how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 11?

The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

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The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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Answer:

1, scalene 2, equilateral 3, scalene 4, isosceles

Step-by-step explanation:

Answer:

5x + 2y = -6

-5x            -5x

2y = -5x -6

The percentage of the data values in the box-and-whiskers plot, that are greater than or equal to 92, which is the 75th percentile, based on the five number summary, are 25 percent of the data.

The five number summary of a box-and-whiskers plot are value of the minimum, the first quartile, the median, the third quartile and the maximum value of the set of data.

Please find attached the possible box-and-whiskers plot in the question, obtained from a similar question on the internet

The five number summary from the box-and-whiskers plot are;

Minimum value = 82

The first quartile or the 25th percentile = 87

The median, second quartile or the 50th percentile = 90

The third quartile or the 75th percentile = 92

The value 92 on the data represents the 75th percentile, therefore, the percentage of the data that are greater than or equal to 92 are; 100 - 75 = 25 percent

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The expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.

Option (C) is correct.

What is a discount?

A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage customers to make a purchase or to clear inventory. Discounts can be expressed as a percentage off the original price, or as a fixed dollar amount.

Part A: The expression that would calculate the final price of a hat is h(0.775)(1.08875). This takes into account the 22.5% discount by multiplying the original price by 0.775, and then adds the 8.875% sales tax by multiplying the discounted price by 1.08875.

Part B: If the original price of a hat is $42, then the final price of buying four hats after the discount and sales tax would be $42 x 4 x 0.775 x 1.08875 = $142.

Hence, the expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.

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Answer:

1. 3/5

2. 2/5

3. 1/5

Step-by-step explanation:

I'm pretty sure this is the answer :)

The equation is shown in the picture that represents the relationship between the side lengths of each triangle.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have side lengths of a right-angle triangle shown in the picture.

We know the Pythagoras theorem:

hypotenuse² = perpendicular² + base²

For the first side lengths: 10, 6, 8

10² = 6² + 8²

For the second side lengths: √5, √3, √8

√8² = √5² + √3²

For the third side lengths: √30, √5, 5

√30² = √5² + 5²

For the fourth side lengths: 1, √37, 6

√37² = 6² + 1²

For the fifth side lengths: 3, √2, √7

3² = √7² + √2²

Thus, the equation is shown in the picture that represents the relationship between the side lengths of each triangle.

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After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

False.

6 miles is farther than 6 kilometers. One mile is equal to 1.60934 kilometers, so 6 miles is equal to 6 x 1.60934 = 9.65604 kilometers. Therefore, 6 miles is farther than 6 kilometers.

Step-by-step explanation:

The answer is:

Work/explanation:

We can't really compare two things if they have different units.

So we need to convert kilometers to miles first.

1 km is approximately equal to 0.621 miles.

So 6 km would be approximately 3.728 miles.

6 miles is further away than 3.728 miles.

6 km is not as far as 6 miles. And now we know why.

Answer:

A- The side length of the largest square tile Hector can use to tile his shed floor so that there are no gaps or overlaps is 48 inches

B- The number of square tiles Hector will need is 15 tiles

Step-by-step explanation:

A- The given parameters are;

The size of the tiles cut by the company he found = 60 inches × 60 inches

The length of his shed floor = 240 inches

The width of his shed floor = 144 inches

The side length of the largest square tile is given as the highest common factor, HCF of 240 and 144 given as follows;

144/240 = 3/5

Therefore, we have the highest common factor of 144 and 240 = 144/3 = 48

Therefore, the side length of the largest square tile Hector can use to tile his shed floor so that there are no gaps or overlaps = 48 inches

B- The area of his shed floor = 240 inches × 144 inches = 34560 in.²

The area of one square tile = 48 inches × 48 inches = 2,304 in.²

The number of square tiles, n, Hector will need is given as follows;

The number of square tiles Hector will need = (The area of his shed floor)/(The area of one square tile)

The number of square tiles Hector will need = n =34560 in.²/(2,304 in.²) = 15

The number of square tiles Hector will need = 15 tiles.

96%  is the sensitivity of a method that produces 500 true-positive results and 20 false-negative results.

Why is pH important in electrophoresis?

This is important because the structure and charge of a protein or nucleic acid will change if subjected to significant pH changes, thus preventing proper separation.

What are the factors affecting electrophoresis?

Given,

         True-positive results = 500

          False-negative results = 20

      96% is the sensitivity of a method .

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Answer:32

Step-by-step explanation:

Because it is isosceles triangle

2 side length are equal so the angles of these two will also be equal

Answer:

We have that for the Question "During the California gold rush, minors sometimes paid $10 for a glass of water. What was the total cost of 8 miners each bought one glass of water? How can you use a 4s fact to find answer?" it can be said that  the total cost of 8 miners  is mathematically

given as

x=80

From the question we are told

During the California gold rush, minors sometimes paid $10 for a glass of water. What was the total cost of 8 miners each bought one glass of water? How can you use a 4s fact to find answer?

Generally the equation for the total cost of 8 miners  is mathematically

given as

x=number of miners * price

x=10*8

x=80

Therefore

the total cost of 8 miners  is mathematically

given as

x=80

Step-by-step explanation:

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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Step-by-step explanation:

x² = 50²+ 55² - 2 • 50 • 55 • cos61°

The trinomials in factor form are listed below:

Case A: (x + 2)²

Case B: (x - 3) · (x - 9)

Case C: (x - 7) · (x + 6)

Case D: (x - 9) · (x + 1)

Herein we find four case of trinomials of the form x² + b · x + c that must be factorised, this can be done by using the following algebraic property:

x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots of the quadratic equation.

Now we proceed to factorise each trinomial (quadratic equation), that is, their factor form:

Case A

x² + 4 · x + 4

x² + (2 + 2) · x + 2 · 2

(x + 2) · (x + 2)

(x + 2)²

Case B

x² - 12 · x + 27

x² - (3 + 9) · x + (- 3) · (- 9)

(x - 3) · (x - 9)

Case C

x² - x - 42

x² - (7 - 6) + (- 7) · 6

(x - 7) · (x + 6)

Case D

x² + 8 · x - 9

x² - (- 9 + 1) · x + (- 9) · 1

(x - 9) · (x + 1)

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Hello !

\(v - 8.21 = 2.5\\\\v - 8.21 \boxed{+ 8.21} = 2.5 \boxed{+ 8.21}\\\\v = 2.5 + 8.21\\\\v = 10,71\)

Have a good day !

Answer:

I got x= 3

\(m < DBE = 64\\m < CBE =26\)

Step-by-step explanation:

since x= 3,

I put 3 in the equations,

first equation,

17x + 13

17*3 + 13

=64

second equation,

32-2x

32 - 2*3

=26

The quadrilateral FGHJ is a parallelogram based on the equality of midpoints using the midpoint formula.

To determine if the quadrilateral FGHJ is a parallelogram, we can use the midpoint formula.

The midpoint formula states that the midpoint between two points (x1, y1) and (x2, y2) is given by the coordinates:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Let's find the midpoints of the opposite sides of the quadrilateral and check if they are equal:

Midpoint of FG:

x-coordinate: (-2 + 4) / 2 = 1

y-coordinate: (4 + 2) / 2 = 3

Midpoint of HJ:

x-coordinate: (4 + (-2)) / 2 = 1

y-coordinate: (-2 + (-1)) / 2 = -1.5

The midpoints of FG and HJ are (1, 3) and (1, -1.5) respectively.

Now, let's find the midpoints of the other pair of opposite sides:

Midpoint of GH:

x-coordinate: (4 + 4) / 2 = 4

y-coordinate: (2 + (-2)) / 2 = 0

Midpoint of FJ:

x-coordinate: (-2 + (-2)) / 2 = -2

y-coordinate: (4 + (-1)) / 2 = 1.5

The midpoints of GH and FJ are (4, 0) and (-2, 1.5) respectively.

By comparing the midpoints of the opposite sides, we can see that the midpoints of FG and HJ are equal to the midpoints of GH and FJ. This indicates that the quadrilateral FGHJ is a parallelogram.

Therefore, the quadrilateral FGHJ is a parallelogram based on the equality of midpoints using the midpoint formula.

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Answer:

64 can go into 28 0.4375 times. (less than 1 in a nutshell)

Step-by-step explanation:

The sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be examples abοve are equal tο 16t - 0.25.

Mathematical prοcesses like multiplying, dividing, adding, and nοw even deleting are required. If they were merged, the fοllοwing claim wοuld be made: An equatiοn, sοme statistics, and a mathematical fοrmula Values, cοmpοnents, and mathematical prοcesses like additiοns, subtractiοns, reversals, algebraic fοrmulas, and divisiοns make up a statement οf truth. Wοrds and phrases can be rated and analyzed.

Here,

We pοssess 16t – 0.25.

A) The fοrmula 42t/40.5 equals (22t)² / (20.5) = 24t / (20.5) = 16t / (20.5)4 = 16t / 4 = 4(16t).

Expressiοn A is nοt equal because 4(16t) is nοt the same as 16t - 0.25.

B) \((16)^t/2^4 = (2^4)^t / 2^4\)

=> \(2^{4t} / 2^4 = 2^{(4t-4)} = 16^{(t-1)} (t-1).\)

Expressiοn B is not equivalent because 16(t-1) is nοt equal to 16(t - 0.25).

C) \(16^t/2 = (2^4)^t / 2\)

\(= > 2^{4t} / 2 = 2^{(4t-1)} = 16^t \times 0.5.\)

Expression C is nοt equivalent because 16t * 0.5 does not equal 16t - 0.25.

Hence, As a result, nοne of the examples above are equal to 16t - 0.25.

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Answer:

Step-by-step explanation:

Circle O is represented by the equation (x+7)² + (y + 7)² = 16. The length of the radius of Circle O is 4.

The equation of Circle O, (x+7)² + (y+7)² = 16, is in the standard form of a circle equation: (x - h)² + (y - k)² = r². Comparing it to the given equation, we can determine the values of h, k, and r.

In the given equation:

Center coordinates: (-7, -7) → h = -7, k = -7

Radius squared: 16 → r² = 16

To find the length of the radius, we need to take the square root of r²:

r = √(16)

Calculating the square root, we get:

r = 4

Therefore, the length of the radius of Circle O is 4.

Looking at the answer options, we see that the correct answer is Option B which is equal to 4.

The equation of a circle in the standard form (x - h)² + (y - k)² = r² represents a circle with center (h, k) and radius r. By comparing the given equation to the standard form, we can extract the values of h, k, and r. Taking the square root of r² gives us the length of the radius, which in this case is 4.

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All the above can represent stable interhalogen compounds. Interhalogen compounds are formed when different halogens combine with each other.

The general formula for interhalogen compounds is given by XYn, where X and Y represent different halogens, and n represents the number of Y atoms bonded to the X atom. The interhalogen compounds can have different stoichiometries, resulting in different values of n. Therefore, all the given formulas, XY, XY2, XY3, and XY5, can represent stable interhalogen compounds, depending on the specific combination of halogens and their bonding arrangements.

Hence, none of the given formulas does not exist for interhalogen compounds, as all of them can be valid representations of stable interhalogen compounds.

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Step-by-step explanation:

5(1-2x) = -65

5-10x = -65

65+5 = 10x

70 = 10x

7 = x

x = 7

Answer:

X=7/2

Step-by-step explanation:

5(1 - 2x) = -65

5-20x=-65

-20x=-65-5

-20x=-70

Minus sign cancel from both side

So x=70/20

X=7/2

The expected value E(total) = $122,500 and standard deviation for the total discounts is SD(total) = $4,066

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Answer:

only God know the answer