PLEASE HELP If the probability that the Islanders will beat the Rangers in a game is 1/6, what is the probability that the Islanders will win at most one out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.

The following solutions with regard to resolving or simplifying the radii of circular ponds are given below.

Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters
Part C: The radius of Pond B is 10√2 meters.
Part D: the radius of Pond B is greater than the radius of Pond A.

Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:

164 = 2 × 2 × 41

So, we can write:

√164 = √(2 × 2 × 41) = 2√41

Using this, we can rewrite Step 1 as:

5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:

5 × 10 + 2√41 meters = 50 + 2√41 meters

So, the radius of Pond A is 50 + 2√41 meters.

Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:

25√200/5 meters = 5√200 meters

We can simplify this further by finding the prime factorization of 200:

200 = 2 × 2 × 2 × 5 × 5

So, we can write:

√200 = √(2 × 2 × 2 × 5 × 5)

= 2 × 5√2

Using this, we can rewrite the expression for the radius of Pond B as:

5 × 2 × √2 meters

= 10√2 meters

Thus, the radius of Pond B is 10√2 meters.

Part D: We can compare the radii of the ponds using the original expressions by writing:

√164 < 25√200/5

Simplifying both sides:

2√41 < 10√2

Dividing both sides by 2:

√41 < 5√2

Squaring both sides (since both sides are positive):

41 < 25 × 2

41 < 50

So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.

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Full Question:

Two circular ponds at a botanical garden have the following radii:

Pond A: Sqrt(164) meters;

Pond B: 25Sqrt(200)/5 meters:

Todd simplified the radius of pond A this way:

5sqrt(164)

Step 1: 5sqrt(100) + Sqrt(164) meters

Step 2: 5(10 + 8)

Step 3: 5(18)

Step 4: 90

One of the steps above is incorrect.

Part A: Rewrite the steps so that it is correct

Part B: Using the corrected step from Part A, simplify the radius of Pond A.

Part C: Simplify the expression for the radius of pond B.

Part D: Write an inequality to compare the radii of the ponds, using the original expressions.

Answer: The area of the living room in square feet is given by:

A = length × width

Before the expansion, the length is 12 feet and the width is 10 feet. Therefore, the initial area is:

A = 12 ft × 10 ft = 120 ft²

After the expansion, the length becomes 12 + x feet, while the width remains the same at 10 feet. Therefore, the area after the expansion is:

A = (12 + x) ft × 10 ft = 120 + 10x ft²

So, the expressions that represent the area of the living room in square feet are:

120 ft²

120 + 10x ft²

Therefore, both expressions are correct.

Step-by-step explanation:

Answer: a Serena and Aaron

Step-by-step explanation:

Answer:

a Serena and Aaron

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

It does not have to be April if there are 30 days. If its not April, it can still have 30 days. April does have 30 days.

y = 5x + 3

-1 = 5(2) + 3

-1 = 13 (wrong)

y = -2x - 4

-1 = -2(2) - 4

-1 = -8 (wrong)

Answer:

\(y=\left \{ {{x < N:x+N}}\right\}\)

\(y=\left \{ {{x > = N:Nx-N}}\right\}\)

Step-by-step explanation:

N stands for a number. I can't read the numbers in the photo.

In brackets start with the if statement and then use a ":" and then write the function.

I tried to make out the numbers. DOUBLE-CHECK! Here is a photo.

Answer:

Simplifying

X + -4 = 2x

Reorder the terms:

-4 + X = 2x

Solving

-4 + X = 2x

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + X = 4 + 2x

Combine like terms: -4 + 4 = 0

0 + X = 4 + 2x

X = 4 + 2x

Simplifying

X = 4 + 2x

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

Answer:

1

Step-by-step explanation:

Answer:

lo siento no se lo siento

Given:

The line perpendicular to the line y = 3x + 3 includes the point (3, 1).

Required:

We need to find the line equation.

Explanation:

The given line y =3x+3 is of the form.

The slope of the line is a negative reciprocal of the perpendicular to the line.

Consider the line equation.

Substitute m=-1/3 in the equation.

Substitute x =3 and y =1 in the equation to find the value of b.

Add 1 to both sides of the equation.

We know that b is the y-intercept.

Final answer:

The y-intercept of the line perpendicular to the line y = 3x + 3 includes the point (3, 1) is 2.

The Task objective chosen is: A Measuring Task

The Objective is: To investigate the fairness of a local athlete's track for runners starting on different lines.

To carry about the investigation, follow the steps given below.

Lastly, make a crossword puzzle that includes mathematical vocabulary in a clever manner.

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```Class IX```

*Mathematics Project work*

*Do any one*

1. *A Measuring Task*

To investigate your local athletes track to see whether it is worked fairly for runners who start on different lines.

2. *Design a crossword puzzle with mathematical terms*

To review mathematics vocabulary, to give the opportunity for creative expression in designing puzzles, to act as a means of motivating the study of a given unit and to given recreation .​

The statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follows:

\(\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}\)

Where s is the standard deviation.

n is the sample size.

α is the significance level.

σ is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

The statement is:

A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval.

As we know,

A 95% confidence interval is narrower than a 99% confidence interval.

Thus, the statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.

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Answer:

h = 20.5 yards

Step-by-step explanation:

Volume of Rectangular Pyramid: lwh/3

492 = (18) * (4) (h) /3

Multiply 3 on both sides

1476 = (18) (4) (h)

1476 = 72h

Flip the equation.

72h = 1476

h = 41/2 or 20.5 yards

To find the hourly rate, we can subtract the cost of two hours by the cost of one hour:

So the hourly rate is $40.

Then, to find the initial fee, we subtract the cost of one hour by the hourly rate:

So the initial fee is $15.

Answer:

ok

Step-by-step explanation:

Answer:

y = -1/2x+7

Step-by-step explanation:

We have a slope of -1/2 and a point of (4,5)

Using the slope intercept form of a line

y = mx+b

y = -1/2 x +b

Substituting the point into the equation

5 = -1/2(4) +b

5 = -2+b

Add 2 to each side

5+2 = -2+2+b

7 = b

The equation of the line is

y = -1/2x+7

Answer:

r = 2.5

Step-by-step explanation:

U= π(r+h)

Where,

U = 16 1/2

h = 2 3/4

π = 3 1/7​

U= π(r+h)

16 1/2 = 3 1/7(r + 2 3/4)

33/2 = 22/7(r + 11/4)

33/2 = 22/7r + (22/7 * 11/4)

33/2 = 22/7r + 242/28

33/2 - 242/28 = 22/7r

(462-242) / 28 = 22/7r

220/28 = 22/7r

r = 220/28 ÷ 22/7

= 220/28 × 7/22

= (220 * 7) / (28 * 22)

= 1540/616

= 2.5

r = 2.5

For a random sample of customers in cellphone company, the probability or p-value that the average excess time used by the 80 customers in the sample is longer than 20 minutes is equals to the 0.5362.

We have a market research analyst for a cell phone company conducts a study of their customers. Now, a random sample of customers

Mean of time, = 22 minutes

Standard deviations, s = 22 minutes

Sample size, n = 80

We have to determine the probability that the average excess time used by the 80 customers in the sample is longer than 20 minutes, P(X > 20). Using the Z-Score formula for distribution is

\(Z = \frac{ X - \mu}{\sigma}\)

Where X --> observed value

μ --> mean

σ --> standard deviations

Now, here x = 20, subsritute all known values, \(Z = \frac{ 20- 22}{22}\)

= - 0.091

Probability is written as P(X > 20)\(= P( \frac{ X - \mu}{\sigma} > \frac{ 20 - 22}{22})\) = P(Z > -0.091)

Using the Z-distribution table the critical value or p-value for Z = - 0.091 is equals to the 0.5362. So, P( Z> - 0.091) = P(X> 20) = 0.5362. Hence, required value is 0.5362.

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Answer:

0.3571

Step-by-step explanation:

Hope this helps!

Answer:line l is the transversal because it intersect both sets of angles. and 7 and 11 are corresponding because they are in the same positions of the intersections.

Step-by-step explanation: usually a transversal is associated with parallel lines and corresponding angles are equal but this is not true with a triangle

If |x z|= 5 , then the value of equation |2x+z z||y w| |2y+w w| is 10| xy + zw/2 + xyw/4 + zwy/4.

Given that |x z|= 5, we need to find the value of |2x+z z||y w| |2y+w w|

Let's start by solving |2x+z z| and |2y+w w|.

|2x+z z| = |2(x + z/2) z/2|

[dividing z/2 on both sides, we get 2x + z = 2(x + z/2)]= 2| x+z/2|.

|2y+w w| = |2(y + w/2) w/2| [dividing w/2 on both sides, we get 2y + w = 2(y + w/2)] = 2| y+w/2|

Now, we need to find the value of |x z||y w|.

|x z||y w| = |x||y| |z||w| = |xy||zw|

As we have the value of |x z|= 5, we get|xy||zw| = 5|y w|

Now, substituting the value of |2x+z z| and |2y+w w| in the equation |2x+z z||y w| |2y+w w|,

we get

2| x+z/2| * | y+w/2| * 5|y w|

= 10| x+z/2|| y+w/2||y w|

= 10| xy + zw/2 + xyw/4 + zwy/4|

Therefore, the value of |2x+z z||y w| |2y+w w| is 10| xy + zw/2 + xyw/4 + zwy/4|.

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Answer:

-10 = a

Step-by-step explanation:

17 = a - 3 - За

Combine like terms

17 = -3 -2a

Add 3 to each side

17+3 = -3-2a+3

20 = -2a

Divide by -2

20/-2 = -2a/-2

-10 = a

Answer:

a=-10

Step-by-step explanation:

17= -3-2a

17+3=-2a

20=-2a

a=-10 hope I helped

Some of the groups of cards that have the same sum are:

Group 1               Group 2                    Sum

{8, 1}                      {7, 2}                         9

{8, 2}                     {7, 3}                         10

{8, 3}                     {7, 3, 1}                      11

{8, 1, 3}                  {7, 3, 2}                     12

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

Numbers: 8 7 6 2 1 3.​

In the above group of numbers, we have

Highest = 8

Least = 1

When these are added, we have

8 + 1 = 9

Another set of numbers that have a sum of 9 is (7, 2)

There are several other numbers that can be created

Some of these numbers are

And several others

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Answer:

If you look back at the formula, you'll see that n – 2 gives the number of triangles in the polygon, and that number is multiplied by 180, the sum of the measures of all the interior angles in a triangle. Do you see where the "n – 2" comes from? It gives us the number of triangles in the polygon.

Have a nice day   :)

Answer:

Question 3: x = 11

Question 4: x = -17

Question 5: x = 26

Question 6: 10 = x

Question 7: x = 36

Question 8: x = 88

Question 9: x = 81

Question 10: n = 36

Step-by-step explanation:

Answer:

slope = -2

Step-by-step explanation:

slope = m = y2-y1/x2-x1

given points (-3,3) and (-1,-1)

plug in to slope formula

m = -1 - 3 / -1 - (-3)

m = -4 / 2

m = - 2

99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.

Using 68-95-99.7 rule, we know that

99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)

(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).

Since the normal distribution is bell-curved and symmetrical,

we can say

0.3/2 = 0.15% values are less than the mean - 3 × standard deviation

and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.

Here,

Mean + 3 × standard deviation.

= 110 + 3 × 10 = 140

So, 0.15% of values  are greater than 140

So, (100 - 0.15) = 99.85% values are less than 140.

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The first four terms and the hundredth term of the sequence whose nth term is given as an=n^2-3 are -2, 1, 6, 13, and 9997, respectively.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

aₙ=n²-3

a₁=-2

a₂=1

a₃=6

a₄=13

a₁₀₀=100²-3

=9997

The first four terms and the 100th term of the sequence whose nth term is given as an=n^2-3 is -2, 1, 6, 13 and 9997.

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