What is the solution of log2x-7(81) = 4

2x-7 is subscript

To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:

1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n

Solution:

1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.

2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.

Now, we need to verify that the product of these series converges:

3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)

4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.

5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.

In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and

summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.

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Answer:

9 23/24

Step-by-step explanation:

Change both mixed fractions to improper fractions

13 5/8=109/8

3 2/3=8

Now substract: 109/8 - 8/3= 10 23/24.

Hope this helps!!

Answer: 90

Step-by-step explanation: I've done this before, this was the correct answer

Answer:90

Step-by-step explanation:

r=2 s=3 t=5

2x3 squared is 2x(3x3)=18

18x5=90

The mean cost for all 5 computer keyboards is $12.80.

The mean cost, also known as the average cost, is a measure of central tendency that represents the typical or average cost of a set of values

To find the mean cost of all 5 computer keyboards, we need to calculate the total cost of all 5 keyboards and then divide by the total number of keyboards.

The total cost of the first 4 keyboards is

= 4 keyboards x $12 each

Multiply the numbers

= $48

The total cost of all 5 keyboards is

= $48 + $16

Add the numbers

= $64

The mean cost of all 5 keyboards is

= $64 / 5 keyboards

Divide the numbers

= $12.80

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The two solutions to e² = 6x using Newton's method are x_left = 1.23151 and x_right = 2.157545.

To find the solutions of e² = 6x using Newton's Method, we will follow these steps:

Let f(x) = e² - 6x. Then we want to find the roots of f(x) = 0, which are the solutions to e² = 6x.

We need to choose a starting point x₀. A good choice is x₀ = 1, since it's a reasonable approximation to the solutions.

Apply Newton's Method to find the next approximation x₁:

x₁ = x₀ - f(x₀)/f'(x₀),

where;

Plugging in the values, we get:

x₁ = x₀ - (e² - 6x₀)/(-6) = x₀ + (e²/6 - x₀)

Use x₁ as the new starting point and repeat the process until we achieve the desired level of accuracy.

In this case, we want to find the solutions to six significant figures, so we will repeat the process until the difference between xₙ and xₙ₋₁ is less than 0.000005 (the sixth decimal place).

Using a calculator, we can apply Newton's Method iteratively to find the two solutions:

Iteration 1:

x₁ = x₀ - f(x₀) / f'(x₀)

x₁ = 1 - (e² - 6)/(-6) = 1.231509

Iteration 2:

x₂ = 1.231509 - (e² - 6)/(-6) = 1.463018

Iteration 3:

x₃ = 1.463018 - (e² - 6)/(-6) = 1.694527

Iteration 4:

x₄ = 1.694527 - (e² - 6)/(-6) = 1.926036

Iteration 5:

x₅ = 1.926036 - (e² - 6)/(-6) = 2.157545

The second solution to six significant figures is x_right = 2.157545

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Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.

We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.

A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.

The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.

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The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.

To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:

ω² = ω₀² + 2αθ

Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).

First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.

Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min

Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad

Now, substitute the values into the kinematic equation:

[tex]0 = (6900π)² + 2α(91.6π)[/tex]

[tex]α = - (6900π)² / (2 × 91.6π)[/tex]

[tex]α ≈ -331283 rad/min²[/tex]

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The distance from each landing point to the boat pulled ashore at point C is given by:-d = sqrt(25^2 (y^2/x^2 + 1))

WHAT IS TRIGONOMETRY ?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving distances, heights, angles, and other geometric measurements. Trigonometric functions such as sine, cosine, and tangent are used to relate the angles of a triangle to its sides. Trigonometry has many practical applications in fields such as engineering, physics, and architecture, and is essential for understanding and solving problems involving waves, oscillations, and periodic phenomena. It is also used in navigation, surveying, and astronomy, among other areas.

To solve this problem, we need to use the concept of right triangle trigonometry.

Let's assume that point C is directly opposite the midpoint of AB, and that the distance from point C to the midpoint of AB is x. Then we can draw a right triangle with legs of length x and 25 (half of 50) and a hypotenuse of length d (the distance from point C to each landing point).

Using the Pythagorean theorem, we can write:

d^2 = x^2 + 25^2

We also know that the angles opposite the legs of the right triangle are complementary, so we can use the tangent function to write:

tan(theta) = x/25

where theta is the angle between the hypotenuse and the side of length 25.

We can rearrange this equation to solve for x:

x = 25 tan(theta)

Now we can substitute this expression for x into the equation for d^2:

d^2 = (25 tan(theta))^2 + 25^2

Simplifying this equation, we get:

d^2 = 25^2 (tan^2(theta) + 1)

Finally, we can use the fact that tan(theta) is equal to the height of the opposite bank divided by the distance from point C to the midpoint of AB. Let's call this distance y. Then we have:

tan(theta) = y/x

Substituting this expression for tan(theta) into the equation for d^2, we get:

d^2 = 25^2 (y^2/x^2 + 1)

So the distance from each landing point to the boat pulled ashore at point C is given by:

d = sqrt(25^2 (y^2/x^2 + 1))

where x and y are the distances from point C to the midpoint of AB and the opposite bank, respectively.

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As a result, the following is the system of equations' solution as  12x - 2y = 20 in the calculation, x = 7/4 and y = 1/2.

A mathematical assertion proving the equality of two expressions is known as an equation. It has two sides—a left side and a right side—that are divided by the equal symbol (=). Variables, constants, and mathematical processes may be used in the expressions on either side of the equal sign. For instance, the expression 2x + 3 on the left is equivalent to the expression 7 on the right, as shown by the equation 2x + 3 = 7.

given

We can use the technique of elimination to solve this system of equations by adding or removing one of the variables from the equations. In this instance, by combining the two equations, we can remove y:

12x - 2y = 20

16x + 2y = 29

28x = 49

We can now find the value of x by multiplying both parts by 28:

28x/28 = 49/28

x = 7/4

We can solve for y by substituting this value of x into either of the initial equations. Let's employ the initial equation:

12x - 2y = 20

12(7/4) - 2y = 20

21 - 2y = 20

-2y = -1

y = 1/2

As a result, the following is the system of equations' solution as  12x - 2y = 20 in the calculation, x = 7/4 and y = 1/2.

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M∠4 is therefore equivalent to 102.5 degrees as Angles 1 and 3 are the opposing interior angles .

Angles are geometric shapes created by two rays that have a similar terminus, or vertex. Often, the rays are depicted as straight lines with arrows pointing in the appropriate directions. Angles are expressed in degrees, with 360 degrees being a full circle. Angles that are less than 90 degrees are referred to as acute angles, those that are precisely 90 degrees are referred to as right angles, those that are between 90 and 180 degrees are referred to as obtuse angles, and those that are exactly 180 degrees are referred to as straight angles.

given

Angles 1 and 3 are the opposing interior angles in this case, and the exterior angle 4 of a triangle is equal to the total of these angles. We thus have:

m∠4 = m∠1 + m∠3\sm∠4 = 45° + 57.5°

m∠4 = 102.5°

M∠4 is therefore equivalent to 102.5 degrees as Angles 1 and 3 are the opposing interior angles .

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The amount to be paid as monthly installment for 24 equal monthly installments is given by 30,278.65 pesos.

Area bought by Vincent =  105. 7 square meters

Cost per square meters =  12,500. 00 pesos per square meter.

The total cost of the lot is the product of the area and the price per square meter,

Cost

= 105.7 sq m ×12,500.00 pesos/sq m

= 1,321,250.00 pesos

Amount paid by Vincent in cash is equals to

= 0.45 × 1,321,250.00 pesos

= 594,562.50 pesos

The remaining balance to be paid in installments is equals to,

= 1,321,250.00 pesos - 594,562.50 pesos

= 726,687.50 pesos

This balance will be paid in 24 equal monthly installments, so the monthly installment amount is equals to,

= 726,687.50 pesos / 24 months

= 30,278.65 pesos per month (rounded to the nearest cent)

Therefore, amount paid by Vincent as monthly installment is equal to 30,278.65 pesos.

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The expected number of boxes of cereal that must be purchased to obtain at least one of each of the four different prizes is 1.

Let X be the number of boxes of cereal that need to be purchased to obtain at least one of each of the four different prizes. We want to find E(X), the expected value of X.

To do this, we can use the concept of the geometric distribution. The probability of obtaining a new prize in a box of cereal is given by:

p = 4/4 = 1 (since there are four different prizes)

The probability of not obtaining a new prize in a box of cereal is

q = 1 - p = 0

Therefore, X follows a geometric distribution with parameter p = 1. The expected value of a geometric distribution with parameter p is

E(X) = 1/p

So in this case, we have

E(X) = 1/1 = 1

This means that on average, the family will need to purchase one box of cereal to obtain at least one of each of the four different prizes.

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The greatest possible integer value of the radius of the circle is 7 inches.

The area of a circle is given by the equation[tex]$A = \pi r^2$[/tex]. We know that the area is less than [tex]$60\pi$[/tex] square inches, so the equation can be written as [tex]$60\pi > \pi r^2$[/tex]. We can solve for the radius by dividing both sides by [tex]$\pi$[/tex], which gives us [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex], which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

To explain this further, we can start with the equation for the area of a circle, which is[tex]$A = \pi r^2$[/tex]. Since the area is less than [tex]$60\pi$[/tex]square inches, this equation can be rewritten as[tex]$60\pi > \pi r^2$[/tex]. We can then divide both sides by [tex]$\pi$[/tex] to get [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex]. This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

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Answer:

The horizontal distance between the two x-intercepts is 7 units.

Step-by-step explanation:

The x-intercepts are the points at which the graph of a function or equation crosses the x-axis.  At these points, the value of y is zero.

Therefore, to find the x-intercepts of the given expression, set the expression equal to zero and solve for x:

(x - 3)(x + 4) = 0

This equation is true if and only if either x - 3 = 0 or x + 4 = 0, which means the x-intercepts are at x = 3 and x = -4.

The horizontal distance between these two points is the absolute value of the difference between the x-coordinates of the x-intercepts:

|3 - (-4)| = |3 + 4| = 7

Therefore, the horizontal distance between the two x-intercepts is 7 units.

Answer:

[tex]2 \sqrt{61} \: in[/tex]

Step-by-step explanation:

Use the Pythagorean theorem (assume, that the length of hypotenuse is x):

[tex] {x}^{2} = {10}^{2} + {12}^{2} = 100 + 144 = 244[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{244} = 2 \sqrt{61} [/tex]

The number of categories of outcomes per trial for a multinomial probability distribution is three or more.

The number of categories of outcomes per trial for a multinomial probability distribution is three or more. A multinomial probability distribution is a probability distribution that can be used to describe the possible outcomes of a trial with multiple categories. Each trial can have two or more categories, with each category having one or more outcomes. Therefore, the number of categories of outcomes per trial for a multinomial probability distribution is three or more.

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The probability that Arianna will lose a turn is impossible.

In probability, impossible events have a probability of 0. This means that there is no chance that the event will occur. In this case, the probability that Arianna will lose a turn on her next turn is 0, which means that it is impossible for her to lose a turn.

In probability theory, the term "probability" refers to the likelihood of an event occurring. It is typically expressed as a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

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Answer:

area=188

Step-by-step explanation:

12×14=168 for the area of the rectangle

2×10=20

20÷2=10 for the area of triangle

168+10+10=188

area=188

The amount accumulated after 8 years is $5,781.84. Rounded to the nearest cent, this is $5,781.84.

What is an amount?

Using the formula A = [tex]P(1 + r/k)^{kt}[/tex], where A is the amount accumulated, P is the principal, r is the annual interest rate, t is the number of years, and k is the number of times the interest is compounded per year, we can calculate the amount accumulated as follows:

P = $3,350 (given)

r = 6.2% = 0.062 (convert to decimal)

t = 8 (given)

k = 365 (given)

A = [tex]P(1 + r/k)^{kt}[/tex]

A = [tex]$3,350(1 + 0.062/365)^{365*8}[/tex]

A = [tex]$3,350(1.000170685)^{2920}[/tex]

A = $5,781.84

Therefore, the amount accumulated after 8 years is $5,781.84. Rounded to the nearest cent, this is $5,781.84.

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Answer:

x

=

−

y

2

+

10

Step-by-step explanation:

Answer:

[tex]\large\boxed{\textsf{Central Angles are made up of 2 Radiuses.}}[/tex]

[tex]\large\underline{\textsf{What are Central Angles?}}[/tex]

[tex]\textsf{Central Angles are angles inside of a circle. They're connected to the center of the circle.}[/tex]

[tex]\textsf{Central Angles have measures determined where the 2 endpoints meet on the circumference.}[/tex]

[tex]\textsf{Central Angles are made of 2 line segments called \underline{Radiuses}. They start at the Center.}[/tex]

[tex]\large\underline{\textsf{What are Radiuses?}}[/tex]

[tex]\textsf{Radiuses are line segments connected from the center of the circle to the circumference.}[/tex]

[tex]\textsf{Hence, Central Angles are made up of 2 Radiuses.}[/tex]

The function rule for this question is d = 90t.

The rate of the cheetah is given as 90 feet per second. The distance travelled by the cheetah is a function of seconds travelled. Let the distance be denoted as d and the time be denoted as t. The function is therefore a linear function of the form y = mx + b.

The equation can be expressed as d = 90t + b. The constant b is the initial distance travelled at time zero since the rate is constant. Therefore, b is zero when the time is zero. The final equation is given as follows: d = 90t, where d is the distance travelled, t is the time and 90 is the rate or speed of the cheetah.

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Answer:

To find out how much more expensive it is, per pound, to buy chicken thighs at Store B than at Store A, we need to compare the cost per pound at each store.

At SuperGrocery B, we know that 3 pounds of chicken thighs cost $34.80, so the cost per pound is:

$34.80 / 3 pounds = $11.60 per pound

At SuperGrocery A, we can use the information in the table to find the cost per pound for each amount of chicken thighs:

For 1.5 pounds of chicken thighs:

$13.52 / 1.5 pounds = $9.01 per pound

For 3 pounds of chicken thighs:

$27.03 / 3 pounds = $9.01 per pound

For 3.5 pounds of chicken thighs:

$31.54 / 3.5 pounds = $9.01 per pound

For 4.5 pounds of chicken thighs:

$40.55 / 4.5 pounds = $9.01 per pound

So the cost per pound of chicken thighs at SuperGrocery A is $9.01 per pound, which is less expensive than the cost per pound at SuperGrocery B, which is $11.60 per pound.

To find the difference between the two prices, we can subtract the cost per pound at SuperGrocery A from the cost per pound at SuperGrocery B:

$11.60 per pound - $9.01 per pound = $2.59 per pound

Therefore, it is $2.59 more expensive, per pound, to buy chicken thighs at SuperGrocery B than at SuperGrocery A.

There are 4 different weekly plans that meet the condition

If Tycho wants to go for a run on the same weekdays every week, there are 7 choices for the first day of the week, 6 choices for the second day of the week, and 5 choices for the third day of the week (since he can't run on two consecutive days).

However, we have to be careful not to overcount the number of plans that meet the conditions. For example, if Tycho chooses Monday and Tuesday as his running days, that's the same as choosing Tuesday and Monday.

To avoid overcounting, let's first count the total number of possible plans, regardless of whether they meet the conditions or not. We can choose any two days of the week for Tycho to run, which can be done in 7 choose 2 ways (or C(7,2) ways), since order doesn't matter.

C(7,2) = 7!/(2!(7-2)!) = 21

So there are 21 possible plans, regardless of whether they meet the conditions or not.

Now let's count the number of plans that meet the conditions. Since Tycho wants to run on two days a week and not on consecutive days, there are only two possible patterns: (1) run on Monday and Thursday, or (2) run on Tuesday and Friday.

Each pattern can be done in 2 ways: either run on Monday and Thursday, or run on Thursday and Monday. Similarly, either run on Tuesday and Friday, or run on Friday and Tuesday.

So there are 4 plans that meet the conditions: (Monday, Thursday), (Thursday, Monday), (Tuesday, Friday), and (Friday, Tuesday).

Therefore, there are 4 different weekly plans that meet the condition

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Answer:

m<CDB = m<GDE

Step-by-step explanation:

This gives us a present value for the company with debt of $35,564 and a present value for the competitor without debt of $36,944. The difference in present values is $1,380, rounded to the nearest dollar. Therefore, the company with debt gives the contract a higher present value of $1,380.

The company with debt will have the higher present value for this contract. This is because, despite having a higher yield, the competitor without debt is only earning 2.3% on their excess money, while the company with debt is earning 8%.

To calculate the difference in present values, we need to first calculate the present value of each company's contract. To do this, we will use the present value formula, which is:

[tex]PV = C / (1 + r)n[/tex]

Where C is the contract amount, r is the rate of return, and n is the number of years. For the company with debt, we can substitute $40,000 for C, 8% for r, and 1.75 for n. For the competitor without debt, we can substitute $40,000 for C, 2.3% for r, and 1.75 for n.

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Answer:

4t - 22

Step-by-step explanation:

To find:-

Answer:-

To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.

The four sides given to us are t-6 , t-5 , t-6 and t-5 .

Hence the perimeter of the quadrilateral would be ,

Perimeter = t-5 + t-6 + t-5 + t-6

Perimeter = 4t - 10 - 12

Perimeter = 4t - 22

Hence the perimeter of the given figure us 4t - 22.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} [/tex]

the property tax on the Weber family's home is $3,999. To find the property tax on the Weber family's home, we can use the formula:

Property tax = assessed value x tax rate

First, we need to convert the tax rate from a percentage to a decimal. We can do this by dividing the tax rate by 100:

2.15% ÷ 100 = 0.0215

Now we can plug in the values we know into the formula:

Property tax = $186,000 x 0.0215

Property tax = $3,999

So the property tax on the Weber family's home is $3,999.

Property taxes are a common way for local governments to generate revenue to fund public services like schools, roads, and emergency services. The tax rate is usually based on the assessed value of the property, which is determined by a local assessor's office. It's important for homeowners to be aware of the property tax rates in their area so they can budget for this expense. Some homeowners may be eligible for property tax exemptions or reductions, so it's also worth checking with the local assessor's office to see if there are any options available.

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Answer:

The rate of interest applied for compound interest is 24.5 %  

The rate of interest applied to simple interest is 37.5 %

Step-by-step explanation:

Given as :

The Principal amount that is deposited = $ 800

The Time period = 24 months = 2 years

The Interest earn = $ 200

Let the rate of interest = R %

So, The Amount = Principal deposited - interest earn

Or, A = $ 800 - $ 200

∴ Amount = $ 600

From compounded method

Amount = Principal ×

Or, $ 600 = $ 200 ×

Or,  =

Or, 3 =

Or,  = (1 +)

Or, 1.245 = (1 +)

or, 1.245 - 1 =

or, 0.245 × 100 = R

So, the rate is = 24.5 %

Hence The rate of interest applied fro compound interest is 24.5 %  Answer

From Simple Interest method

Simple Interest =

Or, $ 600 =

Or,  $ 600 × 100 = $ 800 × R × 2

Or, R =

∴ R = 37.5 %

So, The rate is 37.5 %

Hence The rate of interest applied to simple interest is 37.5 % Answer

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