DPIn a board game, students draw a number, do not replace it, and then draw asecond number. Determine the probability of each event occurring.

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

2,206 yards

Step-by-step explanation:

To find how many yards there are, we can divide by 3.

6618 / 3 = 2206

Best of Luck!

Answer:

6,618 feet is 2,206 yards.

Step-by-step explanation:

a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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Answer:

Step-by-step explanation:

y=mx+b

m= slope and b= y intercept

you'll start with a point on the y axis on -1

and the slope will go up so towards the right corner up but 2/1 points

Answer:

Linear

Step-by-step explanation:

y=x-5/4 is a linear equation.

The number of attempts the tiger made with 10 percent success rate is40 attempt

Percentage is a number that can be expressed as a fraction of 100. To calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

Representing the number of attempt as y

Therefore (10/ 100)× y = 4

10y = 400

therefore

y = 400/10

= 4

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The number of attempts that the tiger made, based on the hunting success rate and the successful hunts was 40 attempts.

The tiger is said to be able to be successful in their hunt by a success rate of 10%. This means that every time a tiger hunts, it has only a 10% chance of being successful.

If the tiger was successful 4 times in a week, then the number of hunting attempts they must have made was:

= Number of successful hunts / Success rat e

= 4 / 10.%

= 4 / 0.1

= 40 attempts

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Answer:

x = 3/2

Step-by-step explanation:

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

(3)(1)+2x=6

Step 1: Simplify both sides of the equation.

(3)(1)+2x=6

3+2x=6

2x+3=6

Step 2: Subtract 3 from both sides.

2x+3−3=6−3

2x=3

Step 3: Divide both sides by 2.

2x/2  3/2

x = 3/2

Hope this helps :)

Answer:

If a coin is tossed 12 times, the maximum probability of getting heads is 12. But, 12 coin tosses leads to 212 , i.e. 4096 number of possible sequences of heads & tails.

Step-by-step explanation:

Answer:

8/13

Step-by-step explanation:

Pam flips a coin 12 times. The coin lands on heads 8 times. What is the theoretical

probability of landing on heads on the next flip?

well it would be 8 and 13

In the above proportions problem, note that the distance of PR is 155.17ft.

To solve for PR, note that

OC/RE = PR/OR

That is:

225/145 = PR/100

To solve for PR, we can cross-multiply the fractions:

225 * 100 = 145 * PR

22,500 = 145PR

Dividing both sides by 145:

PR = 155.17

Therefore, PR is approximately 155.17ft

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The composite solid has a volume of 224 inches³.

Volume is a mathematical notion that indicates how much space in three dimensions a solid, liquid, or gas occupy.

It is commonly measured in cubic length units like cubic metres, cubic feet, or cubic centimetres.

The volume of the cube must be subtracted from the volume of the rectangular prism in order to determine the volume of the composite solid.

Volume of the rectangular prism = length x width x height = 8 x 6 x 6 = 288 cubic inches

Volume of the cube = side \(length^3\) = \(4^3\) = 64 cubic inches

The composite solid's volume is thus:

Volume of rectangular prism - Volume of cube = 288 - 64 = 224 cubic inches.

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An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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Answer:

-1/7 and 3/4

Step-by-step explanation:

1/5(-2/7)  /  2/5

=(-2/35) / (2/5)

=(-2/35) * (5/2) cancel common factors

= -1/7

Question 6

cancel common factors

=(-1/12) / (-1/9)

=(-1/12) * (-9/1)

=9/12

=3/4

Answer:

Question 5: -1/7

Question 6: 3/4

Step-by-step explanation:

For the first one: 1/5(-2/7)= -2/35 divided by 2/5

-2/35 (Flip 2/5 to 5/2) divided by 5/2

-1/7

For the 2nd one: -3/8(2/9)= -1/12

-1/12 divided by -1/9

-1/12x-9/1= 3/4

Answer:

Step-by-step explanation:

How Far Can A Snail Travel In One Hour

If a snail can travel over half an inch per minute, that means in one hour a snail can travel up to 40 inches. If you want to think about how far this is in feet, it means that snails move up to 3.5 feet per hour.

Consider the fact that the average human being can walk about a mile, or 5280 feet, in one hour.

This means that snails can take up to 1,500 days, or over 4 years, to travel just one mile.

Answer:

  A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.

Step-by-step explanation:

The area of a parallelogram is given by the formula ...

  A = bh

So, we have the condition that ...

  A > 42

  bh > 42 . . . . . substitute the expression for area

  14h > 42 . . . . fill in the given base

  h > 3 . . . . . . . divide by 14

Numbers greater than 3 are to the right of 3 on the number line.

_____

The relation is > rather than ≥, so the "or equal to" case is not included. That is why the circle is open, rather than solid.

Answer:

a).

Step-by-step explanation:

s3+5s2+8s+4

Step-by-step explanation:

Answer:

(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)

Where u(t) is the step function

Step-by-step explanation:

use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.

Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.

A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.

The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).

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Answer:

x=80°

Step-by-step explanation:

Straight line=180°

therefore,

180=2x-30+50

minus 50 on both sides

130=2x-30

plus 30 on both sides

160=2x

divide 2 on both sides

x=80

Answer:

m∠A = 130

Step-by-step explanation:

Here, In a given figure

m∠A = 2x - 30°

Now, we know that the sum of all angle is 180° on a straight line

So,

2x - 30° + 50° = 180°

2x + 20° = 180°

2x = 180° - 20°

2x = 160°

x = 160° ÷ 2

x = 80°

Here, we get the value of x is 80°

Now,

m∠A = 2x - 30°

m∠A = 2(80°) - 30°

m∠A = 160° - 30°

m∠A = 130

Thus, m∠A = 130

-TheUnknownScientist

Answer: 176 degrees

Step-by-step explanation:

By the inscribed angle theorem, the measure of arc JML = 88 * 2 = 176 deg.

Answer:

8cm & 514 squared are correct answers

Step-by-step explanation:

Answer:

coefficient..........

Step-by-step explanation:

we have A and B

for A,

95-82 = 13

for B,

95-86 = 9

cost of A = 9

cost of B = 8.5

total = 60

for person

A = 6,

B = 2

Total = 32

setting up objective function:

13x + 9y

constraints:

0≤x≤5, 0≤x≤5

7x + 8.5y ≤ 60

6x + 2y ≤ 32 this can be reduced by 2

3x + y≤16

this would take us to a bounded region which has the corner points and the objective values in the attachment i added.

Answer:

Sarah ate 2, atil ate 2

Step-by-step explanation:

The total number of cookie Sara got = y

Atill got 2 more than Sara so his total cookies is = 2+y

Sarah ate half if hers = y/2

Atil ate 1/3 of his = 2+y/3

We have

Y/2 = 2+y/3

Then we cross multiply

3y = 2(2+y)

3y = 4 + 2y

3y - 2y = 4

Y = 4

Since y = 4,

Sara ate 4/2 cookies = 2

Then atil ate 2+4/3 = 6/3 = 2 cookies

Answer:

20 Feet

Step-by-step explanation:

Answer:

40 feet

Step-by-step explanation:

15 / 3 = 5

5 x 8 = 40

Answer:

B

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .

Answer:

B. \(-\frac{1}{5} x+\frac{4}{5}\)

Step-by-step explanation:

1. Rewrite the function as a linear equation:

y = -5x - 4

2. Swap x and y:

x = -5y - 4

3. Solve for y:

x+4 = -5y - 4+4

x + 4/-5 = -5y/-5

\(\frac{x+4}{-5}\) = y  can be rewritten as \(-\frac{1}{5} x+\frac{4}{5}\)

4. Write in inverse notation:

f(x) = \(-\frac{1}{5} x+\frac{4}{5}\)

Therefore, B is the answer.

Using translation concepts, it is found that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up. Other types of transformations are rotations or dilation.

For the first question, the rule for a reflection over the x-axis is given by:

(x,y) -> (x,-y).

Then:

P': (-5,-3) -> (-5,3).

The coordinates of P' are (-5,3).

For the second question, the rule for a 180º clockwise rotation about the origin is given by:

(x,y) -> (-x,-y).

Hence:

Hence:

The coordinates of the new triangle are P'(5,3),  K'(3,1) and Y'(1,4).

For a dilation by a scale factor of 2, every coordinate is multiplied by 2, hence:

The new coordinates of the dilated triangle are: A'(2,2), B'(10,4) and C'(6,10).

The rule for a translation 5 units down is:

(x,y) -> (x, y - 5).

Hence:

(-1,4) -> (-1,-5).

The new coordinates of C' are (-1,-5).

For the final question, a translation is when just the position of the image changes up/down, having no changes in size or orientation, hence:

The bottom-right image(the one that is already marked) represents a translation.

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Answer:

70

Step-by-step explanation:

Circumference = pi × diameter

219.8 = pi × diameter

219.8/pi = diameter

Diameter = 69.96....

= 70yd

Answer:

274

Step-by-step explanation:

(52 + 4) * 5 - 2 + (-4)

56 * 5 - 2 + (-4)

56 * 5 - 2 - 4

280 - 2 - 4

278 - 4

274

Answer:

274

Step-by-step explanation:

(52+4)*5-2+(-4)

(56)*5-2+(-4)

280-2+(-4)

278+(-4)

274

The blue figure is moved 5 units to the right (T(5, 0)), reflected in the y-axis (r(y-axis)), and then rotated 90 degrees counterclockwise (R(-90)).

Translation: Move the blue figure 5 units to the right (translation of 5 units to the right, denoted as T(5, 0))

Reflection: Reflect the figure in the y-axis (denoted as r(y-axis))

Rotation: Rotate the figure 90 degrees counterclockwise (denoted as R(-90))

The series of transformations that moves the blue figure to the red figure is T(5, 0) followed by r(y-axis) followed by R(-90).To better understand this, let's break down the transformations. The first transformation is a translation, which is a movement of a figure from one location to another. In this case, the figure is being moved 5 units to the right. This is denoted as T(5, 0).The second transformation is a reflection, which is a flip of a figure over a line or axis. In this case, the figure is being reflected in the y-axis. This is denoted as r(y-axis).The third transformation is a rotation, which is a turn of a figure around a point. In this case, the figure is being rotated 90 degrees counterclockwise. This is denoted as R(-90).Therefore, the series of transformations that moves the blue figure to the red figure is T(5, 0) followed by r(y-axis) followed by R(-90).

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