Lana wants to deposit $800 in a certificate of deposit for a maximum of one year. The bank offers her four options. Which offer would earn Lana the most interest?

A. A one-year certificate of deposit with a nominal interest rate of 2 percent.
B. A three-year certificate of deposit with a nominal interest rate of 3 percent
C. A one-year certificate of deposit with a nominal interest rate of 3 percent
D. A three-year certificate of deposit with a nominal interest rate of 4 percent

-----please no links thank you! ------​

Answer:

76

Step-by-step explanation:

(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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\(f(x) = 2(3x + 5)\) is a real valued function and has no restrictions The range of the function is all real numbers from negative infinity to infinity.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

Given, The function f operates on a variable x by tripling it, adding 5, and then doubling that quantity which is \(f(x) = 2(3x + 5)\) and it is a real function.

Now there no restrictions on this function's domain and range

∴ The range of the function is all real numbers from negative infinity to infinity.

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Answer:

coaches students to improve their communication skills

Step-by-step explanation:

Answer:

helps students with speech disabilities

Step-by-step explanation:

Got it right

Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.

The break-even point is the value of x for which:

R(x) = C(x).

In this problem, the functions are:

Hence:

R(x) = C(x)

16x = 12x + 1424

4x = 1424

x = 1424/4

x = 356

The company will break-even when 356 widgets are sold.

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In Bermuda, there are a total of 90 telephones for each 100 people. Also there are a total of 3,76,000 telephones in use in Luxembourg according to simple calculations.

Here, they given that a telephone symbol is equal to 5 telephones.

Then according to the given diagram,

1. There are:

= (5 + 5 + 5 + 3) 5 telephones

= ( 18 ) 5 telephones

= 90 telephones.

Therefore, there are a total of 90 telephones for each 100 people.

2. In 2005, the population of Luxembourg was 470,000.

According to the given diagram, there are 80 telephones available for every 100 people.

For 4,70,000:

100 -------------- 80

4,70,000 ------ (x)

After cross multiplication,

x * 100 = 80 * 470000

x = 8 * 47000

x = 3,76,000

Therefore, there are total of 3,76,000 telephones in use in Luxembourg.

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Answer:

-3 on edg

Step-by-step explanation:

\(\boxed{\boxed{\pink{\bf \leadsto The \ Solution \ of \ the \ given \ equation \ is\ \sqrt{26}\ or \ -\sqrt{26}}}}\)

We need to find the solution of the given logarithmic equation. So the given equation is ,

\(\bf \implies ln ( x^2-25) = 0 \)

Using the Properties of log we can write this as ,

\(\bf \implies e^{ln(x^2-25)} = e^0 \:\:\bigg\lgroup \red{\bf Here \ e \ is \ Euler's \ Number }\bigg\rgroup \\\\\bf\implies x^2-25 = e^0 \\\\\bf\implies x^2-25 = 1 \\\\\bf\implies x^2=25+1\\\\\bf\implies x^2=26 \\\\\bf\implies x = \sqrt{26} \\\\\bf\implies\boxed{\red{\bf x = \sqrt{26},-\sqrt{26}}}\)

In order to prove that ∠E = ∠I, we can use the following statements and reasons:

1. Statement: ∠E = ∠FGL

Reason: Opposite angles in a parallelogram are congruent

2. Statement: ∠FGL = ∠KLG

Reason: Alternate interior angles

3. Statement: ∠KLG = ∠I

Reason: Opposite angles in a parallelogram are congruent

4. Statement: ∠E = ∠I

Reason: Transitive property of the equality (∠E = ∠FGL, ∠FGL = ∠KLG and ∠KLG = ∠I, so ∠E = ∠I)

Answer:

367.75

Step-by-step explanation:

21+23.3+323.45

Add the three terms.

= 367.75

The sum of theses numbers is 367.75.

Answer:

\(= 367.75 \\ \)

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: 21 \\ + \: \: \: \: 23.3 \\ = \: \: 44.3 \\ + 323.45 \\ = 367.75\)

Answer:

What is the best estimation of the equation  

7

8

−

6

11

? Drag the numbers into the boxes. Numbers may be used once, twice, or not at all.

1/2 added to

1/42011/21/8

1

−

1/2

=  

1/2

Step-by-step explanation:

Answer:

A,B

Step-by-step explanation:

I think bc I had the same question well something like this in A in B was it

Answer:

Amount of selling cost = $228

Step-by-step explanation:

Given:

Amount of cost to store = $152

Mark up = 50%

Find:

Amount of selling cost

Computation:

Amount of mark up = Amount of cost to store x Mark up

Amount of mark up = 152 x 50%

Amount of mark up = $76

Amount of selling cost = Amount of cost to store + Amount of mark up

Amount of selling cost = 152 + 76

Amount of selling cost = $228

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

If the acceleration of the object becomes 3 m/s^2, the force is equal to 27 Newton.

Mathematically, a direct proportion can be represented the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 81/9

Constant of proportionality (k) = 9.

For the force when the acceleration of the object becomes 3 m/s^2, we have:

y = kx

y = 9(3)

y = 27 Newton.

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Complete Question:

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 81 N acts on a certain object, the acceleration of the object is 9 m/s^2. If the acceleration of the object becomes 3 m/s^2, what is the force?

90 people

We are told that;

Total number of seats = 10

Number of people in each seat  = 2 Total duration of the Ferris wheel  = 30 minutes

Number of people to ride for the first 15 minutes = 15 × 2 = 30 people

This means that 2 seats will pass per minute and thus;

Number of people to ride for 15 minutes at this double speed = 15 × 2(2) = 60

2(2) was used because a seat can take 2 people.

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The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Answer:

-7 (Not here)

Step-by-step explanation:

1. A negative plus a negative equals a negative/ a negative minus a positive equals a negative so: -10 -4 = -14

2. -14 + 7 = -7 so your answer is -7 and it's not an answer choice so you would select "Not here"

Answer:

D

Step-by-step explanation:

Answer:

x( x-4)(x+3)

Step-by-step explanation:

x^3+x^2−12x

First factor out an x

x(x^2+x^−12)

Now factor inside the parentheses

What two numbers multiply to -12 and add to 1

4*-3 = -12

4+-3 =1

x( x-4)(x+3)

Answer:

x(x - 4)(x + 3)

Step-by-step explanation:

y = x³ + x² - 12x

x(x² + x - 12)

x(x - 4)(x + 3)

The value of m in the limit is (-13 + sqrt(169 + 4ε)) / 2, where -84.875 < ε < 1.

To prove that lim as x approaches 6 of (x^2+x) = 42, we need to find a δ > 0 such that if 0 < |x - 6| < δ, then |(x^2+x) - 42| < ε, where ε > 0 is arbitrary.

We can start by working with the expression |(x^2+x) - 42| and trying to bound it by ε. We have:

|(x^2+x) - 42| = |x^2 + x - 6^2 - 6 + 36| = |(x-6)(x+7)|.

To get a bound on |(x-6)(x+7)|, we can assume that 0 < |x - 6| < δ, where δ > 0 is some quantity we need to determine. This means that:

|x-6| < δ.

We can then use the triangle inequality to bound |x+7| as follows:

|x+7| <= |x-6| + |13| < δ + 13.

Thus, we have:

|(x-6)(x+7)| <= |x-6|*|x+7| < δ(δ+13).

Now, we want to choose δ such that δ(δ+13) < ε. Let's choose:

δ = min(ε/m, 1),

where m is some constant we need to determine. We want to make sure that this choice of δ satisfies δ(δ+13) < ε.

Substituting δ = min(ε/m, 1) into the inequality δ(δ+13) < ε, we get:

min(ε/m, 1)(min(ε/m, 1) + 13) < ε.

Simplifying this inequality gives:

min(ε/m, 1)^2 + 13min(ε/m, 1) - ε < 0.

Since we want to choose the smallest possible value of δ that satisfies this inequality, we want to choose m to be the largest value that satisfies this inequality.

The discriminant of the quadratic equation is:

b^2 - 4ac = 13^2 + 4ε.

Since ε > 0, we know that the discriminant is positive, so there are two roots to the quadratic equation. The largest root is:

(-13 + sqrt(169 + 4ε)) / 2.

So, we can choose:

m = (-13 + sqrt(169 + 4ε)) / 2.

Then, we have:

min(ε/m, 1) = ε/((-13 + sqrt(169 + 4ε)) / 2).

Substituting this value of δ into the inequality δ(δ+13) < ε, we get:

ε^2 / (13 - sqrt(169 + 4ε)) < ε.

This simplifies to:

ε < 13 - sqrt(169 + 4ε).

Squaring both sides and rearranging, we get:

4ε^2 + 338ε - 1444 < 0.

This quadratic inequality holds if and only if:

(-338 - sqrt(338^2 + 441444)) / (24) < ε < (-338 + sqrt(338^2 + 441444)) / (24).

Simplifying this gives:

-84.875 < ε < 1.375.

Thus, we have found that if we choose:

m = (-13 + sqrt(169 + 4ε)) / 2,

where:

-84.875 < ε < 1.

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The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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Answer: C

Step-by-step explanation: I took the test!!

The required distance that the ladder foot away from the base of the wall is √133  meters. Option C is correct.

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and base is Pythagorean triplets.

Here,
Let the base length be x,
According to the question, a 13-meter ladder reach, the foot of the ladder is 6 meters.
So, applying the Pythagoras theorem,
13² = 6² + x²
x = √169 - 36
x = √133

Thus, the required distance that the ladder foot away from the base of the wall is √133  meters.

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Answer:

10.3

Step-by-step explanation:

Answer:10.3

Step-by-step explanation:

Answer:

the number 27 is a composite

Step-by-step explanation:

Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors

Answer:

The number 27 is composite.

Answer:

3. iwjsndudinwksjdj

Step-by-step explanation:

sorry it has to be around 20 letters

Step-by-step explanation:

The total expenses stay the same at $92,039.

The income changes to 12,000 × $35 = $420,000.

So the profit is $420,000 − $92,039 = $327,961.

Answer:

1 km

Step-by-step explanation:

Now we will arrange these lengths from lowest to longest.

30,000 mm < 60,000 mm < 500,000 mm < 1,000,000 mm

Answer:

The value of csc theta is \(\frac{3. 61}{2}\)

It is important to note that the ratio for cot is given as;

Cot theta = adjacent/opposite

cosec theta = hypotenuse/opposite

If cot theta = 3/2, then

Adjacent = 3

Opposite = 2

Using Pythagoras theorem, we have

Hypotenuse square = opposite + adjacent square

\(H = \sqrt{2^2 + 3^2}\)

\(H = \sqrt{4 + 9}\)

\(H = 3. 61\)

Cosec theta = \(\frac{3. 61}{2}\)

Thus, the value of csc theta is \(\frac{3. 61}{2}\)

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Answer:

3.16/2

Step-by-step explanation:

Have a great day