what is the solution to x3 = 64

Answer:

The answer will be, 105.26

\(\huge\blue{\fbox{\tt{Solution:}}}\)

We can simplify the expression using trigonometric identities.

First, we can use the double angle formula for sine to write sin(2x) = 2sin(x)cos(x).

Next, we can use the double angle formula for cosine to write cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x). Rearranging this equation gives 2sin^2(x) - 2cos^2(x) = -cos(2x) + 1.

Substituting these identities into the original expression gives:

tan(x-1) ( sin2x-2cos2x) = tan(x-1) [2sin(x)cos(x) - 2(1 - 2sin^2(x))]

= 2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

We can use the identity tan(x) = sin(x)/cos(x) to simplify this expression further:

2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

= 2sin(x)cos(x)/(cos(x-1)) - 2sin(x)/(cos(x-1)) + 4sin^2(x)/(cos(x-1))

Multiplying both sides of the equation by cos(x-1) gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x-1) = 2(1-2sin(x)cos(x))

Expanding the left-hand side of the equation gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x) - 4sin^2(x) = 2 - 4sin(x)cos(x)

Simplifying this equation gives:

4sin^2(x) - 2sin(x) - 2 = 0

This is a quadratic equation in sin(x), which can be solved using the quadratic formula.

Answer:

The students read 35 pages in the class to start the book.

Step-by-step explanation:

Given: A Language Arts teacher, Mr. Lopez has his students read a certain number of pages out loud in class to start a book, and then a set number of pages for homework each night to complete the book.

The graph displays the total number of pages read each day.

The point (0,35) represents the y-intercept of the function.

Since y axis representing the number of pages read each day.

It implies (0,35) represents  the students read 35 pages in the class to start the book.

Answer:

The students read 35 pages in the class to start the book.

Step-by-step explanation:

on edge

Answer: EDF

Step-by-step explanation:

because if you line it up with XYZ

they are both going to have the same lengths

Answer:

The probability is \(0.3935\)

Step-by-step explanation:

We know that the time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes.

Let's define the random variable ⇒

\(X:\) '' The time it takes a worker on an assembly line to complete a task ''

We know that \(X\) is exponentially distributed with a mean of 8 minutes ⇒

\(X\) ~ Exp (λ)

Where '' λ '' is the parameter of the distribution.

Now, the mean of an exponential distribution is ⇒

\(E(X)=\) 1 / λ  (I)

We have the value of the mean '' \(E(X)\) '' , then we replace that value in the equation (I) to obtain the parameter λ ⇒

\(8=\) 1 / λ  ⇒

λ = \(\frac{1}{8}\)

Then ,  \(X\) ~ \(Exp(\frac{1}{8})\)

The cumulative distribution function of \(X\) is :

\(F_{X}(x)=P(X\leq x)=0\) when \(x<0\) and

\(F_{X}(x)=P(X\leq x)=\) 1 - e ^ ( - λx) when \(x\geq 0\) (II)

If we replace the value of the parameter in (II) :

\(P(X\leq x)=1-e^{-\frac{x}{8}}\)  when \(x\geq 0\)

We need to calculate \(P(X<4)\)

Given that \(X\) is a continuous random variable :

\(P(X<4)=P(X\leq 4)\)

We use the cumulative distribution function to calculate the probability :

\(P(X\leq 4)=F_{X}(4)=1-e^{-\frac{4}{8}}=0.3935\)

The probability is \(0.3935\)

Answer:

The APR of the loan was 18.30%.

Step-by-step explanation:

Given that a student has a total of $ 3000 in student loans that will be paid with a 48-month installment loan with monthly payments of $ 73.94, to determine the APR of the loan to the nearest one-half of a percent the following calculation must be done:

3,000 = 100

(73.94 x 48) = X

3,000 = 100

3,549.12 = X

3,549.12 x 100 / 3,000 = X

354,912 / 3000 = X

118.30 = X

118.30 - 100 = 18.30

Therefore, the APR of the loan was 18.30%.

Answer:

B) AD = 1/3 is the answer.

Answer:

1/15 or 0.0667

Step-by-step explanation:

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bardai

chatgpt

red marble on the first draw is 2/6, or 1/3

red marble on the second draw, given that the first marble was red, is 1/5

(1/3) * (1/5) = 1/15

Answer:

its 10

Step-by-step explanation:

add the numbers, 4 and 6 where you'll get 10

Answer: 1/3

Step-by-step explanation:

Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

The number of times that 9 go into 28 is 3 times with a remainder of 1.

Given the divisor and dividend in the question;

28 ÷ 9

Set up the division problem in a long division format

divisor Γdividend

9Γ28

Divide 28 by 9, place the digit in the quotient on top of the division symbol.

   3

9Γ28

Multiply the newest quotient digit (3 )by the divisor (9)
   3

9Γ28

   27

Subtract 27 from 28

   3

9Γ28

   27

----------

      1

Therefore, the result of the division is 3 with a remainder o 1.

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To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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If you add 10 to each observation, we have that:

a) The mean is increased by 10.

b) The standard deviation remains constant.

Multiplying 10 by each observation, we have that:

a) The mean is multiplied by 10.

b) The standard deviation is multiplied by 10.

If we add 10 to each observation, we have that the sum of the n observations is added to 10n, hence the mean is increased by n.

However, the differences squared between each observation and the mean remain constant, and thus the standard deviation also remains constant.

However, when you multiply every observation in the data-set by 10, the differences squared will also be changed, hence the standard deviation is also multiplied by 10.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.

The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.

To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

Step 1: Go to the chi-square distribution calculator.

Step 2: Enter the degrees of freedom, which is 10 in this case.

Step 3: Enter the confidence level, which is 99% in this case.

Step 4: Click the “Calculate” button.

Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

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Answer:

81 km²

Step-by-step explanation:

so the perimeter of the field is 288 : 8 = 36 km

the perimeter of square is 4 time side

4s = 36

s = 36 : 4 = 9 km

Area = side x side = s²

A = 9² = 81 km²

Answer:

1. you dont add before you multiply

2 they didnt do the parenthesis first...which was their mistake

Step-by-step explanation:

The value of y is 4, so the answer is option A: y = 4.

What is trigonometric ratios ?

Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Using the given diagram, we can use the trigonometric ratios to find the value of y.

First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:

sin(30°) = opposite/hypotenuse

sin(30°) = y/8

y/8 = 1/2

y = 8/2

y = 4

Therefore, the value of y is 4, so the answer is option A: y = 4.

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Answer:

D

Step-by-step explanation:

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┈╱╲▏▎▅▂▅▂▏▎▏▎▏▏

▂▏▎▏▕╭┳┳╮▏┊▏▕╱╲

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Answer:

9

Step-by-step explanation:

18/5 ÷ 2/5 = 18/5 x 5/2 = 9

Answer:

615.832in^2

Step-by-step explanation:

Step one:

given

The radius of a ball is 7 inches.

Required:

the surface area of the ball

Step two:

the formula for the surface area is

SA= 4πr^2

substitute

\(SA=4*3.142*7^2\\\\SA= 4*3.142*49\\\\SA=615.832 in^2\\\\\)

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Answer:

LxWxH

Step-by-step explanation:

Answer:

36 square inches.

Step-by-step explanation:

volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Answer:

5x

Step-by-step explanation:

-6 + 2x + 4 + 3x - (-2)

rearrange to make it easier to solve

2x + 3x - 6 + 4 - (-2)

add like terms, negative time negative is positive

5x - 2 + 2

5x