The numbers 1, 2, 3, 4, and 5 are written on slips of​ paper, and 2 slips are drawn at random one at a time without replacement. Find the given probabilities.

(a) The sum of the numbers is 8.

(b) The sum of the number is 6 or less.

(c) The first number is 2 or the sum is 5

If the initial population is 3800. The population of cockroaches after 3 years will be 1603.

Consider the function:

y = a(1 ± r)ⁿ

where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, there is exponential growth happening by r fraction or r%.

If there is a minus sign, there is exponential decay happening by r fraction or r%.

If the population is currently 3,800 cockroaches.

The expression is given as

y = 3800(0.75)ⁿ

The population of cockroaches after 3 years will be

y = 3800(0.75)³

y = 3800 x 0.4218

y = 1603.125

y ≅ 1603

Hence, the population of cockroaches after 3 years will be 1603.

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The complete question is:

Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.

Answer:

When we multiply by a power of 10 (such as 10, 100, 1000, 10000, etc.), the number of digit zeros in the power of 10 is the number of places we move the decimal point to the right.

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Step-by-step explanation:

The solutions for x, y, z, and w in terms of a, b, c, d, e, and f are: x y = - (a b c d)^-1 (e f z w), z w = - (a b c d)^-1 (e f x y)

To solve for x, y, z, and w in terms of a, b, c, d, e, and f given the equality a b c d x y i 0 = e f z w,

we can rearrange the equation as follows: x y i 0 = - (a b c d)^-1 (e f z w).

Then we can solve for x and y by multiplying both sides by the matrix

(1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 0 1)

to obtain x y = - (a b c d)^-1 (e f z w).

Finally, we can solve for z and w by multiplying both sides by the matrix (

0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0) to obtain z w = - (a b c d)^-1 (e f x y).

Thus, the solutions for x, y, z, and w in terms of a, b, c, d, e, and f are:

x y = - (a b c d)^-1 (e f z w)

z w = - (a b c d)^-1 (e f x y)

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Answer:

1.03

Step-by-step explanation:

Price of phone * 1.03 = Price of phone + Sales tax

Answer:

12, 14, 16, 18

Step-by-step explanation:

(x + (x+2) + (x+4) + (x+6))/4 = 15

^ solve algebraically

you'll get (4x+12)/4 = 15

then: 4x + 12 = 60

then 4x = 60-12

then 4x = 48

then x = 12

x is 12 so then do substitution

so you get

12 + (12+2) + (12+4) + (12+6)

12, 14, 16, 18

The center of mass of the wire is (64/15, 0). To find the mass of the wire, we need to calculate its length first.

Since the wire is bent into the shape of a semicircle, its length is half the circumference of a circle with radius 8 units (since x>=0). Therefore, the length of the wire is πr = π(8) = 8π.

The linear density of the wire is given as k, which means that its mass per unit length is k. Thus, the mass of the wire is the product of its length and linear density: mass = k(8π) = 8kπ.

To find the center of mass, we need to locate the centroid of the semicircle. By symmetry, the centroid lies on the x-axis, and we only need to find its x-coordinate.

The x-coordinate of the centroid can be found using the formula:

x¯ = (1/M) ∫(x dM)

where M is the mass of the wire, and the integral is taken over the semicircle.

Using polar coordinates (x = rcosθ, y = rsinθ), we can rewrite the equation of the semicircle as y = (64-x^2)^0.5.

Then, we have:

dM = kds = k(sqrt(1+(dy/dx)^2))dx = k(1+(x^2/(64-x^2)))^(1/2) dx

Integrating from x=0 to x=8, we have:

x¯ = (1/M) ∫(x dM) = (1/8kπ) ∫(x (1+(x^2/(64-x^2)))^(1/2) dx) = 64/15

Therefore, the center of mass of the wire is (64/15, 0).

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The main difference between an area variance and a use variance is that area variance allows for an exception to zoning regulations related to the physical characteristics of a property, while use variance allows for an exception to regulations related to the intended use of a property.

An area variance is typically granted when a property owner is unable to comply with zoning regulations related to setbacks, building height, lot coverage, or other physical characteristics of a property.

In contrast, a use variance allows a property owner to use their property for a purpose that is not permitted under the current zoning regulations. This may include using a residential property for commercial purposes or using a commercial property for residential purposes.

Use variances are generally more difficult to obtain than area variances, as they require a showing of a unique hardship or practical difficulty that cannot be addressed through other means.

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Answer:

The answer would be 1.38

Step-by-step explanation:

look at the first digit after the decimal point if rounding to one decimal place or the second digit for two decimal places.

draw a vertical line to the right of the place value digit that is required.

look at the next digit.

if it's 5 or more, increase the previous digit by one.

so then once you do all of your math that is required to 1.27 rounded to 2 DP then that would give you 1.38

The number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440 will be 240 tines.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

In thi situation, the simulation shows that the number of times 10 is drawn is 1/6. The number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440 will be:

= 1/6 × 1440

= 240 times.

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Complete question

The simulation shows that the number of times 10 is drawn is 1/6. Use the simulation to predict the number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440.

Answer:

Step-by-step explanation:

a is the base

b is the power

c is the root

a = 7

b = 9

c = 4

System of Equations

Given the system of equations:

2x + y = -6

y = 1/4x + 3

It's required to solve it by graphing.

The graph of a line can be drawn by only knowing two points of it.

To graph the first equation, solve for y:

y = -2x - 6

Now give x two values. For example, x = -5 and x = -1.

For x = -5:

y = -2(-5) - 6

y = 10 - 6 = 4

Point (-5, 4)

For x = -1:

y = -2(-1) - 6

y = 2 - 6 = -4

Point (-1, -4)

With these points, we can graph the first equation. The graph will be shown below in red.

Now graph the second equation:

y = 1/4x + 3

For x = -8

y = 1/4(-8) + 3

y = -2 + 3 = 1

Point (-8, 1)

For x = 0:

y = 1/4(0) + 3

y = 0 + 3 3

y = 3

Point (0,3)

The second line is drawn in blue below.

If two random variables, Y1 and Y2, are independent, the condition that needs to be satisfied is that the joint probability distribution of Y1 and Y2 factors into the product of their individual probability distributions.

Mathematically, for independent random variables Y1 and Y2, the condition can be expressed as:

P(Y1 = y1, Y2 = y2) = P(Y1 = y1) * P(Y2 = y2)

This means that the probability of both events Y1 = y1 and Y2 = y2 occurring together is equal to the product of the probabilities of each event occurring individually.

In simpler terms, knowing the outcome or value of one random variable does not provide any information about the outcome or value of the other random variable if they are independent. They do not influence each other's probability distributions.

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\( {3}^{ - 2} \times {3}^{ - 5} = {3}^{ - 7} \)

Answer:

A) 3^-7

Step-by-step explanation:

Courtney rides for two hours on a bicycle, traveling 24 miles from her home. She has ridden for nine hours and is now 101 miles away. Courtney travels at a speed of 6 mph.

Let x represent the duration in hours and y the distance in miles.

Courtney travels 24 miles from her home after a two-hour ride.

She has traveled 101 miles after riding for nine hours.

rate is the slope

We divide the change in hours by the change in miles to find the rate.

\(Slope=\frac{y_{2} - y_{1} }{x_{2}-x_{1} } \\Slope=\frac{101-24}{9-2} \\Slope= \frac{77}{7} \\Slope=11\)

Therefore, Courtney's speed is 11 mph.

The speed of something or someone is shown to us. If you know how far and how long it took, you can find the average speed of an object.

The distance covered in a given amount of time would also double if one were to speed up. We need to know how far an object has traveled in order to determine its speed, and the slowest speeds are measured over the longest time periods.

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During a chemical reaction mass is conserved.

Only atoms from the reactants can end up in the products of a chemical reaction. No atoms are destroyed or made into new ones. When reactants come into touch with one another, bonds between their atoms are broken, and then the atoms rearrange and form new bonds to create the products.

Atoms in a chemical process are neither formed nor destroyed, according to the law of conservation of mass. The same is true for mass; it cannot be created or destroyed.

This means that both before and after the reaction, the number of atoms in each element must be constant. Atoms in reactants only rearrange to generate products during a chemical reaction.

That is,

During a chemical reaction mass is conserved.

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Answer:

HF

Step-by-step explanation:

Answer: Side HF.

Step-by-step explanation: The corresponding segment to EF in similar triangle HFG is HF, you can confirm it by folding the triangle.

Answer:

127.38

Step-by-step explanation:

Answer:

127.38

Step-by-step explanation:

15 x 3 = 45

(102.38 + 45) - 20 = 127.38

Sine and cosine are both equivalent to x/y, depending on the angle of the point on the circle.

To find two trigonometric functions equivalent to the ratio x/y, we can use the unit circle. Let's assume that x and y are the coordinates of a point on the circle, where x represents the horizontal displacement, and y represents the vertical displacement.

From this, we can find that the sine of the angle that x and y make with the x-axis is y, and the cosine of that angle is x. Therefore, the two trigonometric functions equivalent to the ratio x/y are sine and cosine.

We can write this as sin(angle) = y/y and cos(angle) = x/y. It's important to note that the value of the angle depends on the position of the point on the unit circle.

So, sine and cosine are both equivalent to x/y, depending on the angle of the point on the circle.

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Answer:

The answer is C, hope that helps:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

To make a prediction about the slices of pie the college will need, we can use the proportion of students who prefer pie from the sample of 225 students to estimate the number of students out of the total 4,000.

Number of students surveyed: 225

Number of students who prefer pie: 36

To estimate the number of students who prefer pie out of the total 4,000 students, we can set up a proportion:

225 (surveyed students) is to 36 (students who prefer pie) as 4,000 (total students) is to x (unknown number of students who prefer pie).

225/36 = 4000/x

Cross-multiplying, we get:

225x = 36 * 4000

225x = 144,000

x = 144,000/225

x ≈ 640

Therefore, the best prediction is that the college will have about 640 students who prefer pie.

The correct answer is "The college will have about 640 students who prefer pie."

Answer:

    x = 54

Step-by-step explanation:

Let x be the "mystery number."

If we divide x by 6000 [(x/6000)] and then multiply by 41 [(x/6000)*41] and then add 0.31 [(x/6000)*41 + 0.31], the result is 0.679:

  (x/6000)*41 + 0.31 = 0.679

 ( 41x/6000) + 0.31 = 0.679

( 41x/6000) = 0.369

     x = (0.369*(6000))/41

    x = 54

Answer:

45:63

Step-by-step explanation:

7+5=12

12u-->108

1u--> 9

5u-->45

7u-->63

The average productivity of the workforce, A(x), is given by

A(x) = p(x)/x,

where p(x) is the total value of the production when there are x workers in the plant.

A'(x) is the derivative of A(x) with respect to x.

A'(x) = (p(x)/x)' = (p'(x)x - p(x))/x^2.

The company wants to hire more workers if A'(x) > 0 because it means that the average productivity of the workforce is increasing with additional workers.

A'(x) > 0 if p'(x) is greater than the average productivity, which is p(x)/x.

Therefore, A'(x) > 0 if p'(x) > p(x)/x.
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The probability of the randomly selected point is in the semicircle is equal to 0.1.

Side length of a square = 10inches

Radius of the semicircle = 3 inches

Area of the composite figure = sum of area of semicircle and the area of the square.

The area of the semicircle is equal to,

= (1/2)π(3 in)²

= 4.5π in²

The area of the square is,

=(10 in)²

= 100 in²

The total area of the composite figure is,

= 4.5π + 100

≈ 114.1 sq in (rounded to one decimal place)

The area of the semicircular region is half the area of the semicircle,

= (1/2)(4.5π)

= 2.25π sq in

The probability 'P' of randomly selecting a point within the semicircular region is,

P = (area of semicircular region) / (total area of composite figure)

⇒P = (2.25π sq in) / (114.1 sq in)

⇒P ≈ 0.0619

Rounding to the nearest tenth, the probability is approximately 0.1

Therefore, the probability of randomly selected point is a part of semicircle region is equal to 0.1( nearest tenth ).

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Answer: 12.4%

Step-by-step explanation:

I took the quiz

Answer:

the answer is A

Step-by-step explanation:

just did it

Answer:

a

Step-by-step explanation:

Answer:

5,500

Step-by-step explanation:

2,500 + 3,000:

2000 + 3000 + 500

5000 + 500

5500

Easy!

the probability that at least 5 will do their homework on time in a class of 50 students is 0.1

How do you calculate probability?

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.

the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.

each student does homework independently.

in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?

probability = event occur/ total number of outcomes

                 = 5/50= 1/10=0.1

thus the probability becomes 0.1

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Answer:

\(9 \frac{6}{25}\)

Step-by-step explanation:

0.24 is 6/25.

Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

  1.42 m

Step-by-step explanation:

Each inch is 0.0254 meters, so 56 of them is ...

  56(0.0254 m) = 1.4224 m ≈ 1.42 m