A computer sends a packet of information along a channel and waits for a return signal acknowledging that the packet has been received: If no acknowledgment is received within a certain time, the packet is re-sent: Let X represent the number of times the packet is sent. Assume that the probability mass function of X is given by cx for x S 1,2,3,4, or 5 otherwise p(x) where c is a constant. a Find the value of the constant C so that p(x) is a probability mass function. b. Find P(X = 2). C. Find the mean number of times the packet is sent d. Find the variance of the number of times the packet is sent: e. Find the standard deviation of the number of times the packet is sent:

Answer: How Weather Exists

Step-by-step explanation:

~I think you mean, how weather exists.

You see, "Weather" exists because of the atmosphere. Evidently, weather  is the movement of the atmospheric gases around the planet that creates weather. Places like the Moon or Mercury do not have weather - only temperature changes.

~Hope this helped :)

From knowledge of numerals the answer to the given Question is: a = 3 b = 6 c = 5

What are Numerals?

Numerals are symbols or numerals used to represent numbers. They are used in math and other fields to represent quantities and measurements. Numerals can be written in different forms, such as Arabic numerals (1, 2, 3, etc.) or Roman numerals (I, II, III, etc.). Numerals are also used to label items, such as dates (e.g. May 4th, 2020), addresses (e.g. 1234 Main Street), and telephone numbers (e.g. 555-123-4567). Numerals are an important part of our everyday lives, used to count, measure, and express amounts.

Numerals are just a combination of digits that we know
for example if 0,1,2,3,4,5,6.....9

are the fundamental digits then numbers from these like

12,34,668,389,23,39 etc are called numerals

We can also conclude that all numbers have originated from numerals itself and numerals are basic unit of formation of numbers

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[tex]\stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}}[/tex]

Answer:

24 cherries

Step-by-step explanation:

Greg took the last 50% which left 3 cherries. Since he took half, that means there were 6 before he took any. Mei took 50%, also, which left the 6, so there were 12 before she picked. This was what was left after Jordan took 50%, which means they started with 24 cherries.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (500)(0.032)(1) \implies I = 16[/tex]

Answer:

[tex]S=\{-2,-3\}[/tex]

Step-by-step explanation:

Required integers are: -2 and -3

H represents integer -2 on the number line

Opposite value of -2 is 2

Absolute value of -2 is 2

What is opposite and absolute value of an integer?

Opposite integers: Two numbers that are the same distance from zero but on opposite sides.

Absolute value of integer: The integer’s distance from zero on the number line.

Every integer has an opposite.

The sum of two opposites is always zero.

For example 5 is opposite of -5

According to the given question:

The integer represented by the H lies on the left hand side of zero that is negative side of number line.

H represents -2 on the number line

Opposite value of -2 is 2

Absolute value of -2 is 2

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Answer:

2) ∡1 = 170°

Step-by-step explanation:

1) The angles in red have the same measure, and those in blue have the same measure.

The percentage of the campers that are participating in a nature hike that are females is 57.1% (first option)

Percentage is the fraction out of an amount expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.

Percentage of the campers that are participating in a nature hike that are females = (number of females in the nature hike / total number of campers in the nature hike) x 100

Total number of campers in the nature hike = 20 + 15 = 35

Percentage of the campers that are participating in a nature hike that are females = (20 / 35) X 100 = 57.1%

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The value of x for the given equation is 1.

What is solving an equation?

A General Rule for Equation Solving

Remove parentheses from each side of the equation and combine similar phrases to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Consider the given expression

0.2(x + 1) + 0.5x = -0.3(x - 4)

Simplifying,

0.2x + 0.2 + 0.5x = -0.3x + 1.2

0.7x + 0.2 = -0.3x + 1.2

Add 0.3x on both sides,

0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x

x + 0.2 = 1.2

Subtract 0.2 from both sides,

x + 0.2 - 0.2 = 1.2 - 0.2

x = 1

Hence, the value of x for the given expression is, 1.

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Answer:

Y = 1/4 -1

Step-by-step explanation:

To find slope, count how many units are between points on the line. How many times you count up or down will be found on top of the fraction symbol. How many times you count left or right will be found below the fraction symbol. This line goes to the right four times, and up once to reach its next point. That means our slope will appear as 1/4.

Next, go to the spot where the line hits the Y-axis. That is where the y-intercept is. -1 is where the line crosses the Y-axis, so that's our y-intercept.

Very simply, you find slope by counting, and y-intercept by looking. Up one time, to the right four times; 1/4 for slope. Line crosses at -1; y-intercept. Y = 1/4 -1

The symmetric fraction to 8/4 is given as follows:

1/2.

A fraction is a numerical representation of the division of the two terms, symbolized x and y, as follows:

Fraction = x/y.

The technical terms of x and y are given as follows:

The symmetric fraction is obtained exchanging the numerator and the denominator, hence it is of:

Symmetric fraction = y/x.

The fraction in this problem is given by:

8/4.

Hence the symmetric fraction is of:

4/8 = 1/2.

(as both 4 and 8 are divisible by 4).

The problem asks for the symmetric fraction to 8/4.

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The average rate of  change of f(x) over the interval [-4,-1] is 2  , the value of f(-1) is 3  and value of f(-4) is  -3 .

In the question ,

a linear graph of the function f(x) is given ,

we have to find the rate of change of the function f(x) ,

We know that the Rate Of Change of the function f(x) over interval [a,b] is calculated using the formula ;

Rate Of Change [tex]=[/tex] (f(b) - f(a))/(b - a)

the interval is [-4,-1] ,

So , a = -4 and b = -1 .

From the graph , the value of f(-1) is = 3 ,

and the value of f(-4) is = -3 ,

So , By the Rate Of Change formula ,

we get ,

Rate Of Change = (f(-1) - f(-4))/(-1 -(-4))

= (3 -(-3))/(-1 + 4)

= (3 + 3)/3

= 6/3

= 2

Therefore , the rate of change over the interval [-4,-1] is 2 .

The given question is incomplete , the complete question is

Calculate the average rate of change of f(x) (shown in the graph) over the interval [-4, -1] using the formula. The value of f(-1) is. The value of f(-4) is. The average rate of change of f(x) over the interval [-4, -1] is .

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Answer:

[tex]\huge\boxed{\sf 3 \ baskets}[/tex]

Step-by-step explanation:

Let the baskets missed in game 2 be x.

Says that, the shooting of both the games were accurate.

So,

[tex]\displaystyle \frac{Baskets \ made \ in \ game \ 1}{Baskets \ missed \ in \ game \ 1 } =\frac{Baskets \ made \ in \ game \ 2}{Baskets \ missed \ in \ game 2} \\\\\frac{15}{5} =\frac{x}{1} \\\\Cross \ Multiply\\\\15 \times 1 = 5 \times x\\\\15 = 5x\\\\Divide \ 5 \ to \ both \ sides\\\\3 = x\\\\x = 3\\\\\rule[225]{225}{2}[/tex]

The percentage change in its perimeter would be 36.66%

What is the perimeter of the rectangle?

The perimeter of a shape is the length of its outline. To calculate the perimeter of a rectangle or square, add the lengths of all four sides. In this case, x represents the rectangle's length, while y represents its width. P=x+x+y+y is the perimeter.

Given:

The length of a rectangle is twice its breadth.

Length is increased by 10%.

Breadth is decreased by 10%.

Let the length be x and Breadth be y

By the given condition, we can write

                    x = 2y ------(I)

         Perimeter = 2(x + y)

                           = 2(2y + y)

                           = 4y + 2y

         Perimeter = 6y

Now the length is decreased by 10%,

then the new length will be

                 = x - 10x/100

                 = 9x/10

as x = 2y

                     length =  18y/10.

The breadth is increased by 10%.

then the new breadth will be

                              = y + 10y/100

                breadth = 11y/10

New Perimeter = 2( 18y/10 + 11y/10)

                          = 2(19y/10)

                          = 19y/5

The total change in perimeter = (Old Perimeter - New perimeter)

                                               = 6y - 19y/5

                                              = 11y/5

Percentage change = [tex]\frac{\frac{11y}{5} }{6y}[/tex] * 100

                                 =  11/30 * 100

                                 = 36.66%

Hence, the percentage change in its perimeter would be 36.66%.

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This can be solved through a series of processes!

5(2y - 3) - y = 21

10y - 15 - y = 21

9y - 15 = 21

9y = 36

y = 4

x = 2(4) - 3

x = 8 - 3

= 5

Answer:

I think you are talking about the empirical method if so the answer is

5x - y= 1x= y-3

Answer:

109 degrees

Step-by-step explanation:

all three of those angles will equal 180

42+29+x=180

71+x=180

-71.     -71

x=109

Hopes this helps please mark brainliest

The average rate of change over the interval x = -2 and x = 1 is 4

The equation is given as

f(x) = x² + 5x - 12

The interval is given as:

x = -2 to x = 1

Start by calculating the functions f(-2) and f(1)

So, we have

f(-2) = (-2)² + 5(-2) - 12 = -18

f(1) = (1)² + 5(1) - 12 = -6

So, the average rate over these intervals is calculated as:

Average rate = [f(1) - f(-2)]/[1 - -2]

This gives

Average rate = [-6 - -18]/[1 - -2]

Evaluate

Average rate = 4

Hence, the average rate of change is 4

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Using the ratio principle, the longest stage is Prophase with a duration of 456 minutes

The amount of time spent in each stage of Mitosis can be calculated thus :(Number of onion per stage / total number of onions) × total time spent.

Total time spent = 24 hours = (60 × 24) = 1440 minutes

Time spent per stage :

Anaphase :

(12 / 60) × 1440 = 288 minutes

Prophase :

(19 / 60) × 1440 = 456 minutes

Metaphase :

(14 / 60) × 1440 = 336 minutes

Telophase :

(15 / 60) × 1440 = 360 minutes

Therefore, the stage with the longest duration is the Prophase stage and the duration is 456 minutes

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The 15% discount for home gym, and the $889 cost of the Flex 3,000 gives;

1. f(x) = 0.85•x + 139.95

2. With the deal, Charlotte's before tax cost is $895.6

The deal cost is more than the initial price making the deal not worth it.

1. We are given;

The percentage discount Charlotte gets = 15% = 0.15

Cost of the 6 months subscription = $139.95

Now, to get the function;

f(x) = Final before tax

x = Price of the home gym equipment

Therefore, using the discount of 15%, we will have;

f(x) = (1 - 0.15)x + 139.95

f(x) = 0.85x + 139.95

2. We are told that the cost of the Flex3000 is x = $889

Therefore;

f(889) = (0.85 × 889) + 139.95

f(889) = 895.6

Charlotte's before–tax cost with the deal will therefore be, $895.6

Since the workout channel holds no value to Charlotte, and then the deal cost is higher than the initial cost, then we can say that it isn't worth it for her to pay for the subscription to get the 15% discount

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Complete question is;

Charlotte has been saving up to buy a home gym so she can work out at home without having to pay for a

gym membership or worry about travel when the weather is bad (she lives in Minnesota where it snows

frequently). One day, she sees an ad for a 15% off sale at a fitness equipment store and decides it's a great

time to buy the home gym! She notices the fine print says that to get the 15% off the home gym, she has to

pay $139.95 up front for a 6-month subscription to a workout channel, which holds no value to her.

1. Using function notation, write an expression for the final before-tax cost, f(x), of the purchase

based on the initial price, x, of the home gym equipment with this deal.

2. She was considering purchasing the Awesome Flex3000 for $889. Using your function from

question 1, what would Charlotte be Charlotte's before-tax cost with the deal? Is it worth it for

her to pay for the subscription to get 15% off? Explain your answer.

The number of baseball Mike took to the baseball field is 198

The calculation can be done using one of the mathematical operation called division

Division helps in grouping the baseballs in the baseball bin as follows

= 363 / 11

= 33

Therefore each bin contains 33 baseballs then Mike took 6 bins, the number of baseball in the 6 bins are

= 6 * 33

= 198

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The coordinates of P'Q'R'S' and P"Q"R"S" are P'(-2, 3), Q'(1, 3), R'(1, 1) ,S'(-2, 1) and P''(-6, 1), Q''(-3, 1), R''(-3, -1), S''(-6, -1).

A dilation is a transformation that yields a picture that differs in size while maintaining the original image's shape

The coordinates of the rectangle are P(-6,9), Q(3,9), R(3,3), and S(-6,3).

To find the coordinates of the rectangle after the dilation by a scale factor of 1/3, multiply each coordinate of the original rectangle by 1/3:

P'(-6/3, 9/3), Q'(3/3, 9/3), R'(3/3, 3/3), and S'(-6/3, 3/3)

Simplify the coordinates:

P'(-2, 3), Q'(1, 3), R'(1, 1), and S'(-2, 1)

Now, the coordinates of the rectangle P'Q'R'S' after the translation of 4 units to the left and 2 units down are:

P''(-2 - 4, 3 - 2), Q''(1-4, 3 - 2), R''(1 - 4, 1 - 2), and S''(-2 - 4, 1 - 2)

Simplify the coordinates:

P''(-6, 1), Q''(-3, 1), R''(-3, -1), and S''(-6, -1)

Hence, the coordinates of P'Q'R'S' and P"Q"R"S" are P'(-2, 3), Q'(1, 3), R'(1, 1) ,S'(-2, 1) and P''(-6, 1), Q''(-3, 1), R''(-3, -1), and S''(-6, -1).

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i) The number of participants that would need to attend the forum for Patricia to break even is of: 30.

ii) The number of participants that would need to attend the forum for Patricia to obtain a profit of Ksh 337,500 is of: 75.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

Hence in the context of this problem, the meaning of each coefficient is given as follows:

Hence the values of each coefficient are given as follows:

Hence the profit function is given as follows:

P(x) = 7500x - 225000.

She breaks even when P(x) = 0, hence:

7500x - 225000 = 0

7500x = 225000

x = 225000/7500

x = 30 participants.

She makes a profit of 337500 when:

7500x - 225000 = 337500

x = (337500 + 225000)/7500

x = 75 participants.

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The comparison of the area in inches of these two sections is (d) the area Section 1 is about 24 times greater than the area of section 2​

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

These can be properly expressed as:

The area of these sections is calculated as

Area = Product of lengths

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

Section 1 = 2.4 * 10³ in * 1.5 * 10³ = 3.6 * 10⁶ square inches

Section 2 = 3.6 * 10² in * 4.2 * 10² in = 15.12 * 10⁴ square inches

The ratio of these sections is

Ratio = Section 1/Section 2

So, we have

Ratio = 3.6 * 10⁶ square inches/15.12 * 10⁴ square inches

Evaluate

Ratio = 24 (approximated)

Hence, the relationship between the section areas is (d)

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Answer: the answer is A. 7/2(1/2)

The graph line for function d = 0.25t is added as an attachment

The equation of the function is given as

d = 0.25t

The above function is a linear function

One way to create the graph is to make a list of ordered pairs

So, we have

When t = 0, d = 0.25 * 0 = 0

When t = 1, d = 0.25 * 1 = 0.25

When t = 2, d = 0.25 * 2 = 0.5

So, the ordered pairs are (0, 0), (1, 0.25) and (2, 0.5)

We plot these points on a graph and connect them through a line

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Answer:  a

Step-by-step explanation:

The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

Given: the expression (3√-5 + 2)(4√-5 -1)

(3√-5 + 2)(4√-5 -1)

Clear the parenthesis:

(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)

                             = -60 - 3√-5 + 8√-5 -2

                            = 5√-5 - 62

Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62

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The quadratic equation with the roots  3+i and 3-i is:

x^2 - 6x + 10 = 0

We know that a quadratic equation with the roots a and b is written as:

(x - a)*(x - b) = 0

Here the roots are 3 + i, and 3 - i.

Replacing that we get:

(x - 3 - i)*(x - 3 + i) = 0

Expanding the product on the left we get:

x^2 + x*(-3) + x*i + (-3)*x + (-3)*(-3) + (-3)*i + (-i)*x + (-i)*(-3) - i^2 = 0

Remember that i^2 = -1, then:

x^2 -3x + x*i - 3x + 9 - 3i - x*i + 3i + 1 =0

x^2 - 6x + 10 = 0

That is the equation for the given roots.

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