to find a power series for the function, centered at 0. f(x) = 1 (1 − x)2

concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.

These numbers go from 1 to 10.

5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.

This means that if the card that we turn up is smaller than 6, we discard it.

If the card has the value 6 or larger, we keep it.

In this case, the probability of losing is if one of the other cards has a value larger than 6.

The probability that a random card has a value larger than 6 is:

p = (number of cards with a value larger than 6)/(total number of cards)

p = (16/39)

(The quotient is 39 instead of 40, because we already know one of the cards)

This means that if keep the 6, the probability of winning is:

1 - 16/39 = 0.59

If instead, we got a 7, obviously we keep it, in that case the probability of winning is:

1 - 12/39 = 0.69

And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

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The probability of not rolling a 5 is \(\frac{1}{6}\)

For any event A, the probability of not getting A is given by

\(P(not A)= 1- P(A)\)

A number cube with six sides numbered 1 through 6 is rolled.

Then we have,

The total number of possible outcomes \(= 6\)

Also, it is given that, The probability of rolling a 5 is

P(rolling 5)=\(\frac{1}{6}\).

Now, the probability of not rolling a 5 will be

\(P(\text{not rolling a 5})= 1- P(\text{rolling 5})\)

\(=1-\frac{1}{6}\)

\(=\frac{5}{6}\)

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Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

Solution

Given expression

Required

To find which option represents the expression in factored form

Step 1

Using factorization

The required factors are +9y and +25y

replacing 34y with both factors gives

The required option is (y+1)(25y+9)

Answer:   $33,029.00

Step-by-step explanation: 29700 + 1029 + 2300

sales = $29,700

commission = $1,029

salary = $2,300

Plz mark brainliest:)

When performing hypothesis tests on a population, you need to consider the significance level (alpha) and compare it to the p-value. The significance levels you've mentioned are 0.10, 0.05, and 0.01.

The null hypothesis (H 0) states that there is no significant difference between the sample mean (x-bar) and the population mean.

To determine whether to accept or reject H 0, follow these steps:

1. Calculate the test statistic (e.g., t or z) using the sample data.
2. Determine the p-value associated with the test statistic.
3. Compare the p-value to each of the given alpha levels (0.10, 0.05, 0.01).

Now, for each of the three alpha values, you can decide to accept or reject H 0 as follows:

- If the p-value is less than or equal to the alpha value, you reject H0. This means there is sufficient evidence to suggest a significant difference between the sample mean and the population mean.
- If the p-value is greater than the alpha value, you fail to reject H 0. This means there is not enough evidence to support a significant difference between the sample mean and the population mean.

On the graphs, you can indicate the critical regions (rejection zones) for each alpha value. These regions represent the extreme values where H 0 would be rejected. The critical regions depend on the type of hypothesis test (one-tailed or two-tailed) and the distribution of the test statistic.

For each alpha value, if the test statistic falls within the critical region(s), you would reject H 0; otherwise, you would fail to reject H 0. Remember to maintain a professional, concise, and friendly approach when explaining your conclusions.

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Answer:

Isosceles right triangle.

Step-by-step explanation:

From the given triangle ABM,

AM ≅ MB [Given]

∠AMB is an angle subtended by the diameter AB.

By theorem, angle subtended by a diameter is always 90°.

m∠AMB = 90°

So the given triangle is a right triangle with two equal sides AM and MB.

Therefore, ΔAMB is an isosceles right triangle.

Answer:

15/x

Step-by-step explanation:

x = fish tank

f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

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Answer:

\(\huge\boxed{\sf x = 27\°}\)

Step-by-step explanation:

Since the given triangle is a right-angled triangle, one angle will be equal to 90 degrees.

So,

x + 63 + 90 = 180

x + 153 = 180

x = 180 - 153

\(\rule[225]{225}{2}\)

For the given equation, we created a situation in which the equation would work and analysed it.

What is meant by equations?

A mathematical equation is a formula that uses the equals sign (=) to represent the equality of two expressions. The expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side," respectively, of the equation. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

a ) Given the equation as:

 g + 3 / 16 = 15

Now we have to create a situation that the equations could represent. We have to create a word problem for the equation.

James had a packet of chocolates. There were a total of 16 students in his class. He bought three more chocolates so that each student received 15 chocolates. How many chocolates did James have in the beginning?

To solve this we take g as the number of chocolates in the beginning.

He bought 3 more chocolates.

So number of chocolates = g + 3

Now he divided it among 16 students equally.

So each student received = g + 3 /16 = 15 chocolates.

b) The situation would not work if the denominator of the equation is doubled. That is 16 * 2 = 32.

Because the number of students is 16.

But if the students were 16*2 = 32 then the situation would work.

Therefore for the given equation, we created a situation in which the equation would work and analysed it.

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Answer:

hope it's help you sorry for dirty handwriting

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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David is completing a Rorschach test, which is a type of projective psychological assessment. The test consists of a series of inkblots presented to the participant, and their responses are analyzed by the researcher to gain insights into their personality, thought processes, and emotional functioning.

The Rorschach test is a widely used tool in clinical psychology and has been subject to much controversy and debate over its validity and usefulness in assessment.

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

The first five terms in the sequence cn = 12n - 11 are: c1 = 1, c2 = 13, c3 = 35, c4 = 45 and c5 = 59.

The sequence cn = 12n - 11 represents a sequence where each term (cn) is generated by substituting the value of n into the formula 12n - 11. To find the first five terms of the sequence, we substitute the values of n from 1 to 5 into the formula.

For n = 1, we have c1 = 12(1) - 11 = 1.

For n = 2, we have c2 = 12(2) - 11 = 13.

For n = 3, we have c3 = 12(3) - 11 = 35.

For n = 4, we have c4 = 12(4) - 11 = 45.

For n = 5, we have c5 = 12(5) - 11 = 59.

Therefore, the first five terms in the sequence cn = 12n - 11 are 1, 13, 35, 45, and 59.

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The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given \($m =\frac{y_2 - y_1}{x_2 - x_1}\)  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is \(m*2=-1\)  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.\(m*-1=-1\) i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. \(3=-1/2*3+b\)  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

\(y=-x/2+9/2\)

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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Answer:

15

Step-by-step explanation:

Answer:

$15

Step-by-step explanation:

50% of 30 is 15. When we subtract 15 from 30 we get 15, so the new price of the shirt would be $15.

hope this helps!

Step-by-step explanation:

1kg of grapes = $1.50

=> 3.5kg of grapes = $1.50 * 3.5 = $5.25

1kg of carrots = $1.00

=> 2.25kg of carrots = $1.00 * 2.25 = $2.25

Total cost = $5.25 + $2.25 = $7.50.

Answer:

x = 0 , y = 1

Step-by-step explanation:

x - 5y = -5

  +5y    +5y

-------------------

x = -5 + 5y

4x + 20y = 20​

4(-5 + 5y) + 20y = 20

-20 + 20y + 20y = 20

-20 + 40y = 20

+20             +20

---------------------------------

40y = 40

/40    /40

----------------------------------

y = 1

x = -5 + 5y

x = -5 + 5(1)

x = -5 + 5

x = 0

So, using the method of substitution, we get x = 0 and y = 1.

Answer:

I agree with manamoto13 , the answer is  y= 1  and x=0

One possible function that is a 3-to-1 correspondence from the set {1, 2, ..., 30} to {1, 2, ..., 10} is f(x) = ⌈x/3⌉.where ⌈x/3⌉ denotes the ceiling function of x/3, which rounds up x/3 to the nearest integer.

Intuitively, the function groups every three consecutive integers in the domain {1, 2, ..., 30} into the same integer in the range {1, 2, ..., 10}.

Specifically, the first three integers 1, 2, 3 in the domain map to 1 in the range, the next three integers 4, 5, 6 map to 2, and so on, until the last three integers 28, 29, 30 map to 10.

To see that this function is indeed a 3-to-1 correspondence, we can note that for any integer k in the range {1, 2, ..., 10}, there are three integers in the domain that map to it.

Specifically, if k = 1, then the integers 1, 2, 3 in the domain map to it; if k = 2, then the integers 4, 5, 6 map to it; and so on, until if k = 10, then the integers 28, 29, 30 map to it.

Conversely, for any integer x in the domain {1, 2, ..., 30}, the function f(x) maps it to an integer in the range {1, 2, ..., 10}, and this integer is unique. Therefore, the function f is a 3-to-1 correspondence from the domain to the range.

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Answer:

5000

Step-by-step explanation:

100 × 50

5000

Answer:

--------------------

Find 62% of 45:

Answer:

27.9

Step-by-step explanation:

To find the value of 62% of 45, simply multiply.

\(\sf 45*\dfrac{62}{100} \\\\\sf \dfrac{62*45}{100}\\\\\sf \dfrac{2790}{100}\\\\27.9\)

The unit price for Andy's Hardware varies depending on the length of fencing purchased Unit price for Andy's Hardware: $2.25 per foot, Unit price for Bargain Hardware: $2.50 per foot.

To determine the unit price of fencing for each store, we need to divide the price of the fencing by the length of the fencing.

For Andy's Hardware, the unit price of fencing is:

Unit price = Price / Length = $168.75 / 75 ft = $2.25/ft

For Bargain Hardware, the unit price of fencing is given by the equation y = 2.50x. We can rewrite this equation as:

y/x = 2.50

This gives us the unit price of fencing in dollars per foot. Therefore, the unit price of fencing for Bargain Hardware is:

Unit price = 2.50 dollars per foot

Note that the unit price for Bargain Hardware is constant at $2.50 per foot, while the unit price for Andy's Hardware varies depending on the length of fencing purchased.

To summarize:

Unit price for Andy's Hardware: $2.25 per foot

Unit price for Bargain Hardware: $2.50 per foot

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If the reported p-value is rounded to .03 in a one-sample hypothesis test for a mean, none of the above options (A, B, C, D) can be determined solely based on the p-value.

The p-value in hypothesis testing represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. It is used to assess the strength of evidence against the null hypothesis. The interpretation of the p-value depends on the significance level (α) chosen for the test. Option A suggests being approximately 3% confident that we should reject the null hypothesis based on the rounded p-value of .03.

However, the confidence level is not directly related to the p-value, but rather determined by the significance level chosen. Option B talks about being 97% confident that we would not be committing a type 2 error if we rejected the null hypothesis. However, the p-value does not provide information about type 2 error probabilities.

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Answer:

2673

Step-by-step explanation:

The expression 9cube×4 is counting some numbers like 0300, which are less than 1000. We can fix this as the first digit could be 3, which gives us 9cube possibilities.

The second, third, and fourth digits could be 3, and each of these cases gives us 8×9Square possibilities. (The first digit cannot be 0.)

So the total number of possibilities is

9Cube +8×9Square×3=2673.

Answer:

=x

Step-by-step explanation:

x/y·y

=xy/y

=x

Hope this helps

PLS BRAINLIEST

If the coordimate is reflected over y = -2, hence the resulting coordinate wil be A = (4, -2), B = (2, 3), C = (-6, 2) and D = (2, 2)

Given the coordinate of the quadrilateral shown below

A = (-2, -2)

B = (-1, 3)

C = (3, 2

D = (-1, 2)

Reflecting the coordinates over the y - axis will give:

A = (2, -2)

B = (1, 3)

C = (-3, 2)

D = (1, 2)

If the coordimate is reflected over y = -2, hence the resulting coordinate wil be:

A = (4, -2)

B = (2, 3)

C = (-6, 2)

D = (2, 2)

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Answer:

b is correct

Step-by-step explanation: