1401.

d. The probability that the sample mean will be between $120 and $160 is 0.9356.

e. The symmetrical interval that includes 95% of the sample means is ($116.11, $153.31).

a. The standard error of the mean is calculated using the formula:

SE = σ / √n

where σ is the standard deviation and n is the sample size.

In this case, σ = $30 and n = 10. So, the standard error of the mean is:

SE = 30 / √10

SE = 9.49

b. To find the probability that the sample mean will be less than $125, we need to calculate the z-score:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

In this case, x = $125, μ = $134.71, and SE = 9.49. So, the z-score is:

z = (125 - 134.71) / 9.49

z = -1.02

Using a z-table, we find that the probability of getting a z-score less than -1.02 is 0.1539. So, the probability that the sample mean will be less than $125 is 0.1539.

c. To find the probability that the sample mean will be more than $145, we need to calculate the z-score:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

In this case, x = $145, μ = $134.71, and SE = 9.49. So, the z-score is:

z = (145 - 134.71) / 9.49

z = 1.08

Using a z-table, we find that the probability of getting a z-score less than 1.08 is 0.8599. So, the probability that the sample mean will be more than $145 is 1 - 0.8599 = 0.1401.

d. To find the probability that the sample mean will be between $120 and $160, we need to calculate the z-scores for both values:

z1 = (x1 - μ) / SE

z2 = (x2 - μ) / SE

where x1 and x2 are the sample means, μ is the population mean, and SE is the standard error of the mean.

In this case, x1 = $120, x2 = $160, μ = $134.71, and SE = 9.49. So, the z-scores are:

z1 = (120 - 134.71) / 9.49

z1 = -1.55

z2 = (160 - 134.71) / 9.49

z2 = 2.67

Using a z-table, we find that the probability of getting a z-score less than -1.55 is 0.0606 and the probability of getting a z-score less than 2.67 is 0.9962. So, the probability that the sample mean will be between $120 and $160 is 0.9962 - 0.0606 = 0.9356.

e. To find the symmetrical interval that includes 95% of the sample means, we need to use the formula:

x = μ ± z*SE

where x is the sample mean, μ is the population mean, z is the z-score, and SE is the standard error of the mean.

In this case, μ = $134.71, z = 1.96 (for a 95% confidence interval), and SE = 9.49. So, the symmetrical interval is:

x = 134.71 ± 1.96*9.49

x = 134.71 ± 18.6

x = (116.11, 153.31)

So, the symmetrical interval that includes 95% of the sample means is ($116.11, $153.31).

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Answer:

infinity

Step-by-step explanation:

There are "infinity" rational numbers between 0 and 5​.

What are rational numbers :

A rational number is one that has the form p/q, where p & q are both integers and q is not zero.

How to find rational numbers :

The denominators must be equal to get the rational numbers between two rational numbers with differing denominators.

Finding the LCM of the denominators or multiplying the denominators of one to both the numerator and denominator of the other are two options for equating the denominators.

Answer:

66.5

Step-by-step explanation:

average the 2 together (57+76)/2

The amount after 3 years with an interest rate of 7.5% will be $1,242.3.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Assume the yearly interest rate is 7.5% and the interest is compounded once a year.

If the amount of investment is $1,000 and the amount after 3 years is given as,

A = P(1 + r)ⁿ

A = $1,000 × (1 + 0.075)³

A = $1,000 × (1.075)³

A = $1,000 × 1.24229

A = $1,242.3

The amount after 3 years with an interest rate of 7.5% will be $1,242.3.

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An expression that shows the associative property has been applied to (6+8)+4 is 6+(8+4).

The associative property is a mathematical rule that states that the way numbers are grouped within an expression does not affect the final result. In other words, you can add or multiply numbers in any order, and the result will be the same.

This property is represented as (a+b)+c=a+(b+c) or (a*b)*c=a*(b*c).

In the given expression, (6+8)+4, the associative property can be applied by changing the grouping of the numbers. This can be done by moving the parentheses from the first two numbers to the last two numbers. The new expression would be 6+(8+4).

Therefore, an expression that shows the associative property has been applied to (6+8)+4 is 6+(8+4).

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To rearrange the equation y - 3 = 2x into slope-intercept form, we need to solve for y.

First, we can add 3 to both sides of the equation to isolate y:

y - 3 + 3 = 2x + 3

Simplifying the left side gives:

y = 2x + 3

Now, the equation is in slope-intercept form y = mx + b, where m is the slope (in this case, m = 2) and b is the y-intercept (in this case, b = 3).

The two possible solutions for w are 6 and -3/4.

To solve for w, we need to use algebraic manipulation to isolate w on one side of the equation. Here are the steps:

1. Multiply both sides of the equation by (w+1)(w-7) to clear the fractions: -(7) = 4(w+1)(w-7) + 3(w+1)

2. Distribute the 4 and 3 on the right side of the equation: -(7) = 4w^2 - 24w - 28 + 3w + 3

3. Combine like terms on the right side of the equation: -(7) = 4w^2 - 21w - 25

4. Move all terms to one side of the equation: 4w^2 - 21w - 18 = 0

5. Use the quadratic formula to solve for w: w = (-(-21) ± √((-21)^2 - 4(4)(-18)))/(2(4))

6. Simplify the equation: w = (21 ± √(441 + 288))/(8)

7. Simplify the equation further: w = (21 ± √729)/(8)

8. Solve for the two possible values of w: w = (21 + 27)/(8) or w = (21 - 27)/(8)

9. Simplify the two possible values of w: w = 48/8 or w = -6/8

10. Simplify the two possible values of w further: w = 6 or w = -3/4

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(fog)(-9) value is -9 when  f(x)=2x²-4x-15 and g(x)=x+12

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x)=2x²-4x-15 and g(x)=x+12

We need to find fog(-9)

Before that let us find fog(x)

f(g(x))=2(x+12)²-4(x+12)-15

f(g(-9))=2(-9+12)²-4(-9+12)-15

=2(3)²-4(3)-15

=18-12-15

=-9

Hence, (fog)(-9) value is -9 when  f(x)=2x²-4x-15 and g(x)=x+12

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The slope-intercept form of the equation of the line that has a slope of -1/6 and passes through the point (8,0) is y = -1/6x + 4/3.

To find the slope-intercept form of the equation of the line that has the given slope m and passes through the given point, we can use the point-slope form of a linear equation and then rearrange it to the slope-intercept form.

The point-slope form of a linear equation is given by:

y - y₁ = m(x - x₁)

Where m is the slope and (x₁, y₁) is the point that the line passes through.

In this case, m = -1/6 and the point is (8, 0).

Plugging these values into the point-slope form, we get:

y - 0 = -1/6(x - 8)

Simplifying and rearranging to the slope-intercept form, we get:

y = -1/6x + 8/6

y = -1/6x + 4/3

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The area of the trapezoid is 335 square inches.

What is Trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezoid.

First, we need to convert the lengths of the bases and the perpendicular distance to the same units. Let's convert 6 feet to inches:

6 feet = 6 x 12 inches = 72 inches

Now we can calculate the area of the trapezoid using the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the bases and h is the perpendicular distance between them.

Substituting the given values, we get:

Area = (62 + 72) * 5 / 2

Area = 134 * 5 / 2

Area = 670 / 2

Area = 335 square inches

Therefore, the area of the trapezoid is 335 square inches.

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A floor cannot be tiled using only regular pentagons.

A floor cannot be tiled using only regular pentagons. For a regular hexagon, the measure of each vertex angle is 120°, which means that 3 regular hexagons fit to form 360°, and the plane can be filled. However, for a regular pentagon, the measure of each vertex angle is 108°, so regular pentagons cannot be placed together to fill the plane because the measure of the plane, 360°, is not divisible by the measure of each vertex angle. Therefore, a floor cannot be tiled using only regular pentagons.

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