ESTION I Determine, using the rules of differentiation: dy if y= 플 dx Show ALL calculations. 1. 2 6x³​

The probability of getting a head with her lucky coin is 0.46 and the margin of error for Melissa's estimated probability is 0.218.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. The range of probability is 0 to 1, with 0 representing impossibility and 1 denoting certainty.

Let X be the "number of heads" in a n=13 trial.

The observed percentage of fortunate coins with heads is,

X= 6

The estimated probability of Josue ‘flipping a head’ with his lucky coin is,

p = X/n

p = 6/13

p = 0.46

A statistic called the margin of error measures the degree of random sampling error in a survey's findings. It indicates a likelihood that the results of a sample will be quite close to the findings that one would arrive at if the full population had been surveyed. The margin of error is obtained by multiplying the critical value by the standard deviation.

The estimated probability calculated using Josue's margin of error (ME) assuming,

α = 1 - 0.95= 0.05 is,

ME= Zc x [tex]\sqrt{{p^(1-p^)/n[/tex]

Here, p = 0.46, Zc= z(0.05/2)= 1.96

ME = 1.96 x √0.46⨉0.55/20

ME = 1.96 x √0.01238

ME = 0.21808≅ 0.218

The margin of error is 0.218.

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[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Mean = \dfrac{Sum\: of \: Observations }{No.\:of \:Observations }}\\[/tex]

As per question, we are given -

[tex] \:\:\:\:\:\:\star\:\sf Sum \:of \:observations \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 9+4+8+8+7+x \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 36+x \\[/tex]

Now that, we are given all the values which are required for solving this problem, so we can substitute the values and solve for the sixth datum -

[tex] \:\:\:\:\:\:\longrightarrow \sf Mean = \dfrac{Sum\: of \: Observation }{No.\:of \:Observation }\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 7 = \dfrac{36+x}{6}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 7\times 6 = 36+x \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 42 -36 =x\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{x = 6}\\[/tex]

18/99 simplified is 2/11 by dividing the numerator and denominator by 9.

A mathematical expression can be simplified by replacing it with an equivalent one that is easier (typically shorter), for example. In computer algebra, formulas of algebra are simplified. Boolean equation simplification is also known as logic optimization.

To simplify 18/99

We need to simplify the denominator and numerator by the greatest common factor.

In 18 and 99, 9 is the greatest common factor so, we can divide the numerator and denominator by 9 .

[tex]\frac{18}{99} = \frac{18/9}{99/9} \\\frac{18}{99} = \frac{2}{11}[/tex]

Therefore 18/99 simplified is 2/11

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For given squares, the area of the light greyed figure will be 9²-x² unit².

What are squares?

In mathematics, a square is a geometric shape with four sides of equal length and four right angles. It is also a special case of a rectangle where all sides have the same length. A square can also be defined as a regular quadrilateral, which means all its interior angles are right angles (90 degrees) and all its sides are congruent.

The area of a square can be calculated by multiplying the length of one side by itself, written as A = s², where A is the area and s is the length of a side.

Now,

side of bigger square=9

side of dark greyed square=x

as

Area of light greyed figure will be = area of bigger square - area of dark greyed square

Area(light greyed)=9²-x²

Hence,

           the area of the light greyed figure will be 9²-x² unit².

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The 11th term in the arithmetic sequence 13, 19, 25, 31 is 73.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed number called the common difference (d) to the preceding term.

To find the 11th term in the arithmetic sequence 13, 19, 25, 31, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where:

an is the nth term

a1 is the first term

n is the number of the term we want to find

d is the common difference

In this sequence, the first term (a1) is 13 and the common difference (d) is 6 (we can see that by subtracting each term from the one before it). So we can plug in the values we know:

a11 = 13 + (11 - 1)6

a11 = 13 + 60

a11 = 73

Therefore, the 11th term in the sequence 13, 19, 25, 31 is 73.

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Answer and Step-by-step explanation:

We want to find the measure of angle ABD (∠ABD).

We can tell by looking at this triangle that the array BD creates complementary angles (two angles who's sum equals 90°). ∠CBD is given to us, and we want to find ∠ABD. By knowing that these two angles will add up to 90°, we can create a formula to solve for ∠ABD.

90° = ∠ABD + ∠CBD

Plug in the angle for ∠CBD.

90° = ∠ABD + 45°.

Subtract 45° from both sides of the equation.

90° - 45° = ∠ABD + 45° - 45°

45° = ∠ABD

So, angle ∠ABD is 45°.

Have a great day!

Answer:

∠ABD = 45°

Step-by-step explanation:

∠ABC = 90° (right angle)

∴ ∠ABD = ∠ABC - ∠CBD

             = 90° - 45°

             = 45°

Answer:

Step-by-step explanation:

height x is in the wrong spot of the triangle -90 x 100 then divide sum like that.. (:

We need to find the initial horizontal component of the vector that represents the velocity of the ball. Let us represent that initial horizontal component by, [tex]\bold{v_x}[/tex].

Now, since basketball player shoots the ball with an initial velocity, [tex]\bold{v}[/tex], of 17.0 ft./sec at an angle of 34.1 degrees with the horizontal, we can find the initial horizontal component by, [tex]\bold{v_x}[/tex] using the following formula:

[tex]\bold{v_x}=\bold{v}\text{cos}(\theta)=17.0\times\text{cos}(34.1^\circ)\thickapprox14.1[/tex] ft./sec

Answer: It would be 8 tickets to break even.

Step-by-step explanation: 8×6.75=54

Using the given information, the drama club must sell 50 tickets to break even.

From the question we are to determine the number of tickets that must be sold to at least break even

From the given information,

The drama club has $1262.50 from fund raising

and

They estimated that the entire production will cost $1600.00

Thus,

They need to raise $1600.00 - $1262.50 to break even

$1600.00 - $1262.50 = $337.5

Also from the given information,

Each ticket cost $6.75

Therefore,

The must sell $337.5/$6.75 tickets to break even

$337.5/$6.75 = 50

Hence, the must sell 50 tickets

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Thus, by the property of side side side congruence of triangle, ΔRST ≅ ΔUTS .

Both triangles are considered congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

Given :

The statements are-

RS ≅ UT              Given

RT ≅ US              Given

St  ≅ TS            Common

ΔRST ≅ ΔUTS   By side side side congruence

Thus, by the property of  side side side congruence of triangle, ΔRST ≅ ΔUTS .

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The probability that a person did not see the ad given that they did not purchase the game is 0.146.

Let A be the event that a person has seen the advertisement, and let B be the event that a person has not purchased the game. We are asked to find the probability P(A' | B), which is the probability that a person did not see the ad given that they did not purchase the game.

We can use Bayes' theorem to calculate this probability:

P(A' | B) = P(B | A') * P(A') / P(B)

Where

We know that 47% of the market has seen the ad, so the probability of not seeing the ad is 1 - 0.47 = 0.53. We also know that 48% of those who see the ad purchase the game, so 52% of those who see the ad do not purchase the game. Finally, we know that 86% of those who have not seen the ad have not purchased the game.

Putting all of this information together, we can calculate:

P(B | A') = 86%

P(A') = 53%

P(B) = P(B | A') * P(A') + P(B | A) * P(A) = 0.52 * 0.47 + 0.14 * 0.53 = 0.3111

Substituting these values into Bayes' theorem, we get:

P(A' | B) = (0.86 * 0.53) / 0.3111 = 0.146 (rounded to three decimal places)

Therefore, the probability that a person did not see the ad given that they did not purchase the game is 0.146.

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Normal distribution is symmetric distribution so mean, median and mode are the same. The tails are the same length.

The left tail of such a distribution is longer than the right tail in negative type of asymmetric distribution. The “extremities” of a distribution are precisely what their name suggests - the extensions on either side of a distribution. While this term can be applied to a set of data, it is more easily observable when the data is represented graphically, as the extremities become readily apparent.

The extension on the left is referred to as the left-extremity, and likewise, the one on the right is called the right-extremity. It's not essential for a distribution to have both of these; it can have just one on either side.

Upper and Lower Extremities: Although it's more common to denote the extremities as being on the "left" or "right," this can be problematic if you're not examining a graph. In other words, if you're dealing with a set of data, it may not be immediately clear which data should be placed on the left or right of a graph. The alternative names for the right and left extremities, which address this problem, are upper extremity and lower extremity.

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Answer:

y = -x² + 5

Step-by-step explanation:

If x = -1

y = -(-1²) + 5

y = 4

If x = 0

y = 0 + 5

y = 5

If x = 1

y = -1² + 5

y = 4

If x = 2

y = -2² + 5

y = 1

If x = 3

y = -3² + 5

y = -4

Hope this helps!

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Answer:

Step-by-step explanation:

Middle right = 3

Bottom left = 15t

Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

3 * ( 5t + 4 )

3 * 5t + 3 * 4

15t + 12

Answer:

Step-by-step explanation:

112

If 0.25 inches on the map represents 400 meters in real life, then 1 inch on the map represents 4 * 400 = 1600 meters in real life. Therefore, 4.5 inches on the map represents 4.5 * 1600 = 7200 meters in real life. So, the distance between the towns is 7200 meters.

Answer:

145.68

Step-by-step explanation:

When rounding 145.678 to the nearest hundred, we look at the digit in the tens column, which is 4. Since 4 is less than 5, we round down to the nearest hundred. Therefore, 145.678 rounded to the nearest hundred is 100.

The sixth term is -48672 * x^5.

The coefficient of the fourth term is -2880.

The third term in ascending powers of x is 540 * x^8.

To find the terms and coefficients in the expansion of (3x - 2)^10, we'll use the binomial theorem which states that:

(a + b)^n = Σ [C(n, k) * a^(n-k) * b^k] for k = 0 to n

where C(n, k) is the number of combinations (n! / (k!(n - k)!)) and Σ is the summation symbol.

Here, n = 10, a = 3x, and b = -2.

Sixth term:

To find the sixth term, we'll plug k = 5 into the formula (since the index starts from 0):

C(10, 5) * (3x)^(10 - 5) * (-2)^5 = 252 * (3x)^5 * (-32)

The sixth term is -48672 * x^5.

Coefficient of the 4th term:

To find the coefficient of the fourth term, we'll plug k = 3 into the formula:

C(10, 3) * (3x)^(10 - 3) * (-2)^3 = 120 * (3x)^7 * (-8)

The coefficient of the fourth term is -2880.

Third term in ascending powers of x:

In ascending powers of x, the third term corresponds to x^2. Here, k = 2:

C(10, 2) * (3x)^(10 - 2) * (-2)^2 = 45 * (3x)^8 * 4

The third term in ascending powers of x is 540 * x^8.

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Answer:

50mm²

Step-by-step explanation:

divide it into a rectangle and triangle

rectangle = 7x5 = 35

triangle = 1/2x5x(13-7) = 1/2x5x6 = 15

35+15=50

Answer:

the ratio of boys to girls in Mr Hegarty's class is 5:3 (in its simplest form).

Step-by-step explanation:

For every 3 girls, there are 5 boys, which can be written as a ratio of 5:3 (boys to girls).

To simplify the ratio, we can divide both sides by the greatest common factor of 5 and 3, which is 1.

A marketing company is testing eight different page designs for its new catalogue of clothing. The analysis is most appropriate is ANOVA

The best analysis to use to determine whether there is a noticeable difference in sales amounts between the eight various page designs in the marketing company's new clothing catalogue is Analysis of Variance. In this instance, the averages of the sales figures for each of the eight page designs were compared using the statistical technique known as an ANOVA.

If there is a statistically significant difference between the group means, then at least one of the patterns may be linked to a higher degree of revenue than the others. This can be determined using an ANOVA. The marketing firm can use this data to identify the page designs that are most successful at driving purchases and change their catalogue as necessary to maximise income.

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Answer:

Step-by-step explanation:

The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side.

What is the bisector about?

A bisector is known to be a kind of straight line that cut or divide an angle or a line segment.

Note that The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side as it is the right step to take.

The correct answer to this question is letter b.There are only three steps in constructing a circle circumscribed by a triangle. He is done with the first step.  Use the compass to find the perpendicular bisector for side DF. I hope I have helped you.

The required probability of the given exponential distribution with mean of 10 minutes is equal to 0.39 rounded to two decimal places.

The amount of time spent at a bank follows an exponential distribution with a mean of 10 minutes,

The probability density function (PDF) of the time spent at the bank is given by,

f(x) = (1/10)e^(-x/10), where x ≥ 0

The probability of spending less than 5 minutes at the bank,

Evaluate the cumulative distribution function (CDF) of the exponential distribution up to x=5 minutes,

P(X < 5) = [tex]\int_{0}^{5}[/tex] f(x) dx

=[tex]\int_{0}^{5}[/tex](1/10)e^(-x/10) dx

= [-e^(-x/10)][tex]|_{0}^{5}[/tex]

= -e^(-1/2) + 1

≈ 0.393

Therefore, the probability of spending less than 5 minutes at the bank is approximately 0.39, rounded to two decimal places.

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[tex]0, 1, 1, 2, 2, 2, 2, 3, 3, 5[/tex], minimum: [tex]0[/tex], maximum: [tex]5[/tex], mean: [tex]2.1[/tex], median: [tex]2[/tex], mode: [tex]2[/tex]. I think the data have zero skew. Its mean, median, and mode are based on [tex]2[/tex]. It shows symmetry.

The value that happens most frequently is the mode. The only averaging that is capable of having zero, one, or several values is the mode. Finding the mode is aided by first sorting the numbers.

The mode formula in statistics is used to determine the mode or mode value for a specific collection of data. It is regarded as the number that consistently appears in a particular set. In other words, the mode or mode value in a data collection is the value or quantity that occurs more frequently or with a specific rate.

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The complete question is:

A school sells boxes of cookies each year for a charity fund. The data set shows the number of boxes the 10 families living on Willow Avenue buy, on average, every year. Does this data have negative, positive, or zero skew?

{2,3,2,2,0,5,2,1,1,3}

Answer: x = 50, y = 25

Step-by-step explanation:

Use your trigonometric identities. Sin = Opposite over hypotenuse. Sin(60) = [tex]25\sqrt{3}/x[/tex]. Therefore, [tex]25\sqrt{3}/sin(60) = x[/tex]. Sin(60) = 0.866, so your answer is 50.0014667312, or x = 50. Do the same for the other one, just with tan (Opposite over adjacent). Your answer is 25.  

[tex]p = 5a[/tex]

Answer

P=60

Step by step explanation

a= 12

so according to the formula

p=5(12)

p=60

The perimeter of a pentagon with sides that are each 12 inches long is 60 inches.

The perimeter of a form is the space surrounding its edge.

The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline. Depending on the size, the perimeter of several figures can be the same.

We have,

Sides of Pentagon = 12 inches

We know that Pentagon have 5 sides.

So, Perimeter of Pentagon

= 5 x side

= 5 x 12

= 60 inches

Thus, the Perimeter is 60 inches.

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Dayna will earn $13.43 in interest after 3 months.

Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is usually expressed as an annual percentage rate, interest expense or revenue is frequently expressed as a dollar amount.(APR).

To calculate the interest earned by Dayna after 3 months, we need to convert the interest rate to a monthly rate, since the time period given is in months.

The monthly interest rate can be calculated by dividing the annual interest rate by 12 (the number of months in a year):

monthly interest rate = 1.8% / 12 = 0.15% per month

Now we can use the formula for simple interest to calculate the interest earned:

simple interest = principal x rate x time

Where:

We know the principal is $2,978, the rate is 0.15% per month, and the time is 3 months. We can plug these values into the formula and solve for the simple interest:

simple interest = $2,978 x 0.0015 x 3

Simplifying:

simple interest = $13.43

Therefore, Dayna will earn $13.43 in interest after 3 months.

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"The given statement is option C."The point I is located three-fourths unit to the right and three-fourths unit up from the origin. So the ordered pair that represents point I is (3/4, 3/4).  Which shows (3/4, 3/4) as one of the options.

It is important to remember that the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin.

The signs of the coordinates indicate the direction: positive indicates to the right or up, while negative indicates to the left or down. In this case, the x-axis starts at -2 and goes up to 2 with tick marks every one-fourth unit, and the y-axis starts at -2 and goes up to 2 with tick marks every one-fourth unit.

By following the directions given, we can determine the location of each point and its corresponding ordered pair.The point I is located to the right three-fourths unit and up three-fourths unit from the origin. Therefore, the ordered pair that represents the point labeled as I is (3/4, 3/4).

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Jacki's estimates are reasonable because they make the total of the five winning basketball scores equal to 500 points.

The correct answer is D. It is reasonable because all the scores equal 500.

First, we know that the five winning scores totaled 500 points.
Three of the scores (81, 112, and 97) are already recorded in the team log. We can add these three scores together to find out how many points we need to reach 500:

81 + 112 + 97 = 290 points.

To find the remaining points needed, we can subtract the sum of the known scores (290 points) from the total points (500 points):

500 - 290 = 210 points.
Jacki estimated that the other two scores were 100 and 110 points.

We can add these two scores together to check if they equal the remaining points needed (210 points):

100 + 110 = 210 points.

Since Jacki's estimates add up to the remaining points needed (210 points), we can conclude that her estimates are reasonable.

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