Let $x$ be a real number selected uniformly at random between 100 and 200. If $\lfloor {\sqrt{x}} \rfloor = 12$, find the probability that $\lfloor {\sqrt{100x}} \rfloor = 120$. ($\lfloor {v} \rfloor$ means the greatest integer less than or equal to $v$.)
$\text{(A)} \ \frac{2}{25} \qquad \text{(B)} \ \frac{241}{2500} \qquad \text{(C)} \ \frac{1}{10} \qquad \text{(D)} \ \frac{96}{625} \qquad \text{(E)} \ 1$

Hey there!

Hope this helps!

Answer:

a) even

b) neither

c) odd

Step-by-step explanation:

A function is "even" when there is symmetry about the y-axis.

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

A function is "odd" when there is origin symmetry.

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

From inspection of the graph, the curve appears to be symmetrical about the y-axis. Therefore, the function is even.

This is an absolute value function.  It has no symmetry about the y-axis or the origin.  Therefore, the function is neither.

From inspection of the graph, the curve appears to be symmetric with respect to the origin. Therefore, the function is odd.

The scale factor needed to form ΔA'B'C' from ΔABC is 1/2 or 0.5.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The coordinate points of triangle ABC is -

A(2,6), B(2,2), and C(6,2)

The coordinate points of triangle A'B'C' is -

A'(1,3), B'(1,1), and C'(3,1)

Subtract the coordinate points of A'B'C' from ABC to find the scale factor -

A = (2 - 1, 6 - 3) = (1,3)

B = (2 - 1, 2 - 1) = (1,1)

B = (6 - 3, 2 - 1) = (3,1)

So, it can be seen that to form triangle ABC, the triangle A'B'C' is multiplied by the factor of 2.

A(2,6) = (x/2 , y/2) = A'(1,3)

B(2,2) = (x/2 , y/2) = B'(1,1)

C(6,2) = (x/2 , y/2) = C'(3,1)

Therefore, the scale factor is 1/2 or 0.5.

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A quadrilateral has diagonals that are perpendicular but not congruent

is a rhombus.

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

From the properties of a rhombus, we know,

A rhombus has an equal number of sides. In this case, ABCD equals DA.

At an angle of 90° divides each of the diagonals. In this instance, diagonals AC and BD split at a 90° angle.

A rhombus has parallel opposite sides. In this case, AB || CD and AD || BC.

In a rhombus, the opposite angles are equal. ∠A = ∠C, while ∠B = ∠D.

The sum of adjacent angles is 180°.

Diagonals of a rhombus bisect each other at the right angles but they are not congruent.

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Answer:

Step-by-step explanation:

in the picture

Answer:

c) cryptography

Step-by-step explanation:

Cryptography is a mechanism used to encrypt and decrypt data.

Answer:

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large

Step-by-step explanation:

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large

Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.

The correlation between two variables A and B is exactly the same as the correlation between A and B, and it describes the strength of the association between the two.

A causal relationship exists when an alteration in one variable directly affects an alteration in the other variable. A causal generalization, such as the claim that smoking causes lung cancer, does not refer specifically to any one smoker but rather to the unique connection between the characteristic of smoking and the characteristic of developing lung cancer.

An overview was given as your information is incomplete and can't be found.

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The total weight of the wall and the average dead load per foot of wall length can be calculated.

The total weight of the wall can be calculated by finding the weight of the bricks and frame, then adding the weight of the glass and sash. The total weight of the wall (W) is calculated as follows:

W = (0.25*40ft*11ft)*(weight of bricks + weight of frame) + (0.75*40ft*11ft)*(weight of glass + weight of sash)

The average dead load (F) per foot of wall length is calculated by dividing the total weight of the wall by the total length of the wall (L):

F = W/L = (0.25*40ft*11ft)*(weight of bricks + weight of frame) + (0.75*40ft*11ft)*(weight of glass + weight of sash) / (40ft)

Using the tables in Hibbeler for weights of materials, the total weight of the wall and the average dead load per foot of wall length can be calculated.

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Without graphing the function f(x) = 5 (4)ˣ is an exponential growth

The y intercept is 5

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

The base is what determines exponential growth or decay

when the base is < 1 we have exponential decay nut when the base is > 1 we have exponential growth

Considering the problem,  f(x) = 5 (4)ˣ

the starting = 5

the base = 4 exponential growth

the exponents = x

The y intercept is the starting this is the value at x = 0

f(x) = 5 (4)ˣ

f(x) = 5 (4)⁰

f(x) = 5 * 1

f(x) = 5

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The number of tickets sold for students is 735.

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

Given that, 1415 concert tickets were sold for a total of $26,665. If students paid $15 and non students paid $23,

To solve this problem we will establish a system of equations,

Let the sold ticket for students be x, and that of non students be y,

x+y = 1415

y = 1415-x...(i)

15x + 23y = 26,665...(ii)

Substitute eq(i) in eq(ii)

15x + 23(1415-x) = 26665

15x + 32545 - 23x = 26665

8x = 5880

x = 735

Hence, the number of tickets sold for students is 735.

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Applying the properties of the diagonals of a square, the length of EG ≈ 8.5 units.

The diagonals of a square are line segments that connect opposite corners of the square. They have the following properties:

Therefore, each segment that is formed by the bisection of the diagonals would be equal to 6.

Applying Pythagorean theorem, we have:

EG = √(6² + 6²)

EG = √(36 + 36)

Length of EG ≈ 8.5 units.

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Answer:

a. True

b. False

c. False

d. False

e. True

Step-by-step explanation:

a. True: The graph of f^-1(x) is a reflection of the graph of f(x) over the line y = x. This is because for any point (x,y) on the graph of f(x), the point (y,x) will be on the graph of f^-1(x), and vice versa.

b. False: The inverse function, f^-1(x) does not have to be always increasing. It depends on the original function, f(x) and its properties, A function could be increasing or decreasing, or it could be a combination of both, or none of them. A function which is strictly increasing is guaranteed to have a unique inverse, but that inverse function may or may not be increasing.

c.False: The function y = x^2 does not have an inverse function. Because it is not a one-to-one function. It is not injective, meaning that it maps multiple input values to the same output value, so it cannot be inverted.

d. False: If a function has a y-intercept, it does not mean that its inverse must also have a y-intercept. A y-intercept is a point at which a function crosses the y-axis, which corresponds to x = 0. However, the inverse function of a function will have its x and y coordinates swapped, so the inverse of a function that crosses the y-axis at a particular point will not cross the x-axis at the same point.

e. True: If a function has a y-intercept, it means that the function crosses the y-axis. But since the inverse function of a function will have its x and y coordinates swapped, the inverse of a function that crosses the y-axis at a particular point will cross the x-axis at the same point.

Answer:

Step-by-step explanation:

First write down the decimal number divided by 1 like this:

0.607

1

As we have 3 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 103 = 1000, so that there is no decimal point in the numerator

0.607 × 1000

1 × 1000

=

607

1000

Therefore, 0.607 as a fraction is 607/1000

3/2 is a slope of a line perpendicular to the line whose equation of

2x+3y=-3 .

One specific example of the more broad mathematical concept of orthogonality is the concept of perpendicularity, which is the orthogonality of traditional geometric objects.

As a result, in higher mathematics, the term "perpendicular" is occasionally used to represent considerably more intricate geometric orthogonality criteria, like the relationship between a surface and its normal vector.

If two lines cross at a right angle, they are said to be perpendicular to one another.

A first line is explicitly said to be perpendicular to a second line if the two lines meet and the straight angle on one side of the first line is cut by the second line into two congruent angles at the point of junction.

This can be done by rearranging the equation into the slope intercept form.

2x +3y = -3

3y = -2x -3

y = -2/3x - 1

Thus, the slope of the given line is -2/3.

The slope of the perpendicular line is the negative reciprocal of the given line.

Slope of perpendicular line = 3/2

The slope-intercept form was:

(i) The reciprocal of m is 1/m.

(ii) The negative reciprocal of m is -1/m.

Negative reciprocal of -2/3

= -1 ÷ (- 2/3)

= -1 × (-3/2)

= 3/2

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The algebraic expression will be Y=a+9

Where Y=number of cards Angelica has now, a=added movie cards,

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

As given

Angelica buys 3 packets of movie cards and 6 packets of cartoon cards

and and adds these to the 3 packets of movie cards she already has

Now let a=packets of movies she already has

and Y=number of cards Angelica has now

Therefore, The algebraic expression will be

             Y=a+3+6=a+9

            Y=a+9

             Where a=3

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When there are 12 observations in a small sample, the median is calculated by: b. the average value of the sixth position and the seventh position of an ascending sorted.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the 12 observations from the least to greatest as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

The median for 12 observations is the average of the 6th and 7th number:

Median = (6 + 7)/2

Median = 13/2

Median = 12.5.

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The average of a sample of any data set as given here is an example of a statistic. Hence, option D is the correct answer.

A parameter and a statistic are very similar to one another. Parameters are numerals that are used to describe the properties of total populations. Statistics are numerals that are used to describe the properties of samples. For example, the average age of everyone in a country is a parameter while the average of just 25 peoples' age is a statistic.

Here, we have been told that the researcher recorded the individual change in weight for a small group of 25 freshmen from this college during their first semester, and then, the researcher calculated the average change in weight during the first semester among these 25 students. Hence, we know that the average here is a statistic. So, option D is the correct answer.

The complete question that you might be searching for is given below -

In order for a researcher to obtain a raa researcher is interested in the average first-semester change in weight (gain or loss) for students at a local college. thus, they record the individual change in weight for a small group of 25 freshmen from this college during their first semester. then, the researcher calculates the average change in weight during the first semester among these 25 students. The average is an example of a-

a. constant

b. variable

c. parameter

d. statistic

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Answer:

C. 25.12 inches

Step-by-step explanation:

radius = 4 inches

circumference = 2πr

circumference = 2 × 3.14 × 4 inches

circumference = 25.12 inches

Answer:c is correct 25.12

Step-by-step explanation:

Where the line plot shows the different lengths of nails in your toolbox. If you take all the nails that are less than 2 inches long and lay them end to end, the nails will reach 15 1/2 inches far. (Option C)

A line chart is a type of chart that presents information as a succession of data points called "markers" that are connected by straight-line segments. It is a simple form of a chart that is used in many disciplines.

With regard to the attached line plot, we have the following information.

See the attached line plot

Size inches     Numbers ( frequency)

1/2                     3

1                        5

1 1/2                  6

2                       1

2 1/2                 0

3                       0

3 1/2                 2

4                       1

Nails less than 2 inches in size are 1/2, 1, and 1 1/2

The total length  = 3(1/2)  + 5(1) + 6(1 1/2)

= 3/2 + 5 + (3/2 * 6)

= 3/2 + 5 + 9

= 3/2 + 14

= 1 1/2 + 14

= 15 1/2 Inches.

Therefore, it is correct to state that all the nails that are less than 2 inches will reach 15 1/2 inches. Hence option C is correct.

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Full Question:

See attached image.

We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%.

A confidence interval is a range of values that is possible to include the true population parameter, with a certain level of confidence. In this case, the sample proportion of 47% who indicated they intended to vote for Candidate R was used to construct a 95% confidence interval, with a margin of error of 5%.

This means that if we repeated the sampling process many times, 95% of the intervals constructed would contain the true population proportion of those who intend to vote for Candidate R. In other words, we are 95% confident that the true population proportion falls within the interval of 42% to 52%.

Note that the confidence interval does not indicate that we are 95% confident that the sample proportion is 47% or that 95% of the population intends to vote for Candidate R. It only gives us a range of values that is likely to contain the true population proportion, based on the sample data and the level of confidence.

Hence, the correct answer is B.

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The grapefruit's volume in cubic centimeters to the nearest tenth is equal to 775.8 cubic centimeters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the grapefruit, the diameter of the sphere is given by;

Diameter of sphere = 11.4 cm

Radius = diameter/2 = 11.4/2 = 5.7 cm.

Substituting the given points into the volume of a sphere formula, we have the following;

Volume of sphere = 4/3 × 3.142 × 5.7³

Volume of sphere = 775.8 cubic centimeters.

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The weighted average for A,B and C will be 0.333.

What is weighted average?

Weighted average is a mean calculated by giving values in a data set more influence according to some attribute of the data. It is an important section in CAT quantitative aptitude. Weighted average is an average in which each quantity to be averaged is assigned a weight, and these weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.

Now,

Given weight for A=0.5, B=0.1 and C=0.4

Weighted average=(A+B+C)/3

=(0.5+0.1+0.4)/3

=1/3

Weighted average=0.33

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The length of the missing side is 12cm.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. So if we know the lengths of two sides of a right triangle, we can use the theorem to find the length of the third side.

Given:

Base (b) = 16 cm

Hypotenuse (c) = 20 cm

We can use the Pythagorean theorem to find the length of the missing side (a), which is the side opposite the right angle and adjacent to the base.

c^2 = a^2 + b^2

20^2 = a^2 + 16^2

400 = a^2 + 256

144 = a^2

a = 12cm

once we have the length of the missing side, we can use the values of the base and hypotenuse to find the six trigonometric functions:

Therefore, the length of the missing side is 12cm.

The question is incomplete as it does not include the figure. Hence I have attached the figure for a complete understanding of the problem.

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A significant number of accidents are caused by vehicle equipment failure such as the following except Operative lights.

Operative lights are also called Surgical lights which are medical equipment devices used to illuminate the operating field during surgery.

Surgical lights are referred to by many names: Operating lights, OR lights, operating room lights, surgical lamps, and surgical light heads.

The primary function of surgical lighting is to illuminate the operative site on and/or within a patient for ideal visualization by OR staff during a surgical procedure.

With proper lighting, operating room staff can achieve a higher level of efficacy during surgery and reduce the risk of complications.

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The sides of the triangle ABC are 6, 10, and 8. The sides of the triangle LMN are 12, 20, and 16. The ratio of the respective sides is the same for the two triangles because they are comparable. Therefore, BC is 10 miles long.

Due to the equal ratio of their corresponding sides, the triangles ABC and LMN are comparable. This indicates that the lengths of the sides of LMN may be obtained by multiplying the lengths of the sides of ABC by the same factor. For instance, side AB in ABC is 6 inches long, whereas side LM in LMN is 12 inches long. The lengths are 6:12, or 1:2, apart. The ratio remains the same for all matching. We can examine the other two sides of ABC to verify this response. Ten is the length of AC, and twenty is the length of MN. These two sides must likewise be multiplied by the same factor (1/2), since the ratio of the corresponding sides is the same. This results in AC and MN having lengths of 10 and matching ABC's dimensions. This demonstrates that BC is eight miles long.

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the complete question is

triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer find BC?

Answer:

1224 cm²

Step-by-step explanation:

The picture is a rectangle with length 60 cm and width 30 cm.

area of rectangle = length × width

area of picture = 60 cm × 30 cm = 1800 cm²

Now we add the mat to the picture. The width of the mat is 6 cm, so when you add mat to two opposite sides, the total length of the picture and mat becomes 60 cm + 6 cm + 6 cm = 72 cm. When you add mat to the other two opposite sides, the total width of the picture and mat becomes 30 cm + 6 cm + 6 cm = 42 cm. Now we have a rectangle 72 cm by 42 cm.

area of picture and mat = 72 cm × 42 cm = 3024 cm²

The area of the mat is the difference in area between the picture with mat and the picture without mat.

area of mat = 3024 cm² - 1800 cm² = 1224 cm²

The price of the ABC bond on the previous day is $104 3/4

From the question, we have the following parameters that can be used in our computation:

Rate = $10 per day

Current price = $114 3/4

Using the above as a guide, we have the following:

Previous price = Current price - Rate

Substitute the known values in the above equation, so, we have the following representation

Previous price = $114 3/4 = $10

Evaluate the difference

Previous price = $104 3/4

Hence, the previous price is $104 3/4

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Complete question

ABC bond increase by $10 everyday. If the price on a given is $114 3/4, what was the price of the ABC bond on the previous day?

The solution for the equation 3x²-4x-2=0 is 1.72076 and 0.387426.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3x²-4x-2=0

Now, solving the above Quadratic Equation

D= √b² - 4ac

From the given equation

a= 3, b-4, c=-2

Then, D= √(-4)² - 4(3)(-2)

D= √16 +24

D = √40

Now, x= (-b ±D)/ 2a

x= -(-4) ± √40/ (6)

x= 4+ √40/6  or x= 4-√40/6

x = 1.72076 or x=−0.387426

Hence, the value of x is 1.72076 and 0.387426.

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The value of x from the equation 3(x + 1) = 2(x − 1) is -5

Algebraic expression are defined as expression that are composed of terms, variables, coefficients, factors and constants.

Algebraic expressions are also composed of mathematical operations. Some of these operations are;

From the information given, we have the expression;

3(x + 1) = 2(x − 1)

expand the bracket

3x + 3 = 2x - 2

collect like terms

3x - 2x = -2 - 3

subtract like terms

x = -5

Hence, the value is -4

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