One or more final O's used after the decimal point are always significant. True or flase?

Answer:

To find the odds in favor of Cody being first, we need to divide the probability of him winning (25%) by the probability of him not winning (75%).

Odds in favor of Cody winning = 25% / (100% - 25%) = 25% / 75%

Simplifying, we get:

Odds in favor of Cody winning = 1/3

Therefore, the odds in favor of Cody being first in the 50m backstroke are 1 to 2 (or 1:2).

Note that the rule that describes the translation that was aplied to the trapezoid D.O.G.S to create D'.O'. G'. S' is (x,y) → (x-3, y-7).

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction.

Translation in geometry refers to shifting a form into a different place without affecting it in any manner. Shape translation is presented to Year 5 students by providing them shapes on squared paper that must be moved a specified number of squares up, down, left, or right.

Hence, the  translation rule

that was aplied to the trapezoid D.O.G.S to create D'.O'. G'. S' is (x,y) → (x-3, y-7).

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

The probability that fewer than 11% of the plants in the random sample on this machine is 0.0823.

Given:

The likelihood of a plant having a modern machine is 1/3.

To discover:

The likelihood is that less than 11% of the plants in an arbitrary test have an unused machine.

Let X be the number of plants

out of n plants within the test that has the modern machine.

Since each plant features a likelihood of 1/3 of having the machine, X follows binomial dissemination with parameters n and p=1/3.

We have to discover

P(X < 0.11n).

Utilizing the coherence adjustment, we have:

P(X < 0.11n) = P(X <= 0.10n)

= P(Z <= (0.10n - np)/√(np(1-p))),

where Z may be a standard typical arbitrary variable

Since n isn't given, able to accept a large sufficient test measure such that the binomial dispersion can be approximated by a normal distribution.

A commonly utilized run show of thumb is that this estimation is sensible in case both np and n(1-p) are at the slightest 10.

Since n isn't given, we cannot affirm whether this condition is met or not, but we are going to accept it for the reason of the arrangement.

Utilizing np= n/3 and (1-p)n= (2/3)n, we have:

P(Z <= (0.10n - n/3)/√(n/3 * (2/3)n))

= P(Z <= (0.10 - 1/3)/√(2/9 * n))

= P(Z <= -1.39/√(n))

Employing a standard normal table or calculator, we will discover that P(Z <= -1.39) = 0.0823.

In this manner,

P(X < 0.11n) = P(Z <= -1.39/√(n)) = 0.0823.

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The percentage of values from the z-scores are 29.43% and 5.40%,, respectively

Here, we have

Between z = 0.53 and 2.67

This is represented as

Percentage = (0.53 < z < 2.67)

Using a graphing calculator, we have

Percentage = 29.43%

Next, we have

To the right of z = 1.61

This is represented as

Percentage = x > 1.61

Using a graphing calculator, we have

Percentage = 5.40%

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The requried equation of the line shown in the graph is y = -5x + 6.

From the graph locate 2 points, (0, 6) and (1, 1)

The slope of the line is given as,

m = (1 - 6) / (1 - 0)

m = -5

Using the point-slope form of the equation of a line, we have,

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is a point on the line. Substituting m =-5 and (x₁, y₁) = (0, 6), we get:

y - (6) = -5(x 0)

y = -5x + 6

Therefore, the equation of the line shown in the graph is y = -5x + 6.

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The initial value of the car will be $18,500 initial value and a $2717.85 value after 11 years.

We are Given that the dollar value v (t) of a certain car model that is t years old is given by the following exponential function .

The initial value will be at t= 0,

v (t) = 18,500 (0.84)'

v(t) = 18,500 x (0.84)⁰

v(t) = $18,500

The value of the car after 12 years will be

v(t) = 18,500 (0.84)^11

v(t) = $2717.85

Therefore, the car will have a $18,500 initial value

$2717.85 value after 11 years.

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Answer:

65 feet

Step-by-step explanation:

Let x be the length of the expansion to the north, and y be the width of the expansion to the east.

The current patio has an area of 30 * 30 = 900 square feet.

The total area of the expanded patio will be 2500 square feet.

So, we need to find values of x and y that satisfy the following two conditions:

The area of the expanded patio is 2500 square feet:

xy = 2500

The expanded patio has walls on two sides, so it can only expand to the north and east:

x + 30 = y

We can solve the second equation for x:

x = y - 30

Substitute this expression for x in the first equation:

(y - 30)y = 2500

Simplifying this equation:

y^2 - 30y - 2500 = 0

We can solve for y using the quadratic formula:

y = (30 ± sqrt(30^2 + 4*2500)) / 2

y = (30 ± sqrt(10000)) / 2

y = (30 ± 100) / 2

Since y must be positive, we can ignore the negative solution:

y = (30 + 100) / 2 = 65

Substitute this value for y in the equation x + 30 = y:

x + 30 = 65

x = 35

Therefore, the expansion to the north should be 35 feet, and the expansion to the east should be 65 feet.

The percentage of the students of the class voted for Maria is 36%.

Number of students in Ms. Nguyen's second grade = 25

Number of students voted for Benjamín = 4

Number of students voted for Sahil = 12

Number of students voted for Maria = 9

The total number of students who voted in the class election is,

4 + 12 + 9 = 25

This is the same as the total number of students in the class.

So all students participated in the election.

The percentage of the class that voted for Maria is simply,

= (9/25) ×100

= 36%

Therefore, 36% of the students in Ms. Nguyen's second-grade class voted for Maria.

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The above question is incomplete, the complete question is:

There are 25 students in Ms. Nguyen's second-grade class. In the class election, 4 students voted for Benjamin, 12 voted for Sahil, and 9 voted for Maria. What percentage of the class voted for Maria?

Answer:

Bellow

Step-by-step explanation:

To prove the equation:

(x - 1)/(x - 3) - (x ^ 2 - x + 2)/(x ^ 2 - 2x - 3) = 1/(x + 1)

we need to find a common denominator for the left-hand side of the equation. The common denominator is (x - 3)(x + 1)(x - 3), which is the product of all the factors in the denominators.

Using this common denominator, we can rewrite the left-hand side of the equation as:

[(x - 1)(x + 1)(x - 3) - (x ^ 2 - x + 2)(x + 1)] / [(x - 3)(x + 1)(x - 3)]

Simplifying the numerator using distributive property, we get:

[(x^3 - 2x^2 - 2x + 2) - (x^3 - 2x^2 - x - 2)] / [(x - 3)(x + 1)(x - 3)]

Simplifying the numerator further, we get:

(-x + 4) / [(x - 3)(x + 1)(x - 3)]

Now, we can simplify the right-hand side of the equation by multiplying both the numerator and the denominator by (x - 3)(x + 1), which gives us:

1 / (x + 1) = (x - 3)(x + 3) / [(x - 3)(x + 1)(x - 3)]

Therefore, the original equation can be written as:

(-x + 4) / [(x - 3)(x + 1)(x - 3)] = (x - 3)(x + 3) / [(x - 3)(x + 1)(x - 3)]

Cancelling the common factors on both sides, we get:

-x + 4 = x^2 - 9

Rearranging and simplifying, we get:

x^2 + x - 13 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-1 ± √(1 + 4*13)) / 2

Simplifying, we get:

x = (-1 ± √53) / 2

Therefore, we have proved that the equation:

(x - 1)/(x - 3) - (x ^ 2 - x + 2)/(x ^ 2 - 2x - 3) = 1/(x + 1)

holds true for all values of x except (-1, 3, 3 - √13, 3 + √13).

Answer:

Step-by-step explanation:

(x-1)/(x-3)-(x²-x+2)/(x²-2x-3)=1/(x+1)

[tex]\frac{x-1(x^{2}-2x-3)-x-3(x^{2}-x+2) }{x-3(x^{2} -2x-3)}[/tex] =0

[tex]\frac{(x^{3}-2x^{2} -3x-x^{2} +2x+3)-(x^{3}-x^{2} +2x-3x^{2} +3x-6) }{x^{3}-2x^{2} -3x-3x^{2} +6x+9}[/tex]=0

[tex]\frac{-7x^{2} +2x+9}{x^{3}-5x^{2} +3x+9 }[/tex] =0

-7x²+2x+9=x³-5x²+3x+9

x³-2x²-x=0

The value of measure of angle Q is,

⇒ Q = 58.3 degree

We have to given that;

The triangle above has the following measures. s = 31 cm r = 59 cm

Now, We can formulate;

cos Q = s / r

cos Q = 31 / 59

cos Q = 0.525

Q = 58.3 degree

Thus, The value of measure of angle Q is,

⇒ Q = 58.3 degree

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Answer:

Median: 48

Range: 18

Step-by-step explanation:

The range: is calculated by subtracting the lowest value from the highest value

The median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

Step-by-step explanation:

Two walls are   8x 9   and two walls are 10 x 9

8x9 x2   + 10x9 x2 = 324 ft^2

Using the LCM,  the first customer to receive both a shopping bag and a 25% off coupon is the 45th customer.

To find the first customer who will receive both a free shopping bag and a 25% off coupon, we need to find the least common multiple (LCM) of 15 and 9, since the shopping bags are given every 15th customer and the coupons every 9th customer.

Step 1: Find the prime factors of both numbers.
15 = [tex]3 * 5[/tex]
9 = [tex]3^2[/tex]

Step 2: Identify the highest power of each prime factor in both numbers.
3: [tex]3^2[/tex] (from 9)
5: [tex]5^1[/tex] (from 15)

Step 3: Multiply the highest powers of each prime factor together to find the LCM.
LCM(15, 9) =[tex]3^2 * 5^1[/tex] = [tex]9 * 5[/tex] = 45

So, the first customer who will receive both a free shopping bag and a 25% off coupon is the 45th customer.

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The values of A-B and B-A are 27 and 36.

We are given that;

WA=(x/x=3".n≤6,nEN)

B= (x/x=9",n≤ 4,n € N)

Now,

First, let’s write the sets A and B using roster notation, which means listing all the elements inside curly braces.

A = {x | x = 3n, n ≤ 6, n ∈ N} = {3, 6, 9, 12, 15, 18}

B = {x | x = 9n, n ≤ 4, n ∈ N} = {9, 18, 27, 36}

Now, let’s find A - B by removing the elements that are common to both sets from A.

A - B = {3, 6, 9, 12, 15, 18} - {9, 18, 27, 36} = {3, 6, 12, 15}

Similarly, let’s find B - A by removing the elements that are common to both sets from B.

B - A = {9, 18, 27, 36} - {3, 6, 9, 12, 15, 18} = {27, 36}

Therefore, by the equation the answer will be 27 and 36.

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The equation of the least-squares regression line for predicting the etching rate from the room temperature is 1.77 + 0.23x.

The least squares method is a form of mathematical regression analysis used to determine the line of best fit for a set of data, providing a visual demonstration of the relationship between the data points.

The equation of the least-squares regression line for predicting the etching rate from the room temperature is:

= 6.6 - 0.231 × 20.9 = 1.7721

y = 1.77 + 0.23x.

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Step-by-step explanation:

Continuous compounding formula :

FV = PV e^rt    FV = future value   PV = present value    

                r = decimal interest  rate     t = years

FV = 1000 e^(.045 * 10) = $ 1568.31

The critical value of the statistic for testing the hypothesis of equal treatment means at the 0.05 significance level is approximately option (a) 3.84

To find the critical value of the statistic for testing the hypothesis of equal treatment means at the 0.05 significance level, we can use an analysis of variance (ANOVA test) test

First, we need to calculate the total sum of squares (SST), which represents the total variability in the attendance data:

SST = ∑∑(Xij - X..)2

= (25-31.83)2 + (30-31.83)2 + ... + (30-31.83)2

= 351.83

where Xij is the attendance for the ith day and jth class time, X.. is the grand mean attendance, and the summation is over all observations.

Next, we need to calculate the between-groups sum of squares (SSG), which represents the variability in the attendance data that is due to differences between the class times

SSG = (∑nj(X.j - X..)2) / k

= [(25-32.17)2 + (30-32.17)2 + ... + (30-32.17)2 + (25-32.17)2 + (30-32.17)2 + ... + (30-32.17)2 + (25-32.17)2 + (30-32.17)2 + ... + (40-32.17)2] / 3

= 189.5

where nj is the number of observations for the jth class time, k is the number of groups (i.e., class times), and X.j is the mean attendance for the jth class time

Finally, we can calculate the within-groups sum of squares (SSW), which represents the variability in the attendance data that is due to differences within each class time:

SSW = SST - SSG

= 351.83 - 189.5

= 162.33

The degrees of freedom for the ANOVA test are:

dfG = k - 1 = 3 - 1 = 2 (degrees of freedom for the between-groups sum of squares)

dfW = N - k = 15 - 3 = 12 (degrees of freedom for the within-groups sum of squares)

dfT = N - 1 = 15 - 1 = 14 (total degrees of freedom)

where N is the total number of observations.

The F-statistic for the ANOVA test is

F = (SSG / dfG) / (SSW / dfW)

= (189.5 / 2) / (162.33 / 12)

= 5.87

To find the critical value of the F-statistic for testing the hypothesis of equal treatment means at the 0.05 significance level, we can look it up in an F-distribution table with dfG = 2 and dfW = 12. At the 0.05 level of significance, the critical value of the F-statistic is approximately 3.84.

Therefore, the correct option is (a) 3.84

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Answer:

3/4

Step-by-step explanation:

there are 4 spots and it is on the the third of them

Answer:

Adjacent, supplementary, found in explanation

Step-by-step explanation:

1. The angles above are adjacent.

2. The angles above are supplementary because the angles add up to 180⁰.

3. An equation for this could be

x+35=180

-35 on both sides

x=145⁰

Answer:

AB = √(2^2 + 5^2) = √(4 + 25) = √29 = 5.4

The correct way to explain the solution of the given system of equation is at point ( 1, 7) given by option (c) Line y = −2x + 9 intersects the line y = −x + 8

System of equation are,

y = −2x + 9  and  y = −x + 8

Solution to this system of equations,

The values of x and y should satisfy both the equations.

Equate the two equations to each other and solving for variable x.

⇒ −2x + 9 = −x + 8

like terms on same side of the equation,

⇒ x − 2x  = 8 - 9

Solve for x,

⇒ −x = -1

Dividing both sides of the equation by −1 we get,

⇒ x = 1

Substitute the value of x in either equation of the line and get value of y.

⇒ y = −2x + 9

⇒ y = −2(1) + 9

⇒ y = -2 + 9

⇒ y = 7

Therefore,  the solution representing system of equations is given by coordinate (1, 7) means option c. the line y = −2x + 9 intersects the line y = −x + 8 .

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To find the limit of (x + x²)/(9 − 4x²) as x approaches infinity, we can first try to apply l'Hospital's Rule, which states that if the limit of the ratio of the derivatives exists, then it is equal to the original limit.

However, in this case, a more elementary method is available: dividing both the numerator and denominator by the highest power of x.

1. Divide both the numerator and denominator by x²: lim (x/x² + x²/x²) / (9/x² - 4x²/x²) x→[infinity]

2. Simplify the expressions: lim (1/x + 1) / (9/x² - 4) x→[infinity]

3. As x approaches infinity, the terms with x in the denominator will approach 0: lim (0 + 1) / (0 - 4) x→[infinity]

4. Simplify the expression: (1) / (-4) The limit of (x + x²)/(9 − 4x²) as x approaches infinity is -1/4.

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Answer & Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In the triangle given, we can see that the lengths of the two shorter sides are 8 cm and 10 cm. We want to find the length of the hypotenuse.

Using the Pythagorean theorem, we can set up the equation:

a² + b² = c²

where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.

Substituting in the values we know, we get:

8² + 10² = c²

Simplifying:

64 + 100 = c²

164 = c²

Taking the square root of both sides, we get:

c = sqrt(164)

c ≈ 12.8062

Therefore, the length of the hypotenuse is approximately 12.8062 cm.

Answer: The length of the side of the supply closet is 6 feet

Step-by-step explanation:

1. We can separate the box into 2 rectangles.

3 x 8 and 2 x y

3 x 8 = 24

2. The whole closet is 36

36 - 24 = 12

3. The area of the 2 x y rectangle is 12

12/2 = 6

So the length of the y side is 6 feet.

When there are large differences between robust standard errors and usual standard errors, we can conclude that there may be issues with the assumptions of the statistical model.

Robust standard errors are typically used when there are concerns about heteroscedasticity or the presence of outliers in the data. In contrast, usual standard errors assume that the errors are homoscedastic and normally distributed.

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Answer:

50 degrees Fahrenheit

Step-by-step explanation:

add 15f to cancel -15f and add the 35f left which is 50f

The cost of the brush is $ 1.75 , The cost of the paint set  is $ 10.5 and

The cost of the sketchbook is $ 7

The total amount Emma has is $23.75

Let the cost of paint set = x

Cost of sketchbook = 2x/3

Cost of brush = (1/6)x

23.75 = x + 2x/3 + x/6 + 4.50

23.75 - 4.50 = (6x + 4x +x)/6

19.25 × 6 = 11x

x = 10.5

Cost of sketchbook = 2x/3

Cost of sketchbook = (2 × 10.5)/3

Cost of sketchbook = 7

Cost of brush = (1/6)x

Cost of brush = (1/6)10.5

Cost of brush = 1.75

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