A pair of shoes is regularly priced at $80 and is on sale for 20% off. You have a coupon to receive an additional 15% off the sale price. How much will you pay for the shoes?

Given the Trigonometric Functions:

Using your calculator you get:

By definition, Secant is negative in Quadrant III.

Finds its Reference Angle as follows:

Because:

Then, you get:

Notice that:

Then, you can conclude that it is in Quadrant II.

Therefore its Reference Angle is:

So you can set up:

By definition:

Therefore, you can rewrite it in this form:

Hence, the answer is:

Using Angle Sum property, the measure of 3 angles is ∠Q = 35°, ∠R = 19°, ∠S = 126°.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

As given the measure of 3 angles is -

∠Q = 4x - 17

∠R = x + 6

∠S = 10x - 4

We know that by angle - sum property,

The sum of 3 angles of triangle = 180°

⇒ 4x - 17 + x + 6 + 10x - 4 = 180

⇒ 15x -15 = 180

⇒ 15x = 180 + 15

⇒ 15x = 195

⇒ x = 13

∠Q = 4x - 17 = 4 × 13 - 17 = 35°

∠R = x + 6 = 13 + 6 = 19°

∠S = 10x - 4 = 10 × 13 - 4 = 126°

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Complete question -

The level of measurement of the data can be given as follows:

Interval or ratio.

There are four levels of measurement for the data, given as follows:

The measures of central tendency for each level are given as follows:

For this problem, we have the arithmetic mean, meaning that the level of measurement can be either interval or ratio.

The problem asks for the level of measurement of the data.

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Answer:

138

Step-by-step explanation:

Answer: 138

Step-by-step explanation:

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

A.

1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.

2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.

3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.

4. Mode: No mode. Median: 17. Mean: 18. Range: 28.

5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.

6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.

B.

7. Mode: 4.3. Median: 4.2. Range: 2.1.

8. Mode: 18.6. Median: 18.6. Range: 0.8.

C.

9. Mode: No mode. Median: 4/9.

10. Mode: No mode. Median: 5/24.

For this problem, we are given the attendance graph of three sports centers in the span of 7 months. We need to identify which of the three centers had the largest increase in attendance during this time.

To solve the problem, we need to compare the attendance of each sports center in month 7 with their attendance in month 1.

The Coors field seems to have a growth in attendance of 2.5 horizontal bars, the Petco Park seems to have a growth in attendance of 4.8 bars and the Turner field seems to have a growth in attendance of 3.9 bars. With thi,s we conclude that Petco Park saw the highest growth in attendance.

The answer is Petco Park.

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer: f(8) = 620.6

Step-by-step explanation:

To solve, you must first use substitution, and replace the x value in the given function, with 8.

\(f(8)=\frac{750}{1 + 74e^{-0.734(8)} }\)

Next you follow PEMDAS to solve the rest of the equation to find f(8).

What is PEMDAS?

PEMDAS is the order of operations for mathematical expressions involving more than one operation.

You solve in the following order

In this case our next step is deal with the exponents.

And by doing so, you will be multiplying -0.734 by 8

\(f(8)=\frac{750}{1 + 74e^{-5.872} }\)

And typical with exponents we would raise the number or variable given to the power of the exponent.

However we have a continuous number in this case, which is e.

What is e?

e is a mathematical constant approximately equal to 2.71828

We can now use a calculator to find what e (2.71....) is when raise to the exponent -5.872. Which results to 0.002817 (0.0028172332293320237716146943697).

When continuing to use numbers in calculators, don't use the rounded or shortened of the full number. Make sure to use the all of the numbers (given in the calculator) to its full extent to maintain accuracy.

\(f(8)=\frac{750}{1 + 74(0.002817) }\)

Now multiply 74 and 0.002817.... (use the full number to multiply (0.0028172332293320237716146943697)). The product is (0.2084752589705697590994873833578).

\(f(8)=\frac{750}{1 + 0.2084 }\)

Now lets add 1 + 0.2084.... and you get 1.2084

\(f(8)=\frac{750}{1.2084 }\)

Last you need to divide:

and you get that

f(8) = 620.6167

Now lets go back to the question, and we see that is says for you to round your answer to the nearest tenth.

so your final answer is:

f(8) = 620.6

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

\(f {}^{ - 1} (x) = 4(x + 3)\)

Step-by-step explanation:

We would like to find the inverse of the following function .

\(\longrightarrow f(x) = \dfrac{1}{4}x +3 \)

Step 1 : Replace \(f(x) \) with \(y \) . We have

\(\longrightarrow y =\dfrac{1}{4}x +3 \)

Step 2 : Interchange x and y :-

\(\longrightarrow x = \dfrac{1}{4}y + 3 \)

Step 3 : Solve for y :-

\(\longrightarrow x - 3 =\dfrac{1}{4}y \)

Multiply both sides by 4,

\(\longrightarrow 4(x-3) = y \)

Step 4 : Replace y with f-¹(x) :-

\(\longrightarrow 4(x -3)=f^{-1}(x) \)

Interchange the sides ,

\(\longrightarrow \underline{\underline{ f^{-1}(x)= 4(x-3)}}{}\)

And we are done !

Answer:

The total work done in pulling the bucket to the top of the well is approximately 3,139.1 ft·lb

Step-by-step explanation:

The given parameters are;

The mass of the bucket, W = 3.6 pounds

The depth of the well, h = 78 feet deep

The mass of water in the bucket = 38 ponds

The rate at which the water is pulled up = 2.9 feet per second

The rate at which water is leaking from the bucket, \(\dot m\) = 0.1 pounds per second

We separate and find the work done for lifting the bucket and the water individually, then we add the answers to get the solution to the question as follows;

The work done in lifting bucket empty from the well bottom, \(W_b\) = W × h

∴  \(W_b\) = 3.6 pounds × 78 feet = 280.8 ft-lb

The work done in lifting bucket empty from the well bottom, \(W_b\) = 280.8 ft-lb

The time it takes to lift the bucket from the well bottom to the top, 't', is given as follows;

Time, t = Distance/Velocity

The time it takes to pull the bucket from the well bottom is therefore;

t = 78 ft./(2.9 ft./s) ≈ 26.897

The time it takes to pull the bucket from the well bottom to the top, t ≈ 26.897 s

The mass of water that leaks out from the bucket before it gets to the top, m₂, is therefore;

m₂ = \(\dot m\) × t

∴ m₂ = 0.1 lbs/s × 26.897 s = 2.6897

The mass of the water that leaks, m₂ = 2.6897 lbs

The mass of water that gets to the surface m₃ = m - m₂

∴ m₃ = 38 lbs  - 2.6897 lbs ≈ 35.3103 lbs

Given that the water leaks at a constant rate the equation representing the mass of the water as it is lifted can b represented by a straight line with slope, 'm' given as follows;

The slope of the linear equation m = (38 lbs - 35.3103 lbs)/(78 ft. - 0 ft.) = 0.03448\(\overline 3\) lbs/ft.

Therefore, the equation for the weight of the water 'w' can be expressed as follows;

w = 0.03448\(\overline 3\)·y + c

At the top of the well, y = 0 and w = 38

∴ 35.3103 = 0..03448\(\overline 3\) × 0 + c

c = 35.3103

∴ w = 0.03448\(\overline 3\)·y + 35.3103

The work done in lifting the water through a small distance, dy is given as follows;

(0.03448\(\overline 3\)·y + 38) × dy

The work done in lifting the water from the bottom to the top of the well, \(W_{water}\), is given as follows;

\(W_{water} = \int\limits^{78}_0 {0.03448\overline 3 \cdot y + 35.3103 } \, dy\)

\(\therefore W_{water} = \left [ {\dfrac{0.03448\overline 3 \cdot y^2}{2} + 35.3103 \cdot y\right ]^{78}_0\)

\(W_{water}\) = (0.034483/2 × 78^2 + 35.3103 × 78) - (0.034483 × 0 + 38 × 0)  ≈ 2,859.1

The work done in lifting only the water, \(W_{water}\) ≈ 2,859.1 ft-lb

The total work done, in pulling the bucket to the top of the well, W = \(W_b\) + \(W_{water}\)

∴ W = 2,859.1 ft.·lb + 280.8 ft.·lb ≈ 3,139.1 ft·lb

The total work done, in pulling the bucket to the top of the well, W ≈ 3,139.1 ft·lb.

Answer:

Step-by-step explanation:

\(2^{1/2} - 2^{-1/3} = 2^{1/2 + 1/3} = 2^{3/6} = 2^{1/2} = \sqrt{2}\)

Answer:

\(\sqrt[6]{2}\)

Step-by-step explanation:

2 ^ 1/2 ÷ 2 ^ 1/3

We know that a^b ÷ a^ c = a^(b-c)

2 ^ (1/2 -1/3)

2^ (3/6 - 2/6)

2 ^ 1/6

\(\sqrt[6]{2}\)

To solve for x, we need to isolate the variable (x) on one side of the equation. We can do that by first subtracting 3 from both sides of the equation to get:

11 - 3 = 4x

Simplifying the left side gives:

8 = 4x

Finally, dividing both sides by 4 gives:

x = 2

Therefore, the solution to the equation 11=3+4x is x=2.

the solution to the equation \(11=3+4x\) 11=3+4x is \(x = 2\) X = 2.

The equation \(11=3+4x\) 11=3+4x is a linear equation in one variable \((x)\)(x) with coefficients and constants that are real numbers.

It can be simplified by performing basic algebraic operations, such as isolating the variable term \((4x)\) (4x) and solving for the value of \(x\) x.

to solve for x in the equation  \(11=3+4x\) 11=3+4x, we will follow the steps of algebraic manipulation:

First, we will isolate the variable term \((4x)\) (4x)  by subtracting 3 from both sides of the equation:

\(11 - 3 = 4x\) 11 - 3 = 4x

\(8 = 4x\) 8 = 4x

Next, we will isolate x by dividing both sides by 4:

 \(8/4 = x\) 8/4 = x

   \(2 = x\) 2 = x

Therefore, the solution to the equation \(11=3+4x\) 11=3+4x is \(x=2\) x=2.

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Answer:

No these these result do not differ at 95% confidence level  

Step-by-step explanation:

From the question we are told that

  The first concentrations is  \(c _1= 30.0 \ g/m^3\)

      The second concentrations is  \(c _2 = 52.9 \ g/m^3\)

  The first sample size is  \(n_1 =  32\)

    The second sample size is  \(n_2 =  32\)

   The  first standard deviation is \(\sigma_1 =  30.0 \)

     The  first standard deviation is \(\sigma_1 =  29.0 \)

The mean for  Turnpike is  \(\= x _1 = \frac{c_1}{n} = \frac{31.4}{32} = 0.98125\)

The mean for   Tunnel is  \(\= x _2 = \frac{c_2}{n} = \frac{52.9}{32} = 1.6531\)

The  null hypothesis is  \(H_o : \mu _1 - \mu_2 = 0\)

The  alternative hypothesis is  \(H_a : \mu _1 - \mu_2 \ne 0\)

Generally the test statistics is mathematically represented as

              \(t = \frac{\= x_1 - \= x_2}{ \sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} }}\)

         \(t = \frac{0.98125 - 1.6531}{ \sqrt{\frac{30^2}{32} +\frac{29^2}{32} }}\)

        \(t = - 0.0899\)

Generally the degree of freedom is mathematically represented as

     \(df = 32+ 32 - 2\)

     \(df = 62\)

The  significance \(\alpha\)  is  evaluated as

      \(\alpha = (C - 100 )\%\)

=>   \(\alpha = (95 - 100 )\%\)

=>   \(\alpha =0.05\)

The  critical value  is evaluated as

      \(t_c = 2 * t_{0.05 , 62}\)

From the student t- distribution table  

        \(t_{0.05, 62} = 1.67\)

So

     \(t_c = 2 * 1.67\)

=>  \(t_c = 3.34\)

given that

       \(t_c > t\) we fail to reject the null hypothesis so  this mean that the result do  not differ

the answer is 3 hopw this helps

In order to solve for time, we will solve as follows:

We multiply the movement in the time we want to know (30 ft) times the time it takes to move 5 ft (20 min) and divide it by the 5 ft, that is:

From this, we know it took the voter 120 minutes to move 30 ft.

Digits if four integers.

Formula: 1005 + 10n, n could be 1 , 2, 3 , 4 , etc

S1 = 1005 + 10(1) = 1005 + 10 = 1015

S2 = 1005 + 10(2) = 1005 + 20 = 1025

S3 = 1005 + 10(3) = 1005+ 30 = 1035

S4 = 1005 + 10(4) = 1005 + 40 = 1045

Answer:

option C: 120

Step-by-step explanation:

total marks = 5× 100 = 500

marks he obtained = 380

marks he lost = 500 - 380 = 120

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Answer: 5/6 as a decimal is 0.833

Step-by-step explanation:

just divide 5 by 6

your answer is a

and x equals 20

The coefficient of s/3 is 1/3.

s/3 = (1/3)s

No, 3 is not the coefficient of s/3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

s/3

This can be written as (1/3)s.

The coefficients of an equation are the non-zero values along with the variables.

Example:

ax² + bx + 3

The coefficients of this equation are a, and b.

The coefficient for the expression s/3  is 1/3.

Thus,

The coefficient of s/3 is 1/3.

s/3 = (1/3)s

No, 3 is not the coefficient of s/3.

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