please help I don't undestand

To calculate the number of MADs that the means are apart, we need to find the difference between the two means and then divide that by the MAD.

The difference between the means is 20 - 16 = 4.

Dividing that by the MAD of 2.5, we get:

4 / 2.5 = 1.6

Therefore, the means are 1.6 MADs apart.

1. Find the difference between the two mean ages: 20 years (mean age of second sample) - 16 years (mean age of first sample) = 4 years.

2. Divide the difference by the MAD: 4 years (difference between means) / 2.5 (MAD) = 1.6.

So, the means are 1.6 MADs apart.

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To find the eigenvalues and eigenvectors of a 2x2 matrix, follow these steps:

Calculate the characteristic equation by subtracting the identity matrix I multiplied by the scalar λ from matrix A, and set the determinant of this resulting matrix equal to zero. The characteristic equation is given by det(A - λI) = 0.Solve the characteristic equation to find the eigenvalues (λ).

Let's assume we have a 2x2 matrix A:

  | a  b |

A = | c d |

To find the eigenvalues, we need to calculate the characteristic equation:

det(A - λI) = 0,

where I is the 2x2 identity matrix and λ is the eigenvalue.

A - λI = | a-λ b |

| c d-λ |

The determinant of this matrix is:

(a-λ)(d-λ) - bc = 0,

which simplifies to:

λ² - (a+d)λ + (ad - bc) = 0.

This quadratic equation gives us the eigenvalues.

Solve the quadratic equation to find the values of λ. The solutions will be the eigenvalues.

Once you have the eigenvalues, substitute each value back into the equation (A - λI)v = 0 and solve for v to find the corresponding eigenvectors.

For each eigenvalue, set up the homogeneous system of equations:

(A - λI)v = 0,

where v is the eigenvector.

Solve this system of equations to find the eigenvectors corresponding to each eigenvalue.

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow the steps mentioned above. The characteristic equation gives the eigenvalues, and by solving the corresponding homogeneous system of equations, you can determine the eigenvectors.

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The system is consistent because there is at least one solution.

Your thought process is correct. A system of equations in the form of a11x1 + a12x2 = 0 and a21x1 + a22x2 = 0 must be consistent because both equations must equal 0. This means that the variables will force the rest of the equation to equal 0, and at least one variable, if not both, must be 0.

To further explain, a consistent system of equations is one in which there is at least one solution. In this case, the solution is when both equations equal 0. This can be achieved by setting one or both of the variables to 0. For example, if x1 = 0, then the equations become a12x2 = 0 and a22x2 = 0. Both equations can be solved for x2, and the solution will be x2 = 0. Similarly, if x2 = 0, then the equations become a11x1 = 0 and a21x1 = 0, and the solution will be x1 = 0. Therefore, the system is consistent because there is at least one solution.

In conclusion, a system of equations in the form of a11x1 + a12x2 = 0 and a21x1 + a22x2 = 0 is consistent because at least one variable, if not both, must be 0 in order for both equations to equal 0. This means that there is at least one solution, making the system consistent.

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The plane's angle of elevation at takeoff can be determined by calculating the inverse tangent of the ratio of the change in altitude to the horizontal distance traveled.

To find the angle of elevation at takeoff, we can use the trigonometric function inverse tangent (arctan). The ratio of the change in altitude to the horizontal distance traveled can be represented as the tangent of the angle of elevation. In this case, the plane ascends for a distance of 3,192 feet and is currently flying at an altitude of 1,078 feet. To calculate the angle of elevation, we divide the change in altitude by the horizontal distance traveled: 1,078 feet / 3,192 feet.

Next, we find the inverse tangent (arctan) of this ratio to determine the angle of elevation: arctan(1,078 / 3,192). Using a calculator or trigonometric table, we can find that the approximate angle of elevation at takeoff is approximately 19.77 degrees. Therefore, the plane's angle of elevation at takeoff is approximately 19.77 degrees. This means that the angle between the horizontal ground and the line of sight from the plane to the observer's eye is approximately 19.77 degrees.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

-7 + 47=40

Answer:

-7 + n = 40

Step-by-step explanation:

The angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

The given values are:

AD = 150 mm

AB = 40 mm

CD = 80 mm

The crank AB rotates at 120 r.p.m. clockwise.

BC and AD are of equal length.

To find:

The angular velocity of link CD when angle BAD = 60°.

From the given data, we have to first find the value of angle BCD.

Angle BCD can be calculated as follows:

AB = 40 mm

BC = AD

= 150 mm

In ΔABC,

By using Cosine rule;

AC² = AB² + BC² - 2 × AB × BC × Cos ∠ABC∴ AC² = (40)² + (150)² - 2 × 40 × 150 × Cos 180°

∴ AC = 160.6 mm

In ΔBCD,

By using Cosine rule;

BD² = BC² + CD² - 2 × BC × CD × Cos ∠BCD

∴ BD² = (150)² + (80)² - 2 × 150 × 80 × Cos ∠BCD

In ΔABD,By using Cosine rule;

BD² = AB² + AD² - 2 × AB × AD × Cos ∠BAD

∴ BD² = (40)² + (150)² - 2 × 40 × 150 × Cos 60°

∴ BD = 184.06 mm

In ΔABD,By using Sine rule;

AB / Sin ∠BAD = BD / Sin ∠ABD

∴ Sin ∠ABD = BD × Sin ∠BAD / AB

∴ ∠ABD = Sin⁻¹ [BD × Sin ∠BAD / AB]

∴ ∠ABD = Sin⁻¹ [184.06 × Sin 60° / 40]

∴ ∠ABD = 87.2°∠ACD = ∠ABD - ∠ACB

∴ ∠ACD = 87.2° - 180°

∴ ∠ACD = - 92.8°∠BCD

= 180° - ∠ACD

∴ ∠BCD = 180° - (- 92.8°)

∴ ∠BCD = 272.8°

As we know that for four-bar mechanism, we have a formula for finding the angular velocity of link CD.

ωCD / Sin ∠BCD = ωAB / Sin ∠BADωCD / Sin 272.8°

= ωAB / Sin 60°

Substituting the values, ωCD / Sin 272.8° = ωAB / Sin 60°ωCD

= ωAB × Sin 272.8° / Sin 60°

But, ωAB = 2 × π × N / 60

= 2 × π × 120 / 60

= 4 × π rad/s

∴ ωCD = 4 × π × Sin 272.8° / Sin 60°ωCD

= 21.16 rad/s

Therefore, the angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

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The inequality that represents the situation is:

\(3q + 3 > 51\)

The first assignment had at least 17 questions.

The total number of questions is:

\(T = q + q + 1 + q + 2 = 3q + 3\)

Since the total is greater than 51, the inequality is:

\(3q + 3 > 51\)

Solving the inequality, we have that:

\(3q > 48\)

\(q > \frac{48}{3}\)

\(q > 16\)

Thus, it is found that the first assignment had at least 17 questions.

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Answer:

9674.28 miles

Step-by-step explanation:

From the above question, we are given:

Central angle = 140°

Radius = 3960 miles

We are to solve for the distance = Arc length

The formula for Arc length when your central angle is in radians

r × θ

θ = 140°

Converting 140° to radians

140° × π/180 = 2.443rad

Hence,

3960 × 2.443 rad

= 9674.28 miles

The ship would travel 9674.28 miles.

Answer:

\(n=5\)

Step-by-step explanation:

Given the following question:

\(0=n-5\)

To find the answer we simply add five on both sides because this is a one-step equation.

\(0=n-5\)
\(-5+5=0\)
\(0+5=5\)
\(5=n\)
\(n=5\)

Which means your answer is "n = 5."

Hope this helps.

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Answer: {x=8 , y=0}

Step-by-step explanation:

According to the graph, the x-intercept is eight. Since that is the intercept, the number of candies remaining is zero.

Therefore, the intercept graph would be 8 and 0, which can be written like this:

{x=8 , y=0}

To evaluate the integral ∫√5+x/5-x dx, we first need to simplify the integrand. We can do this by multiplying the numerator and denominator of the fraction by the conjugate of the denominator, which is 5+x. This gives us:

∫√(5+x)(5+x)/(5-x)(5+x) dx

Simplifying further, we get:

∫(5+x)/(√(5-x)(5+x)) dx

We can now make a substitution by letting u = 5-x. This gives us du = -dx, and we can substitute these values into the integral to get:

-∫(4-u)/(√u(9-u)) du

To simplify this expression, we can use partial fraction decomposition to break it up into simpler integrals. We can write:

(4-u)/(√u(9-u)) = A/√u + B/√(9-u)

Multiplying both sides by √u(9-u), we get:

4-u = A√(9-u) + B√u

Squaring both sides and simplifying, we get:

16 - 8u + u^2 = 9A^2 - 18AB + 9B^2

From this equation, we can solve for A and B to get:

A = -B/3
B = 2√2/3

Substituting these values back into the partial fraction decomposition, we get:

(4-u)/(√u(9-u)) = -√(9-u)/3√u + 2√2/3√(9-u)

We can now substitute this expression back into the integral to get:

-∫(-√(9-x)/3√x + 2√2/3√(9-x)) dx

This integral can be evaluated using standard integral formulas, and we get:

(2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C

where C is the constant of integration.

In summary, to evaluate the integral ∫√5+x/5-x dx, we simplified the integrand by multiplying the numerator and denominator by the conjugate of the denominator, made a substitution to simplify the expression further, used partial fraction decomposition to break it up into simpler integrals, and evaluated the integral using standard integral formulas. The final answer is (2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C.

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Answer:

Let's solve your equation step-by-step.

4x−(8−x)−2=9x−20+x−5

Step 1: Simplify both sides of the equation.

4x−(8−x)−2=9x−20+x−5

4x+−8+x+−2=9x+−20+x+−5

(4x+x)+(−8+−2)=(9x+x)+(−20+−5)(Combine Like Terms)

5x+−10=10x+−25

5x−10=10x−25

Step 2: Subtract 10x from both sides.

5x−10−10x=10x−25−10x

−5x−10=−25

Step 3: Add 10 to both sides.

−5x−10+10=−25+10

−5x=−15

Step 4: Divide both sides by -5.

Answer:

x=3

    hope this helps (>'-'<)

The equation in terms of x, for the total time he takes in hours would be 2.48 = 12/x  + 26/10x

Speed can be calculated as the ratio of distance traveled to the time taken

Darpan runs a distance of 12 km and then cycles a distance of 26 km.

Total distance = 12 + 26 = 38km

The running speed is x km/h

A = x

The cycling speed is 10 km/h faster than his running speed

B = 10x

He takes a total time of 2 hours and 48 minutes.

So, the total time he takes

Time = Distance x speed

2.48 = 12/x  + 26/10x

10x(2.48) = 120 + 26

24.8x = 146

x = 5.8

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Out of the given differential equations, only equation 3 is separable, and equation 4 is linear. The rest are nonlinear and neither separable nor linear.

The first-order differential equation dy/dx + exy = x2y2 is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term x2y2 in the equation makes it nonlinear, and the term exy makes it non-separable.

The differential equation y + ex * sin(x) = x3y' is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term ex * sin(x) and the term y' (derivative of y) make it nonlinear, and the term y makes it non-separable.

The differential equation ln(x) - x2y = xy' is separable but not linear. The terms ln(x) and x2y make it nonlinear, but it can be separated into two parts, one containing x and y and the other containing x and y'. Therefore, it is separable.

The differential equation dy/dx + cos(y) = tan(x) is linear but not separable. The terms cos(y) and tan(x) make it nonlinear, but it can be written in the form dy/dx + P(x)y = Q(x), where P(x) = cos(y) and Q(x) = tan(x). Therefore, it is a linear differential equation.

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Complete Question:

Aisha reduced the size of her square driveway. she made one side 10 feet shorter and the other side 15 feet shorter. the smaller rectangular driveway will have an area of no more than 800 square feet. write an inequality to represent the area of the smaller driveway.

Answer:

The inequality that represents the area of the smaller drive way is \(x(x-25) \leq 650\)

Step-by-step explanation:

Let the original length of the sides of Aisha's square driveway be = x

She made one side 10 ft short, i.e. (x - 10) ft

She made the other side 15 ft short, i.e. (x - 15) ft

Since the sides are no longer equal, the driveway is now a rectangle

The question states that the smaller rectangular driveway will have an area of no more than 800 square feet

Area of a rectangle = length * Breadth

Area = (x - 10)*(x - 15)

\(Area = x^{2} - 15x - 10x + 150\\Area = x^{2} - 25x + 150\)

Area ≤ 800

\(x^{2} - 25x + 150 \leq 800\\ x^{2} - 25x - 650\leq 0\\x(x-25) \leq 650\)

Solving the above, x = 40.9 or -15.9

Since the length of a square cannot be negative, x = 40.9 ft

Answer:

(x-10)·(x-15)≤800

Step-by-step explanation:

imagine math

19/3

19/3 ..since 3 isnt a factor of 19..it cant be split further

Answer:

The answer is 6 with a remainder of 2.

Step-by-step explanation:

3 times 6 is 18.

Then if you subtract 18 from 20 you get 2.

So 3 goes into twenty, 6 times, and you get a remainder of 2.

When drawing 3 cards from a standard deck without replacement, there is approximately a 16.60% chance of drawing at least one 3 card.

The probability of drawing at least one 3 card from a standard deck of 52 cards without replacement can be calculated using the concept of complementary probability.

We can find the probability of not drawing any 3 cards and subtract it from 1 to get the probability of drawing at least one 3 card.

To find the probability of not drawing any 3 cards, we first determine the number of ways to choose 3 cards from the 52-card deck without replacement, which is denoted as C(52, 3) or "52 choose 3." This can be calculated as:

C(52, 3) = 52! / (3! * (52-3)!) = 22,100.

Now, let's determine the number of ways to choose 3 cards from the 49 non-3 cards in the deck, which is denoted as C(49, 3) or "49 choose 3." This can be calculated as:

C(49, 3) = 49! / (3! * (49-3)!) = 18,424.

Therefore, the probability of not drawing any 3 cards is given by:

P(not drawing any 3 cards) = C(49, 3) / C(52, 3) = 18,424 / 22,100 = 0.8340 (rounded to four decimal places).

Since we want the probability of drawing at least one 3 card, we can subtract the probability of not drawing any 3 cards from 1:

P(at least one 3 card) = 1 - P(not drawing any 3 cards) = 1 - 0.8340 = 0.1660 (rounded to four decimal places).

Therefore, the probability that at least one of the cards drawn is a 3 is approximately 0.1660 or 16.60%.

To summarize, when drawing 3 cards from a standard deck without replacement, there is approximately a 16.60% chance of drawing at least one 3 card.

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Answer:

4  1/4

Step-by-step explanation:

10 1/3 = 33/3      33/3  divided by 4 = 33/12      so one quarter of your tank can hold 33/12

now just do 33/12 times 3 which is 33/4 or simplified 4  1/4

The correct interpretation of the 95% confidence interval of (-0.056, 0.072) is that we are 95% confident that the difference in the population proportion in 2014 that had a hard time deciding to work overtime is between 0.056 less to 0.072 more than in 2018.

A confidence interval is a range of values that is used to estimate an unknown population parameter with a certain level of confidence.  In this case, the population parameter of interest is the difference in the population proportion in 2014 and 2018 who said that choosing to work overtime is hard. The 95% confidence interval of (-0.056, 0.072) means that if we were to take multiple samples and construct a confidence interval for each sample, then 95% of these intervals would contain the true difference in population proportions. In other words, if we repeated the sampling process many times, we would expect that 95% of the intervals would capture the true difference in population proportions, and 5% of the intervals would not. The confidence interval provides a range of values that is likely to contain the true population difference with a certain level of confidence. The lower and upper bounds of the interval, -0.056 and 0.072 respectively, represent the range of values within which the true difference in population proportions is estimated to lie with a confidence level of 95%.

Therefore, the correct interpretation of the 95% confidence interval of (-0.056, 0.072) is that we are 95% confident that the difference in the population proportion in 2014 that had a hard time deciding to work overtime is between 0.056 less to 0.072 more than in 2018.

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Answer:

angle k = 82°

Step-by-step explanation:

360 - (70 + 118 + 90)

360 - 278 = 82

angle m = 90

angle j = 118 vertical angles are congruent

angle l = 70  Supplemental angles add to 180 (180 - 110)

The cost function that represents the situation is given as C(x) = a + bx.

Given, x represents the number of products sold. To represent the cost function of the situation, we can use the formula,

C(x) = a + bx

where

a is the fixed cost of the product and

b is the variable cost of the product.

x represents the number of products sold.

Here, we are supposed to represent the cost function that represents the situation. However, the values of a and b are not given. Therefore, we can represent the cost function in a general form using a and b as constants.

C(x) = a + bx

Hence, the cost function that represents the situation is given as C(x) = a + bx.

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Answer:

No solution

Step-by-step explanation:

To solve this, we subtract 7x from both sides to get 2=-3. Since 2 does not equal to negative 3, there is no solution.

The term you are looking for is the "z-value." The z-value for a point is the number of standard errors a point is away from the mean.

The z-value for a point is the number of standard errors a point is away from the mean. This is a long answer but it accurately explains the concept.

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The arc length along a circle of radius 8 units subtended by an angle of 19z/12 radians is approximately 12.7 units.

To find the arc length we can use the formula,
Arc Length = radius x angle in radians.
Plugging in the values we have:

Arc Length = 8 x 19z/12

Arc length = (8 × 19z) / 12 = 38z/3

Now, simplify the expression and round to the nearest tenth:

Arc length ≈ (152z) / 12

Arc Length ≈ 12.7

Therefore, approximately 12.7 units is  the arc length along a circle of radius 8 units subtended by an angle of 19z/12 radians .

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Answer:

number 3 or 6 ^w^

your welcome for the help