An engineer is designing a machine to manufacture gloves and she obtains the following sample of hand lengths (mm) of randomly selected adult males based on data gathered: 173 179 207 158 196 195 214 199 Define this data set as discrete or continuous. The hand lengths is what type of level of measurement? Compare the mean and median for this data set and if you can draw any conclusions from these values.

The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Python will return:

True

Step-by-step explanation:

The math function ** is an exponent indicator.

The equation you made was:
\(2^2 =4\)

When you run this in python, it will return as true.

It is run as a Boolean expression because you have already provided the answer to the expression with the "==" statement.

If you had provided an incorrect answer (setting it equal to any number other than 4), it would return False.

It will take approximately 27.7 minutes for the coffee to cool from 54.8°C to 44.9°C when following exponential decay model.

A quantity declines over time proportionate to its existing value through a process known as exponential decay. An exponential function of the form f(t) = ab raised to t, where an is the beginning value, b is the decay factor (a number between 0 and 1), and t represents time, mathematically describes this.

Several real-world circumstances, like population increase, radioactive decay, and the loss of electrical charge in a capacitor, exhibit exponential decay.

Given that the situation follows a exponential decay model.

The exponential decay is given as:

\(T(t) = T0 * e^{(-rt)}\)

Substituting the values T0 = 54.8, r = 0.02, and T(t) = 44.9.

\(44.9 = 54.8 * e^{(-0.02t)}\\0..8208 = e^{(-0.02t)}\\ln(0.8208) = -0.02t\\t = ln(0.8208)/(-0.02) = 27.7 minutes\)

Hence, it will take approximately 27.7 minutes for the coffee to cool from 54.8°C to 44.9°C.

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Step-by-step explanation:

You have selected the correct option

Answer:

.............................

Answer:

1. 80

2. 40

3. 96

4. 160

5. 250 percent of daily recommended vitamin C

Step-by-step explanation:

The mass of the aluminum can be calculated using the change in volume and the density. the mass of the aluminum is approximately 9.415 grams.

The change in volume when the aluminum is added to the graduated cylinder is equal to the volume of the aluminum. The change in volume is obtained by subtracting the initial volume (10.0 mL) from the final volume (13.5 mL), resulting in 3.5 mL.

Since the density of aluminum is given as 2.69 g/mL, we can use this information to calculate the mass of the aluminum. The density of a substance is defined as the mass per unit volume. Therefore, we can multiply the density by the volume to obtain the mass.

Using the given density of 2.69 g/mL and the volume of 3.5 mL, the mass of the aluminum can be calculated as follows:

Mass = Density x Volume = 2.69 g/mL x 3.5 mL = 9.415 g

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Answer:

5 hours and 15 minutes.

Step-by-step explanation:

7:30 - 8:00 is 30 minutes

8:00 - 12:00 is 4 hours

12:00 - 12:45 is 45 minutes

30 minutes plus 45 minutes is 1 hours and 15 minutes

4hours + 1 hour and 15 minutes is

5 hours and 15 minutes

or

5 1/4 hours

or

315 minutes.

I am not sure what form you want.

Answer:

It is 1  4/7

Step-by-step explanation:

The result of the expression is 60.

The given expression can be solved by applying the principle of BODMAS.

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression.

This indicates that numerous operator expressions must only be spelled out in this order, from left to right. We begin by resolving the brackets, then move on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).

Given, 50+20/10*5 = 50+2*5=50+10=60

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Answer:

x=60° , y=30° , z= 75°

Step-by-step explanation:

note...an equilateral triangle has the same angles all equal to 60°. so based on this x is 60°

the angle next to y is on a straight line therefore

60 +y =90

y=90-60

y=30°

the triangle with the y and z angles is an isosceles triangle...so the base angles must be equal

z+z+30=180

2z+30=180

2z=180-30

2z=150

\( \frac{2z}{2} = \frac{150}{2} \)

z=75°

The Answer is 95 miles using distance rule of maths.

What is distance in math?

As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

So if we mark their position in x-y plane. one is not x line and another one is in y line.

So the coordinates of the points are (57,0) and (0,76)

The distance between them is √(y²+x²)

= √(57²+76²)

=√ (3249 + 5776)

= 95 miles

Hence the distance between them is 95 miles.

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Answer:

Step-by-step explanation:

The answer for this is A, C, E

1. Its A because in the question its asking y=5 and is translated doe

2. This should be easy all of them are positive, if you read the question carefully and you pay attention. the same thing for E.

The correct statements of the given ones are -

Translation of image on a graph is the process of movement of graph over the coordinate plane. It can be either horizontally or vertically.

Given is that △ABC has coordinates A(2, 3), B(5, 1), C(4, 4), and △ABC is mapped to △A′B′C′ by a reflection across the line y = 5 followed by a translation 1 unit down.

The correct statements of the given ones are -

Therefore, the correct statements of the given ones are -

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Answer:

~101.5 (area of the shaded area in upper figure)

and

~54.4 (area of the shaded area in lower figure)

Step-by-step explanation:

I attached an image for clarification (please see).

The same approach can be applied to solve these two problems.

As seen in attached image, the shaded area of the 1st figure is the sum of the area of a regular triangle and 3 equal portions.

The area of the regular triangle with side = 12 is:

A1 = side^2 x sqrt(3)/4 = 12^2 x sqrt(3)/4 = 36sqrt(3)

The area of the regular triangle + the area of a portion is:

A2 = pi x radius^2 x (pi/3)/(2pi) = pi x 12^2 x (1/6) = 24pi

=> The area of a porition is:

A3 = A2 - A1 = 24pi - 36sqrt(3)

=> Area of the shade area:

A4 = A1 + 3 x A3 = 36sqrt(3) + 3 x (24pi - 36sqrt(3)) =  ~101.5

**************************

For the second figure, the shaded area could be divided into 6 equal parts, each part is inside a regular triangle and is calculated by:

A = the area of the regular triangle - the area of 2 equal portions (white color).

The area of the regular triangle with side = 6 is:

A1 = side^2 x sqrt(3)/4 = 6^2 x sqrt(3)/4 = 9sqrt(3)

The area of the regular triangle + the area of a portion is:

A2 = pi x radius^2 x (pi/3)/(2pi) = pi x 6^2 x (1/6) = 6pi

=> The area of a porition is:

A3 = A2 - A1 = 6pi - 9sqrt(3)

=> Area of a part (including the regular triangle and excluding 2 equal portions):

A4 = A1 - 2 x A3 = 9sqrt(3) - 2 x (6pi - 9sqrt(3))

=> Area of shaded area:

A5 = 6 x A4 = 6 x [9sqrt(3) - 2 x (6pi - 9sqrt(3)) ] =~54.4

The length of side a is 10/3, and the length of the hypotenuse c is 2√(34)/3.

To find the length of side a, we can use the tangent of angle A. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, tan(A) = 5/12, which means that the length of side a is 5/12 times the length of the adjacent side. Since we know that side b is 2, we can calculate a = \((5/12) * 2 = 10/3\).

To find the length of the hypotenuse c, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we know that side b is 2 and side a is 10/3. Let's denote the length of c as x. Applying the Pythagorean theorem, we have \((10/3)^2 + 2^2 = x^2\). Simplifying this equation, we get \(100/9 + 4 = x^2\). Combining the terms, we have 100/9 + 36/9 = \(x^2\), which gives us \(136/9 = x^2\). Taking the square root of both sides, we have \(x = \sqrt{(136/9)} = \sqrt{(136)/} \sqrt{(9)} = \sqrt{(136)/3} = 2\sqrt{(34)/3}\).

Therefore, the lengths of the missing sides are a = 10/3 and c = \(2 \sqrt{(34)/3}\).

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For a 95% confidence level, the Z-value is 1.96.Hence, the sample size used for the analysis is 124.

Suppose a 95% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$46,872, $53,928]. The population standard deviation used for the analysis is known to be $12,600. Let us answer the given questions:

What is the point estimate of the mean salary of all college graduates in this town?

The midpoint of the confidence interval is the point estimate of the mean salary of all college graduates in this town. Therefore, the point estimate of the mean salary of all college graduates in this town is:

Point estimate = Midpoint of the confidence interval= [(Upper limit of the interval) + (Lower limit of the interval)] / 2= [($53,928) + ($46,872)] / 2= $50,400

Determine the sample size used for the analysis.

The sample size used for the analysis can be determined using the margin of error formula. The margin of error is half the width of the confidence interval.

ME = (Upper limit of the interval - Lower limit of the interval) / 2= ($53,928 - $46,872) / 2= $3,528

Sample size (n) is given by:

n = [(Z-value)² × σ²] / ME²

where Z-value is the Z-score corresponding to the confidence level, σ is the population standard deviation, and ME is the margin of error. For a 95% confidence level, the Z-value is 1.96. Therefore,Sample size (n) = [(1.96)² × ($12,600)²] / ($3,528)²= 123.48≈ 124

Hence, the sample size used for the analysis is 124.

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The total amount comes out to be approximately R9,875.38. This means that Pretty will pay an interest amount of approximately R2,543.38 over the three-year repayment period.

The total interest amount that Pretty will pay can be calculated using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Total amount to be repaid

P = Principal amount (original purchase price)

r = Annual interest rate (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

Given the information:

P = R7,332.00

r = 10.7% = 0.107 (in decimal form)

n = 12 (monthly compounding)

t = 3 years

Plugging in these values into the formula, we can calculate the total amount to be repaid:

A = 7332(1 + 0.107/12)^(12*3)

A ≈ 7332(1.00892)^(36)

A ≈ 7332(1.347003)

A ≈ R9,875.38

Therefore, the total interest amount that Pretty will pay is approximately R9,875.38.

To calculate the total interest amount, we use the compound interest formula. The principal amount is the original purchase price, which is R7,332.00. The annual interest rate is 10.7%, so we convert it to decimal form (0.107). The interest is compounded monthly, so the compounding frequency is 12 times per year. The repayment period is three years.

By plugging these values into the formula, we can calculate the total amount to be repaid, which includes both the principal amount and the interest. In this case, the total amount comes out to be approximately R9,875.38. This means that Pretty will pay an interest amount of approximately R2,543.38 over the three-year repayment period.

It's important to note that this calculation assumes equal monthly installments and that the interest is compounded monthly. The actual repayment schedule and the total amount may vary depending on the terms and conditions of the loan agreement.

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The probability that at least 200 out of 215 college graduates under age 25 are employed is 0.29

In this question we have been given  8% of college graduates, under the age of 25 are unemployed.

We need to find the probability that at least 200 out of 215 college graduates under age 25 are employed.

Here, n = 215

8% of college graduates, under the age of 25 are unemployed.

So, p = 0.08

For graduates under age 25 are employed,

Pr = 1 - 0.08

Pr = 0.92

We use Normal probability distribution

The expected value of the binomial distribution is:

E(x) = n * Pr

E(x) = 215 * 0.92

E(x) = 197.8

So, μ = E(x)

        = 197.8

An the standard deviation would be,

σ = √n * Pr * (1 - Pr)

σ = √(215 * 0.92 * 0.08)

σ = 3.98

An expression for the exact probability that at least  200 out of 215 college graduates under age 25 are employed.

P(x ≥ 200)

which is nothing but the pvalue of Z when x = 200

z = x - μ/σ

z = (200 - 197.8)/3.98

z = 0.55 has p value 0.29

Therefore, the required probability is 0.29

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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The value of a is given by the third root of the function.

The function for this problem is defined as follows:

f(x) = x(x - 2)(x - a).

According to the Factor Theorem, the function is defined as a product of it's linear factors, hence the roots of the function are given as follows:

Hence the value of a is the third root of the function, which is the value on the graph at which the function crosses the x-axis along with x = 0 and x = 2.

The problem is incomplete, hence the general procedure to obtain the value of a is presented.

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(a) A 600-gallon tank starts off containing 300 gallons of water and 40 lbs of salt. Thus, the volume V(t) of water in the tank at any time t is given by V(t) = 2 - 2(1/3) e^(-2t) or V(t) = 2/3 + (4/3)e^(-2t)

Water with a salt concentration of 2lb/gal is added to the tank at a rate of 4gal/min. At the same time, water is removed from the well-mixed tank at a rate of 2gal/min. Consider V(t) as the volume of water in the tank at any time t.The rate of change of volume of water is given by dV/dt = Rate of Inflow - Rate of Outflow . The rate of inflow is the volume of water added per minute, which is given by 4 gallons/min. The rate of outflow is the volume of water removed per minute, which is given by 2 gallons/min.

∴  dV/dt = 4 - 2V(t) is the differential equation for volume of water in the tank at any time t.

The initial condition is V (0) = 300 gallons. As dV/dt = 4 - 2V(t), dV / (4 - 2V(t)) = dt. Integrating both sides, ∫dV / (4 - 2V(t)) = ∫dt. On integrating, we get-1/2 * ln|4 - 2V(t)| = t + C where C is the constant of integration. Rewriting this,|4 - 2V(t)| = e^(-2t - 2C)Multiplying both sides by -1 and removing the modulus sign,4 - 2V(t) = ±e^(-2t - 2C)Solving this equation for V(t),V(t) = 2 - 2e^(-2t - 2C)The initial condition V(0) = 300 gives C = -ln(1/3).Thus, the volume V(t) of water in the tank at any time t is given by V(t) = 2 - 2(1/3) e^(-2t) or V(t) = 2/3 + (4/3) e^(-2t).

(b) Set up an initial value problem for Q(t), the amount of salt (in lbs.) in the tank at any time t. Solving the differential equation, we get Q(t) = 80 - 40e^(-3t)

Q(t) be the amount of salt (in lbs) in the tank at any time t. Let C(t) be the concentration of salt in the tank at any time t. The concentration of salt is defined as C(t) = Q(t) / V(t)The volume of water in the tank at any time t is given by V(t) = 2/3 + (4/3) e^(-2t). The initial volume is V (0) = 300.The amount of salt initially is Q (0) = 40. The rate of inflow of salt is 4 lbs/min. The rate of outflow of salt is given by Q(t)/V(t) * 2. The initial value problem for Q(t) is Q'(t) = 4 - 2Q(t) / (2/3 + (4/3)e^(-2t)) and Q(0) = 40.

(c) Yes, the function Q(t) makes sense for all positive t values. As t → ∞, the volume of the tank approaches 2/3 gallons.

Will the function Q(t) that you would solve for make sense for describing this physical tank for all positive t values? If so, determine the long-term behavior (as t → ∞) of this solution. If not, determine the t value when the connection between the equation and the tank breaks down, as well as what happens physically at this point in time. Yes, the function Q(t) makes sense for all positive t values. As t → ∞, the volume of the tank approaches 2/3 gallons.

As a result, the concentration of salt in the tank approaches 2 lb /gal. The rate of inflow of salt is 4 lbs/min. The rate of outflow of salt is Q(t) / V(t) * 2. Therefore, we can write the differential equation as Q'(t) = 4 - 2Q(t) / (2/3) and Q(0) = 40. Solving the differential equation, we get Q(t) = 80 - 40e^(-3t). Therefore, the long-term behavior of Q(t) is that it approaches 80 lbs. at t = ∞. The connection between the equation and the tank breaks down when the volume of the tank is 0 gallons. This occurs at t = ln(2/3) / 2 = 0.24 min. At this point, the concentration of salt in the tank is infinite, which is not physically possible.

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Answer:

10.

Step-by-step explanation:

median means the "middle" number in a set of numbers.

(I always the meaning of median by remembering "middle" because they rhyme).

NOTE: to find the median of a set of numbers you have to arrange that set of numbers in either ascending order (smallest to biggest value) or descending order (biggest to smallest value) .

sooo....

we were given :

11, 17, 7, 4, 15, 19

let's arrange in ascending order

4, 7, 11, 15, 17 , 19

now you can cancel them out ( cancel left number, right number)

i mean....

cancel out 4, cancel out 19

cancel out 7, cancel out 17

and we are left with 2 numbers which are11 and 15.

NOTE; (when you have two numbers or values remaining instead of one number, add those two numbers and divide by 2).

soooo...

11 + 15 = 20

20/2 = 10

median of the set of numbers is equal to 10.

Hope this helps.

Good luck ✅.

Answer:

87

Step-by-step explanation:

Here g is equalling -1, so substitute -1 for g in the equation. The equation is now 59 - 28(-1) = blank. Multiply 28 by -1 to get -28.

The equation is now 59 - (-28). There are two negatives in a row, so that becomes a plus sign. That makes it 59 + 28. Simply add to get 87 as your answer.

The shortest distance between airports A and B that can be covered by an airplane flying from airport A at a heading of 300 (N 60 W) is =  401 miles.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, is a trigonometric formula that simply establishes a relationship between the length of a triangle and the cosine of one of its angles. The length of the third side of a triangle can be calculated if we know the lengths of the first two sides and the angle between them.

An aircraft takes off from airport A with a heading of 300 (N 60 W). The aircraft changes its direction to 350 (N 10 W) after flying 320 miles, and after flying an additional 112 miles, it reaches airport B.

Below is an attachment with the problem's image. The two sides in this image are 112 miles and 320 miles apart, and the angle between them is 130 degrees. As a result, x has the value

So, by putting the values we get:

\(x=\sqrt{112^{2}+130^{2}-2(112)(130) \cos 130^{\circ}}\)

x = 401 miles.

Therefore, the shortest distance between airports A and B that can be covered by an airplane flying from airport A at a heading of 300 (N 60 W) is 401 miles.

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Answer:

  (b)  56.5 ft

Step-by-step explanation:

The circumference of a circle of diameter d is given by ...

  C = πd

For the given diameter, the circumference of the frame is ...

  C = (3.14)(18 ft) ≈ 56.52 ft

The length of the outside edge of the frame is about 56.5 feet.

Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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During the storming phase of group development, resistance may be aimed at a variety of targets, including: The group leader(s) or facilitator, The group norms or values, Other group members, The group's goals or tasks ,The group process or structure.

The group leader(s) or facilitator: Some group members may resist the authority or leadership of the group facilitator, or may feel that the facilitator is not meeting their needs or expectations.

The group norms or values: As the group begins to establish its norms and values, some members may resist or challenge these norms if they do not align with their own beliefs or values.

Other group members: In some cases, resistance may be aimed at other group members who are perceived as being difficult or uncooperative.

The group's goals or tasks: Group members may resist the goals or tasks set forth by the group if they feel that they are unrealistic, unimportant, or do not align with their personal goals or interests.

The group process or structure: Some members may resist the process or structure of the group, such as the way decisions are made or the frequency of meetings, if they feel that these elements are hindering the group's progress or effectiveness.

It's important to note that resistance during the storming phase is a natural part of group development, and can ultimately lead to greater cohesion and productivity as the group works through its differences and establishes a shared sense of purpose and direction.

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