carl throws a single die twice in a row. for the first throw, carl rolled a 2; for the second throw he rolled a 4. what is the probability of rolling a 2 and then a 4? answer choices are in the form of a percentage, rounded to the nearest whole number.

Answers

Answer 1

To the nearest whole number, the probability of rolling a 2 and a 4 is 2.8%.

A 2 rolling up on the first throw has a 1/6 chance of happening. Given that a 2 was rolled on the first throw, the likelihood of rolling a 4 on the second throw is equally 1/6. We will have to multiply the probabilities to get the probability of both the events happening,

= (1/6)x(1/6)

= 1/36.

We get 2.8% after converting to a percentage and rounding to the next full amount. So, the chance of rolling a 2 and then a 4 is found to be 2.8% chance.

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Related Questions

Make sure you click on the answer in the drop box that goes in the blank for each numbered blank.
BLANK #1 PLEASE ANSWER ALL THE BLANKS 100 points

Answers

1 - THEOREM, 2 - RIGHT, 3 - SUM, 4 - LEGS, 5 - SQUARE, 6 - A, 7 - B, 8 - C, 9 - HYPOTENUSE, 10 - 90-DEGREES

The full statement reads: The pythagoras theorem tells us how the side lengths of right triangles are related. In any right triangle the sum of the squares of the two legs should equal the square of the hypotenuse. The legs are called A and B and the hypotenuse is C. The hypotenuse is always the longest side of a right triangle and its across from the 90-degrees angle.

Some properties of right angled triangles

Let us assume the triangle is ABC, and the angle C is 90 degrees. let the length the side AB = c, the length of side AC = b, the length of side BC is a.

1. The sum of the two non 90 degree angles is equal to 90 degrees.

2. cos(B) = a/c , sin(B) = b/c

3. cos(A) = b/c, sin(A) = a/c

4  [tex]c^2 = a^2 + b^2[/tex]

5 the diameter of the circumcircle of this triangle is c.

6 tan(A) = a/b

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how do i write an inequality for this?​

Answers

The inequality expression representing the area of the shaded region, indicating both the shaded area and the broken line is; y > 0

What is an inequality?

An inequality is a mathematical statement consisting two expressions joined with inequality symbols, which includes; '<', '>', '≠', '≤', and '≥'.

The area of the shaded region is the part of the coordinate plane above the x-axis.

The region shaded can therefore be indicated by the area y > 0

The x-axis on the coordinate plane representing the boundary of the shaded region consists of broken line, which indicates that the line is not included in the shaded region.

The inequality representing the area of the shaded region is therefore;

y > 0

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find the foci of the ellipse with the equation x^2/144+ y^2/100=1

Answers

The foci of the ellipse are at (0, -2√11) and (0, 2√11).

How to find the foci of an ellipse using the equation?

To find the foci of the ellipse with equation x²/144 + y²/100 = 1, we need to use the standard form of the equation of an ellipse:

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center of the ellipse, a is the distance from the center to the vertices in the x-direction, and b is the distance from the center to the vertices in the y-direction.

First, let's rewrite the given equation in standard form by dividing both sides by the constant on the right-hand side:

x²/144 + y²/100 = 1

x²/12² + y²/10² = 1

Comparing this with the standard form, we can see that the center of the ellipse is (0, 0), a = 12, and b = 10.

Thus, the distance from the center to each focus is given by c, where:

c² = a² - b²

c² = 12² - 10²

c² = 144 - 100

c² = 44

c = √44

c = 2√11 units

Thus, the distance from the center to each focus is 2√11.

Since the center is at (0, 0), the foci are located at (0, -2√11 and (0, 2√11).

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a tank contains 60 kg of salt and 2000l of water. a solution of a concentration 0.015 kg of salt per liter enters a tank at the rate 9l/min. the solution is mixed and drains from the tank at the same rate. (a) what is the concentration of our solution in the tank initially? (b) find the amount of salt in the tank after 3.5 hours. (c) find the concentration of salt in the solution in the tank as time approaches infinity.

Answers

(a) The concentration of the solution in the tank will be changing over time.

(b) The amount of salt in the tank after 3.5 hours is 63.292 kg.

(c) When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.

(a) To find the concentration of the solution in the tank initially, we can use the formula:

concentration = mass of salt / volume of solution

The mass of salt in the tank initially is 60 kg, and the volume of solution is 2000 liters.

Therefore, the initial concentration is:

concentration = 60 kg / 2000 L

concentration = 0.03 kg/L

However, we know that a solution with a concentration of 0.015 kg/L is entering the tank at a rate of 9 L/min.

Therefore, the concentration of the solution in the tank will be changing over time.

(b) To find the amount of salt in the tank after 3.5 hours, we can use the formula:

amount of salt = initial amount of salt + (concentration of incoming solution - concentration of solution in tank) x rate x time

The initial amount of salt is 60 kg, and the concentration of the incoming solution is 0.015 kg/L.

We need to find the concentration of the solution in the tank after 3.5 hours.

The rate of flow is 9 L/min, so the total volume of solution that has entered the tank after 3.5 hours is:

volume of solution = rate x time

volume of solution = 9 L/min x 210 min

volume of solution = 1890 L

The total volume of solution in the tank after 3.5 hours is:

total volume = initial volume + volume of incoming solution - volume of drained solution

total volume = 2000 L + 9 L/min x 210 min - 9 L/min x 210 min

total volume = 2000 L

Therefore, the concentration of salt in the tank after 3.5 hours is:

amount of salt = 60 kg + (0.015 kg/L - concentration of solution in tank) x 9 L/min x 210 min

amount of salt - 60 kg = (0.015 kg/L - concentration of solution in tank) x 1890 L

concentration of solution in tank = 0.015 kg/L - (amount of salt - 60 kg) / 1890 L

Now we can substitute the concentration of the solution in the tank into the formula and solve for the amount of salt:

amount of salt = 60 kg + (0.015 kg/L - (0.015 kg/L - (amount of salt - 60 kg) / 1890 L)) x 9 L/min x 210 min

amount of salt = 63.292 kg

Therefore, the amount of salt in the tank after 3.5 hours is 63.292 kg.

(c) To find the concentration of salt in the solution in the tank as time approaches infinity, we need to find the concentration that the solution will reach when the inflow and outflow rates of solution are equal.

At this point, the amount of salt in the tank will remain constant.

Let's denote the concentration of salt in the solution in the tank as c.

We know that the volume of solution in the tank remains constant at 2000 L, and that the inflow and outflow rates are both 9 L/min. Therefore, the amount of salt that enters the tank per minute is 0.015 kg/L x 9 L/min = 0.135 kg/min, and the amount of salt that leaves the tank per minute is c x 9 L/min.

When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.

Therefore, we can set the rate of inflow equal to the rate of outflow and solve for c:

0.015 kg/L x 9.

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What is the value of x?

Right triangle. Vertices are not labeled. The length of one side equals 18.15. The length of the second side equals 17.39. The length of the hypotenuse is unknown, and is labeled x.

Round your final answer to the nearest tenth.

Answers

Answer:

x=25.1

Step-by-step explanation:

by using Pythagorean theorem, [tex]a^{2} +b^{2}=c^{2}[/tex] where c is the hypotenuse

[tex]18.15^{2}[/tex]= 329.4225

[tex]17.39^{2}[/tex]= 302.4121

since those two side lengths are the legs, the sum of the numbers is the length of the hypotenuse squared

therefore, 631.8356 (the sum) = [tex]c^{2}[/tex]

by taking the square root of 631.8356, you will get approx 25.1 for the hypotenuse (aka x)

group the data
1-5,6-10,11-15,16-20 to construct a tally chart and work out the frequency of each group

Answers

To construct a tally chart for the groups 1-5, 6-10, 11-15, 16-20 and work out the frequency of each group, we can do the following:

1-5: ||||| (5)
6-10: ||||| ||||| (10)
11-15: ||||| ||||| ||||| (15)
16-20: ||||| ||||| ||||| (15)

In the tally chart, each vertical line represents one data point. So, for example, the group 1-5 has 5 data points, which we represent with five vertical lines (|||||).

To work out the frequency of each group, we simply count the number of tally marks in each group. The frequency is the number of data points that fall within each group. Based on the above tally chart, we have:

1-5: 5
6-10: 10
11-15: 15
16-20: 15

Therefore, the frequency of each group is 5 for 1-5, 10 for 6-10, 15 for 11-15, and 15 for 16-20.

Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than 5 feathers next festival?

Answers

A reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.

How to estimate the probability of given data?

To estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to use the given data to calculate the mean and standard deviation of the number of feathers she has sold in the past festivals.

The mean, denoted by μ, is calculated by adding up all the number of feathers sold and dividing by the total number of festivals. So,

μ = (3 + 6 + 1 + 4 + 2 + 3 + 7 + 2) / 8 = 3.375

The standard deviation, denoted by σ, is a measure of how spread out the data is. It is calculated by first finding the variance, which is the average of the squared differences between each data point and the mean, and then taking the square root of the variance. So,

Variance = ((3-3.375)² + (6-3.375)²+ (1-3.375)² + (4-3.375)² + (2-3.375)² + (3-3.375)² + (7-3.375)² + (2-3.375)²) / 8 = 4.0898

σ = √(4.0898) = 2.022

Now, to estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to standardize the value by subtracting the mean and dividing by the standard deviation. So, let X be the number of feathers sold at the next festival, then,

Z = (X - μ) / σ

Let's say we want to estimate the probability that Patsy sells fewer than 2 feathers at the next festival. Then,

Z = (2 - 3.375) / 2.022 = -0.679

We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -0.679, which is approximately 0.2485.

Therefore, a reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.

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Correct question is "The number of feathers Patsy 3, 6, 1, 4, 2, 3, 7, 2 Peacock sold at each of the festivals this year. Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than feathers next festival? "

brainlist
show all steps nd i will make u brainlist

Answers

Step-by-step explanation:

There are multiple ways to do this,

  Here is ONE way

This is a RIGHT triangle, so you can use the Pythagorean theorem

  c^2 = a^2 + b^2    

      where c = hypotenuse ( long side) and a and b are the other two sides (legs)

So for this triangle :

15^2  =   x^2 + 12^2

15^2 - 12^2 = x^2

225  - 144 = x^2

81 = x^2

x = 9  cm  ( the missing side length)

can you give me a simple fast answer

Answers

The mapping that is a function will be B). X

How to explain the function

Every function got a set of input values called " Domain " and a set of respective output values as " Range"

And function worked as Function( Input value ) = Output value

There are basic rules for function :

1. There always exist output value for every single input value.

2. Every input value should have one and only one output value

For W : Rule 2 is violated

Here, Input value 6 result to two output value 2 and 4

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Find the nearest 10th the cylinder is 22 inches and 12.5 inches what is the lateral surface ?

Answers

Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².

What is surface area?

Surface area is the total area of the exposed surfaces of a three-dimensional object. It is measured in square units such as square centimeters (cm2) or square meters (m2). Surface area is an important concept in mathematics, science, and engineering, as it is the total area that determines properties such as friction, heat transfer, and fluid dynamics. For example, a larger surface area can increase the rate of heat transfer and allow for more efficient cooling. Similarly, a larger surface area can increase the friction between two objects, allowing them to grip better. Surface area is also important in chemistry, as it affects the amount of gas or liquid that can be absorbed or released by a given object.

The cylinder has a radius of 11 inches and a height of 12.5 inches. To find the lateral surface area of a cylinder, the formula used is A = 2πrℎ, where r is the radius and h is the height of the cylinder. After plugging in the values, the lateral surface area of the cylinder is 821.75 inches². Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².

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CAN I PLEASE GET HELP!

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The result of 10 trials expressed in percentage is 70%.

List out the 10 trials in table format.

We can utilize the random number table to produce 10 random numbers between 0 and 1 to approximate Nestor's performance in the ten races. If a number is less than or equal to 0.79, it is considered a "medal," and if it is larger than 0.79, it is considered a "no medal." This approach can be repeated ten times to get a sense of the range of possible outcomes.

For ten trials, we get the following results using the random number table shown below:

To estimate the likelihood that Nestor will win at least six of the following ten races, we count how many trials resulted in six or more medals. Seven of the ten trials resulted in six or more medals. As a result, we estimate the likelihood to be 7/10, or 70%.

The likelihood is 70% when expressed as a percentage.

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how do i solve this question 4

Answers

A system of equations that model the situation are e = a - 12 and a + e = 100.

The number of tickets Alberto won is 56 tickets.

The number of tickets Elian won is 44 tickets.

How to determine the number of each type of tickets won?

In order to write a system of linear equations to describe this situation, we would assign variables to the number of tickets Alberto won and number of tickets Elian won, and then translate the word problem into an algebraic equation as follows:

Let the variable a represent the number of tickets Alberto won.Let the variable e represent the number of tickets Elian won.

Since Alberto won 12 tickets less than Elian, a linear equation that models this situation is given by:

e = a - 12     .....equation 1.

Additionally, when they put their tickets together they have exactly 100 tickets;

a + e = 100     .....equation 2.

By solving the system of linear equations simultaneously, we have:

a + a - 12 = 100

2a = 112

a = 112/2

a = 56 tickets.

For the number of tickets (e) Elian won, we have:

e = a - 12

e = 56 - 12

e = 44 tickets.

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4/5 x 2 5/12 =?

Needs answered asap

Answers

The answer for 4/5 x 2 5/12 would be 29 over 15

3. A sporting goods store received an order of 64 baseball caps, of which 16 were green. If 1 (1 point)
of the 64 caps is selected at random, what is the probability it will not be green?
25%
75%
80%
50%

Answers

The answer is option (b) 75%.

What is Probability?

Probability is a measure of the likelihood that a particular event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of ways the event can occur by the total number of possible outcomes.

The probability of selecting a non-green cap is the number of non-green caps divided by the total number of caps:

P(non-green) = 48/64 = 3/4 = 0.75

Therefore, the probability that a randomly selected cap will not be green is 0.75 or 75%.

So the answer is option (b) 75%.

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When the function f(x) is divided by 3x + 1, the quotient is 3x² − 4x − 1
and the remainder is -10. Find the function f(x) and write the result in
standard form.

Answers

The function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

When f(x) is divided by 3x + 1, the quotient is 3x² - 4x - 1 and the remainder is -10. We can use polynomial long division to write f(x) in the form:

f(x) = (3x² - 4x - 1)(3x + 1) - 10

Multiplying out the right side gives:

f(x) = 9x³ - 7x² - 13x - 11

Therefore, the function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.

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Choose the word that makes this sentence true.

A square is ____ a rectangle.

Answers

Answer: the same as or equal to

Step-by-step explanation: The shapes are the same one's just stretched

Answer:

A square is a special kind of a rectangle

Step-by-step explanation:

Every Square is a rectangle but not every rectangle is a square.

Triangle PQR has vertex coordinates at P(4, 0), Q(4, 3), R(5, 1). If the triangle is translated so that Q′(4, −5), determine the translation direction and number of units.

8 units down
8 units up
8 units to the right
8 units to the left

Answers

Answer:

To determine the translation direction and number of units, we need to find the vector that connects Q to Q', and then determine the magnitude and direction of that vector.

The vector that connects Q to Q' can be found by subtracting the coordinates of Q from the coordinates of Q':

Q' - Q = (4, -5) - (4, 3) = (0, -8)

This vector indicates a translation 8 units downwards, in the negative y direction. Therefore, the translation direction is downwards and the number of units is 8.

So the correct answer is: 8 units down.

Final answer:

Triangle PQR was translated 8 units down.

Explanation:

In mathematics, particularly in the field of geometry, a translation refers to moving each point in a shape or a figure to a different position by sliding it to a certain direction for a fixed number of spaces. Each point is moved the same distance and in the same direction.

In the case of your Triangle PQR, the Q point moves from (4, 3) to the new coordinate Q'(4, -5). The x-coordinate in both points remains at 4. Hence, there's no left or right movement. But the y-coordinate changes from 3 to -5. This indicates a downward movement. The distance between 3 and -5 on the number line is 8 units. Therefore, the triangle was translated 8 units down.

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im stuck on this need a bit of help

Answers

The author of the poem, "Heritage," is the Jamaican-American poet, Claude McKay. Based on the poem, it is clear that he is nostalgic for the fruits and landscapes of Jamaica.

How to explain the poem

Here is an acrostic list of some of the things he might be nostalgic for:

J - Joyful memories of fruit-trees laden with bananas, cocoa, and alligator pears

A - Awe-inspiring mystical blue skies over the hills

M - Memories of dewy dawns

A - Alligator pears and avocados, also known as butter pears, grown in Jamaica

I - Images of low-singing rills, small streams or brooks

C - Crisp tangerines,

A - Appreciation for the highest prize at parish fairs, which celebrates the bountiful harvests of Jamaica

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PLEASE HELP ME
I’LL GIVE YOU BRAINLIEST

Answers

The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.

How to explain the graph

The key features of the graph of the profit function are the following:

The degree of the polynomial function is 3, which means that the graph is a cubic curve.

The coefficient of the leading term is negative (-4), which means that the graph opens downwards.

The coefficient of the quadratic term is positive (32), which means that the graph is concave up.

The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.

It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:

P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78

Therefore, the maximum profit that the company can make is $23,780.

In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.

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Hi! Please help!

The line plots represent data collected on the travel times to school from two groups of 15 students. Labeled- Bus 47 Travel Times Numbers on the line plot are 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28. One dot is above the number 4. One dot is above the number 6. Two dots are above the number 10. Two dots are above the number 12. One dot is above the number 14. Three dots above the number 16. Two dots above 18. Two dots above 22. One dot above 28.

Second bus- Bus 14 Travel Times
Same numbers as first line plot. Two dots above 8. One dot above 10. Four dots above 12. Two dots above 14. One dot above 16. Three dots above 18. One dot above 20. One dot above 28.

Compare the data and use the correct measure of center to determine which bud typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 47, with a median of 16
Bus 14, with a median of 14
Bus 47, with a mean of 16
Bus 14, with a mean of 14

Answers

Answer:

(A) Bus 47, with a median of 16.

Step-by-step explanation:

To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are small and discrete, we can use either the median or the mean as a measure of center.

For Bus 47, the median is the middle value, which is 16.For Bus 14, the median is also the middle value, which is 14.

Comparing the medians, we can see that Bus 47 has a higher median, which suggests that it typically has a faster travel time than Bus 14.

Therefore, the answer is (A) Bus 47, with a median of 16.

1 County fair admission costs $5. Each game ticket costs $2. Arianna has $21 to
spend at the fair. She writes the inequality 5 + 2g ≤ 21 to represent how many
game tickets, g, she can purchase at the fair. Which values in the set {3, 8, 10, 13)
are solutions of the inequality? Show your work.

Answers

Answer:

3 and 8

Step-by-step explanation:

Ariana has = $21

Fix cost = $5

Each game ticket costs= $2.

Ticket number=g

Then,

[tex]$5 + 2g \leq 21$\\$$2g \leq 21-5$$\\$$g \leq 8$$[/tex]

then, the solution set is {0,1,2,3,4,5,6,7,8}

Plot points between and beyond each​ x-intercept and vertical asymptote. Find the value of the function at the given value of x.
​f(x)= 2/ x^2+3x-10

Answers

the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).

What is function?

a function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

To find the x-intercepts, we set the numerator of the function equal to zero:

[tex]2 / (x^2 + 3x - 10) = 0[/tex]

This is only true if the numerator is equal to zero, so:

2 = 0

This is not possible, so the function has no x-intercepts.

To find the vertical asymptotes, we look for values of x that make the denominator equal to zero:

[tex]x^2 + 3x - 10 = 0[/tex]

We can factor the quadratic as:

(x + 5)(x - 2) = 0

This means that the function has vertical asymptotes at x = -5 and x = 2.

Now, let's plot some points between and beyond each x-intercept and vertical asymptote:

When x = -6, f(x) = 2 / (-6)² + 3(-6) - 10 = -1/2

When x = -4, f(x) = 2 / (-4)² + 3(-4) - 10 = 1/2

When x = 0, f(x) = 2 / (0)² + 3(0) - 10 = -1/5

When x = 3, f(x) = 2 / (3)² + 3(3) - 10 = 1/2

When x = 4, f(x) = 2 / (4)² + 3(4) - 10 = -1/2

When x = 6, f(x) = 2 / (6)² + 3(6) - 10 = 1/5

Therefore, the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).

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How many cuts are necessary to cut the strip of paper until it is approximately 10 nanometers long?

the strip is 10cm in length and 1cm in width​

Answers

Answer: Assuming that we can make each cut with perfect precision and that the thickness of each cut is negligible, we can estimate the number of cuts needed to reduce the strip of paper to approximately 10 nanometers in length as follows:

Convert 10 centimeters to nanometers:

10 cm = 10,000,000,000 nanometers

Divide the length of the strip by the desired final length:

10,000,000,000 / 10 = 1,000,000,000

Therefore, approximately 1 billion cuts would be needed to reduce the strip of paper to approximately 10 nanometers in length. However, this is a theoretical estimate and in reality, it may not be possible to make cuts with such precision or to reduce the strip of paper to such a small length due to physical limitations.

Step-by-step explanation:

If 7/2 litre petrol cost 2163/8 find the cost of 4 litre petrol

Answers

The cost of 4 liters of petrol is 618.

To find the cost of 4 liters of petrol, we can use a proportion. Which means we will equate the two sides of equation having proportions.

We know that 7/2 liters of petrol cost 2163/8. We can write this as,

(7/2) / (2163/8) = 4 / x

where x is the cost of 4 liters of petrol.

To solve for x, we can cross-multiply,

(7/2) * x = (2163/8) * 4

Simplifying both sides, we get,

x = (2163/8) * 4 * (2/7)

x = 309 * 2

x = 618

Therefore, 4 liters of petrol is 618 in price according to question.

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Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose six integers are chosen from A. Must there be two integers whose sum is 11

Answers

When six integers are chosen from the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there must be at least one pair of integers that adds up to 11. This can be proven using a proof by contradiction.

To solve this problem, we can use a proof by contradiction. We assume that there are six integers chosen from A such that no two integers add up to 11.

If there is no pair of integers in the six chosen that sum up to 11, then we can consider the pairs of integers (1,10), (2,9), (3,8), (4,7), and (5,6). These are the only possible pairs of integers in A that add up to 11.

However, since there are five pairs and we can choose at most one integer from each pair, we can choose at most five integers in total. This is a contradiction since we were asked to choose six integers from A. Therefore, our assumption that there are no pairs of integers that add up to 11 is false.

Hence, we conclude that there must be at least one pair of integers among the six chosen that adds up to 11.

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What percent of U.S. vice presidents were at least 60 years old when they took office? Explain how you found your answer.

(Please help asap!!)

Answers

The percent of U.S. vice presidents were at least 60 years old when they took office is 26.5%

How to determine the percentage?

It may interest you that US America has had about 49 vice presidents till date

Out of this 49 vice presidents,

13 of them were more than 60 years at the beginning of their office

This implies that 13/49 * 100 = 26.53%

In conclusion the percentage of US America vice presidents is 26.53%

for clarity, read the article below.

Americans over 60 hold many of the highest offices in the U.S. government. An analysis of the current 117th Congress revealed that it’s the oldest, on average, of any Congress in at least the past 20 years. The average age of U.S.

Presidents are also being elected at older ages than in the past; at 70, President Donald Trump was the oldest to take office, though his record was quickly surpassed by his successor, President Joe Biden, who took office at age 78.

As the average age of elected officials has risen, some have questioned whether we should restrict individuals over a certain age from holding office. In 2019, former President Jimmy Carter expressed concern over the age of the presidential candidates in the 2020 election, stating:

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Directions: find the value of the hypotenuse for each of the following right triangles.

1. a = 5, b = 8
2. a = 6, b = 7
3. a = 4, b = 9
4. a = 3, b = 12
5. a = 11, b = 10
6. a = 8, b = 7
7. a = 9, b = 4
8. a = 7, b = 11
9. a = 13, b = 15
10. a = 5, b = 6

Answers

By Pythagoras Hypotenuse for 1.   9.43 , 2.   9.22 , 3.    9.85 , 4.   12.37, 5.   14.87 , 6.   10.63

7. 9.85 ,   8. 13.04 ,  9. 19.85 ,  10.    7.81

Theorem of Pythagoras defined?

The Pythagorean theorem, commonly referred to as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. It declares that the hypotenuse's square, which is the side that is opposite the right angle, is equal to the sum of the squares of the other two sides. In other words, if the hypotenuse is length c and the legs of a right triangle are lengths a and b, then a² + b² = c².

The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the other two sides, can be used to determine the hypotenuse of a right triangle.

This theorem allows us to calculate the hypotenuse value for each of the right triangles presented as follows:

1. a = 5, b = 8

  c = √(a² + b²) = √(5² + 8²) = √(25 + 64) =√(89) ≈ 9.43

2. a = 6, b = 7

  c = √(a² + b²) = √(6² + 7²) = √(36 + 49) = √(85) ≈ 9.22

3. a = 4, b = 9

  c = √(a² + b²) = √(4² + 9²) = √16 + 81) = √(97) ≈ 9.85

4. a = 3, b = 12

  c =√(a² + b²) = √(3² + 12²) = √(9 + 144) = √(153) ≈ 12.37

5. a = 11, b = 10

  c = sqrt(a^2 + b^2) = sqrt(11^2 + 10^2) = sqrt(121 + 100) = sqrt(221) ≈ 14.87

6. a = 8, b = 7

  c = √(a² + b²)= √(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63

7. a = 9, b = 4

  c =√(a² + b²)=√(9² + 4²) = √(81 + 16) = √(97) ≈ 9.85

8. a = 7, b = 11

  c = √(a² + b²)= √(7² + 11²) = √(49 + 121) ≈√(170) ≈ 13.04

9. a=13,b=15

  c=√(a² + b²)=√((13²)+(15²))=√((169)+(225))=√(394))≈19.85

10.a=5,b=6

  c=√(a²+b²)=sqrt((5²)+(6²))=s√((25)+(36))=√(61))≈7.81

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If you were to use the substitution method to solve the following
system, choose the new equation after the expression equivalent to x
from the second equation is substituted into the first equation.
3x + 2y = -21
x-3y = 4 (6 points)

Answers

Answer:

Step-by-step explanation:

Making x the subject in the second equation gives:

x = 4+3y

substituting x = 4 +3y into the first one gives:

3(4 + 3y) + 2y = -21

12 + 9y +2y = -21

11y = -33

y = -3

PLEASE HELP AND EXPLAIN AND SHOW WORK OF HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST

Answers

Answer: 5 & 12

Step-by-step explanation: The formula for the Pythagorean theorem is a^2 + b^2 = c^2. So if 5^2 + 12^ = 13^, 5 & 12 must be the side lengths that form the right angle.

An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1850 feet apart. As the airplane
passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane,
as indicated in the figure. If A=25°, and B=25°, how high is the airplane?

Answers

Answer: We can use trigonometry to solve this problem. Let's call the height of the airplane H, and let's call the distance from observer X to the airplane D. Then the distance from observer Y to the airplane is L - D.

From the point of view of observer X, we can write:

tan(A) = H / D

tan(25°) = H / D

From the point of view of observer Y, we can write:

tan(B) = H / (L - D)

tan(25°) = H / (L - D)

We now have two equations with two unknowns (H and D). We can solve for one of the unknowns in terms of the other, and then substitute that expression into the other equation to eliminate one of the unknowns.

Let's solve the first equation for D:

D = H / tan(25°)

Substituting this expression for D into the second equation, we get:

tan(25°) = H / (L - H / tan(25°))

Multiplying both sides by (L - H / tan(25°)), we get:

tan(25°) (L - H / tan(25°)) = H

Expanding the left-hand side, we get:

tan(25°) L - H = H tan^2(25°)

Adding H to both sides, we get:

tan(25°) L = H (1 + tan^2(25°))

Dividing both sides by (1 + tan^2(25°)), we get:

H = (tan(25°) L) / (1 + tan^2(25°))

Now we can substitute this expression for H into the equation D = H / tan(25°) to get:

D = ((tan(25°) L) / (1 + tan^2(25°))) / tan(25°)

Simplifying, we get:

D = L / (1 + tan^2(25°))

Now that we know the distance D, we can use the equation tan(A) = H / D to find H:

tan(25°) = H / D

H = D tan(25°)

Substituting D = L / (1 + tan^2(25°)), we get:

H = (L / (1 + tan^2(25°))) tan(25°)

Plugging in the given values L = 1850 feet and A = B = 25°, we get:

H = (1850 / (1 + tan^2(25°))) tan(25°)

H ≈ 697.3 feet

Therefore, the airplane is about 697.3 feet high.

Step-by-step explanation:

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