Side panel MF Open course index Open block drawer Learnership Pre-Assessment and Evaluation v1 Figure Classification Assessment  QUIZ Figure Classification Assessment Back Time left 0:59:33 Question 1 Not yet answered Not graded Flag question Question text This test consists of several different items. Each item of the test appears in a separate question. The form of an item - item 25, say, is as follows:  You will notice that there are six boxes: 1 box in the first row 2 boxes in the second row, and 3 boxes in the third row In the top left-hand corner of each box, there is a letter labelling each box. For example, the letter ‚"A" labels the box in the first row. The number, which appears to the left of the box ‚"A" is the number of the item. In this example, it is item 25. Every item of the test will have this form, with each box containing a drawing of shapes or patterns. The following is an example of an item:  You must group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together.   In the example  - item 25 - drawings A, B and F belong together because they are shaded the same way, and drawing C, D and E belong together because their shadings are the same. Now turn to your answer sheet and look at it carefully.   At the top of the page is 2 rows of 6 boxes. The first row of the boxes refers to the item "Example (i)" and the second row of the boxes refer to the item "Example (ii)."   Below these two rows are 24 rows of 6 boxes. Each row refers to a particular item of the test. The number which appears to the left of each row of boxes refers to the item number in the test.   Each row of 6 boxes is divided into 2 groups of 3 boxes.    The first box of each row contains the letter "A".   In the following two empty boxes, you insert the letters of the two drawings which belongs to the same group as that to which drawing A belongs.   In the second group of 3 empty boxes you must insert the letters of the other 3 drawings which belong together. Here is another example of an item - item 26.  In this item, drawings A, D and E belong together because their outlines consist of single lines. Drawings B, C and F belong together because their outlines consist of double lines.   The answer to this practice item should be filled in as follows:  Please note the following:   1.       It is NOT correct to find a reason for grouping together 3 drawings of an item, and assume that the other 3 drawings belong together.   For example, when solving item 26 (Previous page), it would be incorrect to group together drawings A, E and F on the basis that each of these is a 4-sided figure, and drawings B, C and D on the basis that they do not have 4 sides.   You must be able to find something common to the 3 drawings of each group.   2.       A drawing may NOT belong to both groups. For example, the response-  would be incorrect since the drawing "D" is common to both groups.   Select one: a. Continue b. Ask for assistance Clear my choice Question 2 Not yet answered Not graded Flag question Question text You must now do two example items on your own. These examples are on the next two pages. Please fill in the answers to the two examples in the first two rows of the answer sheet. These two rows are labelled “Example (i)" and “Example (ii)". Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. Hint: Type the answer as one word e.g. ABC  Answeris the first group. Answeris the second group.​

Answer:

from 3 o’clock until 3:20, the minute hand will move 1/3 of the way around the circle or 120 degrees. But the hour hand has also moved 1/3 of the way to the next number, or 10 degrees.

Answer:

42deg

Step-by-step explanation:

Let's see.

We'll consider 12:00 the "starting position"

The minute hand moves with the speed of 360deg in an hour, so 6deg per minute.

The hour hand moves with the speed of 360deg in 12hours, so 30deg per hour, so 0.5deg per minute.

at 3:24, the minute hand has moved 24*6deg=144deg from the starting position, while the hour hand has moved by 3*30deg + 24*0.5deg = 102deg

The absolute difference of the angles is 144deg-102deg = 42deg and it's the angle between the hands.

Answer:

d

Step-by-step explanation:

The segment inside the triangle bisects the angle and divides the opposite sides into segments that are proportional to the other two sides, that is

\(\frac{x}{17}\) = \(\frac{37.5}{52.5-37.5}\) = \(\frac{37.5}{15}\) ( cross- multiply )

15x = 637.5 ( divide both sides by 15 )

x = 42.5 → d

Answer:

Step-by-step explanation:

A=100

Answer:

1:72

Step-by-step explanation:

The scale of a drawing is the ratio of the length in the drawing to the real length.

Drawing length: 7 inches

Real length: 42 ft × 12 in. / ft = 504 in.

Scale:

7 in. to 504 in.

Divide both numbers by 7:

1 in. to 72 in.

Scale: 1:72

The given line is tangent to the circle at the point (-2, 1).

Here we have the circle equation:

\(x^2 + y^2 = 5\)

Writing that as a function (actually two functions) we get:

\(x = \pm\sqrt{5 - y^2}\)

If we differentiate the part with positive sign, we get:

\(\frac{dx}{dy} = (-1/2)*(5 - y^2)^{-1/2}*(-2y)\)

Now, in which value of y we need to evalute that to get a 2?

If we use y = -2 we get:

\(\frac{dx}{dy} = (1/2)*(5 - 2^2)^{-1/2}*(-2*-2) = 2\)

now, when y = -2 in the circle we get:

\(x^2 + (-2)^2 = 5\\x^2 = 5 - 4 = 1\\x = \pm 1\)

This means that the tangent line of the form:

x = 2y + b

Needs to pass through the point (-2, 1) or (-2, -1) to be tangent to the circle.

When evaluating in -2 we get:

x = 2*(-2) + b

x = -4 + b

Then we can have either b = 3 or b = 5.

So the line:

x = 2x + 5

Is tangent to the circle at the point (-2, 1)

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Answer:

24.3

Step-by-step explanation:

area of a rectangle =length*width

if we know at least the 2 quantities already

total area = 656.1

and one of the sides = 27

we have to divide the are by one of the sides to get the remaining side

width = area/length

656.1 divided by 27 equals 24.3

Answer:

24.3 he was rii i got my answer frm here

Step-by-step explanation:

A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

Answer: They're the same angles/measurements.

Step-by-step explanation: Look closely at both the angles. If you measure them, they will be the same because both angles look the same, but ΔADC's side is flipped.

Let me know if you have any questions.

~ Lily, from Brainly.

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:

108 inches

Step-by-step explaination:
Looking at the picture I drew, we can assume that 24 = 4x
and so x=6 and 3x=18.
6 times 18 is 108.

Answer:

\(y=\dfrac{5}{4}x^3+10\)

Step-by-step explanation:

Given information:

Create two equations by substituting the given points into the given equation:

Equation 1:  point (0, 10)

\(\implies a(0)^3+d=10\)

\(\implies 0+d=10\)

\(\implies d=10\)

Equation 2:  point (2, 20)

\(\implies a(2)^3+d=20\)

\(\implies 8a+d=20\)

Substitute Equation 1 into Equation 2 and solve for a:

\(\implies 8a+d=20\)

\(\implies 8a+10=20\)

\(\implies 8a+10-10=20-10\)

\(\implies 8a=10\)

\(\implies \dfrac{8a}{8}=\dfrac{10}{8}\)

\(\implies a=\dfrac{10}{8}\)

\(\implies a=\dfrac{5}{4}\)

Finally, substitute the found values of a and d into the original formula:

\(\implies y=\dfrac{5}{4}x^3+10\)

Check by substituting the x-values of the two given points into the found equation:

\(x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}\)

\(x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}\)

Put(0,10)

Now

Put again (2,20) this time

Given:

The vector (-3,2) describes the translations:

From the first translation, we will find the values of (x) and (y)

So, we have the rule:

The sum of the x-coordinates from the left will equal the x-coordinates from the right

Solve the equation to find y

Now, The sum of the y-coordinates from the left will equal the y-coordinates from the right

Subtract 2 from both sides:

From the second translation, we will find the value of z:

so, the answer will be:

See the following figure:

Answer:

A

Step-by-step explanation:

Because the cost per pie is less.

Answer:

At most one of the adults has high blood pressure.

Step-by-step explanation:

The solution to the system of equation is the point where both lines intersect and it is at (3, 0)

Given the following system of equations

x + y = 3

- 2x + y = -6

Graphically, the point where both lines intersect on the place is the solution to the given system of equation.

From equation 1, x = 3 - y

Substitute into equation 2:

- 2(3-y) + y = -6

-6 + 2y + y = -6

3y = -6 + 6

y = 0

Substitute y = 0 into any of the equation

x + y = 3

x + 0 = 3

x = 3

Hence the solution to the given system of equation is (3, 0)

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The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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Answer:

4in

Step-by-step explanation:

Given parameters:

  Volume of can  = 314in

  Radius  = 5in

Unknown:

Height of the cylinder = ?

Solution:

The height of a cylinder is mathematically given as;

   V = πr²h

Where r is the radius

           h is the height

Input the parameters and solve for h;

          314  = 3.142 x 5² x h

     h  = 4in

The height of the cylinder is 4in

The surface area of the rectangular prism is 1476 square units

From the question, we have the following parameters that can be used in our computation:

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

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length = 7 in

- Surface area

Calculate the area of one side

Area = 7 x 7

= 49 in^2

Multiply the area by 6 because a cube has 6 sides

Total area = 49 x 6

= 294 in^2

-Volume

Volume = 7^3

= 343 in^3

Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

The interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

In this question we have an expression that combines polynomic and exponential expression, whose variable x cannot be cleared by analytical approaches, but by numerical and graphical methods. Herein we decide to find the interval by graphical methods, using a graphing tool:

First, write the function in explicit form (f(x) = 3 · x - eˣ). Second, find the two points such that the function goes through the x-axis (horizontal axis). Third, define the set of possible x-values by interval notation such that y > 0.

Then, the points of the function that are on the x-axis are (x₁, y₁) = (0.6191, 0) and (x₂, y₂) = (1.5121, 0). Then, the interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

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Answer:

243

Have a good day!

Answer:

1 hour and 50 minutes

Step-by-step explanation:

Time Connie takes to clean the house: 210 minutes

Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes

Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.

Answer:Alvaro can clean the house alone in approximately 3.89 hours.

Step-by-step explanation:

If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.

To find how long it would take Alvaro to clean the house alone, we can use the formula:

combined rate of work = sum of individual rates of work

So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.

Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).

Answer:

Answer:

which class Of question is this

Answer:

a. Expected frequency of losses per semester = 0*0.08 + 5*0.16 + 10*0.28 + 15*0.32 + 20*0.14 + 25*0.02

Expected frequency of losses per semester = 11.7 losses per semester

b. Variance = (0-11.7)²*0.08 + (5-11.7)²*016 + (10-11.7)²*0.28 + (15-11.7)²*0.32 + (20-11.7)²*0.14 + (15-11.7)²*0.02

Variance = 10.9512 + 7.1824 + 0.8092 + 3.7848 + 9.6446 + 3.5378

Variance = 35.61

c. As losses equal $60, expected losses per semester = 11.7*$60 = $702

d. Expected losses of all textbooks per semester = 250*11.7*$60 = $175,500

You answered 6,9 and 10,13. The correct answer is 6,9 and 7,13 to find the equation of the linear model.

(a) The two points you selected are (6,9) and (10,13). This is correct.

(b) To find the slope of the linear model, we can use the formula: slope = (change in y) / (change in x). By using the points (6,9) and (10,13), we have (13-9) / (10-6) = 4/4 = 1. So, the slope is indeed 1. This is correct.

(c) The equation of the linear model in point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6,9) as the point and 1 as the slope, we get y - 9 = 1(x - 6). This simplifies to y - 9 = x - 6. This is not the same as the equation you provided. It seems you made a mistake here.

(d) The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert the equation y - 9 = x - 6 to slope-intercept form, we can add 9 to both sides: y = x - 6 + 9, which simplifies to y = x + 3. This matches the equation you provided. So, this is correct.

(e) The equation for the least squares regression line is in the form y = bx + a, where b is the slope and a is the y-intercept. In this case, the slope is 1, and we need to find the y-intercept.

We can use the point (6,9) and the slope-intercept form equation y = x + 3 to find the y-intercept: 9 = 6 + 3. Solving this equation, we find that the y-intercept is 3.

Therefore, the equation for the least squares regression line is y = x + 3. This does not match the equation you provided. It seems you made a mistake here.

(f) Based on the correct equation from part (d) (y = x + 3), the correct equation for the least squares regression line is y = 1x + 3. When rounded to three decimal places, this would be y = 1.000x + 3.000.

The equation you provided (Y = 1.028x + 2.271) is slightly different, so it appears you made a mistake in the calculations or rounding.

To summarize, your answers in parts (a) and (b) are correct. However, there are mistakes in parts (c), (e), and (f). The corrected answers are:

(c) The equation of the linear model in point-slope form: y - 9 = x - 6.

(d) The slope-intercept form of the equation: y = x + 3.

(e) The equation for the least squares regression line: y = 1x + 3.

(f) When rounded to three decimal places, the equation is: y = 1.000x + 3.000.

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Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

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