what is the factor?\(36y ^{2} - 1\)

The expected value of your third punch is 5660.

What is probability?

A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.

Given that,

This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.

E(third punch) = Σ  x  p(x)

=  100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50)     + 100000 × (2/50) + 25000 × (1/50)

=  5660

Let us find the median of the given possibilities,

5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000

There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.

25th term = 500

26th term = 1000

Median = (500 + 1000) / 2 = 750

The next available possibility greater than 750 is 1000.

Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes                                                                                                         = 15 / 50 = 0.3

Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes                                                                                                                

= 25 / 50 = 0.5

Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.

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Answer:

4.5

Step-by-step explanation:

Diameter is equal to 2r. In other words, to find radius from the diameter, you divide the diameter by two. In this case, its 9/2. That gives you 4.5

Answer:

4 1/2 feet

Step-by-step explanation:

The radius fo the circle is half of the diameter so 4 1/2 Feet.

Rested numbers in group is 33 out of 76.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

Total numbers in a group = 76.

44% of them were rested.

That is 44% of 76.

To find how many are rested we have to find the value in numbers.

Convert 44% of 76 to numbers.

For this, it can be written as

\(\frac{44}{100} *76\) = 33.44

Therefore 44% of 76  ≅ 33 numbers.(approximately)

Hence, rested numbers in group is 33.

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Answer:

-2

Step-by-step explanation:

Answer:

Investment is a source of Income.

Self Employment Income

Answer: Business ownership

Step-by-step explanation: took the quiz

Answer:

-2/3 or -0.6666

Step-by-step explanation:

-3x + 6 = 4 -6x

Let's move the x to one side

-3x +6x=4-6

Combine like terms

3x = -2

Divide both sides by 3

-2/3=x

or -0.666666

The value of the radius of the cone is, 5 inches

We have to given that;

The volume of a cone is 35π cubic inches.

And, the height is 4.2 inches.

Now, We know that;

Volume of cone is,

V = πr²h/3

Hence, We get;

35π = π × r² × 4.2 / 3

105 = 4.2r²

r² = 105/4.2

r² = 25

r = 5 inches

Thus, The value of the radius of the cone is, 5 inches

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Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

Answer:

1/2 is the answer

step-by-step explqnation:

Answer:

The answer is 1/2.

Answer:

cool

Step-by-step explanation:

Answer:

LOL that's just

Step-by-step explanation:

epik uhhh wsg?

Answer:

a = - 2

Step-by-step explanation:

Givens

y2 = 4

y1 = a

x2 = 5

x1 = 3

Formula

m  = (y2 - y1)/(x2 - x1)

Solution

3 = (4 - a)/(5 - 3)      Combine the denominator on the right

3 = (4 - a)/2             Multiply both sides by 2

3*2 = 4 - a               Subtract 4 from both sides

6 - 4 = - a

2 = - a                     Multiply both sides by - 1

-2 = a

The level of agreement between judge X and judge Y is also determine by rank correlation which is 0.8787.

A technique for determining the degree of association between two variables is rank correlation. Similar to the Pearson correlation coefficient, the rank correlation coefficient is calculated using the observations' ranks rather than their numerical values. When there is sufficient information to rank the data but the data are not available in numerical form, this method is useful.

See the attached table for the solution at last find:

∑d² = 20

The rank correlation, R = 1- [6∑d² ÷ n(n²-1)]

R = 1- [6×20 ÷ 10(100-1)]  = 0.8787

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Answer: The required sample size = 97

Step-by-step explanation:

If prior population standard deviation is known, then the minimum sample size can be computed as:

\(n=(\frac{z^*\times\sigma}{E})^2\)

,where z* = critical z-value

\(\sigma\) = population standard deviation

E = Margin of error

As per given,

\(\sigma=20,\ E= 4\)

Critical value for 95% confidence = 1.96

\(n=(\frac{1.96\times20}{4})^2\\= (1.96\times 5)^2\\= (9.8)^2\\=96.04\approx97\)

Hence, the required sample size = 97

Answer:

8%

Step-by-step explanation:

P(X<79) = normalcdf(0,79,100,15) = 0.0807567112 ≈ 0.08 ≈ 8%

Therefore, the probability, rounded to the hundredth, that a person from Montana will have an IQ less than 79 is 0.08 or 8%

The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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The factor of the trinomial 9x² + 30x + 25 is (3x + 5).

When you factor a trinomial, you change an algebraic expression from a trinomial to a binomial. ax² + bx + c, where a and b are coefficients and c is a constant, is the general expression for a trinomial, which is a polynomial with three terms.

Given trinomial: 9x² + 30x + 25

Factoring the trinomial, we get

9x² + 30x + 25

9x² + 15x + 15x + 25

3x(3x + 5) + 5(3x + 5)

(3x + 5)²

Therefore, (3x + 5) is the factor of the given trinomial.

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Answer:

\(g(2) = 4(2) + 6 = 14\)

\(f(2) = 2(2) + 3 = 7\)

\((g - f)(2) = 14 - 7 = 7\)

problem decoded dude

thank and follow meh

Step-by-step explanation:

a)

0.00000000007

b)

0.00000001

Approximately 733395 babies were born in the UK in 2018.

Given,

In the UK in 2018 a baby was born every 43 seconds.

We have to find the total number of babies in the UK in 2018.

A baby in every 43 seconds.

There is 3600 seconds in an hour.

There is 24 hours in a day.

In 2018 there were 365 days.

So, the total number of babies born in 2018 in the UK:

= (Seconds in an hour × hours in a day × total days in 2018) ÷ 43

= (3600 × 24 × 365) ÷ 43

= 31536000 ÷ 43

= 733395.3488

≈ 733395

That is, in the UK in 2018 approximately 733395 babies were born.

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 95% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

xbar = $1,465,752

SD = $1,346,046.2

lower bound of confidence interval ________

upper bound of confidence interval _______

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 95% confidence interval using the remaining 61 salaries.

xbar = $1,371,191

SD = $1,130,666.5

lower bound of confidence interval _________

upper bound of confidence interval. ________

Answer:

Question 1:

lower bound of confidence interval = $1,124,027

upper bound of confidence interval = $1,807,477

Question 2:

lower bound of confidence interval = $1,081,512

upper bound of confidence interval = $1,660,870

Step-by-step explanation:

Question 1:

The sample mean salary of 62 couches is

 \(\bar{x} = 1,465,752\)

The standard deviation of mean salary is

 \(s = 1,346,046.2\)

The confidence interval for the mean salary of all basketball coaches is given by

 \($ CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\)

Where \(\bar{x}\) is the sample mean, n is the sample size, s is the sample standard deviation and  \(t_{\alpha/2}\) is the t-score corresponding to a 95% confidence level.  

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 62 - 1 = 61

From the t-table at α = 0.025 and DoF = 61

t-score = 1.999

So the required 95% confidence interval is  

\(CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (\frac{1,346,046.2}{\sqrt{62} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (170948.04 ) \\\\CI = 1,465,752 \pm 341,725 \\\\LCI = 1,465,752 - 341,725 = 1,124,027 \\\\UCI = 1,465,752 + 341,725 = 1,807,477\\\\\)

Question 2:

After removing the Coach Krzyzewski's salary from the data

The sample mean salary of 61 couches is

\(\bar{x} = 1,371,191\)

The standard deviation of the mean salary is

\(s = 1,130,666.5\)

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 61 - 1 = 60

From the t-table at α = 0.025 and DoF = 60

t-score = 2.001

So the required 95% confidence interval is  

\(CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (\frac{1,130,666.5}{\sqrt{61} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (144767 ) \\\\CI = 1,371,191 \pm 289,678.8 \\\\LCI = 1,371,191 - 289,678.8 = 1,081,512 \\\\UCI = 1,371,191 + 289,678.8 = 1,660,870\\\\\)

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

Step-by-step explanation:

The first time:

The second time and each time after, half of the previous distance

This is a GP with the first 6 terms:

Sum of the distances:

Answer:

Solution given:

For first time:

ball goes 16 m up and 16 m down = 32 m

The second time and each time after, half of the previous distance

since it is in a GP with the first 6 terms:

32, 16, 8, 4, 2, 1

now

Sum of the distances:32 + 16 + 8 +4+2+1= 63 m

63 m is your answer.

Answer:

\(( {2}^{ - 6} )(5)( {2}^{3} \times 5) {}^{2} \\ \\ = 2 {}^{( - 6 + (3 \times 2))} \times {5}^{(1 + 2)} \\ \\ = {2}^{0} \times {5}^{3} \\ \\ = 1 \times {5}^{3} \\ \\ = {5}^{3} \)

Answer:

k = -0.4

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

2k + 9 = 7 - 3k

Step 2: Solve for k