Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)

\(12>-2(y-4)\\\\\implies -\dfrac{12}2 <y-4~~~;[\text{Dividing by a negative number, so reverse the inequality.}]\\\\\implies -6<y-4\\\\\implies -6+4<y\\\\\implies -2<y\\\\\implies y>-2\\\\\text{Interval,}~ (-2,\infty)\)

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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44 percentage of scanners can be expected to fail between 40 and 45 months of service.

The percentage of scanners that can be expected to fail between 40 and 45 months of service, we need to calculate the probability within this range using the normal distribution.

Mean (μ) = 41 months

Standard deviation (σ) = 4 months

We can use the standard normal distribution to calculate the probability. However, since the distribution is given as normally distributed with a specific mean and standard deviation, we need to standardize the values before using the standard normal distribution table.

To standardize a value (x) in a normal distribution, we use the formula:

Z = (x - μ) / σ

For the lower limit of 40 months:

Z₁ = (40 - 41) / 4 = -0.25

For the upper limit of 45 months:

Z₂ = (45 - 41) / 4 = 1

Next, we look up the probabilities associated with these standardized values in the standard normal distribution table.

The probability of a z-score less than or equal to -0.25 is P(Z ≤ -0.25), and the probability of a z-score less than or equal to 1 is P(Z ≤ 1).

Using the standard normal distribution table, we find:

P(Z ≤ -0.25) ≈ 0.4013

P(Z ≤ 1) ≈ 0.8413

To find the probability within the range of 40 to 45 months, we subtract the lower probability from the upper probability:

P(40 ≤ X ≤ 45) = P(Z ≤ 1) - P(Z ≤ -0.25)

P(40 ≤ X ≤ 45) ≈ 0.8413 - 0.4013 = 0.44

Therefore, approximately 44% of scanners can be expected to fail between 40 and 45 months of service.

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Solving the operations:

Now we multiply by 100 to convert to percentage:

Therefore, oct-dec sales are 17.4% of the total sales.

For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.

A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.

The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.

A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.

Given 300 2   and p 0.45

p = 0.45 Up

and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287

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Answer:

.05

Step-by-step explanation:

you divide 5 by 100 which makes it .05

Answer:

I think the answer is D. 2

Answer:

The answer is A

Step-by-step explanation:

x is equal to - 4

so the the x is replaced by the- 4 and then you will group like- items

Divide both sides by - 5 to get - 2

The Central Angle of the sector in radians is  0.3184 π  .

In the question ,

it is given that ,

the radius of the sector = 24 m

the area of the sector = 288 m²

we know that the Area of the sector of the circle is given by the formula

Area = πr²(θ/360)

Substituting the values , we get

288 = (3.14)*(24)²*(θ/360)

θ = (288*360)/((3.14)*(24)²)

θ = 1,03,680/1808.64

θ = 57.32°

converting the angle to radian ,

we get

θ = 57.32° ×  π/180 radian

= 0.3184 π

Therefore  , The Central Angle of the sector in radians is  0.3184 π  .

The given question is incomplete , the complete question is

A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .

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Answer: It actually 18

The value of x is 18°.

It is required to find the value of given angle.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given that:

m <AOB=28° ,

m < BOC=3x-2,

m< AOD=6x

It is given that

m <AOB=m< COD

so,

m< AOD=m <AOB+ m < BOC+ m< COD

By putting the value, we get

6x=28°+3x-2+28°

6x=54°+3x

3x=54°

x=54°/3

x=18°

∴m <AOB=28° ,

m < BOC=3x-2

m < BOC=3*18-2=52°

m< COD=28°

Therefore, the value of x is 18°.

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From the hypothesis test conducted, the calculated t-statistic of -3.57 is less than the lower critical t-value of -2.064. This tells us that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level. Therefore, the null hypothesis can be rejected and conclusions can be made that that there is enough evidence to suggest that the average grade of the students in the Algebra 2 class this year is not equal to the average grade of the same students in the Algebra 1 class two years ago.

To determine whether there is enough evidence to reject the teacher's claim, we can conduct a hypothesis test. A one-sample t-test will be us to compare sample mean.

Here are the sample statistics:

Sample size (n) = 25

Sample mean (X) = 87%

Sample standard deviation (s) = 7%

A significance level (α) of 0.05, wil be used

We first calculate the t-statistic, with  (X - μ) / (s/√n),

t = (87 - 92) / (7/√25) = -5 / (7/5) = -3.57

Then, we check this value against the critical t-value for a two-tailed test with 24 degrees of freedom (n-1), and α = 0.05.

The critical t-values for a two-tailed test at α = 0.05 and df = 24 are approximately -2.064 and +2.064.

-3.57 t-test is less than the lower critical t-value of -2.064. This means that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level.

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After calculating the total distances for each scenario, we can compare them to find the worst-case scenario that minimizes the total distance traveled. The scenario with the smallest total distance will be the best option.

To determine the worst-case scenario that minimizes the total distance traveled in two-way trips to and from the existing departments, we need to calculate the total distance for each possible combination of facility locations (F1 and F2).

Let's calculate the total distance for each scenario:

F1 to A, and F2 to B:

Total distance = distance(D1 to F1) + distance(F1 to A) + distance(D2 to F2) + distance(F2 to B) + distance(D3 to F2) + distance(D4 to F2) + distance(D5 to F1)

Calculate the distances using the coordinates provided and sum them up.

F2 to A, and F1 to B:

Total distance = distance(D1 to F2) + distance(F2 to A) + distance(D2 to F1) + distance(F1 to B) + distance(D3 to F1) + distance(D4 to F1) + distance(D5 to F2)

Calculate the distances using the coordinates provided and sum them up.

F1 to C, and F2 to B:

Total distance = distance(D1 to F1) + distance(F1 to C) + distance(D2 to F2) + distance(F2 to B) + distance(D3 to F2) + distance(D4 to F2) + distance(D5 to F1)

Calculate the distances using the coordinates provided and sum them up.

None of them (No facility locations specified)

F1 to B, and F2 to C:

Total distance = distance(D1 to F1) + distance(F1 to B) + distance(D2 to F1) + distance(F2 to C) + distance(D3 to F2) + distance(D4 to F2) + distance(D5 to F1)

Calculate the distances using the coordinates provided and sum them up.

After calculating the total distances for each scenario, we can compare them to find the worst-case scenario that minimizes the total distance traveled. The scenario with the smallest total distance will be the best option.

Please note that to calculate the distance between two points, you can use the Euclidean distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Perform the calculations for each scenario to determine the worst-case scenario that minimizes the total distance traveled.

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Answer:

See Explanation

Step-by-step explanation:

Given

The function is not clear, so I will use:

\(x(t) = 2+ 3t + t^2\)

Required

Speed over 2 to 10s

This is calculated as:

\(Speed = \frac{x(a) - x(b)}{a - b}\)

Where

\((a,b) =(2,10)\)

So, we have:

\(Speed = \frac{x(2) - x(10)}{2 - 10}\)

\(Speed = \frac{x(2) - x(10)}{-8}\)

Calculate x(2) and x(10)

\(x(2) = 2+ 3*2 + 2^2 =12\)

\(x(10) = 2+ 3*10 + 10^2 =132\)

So, we have:

\(Speed = \frac{12 - 132}{-8}\)

\(Speed = \frac{-120}{-8}\)

\(Speed = 15\)

#6

Ordered pairs

And

Ordered pairs

Remember parallel lines have no solutions

Answer:

Step-by-step explanation:

Given system of equations

\(\textsf{Equation 1}:\quad x-y=-2\)

\(\textsf{Equation 2}:\quad x-y=2\)

Rewrite each equation to make y the subject.

Input x = 0 into the equation to find the y-intercept.

Input y = 0 into the equation to find the x-intercept.

Input x = 4 into the equation to find a third ordered pair.

Plots the points on the graph and draw a line through them.

Equation 1

\(\begin{aligned}x-y &=-2\\ \implies -y&=-x-2\\y&=x+2\end{aligned}\)

\(x=0 \implies y=0+2=2 \implies (0,2)\)

\(y=0 \implies x+2=0 \implies x=-2 \implies (-2,0)\)

\(x=4 \implies y=4+2=6 \implies (4,6)\)

Equation 2

\(\begin{aligned}x-y& =2\\\implies -y &=-x+2\\y & = x-2\end{aligned}\)

\(x=0 \implies y=0-2=-2 \implies (0,-2)\)

\(y=0 \implies x-2=0 \implies x=2 \implies (2,0)\)

\(x=4 \implies y=4-2=2 \implies (4,2)\)

Slope-intercept form of a linear equation:  \(y=mx+b\)

(where m is the slope and b is the y-intercept)

Comparing both equations:

Therefore, the lines are parallel. This is called Inconsistent and means the system of equations has no solution (since the lines never intersect).

Value of P(5) is 0.058 by probability.

What is a math illustration of probability?

Given that ,

p = 1 / 4 = 0.25

1 - p = 1 - 0.25 = 0.75

n = 10

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

(a) x = 5

P(X = 5) = ((10! / 5! (10 - 5)!) * 0.255 * (0.75)10 - 5

              =  ((10! / 5! (5)!) * 0.255 * (0.75)5

              =  0.058

P(5) = 0.058

(b)

P(X > 3) = 1 - P(X \leq 3)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= 1 - 0.776

= 0.224

P(ore than 3) = 0.224

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The complete question is-

Take another guess: A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)

b. 9.2

Step-by-step explanation:

cos(52) × 15 gives you the adjacent which is 9.2

In the line of symetry for this parabola is x = -1.

The maxima or minima of the parabola is \(-\frac{21}{4}\)

Estimate the gradient of the curve at x = 4 is 5.

The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.

The gradient of the curve at the point (-1, 1) is -1.

The steps are as follows:

The function of parabola y = x² - 3x - 3

(i) In the line of symetry for this parabola.

Symetry of the parabola:

x =  \(-\frac{b}{2a}\)    → for y = ax² + bx + c

x =  \(-\frac{-3}{-3}\)

x = -1

(ii) The maxima or minima of the parabola.

The maximum or minimum parabola can be found when the derivative is 0

y = x² - 3x - 3

y' = 2x - 3

0 = 2x - 3

2x = 3

x =  \(\frac{3}{2}\)

The maxima or minima of the parabola

y = x² - 3x - 3

  = ( \(\frac{3}{2}\) )² - 3 (  \(\frac{3}{2}\) ) - 3

  =  \(\frac{9}{4}\)  -   \(\frac{9}{2}\)  - 3

  =   \(\frac{9}{4}\)  -  \(\frac{18}{4}\)  -  \(\frac{12}{4}\)

  = \(-\frac{21}{4}\)

(iii) Estimate the gradient of the curve at x = 4

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(4) - 3

          = 8 - 3

          = 5

y = x² - 3x - 3

y = 4² - 3(4) - 3

  = 16 - 12 - 3

  = 1

(iv) The equation of the tangent of the point (4, 1)

(y - b)² = m (x - a)²

(y - 1)² = 5 (x - 4)²

y² - 2y + 1 = 5 (x² - 8x + 16)

y² - 2y + 1 = 5x² - 40x + 90

5x² - y² - 40x + 2y + 90 - 1 = 0

5x² - y² - 40x + 2y + 89 = 0

(v) The gradient of the curve at the point (-1, 1)

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(1) - 3

          = 2 - 3

          = -1

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Answer:

Answer is 235/45

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

8x+4=24-2x.

Add 2 to each side.

10x+4=24

Subtract 4 to each side.

10x=20

Divide.

x=2.

Answer:

Step-by-step explanation:

You are given several lists from which to choose (share them, please) and in each case you must decide whether or not the numbers are in ordere from least to greatest.

Using 37/6, -5.1717, √33, -26/5 as an example (since it is only one of several llsts), we convert all the numbers into mixed decimal fractions:

37/6 = +6.17

-5.172

5.74

-5.3

This particular list has NOT been arranged in order from least to greatest.

You must now perform the same test on the other lists and then choose the list whose numbers are shown in order from least to greatest.

The list that shows these numbers in order from least to greatest is to be considered as the -5.17, 26/5, √33, 37/6.

Since

If we divide 37 by 6 so it comes 6.1666

The next value is -5.1717

The root of 33 is 5.744

And, the value of  -26/5 is 5.2

So based on this, we can say that The list that shows these numbers in order from least to greatest is to be considered as the -5.17, 26/5, √33, 37/6.

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\(f(0) = 2 \cdot 0 - 3 = 0 - 3 = -3\\f(-2) = 2 \cdot (-2) - 3 = -4 - 3 = -7\\f(5) = 2 \cdot 5 - 3 = 10 - 3 = 7\)

the expression \(10x^2 - 14x^3 + 18x^4 as 18x^2(x - 5/18)(x - 2/3).\)\(10x^2 - 14x^3 + 18x^4\) To factorise the expression we can first factor out the common factor of \(2x^\\2\):

\(2x^2(5 - 7x + 9x^2)\)

Now, we need to factorise the quadratic expression in parentheses, \(5 - 7x + 9x^2.\) We can use the quadratic formula to find the roots of this expression:

\(x = (-(-7) ± sqrt((-7)^2 - 4(5)(9)))/(2(9))\)

\(x = (7 ± sqrt(169))/18\)

\(x = (7 ± 13)/18\)

Therefore, the roots are x = 5/18 and x = 2/3.

We can use these roots to factorise the quadratic expression as follows:

5 - 7x + 9x{power}2 = 9(x - 5/18)(x - 2/3)

Substituting this into our original expression, we get:

\(10x^2 - 14x^3 + 18x^4 = 2x^2(5 - 7x + 9x^2)\)

=\(2x^2(9)(x - 5/18)(x - 2/3)\)

= \(18x^2(x - 5/18)(x - 2/3)\)

Therefore, we have successfully factorised the expression\(10x^2 - 14x^3 + 18x^4 as 18x^2(x - 5/18)(x - 2/3).\)

Factorising expressions is an important skill in algebra and can be useful in solving equations and simplifying complex expressions. In this case, we used the method of factoring by grouping and the quadratic formula to factorise the expression into a product of simpler expressions.

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Answer:

28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

80% × 35 =

(80 ÷ 100) × 35 =

(80 × 35) ÷ 100 =

2,800 ÷ 100 =

28

hope this helps

Answer: Here, m angle KEF = 80 Degrees

Time taken to complete 10.3 half lives is 10.3 × 122 s = 1257 s which is equal to for the number of 15 8 O nuclei in a given sample to decrease to a factor of 8 × 10⁻⁴of the initial value.

Now, According to the question:

Radioactive Decay:

The rate of decay of nuclei of a radioactive element is directly proportional to the number of radioactive nuclei present at that moment in the sample.

The equation which determines the disintegration of atoms is,

N = N₀ e⁻(λt)

where, N is the number of atoms undergoing decay

N₀ is the initial number of atoms present

λ is the rate constant

t is the time

For the number of 15 8 O nuclei in a given sample to decrease to a factor of 8 × 10⁻⁴ of the initial value, the number of half-lives decay took place be n which is given by,

2⁻ⁿ = 8 × 10⁻⁴

Taking log on both sides we have,

- n ln 2 = ln(8 × 10⁻⁴)

n = 10.3

Time taken to complete 10.3 half lives is 10.3 × 122 s = 1257 s which is equal to for the number of 15 8 O nuclei in a given sample to decrease to a factor of 8 × 10⁻⁴ of the initial value.

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The rate at which the area of the illuminated circular region is increasing when the radius is 50m is 800π m²/s.


To find the rate at which the area of the illuminated circular region is increasing, we can use the formula for the rate of change of area with respect to time. This formula is given by dA/dt = 2πr(dr/dt), where A is the area, t is time, r is the radius, and dr/dt is the rate of change of the radius with respect to time.

Given that the radius is increasing at a rate of 4 m/s, we have dr/dt = 4. Substituting this value and the radius of 50m into the formula, we get dA/dt = 2π(50)(4) = 800π m²/s.

Therefore, when the radius is 50m, the area of the illuminated region is increasing at a rate of 800π m²/s. This means that the illuminated area is expanding rapidly as the helicopter continues to rise vertically.

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The predicate in the conditional statement checks whether the value of variable "a" is less than or equal to 1. However, it does not directly determine if "a" is of type double.

In this specific case, let's break down the code:

1. The expression `(2 + 1) / 2` is evaluated first. Since both 2 and 1 are integers, the division operation `/` results in a floating-point value, specifically 1.5.

2. The result of the expression is then assigned to variable "a" with the statement `a = (2 + 1) / 2`. The value of "a" becomes 1.5.

3. The conditional statement `if (a <= 1)` is evaluated. The comparison `1.5 <= 1` is false because 1.5 is greater than 1.

Therefore, the predicate result for the variable "a" to be a double primitive type in this case is false.

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Answer:

y= 3x - 4

Step-by-step explanation:

hope this helps.