A rectangle is 16 feet long and 12 feet wide. How long is the diagonal from one corner to the other?

Answer:

5,181

Step-by-step explanation:

The arithmetic sequence has a common difference d = 9 which is the difference between successive terms

The sum of the first n terms of an arithmetic sequence is given by
[tex]S_n = \dfrac{n(a_1 + a_n)}{2}[/tex]

The nth term of an arithmetic sequence is given by
aₙ = a₁ + d(n - 1)

where a₁ = first term

In this particular sequence, a₁ = 13 and d = 9

Therefore
a₃₃ = 13 + 9(33-1)
= 13 + 9(32)

= 13 + 288

= 301

Therefore

If Zanele realized that the questionnaire is not suitable, it could be for various reasons, such as:

The questions may not be relevant to her specific situation or goals.

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What is your name?

Name may not be needed to provide advice on taking a gap year.

Why do you think that it is wise to take a gap year after school?

Taking a gap year after school can provide students with a break from academic studies, help them gain life experience, and give them time to explore their interests before committing to a university degree.

What are the benefits of taking a gap year?

The benefits of taking a gap year include personal and academic growth, increased independence, cultural exposure, and the opportunity to gain valuable work or volunteer experience.

What are the reasons for delaying a gap year than first pursuing a university degree?

Some students choose to delay taking a gap year to pursue a university degree first so that they can stay on track with their academic and career goals. Others may want to save money or avoid interrupting their academic momentum.

What is the best way to spend a gap year?

The best way to spend a gap year depends on your interests and goals. Some popular gap year activities include traveling, volunteering, interning, working, learning a new language or skill, or pursuing a passion project.

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Answer:

Step-by-step explanation:

The statement less than 1/2 of the bags are plain chips is true, Option D is correct.

Two or more expressions with an Equal sign is called as Equation.

Let's find the fraction of bags that are plain chips.

We know that the barbecue-flavored chips make up 1/3 of the bags, and Cheese-flavored chips make up 3/5 of the bags.

The fraction of bags that are plain chips is:

1 - 1/3 - 3/5

Lets convert the fractions with same denominator.

= 15/15 - 5/15 - 9/15

=15-5-9/15

= 1/15

1/15 is less than 1/2.

Therefore, less than 1/2 of the bags are plain chips, Option D is correct.

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So, after 4 years, a £230 investment will be worth roughly £283.52 at a 5% yearly income rate compounded annually.

Let's assume you spend $1,000 (your capital) and it makes 5% once a year in interest or profits (the compounding frequency). You would've had $1,050 at the end of the first year, which is your initial capital plus an additional $5, or $50. You would also have $1,102.50 in the following year.

We can use the compound interest algorithm to find a solution to this issue:

[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]

where A is the final amount, P is the initial investment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have:

P = £230 (the initial investment)

r = 5% = 0.05 (the annual interest rate as a decimal)

n = 1 (since the interest is increased yearly) (since the interest is compounded annually)

Given that we're searching for a number after four years, t = 4.

With these numbers entered into the algorithm, we obtain:

A = 230(1 + 0.05/1)⁴

A = 230(1.05)⁴

A = £283.52

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The weight of the fluid displaced is equivalent to the weight of the object that is submerged in the fluid.

Volume of the water displaced by the Oar = 3878 cm^3  -  2525 cm^3

= 1353 cm^3

Mass of the water = 1353  g

Weight of water displaced = Weight of the oar

Weight of oar = 1353 g

2)

Let the age of the pet be x

3x = 13

x = 13/3

x = 4 1/3 years

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The weight of cocoa in Rueben’s chocolate bar is found as  27.47 grams.

Percentage of cocoa in Rueben’s chocolate bar = 41%.

Weight of the chocolate bar = 67 grams.

Grams of cocoa in chocolate bar  = 0.41*67

Grams of cocoa in chocolate bar  = 27.47 grams

Thus, weight of cocoa in Rueben’s chocolate bar is found as  27.47 grams.

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Answer:

Step-by-step explanation:

If y varies jointly with x and the square of z, we can express this relationship as:

y = kx z^2

where k is the constant of variation. To find the value of k, we can use the given information that y = 90 when x = 5 and z = 3:

90 = k(5)(3)^2

Simplifying, we get:

90 = 45k

Dividing both sides by 45, we get:

k = 2

Now we can substitute this value of k into our equation to get:

y = 2xz^2

Therefore, the equation that represents the relationship between y, x, and z is:

y = 2xz^2

Answer: 3,500

Step-by-step explanation: 70% of 20,000 is 14,000 25% of 14,000 is 3,500

From the given graph the function obtained is [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The graph g(x) given is a graph of function g(x) = √x.

The graph when drawn for g(x) = √x, starts from the origin (0,0).

In the graph it can be seen that the function is moved 3 units left and 1 units down.

For a function f(x) moving left with k units the formula is -

y = f(x + k)

For a function f(x) moving down with k units the formula is -

y = f(x) - k

Apply these formula to our basic function g(x) = √x.

So since the graph is moved  3 units left and 1 units down, the function will be -

[tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].

Therefore, the function is obtained as [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].

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A polynomial function with real coefficients and roots 1, 3i is f(x) = x^3 - x^2 + 9x - 9.

If a polynomial function has real coefficients, then complex roots must come in conjugate pairs. That is, if 3i is a root, then -3i must also be a root. Therefore, the polynomial with roots 1, 3i, and -3i is:

(x - 1)(x - 3i)(x + 3i)

Multiplying this out using the difference of squares, we get:

(x - 1)(x^2 - (3i)^2)

Simplifying the expression using (3i)^2 = -9, we get:

(x - 1)(x^2 + 9)

Expanding the expression using FOIL, we get:

x^3 + 9x - x^2 - 9

Simplifying this expression, we get:

f(x) = x^3 - x^2 + 9x - 9

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Answer: 17 dimes or 23 nickels

Step-by-step explanation:

Let's use two variables to represent the number of nickels and dimes that Daniel has. Let: n be the number of nickels, and d be the number of dimes.

We can write two equations based on the information given in the problem:

n + d = 40 (because Daniel has a total of 40 coins)
0.05n + 0.1d = 2.85 (because the total value of the coins is $2.85)
To solve for n and d, we can use the first equation to express one variable in terms of the other, and substitute that expression into the second equation:n + d = 40

n = 40 - d0.05n + 0.1d = 2.85

0.05(40 - d) + 0.1d = 2.85

2 - 0.05d + 0.1d = 2.85

0.05d = 0.85

d = 17
So Daniel has 17 dimes. We can substitute this value back into the first equation to solve for n:n + d = 40

n + 17 = 40

n = 23
So Daniel has 23 nickels.
Therefore, Daniel has 23 nickels and 17 dimes.

The tοtal payment οver the term οf the lοan, 44% is paid tοward the principal and 56% is paid tοward the interest.

Tο sοlve this prοblem, we need tο use the fοrmula fοr a fixed-rate mοrtgage payment:

[tex]P = (Pv \times r) / (1 - (1 + r)^{(-n))[/tex]

Where:

Pv = present value οf the mοrtgage (in this case, $200,000)

r = mοnthly interest rate (APR divided by 12)

n = tοtal number οf payments (20 years × 12 mοnths per year = 240)

First, we need tο find the mοnthly interest rate:

r = 9% / 12 = 0.0075

Next, we can plug in the values and simplify the fοrmula:

[tex]P = (200,000\times 0.0075) / (1 - (1 + 0.0075)^{(-240))[/tex]

P ≈ $1,734.84

Therefοre, the mοnthly payment οn the mοrtgage is apprοximately $1,734.84.

Tο determine the percentage οf the payment that gοes tοward principal and interest, we need tο lοοk at the amοrtizatiοn schedule fοr the mοrtgage. This will shοw hοw much οf each payment gοes tοward principal and interest οver time.

Using an οnline amοrtizatiοn calculatοr, we can see that οver the 20-year term οf the mοrtgage, apprοximately 44% οf the tοtal payments gο tοward principal and 56% gο tοward interest.

Therefοre, οf the tοtal payment οver the term οf the lοan, 44% is paid tοward the principal and 56% is paid tοward the interest.

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Answer: whole = 45; part = 15%

Step-by-step explanation:

The part ( a.k.a the fraction) is the percentage.

15% can be expressed as 15/100 = 3/20.

The whole is 45.

Hope this helps! :)

The bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.

First, we need tο calculate the amοunt οf DDE in the 200g οf seal that the bald eagle eats:

If a delay differential equatiοn (DDE) equilibrium is lοcally asymptοtically stable fοr all delays, it is said tο be tοtally stable. We οutline standards fοr DDEs with discrete time delays' absοlute stability.

Calculate the amοunt οf DDE in 1 gram οf fish:

1.0 micrοgram οf DDE per gram οf fish

Calculate the amοunt οf fish the seal eats tο accumulate 2.0 micrοgrams οf DDE in its tissue:

2.0 micrοgrams οf DDE per gram οf seal / 1.0 micrοgram οf DDE per gram οf fish = 2.0 grams οf fish per gram οf seal

Calculate the amοunt οf seal that the bald eagle eats:

200g οf seal

Calculate the amοunt οf fish the bald eagle cοnsumes frοm the 200g οf seal:

200g οf seal * (1 gram οf fish / 2.0 grams οf fish per gram οf seal) = 100g οf fish

Calculate the amοunt οf DDE the bald eagle cοnsumes frοm the fish it ate frοm the seal:

100g οf fish * 1.0 micrοgram οf DDE per gram οf fish = 100 micrοgrams οf DDE

Therefοre, the bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.

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The exponential function that models the height of the ball after n bounds is given as follows:

b) [tex]H(n) = 650(0.72)^{(n - 1)}[/tex],  where n = 1, 2, 3, …

The general format of an exponential function is given as follows:

y = ab^x.

In which the parameters are given as follows:

Some students performed an experiment in which they dropped a rubber ball from a height of 650 centimeters, hence the parameter a is given as follows:

a = 650.

They noticed that after each bounce, it reached 72% of its previous height, hence the parameter b is given as follows:

b = 0.72.

Considering that the first bounce is the reference bounce, the equation is given as follows:

[tex]H(n) = 650(0.72)^{(n - 1)}[/tex]

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Based on the given information, Madras Limited Liability Company (LLC) needs to make certain adjustments in their financial statements. Firstly, the company should make a provision for the legal costs of P50,000 related to the wrongful dismissal case. Even though the legal team is confident that the ex-employee will not be successful, the provision must be made as the costs are to be incurred regardless of the outcome. This will reflect the true financial position of the company and will ensure that the financial statements present a fair view of the company's affairs.

Secondly, the company needs to make a provision for the settlement of P150,000 if the ex-employee's case is successful. This provision needs to be made because there is a likelihood of an outflow of economic resources in the future, as a result of the company losing the case. This provision will reduce the company's profit and hence its tax liability.

Thirdly, the company needs to recognize the refunds of P48,000 made to dissatisfied customers as a liability. Even though Madras LLC is under no legal obligation to make refunds, their policy of making refunds is generally known. Hence, the company has a constructive obligation to make refunds and therefore, the refunds should be recognized as a liability in the financial statements.

Lastly, the company needs to make a provision for the damages payable to the pedestrian injured on their building site. The legal advisers have confirmed that the company will have to pay damages of P100,000. Hence, the company needs to make a provision for this amount as there is a likelihood of an outflow of economic resources in the future. However, as the company has a counterclaim against the building subcontractors for P50,000, this amount can be netted off against the provision. Therefore, Madras LLC needs to make a provision of P50,000 for the net amount of damages payable to the pedestrian.

In conclusion, Madras LLC needs to make the above-mentioned adjustments to their financial statements to ensure that the financial statements present a fair view of the company's affairs. These adjustments will also ensure that the company complies with the Generally Accepted Accounting Principles (GAAP) and will help stakeholders in making informed decisions based on the financial statements.

Therefore , the solution of the given problem of expressions comes out to be it is 4 units between locations C and D.

Calculations like arbitrary division, joining, multiplication variable and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.

Here,

We can apply the distance calculation to determine the separation between two points:

=> distance=  √((x2 - x1)² + y2 - y1)²)

where the coordinates for the two points are (x1, y1) and (x2, y2).

This formula allows us to determine the separation between points

C (6, -4) and D (6, -8) as follows:

=> distance = √[(6 - 6)^2 + (-8 - (-4))^2]

=> distance = √[0^2 + (-4)^2]

=> distance = √[16]

=> distance = 4

As a result, it is 4 units between locations C and D. Both of the available answer options are incorrect.

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Answer:

Step-by-step explanation:

To convert degrees to radians we use this formula

number of degrees x [tex]\frac{\pi}{180}[/tex]

1. [tex]-415 * \frac{\pi}{180} =[/tex][tex]\frac{-83}{36} \pi[/tex]

3. [tex]570 * \frac{\pi}{180} =[/tex][tex]\frac{19}{6} \pi[/tex]

5. [tex]473 * \frac{\pi}{180} =[/tex][tex]\frac{473}{180} \pi[/tex]

7. [tex]-799 * \frac{\pi}{180} =[/tex][tex]\frac{-799}{180} \pi[/tex]

9. [tex]44 * \frac{\pi}{180} =[/tex][tex]\frac{11}{45} \pi[/tex]

11. [tex]270 * \frac{\pi}{180} =[/tex][tex]\frac{3}{2} \pi[/tex]

13. [tex]-712 * \frac{\pi}{180} =[/tex][tex]\frac{-178}{45}[/tex]

15. [tex]-332 * \frac{\pi}{180} =[/tex][tex]\frac{-83}{45} \pi[/tex]

17. [tex]-54 * \frac{\pi}{180} =[/tex][tex]\frac{-3}{10} \pi[/tex]

19. [tex]-875 * \frac{\pi}{180} =[/tex][tex]\frac{-175}{36} \pi[/tex]

21. [tex]763 * \frac{\pi}{180} =[/tex][tex]\frac{763}{180} \pi[/tex]

23. [tex]299 * \frac{\pi}{180} =[/tex][tex]\frac{299}{180} \pi[/tex]

25. [tex]-705 * \frac{\pi}{180} =[/tex][tex]\frac{-47}{12} \pi[/tex]

27.[tex]374 * \frac{\pi}{180} =[/tex][tex]\frac{187}{90} \pi[/tex]

29. [tex]-239 * \frac{\pi}{180} =[/tex][tex]\frac{-239}{180} \pi[/tex]

Hope this helps!

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Answer:

5/12

Step-by-step explanation:

3/4 - 1/3

We need to use the common denominator of 12

3/4 * 3/3 = 9/12

1/3 * 4/4 = 4/12

9/12 - 4/12 = 5/12

First we find the difference of y values. Then Find the difference of the differences. If the difference of the differences is a constant then the data represents a quadratic function.

Answer: I would use tan or cot

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know that the sine of an angle is negative in the third and fourth quadrants. So, since β is in the third quadrant (pi < β < (3pi/2)), we know that sin(β) is negative.

Given sin(β) = -√(3)/2, we can use the half-angle formulas for sine to find sin(β/2):

sin(β/2) = ±√[(1 - cos(β))/2]

Since β is in the third quadrant, we know that cos(β) is negative. We can use the Pythagorean identity to find cos(β):

cos²(β) + sin²(β) = 1

cos²(β) = 1 - sin²(β)

cos(β) = -√(1 - sin²(β))

cos(β) = -√(1 - (3/4))

cos(β) = -√(1/4)

cos(β) = -1/2

Now we can substitute cos(β) into the half-angle formula for sine:

sin(β/2) = ±√[(1 - cos(β))/2]

sin(β/2) = ±√[(1 - (-1/2))/2]

sin(β/2) = ±√(3/4)

sin(β/2) = ±(√3/2)

Since β is in the third quadrant, we know that cos(β/2) is negative. So we can use the half-angle formula for cosine to find cos(β/2):

cos(β/2) = ±√[(1 + cos(β))/2]

cos(β/2) = ±√[(1 - 1/2)/2]

cos(β/2) = ±√(1/4)

cos(β/2) = ±(1/2)

Since β is in the third quadrant, we know that cot(β/2) is negative. We can use the half-angle formulas for cosine and tangent to find cot(β/2):

cos(β/2) = ±√[(1 + cos(β))/2]

cos(β/2) = ±√[(1 - 1/2)/2]

cos(β/2) = ±√(1/4)

cos(β/2) = ±(1/2)

cot(β/2) = cos(β/2) / sin(β/2)

cot(β/2) = (±1/2) / (±(√3/2))

cot(β/2) = ±(1/√3)

cot(β/2) = ±(√3/3)

Therefore, cos(β/2) is either -1/2 or 1/2, and cot(β/2) is either -√3/3 or √3/3, depending on the choice of sign for the square roots.

answer: cos(β/2) = 1/2 and cot(β/2) = -sqrt(3,

Given sin()=-((3)/2, we can use the Pythagorean identity to calculate the value of cos():

cos(β) sqrt(1 - sin2()) sqrt(1 - sqrt(3)/2) = square (1 - 3/4) Equals square (1/4) = square 1/2

We know that is in the third quadrant, where cosine is negative, since pi (3pi/2). As a result, we have:

cos(β) = -1/2

Now we can calculate cos(/2) and cot(/2) using the half-angle formulas:

sqrt((1 + cos())/2) = cos(/2) = ±sqrt((1 - 1/2)/2) = ±sqrt(1/4) = ±1/2

We know that /2 is in the fourth quadrant, where tangent is negative, because is in the third quadrant. As a result, we have:

Tan(1/2) = -1/tan(1/2) = -1/sqrt((1 + cos())/1 - cos()) = -1/sqrt((1 - 1/2)/(1 + 1/2)) = -1/sqrt(1/3) = -sqrt (3)

The answers are therefore cos(/2) = 1/2 and cot(/2) = -sqrt (3). Nonetheless, we must establish the sign of cos(/2). We can exploit the fact that sine is negative in the third quadrant, where is located, to accomplish this. As a result, we have:

Sin(/2) is equal to sqrt((1 - cos())/2). = -sqrt((1 + 1/2)/2) = squared(3/4) = squared(3)/2

Given that cosine is positive and /2 is in the fourth quadrant, we have:

sqrt(1 - sin2(/2)) = cos(/2) 1/2 = sqrt(1 - 3/4) = sqrt(1/4)

Therefore, the solutions are cos(β/2) = 1/2 and cot(β/2) = -sqrt(3,

Answer:

222.4 cm

Step-by-step explanation:

16cm x 13.9 cm =222.4 cm

hope this helped! :D

Answer:

Step-by-step explanation:

To simplify the expression 24 + b/b + 24 x 53.72, we first need to substitute the given value of b into the expression. For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72. Next, we can simplify the division by evaluating 5/5, which equals 1. Then, we can multiply 24 and 53.72 to get a product of 1288.28. Finally, we can add the simplified terms to get a final result of 1312.28. Therefore, the simplified expression, given that b is equal to 5, is 1312.28.

The estimated intercepts are:

x-intercepts: (-1, 0) and (2, 0)

y-intercept: (0, 2).

We may take an approximation reading from the graph and use it to estimate the intercepts of the graph of the function y = -x2 - x + 2:

The graph's x-intercepts are the locations where it crosses the x-axis, indicating that y = 0. We can see from the graph that the x-intercepts are about at x = -1 and x = 2.

The graph's intersection with the y-axis, known as the y-intercept, indicates that x = 0. The graph indicates that the y-intercept is roughly at y = 2.

The estimated intercepts are as follows:

x-intercepts: (-1, 0) and (2, 0)

y-intercept: (0, 2)

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The required 1-st section: 6 ft;  2-nd section: 6+9 = 15 ft;  3-rd section: 4*6 = 24 ft.

The 40 or 80 ft. (12-24 m) lengths of steel pipe sections, or joints, are trucked to the building site and strung out along the path in the locations where they are to be welded together.

The 45-foot conduit is divided into three pieces. The middle-sized section is 9 feet longer than the shortest segment, and the longest section is 4 times as long as the shortest. Finish the design.

x + (x+9) + 4x = 45,   or

6x = 45-9

6x = 36,

x = 6.

Thus,1-st section: 6 ft;  2-nd section: 6+9 = 15 ft;  3-rd section: 4*6 = 24 ft.

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Complete Question:

A 45 foot pipe is cut into three sections. The longest section is 4 times as long as the shortest, and the middle-sized section is 9 feet longer than the shortest. Complete the diagram.