Prove that
cos 75° = √2 (√3-1)÷4​

The proportion of oil tankers that had spills is:

1 - (445/563) = 0.208

Rounded to three decimal places, the answer is 0.208. Alternatively, this can be expressed as the fraction 52/253.

A: The expression to represent the average change in temperature is -11/10 °F per minute.

B: The average change in temperature is -1.1 °F per minute,

C:  For the second attempt average change is -0.1 per minute.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given temp. at beginning = 23°F

He monitors the temperature of the solution every minute for 10 minutes, and

He records the change in temperature from his previous reading. His data show a decrease of 2 degrees Fahrenheit four times, a decrease of 3 degrees Fahrenheit three times, no temperature change two times, and an increase of 6 degrees Fahrenheit

A) The expression to represent the average change in temperature each minute is given as follows:

The observations are given as follows:

-2, -2, -2, -2, -3, -3, -3, 0, 0, 6.

Mean = (4 x (-2) + 3 x (-3) + 0(2) + 6)/10.

Mean = -11/10

B) The average change in temperature for the first trial is given as follows:

The observations are given as follows:

-2, -2, -2, -2, -3, -3, -3, 0, 0, 6.

The average change  = -11/10

The average change  =  -1.1ºF per minute.

C) In the second attempt of the experiment, the average change in temperature per minute,

A data set's mean is computed as the total number of observations divided by the total number of observations in the data set.

There are 10 observations in total in this problem.

The observations are given as follows:

-2, -2, -2, -2, -3, -3, -3, 0, 0, 6.

Hence, the mean is calculated as follows:

Mean = (4 x (-2) + 3 x (-3) + 6)/10

Mean = -1.1ºF per minute

1ºF greater than this for the second trial is given as follows:

-1.1 + 1 = -0.1 ºF per minute.

Hence the average change in temperature is -1.1 °F per minute,

C: For the second attempt average change is -0.1 per minute.

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The question is incomplete. The complete question is 'Edgar measures the temperature of a solution at the beginning of an experiment to be 23 degrees Fahrenheit . He monitors the temperature of the solution every minute for 10 minutes. He records the change in temperature from his previous reading. His data show a decrease of 2 degrees Fahrenheit four times, a decrease of 3 degrees Fahrenheit three times, no temperature change two times, and an increase of 6 degrees Fahrenheit once. (a) Write an expression to represent the average change in temperature each minute. (b) Using your expression from Part (a), determine the average change in temperature for the first trial(c) Edgar repeats the experiment and finds the average change in temperature each minute is 1 degrees Fahrenheit greater in the second trial than in the first trial. What is the average change in temperature each minute in the second trial of the experiment?'

The demand equation, by assuming it is linear. The equation expresses price p in terms of quantity q, q  =  -10000/3p + 52000

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

An album is downloaded 12000 times per week when its price is $12

It is downloaded 22000 times per week when the price drops to $9

The demand equation = ?

Suppose, price is expressed as p and quantity as q

Formula of linear relationship,

y = mx + c

So,

q  = mp + c

when,  p = 12 then q = 12000

12000 = 12m + c  _________(i)

when, p = 9 then q = 22000

22000 = 9m + c  _________ (ii)

Now by using elimination method solve equation i & ii

12m + c    =   12000

- 9m + (-c) =  -22000

3m  = -10000

m  = -10000/3

12m + c = 12000

c  = 12000 - 12 x (-10000/3)

c  =  12000 + 40000

c  =   52000

q  = -10000/3p + 52000

The equation is q  =  -10000/3p + 52000

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The multiplication inequality that shows the number of bags (b) the wheelbarrow can carry is 20b ≤ 300.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The wheelbarrow can carry upto = 300 lbs

The bag of soil weighs = 20 lbs.

Now,

Number of bags of soil = b

We can write an inequality for the number of bags of soil the wheelbarrow can carry.

20b ≤ 300

Thus,

20b ≤ 300 is the multiplication inequality to show the number of bags (b) the wheelbarrow can carry.

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We compute the functions as follows

1. g(f(0)) = -3

2. f(f(2)) = 5

3. f(g(x)) = 6x - 1

4. g(h(x)) = 3x² + 3

5. g(f(x)) = 6x - 3

6.  f(f(x)) = 4x - 3

7. g(g(x)) = 9x

A function is a  mathematical equation that shows the relationship between two variables.

Given that

Let's compute the given functions.

To compute the function g(f(0)), we first compute g(f(x)).

So, g(f(x)) = 3f(x)

= 3(2x - 1)

= 6x - 3

So, g(f(0)) = 6(0) - 3

= 0 - 3

= -3

So, g(f(0)) = -3

To compute the function f(f(2)), we first compute f(f(x)).

So, f(f(x)) = 2(f(x)) - 1

= 2(2x - 1) - 1

= 4x - 2 - 1

= 4x - 3

So, f(f(2)) = 4(2) - 3

= 8 - 3

= 5

So, f(f(2)) = 5

To compute the function f(g(x)), since we have

So, f(g(x)) = 2(g(x)) - 1

= 2(3x) - 1

= 6x - 1

So, f(g(x)) = 6x - 1

To compute the function g(h(x)), Since

So, g(h(x)) = 3(h(x))

= 3(x² + 1)

= 3x² + 3

So, g(h(x)) = 3x² + 3

To compute the function g(f(x)), Since

So, g(f(x)) = 3(f(x))

= 3(2x - 1)

= 6x - 3

So, g(f(x)) = 6x - 3

To compute the function f(f(x)), Since f(x) = 2x - 1,

So, f(f(x)) = 2(f(x)) - 1

= 2(2x - 1) - 1

= 4x - 2 - 1

= 4x - 3

So, f(f(x)) = 4x - 3

To compute the function g(g(x)), Since g(x) = 3x

So, g(g(x)) = 3(g(x))

= 3(3x)

= 9x

So, g(g(x)) = 9x

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Answer:

44117/245 or 180 17/245

Answer:

1700/49×5 + 33/5

173.45 + 6.6

180

The equation for Harper's situation is 10x = 150 + 5x. The number of t-shirts Harper needs to sell so that the amount of money she spends to start her business and the amount of money she earns are the same is 30 t-shirts.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The price of one plane t-shirt is = $5

The money spent on printing equipment is = $150

The price for printed t-shirt is = $10

Let the number of t-shirts to be sold be x.

The expression for earning money is 10x

The amount she spends on starting the business is -

150 + 5x

So, according to question the equation is -

10x = 150 + 5x

10x - 5x = 150

5x = 150

x = 150 / 5

x = 30

Therefore, 30 t-shirts needs to be sold.

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Mr. Doyle washed most of the laundry. And the amount of the laundry that still needs to be washed will be 1/2.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Mr. Doyle washed 2/5 of his laundry. His son washed 1/4 of it. The laundry done by the son is given as,

⇒ (1/4) x (2/5)

⇒ 1 / 10

The amount of the laundry that still needs to be washed is given as,

⇒ 1 - 1/10 - 2/5

⇒ 1 - 1/10 - 4/10

⇒ (10 - 1 - 4) / 10

⇒ 5 / 10

⇒ 1/2

Mr. Doyle washed most of the laundry. And the amount of the laundry that still needs to be washed will be 1/2.

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Answer:

Step-by-step explanation:

The number of ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties, is calculated using the combination formula. The combination formula is:

C(n, r) = n! / (r! (n-r)!)

Where n is the total number of items, and r is the number of items to choose. In this case, n = 10 and r = 3.

So, the number of ways to choose 3 students out of 10 is:

C(10, 3) = 10! / (3! (10-3)!) = 10! / (3! 7!) = 10 x 9 x 8 / (3 x 2 x 1) = 120.

Therefore, there are 120 different ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties.

The fixed costs per unit when 18,349 units are produced is $18.00.

First we need to determine the total costs of production at that level of output.

Given that fixed costs are $18 per unit and variable costs are $10 per unit, the total costs when 15,637 units are produced are:

Fixed costs = $18 * 15,637 = $281,866

Variable costs = $10 * 15,637 = $156,370

Total costs = $281,866 + $156,370 = $438,236

When 18,349 units are produced, the total costs are:

Fixed costs = $18 * 18,349 = $328,882

Variable costs = $10 * 18,349 = $183,490

Total costs = $328,882 + $183,490 = $512,372

Next, we can calculate the fixed costs per unit by dividing the fixed costs by the number of units produced:

Fixed costs per unit = $328,882 / 18,349 = $18.00

Therefore, The fixed costs per unit when 18,349 units are produced is $18.00.

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The statement about the standard deviation that is false is -

a. The standard deviation can never be 0.

What is standard deviation?

The standard deviation is a measure of variance from the mean that includes spread, dispersion, and spread. The standard deviation displays a "typical" deviation from the mean. It is a well-liked measure of variability because it retains the original units of measurement from the data set.

When all of the observations are identical, the standard deviation can be zero

(a). This is due to the fact that if all of the observations are identical, their mean will be the observation itself, resulting in a standard deviation of 0.

As a result, the assertion is untrue.

(b) The deviations of each observation are indeed calculated from the average, which is the measure of the centre.

As a result, the assertion is accurate.

(c) The standard deviation is given by:

[tex]\frac{1}{n}E(X_i-X')^2[/tex]

So, as the individual data points or data observations get farther away from the mean, the term [tex](X_i-X')^2[/tex]keeps becoming larger which causes the overall value of the standard deviation to be large.

Therefore, the given statement is true.

(d)

The standard deviation measures the spread of the data around the mean.

This is the basic definition of the standard deviation itself.

Therefore, the given statement is true.

(e)

When an outlier is taken into account, the difference between the observation and mean value will be greater, and the square term will intensify the term's value even more. The standard deviation will rise dramatically as a result.

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Complete question:

The standard deviation is a useful measure of a characteristic of a distribution of data values. Which of the following statements about the standard deviation is false?

a. The standard deviation can never be 0.

b. The standard deviation is appropriate as a measure of spread when the mean is chosen as the measure of center.

c. As the data values get farther away from the mean, the standard deviation becomes larger.

d. The standard deviation measures the spread of the data around the mean.

e. The standard deviation can be made very large by an outlier.

The alternative hypothesis H1 and the null hypothesis H0. H0: H1: the mean systolic blood pressure of senior ladies is 120.

An declaration that a certain group of data has no significance level is known as a null. Hypotheses are analyzed for viability using sample data. known as "zero" at times is represented by that of the letter H0. The premise used by researchers is that all variables have a relationship. The alternate hypothesis, on the other extreme, asserts that there's no such link. The h0 is an important component of research, despite embodies insignificance.

given

a) H1. H0: H1: as μο = 120

μ >120

b) one sample t - test

c) t = 2.213

d) = no

The alternative hypothesis H1 and the null hypothesis H0. H0: H1: the mean systolic blood pressure of senior ladies is 120.

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Answer: Sorry ching cong ling long aoa

Step-by-step explanation:

Answer:t

Step-by-step explanation:

R5

f⁻¹(x) = 4x + 7

This can be solved using the concept of function.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

Given that,

f(x) = x -7/4

f⁻¹(x) = 4x + 7

Now, f (f⁻¹(x)) = f (4x + 7)

=  [{(x - 7) / 4} ÷ 4] + 7

= x          [Proved]

Next, f⁻¹(f(x))

= f⁻¹ (x -7/4)

= 4 × [(x -7/4)] + 7

= x          [Proved]

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You can deduce from your facts that assertion A is correct. Statement B is not conclusive. Statement C is incorrect. Statement D is not conclusive. statement E is false.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.

Here,

From your data, you can conclude that:

A. A parent-offspring regression for trait C will have the highest slope.

Heritability is the proportion of variation in a trait that can be explained by genetic variation. A higher heritability indicates that more of the variation in a trait is due to genetic differences, and less is due to environmental differences. If the heritability of a trait is 0.8, this means that 80% of the variation in the trait is due to genetic differences, and a parent-offspring regression would have a steeper slope than if the heritability was lower.

B. Selection of trait A will have no effect on the population mean for this trait.

This statement cannot be concluded from the data. Heritability of a trait does not dictate the responsiveness of a trait to selection. Even if the heritability of a trait is low, it can still respond to selection, and even if the heritability of a trait is high, it may not respond much to selection, depending on the presence of other factors such as the distribution of the trait in the population, the presence of linkage disequilibrium, and the presence of genetic constraints.

C. A parent-offspring regression for trait B will be a flat line.

This statement is false. If the heritability of a trait is 0.5, this means that half of the variation in the trait is due to genetic differences, and half is due to environmental differences. A parent-offspring regression would not be a flat line, but would still have a slope, albeit not as steep as if the heritability was higher.

D. Selection on each behavior will result in similar changes in the population mean for each trait.

This statement cannot be concluded from the data. Heritability is only one of many factors that affects the responsiveness of a trait to selection, and the responsiveness of each trait will depend on other factors as well.

E. A parent-offspring regression on trait A will have a slope of 0.9.

This statement is false. Heritability is the proportion of variation in a trait that can be explained by genetic differences, not the slope of a regression. The slope of a parent-offspring regression would depend on other factors such as the distribution of the trait in the population and the presence of environmental factors.

From your data, you can conclude that: statement A is true. statement B cannot be concluded. statement C is false. statement D cannot be concluded. statement E is false.

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The measure of <OXY is 90 degree.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent.

Given:

As, A line that crosses a circle at precisely one point, known as the point of tangency or tangency point, is said to be tangent to the circle.

The fact that the radius is perpendicular to the tangent line from the circle's center to the point of tangency is a significant outcome.

So, according to this tangent XY toucehes the circle at point X.

Thus, <OXY is perpendicular i.e., <OXY = 90

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The conversion of the units gives:

NUMBER 1: 75 mi/hr = 36.957 m/s

NUMBER 2: 5d = 432000 seconds

Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement. For example, converting a distance measured in meters to feet, or converting a weight measured in kilograms to pounds.

NUMBER 1

1 mile = 5820 feet, 1 feet = 0.3048 meter.

1 hour = 60 minutes = 60 * 60 seconds = 3600 seconds

To convert 75 mi/hr to m/s, we have:
75 mi/hr = (75 * 5820 * 0.3048)m / (60 * 60)s = 36.957 m/s

NUMBER 2

Since we have 24 hours in a day, 60 minutes in 1 hour and 60 seconds in a minute. Thus, 5 days can be written as:

5d = 5 * 24 * 60 * 60 = 432000 seconds

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ V=11.25\pi \end{cases}\implies 11.25\pi =\pi (1.5)^2 h \\\\\\ \cfrac{11.25\pi }{\pi (1.5)^2}=h\implies 5=h[/tex]

Correct answer to the question is: operating profit will be the same on both statements; marketing and administrative costs will be the same on both statements.

A gross margin income statement focuses on the difference between the cost of goods sold (COGS) and the selling price of the products. It shows the gross profit as a percentage of sales, which can be used to evaluate the company's ability to generate revenue and cover its costs.

Both the gross margin and the contribution margin income statements provide important information to the company, but they offer different perspectives on the company's profitability. The gross margin income statement is useful for evaluating the overall efficiency of the company's sales and production processes, while the contribution margin income statement is useful for evaluating the potential profit from selling additional units.

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The complete question is :

Assume total units produced equals total units sold. If the company prepares a gross margin income statement and a contribution margin income statement, _____.

Answer: x = -22/7

Step-by-step explanation: Basically, all angles are the same as indicated in the image, this means that the triangle is equilateral and that all sidelengths will  be the same lengths

we can now set up an equation that equals both side lengths to find x

4x+16 = -3x -6

4x+16-16= -3x -6 -16

4x = -3x - 22

4x +3x= -3x + 3x -22

7x/7 = -22/7

x = -22/7

The turning points of the given equation are:

(3, 27 + 1/45) and (-3, 27 + 1/45), and (4, 27 + 4/243) and (-4, 27 + 4/243).

The turning point of a parabolic equation in the form of y = ax^2 + bx + c can be found by setting the derivative equal to zero and solving for x. The derivative of the given equation y = 4/(4x^2 + 27x + 27) + 27 is:

dy/dx = -16x/(4x^2 + 27x + 27)^2 + 27

Setting the derivative equal to zero, we can solve for x:

-16x/(4x^2 + 27x + 27)^2 + 27 = 0

-16x = (4x^2 + 27x + 27)^2 - 27 * (4x^2 + 27x + 27)

-16x = 16x^4 + 216x^3 + 1044x^2 + 729x + 729 - 108x^2 - 729x - 729

8x^4 - 288x^3 - 336x^2 = 0

x = ±3, ±4

For these values of x, we can find the corresponding y-values using the original equation:

y = 4/(4x^2 + 27x + 27) + 27

At x = 3, y = 4/(4 * 9 + 27 * 3 + 27) + 27 = 4/180 + 27 = 27 + 1/45

At x = -3, y = 4/(4 * 9 + 27 * -3 + 27) + 27 = 4/180 + 27 = 27 + 1/45

At x = 4, y = 4/(4 * 16 + 27 * 4 + 27) + 27 = 4/243 + 27 = 27 + 4/243

At x = -4, y = 4/(4 * 16 + 27 * -4 + 27) + 27 = 4/243 + 27 = 27 + 4/243

So, the turning points of the given equation are:

(3, 27 + 1/45) and (-3, 27 + 1/45), and (4, 27 + 4/243) and (-4, 27 + 4/243).

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Answer:

Therefore, you will need to order approximately 9.07 cubic yards of topsoil to fill the garden to a depth of 6 inches.

Step-by-step explanation:

To calculate the amount of topsoil needed, we need to find the volume of the garden in cubic yards, since topsoil is sold by the cubic yard.

The garden is 35 feet by 14 feet and 6 inches (or 0.5 feet) deep.

Volume of the garden = length x width x depth

= 35 feet x 14 feet x 0.5 feet

= 245 cubic feet

To convert cubic feet to cubic yards, we divide by 27 (since 1 cubic yard = 27 cubic feet):

Volume in cubic yards = 245 cubic feet / 27

= 9.07 cubic yards (rounded to two decimal places)

Therefore, you will need to order approximately 9.07 cubic yards of topsoil to fill the garden to a depth of 6 inches.

None of them is correct and the value of f(5/2) is 1.6 to 1 decimal place

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

f(x) = √x

Substitute 5/2 for x

So, we have

f(5/2) = √5/2

When the above is compared to their functions, we have no equivalent expression

This means that none of the notations is correct

Next. we have

f(5/2) = 1.6

Hence, the value is 1.6

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The cubic yards of concrete needed to fill the form is 5, 746.2 cubic yards

The formula for calculating the volume of a cylinder is expressed with the formula.

V = πr²h

Given that the parameter are;

Note that;

Radius = diameter/2

Radius = 20/2 = 10 yards

From the information, let's substitute the values, we get;

Volume = 3.1 4 × 10² × 18.3

find the square

Volume = 3.1 4× 100 × 18.3

multiply the values

Volume = 5, 746.2 cubic yards

Hence, the value is 5, 746.2 cubic yards

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Answer:

Step-by-step explanation:

Let's say the enrollment in the Spanish class is x.

According to the information given, the enrollment in the French class is 0.72 of the enrollment in the Spanish class, which means the enrollment in the French class is 0.72x.

The enrollment compared to Spanish class as a fraction is 0.72x / x = 0.72.

The enrollment compared to Spanish class as a percent is 0.72 x 100% = 72%.

The solution is, The enrollment compared to Spanish class as a percent is

72%.

Here, we have,

Let's say the enrollment in the Spanish class is x.

According to the information given, the enrollment in the French class is 0.72 of the enrollment in the Spanish class, which means the enrollment in the French class is 0.72x.

The enrollment compared to Spanish class as a fraction is,

0.72x / x = 0.72.

The enrollment compared to Spanish class as a percent is,

0.72 x 100% = 72%.

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A coterminal angle of θ such that 0 ≤ θ ≤ 2π is 3π/4

A. A coterminal angle of θ such that 0 ≤ theta  ≤ 2π is

= theta + 2π

= -11π/4 + 2π

= 3π/4.

B. The exact values of the six trigonometric functions evaluated at θ are as follows:

sin(θ) = sin(-11π/4) = -√2/2

cosec (θ) = cosec (-11π/4) = -2/√2

cos(θ) = cos(-11π/4) = -√2/2

sec (θ) = sec (-11π/4) = -√2/2

tan(θ) = tan(-11π) = 1

cotan (θ) = cotan (-11π) = 1

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The solution to the equation x - 25 = 2 is x = 27.

What is the equation?

An equation is a mathematical statement that asserts the equality of two expressions. In other words, it is a statement that states that two values are equal.

To solve the equation x - 25 = 2, we first add 25 to each side of the equation:

x - 25 + 25 = 2 + 25

Simplifying the right side of the equation, we get:

x = 27

Hence, The solution to the equation x - 25 = 2 is x = 27.

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Answer:

Step-by-step explanation:

56.6