which is equivalent to 3 square root 8 x

Answer:

0.8

Step-by-step explanation:

36/45

4/5

80/100

0.8

2(x - 2)

The given expression is:

3x−6x+x−4+4x

Collect like terms

3x - 6x + x + 4x - 4

Simplify the resulting expression

2x - 4

Factor out the common term (2) from the expression

2(x - 2)

Answer:

2(x−2)

Step-by-step explanation:

Solution Steps

3x−6x+x−4+4x

Combine 3x and −6x to get −3x.

−3x+x−4+4x

Combine −3x and x to get −2x.

−2x−4+4x

Combine −2x and 4x to get 2x.

2x−4

a) The probability that the length of a randomly selected axle is less than 595 mm is approximately 0.3528.

b) The probability that the mean length of 20 axles is less than 595 mm is extremely low.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center.

(a) Using the normal distribution with mean μ = 597 mm and standard deviation σ = 5.3 mm, we can calculate the z-score for a length of 595 mm:

z = (x - μ) / σ

= (595 - 597) / 5.3

= -0.3774

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -0.3774 is 0.3528.

Therefore, the probability that the length of a randomly selected axle is less than 595 mm is approximately 0.3528.

(b) The mean of a sample of 20 axles will also follow a normal distribution, with mean μ = 597 mm and standard deviation σ = 5.3 / sqrt(20) = 1.1847 mm (using the formula for the standard deviation of the sample mean).

To find the probability that the mean length of 20 axles is less than 595 mm, we can calculate the z-score for this value:

z = (x - μ) / (σ / √(n))

= (595 - 597) / (5.3 / √(20))

= -4.1054

Using a standard normal distribution table or calculator, we can find that the probability that a z-score is less than -4.1054 is essentially 0.

Therefore, the probability that the mean length of 20 axles is less than 595 mm is extremely low.

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Option (B) is the correct answer.

A company plans to spend $8,000 in year 2 and $10,000 in year 4. At an interest rate of 10% per year, compounded semiannually. The equation that represents the equivalent annual worth A in years I through 4 is given by option (B).That is;Option (B) represents the equation that represents the equivalent annual worth A in years I through 4.

The formula for equivalent annual worth is given by;A = PW (A/P, i, n) + F(A/F, i, n)where,PW = Present WorthF = Future WorthA/P = Present Worth FactorA/F = Future Worth Factori = interest raten = number of yearsSo,A = 8000(P/A, 10/2,2) + 10000(F/A, 10/2,4)A = 8000(3.1051) + 10000(0.6848)A = 24,840.80 + 6848A = $31,688.80The equation that represents the equivalent annual worth A in years I through 4 is represented by the option (B);A = 8000(P/A, 10.25/2,2) + 10000(F/A, 10.25/2,4).

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The integral ∫(4x - 2)dx from [-2, 2] is equal to the area between the x-axis and the function 4x - 2 over the interval [-2, 2], which is 32.

The integrand is 4x - 2.

To evaluate the integral geometrically in terms of area, we can interpret the integral as the area between the x-axis and the function 4x - 2 over the interval [-2, 2]. We can break this area into two parts: the area under the line y = 4x and the area under the line y = 4x - 2.

The area under the line y = 4x is given by the integral ∫4x dx from -2 to 2, which is equal to [2x^2] from -2 to 2, or 2(2^2) - 2(-2^2) = 16.

The area under the line y = 4x - 2 is given by the integral ∫(4x - 2) dx from -2 to 2, which is equal to [2x^2 - 2x] from -2 to 2, or 2(2^2) - 2(2) - [2(-2^2) - 2(-2)] = 8 - (-8) = 16.

Therefore, the total area between the x-axis and the function 4x - 2 over the interval [-2, 2] is 16 + 16 = 32.

So, the integral ∫(4x - 2)dx from [-2, 2] is equal to the area between the x-axis and the function 4x - 2 over the interval [-2, 2], which is 32.

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The upper control limit (UCL) at a 99% confidence interval with a z value of 3 is 0.165.(option c)

In statistical process control, the UCL is a key parameter used to determine the upper boundary for acceptable variation in a process. To calculate the UCL for a defect rate, we use the formula UCL = p' + z * sqrt(p'(1-p')/n), where p' is the proportion of defects in the sample, z is the z value corresponding to the desired confidence level, and n is the sample size.

In this case, we have collected 20 samples of 100 items each, and the total number of defective items is 75. Therefore, the proportion of defects in the sample is 75/2000 = 0.0375. Using the formula mentioned earlier, with a z value of 3 and n value of 100, we can calculate the UCL as follows: UCL = 0.0375 + 3 * sqrt(0.0375 * (1-0.0375)/100) ≈ 0.165.

Therefore, the correct answer is C. 0.165.

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It will take Aidan approximately 9.70 years to save enough to buy the $29,000 speed boat.

To calculate the time it will take for Aidan to save enough for the speed boat, we can use the formula for compound interest. The formula is given by:

\(Future Value = Present Value * (1 + interest rate)^{(number of periods)}\)

In this case, Aidan currently has $2,600 saved, and he saves an additional $205 per month. The future value (FV) is $29,000, and the interest rate (r) is 1.7% per year. We need to find the number of periods (t) in years. Rearranging the formula, we get:

t = log(FV / PV) / log(1 + r)

Plugging in the values, we have:

t = log((29000 - 2600) / 205) / log(1 + 0.017)

≈ 9.70 years

Therefore, it will take Aidan approximately 9.70 years to save enough to buy the $29,000 speed boat.

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The quotient in scientific notation is \(3.6 * 10^2\). Hence, the correct option is \(3.6 * 10^2\).

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

For example, 650,000,000 can be written in scientific notation as \(6.5 * 10^8.\)

To divide numbers in scientific notation, you divide their coefficients and subtract their exponents.

The expression is as follows:

\((a x 10^m) / (b x 10^n)\)

=\((a / b) x 10^_(m - n).\)

Consider the given division of numbers in scientific notation:

\((8.64 * 10^4) / (2.4 * 10^2)\)

= \((8.64 / 2.4) * 10^_(4 - 2)\)

=\(3.6 * 10^2\).

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Answer:

62 mph

Step-by-step explanation:

Decimal Answer: 7.23

Step-by-step explanation: 7+23/100 = 7.23

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The limit of the function is infinity.

The limit of a function is the value that the function approaches as the input values get closer and closer to a particular point. In this problem, the input value is approaching infinity, and we need to find the limit of the given function as x approaches infinity.

To find the limit, we need to examine the behavior of the function as x gets larger and larger. We can do this by looking at the dominant terms in the function, which are the terms with the highest powers of x. In this case, the dominant terms are 5x³ and 20x³.

As x gets larger and larger, the term 4/20x³ becomes insignificant compared to the dominant terms, so we can ignore it. Similarly, the term -9x^2 becomes smaller compared to the dominant terms, and we can also ignore it. Therefore, the function approaches the value of 5x³ as x approaches infinity.

Now, as x gets larger and larger, the value of 5x³ also gets larger and larger without bound.

Therefore, we can say that the limit of the function as x approaches infinity does not exist. In other words, the function does not approach a particular value as x gets larger and larger.

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Answer: Angles C and E are same side interior angles.

Step-by-step explanation:

The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

either d or b???

The numeric values of the graphed function are given as follows:

To obtain the numeric values of a function from its graph, you can use the following steps:

When x = 1, the point with a closed circle is at y = 4, hence the numeric value is given as follows:

g(1) = 4.

When x = -12, we have that y = -10, hence the numeric value is given as follows:

g(-12) = -10.

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Answer:

5 degrees per hour

Step-by-step explanation:

-5+n=10

+5. +5

n=15

15/3=5

If this is a sample of 4 scores, then By using the definitional formula, SS equals 5. Your answer: 5.

Using the definitional formula, SS can be calculated as:

SS = ∑(x - X)2

where X is the sample mean.

To find X, we can use the formula:

X = ∑x / n

where n is the sample size.

Given that ∑x = 22 and n = 4, we can calculate X as:

X = 22 / 4 = 5.5

Now, we'll plug these values into the formula:

SS = 126 - (22)² / 4

Calculate (∑x)² / n:

(22)² / 4 = 484 / 4 = 121
Now we can plug in the values into the formula for SS:

SS = ∑(x - X)2
  = (1-5.5)2 + (2-5.5)2 + (3-5.5)2 + (4-5.5)2
  = (-4.5)2 + (-3.5)2 + (-2.5)2 + (-1.5)2
  = 20.5

Therefore, SS equals 20.5.

So, using the definitional formula, SS equals 5. Your answer: 5.

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We have two sets from which we get the coordinates of the ordered pair. We know that a set of ordered pair is called a relation, and that the set from which the first coordinate comes from is the domain while the set where the second coordinate comes from is called the range.

Thus, the given set is a relation.

Also we know that there are special kinds of relations--those whose first coordinate only has one corresponding second coordinate. They are called functions.

In this set, -6 corresponds to 3, 0 corresponds to 7, and 6 corresponds to 5. There is a one-to-one relation.

Therefore, this set is also a function.

The answer is the second option--it is both a function and a relation.

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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(a) Linear depreciation function: f(x) = -2,731x + 24,790.

(b) Estimated value of the car 7 years from now: $5,673.

(c) Depreciation rate: $2,731 per year.

To find the linear depreciation function for the car, we can use the formula for the equation of a straight line: y = mx + b, where y represents the value of the car, x represents the number of years, m is the slope (depreciation rate), and b is the y-intercept (initial value).

Initial value (when x = 0): $24,790

Value after 4 years (when x = 4): $13,866

We can use these two points to find the slope (m):

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

m = (13,866 - 24,790) / (4 - 0)

m = -10,924 / 4

m = -2,731

The slope (depreciation rate) is -2,731.

To find the y-intercept (b), we can substitute one of the points into the equation:

24,790 = (-2,731)(0) + b

b = 24,790

Therefore, the linear depreciation function for this car is:

f(x) = -2,731x + 24,790

(b) To estimate the value of the car 7 years from now (x = 7), we can substitute x = 7 into the linear depreciation function:

f(7) = -2,731(7) + 24,790

f(7) = -19,117 + 24,790

f(7) ≈ $5,673

The estimated value of the car 7 years from now is approximately $5,673.

(c) The rate at which the car is depreciating is given by the slope of the linear depreciation function, which is -2,731.

Therefore, the car is depreciating at a rate of $2,731 per year.

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Answer:

Step-by-step explanation:The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle. Example: In the triangle shown, tan(A)=68 or 34 and tan(B)=86 or 43 .

Given two sides

if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)

if leg b is unknown, then. b = √(c² - a²)

for hypotenuse c missing, the formula is. c = √(a² + b²)

Answer:

it’s 3/4

Step-by-step explanation:

it’s right for khan (trigonometric ratios in right triangles)

Answer:

d

Step-by-step explanation:

The probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

A regular octagon has 8 sides, and a triangle has 3 sides

Assume that there is a point on the triangle.

Then we select (3 - 1) points from the (8 - 1) sides.

8 - 1 = 7

3 - 1 = 2

So, the total number of selection is:

Selection = 7C2

Evaluate the combination expression

Selection = 21

Adjacent triangles have 5 lines (one line in common).

So, we have:'

n = 5 - 1

n = 4

The number of ways this points can be selected is:

Selection = 4C2

Evaluate

Selection = 6

The probability that the triangle and the octagon do noth have the same side is:

P= 6/21

The probability that at least one of the sides of the triangle is also a side of the octagon is calculated using the following complement rule

P = 1 - 6/21

Evaluate the difference

P = (21 -6)/21

P = 15/21

Reduce fraction

P = 5/7

Hence, the probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

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Answer:

Step-by-step explanation:

The more common way of writing this equation would be the following way

y = 2x + 1

This is a linear equation in slope-intercept form, meaning that 2 is the slope when graphed while 1 is the point where the line intercepts the y-axis when x is equal to 0. This equation has only 1 input (x) and 1 output (y). You can see the equation graphed in the picture attached below. As you can see the line crosses the y-axis at point (0,1) and crosses the x-axis at point (-0.5,0)

The revised values of the mean and standard deviation are respectively; 154 cm and 5 cm

Let us assume that the number of Patients is denoted as P. We are given;

Mean = 156 cm

We know that mean here is gotten from the formula;

Mean = Total height/number of patients

Thus;

Total Height = 156P  cm

We are told that each height was measured 2 cm more. Thus;

Total height reduction = 2P cm

Thus;

Actual Total Height = 156P - 2P = 154P cm

Mean = 154P/P  = 154  cm

Therefore, as each reading and mean both have shifted by 2 then Standard deviation will remain same as 5cm

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Answer: x=4 hope this helps:)

Step-by-step explanation:

Answer:

x=-4

Step-by-step explanation:

9x-17=5x-1 isolate X

9x-17=5x-1 add +1 to each side of the equation 9x-17+1=5x-1+1 the ones cancels out... 9x-16=5x

add -9x to both sides..... 9x-16+9x=5x-9x...... 9x-9x-16=5x-9x

-16=5x-9x subtract 5x-9x

-16= - 4x divide both sides by -4

-4=x or x=-4

-