A lottery has a very large number of tickets, one in every 500 of which entitles the purchaser to prize. Find the minimum number of tickets the agent must sell to have 95% chance of selling at least one prize winning ticket. ​

The required length is 11 units for the given triangle.

The sine rule defines the side length ratios of triangles to their opposing angles. This proportion is true for all three sides and opposing angles.

a/sinA = b/sinB = c/sinC

The triangle is given in the question, as follows:

In ΔABC, ∠A=120°, ∠B=37°, and c = 5 units

Here, ∠C= 180° - 120° - 37° = 23.

We have to determine the length of a.

As per the sine rule, the required solution would be as:

a/sin∠A = c/sin∠C

Substitute the known values and we get

a/sin 120° = 5/sin 23°

a = (18/sin 1240°) × sin 23°

k ≈ 11

Thus, the length of c is 11 units.

Hence, the number that belongs in the green box is 11.

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Answer:

1×1=1

2×2=4

3×3=9

4×4=16

The equations to have infinite solutions and no solutions are 3x + 5 = 3x + 5 and 3x + 5 = 3x + 6

Infinite many solutions

From the question, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have infinite many solutions, both sides must be equal

So, we have

[1] x + 2x + 5 = [3] x+ [5]

Evaluate

3x + 5 = 3x + 5

No solution

Here, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have no solutions, both sides must be unequal

So, we have

[1] x + 2x + 5 = [3] x+ [6]

Evaluate

3x + 5 = 3x + 6

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BIVE & is a company that provides a platform for businesses to connect with and engage with their customers.

The company was founded in 2015 by two entrepreneurs, and it has since raised over $10 million in funding. BIVE & offers a variety of features that allow businesses to create and manage their own social media profiles, as well as to track and measure their social media engagement. The company also offers a variety of tools that allow businesses to create and manage their own email marketing campaigns.

BIVE &'s employee data is not publicly available. However, the company has stated that it has over 50 employees. BIVE &'s products and services are similar to those offered by other social media marketing platforms, such as Hootsuite and Buffer. However, BIVE &'s platform is designed specifically for businesses that want to connect with and engage with their customers on a social level.

BIVE &'s main source of revenue is from its subscription fees. The company offers a variety of subscription plans, starting at $29 per month. BIVE & also offers a free trial of its platform.

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You answered 6,9 and 10,13. The correct answer is 6,9 and 7,13 to find the equation of the linear model.

(a) The two points you selected are (6,9) and (10,13). This is correct.

(b) To find the slope of the linear model, we can use the formula: slope = (change in y) / (change in x). By using the points (6,9) and (10,13), we have (13-9) / (10-6) = 4/4 = 1. So, the slope is indeed 1. This is correct.

(c) The equation of the linear model in point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6,9) as the point and 1 as the slope, we get y - 9 = 1(x - 6). This simplifies to y - 9 = x - 6. This is not the same as the equation you provided. It seems you made a mistake here.

(d) The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert the equation y - 9 = x - 6 to slope-intercept form, we can add 9 to both sides: y = x - 6 + 9, which simplifies to y = x + 3. This matches the equation you provided. So, this is correct.

(e) The equation for the least squares regression line is in the form y = bx + a, where b is the slope and a is the y-intercept. In this case, the slope is 1, and we need to find the y-intercept.

We can use the point (6,9) and the slope-intercept form equation y = x + 3 to find the y-intercept: 9 = 6 + 3. Solving this equation, we find that the y-intercept is 3.

Therefore, the equation for the least squares regression line is y = x + 3. This does not match the equation you provided. It seems you made a mistake here.

(f) Based on the correct equation from part (d) (y = x + 3), the correct equation for the least squares regression line is y = 1x + 3. When rounded to three decimal places, this would be y = 1.000x + 3.000.

The equation you provided (Y = 1.028x + 2.271) is slightly different, so it appears you made a mistake in the calculations or rounding.

To summarize, your answers in parts (a) and (b) are correct. However, there are mistakes in parts (c), (e), and (f). The corrected answers are:

(c) The equation of the linear model in point-slope form: y - 9 = x - 6.

(d) The slope-intercept form of the equation: y = x + 3.

(e) The equation for the least squares regression line: y = 1x + 3.

(f) When rounded to three decimal places, the equation is: y = 1.000x + 3.000.

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Vertical Angles

---Vertical angles are congruent and can often be found where two lines intersect and make an "X" shape.

The vertical angles in this figure are XAW and UAY.

Adjacent angles that are neither complementary nor supplementary

---Adjacent angles are angles that share a line and are, as a result, next to each other.

Two adjacent angles in this figure that are neither complementary nor supplementary are XAW and ZAY.

Supplementary Angles

---Supplementary angles form a straight line, or 180 degree angle.

The supplementary angles in this figure are XAW and WAU.

Complementary Angles

---Complementary angles form a right, or 90 degree angle.

The complementary angles in this figure are XAW and XAZ.

Hope this helps!

Step-by-step explanation:

See image

Answer:

18 more sessions

Step-by-step explanation:

Her goal is to practice 800 minutes.

She already did 175 minutes.

That means she has 800 - 175 = 625 minutes remaining, and she says that she will only practice in 35 minute sessions.

To determine the number of sessions she has left, just divide 625 by 35.

[tex]\frac{625}{35}[/tex]

= 17.85714

However, you can't have a portion of a session, as she only does 35 mins every session. Therfore, she must do 18 more sessions.

~~~Harsha~~~

The number of ways to choose the letters is given as follows:

First we must decide which formula to use, depending if the order matters, as follows:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P(n,x) = \frac{n!}{(n-x)!}[/tex]

Hence, if the order matters, the number of ways is given as follows:

P(3,2) = 3!/(3 - 2)! = 6.

The combination formula is given as follows:

[tex]C(n,x) = \frac{n!}x!{(n-x)!}[/tex]

Hence, if the order does not matter, the number of ways is given as follows:

C(3,2) = 3!/(2! x 1!) = 3.

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1) The translation made is 2 units up, 1 units left.

2) The translation made is 2 units right, 1 unit up.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Chess player moves a knight from the location (3,2) to (5,1) on a chessboard.

And, the player moves the knight from (5,1) to (6,3),

Since, Translation for (3,2) to (5,1|) is,

⇒ 2 units up, 1 units left.

And, Translation for (5,1) to (6,3) is,

⇒ 2 units right, 1 units up.

Hence, When a player moves a knight from the location (3, 2) to (5, 1) on a chessboard the translation made is 2 units up, 1 units left.

And, When the player moves the knight from (5, 1) to (6, 3), the translation made is 2 units right, 1 units up.

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Answer:

2816 ft^3

Step-by-step explanation:

Solution Given:

Radius(r)=8ft.

Height(h)=14 ft.

Now

To find the volume of a cylinder, you can use the formula:

[tex]\boxed{\bold{Volume = \pi * r^2 * h}}[/tex]

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

[tex]Volume = \pi * r^2 * h\\Volume=3.14*8^2*14\\Volume=2816 ft^3[/tex]

The required equation of the function with the given characteristics is y = (2/9)|x| whose height will be compressed to 2/9 of the original height.

As per the question, the absolute value function y = |x| looks like a "V" shape with its vertex at the origin and opening upward.

To shrink it vertically by a factor of 2/9, we need to multiply the function by this factor.

Thus, the equation of the function with the given characteristics is:

y = (2/9)|x|

The resulting graph will still have a "V" shape, but its height will be compressed to 2/9 of the original height.

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The equation subject to p is P = (n - 7/2)/q.

To solve for p, we need to isolate it on one side of the equation.

Starting with:

Pq+7/2=n

Subtract 7/2 from both sides:

Pq = n - 7/2

Divide both sides by q:

P = (n - 7/2) / q

Therefore, the solution for p is:

P = (n - 7/2) / q

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The probability that the husband has more than $150,000 of insurance is 1.4577

Looking at the row where the husband's insurance is between $50,000 and $100,000, we can see that there are a total of 329 policies.

Out of these policies, the number of policies where the husband has more than $150,000 of insurance is 249+30+25+176 = 480.

Therefore, the probability that the husband has more than $150,000 of insurance given that his insurance is between $50,000 and $100,000 is:

480/329 ≈ 1.4577

Rounded to four decimal places, the probability is 1.4577.

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Norbit is looking to buy a car for $32,550 and finance it over 4 years. Using an annual interest rate of 8%, we can calculate his monthly payment.

First, we will calculate the total amount of interest over the 4-year period. To do this, we multiply the interest rate (8%) by the amount borrowed ($32,550) and then by the number of years (4).

Next, we need to find the total amount that Norbit will pay over the 4-year period. To do this, we add the amount borrowed ($32,550) to the total interest ($10,620).

Finally, to calculate the monthly payment, we divide the total amount by the number of months in 4 years (48). q

Therefore, if Norbit finances his car for 4 years at an annual interest rate of 8%, his monthly payment will be $899.37

The probability to the nearest thousand that all three marbles drawn will be red is approximately 0.080.

There are 8 red marbles, 3 blue marbles, and 6 green marbles in the bag so the total possible outcomes in this scenario are:

8+3+6=17.

The probability of getting a red marble on the first draw is simply equal to:

= 8/17

The probability of getting a red marble on the second draw without replacement is equal to:

= 7/16

The probability of getting a red marble on the third draw without replacement is equal to:

= 6/15

The probability of getting three red marbles in a row is:

= [tex]\frac{8}{17}*\frac{7}{16}*\frac{6}{15}[/tex]

=[tex]\frac{7}{85}[/tex]

or 0.082

after rounding it to the nearest thousand, we get the probability [tex]^\sim_\sim[/tex] 0.080

Therefore, the probability to the nearest thousand that all three marbles drawn will be red is approximately 0.080.

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Answer: 72

800/11 = 72.272727272

11 is 6ft plus 5 feet in between each barricade since you need 5 ft for each barricade including the 6ft itself.

Therefore, 800ft can have no more than 72 barricades.

The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

The set is {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5}.

The range first need to identify the smallest and largest numbers in the set.

The smallest number is 0 appears three times.

The largest number is 5.

The range is:

5 - 0 = 5

The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.

The range is a measure of the spread or variability of a set of numbers.

It tells us how much the values in the set differ from each other.

The range of 5 indicates that the values in the set are spread out over a range of 5 units.

The set includes consecutive integers from 0 to 5 with multiple occurrences of some of these integers.

While the range provides a measure of the spread it is only one of many measures that can be used to describe the characteristics of a set of data.

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Answer:

62.25

Step-by-step explanation:

Rectangle Area Formula: A=l•w

7.5•5=37.5

=hbb/2=7.5·4.2/2=15.75

=hbb/2=7.5·2.4/2=

Add all three =62.25

The set of results that could not have been drawn from the bag is 3, 5, 5.

Let's assume there are three balls in the bag, labeled A, B, and C. The possible combinations are:

ABC, ACB, BAC, BCA, CAB, CBA

Now, let's analyze each set of results:

2, 3, 7: This set of results could have been drawn from the bag. For example, if A = 2, B = 3, and C = 7, the results would be 2, 3, 7.

10, 4, 3: This set of results could have been drawn from the bag. For example, if A = 10, B = 4, and C = 3, the results would be 10, 4, 3.

3, 5, 5: This set of results could not have been drawn from the bag, because there is only one ball labeled 3 in the bag. Therefore, it is impossible to draw two balls labeled 5 and one ball labeled 3.

8, 6, 10: This set of results could not have been drawn from the bag, because there is no ball labeled 8 in the bag. Therefore, it is impossible to draw a ball labeled 8.

So, the set of results that could not have been drawn from the bag is 3, 5, 5.

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 7} \implies \boxed{A \approx 3969.39} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2800\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A = 2800\left(1+\frac{0.052}{4}\right)^{4\cdot 7}\implies A=2800(1.013)^{28} \implies \boxed{A \approx 4019.97} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 4019.97 ~~ > ~~ 3969.39 \end{array}}~\hfill[/tex]

Answer:

7.638m

Step-by-step explanation:

The solution of the expression is,

⇒ - 37/14

We have to given that;

Expression to solve is,

⇒ 6 - 5/4 × 6 - 8/7

Now, We can simplify the expression as,

⇒ 6 - 5/4 × 6 - 8/7

⇒ 6 - 5/2 × 3 - 8/7

⇒ 6 - 15/2 - 8/7

⇒ (12 - 15)/2 - 8/7

⇒ - 3/2 - 8/7

⇒ (- 21 - 16) / 14

⇒ - 37/14

Thus, The solution of the expression is,

⇒ - 37/14

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Answer: 260(0.962)^8

Step-by-step explanation:

Pretty simple. We have a base of 260, which all of the answers include. Then for a decay rate of 3.8, we reduce to percentage form ( 0.038 ) and subtract that from 1 ( or 100 in standard form ). Then we get 0.962. We choose the second option because it includes both these terms and 8 ( which I'm assuming is an exponent )

The total area of the figure formed by the congruent triangles and the square is 60 sq in

For square

A = s²

where s is the side

Given:

s = 6 in

Area = 6 * 6

= 36 sq in

Area of triangle = 0.5bh

where b is the base

h is the height

Given:

b = 6 in

h = 4 in

A = 0.5 * 6 * 4

= 12 sq in

Total area of the figure = 2 * Area of triangle + area of square

= 2 * 12 + 36

= 24 + 36

= 60 sq in

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Answer:

8 more red counters

Step-by-step explanation:

It would make it 9:3, which, when simplified, is 3:1.

Answer:

A

Step-by-step explanation:

We can factor 625x^4 - 81 by recognizing it as the difference of two squares:

625x^4 - 81 = (25x^2)^2 - 9^2

This can be further simplified using the formula for the difference of squares, which states that:

a^2 - b^2 = (a + b)(a - b)

In this case, a = 25x^2 and b = 9, so we have:

(25x^2 + 9)(25x^2 - 9)

We can then use the difference of squares formula again to factor 25x^2 - 9:

25x^2 - 9 = (5x)^2 - 3^2 = (5x + 3)(5x - 3)

Substituting this into our original expression, we get:

625x^4 - 81 = (25x^2 + 9)(25x^2 - 9) = (25x^2 + 9)(5x + 3)(5x - 3)

Therefore, the fully factored form of 625x^4 - 81 is (25x^2 + 9)(5x + 3)(5x - 3). Answer: (A) (5x - 3)(5x - 3)(25x² + 9)