Find the values of the trigonometric functions of t from the given information. tan(t) = -12/5 , sin(t) > 0 ,sin(t),cos(t),csc(t),sec(t),cot(t).
Find the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5
π
/7 rad. (Round your answer to two decimal places.)

The original cost of the shoes​ is $0.31. A pair of workout sneakers is being sold for $15.50 at a shoe retailer, which is one third of its original cost.

How can you determine the original price based on the sale price?

The original cost, for instance $90, should be located. Obtain the discounted amount, say 20%. Create a savings estimate: 20% of $90 = $18. Get the sale price by deducting the savings from the original cost: $90 - $18 = $72. Finally, revenue = cost + cost * markup / 100 should work if you need the selling price. This is perhaps the most frequent scenario: you know the purchase price of an item, along with the intended markup, thus you're trying to determine the sale price.

Enter several numbers into the markup calculator if you want to. $15.50 + $15.50 =$ 31/100 =$0.31.

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Answer:

(-2, 4/7)

Step-by-step explanation:

Ahh the wonderful world of substitution:

x = 7y - 6

x + 7y = 2

So, we need to find what x and y are. Since we know what x is equal to because of the first equation, we can plug that into the second equation:

7y - 6 + 7y = 2

Now let's solve this

14y - 6 = 2

       +6     +6

14y = 8

/14      /14

y = 4/7

Now that we know what y is equal to, we can plug this into the equation. I'll choose the first one, since it is much easier:

x = 7(4/7) - 6

x = 4 - 6

x = -2

Therefore, x is equal to -2 and y is equal to 4/7, final answer.

Hope this helps :D

It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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The value of a such that f(x) is continuous at x = 1 is given as follows:

a = 2.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

To the left of x = 1, the lateral limit is given as follows:

lim x -> 1^- f(x) = lim x -> 1^- x² + a = 1² + a = a + 1.

To the right of x = 1, the lateral limit is given as follows:

lim x -> 1^+ f(x) = lim x -> 1^+ -2ax + 7 = -2a + 7.

The function f(x) is only continuous at x = 1 if the lateral limits are equal, hence the value of x is obtained as follows:

a + 1 = -2a + 7

3a = 6

a = 6/3

a = 2.

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The required second-degree polynomial in the given situation is f(x)=14x²+14x+8.

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Sums of terms of the form k-xⁿ, where k is any number and n is a positive integer, make up polynomials.

For instance, the polynomial 3x+2x-5. a description of polynomials.

So, we have:

p(2) = 14, p'(2) = 14, and p''(2) = 8

So, the equation would be in the form:

f(x) = ax² + bx + x

Now, insert values as follows:

f(x) = ax² + bx + x

f(x) = 14x² + 14x + 8

Therefore, the required second-degree polynomial in the given situation is f(x) = 14x² + 14x + 8.

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The function with the asymptotes as x = 2 , x = 4 and y = 2 is given by the relation f(x) = 2 / [(x - 2)(x - 4)]

Given data,

To find a function that has vertical asymptotes at x = 2 and x = 4, and a horizontal asymptote at y = 2, we can start by considering the basic form of a rational function:

f(x) = (ax + b) / (cx + d)

To satisfy the given conditions, we need the denominator of the rational function to have factors of (x - 2) and (x - 4) since these will create the vertical asymptotes at x = 2 and x = 4.

So, f(x) = (ax + b) / [(x - 2)(x - 4)]

Now, let's consider the horizontal asymptote at y = 2. For a rational function, the horizontal asymptote occurs when the degree of the numerator is less than or equal to the degree of the denominator. Since we want a horizontal asymptote at y = 2, which is a horizontal line, the numerator needs to be a constant, and the denominator needs to be linear.

Let's choose a = 0 and b = 2 so that the numerator is a constant equal to 2.

f(x) = 2 / [(x - 2)(x - 4)]

Hence , a formula for the function that satisfies the given conditions is given by f(x) = 2 / [(x - 2)(x - 4)].

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For the quadratic function f(x) = 3x² - 8x + 2, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The given quadratic function is - f(x) = 3x² - 8x + 2.

The quadratic function is in the standard form ax² + bx + c = 0.

Here, a = 3, b = -8 and c = 2.

The x-intercepts can be found using the formula -

x1 = (-b + √Δ) / (2a)

x2 = (- b - √Δ) / (2a)

Here, Δ = b² - 4ac.

Substitute the values in the above equation -

Δ = b² - 4ac

Δ = (-8)² - 4(3)(2)

Δ = 64 - 24

Δ = 40

Now, substitute the value of Δ in the x-intercepts formula -

x1 = [-(-8) + √40) / [2(3)]                x2 = [-(-8) - √40) / [2(3)]

Open the brackets and use arithmetic operation of multiplication -

x1 = (8 + √40) / 6                          x2 = (8 - √40) / 6

Take out the common value -

x1 = (8 + 4√10) / 6                         x2 = (8 - 4√10) / 6

Use arithmetic operation of division -

x1 = (4 + √10) / 3                           x2 = (4 - √10) / 3    

Therefore, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.

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The equation of the line in slope intercept form is A. 5x - 6y - 8 = 0.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Equation of a line in slope intercept form is,

y = mx + d

m : slope

d : y intercept

y intercept is the y coordinate of the point where the line touches the Y axis.

Given are two points (4, 2) and (-2, -3).

Slope = (-3 - 2) / (-2 - 4) = -5 / -6 = 5/6

So the equation becomes,

y = 5/6 x + d

Substitute one of the points given in the above equation.

2 = (5/6) 4 + d

d = 2 - 10/3

d = -4/3

Equation is,

y = 5/6 x - 4/3

Multiplying throughout the equation with 6,

6y = 5x - 8

5x - 6y - 8 = 0

Hence the required equation is 5x - 6y - 8 = 0.

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Answer: To find out how much Moira would have been paid after working for 18 weeks, we need to multiply her fortnightly pay by the number of fortnights in 18 weeks.

Since there are 26 fortnights in a year, 18 weeks is equivalent to 18/26 = 9/13 of a year.

So, Moira's total pay after 18 weeks would be:

891.60 * 9/13 = $584.40

So, Moira would have been paid $584.40 after working for 18 weeks.

Step-by-step explanation:

The unknown number is -9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the product of a number and -7 is 63.

Let the unknown number be x.

Now, -7×x=63

-7x=63

x= -9

Therefore, the unknown number is -9.

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Solving a system of equations we will see that she has 250 quarters and 200 dimes.

Let's define the variables:

d = number of dimes.

q = number of quarters.

We know that:

q = 50 + d

And:

0.25*q + 0.10*d = 82.50

Then we can write the system of equations:

q = 50 + d

0.25*q + 0.10*d = 82.50

Replacing the first equtaion into the second one we will get:

0.25*(50 + d) + 0.10*d = 82.50

12.5 + 0.35*d = 82.5

0.35*d = 82.5 - 12.5

0.35*d = 70

d = 70/0.35 = 200

And:

q = 50 + d

q = 50 + 200 = 250

So she has 250 quarters and 200 dimes.

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The probability that a professional would accept the promotion is 0.7435.

The total row represents the sum of the probabilities of each event for all the categories, and in this case, the probability of accepting the promotion is the sum of the probabilities of accepting the promotion for each category, which is 0.276 + 0.3145 + 0.1530 = 0.7435.

This means that if we randomly select a professional, there is a 0.7435, or 74.35%, chance that they would accept the promotion. The probability is calculated by taking the sum of the probabilities for each category that corresponds to accepting the promotion and dividing it by the total number of professionals surveyed.

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Answer: Your mom?

Step-by-step explanation: Your mom?

Using a linear equation, since Bella currently has $52 and saves $14 weekly, for the first 5 weeks, she will have $122.

We can use a linear equation to determine the total savings that Bella will have after x weeks.

A linear equation is an algebraic equation that can be modeled on a graph line and written in the form of y = mx + b, where m is the slope, x is a variable and the x-intercept, and b is the y-intercept.

The current savings = $52

The weekly savings = $14

The number of weeks = 5 weeks

The total savings in five weeks = $122 ($52 + 14(5)

= 52 + 14x, where x is the number of weeks

Thus, we can conclude that Bella will have $122 in her savings after 5 weeks.

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dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!) By applying the chain rule, we can calculate the derivative dz/dr.

The derivative of z with respect to r is given by the chain rule:

dz/dr = (∂z/∂x) * (∂x/∂r) + (∂z/∂y) * (∂y/∂r)

Where (∂z/∂x) and (∂z/∂y) are the partial derivatives of z with respect to x and y respectively, and (∂x/∂r) and (∂y/∂r) are the partial derivatives of x and y with respect to r.

Since x = r cos! and y = rsin!, we can substitute these values into the above equation to get:

dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!)

Thus, by applying the chain rule, we can calculate the derivative dz/dr if we know the partial derivatives of z with respect to x and y.

dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!) By applying the chain rule, we can calculate the derivative dz/dr if we know the partial derivatives of z with respect to x and y.

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The cost of the tiles and carpet will be $1,600 and $640, respectively.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The area of the bedroom is given as,

A = (5 x 1/4 x 16) x (4 x 1/4 x 16)

A = 20 x 16

A = 320 square feet

A = 320 / 9

A = 35.56 square yards

Ceramic tile costs $5 per square foot. Then the cost of tiles is given as,

⇒ 320 x 5

⇒ $1,600

The carpet costs $18 per square yard. Then the cost of the carpet is given as,

⇒ 35.56 x 18

⇒ $640

The cost of the tiles and carpet will be $1,600 and $640, respectively.

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Solving the provided question, we can say that The quadratic equation we have is -  [tex]p^2 + 2p - (q+1)(1-1)[/tex] => p = [tex]\sqrt{-2p}[/tex]

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

The quadratic equation we have is -

[tex]p^2 + 2p - (q+1)(1-1)[/tex]

[tex]p^2 + 2p - (q+1)*0[/tex]

[tex]p^2 + 2p = 0[/tex]

[tex]p^2 = -2p[/tex]

p = [tex]\sqrt{-2p}[/tex]

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Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).

What is rate ?

Rate is a measure of the change of a quantity per unit of time or per unit of another quantity. It can refer to various physical or abstract quantities, such as speed, velocity, frequency, interest rate, growth rate, etc. It is often expressed as a ratio or a fraction and has units specific to the quantity being measured.

The mean time to failure (MTTF) can be calculated as the reciprocal of the failure rate. The failure rate can be calculated as the number of failures per unit of operating time.

In this case, the failure rate is 12% per 235 hours, or 0.12 / 235 = 0.00051 failures per hour.

So, the MTTF would be:

MTTF = 1 / failure rate = 1 / 0.00051 = 1952 hours.

Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).

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Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).

Rate is a measure of the change of a quantity per unit of time or per unit of another quantity. It can refer to various physical or abstract quantities, such as speed, velocity, frequency, interest rate, growth rate, etc. It is often expressed as a ratio or a fraction and has units specific to the quantity being measured.

The mean time to failure (MTTF) can be calculated as the reciprocal of the failure rate. The failure rate can be calculated as the number of failures per unit of operating time.

In this case, the failure rate is 12% per 235 hours, or 0.12 / 235 = 0.00051 failures per hour.

So, the MTTF would be:

MTTF = 1 / failure rate = 1 / 0.00051 = 1952 hours.

Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).

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The scalars 1 and 2 in the equation w = 1u + 2v can be found by knowing the components of the vectors u and v.

Given the equation w = 1u + 2v, the scalars 1 and 2 can be found by knowing the components of the vectors u and v. Let's assume that u has the components (a, b) and v has the components (c, d). Then, the vector w can be written as (a + 2c, b + 2d).

Comparing the components of w with the equation w = 1u + 2v, we can see that 1 = 1 and 2 = 2. This means that the scalars 1 and 2 are simply equal to 1 and 2, respectively.

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The number outside of the radical symbol is called the index or the radicand.

In your photo, the letter "K" appears to be a variable and is not commonly referred to as a specific term. However, in some contexts, the letter "K" may represent a constant value.

The horizontal line of the radical symbol is referred to as the vinculum, the quantity underneath it as the radicand, and the number n written to the left as the index.

The term "radical" is used to represent the square root or nth roots.

Radicand: A value or phrase included within the radical symbol.

Therefore, the number outside of the radical symbol is called the index or the radicand

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From the question, we can conclude that the survey produced the following results.

Employed Full Time, Yes doctor = 70

Employed Full Time, No doctor = 15

Employed Part Time, Yes doctor = 25

Employed Part-Time, No doctor = 25

The question states that there are:-

135 adults

85 fully employed, which also means that there are

135 - 85 = 50 part employed

Full employed, 70 = yes doctor

Part employed, 25 = yes doctor

From the above, we can subtract that

Full employed = 85

Yes doctor = 70

No doctor = 85 - 70 = 15

Part employed = 50

Yes doctor = 25

No doctor = 50 - 25 = 25

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The sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.

The formula for the sum of the first n consecutive odd numbers is n^2. This can be proven by induction.

Let n = 2k – 1.

Base case: When k = 1, then n = 2k – 1 = 1. The sum of the first 1 consecutive odd numbers is 1^2 = 1.

Inductive step: Assume that for some k = p, the sum of the first 2p – 1 consecutive odd numbers is (2p – 1)^2.

Now, consider the case when k = p + 1. The sum of the first 2(p + 1) – 1 consecutive odd numbers is:

(2p – 1)^2 + (2p + 1) + (2p + 3) + … + (4p + 1).

This can be written as (2p – 1)^2 + 2(1 + 2 + … + (p + 1)) (2p + 1).

By the sum of an arithmetic sequence, the expression in the parentheses is equal to (p + 1)(2p + 2).

Therefore, the sum of the first 2(p + 1) – 1 consecutive odd numbers is (2p – 1)^2 + 2(p + 1)(2p + 2).

Simplifying, this is equal to (2p + 1)^2.

Therefore, the statement holds for k = p + 1, and by induction, it holds for all positive integers k.

Therefore, the sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.

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4706 revolutions are made by the wheel over the course of 7 miles.

The wheel is a circular, therefore one revolution covers its entire circumference.

So, circumference C = d, where d is the wheel's diameter in inches, which is 30.

So, C = πd

= π × 30 in

= 30π in

= 94.25 in

Now that the tractor has traveled D = 7 miles, we need to determine how many revolutions the wheel completes.

As 1 mile equals 63360 inches,

D = 7 miles when converting miles to inches

= 7 × 1 mile

= 7 × 63360 in

= 443520 in

N = D/C is the number of revolutions the wheel completes in 7 kilometers.

= 443520 in/94.25

= 4705.89

To the nearest whole number, enter 4706.

Therefore, 4706 revolutions are made by the wheel over the course of 7 miles.

The Complete Question.

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The correct answer is "median, because the histogram is skewed to the right."

It depends on the shape of the histogram and the specific characteristics of the data set.

If the histogram is roughly symmetrical and resembles a bell-shaped curve, it is considered normal or approximately normal, and the mean and median are appropriate measures of center. In this case, both the mean and median would give similar values and could be used to describe the center of the data.

If the histogram is skewed to the right, with a longer tail on the right side, the mean will be larger than the median. In this case, the median is considered the most appropriate measure of center because it is not influenced by outliers or extreme values, which can have a significant impact on the mean.

Therefore, the correct answer is "median, because the histogram is skewed to the right."

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The correct answer is "median, because the histogram is skewed to the right."

It depends on the shape of the histogram and the specific characteristics of the data set.

If the histogram is roughly symmetrical and resembles a bell-shaped curve, it is considered normal or approximately normal, and the mean and median are appropriate measures of center. In this case, both the mean and median would give similar values and could be used to describe the center of the data.

If the histogram is skewed to the right, with a longer tail on the right side, the mean will be larger than the median. In this case, the median is considered the most appropriate measure of center because it is not influenced by outliers or extreme values, which can have a significant impact on the mean.

Therefore, the correct answer is "median, because the histogram is skewed to the right."

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Rounding to the nearest hundred dollars, the amount Mason needs to invest is $144,000.

To determine the amount Mason needs to invest, you can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = initial investment (principal)

r = annual interest rate (5.3%)

n = number of times interest is compounded per year (quarterly = 4 times)

t = number of years

Setting A = 205,000 and solving for P:

205,000 = P * (1 + 0.053/4)^(4 * 14)

P = 205,000 / (1 + 0.053/4)^(4 * 14)

Rounding to the nearest hundred dollars, the amount Mason needs to invest is $144,000.

The information provided is about calculating the initial investment (or principal) that Mason needs to make in an account paying an interest rate of 5.3% compounded quarterly, in order to reach a target amount of $205,000 in 14 years. The calculation uses the formula for compound interest, which takes into account the initial investment, the interest rate, the number of times the interest is compounded in a year, and the number of years the investment will grow.

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You did not include enough information to figure out the answer!!

In caring for A.N., we will perform a number of interventions. The first is to shave all hair within the wound beds, to minimize the risk of infection and reduce the amount of bacteria around the wound.

We will also maintain the room temperature at 85 degrees Fahrenheit (29.4 degrees Celsius) to ensure a warm and comfortable environment for A.N. when she is receiving treatment. We will also use clean technique when changing A.N.'s dressings to reduce the risk of infection. Additionally, we will monitor the CBC and WBC with differential frequently to ensure A.N. is receiving adequate treatment.

Furthermore, we will not allow her to bathe for the initial 72 hours after injury to reduce the chances of infection. Lastly, we will apply a 1/16-inch film of medication, covering the entire burn, to help aid in the healing process and reduce the risk of infection.

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Answer:

Convert from degrees to radians using the ratio

π

180.001989675

radians

Answer:y = 4x-5.

Step-by-step explanation: