Which trigonometric function is equivalent to sec(-270) ?

There were 490 walkers at the 10k fund-raiser.

The ratio of runners to walkers is 5:7, that means that the every five runners, there are 7 walkers so therefore we will use ratio formula.

If there have been 350 runners, we can use this ratio to discover what number of walkers there were:

5/7 = 350/x

Where x is the number of walkers.

To solve for x, we will cross-multiply:

5x = 7 * 350

5x = 2450

x = 490

Consequently, there were 490 walkers at the 10k fund-raiser.

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The critical points of the given function f(x) = ** + 5x/ (10x-60) are x = 6 and x = -6/5. The function is decreasing on (-∞, -6/5) and increasing on (-6/5, 6) and (6, ∞). The First Derivative Test shows that x = -6/5 is a local maximum and x = 6 is a local minimum.

To find the critical points, we need to first find the derivative of the function. Using the quotient rule, we get:

f'(x) = (10x - 60)(**)' - **(10x - 60)' / (10x - 60)²

Simplifying, we get:

f'(x) = 50 / (10x - 60)²

The critical points occur where the derivative is zero or undefined. Here, the derivative is never undefined, so we only need to find where it is zero:

50 / (10x - 60)² = 0

This occurs when x = 6 and x = -6/5.

Next, we need to determine the intervals on which the function is increasing or decreasing. To do this, we can use the first derivative test. We test a value in each interval of interest to see if the derivative is positive or negative:

For x < -6/5, we choose x = -2:

f'(-2) = 50 / (10(-2) - 60)² = -5/81 < 0

Therefore, the function is decreasing on (-∞, -6/5).

For -6/5 < x < 6, we choose x = 0:

f'(0) = 50 / (10(0) - 60)² = 5/9 > 0

Therefore, the function is increasing on (-6/5, 6).

For x > 6, we choose x = 10:

f'(10) = 50 / (10(10) - 60)² = 5/81 > 0

Therefore, the function is increasing on (6, ∞).

Finally, we can use the First Derivative Test to determine the nature of the critical points.

For x = -6/5:

f'(-6/5 - ε) < 0 and f'(-6/5 + ε) > 0, for small values of ε.

Therefore, x = -6/5 is a local maximum.

For x = 6:

f'(6 - ε) < 0 and f'(6 + ε) > 0, for small values of ε.

Therefore, x = 6 is a local minimum.

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The inequalities in the given options are: B) t > 0, C) 3 < a, E) k < -5/7, The correct option is B,C,E.

B) t > 0: This represents an inequality because the symbol ">" indicates "greater than." It states that the variable "t" is greater than zero. In other words, it means that "t" has to be a positive number and cannot be zero or negative.

C) 3 < a: This represents an inequality because the symbol "<" indicates "less than." It states that the number 3 is less than the variable "a." In other words, it means that "a" has to be greater than 3 for the inequality to hold true.

E) k < -5/7: This represents an inequality because the symbol "<" indicates "less than." It states that the variable "k" is less than -5/7. In other words, it means that "k" has to be a value smaller than -5/7 for the inequality to be true.

The other options, such as -3 = y, g = 5 and one-half, and x = 1, do not represent inequalities because they either show an equation (equality) or simply assign values to variables without any comparison.

Therefore the correct option is B,C,E.

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The carbon dioxide level in the atmosphere is modeled using two possible derivative functions. Using Model I, the level in 2050 is approximately 426.25 ppm, and using Model II, it is approximately 522.73 ppm.

Using Model I

We need to integrate the derivative function C'(t) = 0.5 + 0.025t to get C(t).

∫C'(t) dt = ∫0.5 + 0.025t dt

C(t) = 0.5t + (0.025/2)t^2 + C

Using the initial condition that C(0) = 370, we get

370 = 0 + 0 + C

C = 370

So, C(t) = 0.5t + (0.025/2)t^2 + 370

To find the carbon dioxide level in 2050 using Model I

C(50) = 0.5(50) + (0.025/2)(50)^2 + 370

C(50) = 25 + 31.25 + 370

C(50) = 426.25 ppm

Using Model II

We need to integrate the derivative function C'(t) = 0.5e^(0.025t) to get C(t).

∫C'(t) dt = ∫0.5e^(0.025t) dt

C(t) = (20e^(0.025t))/ln(10) + C

Using the initial condition that C(0) = 370, we get

370 = (20e^(0))/ln(10) + C

C = 370 - (20/ln(10))

So, C(t) = (20e^(0.025t))/ln(10) + (370 - (20/ln(10)))

To find the carbon dioxide level in 2050 using Model II

C(50) = (20e^(0.025(50)))/ln(10) + (370 - (20/ln(10)))

C(50) = 522.73 ppm (rounded to two decimal places)

Therefore, the carbon dioxide level in 2050 is approximately 426.25 ppm using Model I, and approximately 522.73 ppm using Model II.

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Applying the Equidistant Chords Theorem, the value of x in the circle given above is calculated as: b. 50.

The Equidistant Chords Theorem states that If two chords in a circle, or in congruent circles, are equally distant from the center, then the chords are congruent.

The image given reveals that the two chords are equidistant from the center of the circle, therefore:

x = 2(25)

x = 50.

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The length of the hypotenuse is approximately 7.21 ft.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In mathematical terms, it looks like this:

a² + b² = c²

Where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

In your case, we can substitute the given values into the equation:

6² + 4² = c²

Simplifying:

36 + 16 = c²

52 = c²

To solve for "c," we need to take the square root of both sides of the equation:

√(52) = c

We can simplify the square root of 52 to be 2 times the square root of 13. Therefore:

c ≈ 7.21 ft

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Complete Question:

Find the value of hypotenuse of the given triangle by using the Pythagoras theorem.

The probability that Nguyen will choose a can of chicken noodle soup is 1/3. Therefore, the correct option is B.

To find the probability, you need to divide the number of favorable outcomes (chicken noodle soup cans) by the total number of possible outcomes (total cans of soup). Hence,

1. Count the total number of cans of soup: 4 chicken noodle + 2 tomato + 3 vegetable + 3 potato = 12 cans in total.

2. Count the number of chicken noodle soup cans: 4 cans.

3. Divide the number of chicken noodle soup cans (4) by the total number of cans (12): 4/12.

4. Simplify the fraction: 4/12 can be simplified to 1/3.

Therefore, the probability of choosing a chicken noodle soup is option B: 1/3.

Note: The question is incomplete. The complete question probably is: Nguyen has the following cans of soup in his pantry: 4 cans of chicken noodle soup; 2 cans of tomato soup; 3 cans of vegetable soup; 3 cans of potato soup. He randomly chooses a can of soup for lunch. What is the probability that he will choose chicken noodle soup? a. ½ b. 1/3 c. 1/6 d. ¼.

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After depreciating for 3 years at a rate of 16% per year, the computer is worth approximately $788.26.

To find the worth of the computer after depreciating for 3 years at a rate of 16% per year, we can use the formula for compound interest with depreciation.

Given:

Initial value (cost of the computer) = $1,495

Depreciation rate = 16% per year

Number of years = 3

1. Convert the depreciation rate to a decimal: 16% = 0.16.

2. Calculate the depreciation factor, which is (1 - depreciation rate):

Depreciation factor = 1 - 0.16 = 0.84.

3. Apply the formula for compound interest with depreciation:

Worth = Initial value * (Depreciation factor)^(Number of years).

Substituting the given values into the formula:

Worth = $1,495 * (0.84)^3.

Calculating the exponent:

Worth = $1,495 * 0.84 * 0.84 * 0.84.

Simplifying the expression:

Worth ≈ $788.26.

Therefore, after depreciating for 3 years at a rate of 16% per year, the computer is worth approximately $788.26.

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The area under the standard normal distribution curve between z = 0 and z = 0.98 is:

                         0.8365 - 0.5000 = 0.3365

To find the area under the standard normal distribution curve between z = 0 and z = 0.98, we can use a standard normal distribution table or a calculator that can compute normal probabilities.

Using a standard normal distribution table, we can look up the area corresponding to a z-score of 0 and a z-score of 0.98 separately and then subtract the two areas to find the area between them.

The area under the standard normal distribution curve to the left of z = 0 is 0.5000 (by definition). The area under the curve to the left of z = 0.98 is 0.8365 (from the standard normal distribution table).

So the area under the standard normal distribution curve between z=0 and z=0.98 is approximately 0.3365.

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Acute angle ⇒ 0⁰ < m < 90⁰

Straight angle ⇒  m = 180⁰

Obtuse angle ⇒ 90⁰ < m < 180⁰

Right angle ⇒ m = 90⁰

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. In other words, an obtuse angle is an angle that is wider than a right angle (90 degrees), but not as wide as a straight angle (180 degrees).

When two rays or line segments intersect at a point, they form an angle. If the angle formed is less than 90 degrees, it is called an acute angle. If the angle is exactly 90 degrees, it is called a right angle.

If the angle is greater than 90 degrees but less than 180 degrees, it is called an obtuse angle. Finally, if the angle measures exactly 180 degrees, it is called a straight angle.

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"Based on the data Stephanie collected, the best conclusion she can make is that her commute time varies between walking from home to work and walking from work to home."

Stephanie recorded the time it took for her to walk from home to work and from work to home. The recorded times for walking from home to work are 15, 16, 18, 20, and 21 minutes. The recorded times for walking from work to home are 14, 21, 21, 25, and 27 minutes.

From the given data, we can see that Stephanie's commute time is not consistent. The time it takes for her to walk from home to work varies between 15 and 21 minutes, and the time it takes for her to walk from work to home varies between 14 and 27 minutes. There is no clear pattern or trend in the data.

Therefore, the best conclusion Stephanie can make is that her commute time fluctuates, and it is not fixed or predictable. The specific duration of her commute can vary from day to day.

In conclusion, Stephanie's commute time varies between walking from home to work and walking from work to home, as indicated by the range of recorded times for each direction.

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To find the derivative of sin(y²)+x=eʸ using implicit differentiation, we need to differentiate both sides of the equation with respect to x.

Starting with the left side, we use the chain rule and the derivative of sin(u), which is cos(u) times the derivative of u with respect to x:

d/dx(sin(y²)) = cos(y²) * d/dx(y²)

Using the power rule, we get:

d/dx(y²) = 2y * d/dx(y)

Putting it all together:

d/dx(sin(y²)) = 2y * cos(y²) * d/dx(y)

Now let's move on to the right side of the equation. The derivative of implicit function eʸ with respect to x is simply eʸ times the derivative of y with respect to x:

d/dx(eʸ) = eʸ * d/dx(y)

Putting it all together, we have:

2y * cos(y²) * d/dx(y) + 1 = eʸ * d/dx(y)

We can now solve for d/dx(y):

d/dx(y) = (1 - 2y * cos(y²)) / eʸ

Therefore, the derivative of sin(y²)+x=eʸ is:

d/dx(y) = (1 - 2y * cos(y²)) / eʸ.

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Answer:

y = 8 - 4x

" is" is express the equal sighn

"less than" express - sighn so you will write the equestion as

y = 8 - 4x

The cost of one hamburger is $2.50 and the cost of one order of fries is $1.50.

Let's use h to represent the cost of one hamburger and f to represent the cost of one order of fries.

The Smith family's order can be represented by the equation:

6h + 3f = 19.50

The Jansen family's order can be represented by the equation:

8h + 6f = 29.00

We now have a system of two linear equations with two variables:

6h + 3f = 19.50

8h + 6f = 29.00

To solve for h and f, we can use the elimination method. We can start by multiplying the first equation by 2 to eliminate the variable f:

12h + 6f = 39.00

8h + 6f = 29.00

Subtracting the second equation from the first, we get:

4h = 10.00

Solving for h, we get:

h = 2.50

Now that we know the cost of one hamburger, we can substitute this value back into one of the original equations to solve for f. Using the first equation:

6h + 3f = 19.50

6(2.50) + 3f = 19.50

15 + 3f = 19.50

3f = 4.50

f = 1.50

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The length of CB is 3 unit.

In the given figure ;

By SAS property of similar of triangles,

ΔCED and ΔCAB are similar.

Therefore,

CE/CB = DE/AB = DC/AC

⇒ CE/CB = DC/AC

⇒ 2/CB = 2.4/3.6

⇒ CB = (3.6/2.4)X2 = 3

Hence CB = 3

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The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:

C. 57 x 1,000.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

In the given question,

The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:

C. 57 x 1,000

Since 1 km equals 1,000 meters, we can convert the distance of 57 km to meters by multiplying it by 1,000. This gives us:

57 km x 1,000 meters/km = 57,000 meters

Therefore, the distance from Washington, D.C., to Baltimore is 57,000 meters.

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The equation of the line that is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) is expressed as: y = (2/3)x - 1.

To find the equation of a line that is parallel to the graph of 2x - 3y = 7, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form:

2x - 3y = 7

-3y = -2x + 7

y = (2/3)x - 7/3

This implies that the slope of this line is m = 2/3.

Thus, the equation of the line we are to find will take the following form:

y = (2/3)x + b

where b is the y-intercept of the line.

To find the y-intercept (b), substitute (x, y) = (-3, -3) and m = 2/3 into y = mx + b:

-3 = (2/3)(-3) + b

-3 = -2 + b

b = -1

Substitute m = 2/3 and b = -1 into y = mx + b:

y = (2/3)x - 1

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Answer:

Radius = 18 m

Step-by-step explanation:

Given:

Diameter = 36 m

To find:

Radius

Explanation:

We know that,

Radius = Diameter/2 = 36/2 = 18 m

Final Answer:

18 m

The expression that represents the change in Emilio's savings each week is $7.50.

Emilio saving 25% of the money he earns babysitting, which means that he saves a quarter of his earnings. This can be expressed mathematically as:

savings = 0.25 x earnings

where "savings" is the amount Emilio saves and "earnings" is the amount he earns each week.

Substituting the given value of Emilio's average weekly earnings of $30, we get:

savings = 0.25 x $30

savings = $7.50

Therefore, Emilio saves $7.50 each week.

Since the question asks for the change in Emilio's savings each week, the expression that represents this is simply:

$7.50

This means that Emilio's savings increase by $7.50 each week.

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The best estimate of the charge Zachary will later find on his credit card statement is $20

The formula to be used is -

Amount in USD = Amount of MYR/Value of one MYR

As, 3.04 MYR is 1 USD performing money conversion of 58 MYR

So, 58 MYR will be = 58/3.04

Divide the values in Right Hand Side of the equation to find the value of MYR in USD

Value in USD = $19.07

Hence, the credit card statement will reflect usage of $20 (since it is the closes correct option and we have been asked the best estimate).

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The coordinates of the other trees that must also be on the boundary are (-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).

The coordinates of the other trees that must be on the boundary of the circular orchard, given that the tree at (5, 12) is on the boundary and the center of the orchard is at (0, 0) can be determined as follows.

1. Calculate the radius of the orchard using the distance formula:

sqrt((x2-x1)^2 + (y2-y1)^2).

In this case, (x1, y1) = (0, 0) and (x2, y2) = (5, 12).

2. Radius = sqrt((5-0)^2 + (12-0)^2) = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13.

Now, we know the radius of the orchard is 13. To find the other boundary points, we can use the property of circles that states that the points on the boundary are equidistant from the center.

Since the coordinates are integers and symmetric, we can list the other points as follows:

3. The coordinates of the other trees on the boundary are:

(-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).

These points are also 13 units away from the center, making them equidistant from the center and thus on the boundary of the circular orchard.

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The probability of 3 rainy days in a row when the probability of rain on each single day is 56% ≈ 17.6%

The probability of 3 sunny days in a row when the probability of rain on each single day is 56% ≈ 8.5%

To determine the probability of 3 rainy days in a row, you need to multiply the probability of rain on each single day (56%). In percent form, this would be:

56% × 56% × 56% = 0.56 × 0.56 × 0.56 ≈ 0.175616

To express this as a percentage rounded to the nearest tenth, we have:

0.175616 × 100% ≈ 17.6%

Now, to determine the probability of 3 sunny days in a row, you first need to find the probability of a sunny day, which is the complement of the probability of rain:

100% - 56% = 44%

Next, multiply the probability of a sunny day (44%) for three days:

44% × 44% × 44% = 0.44 × 0.44 × 0.44 ≈ 0.085184

To express this as a percentage rounded to the nearest tenth, we have:

0.085184 × 100% ≈ 8.5%

So, the probability of 3 rainy days in a row is approximately 17.6%, and the probability of 3 sunny days in a row is approximately 8.5%.

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The value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3

Given, [tex]\lim_{x \to 3} f(x)=0[/tex]

[tex]\lim_{x \to 3} g(x)=4[/tex]

[tex]\lim_{x \to 3} h(x)=2[/tex]

We have to find the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex]

[tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)=\lim_{x \to 3} \frac{6h(x)}{4f(x)+g(x)}[/tex]

[tex]= \frac{\lim_{x \to 3}6h(x)}{\lim_{x \to 3}4f(x)+\lim_{x \to 3}g(x)}[/tex]

[tex]=\frac{6\times 2}{4\times0+4}[/tex]

= 12/4

= 3

Hence, the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3

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Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.

To find the number of different outfits that Lindsey can put together, we need to use the counting principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

In this case, there are 3 ways for Lindsey to choose a top, 3 ways to choose a bottom, and 3 ways to choose a scarf. To find the total number of outfits, we multiply these numbers together:

Total number of outfits = number of tops x number of bottoms x number of scarves

Total number of outfits = 3 x 3 x 3

Total number of outfits = 27

Therefore, Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.

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The constant hourly rate using the given data points is  $100 per hour.

To calculate the constant hourly rate, we can use the given data points. For example, let's use the 5-hour rental for $500:

Hourly rate = Total cost / Number of hours
Hourly rate = $500 / 5 hours
Hourly rate = $100 per hour

Now, we can use this hourly rate to find the cost for the missing hour value in the table:

Cost = Hourly rate × Number of hours
Cost = $100 per hour × 9 hours
Cost = $900

So, the table will look like this:

Hours: _______ 5   |   9   |   _______
Cost (in dollars): 500 | 1,250 | 3,500

Now we can calculate the missing hours for the $3,500 cost:

Number of hours = Total cost / Hourly rate
Number of hours = $3,500 / $100 per hour
Number of hours = 35 hours

Now, the completed table is:

Hours: _______ 5   |   9   |   35
Cost (in dollars): 500 | 1,250 | 3,500

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The statement that must be true is the original prices of the refrigerator and the stove were the same. So the answer is option B.

Let x represent the original cost of the refrigerator and y represent the original cost of the stove. The refrigerator's sale price is 0.6x (40% off means paying 60% of the original price), while the stove's sale price is 0.8y (20% off means paying 80% of the original price).

To get the overall discount, multiply the total cost after the discount by the original total cost:

(0.6x + 0.8y) / (x + y)

We want this fraction to equal 0.7 (or 30% off), so we can set up the equation:

(0.6x + 0.8y) / (x + y) = 0.7

Simplifying this equation, we get:

0.6x + 0.8y = 0.7(x + y)

0.6x + 0.8y = 0.7x + 0.7y

0.1x = 0.1y

x = y

Therefore, the statement that must be true to conclude that Alfonso received a 30% overall discount on the refrigerator and stove together is: The original prices of the refrigerator and the stove were the same.

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The weight of Harry Skyes on Mercury is 32.8 kg, under the condition that Mercury's gravity = 3. 70 m/s².

The weight of astronaut Harry Skyes on Mercury can be evaluated using the formula:

Weight on Mercury = (Weight on Earth / 9.81 m/s²) × 3.7 m/s²

Given that Harry Skyes has a mass of approximately 85.0 kg, his weight on Mercury would be:

Weight on Mercury = (85.0 kg / 9.81 m/s²) × 3.7 m/s²

Weight on Mercury = 32.8 kg

Gravity affects weight severely and causes its change . Objects have mass, which is specified as how much matter an object contains. Weight is known as the pull of gravity on mass. The relation between weight and gravitational pull is such that, when on another celestial body, the difference in gravity would alter a person’s weight.

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Answer:

Step-by-step explanation:

We can simplify the fractions first:

(3r + 9)(r+6) / (r+6) = 3r + 9

6r + 3 / (r + 6) = 3(2r + 1) / (r + 6)

(r^2 + 9r + 18) / (2r + 1) = (r^2 + 6r + 3r + 18) / (2r + 1) = [(r+3)(r+6)] / (2r + 1)

So the expression becomes:

[3(2r + 1) / (r + 6)] * [(r+3)(r+6) / (2r + 1)]

We can now cancel out the common factors:

[3 * (r+3)] = 3r + 9

Therefore, the simplified product is:

(3r + 9)(r+6) / (r+6) = 3r + 9