A museum surveyed three groups of 5 members to find out how many times the members visited the museum in the past year. This table shows the results of the three samples. Survey Visits to the Museum Group 1 {4, 10, 6, 3, 8} Group 2 {3, 1, 2, 1, 2} Group 3 {7, 9, 3, 4, 7} Identify any surveys that are likely biased. Based on the unbiased surveys, estimate the mean number of visits per member in the past year. Enter your answer in the box. Round to the nearest whole number. Visits.

The probability that a randomly chosen part is defective is 0.16, or 16%.

The probability that a randomly chosen part is defective, we need to use the law of total probability.

Let \($D$\) be the event that a part is defective and let \($M_i$\) be the event that the part came from machine \($i$\), for \($i = A, B, C$\).

Then we have:

\($P(D) = P(D|M_A)P(M_A) + P(D|M_B)P(M_B) + P(D|M_C)P(M_C)$\)

60% of the products come from machine A, 30% from machine B, and 10% from machine C.

Therefore:

\($P(M_A) = 0.6$\)

\($P(M_B) = 0.3$\)

\($P(M_C) = 0.1$\)

The probability of a part being defective is 10% if it comes from machine A, 30% if it comes from machine B, and 40% if it comes from machine C.

Therefore:

\($P(D|M_A) = 0.1$\)

\($P(D|M_B) = 0.3$\)

\($P(D|M_C) = 0.4$\)

Substituting these values into the law of total probability, we get:

\($P(D) = 0.1 \cdot 0.6 + 0.3 \cdot 0.3 + 0.4 \cdot 0.1 = 0.16$\)

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Answer:

a. Morgan's current average is (84+76)/2=80.

b. To maintain her current letter grade, Morgan needs to score at least a 76 on the final exam.

c. To move up a letter grade, Morgan needs to score at least a 92 on the final exam.

d. It is not possible for Morgan to fail the course. Even if she scores a 0 on the final exam, her overall grade will still be a 68, which is a passing grade.

Here is the work to support my answer:

Answer:

The correct answer is

x= 4

y=-3

Answer:

  (x, y) = (4, -3)

Step-by-step explanation:

You want to solve this system of equations using substitution.

The substitution method requires that you find an expression for one of the variables that you can use to replace that variable in the other equation.

Here, we choose to use the second equation to write an expression for y. This makes the resulting coefficients be decimal values.

  5y = 9 -6x . . . . subtract 6x

  y = 1.8 -1.2x . . . . divide by 5

Substituting this for y in the first equation gives ...

  4x -3(1.8 -1.2x) = 25

  7.6x -5.4 = 25 . . . . . . . simplify

  7.6x = 30.4 . . . . . . . . add 5.4

  x = 4 . . . . . . . . . . divide by 7.6

  y = 1.8 -1.2(4) = 1.8 -4.8

  y = -3

The solution is (x, y) = (4, -3).

__

Additional comment

We could have used the first equation to write an expression for x. That would also make the coefficients be terminating decimal values. Using the first equation to write an expression for y leaves coefficients that are multiples of 1/3, not nice decimals. Similarly, solving the second equation for x would result in coefficients that are multiples of 1/6, also not nice decimals.

These "not nice" values can be used to get the same result. It just depends on what kind of arithmetic you want to do: fractions or decimals.

This set of coefficients would generally indicate that some other method would be more desirable to use: graphing, or matrix methods, for example. The attachment shows a matrix method.

Answer:

40% = 0.40

800 / 0.40 = 2000 total tickets were sold

Step-by-step explanation:

Answer:

x=15/19

Step-by-step explanation:

You have to start by multiplying the denominators by the numerators. I doesn't matter which you do first, as you can see, I chose to multiply the 6 by the 4x first.

Once that is completed, it is a simple matter of rearranging the equation so it begins with x=...

To do this, just subtract 5x and then divide by 19 on both sides to get the final fraction.

I have attached a photograph of my workings.

Yes.

You can add them together to get 13x.

because you can add them together, they are alike terms.

Ordering the numbers,

28,31,31,35,37

the median is the middlemost number, which is 31

Since girls and boys have equal probability, iin a family with four children, they have probability equal to

so, the probability of having 3 boys and 1 girls is

that is, the answer is 3/16 which is equal to 0.19.

The exact measurements for the largest side is 12√10 inches. Hence option a is the correct option.

What is the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Given that the angles of a triangle are 30-60-90.

The smallest angle is always opposite the shortest side, and vice versa. The longest side is also opposite the largest angle, and vice versa.

The opposite side of angle 30 is the shortest side of the triangle.

The opposite side of angle 90 is the longest side of the triangle.

Sine law:

a/sin A = b/ sin B =c/sin C

a is the opposite side of angle A, b is the opposite side of angle B, c is the opposite side of angle C.

Assume that the length of the longest side is a.

Applying sine law in the given triangle:

6√10/sin 30 = a/sin 90

6√10/(1/2)= a/1

a = 12√10

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Answer:

B

Step-by-step explanation:

8 weeks, 2 sessions per week =16 sessions

45mins each = 16*45=720 mins = 12 hours

52 /12 =4.33 / hour

B: $4.33/hour is the closest to the charge per hour for the courses. Hence, the correct option is (B)

The total charge for the 8-week course is $52, which means each 45-minute session costs $52 / (2 sessions/week * 8 weeks) = $1.67.

To convert this to an hourly rate, we divide by 45 minutes to get an hourly rate of $1.67 / (45 minutes/hour) = $3.93/hour.

Therefore, the answer closest to this is $4.00/hour, which is not one of the options, but we can see that $3.93/hour is closest to option B: $4.33/hour.

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The denominator has a single first-order term the closed-loop system has a single pole at:

s = -G(s) × (Kp + Kd × s) / Ki

The transfer function from the reference input θr to the Hapkit output θ for a closed-loop system with a unity gain negative feedback and a PID controller can be derived as follows:

Let's denote the transfer function of the plant (Hapkit) by G(s) the transfer function of the PID controller by C(s) and the transfer function of the feedback path by H(s).

The closed-loop transfer function T(s) is given by:

T(s) = θ(s) / θr(s)

= G(s) × C(s) / [1 + G(s) × C(s) × H(s)]

Since the feedback path has unity gain we have H(s) = 1.

Also, the transfer function of a PID controller with proportional gain Kp, integral gain Ki and derivative gain Kd is:

C(s) = Kp + Ki/s + Kd × s

Substituting these into the expression for T(s), we get:

T(s) = θ(s) / θr(s)

= G(s) × [Kp + Ki/s + Kds] / [1 + G(s) × [Kp + Ki/s + Kds]]

Multiplying both the numerator and denominator by s, and simplifying, we get:

T(s) = θ(s) / θr(s)

= G(s) × Kps / [s + G(s) × (Kp + Ki/s + Kds)]

This is the transfer function from the reference input θr to the Hapkit output θ for the closed-loop system.

The closed-loop system has as many poles as the order of the denominator of the transfer function T(s).

Since the denominator has a single first-order term the closed-loop system has a single pole at:

s = -G(s) × (Kp + Kd × s) / Ki

The pole may change as a function of the frequency s due to the frequency dependence of G(s).

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Answer:

B

Step-by-step explanation:

The Domain is the X- value so that makes it the domain and you have to order it correctly

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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Answer: 80 degrees because a line is 180°.

So if you subtract

180 - 100 = 80°

Answer:

x=80°

Step-by-step explanation:

The measures of angle x and the 100° angle form a straight angle.

This straight angle is 180°.

You can subtract the measure of one angle from the whole to find the measure of the other angle.

180°-100°=80°

This means angle x is 80°.

Answer:

5:3....added = 8

5/8(144) = 720/8 = 90 adults

3/8(144) = 432/8 = 54 children

Answer:see below

Step-by-step explanation:

10.600

11.80000

12.17

13.48

14.4000

21. 1km=100m;0.5km=500m;0.1km=100m

22.50m=5000cm; 5m=500cm; 0.5m=50cm

Answer:

6. From speed vs. time graphs, we know that in order to find the distance, we need to look at the area covered. Given the rectangular shape below, we know that it would be A=lw so A=60mph(2.5h).

7. A=60mph(2.5h)= 150 miles.

Answer:

\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)

There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

Now,

Substituting values,

We get,

\(^5N_5 = \frac{5!}{(5-5)!}\)

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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Answer:

yes!

Step-by-step explanation:

hi, that is correct. 3800 is a constant, meaning it is consistent and the initial height of the plane before it starts its descent.

\(\\ \sf\dashrightarrow 4(x-1)+1=6x-2(4+x)\)

\(\\ \sf\dashrightarrow 4x-4+1=6x-8-2x\)

\(\\ \sf\dashrightarrow 4x-3=4x-8\)

\(\\ \sf\dashrightarrow 4x-4x=-8+3\)

\(\\ \sf\dashrightarrow 0=-5\)

Answer:

Formula used : (a^m)^n = a^(m×n)

\( →{( {d}^{ \frac{1}{8} }) }^{5} = {d}^{( \frac{1}{8}\times 5) } = \boxed{{d}^{ \frac{5}{8} } }✓ \\ \)

The value of 'x' is highlighted in the box

The balloon is receding from the observer at a rate of approximately 56.47 ft/s, which is closest to answer choice C. 23 ft/s.

We can use the Pythagorean theorem to find the distance between the observer and the balloon after 10 seconds.

The distance the balloon has traveled vertically is 15 ft/s x 10 s = 150 ft.

Using the Pythagorean theorem:

\(distance = sqrt((80 ft)^2 + (150 ft)^2) = 170 ft\)

To find the rate at which the balloon is receding from the observer, we can differentiate this distance with respect to time:

\(d(distance)/dt = (80 ft)/sqrt((80 ft)^2 + (150 ft)^2) x d/dt(sqrt((80 ft)^2 + (150 ft)^2)) + (150 ft)/sqrt((80 ft)^2 + (150 ft)^2) x d/dt(150 ft)\)

\(d(distance)/dt = (80 ft)/170 ft x (1/2) x (2 x 80 ft x 0 ft/s + 2 x 150 ft x 15 ft/s)/(sqrt((80 ft)^2 + (150 ft)^2)) + (150 ft)/170 ft x 15 ft/s\)

\(d(distance)/dt = (9600 ft^2/s)/(170 ft) + (2250 ft^2/s)/(170 ft)\)

\(d(distance)/dt = 56.47 ft/s\)

Therefore, The balloon is receding from the observer at a rate of approximately 56.47 ft/s, which is closest to answer choice C. 23 ft/s.

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Answer:

Step-by-step explanation:

2x4=8

4+4=8

Or

2+2+2+2=8

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

slope = 2/7

y-intercept = -16/7

Step-by-step explanation:

We rewrite this equation in slope-intercept form as follows:

\( - 2x + 7y = - 16\)

\(7y = 2x - 16\)

\(y = \frac{2}{7} x - \frac{16}{7} \)

The slope is 2/7, and the y-intercept is -16/7.