Ellis's backyard has a 6.25m by 6.25m patio. She would like to build a 1.5m wide extension around 3 sides of the patio. She will buy 0.25m b 0.25m tiles that come 25 to a package. How many packages does Ellis need to buy to build the extension?

The true proportion of adults is in the interval 0.4026< P< 0.4594.

Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.

Data provided:

selected (x) = 329

Total(n) = 763

Sample proportion (p') = x/n

                                       = 329/ 763

                                       = 0.431

Critical z-value = 1.59

margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]

                             = 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]

                             = 1.59 × 0.0179

                             = 0.0284

88% confidence interval is:

(p' ± E) = ( 0.431 ± 0.0284)

          = 0.4594 and 0.4026

Therefore the estimate is 0.4026< P< 0.4594.

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The solution for r in the equation is r = 3

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

\dfrac12r-3=3\left(4-\dfrac32r\right)

Rewrite the above expression properly, as a fraction

So, we have the following representation

1/2r - 3 = 3(4 - 3/2r)

To start with, we need to open the brackets

So, we have the following representation

1/2r - 3 = 12 - 9/2r

Next, we multiply through by 2 to eliminate the fraction

This gives

r - 6 = 24 - 9r

Solving further, we collect the like terms

So, we have

r + 9r = 24 + 6

Evaluate the like terms

10r = 30

So, we have

r = 3 --- by dividing both sides by 10

Hence, the solution is 3

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The diameter of IC 1101 is 50 times greater than the diameter of the Milky way.

Diameter is a measurement that goes all the way around from starting point to the end point.

Given, the largest galaxy IC 1101 has a diameter of 5 * 10²² and the Milky way has a diameter of 1 * 10²¹.

Diameter of IC 1101 = 5 * 10²²

Rearranging the above term;

Diameter of IC 1101 = 1 * 5 * 10²¹ * 10

Diameter of IC 1101 = 1 * 10²¹ * 50

Diameter of IC 1101 = 50 * diameter of Milky way

Therefore, the answer is 50 times.

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By using the concept of probability, it can be calculated that

Probability that the flight arrives on time =  [tex]\frac{399}{500}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Total number of flights = 1000

Number of flights arriving on time = 798

Probability that the flight arrives on time = [tex]\frac{798}{1000}[/tex]

                                                                   = [tex]\frac{399}{500}[/tex]

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Answer:

[tex] \huge{ \boxed{f(g(x)) = - 75 {x}^{2} - 1}}[/tex]

Step-by-step explanation:

To find f(g(x)), substitute g(x) into f(x). That is for every x found in f(x), replace it by g(x) and solve.

[tex]f(x) = - 3 {x}^{2} - 1 \\ g(x) = - 5x[/tex]

[tex]f(g(x) )= - 3 ({ - 5x})^{2} - 1 \\ = - 3(25 {x}^{2} ) -1 \\ = - 75 {x}^{2} - 1 \: \: \: \: \: \: [/tex]

We have the final answer as

[tex] \bold{f(g(x)) = - 75 {x}^{2} - 1}[/tex]

Answer: -10

Step-by-step explanation:

Substitute the numbers in for the variables.

np + n = (2)(-6) + 2

-12 + 2

-10

The value of m and n from the obtained probability is equal to 3 and 14 respectively.

As given in the question,

Nine tiles numbered 1, 2, .....9

Number of odd numbered tiles are 1,3,5,7,9 = 5

Number of even numbered tiles are 2,4,6,8 = 4

Number of players =3

Possibility to choose 3 tiles by first player out of 9 tiles = ⁹C₃

                                                                                            = 84 ways

Possibility to choose 3 tiles by second player out of 6 tiles = ⁶C₃

                                                                                                 =20 ways

Possibility to choose 3 tiles by third player out of 3 tiles = ³C₃

                                                                                             = 1 way

Total number of ways = 84× 20 ×1

                                     = 1680

To have a sum of 3 tiles is odd number at least one tile should be odd.

Chances of first player all the 3 tiles are 0dd out of 5 = ⁵C₃

Next two players must 2 even tiles and 1 odd tile.= ²C₁

One player can be selected in ³C₁ way

Remaining 4 even tiles distributed equally = (4!)(2!)/ (2!)² ( 2!)

Number of favourable outcomes =  ⁵C₃ × ²C₁ ׳C₁  × (4!)(2!)/ (2!)² ( 2!)

                                                       = 10 × 2 × 3 × 6

                                                       = 360

Probability (m/n) =  360 /1680

                            = 3/14

m = 3 and n = 14.

Therefore, from the probability that all three players obtain an odd sum is m/n , the value m = 3 and n = 14.

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There are 20,000 different phone numbers possible that is 7-digits long and start with either 824 or 825.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Based on the given information, all phone numbers are 7-digits long and starts with either 824 or 825. Hence, the four last digits will be the combination of numbers from 0 to 9.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is 20,000.

= (number of phone numbers starting with 824) + (number of phone numbers starting with 825)

= (10 x 10 x 10 x 10) + (10 x 10 x 10 x 10)

= 20,000

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Answer: 270 I think

Step-by-step explanation:

try it you can get this right

Answer:

R= 2sqrt(13) = about 7.2

Step-by-step explanation:

D^2= 12^2 + 8^2

 = 144+64=208

D=4sqrt(13)

R= D/2= 2sqrt(13)

Answer:

  4/39

Step-by-step explanation:

You want to know the fraction of 39 students represented by the 4 that have blue eyes.

The fraction is the ratio of the part of interest to the whole.

  (students with blue eyes)/(total number of students) = 4/39

Given that the dividend is 15a²-a-28 and the divisor is 3a+4, the quotient will be 5a-7 and the remainder will be 0.

A multi-term algebraic statement is referred to as a polynomial. It contains exponents, coefficients, variables, constants, and arithmetic operators. It uses a polynomial long division algorithm to divide the polynomials. It is the long division technique in a more generalized form. In this method, a polynomial is divided by other polynomials of the same degree or lower. Synthetic division method is a simple and quick technique that is occasionally employed as well.

Here,

dividend=15a²-a-28

divisor=3a+4

remainder=0

15a²-a-28=(3a+4)(5a-7)

quotient=5a-7

The quotient will be 5a-7 and remainder will be 0 as dividend is 15a²-a-28 and divisor is 3a+4.

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Answer:

18

Step-by-step explanation:

1)since 9*9 = 81 the square root of 81 is  9

9*2

2)simplify

18

The answer to following questions are as follows:-A)experiment

B)meaning “statistically non significant” C)explained below

A wave is a dynamic disturbance that propagates over one or more quantities in the domains of physics, mathematics, and allied sciences. When waves are periodic, those parameters repeatedly oscillate around an equilibrium value at a certain frequency.

The answers are: a) It is an experiment since some claims are not supported by evidence.

b) When the analysis reveals that there are substantial variations between the observed, "not statistically significant" refers to "statistically non significant." And we are unable to analyse any of the statistics' results.

c) The fact that Motorola, a cell phone company, funded this research reveals to us that this claim is untrue because Motorola conducts this research to boost their sales.

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Answer

$1,580.54

1215.80×(1+0.3)= 1580.54

Answer: 70%

Step-by-step explanation:

Answer:

y = 2x - 9

Step-by-step explanation:

The slope is the change in y over the change in x.  From the 2 points, the y's are 7 and 5.  The x's are 8 and 7.

[tex]\frac{7-5}{8-7}[/tex] = [tex]\frac{2}{1}[/tex] = 2

2 is the slope.

Now we need to find the y intercept (b).  Use one of the points on the line.  It does not matter which one.  I am going to use (8,7)

slope (m) = 2

x = 8

y = 7

y=mx + b

7 = 2(8) + b  Plug in what we know and solve for b

7 = 16 + b  Subtract 16 from both sides

-9 = b

The y intercept (b) is -9

y = mx + b

y = 2x -9

Answer:

Step-by-step explanation: 10.75

Because it diverges using a comparison test, the correct answer is an option (E).

The comparison test, also known as the direct comparison test to distinguish it from other closely related tests, offers a method for determining whether an infinite series or an improper integral will converge or diverge.

The test is effective in both situations by contrasting the given series or integral with one whose convergence characteristics are known.

So, refer to the image attached below.

According to the image which has the reason for convergence and divergence, we know that the correct answer would be option (E).

The reason is the comparison test.

Therefore, because it diverges using a comparison test, the correct answer is an option (E).

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Answer: I think it's 2/5, it is closest to the answer I came up with

The first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.

Given, A Tomato juice 46 oz. Cans cost $2. 53

B Tomato juice 6-pack of 10 oz. Cans costs $4. 50

we have to find the best buy between the given two.

In first case,

46 cans cost $2.53

46 cans = $2.53

1 can = 2.53/46

1 can costs $0.055

In second case,

60 cans cost $4.50

60 cans = $4.50

1 can = 4.50/60

1 can costs $0.075

So, it is clear that first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.

Hence, the first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.

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Answer: 315 children and 15 adults

Step-by-step explanation:

15 x 21 = 315
315 + 15 = 330
c = 315
a = 15

The equations represent the given situation is:

2x - y = -6

3x - y = -5

where, x is the smaller number and y is the larger number.

Let the smaller number be x.

We have been given a number, y, is equal to twice the sum of a smaller number and 3

So, we get an equation,

y = 2(x + 3)

y = 2x + 6                        

2x - y = -6

The larger number is also equal to 5 more than 3 times the smaller number.

So, we get an equation,

y = 5 + 3x                        

3x - y = -5

Therefore, the equations represent the situation:

2x - y = -6

3x - y = -5

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The largest value less than 500 that both sets have common is 479.

We have given two arithmetic progression such that,

{2,5,8,11,...} and {3,10,17,24,...}

and we have to find the largest value less than 500 that they have in common.

We know the formula for the nth term of the arithmetic progression,

i.e, an = a + (n - 1)d

for the arithmetic progression {2,5,8,11,...} the formula become

am = 2 + (m - 1)3 ----------- (1)

and for the arithmetic progression {3,10,17,24,...} the formula become

an = 3 + (n - 1)7 ------------- (2)

by solving for m and n we get,

m = 160 and n = 69

so equation (1) implies that,

a(160) = 2 + (159)3 = 479

this is the 160th term in the 1st arithmetic progression

and equation (2) implies that,

a(69) = 3 + (68)7 = 479

this is the 69th term in the 2nd arithmetic expression.

Therefore, the value which less than 500 that both the progressions have in common is 479.

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We want to finish each statement by analyzing the graph provided.

The function's y-intercept is y =2.

y = 3x+2 is the equation.

The line connects (0, 2) and (2, 6).

The earliest known attempt to the concept of function may be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity. The position of a planet, for example, is a function of time.

So, first, we need to find the y-intercept. We know that the y-intercept is the y-value at which the function intersects the y-axis, and we can see from the graph that the y-intercept is y = 2.

Then we'd like to see the line's equation.

Remember that y = ax + b is a generic line.

Where a denotes the slope and b the y-intercept, we may deduce:

y = ax + 2

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a=(y₂-y₁)/(x₂-x₁)

Given that the line passes through (0, 2) and (-2/3, 0), the slope is as follows:

a=(-2/3)/(-2)

a=1/3

The equation of the line is:

y =3x+2

And using that equation, we can show that the line does indeed pass through the points (0, 2) and (2, 6)

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Answer: 84

Step-by-step explanation: so 7:8 increased by some number is 180 degrees. add 7 and 8 to get 15. 180/15 is 12 so x = 12 7*12 is 84.

If Aquataste sticks to the agreement, Waterland has an incentive to renege on the agreement by producing 350 gallons because Waterland’s profits would then increase from $375 to $525.

If Waterland and Aquataste both produce 250 gallons each and charge $1.50 per gallon.

There would be 500 gallons in total, and the total revenue would be

$1.50 × 500 = $750

which when shared equally between Waterland and Aquataste would result in each of them getting $375 each.

But if Aquataste sticks to the agreement, Waterland has an incentive to renege on the agreement by producing 350 gallons, still charging $1.50 and Waterland’s profits would then be

$1.50 × 350 = $525

If one cheats they will get sell 350 gallons at the new market price of $1.25 '.

Then, a total quantity of 250+350=600.

Total profit $1.25 × 350 = $437.50

If Waterland also reneges and produces 350, market qty supplied is now 700 and price is $1. Each firm earns profit of $350 ($1*350). This is better for waterland than before since they were selling the 250 gallons at $1.25

Therefore, Profit = 250 × 1.25

                           =312.50

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Answer: 89.7

Step-by-step explanation: