Calculate the discount and selling price
$980 mark price
discount 12 1/2%

24. 98 mark price
discount 16 2/3%​

By definition, the x-coordinate of the terminal point is equal to cos t and the y-coordinate is equal to sin t. This allows us to easily find the values of sin t and cos t. To find tan t, we use the formula tan t = sin t / cos t, which we can substitute with our previously found values for sin t and cos t.

First need to understand what is meant by the terms "terminal point" and "unit circle". The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane. The terminal point is the point where the circle intersects with a line that starts at the origin and passes through an angle t measured in radians.
To find sin t and cos t, we need to look at the coordinates of the terminal point. Let's call the x-coordinate of the terminal point x' and the y-coordinate y'. By definition, x' = cos t and y' = sin t. Therefore, sin t = y' and cos t = x'.
To find tan t, we use the formula tan t = sin t / cos t. Substituting in our values for sin t and cos t, we get:
tan t = y' / x'
So, to summarize:
- sin t = y'
- cos t = x'
- tan t = y' / x'
In summary, we can use the unit circle to determine the values of sin t, cos t, and tan t for any angle t measured in radians. The terminal point on the unit circle is the point where the circle intersects with a line passing through the origin at angle t.

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The value of the variable x in the given right angle expression is; x = 11

We know that a right angle simply means an angle that is equal to 90 degrees.

Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.

Thus;

5x + 35 = 90

Subtract 35 from both sides to get;

5x = 55

x = 55/5

x = 11

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The statement that best describes the composition of most foods is: "They contain mixtures of the three energy nutrients, although only one or two may predominate."

Most foods contain mixtures of the three energy nutrients, namely carbohydrates, proteins, and fats. However, the relative proportions of these nutrients can vary significantly from one food to another. In some foods, one or two of these nutrients may predominate, while others may contain relatively equal amounts of all three.

Carbohydrates are a primary source of energy for the body and can be found in various forms such as sugars, starches, and fibers. Foods like grains (e.g., rice, wheat, oats), fruits, vegetables, and legumes tend to be rich in carbohydrates. However, the specific types and amounts of carbohydrates can vary widely.

Proteins are crucial for building and repairing tissues, as well as for various metabolic functions. Foods like meat, poultry, fish, eggs, dairy products, legumes, nuts, and seeds are excellent sources of protein. Again, the protein content in different foods can vary.

Fats, also known as lipids, are an important energy source and provide essential fatty acids. Foods such as oils, butter, avocados, nuts, and fatty meats are high in fats. Like carbohydrates and proteins, the fat content in foods can differ significantly.

It's worth noting that some foods may predominantly consist of one specific nutrient. For example, pure sugar is almost entirely composed of carbohydrates, while pure oil is almost entirely composed of fats. However, most whole foods, such as fruits, vegetables, grains, meats, and dairy products, contain a mixture of these energy nutrients.

Furthermore, a balanced diet typically includes a combination of these nutrients in appropriate proportions. A varied diet that incorporates a range of foods from different food groups helps ensure an adequate intake of carbohydrates, proteins, and fats, along with other essential nutrients required for optimal health.

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The metric unit from pounds to tons is 250 pounds = 0.125 tons

From the question, we have the following parameters that can be used in our computation:

250 pounds = how many tons

As a general rule, we have

1 pound = 0.0005 tons

Multiply both sides of the equation by 250

So, we have

250 * 1 pound = 0.0005 tons * 250

Evaluate the products

250 pounds = 0.125 tons

Hence, the conversion is 250 pounds = 0.125 tons

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Answer in fraction form:  x = 87/2

Answer in decimal form:  x = 43.5

========================================================

Work Shown:

Supplementary angles always add to 180.

angleA+angleB = 180

(3x-5)+(x+11) = 180

(3x+x) + (-5+11) = 180

4x+6 = 180

4x = 180-6

4x = 174

x = 174/4

x = 87/2

x = 43.5

----------

Extra info:

Based on that x value, we can write,

As a check, angleA+angleB = 125.5+54.5 = 180. The answer is confirmed.

Answer:

6.2x10^3

Step-by-step explanation:

I just used a scientific calculator

Answer:

325

Step-by-step explanation:

I got it right before

Answer:

325

Step-by-step explanation:

The mean and the standard deviations values are calculated to be

Mean = 22; Standard deviation = 8.32

Information from the question include

The East Bay traps produce a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds.

The West Bay traps produce a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds.

the sum of the mean for the total weight of the lobsters is calculated by simple addition

= 12 + 10

= 22 pounds of lobsters per day

The standard deviation is not by simple addition it is solved as follows

= √(7² + 4.5²)

= 8.32 pounds

Therefore the mean and the standard deviation are 22 and 8.32 respectively

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we can use the concept of the time value of money and the formula for compound interest. By solving for the number of periods, we can find the answer. Starting with an initial investment of $1, we want to find the time it takes for the investment to reach $6.

The formula for compound interest is given by:

Future Value = Present Value * (1 + Interest Rate)^n,

where Future Value is the desired value ($6), Present Value is the initial investment ($1), Interest Rate is the monthly interest rate (16%/12), and n is the number of periods (in months).

Solving for n, we have:

$6 = $1 * (1 + 0.16/12)^n.

Taking the logarithm of both sides and rearranging the equation, we can solve for n:

n = (log($6) - log($1)) / log(1 + 0.16/12).

Using a calculator, we find that n ≈ 22.35 months.

Since we are interested in the time in years, we divide the number of months by 12:

n ≈ 22.35 / 12 ≈ 1.86 years.

Therefore, it would take approximately 1.86 years for the investment to grow sixfold at a compounded monthly interest rate of 16 percent, starting with an initial investment of $1.

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The maximum likelihood estimator of 0 in the Uniform(0,0) distribution is 0.

The maximum likelihood estimator (MLE) is a method used to estimate the parameter(s) of a statistical distribution based on the observed data. In this case, we are looking for the MLE of the parameter 0 in a Uniform(0,0) distribution.

Since the probability density function (PDF) of the Uniform(0,0) distribution is defined as 1/0 for 0 ≤ x ≤ 0 and 0 otherwise, the likelihood function for the sample X₁, X₂, ..., Xₙ can be written as:

L(0) = (1/0)ᵏ \(\times\) 0ᵐ \(\times\) (1/0)ⁿ₋ᵏ₋ₘ

where k is the number of observations falling in the interval (0, 0), m is the number of observations falling outside the interval (0, 0), and n is the total number of observations.

To maximize the likelihood function, we need to maximize (1/0)ᵏ * 0ᵐ, which is only possible if k = n (all observations fall in the interval (0, 0)) and m = 0 (no observations fall outside the interval).

Therefore, the maximum likelihood estimator of 0 in the Uniform(0,0) distribution is 0.

In summary, the MLE of 0 is 0, as all the observations are within the interval (0, 0) according to the given distribution.

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Answer: -5

Step-by-step explanation: whichever number repeats the most is the mode. In this case, -5 repeats 2 times, while the other numbers dont repeat at all.

If we want to write to the mode of -5, -2, -5, -9, -7, 4 is -5

Identity theft is a crime where someone wrongfully obtains and uses another person's personal information for fraudulent purposes.

Identity theft are be committed through means such as phishing scams, data breaches, social engineering and physical theft of personal documents. Once the perpetrator obtains the victim's information, they can use it to open credit accounts, make unauthorized purchases, apply for loans, file fraudulent tax returns, commit crimes in the victim's name etc.

The consequences for the victim can be devastating. They may experience financial loss, damage to their credit score, legal issues and emotional distress. It can take long amount of time and effort to rectify the damage caused by identity theft often requiring extensive documentation, contacting financial institutions and working with law enforcement agencies.

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​(a) 9.3875 response represents the 94th ​percentile.

​(b)  6.2625 response represents the 62nd percentile.

(c) 3.8150 response represents the first quartile.

Given:

µ =     5.5

σ =    2.5

a) 94th percentile                                    

P(X < x) =    94%                                    

P(Z < z) =    0.94                                    

z =    1.555  [ from z-table or excel command: =NORM.S.INV(probability) ]                        

x = µ + z σ  = 5.5 + (1.555 × 2.5)  

                  = 9.3875    

b) 62nd percentile                                    

P(X < x) = 62%                                    

P(Z < z) = 0.62                                    

z = 0.305 [from z-table or excel command: = NORM.S.INV(probability) ]                        

x = µ + z σ = 5.5 + ( 0.305× 2.5 )

                 = 6.2625    

c) first quartile

25th percentile                                    

P(X < x) = 25%                                    

P(Z < z) = 0.25                                    

z = -0.674 [from z-table or excel command: = NORM.S.INV(probability) ]                        

x = µ + z σ = 5.5 + ( -0.674 × 2.5)

                 = 3.8150    

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Complete Question:

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.5 with a standard deviation of 2.5.

​(a) What response represents the 94th ​percentile?

​(b) What response represents the 62nd percentile?

(c) What response represents the first quartile?

To find the response that represents a specific percentile or quartile, convert the percentage to a decimal, multiply it by the total number of responses, and use the result to locate the corresponding position in the data set.

(a) To find the response that represents the nth percentile, we need to determine the score below which n% of the responses fall. Let's say we want to find the response that represents the 75th percentile. We start by converting the percentile into a decimal, so 75% becomes 0.75.

Next, we calculate the position of the response in the data set. We multiply the decimal by the total number of responses. For example, if there were 100 participants, 0.75 x 100 = 75. This means that the response at position 75 would represent the 75th percentile.

(b) Similarly, if we want to find the response that represents the 90th percentile, we convert 90% to 0.90. Then we multiply it by the total number of responses to find the position of the response in the data set.

(c) To find the response that represents a specific quartile, we divide the data set into four equal parts.

The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) represents the 50th percentile (also known as the median), and the third quartile (Q3) represents the 75th percentile. We can use the same method mentioned in part (a) to find the responses that represent these quartiles.

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For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.

At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.

Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.

The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.

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Answer:

V = π(8^2)(31) = 6,232.9 m^3

(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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Answer:

-4 ≤ x <7

x is greater than or equal to -4, and x is less than 7

Step-by-step explanation:

Take each side and solve

-12 ≤ 2x -4

subtract 4 on both sides

-8 ≤ 2x

divide by 2 on both sides

-4 ≤ x

2x -4 < 10

add 4 on both sides

2x < 14

divide by two on both sides

x < 7

Final answer:

-4 ≤ x <7

Answer:

-4 ≤ x < 7

Step-by-step explanation:

Method 1: Split the inequality into two parts,

-12 ≤ 2x-4

and

2x -4 < 10

Solve.

-8 ≤ 2x

2x ≥ -8

x ≥ -4

and

2x < 14

x < 7

So, x is greater than (or equal to) -4, but less than 7.

-4 ≤ x < 7

Method 2:

-12 ≤ 2x - 4 < 10

Add 4 to both sides.

-8 ≤ 2x < 14

Divide both sides by 2.

-4 ≤ x < 7

Combining the above results, we have shown that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number.

To prove that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number, we need to show two things:

The direct image f([a, b]) is a closed set.

The direct image f([a, b]) is a bounded set.

Let's prove each of these statements:

The direct image f([a, b]) is a closed set:

To show that f([a, b]) is closed, we need to prove that it contains all its limit points.

Let y be a limit point of f([a, b]). This means that there exists a sequence (yₙ) in f([a, b]) such that yₙ → y as n approaches infinity.

Since (yₙ) is a sequence in f([a, b]), there exists a sequence (xₙ) in [a, b] such that f(xₙ) = yₙ.

Since [a, b] is a closed and bounded interval, the sequence (xₙ) has a subsequence (xₙₖ) that converges to some x ∈ [a, b] (by the Bolzano-Weierstrass theorem).

Since f is continuous, we have f(xₙₖ) → f(x) as k approaches infinity. But f(xₙₖ) = yₙₖ, and since yₙₖ → y, we have f(xₙₖ) → y as k approaches infinity.

Therefore, we have shown that for any limit point y of f([a, b]), there exists a corresponding point x in [a, b] such that f(x) = y. Hence, y is in f([a, b]), and f([a, b]) contains all its limit points. Thus, f([a, b]) is a closed set.

The direct image f([a, b]) is a bounded set:

Since [a, b] is a closed and bounded interval, the continuous function f([a, b]) is also bounded by the Extreme Value Theorem. In other words, there exist M, m ∈ R such that for all x ∈ [a, b], m ≤ f(x) ≤ M.

Therefore, f([a, b]) is a bounded set.

Therefore, Combining the above results, we have shown that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number.

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Incomplete question:

Suppose that f : [a, b] → R is a continuous function. Prove that the direct image f ([a, b]) is a closed and bounded interval or a single number.

Answer:

Adult ticket: $18

Child ticket: $15

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

The group of volunteers can make a total of 200 masks out of 25 yards of fabric.

To calculate the number of masks that can be made, we divide the total amount of fabric (25 yards) by the amount of fabric required per mask (1/8 yard). To do this, we first convert the fraction 1/8 to decimal form, which is 0.125. Then, we divide the total fabric (25 yards) by the fabric required per mask (0.125 yards). This can be done by dividing 25 by 0.125, which equals 200. Therefore, the group of volunteers can make a total of 200 masks out of 25 yards of fabric. Each mask requires 1/8 yard of fabric, so dividing the total fabric by the fabric required per mask gives us the total number of masks that can be made.

Calculation steps:
1. Convert the fraction 1/8 to decimal form: 1/8 = 0.125.
2. Divide the total fabric (25 yards) by the fabric required per mask (0.125 yards):
  25 / 0.125 = 200.


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Answer:

You must produce 12 units

Step-by-step explanation:

19.35 - 9.75=9.60

9.6/0.8=12

Answer:

the answer is 12 units  

Step-by-step explanation:

u get 9.75 an hour and 0.80 for every unit so subtract 9.75 from 19.35 and u get 9.60 now divide that by 0.80 and u  get 12 units

Note that function f'(x) is always positive for x > 1 because ln(x) > 0. Therefore, f(x) is strictly increasing for x > 1 and has only one root on its entire domain.

To find an interval of length 1 which has integer endpoints on which the function has a root, we can check the function values at integer points starting from 1.

f(1) = ln(1) - 1/1 = -1

f(2) = ln(2) - 1/2 > 0

f(3) = ln(3) - 1/3 < 0

Since f(1) is negative and f(3) is positive, there must be a root of f(x) between x = 1 and x = 3. Let's check the derivative to prove that there is only one root on the entire domain.

f'(x) = 1/x^2 - 1/x^2 * ln(x)^2 = 1/x^2 * (1 - ln(x)^2)

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Answer:

One cup of juice would cost about $1.05.

Step-by-step explanation:

Since there are 4 cups per quart, and there are 2 quarts, then there are 8 cups of juice in total.

To find how much one cup of juice would cost in an $8.42 carton of juice, you must do the following equation -

8.42 ÷ 8 = x

x = 1.0525.

You can write 1.0525 as 1.05. So, in an $8.42 2 quart carton of juice, 1 cup would cost about $1.05.

:)

The correct option will be option C: Multiply/divide both sides by the same non-zero constant.

To solve the linear equation of one variable;

Step-1: we have to balance each side by simplifying the equation

Step-2: add/subtract constant term on both sides of the equation to separate variable and constant term on both sides

Step-3: divide the coefficient of the variables on both sides.

So according to the question,

the given equations are:

AAA: 3(x+2)=18

BBB: x+2=6

We have to find a way from equation AAA to Equation BBB

from the above equation, it is clear BBB is factor AAA.

to get BBB from equation AAA, we have to just divide 3 on both sides of the equation AAA.

Therefore option C, will be correct as 3 is a non-zero constant. we have to divide both sides by this same non-zero constant.

Therefore The correct option will be option C:

Multiply/divide both sides by the same non-zero constant.

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Answer:

i can't find the answer

Step-by-step explanation:

The surface area is increasing at the rate of (60 x + 150) cm² per second.

Let the side of the cube be x cm.

s = x cm

Surface area of the cube will be:

S = 6 x² cm²

Now, we are given that, the side of the cube is expanding 5 cm per second.

So, the side of the cube after 1 second will be:

s' = x + 5 cm

Surface area will be:

S' = 6 (x + 5)² cm²

S' = (6x² + 150 + 60 x) cm²

Change in the surface area is:

ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²

ΔS = (60 x + 150) cm²

Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.

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Answer:

c) 27.9

Step-by-step explanation:

Since MN is the midsegment ,

MN = (AB + CD)/2

21.1 = (AB + 14.3)/2

21.1*2 = AB + 14.2

AB = 42.2 - 14.2

AB = 27.9

Answer:

C

Step-by-step explanation:

the midsegment is equal to half the sum of the parallel bases, that is

\(\frac{1}{2}\) (AB + CD) = MN ( substitute values )

\(\frac{1}{2}\) (AB + 14.3) = 21.1 ( multiply both sides by 2 to clear the fraction )

AB + 14.3 = 42.2 ( subtract 14.3 from both sides )

AB = 27.9 cm

Based on the calculation of the index of the 65th percentile using the formula and the ordered list of bills, the 65th percentile of the bills for the sample of 20 couples at the restaurant is 63 dollars.

We must arrange the bills in ascending order in order to determine the sample's 65th percentile:

6, 15, 21, 21, 23, 23, 24, 26, 27, 30, 30, 31, 37, 56, 61, 62, 63, 63, 64, 65

The formula for calculating the index of the 65th percentile is as follows:

Index = (Percentile / 100) * (N + 1)

where N is the sample size (which is 20 in this case).

So, for the 65th percentile, we have:

Index = (65 / 100) * (20 + 1) = 13.65

We require the index of the bill that is more than or equal to the 65th percentile, so we must round up this value to the nearest integer.

Therefore, the 65th percentile is the 14th bill in the ordered list:

6, 15, 21, 21, 23, 23, 24, 26, 27, 30, 30, 31, 37, 56, 61, 62, 63, 63, 64, 65

So, The 14th banknote on the ordered list, with a value of 63 dollars, represents the 65th percentile.

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