i have 18 distinguishable socks in my drawer: 8 white, 6 brown, and 4 blue. in how many ways can i choose a pair of socks, provided that i get two socks of the same color?

The expression for a  90% confidence interval, given a sample of 50 people with a sample proportion of 0.65 is B. [tex]0.65\pm1.645\sqrt{\frac{0.65(1 -0.65)}{50}[/tex].

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

We know the confidence interval for a population proportion is given by the formula [tex]p\pm{Z_\frac{\alpha}{2}}\sqrt{\frac{p(1 -p)}{n}[/tex], where p = population proportion,

n = The number of samples and [tex]Z_\frac{\alpha}{2}[/tex] is the area value corresponding to the context.

Given, The 90% confidence interval, given a sample of 50 people with a sample proportion of 0.65.

We know at 90% confidence interval [tex]Z_\frac{\alpha}{2}[/tex] = 1.645.

Therefore it should be [tex]0.65\pm1.645\sqrt{\frac{0.65(1 -0.65)}{50}[/tex].

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We can see here that assuming is solving a linear system and in the process of solving it, the person gets a final statement of 5 = 0, the true statement will  be: D. None of these statements are true.

A linear system is a set of one or more linear equations involving the same variables. The goal is to find the values of the variables that simultaneously satisfy all the equations in the system.

A linear equation of the form 5 = 0 has no solutions, since 5 is not equal to 0. In this case, if you graph the equation on a coordinate plane, it will be a straight line with no points on the line satisfying the equation.

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Answer:

Gia has 85 beads in the end

Step-by-step explanation:

28+17 beads = 45 beads

94 beads - 45 beads = 49 beads

49 beads + 36 beads = 85 beads

Since Paul's English class is located in the same quadrant as the library, the coordinates of the English classroom include the following: B: (−4, 5).

In Mathematics, the translation of a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image or function.

On the other hand (conversely), the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

Since the library is located in the fourth quadrant in which the value on the x-coordinate (x-axis) is positive while the value on the y-coordinate (y-axis) is negative, we can reasonably infer and logically deduce that its coordinates would be translated to the right and then downward.

In conclusion, the coordinates of the English classroom would most likely have negative x-coordinate (x-axis) and a positive y-coordinate (y-axis);

Coordinates of the English classroom = (-4, 5).

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Complete Question:

The map shows the location of four places in a school.

A coordinate plane is shown. There is a point at 5, 2 labeled Front office. There is a point at negative 6, 4 labeled Gym. There is a point at negative 4, negative 3 labeled Auditorium. There is a point at 6, negative 4 labeled Library.

Paul's English class is located in the same quadrant as the library. Which of the following could be the coordinates of the English classroom?

A: (4, 5)

B: (−4, 5)

C: (−4, −5)

D: (4, −5)

Answer:

16 ounces of $400 alloy

Step-by-step explanation:

The amount of each solution that should be mixed together to obtain the desired target solution is;

160 quarts of the solution that contains 3 parts salt to 5 parts water

120 quarts of the solution that contains 2 parts salt to 8 parts water

The parameters are;

Solution A contains 2 parts salt to 8 parts water

Solution B contains 3 parts salt to 5 parts water

Target Mixture contains 3 parts salt to 7 parts water:

Expressing the salt concentration in decimal form;

Solution A: 2/(2 + 8) = 2/10

= 0.20 salt

Solution B: 3/(3 + 5) = 3/8

= 0.375 salt

Mixed Solution: s/(3 + 7) = 3/10

= 0.30 salt

Since target mixture is 280 quarts;

If the amount of 0.375 salt present in mixed solution is denoted by x

Then, the amount of 0.20 salt is expressed as;

y = 280 – x

Using a general mixture equation, we will have;

0.375x + 0.20(280 - x) = 0.30(280)

0.375x + 56 - 0.20x = 84

Subtract 56 from both sides of the equation

0.375x - 0.20x + 56 – 56 = 84 – 56

0.375x - 0.20x = 28

0.175x = 28

Divide both sides of the equation by 0.175

0.175x/0.175 = 28/0.175

x = 160

Thus;

y = 280 – x

y = 280 – 160

y = 120

Therefore,

x = 160 quarts of the solution that contains 3 parts salt to 5 parts water

y = 120 quarts of the solution that contains 2 parts salt to 8 parts water

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Conduct additional surveys to increase the total number of responses.

Remove duplicates from the dataset to eliminate skewing of results

Use caution when interpreting the results and consider them exploratory rather than conclusive

Consider using a different methodology for gathering data, such as focus groups or interviews

Adjust the confidence level for the survey results to account for the smaller sample size

Use a different data analysis technique, such as bootstrapping, to account for the limitations of the dataset

Consider using a sample survey method, like stratified sampling or cluster sampling.

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0.115 is the quotient of  9.43/82

A division is a process of splitting a specific amount into equal parts.

In division, we divide a number by any other number to get another number as a result.

The number which is getting divided here is called the dividend.

The number which divides a given number is the divisor.

The number which we get as a result is known as the quotient.

9.43/82 we have to find quotient

9.43 is the dividend and 82 is the divisor

9.43/82=0.115

Hence, 0.115 is the quotient of  9.43/82

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Answer:

1.  Rotation 90° counterclockwise

    (x, y) → (-y, x)

2.  Translation 2 right and 2 down

    (x, y) → (x + 2, y – 2)

3.  Reflection over the x-axis

    (x, y) → (x, -y)

4.  Translation 2 left and 2 up

    (x, y) → (x – 2, y + 2)

Step-by-step explanation:

Translation 2 left and 2 up

To translate (move) a point two units to the left, we subtract 2 from its x-value.  Similarly, to translate (move) a point two units up, we add 2 to its y-value.

Rotation 90° counterclockwise

When rotating a point 90° counterclockwise, the y-value becomes negative, and the x and y switch:

Translation 2 right and 2 down

To translate (move) a point two units to the right, we add 2 to its x-value.  Similarly, to translate (move) a point two units down, we subtract 2 from its y-value.

Reflection over the x-axis

When a point is reflected over the x-axis, the y-value is negated but the x-value stays the same:

On solving the provided question, we can say that a set's elements can be arranged in any sequence.

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

Set Representation

A capital letter indicates a set. For instance, consider sets A, B, N, etc.

Small letters are used to identify the components of a set. Each element is written using curly brackets and a comma in between.

Elements are not repeated in set notation.

A set's elements can be arranged in any sequence.

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One is not considered a prime factor.

One has only a single element, which is itself, hence it is not regarded as a prime number. A prime number is a positive integer greater than 1 with just itself and the number one as its other positive divisors. Since there is only one divisor of one, one is not regarded as a prime number. Additionally, 1 does not adhere to the conventional characteristics of prime numbers and is regarded as a unit in mathematics.

For instance, a number's value is unaffected by division or multiplication by one, and it is always one when raised to any power. Since one does not meet the criteria for primes and does not share their characteristics, it is likewise excluded from the set of prime numbers.

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Answer:

The slope: 2/5

The point is on the graph below

Step-by-step explanation:

y−4=2/5(x+3)

y - 4 = 2/5x + 3

y = 2/5x + 7

The equation is y = mx + b

m = the slope

m = 2/5

Answer:

[tex]point=(-3,4)\\\\slope=\frac{2}{5}[/tex]

Step-by-step explanation:

[tex]y-y_0=m(x-x_0)[/tex]

[tex]y_o:y-point\\x_o:x-point\\m=slope[/tex]

[tex]y-4=\frac{2}{5}(x+3) \\\\y_0=4\\x_0=-3\\\\slope=\frac{2}{5}[/tex]

The angle formed by the intersection of secant and tangent is as follows:

m∠P = 51.83 degrees.

A line that touches the circle at a single point is known as a tangent to a circle. Secant is straight line that intersects a curve at two or more points.

Therefore, the measure of the angle formed by the intersection of a tangent and a secant is equals to half the difference of the intercepted arcs.

Hence,

m∠P = 1 / 2 (125.83 - 22.17)

m∠P = 1 / 2 (103.66)

m∠P = 1 / 2 × 103.66

m∠P = 51.83 degrees

Therefore, the angle formed by the intersected secant and tangent is 51.83 degrees.

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Yes, the  intersection of all of those intervals always be ope

The mathematical concept of well-defined groupings of objects, or sets, that are referred to as members or elements of the set. The only sets that are taken into consideration are those whose members are also sets because pure set theory only deals with sets.

Any union of open sets, or an unlimited number of open sets, is open. It is open where a finite number of open sets intersect.

A closed set is the complement of an open set (according to the space that the topology is specified on).

Thus, the intersection of all of those intervals always be open.

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Answer:

by finding the angles and sides using law of sines

Step-by-step explanation:

basically you have to use the law of sines to find the angles and sides, after that you will find the angles and sides using law of sines

Hyperbola will form out from the cone.

The generator, vertex, and vertical axis are three crucial components of the double-napped cone. Conic sections or conics are the curves that result from the division of a double-napped cone into sections by a plane.

A plane intersects with both parts of a double cone to form a hyperbola, which is an open curve with two branches. The hyperbola will be symmetrical regardless of whether the plane is parallel to the axis of the cone or not.

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Answer:

2^845 is greater than 5^362.

Step-by-step explanation:

To compare the two numbers, we can evaluate them using the logarithm function with base 2 and base 5 respectively.

2^845 = 2^(845 * log2(2)) = 2^(845 * 1) = 2^845

5^362 = 5^(362 * log5(5)) = 5^(362 * 1) = 5^362

The logarithm of a number is the exponent to which the base must be raised to give that number. Since logarithm function is a monotonically increasing function, if we compare log base a of x to log base a of y, logarithm of x is greater than y if x is greater than y.

So 2^845 > 5^362 if 845 > 362 * log5(2)

We can calculate log5(2) = log5(2)/log5(2) = 0.6309

so 845 > 362 * 0.6309

845 > 229.8198

so 845 is greater than 229.8198, therefore 2^845 is greater than 5^362.

Answer:

Step-by-step explanation:

2^845 = 2^5(2^7)^120 = 32(128)^120,

5^362 = 5^2(5^3)^120 = 25(125)^120,

2^845 is bigger.

The title is explains what the graph is about. Scale: The scale is the numbers that show the units used on the bar graph. Labels: Both the side and the bottom of the bar graph have a label that tells what kind of data is shown.

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Answer:

63

Step-by-step explanation:

b*h/2

b= 18

h=7

(7*18)/2 = 63

An average swimmer covers a distance of 1 / 30 miles in a minute, while an Olympic swimmer covers a distance of 1 / 10 miles.

This is a classic example of an open question, since there are answers as many as possible assumptions. In this case, answer change if swimmer's speed is changed. We shall consider two cases: (i) Average swimmer (v = 2 miles per hour), (ii) Olympic swimmer (v = 6 miles per hour).

Under the assumption of uniform motion, distance (s), in miles, is the product of speed (v), in miles per hour, and time (t), in hours (please notice that an hour is equal to 60 minutes):

s = v · t

Average swimmer (v = 2 mi / h, t = 1 / 60 h)

s = 2 · (1 / 60)

s = 2 / 60

s = 1 / 30 mi

Olympic swimmer (v = 6 mi / h, t = 1 / 60 h)

s = 6 · (1 / 60)

s = 6 / 60 mi

s = 1 / 10 mi

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The slope and y-intercept can provide important information about the relationship between the variables being modeled.

What are the slope and y-intercept?

The slope and y-intercept are both elements of a linear equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept of the line.

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It tells us how much the y-value changes for a given change in the x-value. The slope can be positive, negative, or zero, and it is often represented as a ratio, such as "rise over run" or "rise/run". A positive slope indicates that the line rises as x increases and a negative slope indicates that the line falls as x increases.

The y-intercept (b) represents the point at which the line crosses the y-axis. It tells us the value of y when x = 0. In other words, the y-intercept is the value of the dependent variable when the independent variable is zero.

Hence, the slope and y-intercept can provide important information about the relationship between the variables being modeled.

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The rate of change of volume with respect to R is 4πR².

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity. The rate of change from the coordinates of y to the coordinates of x can be found out as Δy/ Δx = (y2 - y1 )/ (x2 - x1 ). For a linear function, the rate of change m is represented in the slope-intercept form for a line: y=mx+b whereas the rate of change of functions is otherwise defined as, (f(b)-f(a))/ b-a.

The volume of the sphere is:

V = (4π/3)(R³)

Differentiating volume with respect to radius gives:

dV/dR  = (4π/3)× (3R²) = 4πR²

Thus, the rate of change of volume with respect to R is 4πR².

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Solution for the given expression is x = 16y^2 -5.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given an expression in terms of x where y and x both are variables

To make x the subject we need to calculate the value of x in terms of y

Thus,

√(x +5) / 4 = y

multiply by 4 both sides

√(x + 5 ) = 4y

take square

x + 5 = 16 y²

x = 16y² - 5

therefore, given expression in terms of y is  x = 16y² - 5.

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Therefore, correct response is percentage C. "For comedies that college students enjoy, she estimated the conditional relative frequency. The right response is 28%.

A number or figure that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the "%" symbol used to represent it is often employed. No dimensions exist; the % amount is flat. Percentages are essentially fractions because their numerator is 100. A percent symbol (%) should be placed in front of a number to indicate that it is a percentage. For instance, if you answered correctly 75 out of questions in total on a test, you'd get a 75%.

Here,

Given :

She determined the combined relative frequency for humor and college. For college students who enjoy comedy, the appropriate conditional relative frequency value is 28%.

For comedies that college students enjoy, she determined the conditional relative frequency. For college students who enjoy comedy, the appropriate conditional relative frequency value is 16%.

For comedies that college students enjoy, she determined the conditional relative frequency. The right response is 28%.

She determined the combined relative frequency for humor and college. The right response is 16%.

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well, the triangle is an equilateral, so all sides are equal, we know that the segment "x" stems out of the vertex and drops perpendicular to the other side, now, the vertex "x" stems from has two equal sides.

what the hell all that means?  well it means that "x" is an altitude and is also  an angle bisector and likewise is also cutting the opposite side into two equal halves, meaning that one side is really 8 + 8 = 16, so then

[tex]\stackrel{altitude}{height}\textit{ of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=16 \end{cases}\implies h=\cfrac{16\sqrt{3}}{2}\implies h=8\sqrt{3}[/tex]

the length of DG in this cuboid is 46.53 cm

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

from the given figure,

we get,

by Pythagorean theorem,

DG =√41²+22²

     =46.53

hence, the length of DG in this cuboid is 46.53 cm

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Answer:

Below in bold.

Step-by-step explanation:

m < DAC  = 360 -15 - 155 - 166

                = 24⁰

The bearing of D from A

                = 180 + 15 + 24

                 =  219⁰

or S 39⁰ W.

Answer:

No.

Step-by-step explanation:

Using the Pythagorean Theorem, a^2 + b^2 = c^2, this would not be possible, because 4 + 9 does not equal 16.

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

Answer:

No.

Step-by-step explanation:

the Pythagorean Theorem states that a²+b²=c²

where a and b are the legs and c is the hypotenuse of a right triangle

in this case we need to know if 2²+3²=4²

2²=4

3²=9

4²=16

4+9=13

13≠16

so no, the hypotenuse cannot be 4 inches long.

Answer:

9 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{4}{1}[/tex] x [tex]\frac{7}{3}[/tex] = [tex]\frac{28}{3}[/tex] = 9 [tex]\frac{1}{3}[/tex]