Given that sec n - tan n = ¼ , find sec n + tan n

The dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.

The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.A rectangular poster is given that is to contain 450 square inches of print. The margins at the top and bottom of the poster are 2 inches, and the margins on the left and right are 1 inch. Let us suppose the width of the poster is x in and the length of the poster is y in. Also, we need to find the least amount of poster used.Therefore, the dimensions of the poster be x in × y in. The printable area of the poster is given as 450 sq in. Hence, the area of the poster minus the area of the margins should be 450 sq in. Therefore,x × y = (x - 2) (y - 4) + 450x × y = xy - 2x - 4y + 8 + 450xy - xy - 2x + 4y = 8 + 450(y - 4)x = (450(y - 4) - 8) / (y - 1)x = (450y - 1808) / (y - 1)Now we need to calculate the dimensions of the rectangular poster. We need to find the value of x and y. Substituting the value of x in the first equation we get,y = (450 / (x - 2)) + 4We also know that x > 2 and y > 4. We need to minimize the amount of poster used. Hence we need to minimize x × y. The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.Therefore, the dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.

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Answer:

37

Step-by-step explanation:

we know that:

C=?

c=17

b=26

a=14

using the law of cosine:

[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]

[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]

Answer: -109

Step-by-step explanation:

Concept : First take note of what operations are in play and how they relate to y. In this case, -10 is being multiplied to y and then 19 is subtracted from the product of -10 and y.

Steps:

Plug 9 in for y (parentheses just mean multiply):

-10(9)-19

Simplify using correct order of operations:

-90-19

-109

Hope this helps :)

The probability the length of the display will exceed 154 inches is 0.1292

The probability that the length of the display shelf given to each bar of soap will exceed 154 inches when there are 50 bars of soap is 0.0062 or 0.62%. This is because the mean is 3 inches and the standard deviation is 0.5 inches, which means that the length of the display will have a normal distribution.

We can calculate this probability by using the following formula:

P(x > 154) = P (x > 154 - 50 × 3/√(50×0.5)) = P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.870 = 0.1292

The probability the length of the display will exceed 154 inches is 0.1292.

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The answer to the question is 334 kittens.

Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.

First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g

Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.

Therefore, the answer to the question is 334 kittens.

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Answer: £43.50

Step-by-step explanation:

each ticket from samuel is £12 if erica is spending £2.50 more per ticket that is £14.50 per ticket. £14.50 x 3 = £43.50

The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.

Using the distance formula, we have:

d(P,Q) = √((x2-x1)² + (y2-y1)²)

= √((-4-(-12))² + (-9-7)²)

= √(8² + (-16)²)

= √(320)

= 8 √(5)

Since PR:QR is 3:5, we can set up the following equation:

d(P,R)/d(R,Q) = 3/5

Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.

Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)

Using the distance formula again, we can find the distance between P and R:

d(P,R) = (3/8) d(P,Q)

= (3/8) (8 √(5))

= 3 √(5)

Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:

d(R,Q) = (5/3) d(P,R)

= (5/3) (3 √(5))

= 5 √(5)

Finally, we can use the midpoint formula to find the coordinates of R:

x = (-12 + (3/8) (8))/2 = -8

y = (7 + (-1))/2 = 3

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Complete Question:

The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?

The selling price of laptop after VAT (15 percent) is Rs 4830.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

A number that is expressed as a fraction of hundred is what it is.

it is mostly used to compare and determine ratios and is represented by the symbol %.

We are given that:-

so the amount after VAT = 4200+4200*15%

= 4200+4200+0.15

= 4200+630= 4830.

therefore, the selling price of laptop after VAT is Rs 4830.

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We have to find the minimum number, k, of z in (a, b) such that g'(z) = 0. The function g is continuous on the interval [a, b] and is differentiable on (a, b). Suppose that g(x) = 0 for 4 distinct values of x in (a, b).

Let x1, x2, x3, and x4 be the four distinct values of x such that g(x) = 0.Now consider the following cases:Case 1: All four x1, x2, x3, x4 are local extrema of g(x).If this is the case, then g′(x1)=g′(x2)=g′(x3)=g′(x4)=0. Therefore, the minimum number, k, of z in (a, b) such that g′(z) = 0 is 4.Case 2:

There are less than four local extrema of g(x).In this case, by Rolle's Theorem, there exists at least one point z in (a, b) such that g′(z)=0. Since there are less than four local extrema of g(x), this point z is not equal to any of x1, x2, x3, and x4. Therefore, the minimum number, k, of z in (a, b) such that g′(z) = 0 is 1.In conclusion, the minimum number, k, of z in (a, b) such that g′(z) = 0 is either 1 or 4 depending on whether there are less than four local extrema of g(x) or all four x1, x2, x3, and x4 are local extrema of g(x).

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In both cases, the slope (m) is the coefficient of the x-variable, and the y-intercept (b) is the constant. In the first equation, the slope (m) is 2, and the y-intercept (b) is -3. In the second equation, the slope (m) is 3, and the y-intercept (b) is 6.

Graph is a data structure that consists of nodes (vertices) and edges (connections between nodes). Graphs are used to represent networks, such as social networks, transportation networks, and communication networks. Graphs provide a way to visualize relationships between data points and can be used to discover patterns in data and make predictions. Graphs are a powerful tool in data science and can be used to analyze complex systems.

This is happening because the equations represent the linear relationships between the variables of the graphs. The first equation is in slope-intercept form, and can be used to calculate the y-value of a given x-value. The equation for the second graph is also in slope-intercept form, and can be used to calculate the y-value of a given x-value.

In both cases, the slope (m) is the coefficient of the x-variable, and the y-intercept (b) is the constant. In the first equation, the slope (m) is 2, and the y-intercept (b) is -3. In the second equation, the slope (m) is 3, and the y-intercept (b) is 6.

These equations represent the linear relationships between the variables of the graphs. The slope of the line is the rate of change between the x- and y-values, while the y-intercept is the starting point of the line. By using the equations, we can calculate the y-value of any given x-value on the graph, and thus accurately represent the linear relationships between the variables.

The diagram is given below.

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Complete questions as follows-

After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.

Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.

The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.

If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.

The number of generations (n) in seven hours is calculated as:

n = t/g

n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations

The number of cells in the cream pie after 7 hours is calculated as :

N = N₀ × 2ⁿ

N = 6 cells × 2⁷

N = 768 cells

Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.

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The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.

As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.

We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:

Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:

Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)

Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)

(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)

Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)

(b), we can use the just-proven formula:

A = ln(1, 2,...) + ln + ln (89)

= ln(j=1 to 89) prod

sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).

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Answer: 8377828766289

Step-by-step explanation:

Answer:

The sum is:

74569273469287465294875629837469523746539287465927346592873654987264982768

999999999999999999292929292929923798341038701384710348710387017

= 74569273469287465294875629837469523746539287465927346592873655087264969785

3. The statement is true,  the correlation coefficient is close to -1. 4. temperature for a city with a latitude of 48 is 43. 5. The statement is false. 6. cannot make a reasonable estimate

Equations can be used to model real-world situations and solve problems in many fields, including science, engineering, finance, and more. They are an essential tool in mathematics and are used extensively in algebra, calculus, and other advanced branches of math.

Equations can involve various mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and others.

Question 3:

The statement is true. We can check this by calculating the correlation coefficient between the latitude and temperature data points, which should be close to -1. The calculated line of best fit is also consistent with the given data.

Question 4:

To estimate the temperature for a city with a latitude of 48, we can use the equation of the line of best fit:

y = -1.07x + 92.87

Substituting x = 48, we get:

y = -1.07(48) + 92.87

y = 42.79

Rounding to the nearest whole number, the estimated temperature for a city with a latitude of 48 is 43.

Question 5:

The statement is false. We can check this by calculating the correlation coefficient between the passengers and suitcases data points, which should be close to 1. The given line of best fit has a negative slope, which is inconsistent with the positive correlation between the variables.

Question 6:

To estimate the number of suitcases for a flight carrying 250 people, we can use the equation of the line of best fit:

y = -1.98x + 7.97

Substituting x = 250, we get:

y = -1.98(250) + 7.97

y = -485.03

However, it does not make sense for the number of suitcases to be negative. Therefore, we cannot make a reasonable estimate for the number of suitcases on a flight carrying 250 people using this line of best fit.

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It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

First, we need to convert the dimensions of the tank from inches to feet:

68 inches diameter = 68/12 feet = 5.67 feet diameter

24 feet long = 24 feet long

Next, we can calculate the volume of the tank in cubic feet:

Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:

To find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:

Finally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:

Therefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

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Answer:

2)She could either divide by 3 or distribute 3 into the parenthesis

As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.

A mathematical relationship called proportionality asserts that two values are related in such a way that if one quantity rises or falls, the other quantity rises or falls by a fixed amount. The proportionality constant, also known as this constant factor, is typically represented by the letter "k".

given

The remaining 70% of Jerome's 1,040 songs are not country songs if only 30% of them are.

We can use the following calculation to get the proportion of non-country songs:

70% of 1,040 = 0.7 x 1,040 = 728

As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.

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Answer: So that means the answer is $112.5

Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.

YES THIS IS RIGHT!!!!

The shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it has magnitude but no direction. Distance is usually measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement used.

Sound is a type of physical energy that is produced by vibrating objects and travels through a medium, such as air, water, or solids, as a series of pressure waves. When an object vibrates, it creates a disturbance in the surrounding medium that causes molecules to move back and forth, creating areas of high and low pressure that propagate outward from the source of the sound.

In the given question,

Let d be the distance between Alan and Ryan in miles. Then, the time it takes for sound to travel this distance is given by d/768. Therefore, we have:

d/768 = 45 - 30 = 15

Solving for d, we get:

d = 15 x 768 = 11520

So the distance between Alan and Ryan is 11520 miles.

If we take the lower bound of 750 miles per hour, we can calculate the minimum distance between Alan and Ryan as follows:

d/750 = 15

d = 15 x 750 = 11250

Therefore, the minimum distance between Alan and Ryan is 11250 miles.

If we take the upper bound of 800 miles per hour, we can calculate the maximum distance between Alan and Ryan as follows:

d/800 = 15

d = 15 x 800 = 12000

Therefore, the maximum distance between Alan and Ryan is 12000 miles.

Therefore, the shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles.

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The normal distribution that best approximates X is N(42, 21).

In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).

In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)

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Answer:

4 apples

Step-by-step explanation:

We know

John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.

How many apples does he have now​?

3 - 2 + 4 - 1 = 4 apples

So, he has 4 apples now.

Answer:

4 apples

Step-by-step explanation:

We know that John had 3 apples

but then he had dropped 2 of them

he then found 4

then he gave 1 to his friend

3-2=1

1+4=5

5-1=4

The answer is 4

Hope this helps!

Boolean expressions that are equivalent to the expression num ≥ 15 are (B) (num > 15) OR (num = 15) and (D) NOT (num < 16).

In Boolean algebra, a Boolean expression is an algebraic expression made up of Boolean variables and logical operations. Boolean logic deals with logical variables and has only two values: 1 or 0 or TRUE or FALSE. Boolean expressions evaluate to a Boolean value of either 0 or 1 or TRUE or FALSE.(A) (num > 15) AND (num = 15) - this expression is not equivalent to num ≥ 15 because (num > 15) is false for all values of num that are less than or equal to 15.

However, num ≥ 15 is true for all values of num that are greater than or equal to 15.(C) NOT (num < 15) - this expression is not equivalent to num ≥ 15 because NOT (num < 15) is true for all values of num that are greater than or equal to 15. However, num ≥ 15 is true for all values of num that are greater than or equal to 15.(B) (num > 15) OR (num = 15) - this expression is equivalent to num ≥ 15 because if num is greater than 15, then (num > 15) is true and (num = 15) is false. However, if num is equal to 15, then (num > 15) is false and (num = 15) is true.

In either case, (num > 15) OR (num = 15) is true, which means that num ≥ 15 is true.(D) NOT (num < 16) - this expression is equivalent to num ≥ 15 because if num is less than 16, then (num < 16) is true and NOT (num < 16) is false. However, if num is greater than or equal to 16, then (num < 16) is false and NOT (num < 16) is true. In either case, NOT (num < 16) is true, which means that num ≥ 15 is true.

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Answer: Total number of males= C

Step-by-step explanation:

Answer: In 2030, the population will be 16,800 and in 2040 the population will be 18,816.

Step-by-step explanation: To find the population in 2030, we need to calculate one decade of growth from 2020 to 2030:

Population in 2030 = 15,000 x (1 + 0.12)^1 = 16,800

Therefore, the population in Gastonia is expected to be 16,800 in 2030.

To find the population in 2040, we need to calculate two decades of growth from 2020 to 2040:

Population in 2040 = 15,000 x (1 + 0.12)^2 = 18,816

Therefore, the population in Gastonia is expected to be 18,816 in 2040.

Yes, every odd integer can be written as the difference of two squares.

To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.

To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.

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Work Shown:

x = previous total weight

2% of x = 0.02x = amount of weight lost

x - 0.02x = 0.98x = current total weight

0.98x = 1519

x = 1519/0.98

x = 1550 pounds

Check:

2% of 1550 = 0.02*1550 = 31

The group collectively lost 31 pounds.

1550-31 = 1519

The answer is confirmed.

Note that 98% of 1550 = 0.98*1550 = 1519

Answer: 36.8

Step-by-step explanation:

First convert 7/19 to a decimal.

7/19 = 0.368421...

Then to convert a decimal a percent by multiplying by 100

0.3684... x 100 = 36.8

The chance that a randomly selected individual found to have a positive result actually has the disease is called the Positive Predictive Value (PPV). What is the chance that a randomly selected individual found to have a positive result actually has the disease?

The probability that a randomly chosen individual with a positive test result really has the disease is referred to as the Positive Predictive Value (PPV). It reflects how well the test can detect disease in those who have it. In statistics, the PPV is calculated as follows:

PPV = True Positives / (True Positives + False Positives) x 100

In addition, the PPV is influenced by a variety of factors, including the disease's prevalence, the sensitivity and specificity of the test, and the prevalence of the disease in the population.

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the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".

How to solve and what is subtraction?

To write the subtraction problem "-3 - 4" as an addition problem using negative numbers, we can rewrite it as follows:

-3 - 4 = -3 + (-4)

So, the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".

Subtraction is a fundamental arithmetic operation used to find the difference between two values or quantities. It involves taking away a certain amount from a starting value, resulting in a lower value.

The starting value is called the minuend, the amount being subtracted is called the subtrahend, and the result is called the difference. Subtraction is commonly used in everyday life, such as in calculating change when making a purchase or determining how much time has elapsed between two events. It is also an important concept in more advanced mathematical topics such as algebra and calculus.

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The value of k in the cubic equation is 2 and factorization of the equation is 2(x-1)^2(x+1)

If 2x^3 + 15x^2 + 24x + k has three linear factors, then it must be in the form:

[tex]2x^3 + 15x^2 + 24x + k = a(x-b)(x-c)^2[/tex]

where a, b, and c are constants, and (x-c)^2 means that (x-c) is a repeated factor.

Expanding the right side, we get:

[tex]2x^3 + 15x^2 + 24x + k = a(x^3 - 2cx^2 + cx^2 - 2cx + c^2x - c^2)[/tex]

Simplifying, we get:

[tex]2x^3 + 15x^2 + 24x + k = ax^3 - 2acx^2 + ac^2x - 2acx + ac^2 + a(-c^2)\\2x^3 + 15x^2 + 24x + k = ax^3 + (-2ac + ac^2)x^2 + (-2ac + ac^2)x - ac^2[/tex]

Equating the coefficients of each power of x on both sides, we get:

[tex]a = 2\\-2ac + ac^2 = 15\\-2ac + ac^2 = 24\\-ac^2 = k\\\\[/tex]

From the second and third equations, we can see that -2ac + ac^2 = 15 and -2ac + ac^2 = 24. These equations are equivalent, so we can set them equal to each other:

[tex]-2ac + ac^2 = 15 = 24[/tex]

Simplifying, we get:

ac^2 - 2ac + 9 = 0

This is a quadratic equation in ac. Solving for ac using the quadratic formula, we get:

[tex]ac = [2 \± \sqrt(4 - 4(1)(9))] / 2[/tex]

[tex]ac = 1 \± \sqrt(-5)[/tex]

Since ac is the product of two real numbers (b and c), we know that the square root of -5 must cancel out. This is only possible if ac = 1 and c = -1. Therefore, b = -c = 1, and we can find k by setting ac^2 = -k:

[tex]1 = 2a\\15 = -2ac + ac^2 = -2a + a^2\\24 = -2ac + ac^2 = -2a + a^2\\-k = -ac^2 = 2(-1)^2 = 2\\[/tex]

Therefore, k = -2, and the factorization of 2x^3 + 15x^2 + 24x - 2 is:

2x^3 + 15x^2 + 24x - 2 = 2(x-1)^2(x+1)

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