Can someone please help I really need help

b. Central Limit Theorem. in this scenario, we would use the Central Limit Theorem to determine the probability that the mean life expectancy will be less than 70 years.

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution. In this case, a sample of 50 people is selected, which is reasonably large.

Since the mean and standard deviation of the population are known, we can calculate the z-score for a sample mean of 70 years. The z-score is calculated as:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

= (70 - 72) / (5.3 / sqrt(50))

≈ -1.19

By referring to a standard normal distribution table or using a calculator, we can find the probability of a z-score less than -1.19. This probability corresponds to the probability that the sample mean will be less than 70 years.

Using the Central Limit Theorem, we can approximate the distribution of the sample mean as a normal distribution and calculate the desired probability.

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The value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We will use Taylor's theorem to derive this result.

Taylor's theorem, also known as the Taylor series theorem, is a mathematical formula used to represent functions as a sum of infinitely many derivatives in order to approximate them over a certain interval.

This formula allows us to derive the value of a function at a point using information about its derivatives at that point.

In essence, Taylor's theorem is a tool used in calculus to model complex functions that cannot be easily solved.

Using Taylor's theorem to solve the question:

We know that the Taylor series expansion of cos(x) is given by the formula:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

To get an accurate value of cos(x), we need to keep adding terms in the series until the absolute value of the next term is less than our required accuracy.

Using |x| ≤ 1/12 and rounding to 12 decimal places, we have an error tolerance of 0.000000000001.

Therefore, we need to find the smallest value of n such that \(|x^(n+1)/(n+1)!| ≤ 0.000000000001,\)

where x = 1/12.

Substituting x = 1/12,

we have |(1/12)^(n+1)/(n+1)!| ≤ 0.000000000001

Using a calculator, we can find that n = 4 satisfies this inequality.

Therefore, we need at least 5 terms in the series of cos(x) to compute the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded).

Conclusion:

To calculate the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We used Taylor's theorem to derive this result.

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Answer: C. 00:00 $927; Vince wrote the wrong number to represent the interest rate.

Step-by-step explanation:

Given that:

Amount borrowed (p) = 900

Simple interest (r) = 1.5% = 0.015

Time (t) = 2 years

Amount he'll pay back (A) :

A = P(1 + rt)

A = 900(1 + 0.015(2))

A = 900(1 + 0.03)

A = 900(1.03)

A = $927

Answer: The Y-intercept: (0,12)

The X-intercept: (4,0)

Answer:

y - intercept (0, 12)

x - intercept (4,0)

Step-by-step explanation:

Y intercept means the x-coordinate is 0

X intercept means the y-coordinate is 0

y-intercept (0, 12)

Plug in, y = -3*0 +12

y = 0 +12

y = 12

x - intercept (4,0)

0 = -3x + 12

Minus 12 on both sides

-12 = -3x

x = 4

Answer:

The variable can be any letter.

Step-by-step explanation:

The value of z is 4.

Given that,

Based on the above information, the calculation is as follows:

4z = 16

z = 4

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The assumption/condition that is not required for the paired t-test is the Independent Groups Assumption.

The paired t-test, also known as the dependent t-test, is used to compare the means of two related samples. It is appropriate when the data are paired or matched in some way, such as when the same subjects are measured before and after a treatment.

The nearly normal condition refers to the assumption that the differences between the paired observations should be approximately normally distributed. This assumption can be checked by examining a histogram or conducting a normality test on the differences.

The paired data assumption is a requirement for the paired t-test, as it involves comparing the measurements from the same subjects or items. The data should be paired in a meaningful and appropriate way.

The randomization condition is not specific to the paired t-test, but it is a fundamental assumption in hypothesis testing. It assumes that the data were collected randomly from the population of interest, which helps ensure that the sample is representative of the population.

In summary, the assumption/condition that is not necessary for the paired t-test is the Independent Groups Assumption. The other assumptions/conditions, such as the nearly normal condition, paired data assumption, and randomization condition, are important considerations when performing and interpreting the results of a paired t-test.

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The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, the conversion factors are given as

1 kilometer = 0.62 mile

36 inches = 1 yard

1 mile = 1760 yards

To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile

1 km = 0.62 miles

Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards

1 km = 0.62 miles = 0.62 (1760 yards)

1 km = 0.62 miles = 1091.2 yards

Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard

1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)

1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches

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Answer:

60 is the answer

Step-by-step explanation:

The complement of this angle is 30 degrees.

The supplement is 120 degrees. I hope it helps!:-)

Turn the fraction into an improper fraction.

4 13/25 -> 113/25

Divide both numbers.

113 / 25 = 4.52

Best of Luck!

Answer: 1 in 2 chance

Step-by-step explanation:

Answer:

Katie made more money. Her hourly rate was $9.25 per hour.

Step-by-step explanation:

Answer:

Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?

y = –3(x + 2)2 + 10

y = –3(x – 2)2 + 10

y = –3(x + 2)2 – 14

y = –3(x – 2)2 – 2

Step-by-step explanation:

Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?

y = –3(x + 2)2 + 10

y = –3(x – 2)2 + 10

y = –3(x + 2)2 – 14

y = –3(x – 2)2 – 2

The simplified polynomial in standard form that results when (3x³)² is subtracted from 4x².

To simplify the polynomial expression (4x² - (3x³)²) in standard form, we first need to square the quantity (3x³):

(3x³)² = (3x³) * (3x³) = 9x^6

Now we can substitute 9x^6 for (3x³)² in the original expression:

4x² - (3x³)² = 4x² - 9x^6

This is the simplified polynomial in standard form that results when (3x³)² is subtracted from 4x².

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The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

In the given graph two lines are plotted.

Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).

Part B: Slope and y-intercept

Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.

For the equation y=3/4 x+1,

Compare, y=3/4 x+1 with y=mx+c, we get

Slope (m)= 3/4 and the y-intercept (c)=1

For the equation y= -4/3 x-2,

Compare, y= -4/3 x-2 with y=mx+c, we get

Slope (m)= -4/3 and the y-intercept (c)=-2

Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

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To make the cooldrink with a concentrate-to-water ratio of 1:3, you will need to use 1200ml of water.

The ratio of 1:3 means that for every 1 part of concentrate, you need 3 parts of water. In this case, you have 400ml of concentrate, which represents 1 part. To find the amount of water needed, you can multiply the amount of concentrate by the ratio of water to concentrate, which is 3. So, 400ml multiplied by 3 equals 1200ml. Therefore, you will need to use 1200ml of water to mix with the 400ml of concentrate in order to make the cooldrink. This ratio ensures the desired concentration and taste of the cooldrink.

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⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀

Answer:

(c)

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0

Then the product of the roots = \(\frac{c}{a}\)

(k - 2)x² - 6x + 12 = 0 ← is in standard form

with a = k - 2 and c = 12 , thus

\(\frac{12}{k-2}\) = 3 ( multiply both sides by (k - 1) )

12 = 3(k - 2) = 3k - 6 ( add 6 to both sides )

18 = 3k ( divide both sides by 3 )

6 = k → (c)

Answer:

Step-by-step explanation:

3===o===2=======1========0========-1=======x-2

I know this is backwards, but the question makes the choice of which direction is plus. o represents where anna lives.

Ben should be right at -2 where the x is.

e^(-10) ≈ 1/e^(10) ≈ 0.001809.. To approximate e^0.5 using Taylor series, we can start with the definition of the Taylor series for e^x:

e^x = Σ[n=0 to ∞] (x^n / n!)

Taking x = 0.5, we get:

e^0.5 = Σ[n=0 to ∞] (0.5^n / n!)

To approximate this value, we can truncate the series after a certain number of terms. For example, if we use the first four terms of the series, we get:

e^0.5 ≈ 1 + 0.5 + 0.125 + 0.0208... ≈ 1.6487

To approximate e^(-10) using Taylor series for e^x and then using the fact that e^(-x) = 1/e^x, we can start with the Taylor series for e^x as before:

e^x = Σ[n=0 to ∞] (x^n / n!)

Taking x = -10, we get:

e^(-10) = Σ[n=0 to ∞] ((-10)^n / n!)

Then, using the fact that e^(-x) = 1/e^x, we have:

e^(-10) = 1/e^(10)

We can approximate e^(10) by truncating the Taylor series after a certain number of terms. For example, if we use the first three terms of the series, we get:

e^(10) ≈ 1 + 10 + 500/3 ≈ 552.67

Therefore,

e^(-10) ≈ 1/e^(10) ≈ 0.001809

This is an approximation of e^(-10) using the first three terms of the Taylor series for e^x and then evaluating the reciprocal of the result. Note that this approximation is not very accurate, as we are only using a few terms of the series.

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The cost of one rose bush is $2 and the cost of one bunch of grass is $17.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, Norachai and Rain each improved their yards by planting rose bushes and grass.

Let the cost of rose bushes be x and the cost of bunches of grass be y.

Norachai spent $209 on 11 rose bushes and 11 bunches of grass.

Now, 11x+11y=209

x+y=19 --------(i)

Rain spent $40 on 3 rose bushes and 2 bunches of grass.

3x+2y=40 --------(ii)

Substitute x=19-y in equation (ii), we get

3(19-y)+2y=40

57-3y+2y=40

57-40=y

y=17

Substitute y=17 in equation (i), we get

x=2

Therefore, the cost of one rose bush is $2 and the cost of one bunch of grass is $17.

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Answer:

4

Step-by-step explanation:

Answer:

4 because half of 8 is 4

Answer:

Kevin's unit rate is 8.5.  This means Kevin earns $8.5 ever hour.

Step-by-step explanation:

51.00/6.

Hope this helps! :)

Answer:

He earns 8.5 every hour.

Step-by-step explanation:

You would have to find how much he earns every hour

6:51, divide 6 on both sides

1:8.5, earns 8.5 every 1 hour.

18a+15

making a subject of formular

a=18-15

=3

After considering the given data we conclude the solution to the given IVP is \(y(t) = (-1/6)sin(3t) + (1/3)e^{t} + (1/6)e^{(-2t)} .\)

To evaluate the given IVP \(y"+y' - 2y = 3 cos (3t) - 11sin (3t), y(0) = 0, y'(0) = 6\)applying Laplace transform,

we can take the Laplace transform of both sides of the equation, applying the fact that the Laplace transform of a derivative is given by

\(L{y'} = s_Y(s) - y(0) and L{y"} = s^2_Y(s) - s_y(0) - y'(0).\)

Taking the Laplace transform of both sides of the equation, we get:

\(s^2_Y(s) - sy(0) - y'(0) + s_Y(s) - y(0) - 2_Y(s) = 3_L{cos(3t)} - 11_L{sin(3t)}\)

Staging the Laplace transforms of cos(3t) and sin(3t), we get:

\(s^2_Y(s) - 6s + s_Y(s) - 0 - 2_Y(s) = 3(s/(s^2 + 9)) - 11(3/(s^2 + 9))\)

Applying simplification on the right-hand side, we get:

\(s^2_Y(s) + s_Y(s) - 2_Y(s) = (3_s - 33)/(s^2 + 9)\)

Combining like terms on the left-hand side, we get:

\(s^2_Y(s) + s_Y(s) - 2_Y(s) = (3_s - 33)/(s^2 + 9)\)

\(Y(s)(s^2 + s - 2) = (3_s - 33)/(s^2 + 9)\)

Solving for Y(s), we get:

\(Y(s) = (3_s - 33)/(s^2 + 9)(s^2 + s - 2)\)

To evaluate the inverse Laplace transform of Y(s), we can apply partial fraction decomposition:

\((3s - 33)/(s^2 + 9)(s^2 + s - 2) = A/(s^2 + 9) + B/(s - 1) + C/(s + 2)\)

Applying multiplication on both sides by \((s^2 + 9)(s - 1)(s + 2),\) we get:

\(3s - 33 = A(s - 1)(s + 2) + B(s^2 + 9)(s + 2) + C(s^2 + 9)(s - 1)\)

Staging s = 1, s = -2, and s = i3, we get:

A = -1/6, B = 1/3, C = 1/6

Hence, we can write Y(s) as:

\(Y(s) = (-1/6)/(s^2 + 9) + (1/3)/(s - 1) + (1/6)/(s + 2)\)

Taking the inverse Laplace transform of Y(s), we get:

\(y(t) = (-1/6)sin(3t) + (1/3)e^t + (1/6)e^{(-2t)}\)

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Here is a diagram of the points described:

(2,3)      (2, -3)

  |             |

  |             |

  c----------d

Based on the given points, let's consider the following:

Point A: A (2, 3)

Point B: B (2, -3)

Points A and B have the same x-coordinate, indicating that they lie on a vertical line. The y-coordinate of A is greater than the y-coordinate of B, suggesting that A is located above B on the y-axis.

Now, you mentioned that points C and D are collinear. Collinear points lie on the same line. Assuming that points C and D lie on the same vertical line as A and B, but at different positions.

The points A (2,3) and B (2, -3) are collinear, but the points A, B, C, D, and F are not. This is because the points A and B have the same x-coordinate, so they lie on the same vertical line. The points C and D also have the same x-coordinate, so they lie on the same vertical line. However, the point F does not have the same x-coordinate as any of the other points, so it does not lie on the same vertical line as any of them.

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Answer:

g(x) =1

x-1

it's either g(x) or f(x)