Find the first five terms in sequence with the following a. 2n^2+6

Answer:

4 cookies

Step-by-step explanation:

The remainder of (7x12)/5 is your answer.

Answer:

d

Step-by-step explanation:

To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:

Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5

Next year's estimated budget is £6,032 per quarter.

To calculate the percentage difference, we can use the following formula:

Percentage difference = (new value - old value) / old value x 100%

Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%

Therefore, the answer is (d) 3.9%.

We can use the given formula for the rate of change of the weight of the solid to estimate the amount of solid 1 second later.

If there is 6 grams of solid at time t, then f(t) = 6 g.

To estimate the amount of solid 1 second later, we can use the derivative formula:

f'(t) = −2f(t)(5+ f(t))

We want to estimate the value of f(t+1), which represents the weight of the solid 1 second later.

To do this, we can use Euler's method, which is an approximation method for solving differential equations.

Euler's method uses the formula:

f(t+1) ≈ f(t) + f'(t)Δt

where Δt is the time step (in minutes).

Since we want to estimate the amount of solid 1 second later, we can set Δt = 1 minute.

Plugging in the values for f(t) and f'(t), we get:

f(t+1) ≈ f(t) + f'(t)Δt

f(t+1) ≈ 6 - 2(6)(5+6)

f(t+1) ≈ -66

Therefore, the estimated weight of the solid 1 second later is -66 grams. However, this result does not make physical sense since weight cannot be negative.

It is possible that the given formula for f'(t) does not accurately describe the behavior of the solid, or that there was an error in the calculation.

or maybe im just bad at maths

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

If the length of the leg of the isosceles triangle is 17 cm and the base is 16 cm then the length of altitude to the base is  15cm .

An Isosceles triangle is defined as a triangle in which any two side are of  equal length .

The Length of the leg is = 17cm ,

the base of the triangle is = 16cm ;

let the length of the altitude to the base be = x cm ,

The altitude to the base of the triangle divides it into two right angle triangle.

So , in one of the right angle triangles, Base = 16/2 = 8 cm

the Hypotenuse of triangle = length of the leg = 17 cm

By Applying Pythagoras theorem,

we get ,

17² = 8² + x²   ,

289 = 64 + x² ,

x² = 289 - 64

x² = 225 ,

taking Square root(√) on both the sides ,

we get , x = 15 .

Therefore , the length of the altitude to the base is = 15 cm .

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To find the altitude of an isoceles triangle with a base length of 16 cm and a leg length of 17 cm, use the Pythagorean Theorem. Calculate 17² + 16² = c², then solve for c² to get c = √545 = 23.3 cm.

The altitude of the triangle can be found using the Pythagorean Theorem.

a² + b² = c²

17² + 16² = c²

289 + 256 = c²

545 = c²

c = 23.3 cm

(or)

17² + 16² = c² => 289 + 256 = c²

=> 545 = c²

=> c = √545 = 23.3 cm

The altitude of an isoceles triangle can be found by using the Pythagorean Theorem. The formula for the theorem is a² + b² = c², where a and b are the two sides and c is the hypotenuse, which is the altitude. In this situation, a is the leg length of 17 cm and b is the base length of 16 cm. Substituting these values into the equation gives 17² + 16² = c². Solving for c² gives c = √545 = 23.3 cm, which is the length of the altitude.

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Answer:

B.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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As a result, it is discovered that the answer to the given function problem is slant sample points of y = x -4.

Mathematical studies cover the areas and prospective applications of geometry as well as numbers and their variants, equations, and related structures. A group of inputs that collectively produce a similar result is referred to as a "function." Each input contributes to a single, distinguishable consequence in an output-input connection known as a function. Each activity has a scope, which is also known as a region or city or municipality. Commonly, functions are denoted by the letter f. (x). The origin is X. Across operations, one-to-one action, many-to-one activity, on activity, and on

Here,

Every one of the three asymptotes can be used to construct a rational function because rational functions can take any form.

This is depicted in both the linked graph and the graph of the function f(x that serves as a representation. The function's asymptotes are as follows.

The asymptotes for the vertical slope are x = -4,

The horizontal asymptotes are Y = 0 and.

Slant has an asymptote of Y = x -4.

An exponential function is used in our example function. That isn't generally perceived of as a polynomial, but it may be expressed as an endless degree polynomial. A rational function is typically described in publications as the percentage of polynomials.

As a consequence, the solution to the given function problem is slant sampling points, which are y.

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$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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Answer:

201.1 km²

Step-by-step explanation:

Surface area of a sphere= 4πr², where r = radius

so,

4πr²

= 4×π×4²

= 64π

= 201.1 km² (rounded to the nearest tenth)

Answer: Continuous

If X is the random variable denoting the weights of employees,  X is a continuous random variable.

Step-by-step explanation:

Given: An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs.

here weights of the employees vary.

Also, weight is measured not counted , that means weight is a continuous variable.

If X is the random variable denoting the weights of employees,  X is a continuous random variable.

The weights of employees, X, is a: continuous random variable.

Therefore, the weights of employees, X, is a: continuous random variable.

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Step-by-step explanation:

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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Answer: 6.6 meters a week

Step-by-step explanation:

This problem is quite simple

You take 80 and divide it by 12

80/12

which equals

6.6

Answer:

125 ft^3

Step-by-step explanation:

V = length x width x height so for a cube V= side^3

V= 5 x 5 x 5 or 5^3 = 125

Hope this helps!

Answer:

B. 4

Step-by-step explanation:

First, make the equation. We will use H as a variable (An unknown number, represented with a letter.) to represent how many hours he has to work, so that will be the solution.

12 +7.5H = 42

First, subtract 12 from both sides to isolate the variable.

12 +7.5H = 42

-12             -12

7.5H = 30.

Next, divide both sides by the coefficient (Number next to the variable.).

7.5H = 30

/7.5      /7.5

H = 4

He has to work 4 hours to make $42. Check your solution by putting it back in the original equation.

12 + 7.5(4) = 42

7.5*4 = 30.

12+30 = 42.

This is how we know the answer is correct.

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer: cos4

Step-by-step explanation: 50 meters

B. 50-√3 meters

C. 100 meters

D. 100-√3 meters

40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.

The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."

A. sin 22

B. cos 22

C. tan 22

D. cot 22

Answer:

The square has the greatest area.

Step-by-step explanation:

Reason:

Rectangle: The area is 5.25 in2

3/4= 0.75

7 in x 0.75 in= 5.25 in2

Square: The area is 6.25 in2

2 1/2= 2.5

2.5 in x 2.5 in= 6.25 in2

In 2012, a company made $410,000 in sales in Seattle but only making $255,000 in sales in Portland. Fulfill each of the following claims:

a. Seattle outsold Portland in sales by 60.78%.

b. Portland's sales lagged Seattle's by 60.78%.

c. Sales in Portland were 62.2% of those in Seattle.

a. Seattle's sales were ___% larger than Portland's.

To calculate the percentage difference between the two sales figures, we can use the following formula:

Percentage difference = ((larger value - smaller value) / smaller value) x 100%

Substituting the values, we get:

Percentage difference = ((410,000 - 255,000) / 255,000) x 100%

Percentage difference = 155,000 / 255,000 x 100%

Percentage difference = 0.6078 x 100%

Percentage difference = 60.78%

Therefore, Seattle's sales were 60.78% larger than Portland's.

b. The sales in Portland were ___% less than those in Seattle.

Since Portland's sales were smaller than Seattle's, we can simply use the percentage difference we calculated above to find the percentage by which Portland's sales were smaller:

Portland sales were 60.78% smaller than Seattle's.

c. Portland sales were ___ % of Seattle's.

To calculate the percentage of Seattle's sales that Portland's sales represent, we can use the following formula:

Percentage = (smaller value / larger value) x 100%

Percentage = 0.62195 x 100%

Substituting the values, we get:

Percentage = (255,000 / 410,000) x 100%

Percentage = 62.2%

Therefore, Portland's sales were 62.2% of Seattle's.

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Without using a calculator, the only solution to the equation    \((x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}\) is 10.1136.

To solve this equation without using a calculator, we need to simplify both sides of the equation and then use algebraic techniques to isolate x.

\((x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}\)

square both sides of the equation and cube both sides of the equation, we will have;

(x³ - 1000)³ = (x² + 100)²

We can simplify the left-hand side of the equation by applying the cube of a binomial formula, which states that:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Let's apply this formula with a = x³ and b = -1000:

(x³ - 1000)³ = x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³

Next, let's simplify the right-hand side of the equation:

(x² + 100)² = x⁴ + 200x² + 10000

Now we can substitute these expressions back into the original equation:

x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³ = x⁴ + 200x² + 10000

We can then rearrange the terms to get a polynomial equation in x:

x⁹ - 3x⁶(1000) + 3x³(1000)² - x⁴ - 200x² - 10000 - 1000³ = 0

This equation is difficult to solve exactly, but we can make an educated guess that x is close to 10. If we substitute x = 10, we get:

(10³ - 1000)³ ≠ (10² + 100)²

Increase the value of x a little, say 10.1136

(10.1136³ - 1000)³ ≈ (10.1136² + 100)²

This is true, so x = 10.1136 is a solution to the equation. We can check that there are no other integer solutions by noting that the left-hand side of the equation is always larger than the right-hand side for x > 10, and smaller than the right-hand side for x < 10.

Therefore, the only solution to the equation is x = 10.1136.

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A function assigns the values. The interval for which the given function will be decreasing is (-∞, -1)∪(0,∞).

A function assigns the value of each element of one set to the other specific element of another set.

The interval for which the given function will be decreasing is from point A to point B, and then from point C to point D. Therefore, the interval will be (-∞, -1) and (0,∞). Hence, The interval for which the given function will be decreasing is (-∞, -1)∪(0,∞).

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Step-by-step explanation:

The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) − b shifts the function b units downward. f (x + b) shifts the function b units to the left

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

I think its false but iam not sure but you can try it