How many times larger is 1.71 x 10^7 than 9.98 x 10^6?

Answer:

"sixty-three hundredths of a Kilometer"

Step-by-step explanation:

Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"

Answer:

1. Diego has to move 2 places back to be 25th .

2.a. Jade is right. She'll get 2 prizes .

2.b.The blueberry muffin and the carrot cake

Step-by-step explanation:

[Every fifth customer will get a free bagel.]`-------

This means that anyone on the line who is a multiple of 5 will get a free bagel. Example-  5th customer,10th customer, or the 15th customer and so on..

[Every ninth customer will get a free blueberry muffin]--------

This means that anyone on line who is a multiple of 9 will get a free blueberry muffin. Example- the 9th customer, 18th customer etc...

[Every 12th customer will get a free slice of carrot cake. ]----------

This means that anyone on line who is a multiple of 12 will get a free carrot cake. Example- the 12th customer, 24th customer, 36th customer etc...

THEREFORE, (ANSWERS TO THE QUESTION)

1. Yes, he is right  in order to get the prize. To get at least one prize, he should go two places behind and become the 25th customer {since he s a multiple of 5}.He will get a free bagel.

2.a. Yes, Jade will get a prize. She can get a free blueberry muffin and a free slice of carrot cake .

2.b. Yes, it is possible for Jade to win more than one prize because she is the 36th customer and 36 is a multiple of both 9 and 12

\(\\\)

Answer:

3.5 Points

Step-by-step explanation:

Change means how many more points did you gain. 6.4 - 2.9= 3.5

The stocks overall change in points over the two days is 3.5 points.

Therefore,  The pdf of e^(−x) for x ∼ expo(1) is f(x) = e^(−x) for x ≥ 0. The pdf is a decreasing function that approaches zero as x increases.

The probability density function (pdf) of an exponential distribution with parameter λ is f(x) = λe^(−λx) for x ≥ 0. In this case, λ = 1, so the pdf of e^(−x) for x ∼ expo(1) is f(x) = e^(−x) for x ≥ 0. This means that the probability of observing a value of e^(−x) between a and b is given by the integral of e^(−x) from a to b, which is equal to e^(−a) − e^(−b). The graph of this pdf shows that it is a decreasing function that approaches zero as x increases.

Therefore,  The pdf of e^(−x) for x ∼ expo(1) is f(x) = e^(−x) for x ≥ 0. The pdf is a decreasing function that approaches zero as x increases.

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Answer: 36 degrees

Step-by-step explanation:

PART A:

To find the rate of change, put change in y over change in x. In order to first find the changes, you must subtract two y values from each other and two x values from each other, like this:

Change in y = 20-10

Change in x = 4-2

Then you can put these over each other:

20-10/4-2

Then simplify

20-10/4-2 = 10/2 = 5/1 = 5

So, this means the rate of change is 5. $5 per bushel.

If you also need part B it would be helpful to see the other chart because it's hard to understand in the writing you included. :) Comment and let me know if you post it so I can help you out!

Part A: 7 dollars  

- The graph shows that 2 bushels is 14 dollars,  because the graph has a straight line, the rate remains constant you must divide the sides by two to find the amount for one bushel which would be 7 dollars.

- And to double check you would divide 28 by 4, 42 by 6, 56 by 8, 70 by 10, 84 by 11, and 98 by 12. they all equals 7 dollars So, the equation would be y = 7x.

- 7 can be known as the slope and  rate of change.

Part B:2 dollars

- The years before show 2 bushes was 10 dollars

-so you would divide 10 by two you would get five  To double check you would do the same thing with 20 by 4, 30 by 6 and 40 by 8, and they all equal 5 dollars.

-if you use this answer be sure to reword it so you dont get copy write and integrity. have a great day or night.

The function which will represent the given Translation will be T(x, y) = (x + 3, y - 2).

Translation may be defined as the shifting of the curve on a graph or shifting of the plotted points on a graph. The translation can be horizontal or vertical. In horizontal direction it can be shifted either left or right and in vertical direction it can be shifted either up or down. Horizontal translation always occurs on the x axis and vertical translation always occurs on the y axis. A function may be defined as an expression in which for input variable x there is output variable y. We need to translate a function T(x, y) 3 units right so the new coordinate will be T(x + 3, y). Now, translation occurs 2 units down. so, new coordinates will be T(x + 3, y -2) which is the required function.

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Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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we start by opening the brackets so it will be -25 plus 15 v is equals to 115. negative times a negative is a positive so -5 times -3 we we have gotten positive 15v there I hope you understood so our new equation is -25 + 15v is equals to 115 collect the like terms 15v is equals to 115 + 25 15 v is equals to 140 divide both sides by 15 so v is equals to 9 and 1/3

If Mirka is 5 years old, her parents start to give her pocket money of 50p per week , then the amount of pocket money does Mirka get in the first year is £26 .

the amount that Mirka gets per week is = 50p ;

Age of Mirka is = 5 years ;

When Mirka is 5 years old, she starts to receive 50p per week in pocket money. On her birthday, her parents increase her pocket money by 50p.

that means ;

So, for the first year, the pocket money will be 50p per week for 52 weeks (1 year),

Pocket money in the first year = 50p × 52 weeks = £26 .

Therefore , Mirka will get £26 in the first year of her birthday .

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The additive inverse of a number gives zero. The additive inverse of the complex number -8+3i is 8-3i.

The additive inverse of a number is the other number which when added to the initial number gives the output as zero.

As we know about the additive inverse, therefore, we need a number that will return zero when added to the complex number.

The additive inverse of the complex number -8+3i will be,

\((-8+3i) + (8-3i) = 0\)

Thus, the additive inverse of the complex number -8+3i is 8-3i.

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Answer:

8-3i

Step-by-step explanation:

got it right

Given the provided information, if a woman over 35 tests positive for ovarian cancer, the probability that she actually has cancer is approximately 1.96%.

To determine the probability that a woman over 35 actually has ovarian cancer given a positive test result, we can create a contingency table and use conditional probability. Let's consider a hypothetical sample of 100,000 women:

Out of 100,000 women, 1 in every 2,500 (or 40 out of 100,000) actually has ovarian cancer. Since the test has a 0% rate of false negatives, all the women with ovarian cancer will test positive.

The test also has a 5% rate of false positives. This means that out of the remaining 99,960 women who do not have ovarian cancer, approximately 5% (or 4,998) will test positive incorrectly.

Therefore, out of a total of 5,038 positive test results (40 true positives + 4,998 false positives), only 40 are true positives for ovarian cancer. The probability that a woman who tests positive actually has ovarian cancer can be calculated as the ratio of true positives to the total positive tests:

Probability = (True Positives) / (Total Positive Tests) = 40 / 5,038 ≈ 0.00795 ≈ 0.795%

Thus, the probability that a woman over 35 actually has ovarian cancer given a positive test result is approximately 1.96%. This calculation highlights the importance of considering both the prevalence of the disease and the accuracy of the test in interpreting the results correctly.

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The complete solution to the inhomogeneous recurrence tₙ + 3tₙ₋₁ + 2tₙ₋₂ = 3ⁿ consists of the homogeneous solution (combinations of the roots) and the particular solution: tₙ = A(-2)ⁿ + B(-1)ⁿ + tₚ

To find the characteristic polynomial for the given inhomogeneous recurrence, we first need to solve the associated homogeneous recurrence, which is obtained by setting the right-hand side (RHS) equal to zero:

tₙ + 3tₙ₋₁ + 2tₙ₋₂ = 0

The characteristic polynomial is derived by replacing each term in the homogeneous recurrence with a variable, let's say r:

r² + 3r + 2 = 0

Now we can solve this quadratic equation to find the roots:

(r + 2)(r + 1) = 0

This equation has two roots:

r₁ = -2

r₂ = -1

The roots of the characteristic polynomial represent the solutions to the homogeneous recurrence. Since the equation is second-order, there are two distinct roots.

Next, we need to consider the inhomogeneous part of the recurrence, which is 3ⁿ. The inhomogeneous part does not affect the roots of the characteristic polynomial but instead contributes to the particular solution.

Since the inhomogeneous part can be parsed as 1 * 3ⁿ, we have p(n) = 1 and b = 3.

The characteristic polynomial remains unchanged:

(r + 2)(r + 1) = 0

The roots of the characteristic polynomial are:

r₁ = -2 (with multiplicity 1)

r₂ = -1 (with multiplicity 1)

These roots represent the solutions to the homogeneous recurrence.

To find the particular solution, we use the fact that b/p(n) = 3/1 = 3. Since p(n) = 1, the particular solution is a constant, which we can denote as tₚ.

Therefore, the complete solution to the inhomogeneous recurrence tₙ + 3tₙ₋₁ + 2tₙ₋₂ = 3ⁿ consists of the homogeneous solution (combinations of the roots) and the particular solution:

tₙ = A(-2)ⁿ + B(-1)ⁿ + tₚ

where A and B are constants determined by initial conditions, and tₚ is the particular solution.

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Answer:

b = 9√5 (see below)

Step-by-step explanation:

Using the Pythagorean Theorem, you can find the missing side. The two sides connect to the right angle are the legs, and the sloping side across from the right angle is the hypotenuse.

We know that:

a² + b² = c²

—where a and b are legs and c is the hypotenuse.

Plug in the known values:

a² + b² = c²

18² + b² = 27²

324 + b² = 729

b² = 405

√b² = √405

b = √81 √5

b = 9√5

Answer:

20

Step-by-step explanation:

A^2+B^2=C^2

18^2+B^2= 27^2

324+B^2= 729

-324           -324

        B^2  = 405

         B= \(\sqrt{405)\\\)

B=20

Answer:

B and D

Step-by-step explanation:

check where the points are. If they are in shaded triangle they are solutions

The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).

The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:

kx + 2y = 3   -- (1)

3x + 6y = 10  -- (2)

To have a unique solution, the determinant of the coefficients of x and y must not be zero.

The determinant of the coefficient matrix for the system is:

D = | k   2 |

       | 3   6 |

By calculating the determinant, we have:

D = (k * 6) - (2 * 3)

D = 6k - 6

For the system to have a unique solution, the determinant D must not equal zero.

6k - 6 ≠ 0

Simplifying the inequality:

6k ≠ 6

Dividing both sides by 6:

k ≠ 1

Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).

In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.

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Step-by-step explanation:

a) 1.16× 10^-6

standard form should be less than 10. therefore, count decimal places from where the decimal point is located to the right until you reach a number less than 10 ....count the number of shifts in the above is 6 shifts to the right. when moving to the right, power will be negative.(-6)

1.157/1.16 ×10^-6

b) 6.79 × 10^10

67890000000....count till a number less than 10.there will be 10 shifts to the left. the 10 will be your power,(positive) since u r moving to the left exponent is positive

6.789/6.79 × 10^10

\(1.157 \times {10}^{ - 6} \)

\(6.79 \times {10}^{10} \)

Step-by-step explanation:

\(mark \: me \: as \: brainliest\)

the mathematical property demonstrated is associative property (3rd option)

Given:

To find:

the mathematical property

The property with the same arrangement as the given expression is associative property as it has to do with grouping.

Hence, the mathematical property demonstarted is associative property (3rd option)

Outcomes where a green ball is drawn on the third draw, given at least one red ball is drawn, are RBG, GBR, GRR, RRG, and GRG.



Let's analyze each option and identify the outcomes where a green ball is drawn on the third draw, given at least one red ball is drawn:

A. RRR B. RBG In option A, all three balls are red, so a green ball cannot be drawn on the third draw. In option B, there is a red ball in the first draw, so it's possible to draw a green ball on the third draw.

C. GBR D. BRG In option C, the first ball drawn is green, so a green ball is already drawn on the first draw, making it possible to draw a green ball on the third draw. In option D, no red ball is drawn, so it's not possible to draw a green ball on the third draw given the condition.

E. GRR OF. RRG G. GRG In options E, F, and G, there is at least one red ball drawn, allowing the possibility of drawing a green ball on the third draw.

H. RYB  In option H, there are no red balls drawn, so it's not possible to draw a green ball on the third draw given the condition.

Therefore, the outcomes where a green ball is drawn on the third draw given at least one red ball is drawn are: RBG, GBR, GRR, RRG, and GRG.

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Answer: 1- 2:3

2- 4:7

3- draw 5 of something, then one of something else

4- same as 3

5- 10, 3, and 20

6- 14, 21, and 4

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Area 1 = 3 x 3 = 9 m²

Area 2 = 4 x 4 = 16 m²

Area 3 = 5 x 5 = 25 m²

The areas are 16 unit², 9 unit² and 25 unit² respectively.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. Square units are used to measure it as well.

As per the given diagram:

We are given 3 squares, and we have to find out the area of each square.

The area of a square is given by a², where a is the length of the side of the square.

For area of the square with length of the side, 4 units.

A = (4)² unit² = 16 unit²

For area of the square with length of the side, 3 units.

A = (3)² unit² = 9 unit²

For area of the square with length of the side, 5 units.

A = (5)² unit² = 25 unit²

The areas are 16 unit², 9 unit² and 25 unit² respectively.

Hence, The areas are 16 unit², 9 unit² and 25 unit² respectively.

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A. The probability that exactly 5 adults meet the criteria for hypertension is approximately 0.0916 or 9.16%.

B. The probability that none of the adults meet the criteria for hypertension is approximately 0.0255 or 2.55%.

C.  The probability that less than or equal to 7 adults meet the criteria for hypertension is approximately 0.9999 or 99.99%.

To calculate the probabilities,

Use the binomial probability formula.

The binomial probability formula is,

P(X = k) = C (n ,k) × \(p^k\) × \((1 - p)^{(n - k)\)

Where,

P(X = k) is the probability of exactly k successes

n is the number of trials

k is the number of successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

C(n, k) represents the binomial coefficient,

which can be calculated as n! / (k! × (n - k)!)

A. To calculate the probability that exactly 5 adults meet the criteria for hypertension,

n = 15 (number of adults assessed)

k = 5 (number of adults meeting the criteria)

p = 0.30 (probability of meeting the criteria)

A. Probability that exactly 5 adults meet the criteria for hypertension,

n = 15

k = 5

p = 0.30

P(X = 5) = C( 15, 5) × 0.30⁵ × (1 - 0.30)¹⁵⁻⁵

Using the binomial coefficient formula C (n ,k) = n! / (k! × (n - k)!), we have,

(¹⁵C₅) = 15! / (5! × (15 - 5)!) = 3003

P(X = 5) = 3003 × 0.30⁵ × 0.70¹⁰

Calculating the probability,

P(X = 5) = 0.0916 (approximately)

B. Probability that none of the adults meet the criteria for hypertension,

n = 15

k = 0

p = 0.30

P(X = 0) = (¹⁵C₀) × 0.30⁰× (1 - 0.30)¹⁵⁻⁰

(¹⁵C₀) = 1 (since choosing 0 from any set results in 1)

P(X = 0) = 1 × 0.30⁰ × 0.70¹⁵

Calculating the probability,

P(X = 0) = 0.0255 (approximately)

C. Probability that less than or equal to 7 adults meet the criteria for hypertension,

n = 15

k = 0, 1, 2, 3, 4, 5, 6, 7

p = 0.30

P(X ≤7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Calculate each individual probability using the binomial probability formula and sum them up.

P(X ≤7) = (¹⁵C₀) × 0.30⁰ × 0.70¹⁵ + ¹⁵C₁× 0.30¹× 0.70¹⁴+ (¹⁵C₂) × 0.30²× 0.70¹³ + (¹⁵C₃) × 0.30³ × 0.70¹² + (¹⁵C₄) ×0.30⁴ × 0.70¹¹ + (¹⁵C₅) × 0.30⁵× 0.70¹⁰ + (¹⁵C₆) × 0.30⁶× 0.70⁹ + (¹⁵C₇) × 0.30⁷ ×0.70⁸

Calculating the probability,

P(X ≤ 7) ≈ 0.9999

Therefore, the probabilities for different conditions are,

A. For exactly 5 adults is 0.0916 or 9.16%.

B. For none of the adults is 0.0255 or 2.55%.

C. less than or equal to 7 adults is 0.9999 or 99.99%.

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a) The probability of a very good poker player earning a profit (more than $0) after playing 40 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31). b) The proportion of the time a very good poker player can expect to earn at least $500 after playing 100 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31).

To compute these probabilities, we need to make some assumptions and use probability distribution calculations based on the given information.

a) To determine the probability of a profit after playing 40 hands, we can use the concept of the normal distribution. We need to calculate the z-score using the formula: z = (x - μ) / σ, where x is the desired profit, μ is the expected profit per hand, and σ is the standard deviation. In this case, x = $0, μ = $1, and σ = $31.

Once we have the z-score, we can use a standard normal distribution table or calculator to find the corresponding probability.

b) Similarly, to find the proportion of the time a player can expect to earn at least $500 after playing 100 hands, we need to calculate the z-score for x = $500, using the same formula as in part (a). Then, we can use the standard normal distribution table or calculator to find the corresponding proportion.

c) To determine the probability of earning a profit during a 14-hour session, we need to calculate the number of hands played, which is 20 hands per hour multiplied by 14 hours. Let's denote it as N. Then, we can calculate the mean profit for the 14-hour session by multiplying the expected profit per hand ($1) by N.

The standard deviation for the session can be calculated by multiplying the standard deviation per hand ($31) by the square root of N. Finally, we can use the normal distribution and the same z-score calculation as in part (a) to find the probability.

Please note that the above calculations assume that the profits from each hand are independent and follow a normal distribution. Real poker outcomes may deviate from these assumptions.

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Answer:6/5x=7/x+2 Two solutions were found : x =(10-√940)/12=(5-√ 235 )/6= -1.722 x =(10+√940)/12=(5+√ 235 )/6= 3.388 Rearrange: Rearrange the equation by subtracting what is to the right

Step-by-step explanation:

Answer: 120000

Step-by-step explanation:

To prove the equation 1 · 1! + 2 · 2! + ··+ n · n! = (n + 1)! - 1 for a positive integer n, we can use mathematical induction. The base case is n = 1, where the equation holds true.

Explanation:

We start with the base case n = 1:

1 · 1! = (1 + 1)! - 1

1 = 2 - 1

1 = 1

The equation holds true for n = 1.

Next, we assume that the equation holds for some positive integer k:

1 · 1! + 2 · 2! + ··+ k · k! = (k + 1)! - 1

Now, we need to prove that the equation holds for k + 1:

1 · 1! + 2 · 2! + ··+ k · k! + (k + 1) · (k + 1)! = ((k + 1) + 1)! - 1

Simplifying the left side of the equation, we have:

(k + 1)! + (k + 1) · (k + 1)! = (k + 2)! - 1

Factoring out (k + 1)! from the left side, we get:

(k + 1)! (1 + (k + 1)) = (k + 2)! - 1

Simplifying further, we have:

(k + 2)! = (k + 2)! - 1

Since the equation holds true for k, it also holds true for k + 1.

By using mathematical induction, we have proven that 1 · 1! + 2 · 2! + ··+ n · n! = (n + 1)! - 1 for all positive integers n.

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