dragon selects three positive real numbers with sum 100, uniformly at random. he asks cat to copy them down, but cat gets lazy and rounds them all to the nearest tenth during transcription. find the probability the three new numbers still sum to 100.

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.

Therefore, the vertically scale factor is equal to 1/2:

=> y = (1/2)f(x)

This problem can be solved by multiplying it by two and yields the following solution:

=> 2y = f(x)

thus , option c is correct

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

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The values 16, and 8 are the two common denominators. If you want the answer for the question it's 7/8

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The calculation of the fraction will be calculated by simply adding the sum of 1/2 together with that of 3/8. Therefore, it should be noted that the addition of the fraction will be:

= 1/2 + 3/8

= 4/8 + 3/8

= 7/8

The value of the addition of the fraction is 7/8.

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What is a different common denominator you could use in problem 2? Describe how you would

add the fractions using this different common denominator. Is the result equivalent to the sum

found in problem 2?

There’s problem 2 given as 1/2 + 3/8

A logarithmic function is the inverse of an exponential function. The foundation of an exponential function is equal to that of a log function.

Slope is the difference in log(Y) when log(X) varies by a factor of 1.0. The Y value at 0.0 for log(X) is known as the Y intercept. Consequently, it is the Y value at 1.0 for X.

On logarithmic graph paper, power functions are represented as straight lines. Exponent in the equation is determined by the slope of the line (m), and k is determined by the value of y at the point where the line crosses the x = 1 axis.

An exponential function's inverse is a logarithmic function. An exponential function's basis is the same as that of a log function. Exponents include logarithms. f(x) = [tex]$$b^x[/tex] is the formula for the exponential function. f(x) = log base b of x is how the logarithmic function is expressed.

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Demi notices that the average unemployment rate is 7.1% and that there are 21.3 unemployed persons for every 300 people.

In mathematics, a percentile is a variable or ratio that will be given as a fraction or 100. Every once in a while, the symbols "pct.," "pct," and "pc" are also used. But it is classified in four by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions only when denominator is 100. Were using the percent sign (%) to indicate that a number is a percentage by positioning it next to it. For instance, you score a 75% if you properly answer 75 outside from 100 questions on a test (75/100). Divide the money by the total and multiplied the result by 100 to calculate percentages.

given

[Percentage] x [Number Given] = [New number]

7.1 % * 300

= 21.3

Demi notices that the average unemployment rate is 7.1% and that there are 21.3 unemployed persons for every 300 people.

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The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 has no solution.

To find the number of solutions that a pair of linear equations will have, we can use the concept of the ratio of coefficients.

For the pair of linear equations:

3x + 4y + 5 = 0

12x + 16y + 15 = 0

We can find the ratio of the coefficients of x in both equations.

In the first equation, the coefficient of x is 3 and in the second equation, the coefficient of x is 12. The ratio of these coefficients is

3/12 = 1/4

We can also find the ratio of the coefficients of y in both equations.

In the first equation, the coefficient of y is 4 and in the second equation, the coefficient of y is 16. The ratio of these coefficients is

4/16 = 1/4

As both ratio are equal, let us check ratio of constants.

5/15 = 1/3

So the ratio of constants is not equal, so there is no solution for this system of linear equations.

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In a shop where everything in the store is 16% off and the regular price of a t-shirt is $19 therefore the discount price to the nearest cent will be $16.

This is referred to as the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

We were told that there is a discount of  16%  which means:

16/100 × $19 = $3.04

The discount price is $19 - $3.04 = $15.96

≈ $16

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The scale factor is 2. Then the perimeter of the triangle ΔCBF will be 64 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

Triangle DEF ~ triangle CBE. Then the scale factor is given as,

Scale factor = 16 / 8

Scale factor = 2

The perimeter of the triangle ΔDEF is 32 units. Then the perimeter of the triangle ΔCBF will be given as,

P = (Scale factor) x (Perimeter of triangle ΔDEF)

P = 2 x 32

P = 64 units

The perimeter of the triangle ΔCBF will be 64 units.

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The number of days until all of them will have a day off together is given as follows:

105 days.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for each person are given as follows:

The least common factor of 3, 5 and 7 is given as follows:

3 x 5 x 7 = 105 days.

(as 3, 5 and 7 are prime numbers, hence we just multiply them).

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Quadratic equations can be expressed in three different ways:

1. Standard form

2. Factor form

3. Vertex Form

a[tex]x^2[/tex] + bx + c = 0 is the quadratic equation's standard form, where 'a' is the leading coefficient and a non-zero real number. Due to the word "quad" meaning "square," this equation, whose degree is 2, is referred to as "quadratic." A quadratic equation can be expressed in other ways in addition to the usual form.

1. Standard form: An equation with a quadratic term has the following standard form y = a[tex]x^2[/tex] + bx + c where a, b and c  are just the numbers.

2. Factor form: An equation with a quadratic term has the following factor forma (x - p)(x - q) = 0

3. Vertex Form: An equation with a quadratic term has the following vertex form a[tex](x-h)^2[/tex] + k = 0

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The nearest ten of 999 is 1000.

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations.

In mathematics, there are various number systems such as the decimal number system, binary number system, octal number system, and hexadecimal number system.

Round the number to the nearest ten. 999 is between 990 and 1000.

Looking at the 1 in the one's place. It's more than 5, so round up to 1000.

Thus, the nearest ten of 999 is 1000.

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Answer: 3=5, 6=10

Step-by-step explanation:

Basic Logic)

Three times two equals six, therefore the correspondent must also double itself.

Five times two equals ten.

Alternate Logic)

Three plus two-thirds of itself is five(3+2=5)

Six plus two-thirds of itself is four(6+4=10)

Answer:

10

Step-by-step explanation:

3=5

3+2

3x2= 6

2x2=4

6+4=10

Answer:

Step-by-step explanation:

The equation x^2 + kx + 5 = 0 has real roots if and only if the discriminant b^2 - 4ac is greater or equal to zero.

In this case, the discriminant is k^2 - 415 = k^2 - 20.

So we know that k^2 - 20 >= 0

therefore k >= sqrt(20) or k <= -sqrt(20)

Two positive values of k are:

k = sqrt(20)

k = sqrt(20) + n, where n is an integer greater than 0

Please note that this is an algebraic solution and doesn't account for any other possibilities that the problem or context may have.

Answer:

1.5

Step-by-step explanation:

Since, 400 is not half of 600 but past it, it would be:

1.0

Since it is half way to 600 it would equal:

1.5.

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Answer: m∠ABC and m∠ABD are the measures of angles in a triangle. The sum of the measures of the angles in a triangle is always 180°.

So if we know two of the angles, we can use this information to find the measure of the third angle.

Given that m∠ABC= (8x-48)°, m∠ABD=44°

we can find the measure of the third angle, m∠BCD by:

m∠ABC + m∠ABD + m∠BCD = 180

(8x-48) + 44 + m∠BCD = 180

m∠BCD = 180 - (8x-48) - 44

m∠BCD = 180 - 8x + 4

m∠BCD = (180 - 8x + 4)°

However, Since we don't know the value of x, the measure of angle BCD is not determined.

Step-by-step explanation:

Answer:

Out of the 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 total students, 4 + 3 = 7 are freshmen so the answer is 7 / 30 * 100 = 23%.

Step-by-step explanation:

The required value of f (x) / g (x) is (7 - 7i)/10 for the given functions.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows;

f (x) = 2 - 3i and g (x) = 3 - i

we have to determine the value of f (x) / g (x)

As per the question, we have

⇒ f (x) / g (x)

Substitute the values of f (x) and  g (x), and we get

⇒ (2 - 3i) / (3 - i)

⇒ (2 - 3i)(3 + i) / (3 - i)(3 + i)       [∵i²= -1]

⇒ (6 +2i - 9i - i²) / (9 - i²)

⇒ (6 -7i + 1) / (9  + 1)

⇒ (7 - 7i)/10

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The base graph is moved up or down in the y-axis direction when a graph is vertically translated.

A vertical translation results from the equation y = f(x-h) if y = f(x). When the value of h is positive or negative, respectively, the translation h shifts the graph to the left and the right. It's important to keep in mind that these translations don't always occur separately.

Shifting the base graph to the left or right in the x-axis direction is the same as translating a graph horizontally. Each point on a graph is translated by k units in the horizontal direction. By shifting f (x) k units horizontally, it is possible to sketch g(x) = f (x - k).

The base graph is moved up or down in the y-axis direction when a graph is vertically translated. Each point on a graph is moved k units up the graph to translate it vertically. Shifting the f (x) k units vertically will allow you to sketch the equation g (x) = f (x) + k.

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Answer: We can solve this problem using the technique of combinatorics known as the "Stars and Bars" method.

We can think of the 3 boys and 4 girls as 7 distinguishable objects and 3 "bars" that separate them. We are trying to find the number of ways to place the 3 bars among the 7 objects.

For example, if the 3 bars are represented by the symbols |, |, |

BB|G|GBG|G|GBG

The leftmost and rightmost spaces always contain a boy or a girl, so there are a total of 9 spaces to put the 3 bars.

This means that there are C(9,3) = 84 ways to place the 3 bars among the 7 people.

So, there are 84 ways in which 3 boys and 4 girls can sit in a row such that no two people of the same sex sit together.

Step-by-step explanation:

The formula for the distance between the points (a,b) and (c,d) is square root of (a,c)2 + (b,d)2. The distance in three dimensions between points (a, b, c) and (d, e, f) is equal to the square root of (a, d), (b, e), and (c, f)2.

You're going to travel for four hours at an average speed of 70 km/h. Speed is equal to time times distance, therefore 70 km/h times 4 hours is 280 km.

Alexis Clairaut published the distance formula itself for the first time in 1731.

To calculate the shortest path between a point and a plane, we use the formula d = |Ax0 + By0 + Cz0 + D |/(A2 + B2 + C2). In this equation, the supplied point is represented by (x0, y0, z0), while the given plane's equation is Ax + By + Cz + D = 0.

Minimum=5

Low Quartile: 11; Median: 23

Higher Quartile: 34

Maximum=38

24 to 23 percentiles

least is the smallest number

largest number is maximum.

The data set's median is its middle number.

Middle value between the minimum and the median is a lower quartile.

Middle number from the median to the maximum is the upper quartile.

Upper quartile - Lower quartile, or Q3 - Q1, is the interquartile range.

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The recurrence relation is C(n) = (2n)! / ((n+1)! * n!)

A recurrence relation for the number of ways to fully parenthesize an expression of n variables can be found using the formula of the Catalan numbers. The Catalan numbers, C(n) represent the number of ways to fully parenthesize an expression of n variables. The recurrence relation for the Catalan numbers is C(n) = C(0)*C(n-1) + C(1)*C(n-2) + ... + C(n-1)*C(0) which can be simplified to C(n) = (2n)! / ((n+1)! * n!).

We can also find it by using the following recurrence relation:

C(n) = (2n-1)C(n-1) / n; This recurrence relation is based on the observation that we can insert a pair of matching parentheses in 2n-1 positions in an expression of n variables, and the number of ways to parenthesize the expression inside the pair of parentheses is given by C(n-1).

It's important to note that the above recurrence relation is for fully parenthesizing an expression, if you need to find several ways to partially parenthesize an expression, different recurrence relations should be used.

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The sum of three non-contiguous segments is the same as the sum of the other three.

The Theorem of Menelaus states that six segments are cut off on either side of every line that transverses (crosses) a triangle's three sides (one of them must be extended). This theorem only applies to plane geometry. The sum of three non-contiguous segments is the same as the sum of the other three.

Menelaus' theorem relates ratios that can be derived by cutting a triangle in half. The inverse of the theorem, which states that three points on a triangle are only coincident if and only if they meet certain requirements, is also accurate and very effective in demonstrating the existence of three congruent points.

By using Menelaus' Theorem for triangle ADC and line F - E - B:

[tex]$$\begin{gathered}\frac{A F}{F C} \cdot \frac{C B}{B D} \cdot \frac{D E}{E A}=1 \\\frac{A F}{F C} \cdot \frac{2}{1} \cdot \frac{1}{1}=1 \\\frac{A F}{F C}=\frac{1}{2}\end{gathered}$$[/tex]

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The required sample spaces for the given chance experiment, are as follows:  flipping a coin: {heads, tails}, selecting a random season of the year: {spring, summer, fall, winter}, and selecting a random day of the week: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The sample space for flipping a coin: {heads, tails}

The sample space for selecting a random season of the year: {spring, summer, fall, winter}

The sample space for selecting a random day of the week: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

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5 x 5 = 25 possible pairings. The five boys can be paired with any of the five girls, and the five girls can be paired with any of the five boys, creating 25 possible pairings. To explain this mathematically, we can use permutations.  

A permutation is an arrangement of objects or symbols in which the order of the arrangement matters. In this case, the order of the arrangement matters because the pairings have to be specific boy-girl pairs.  We can also use factorials to explain the answer. Factorials are used to calculate the number of possible arrangements for a given set.

In this case, the set consists of five boys and five girls, and the factorial calculation would be 5! x 5! = 5 x 4 x 3 x 2 x 1 x 5 x 4 x 3 x 2 x 1 = 25, which is the same answer as the permutation calculation.  The final answer of 25 possible pairings can be explained using both permutations and factorials. Both methods of calculation show that there are 25 possible pairings, with each pairing consisting of one boy and one girl.

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Answer:

[tex]6^{5}[/tex]

Better-than-average illusion is the propensity to assume that one is superior to the majority within a certain group.

The disparity between the parameter's actual value and its expected value is known as bias. Anything that causes a systematic discrepancy between the statistics used to estimate the parameters of a population and their true parameters is considered statistical bias.

Truth is warped by bias. It is a flaw in the system that we don't frequently notice since it is wrapped up in our humanity. The definition of bias is as basic as "unconscious preference," yet it can be benign or evil. Whatever form they take, though, the biases we have prevent us from seeing the world as it really is.

Better-than-average illusion is the propensity to think that one is superior to the majority in a specific group.

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The measure of angle m ∠C is 24°.

Congruent triangles have both the same shape and the same size.

Given is that △DSJ ≅ △RCW and m ∠D = 114 and m ∠J = 42.

Since △DSJ ≅ △RCW, we can write -

m ∠S = m ∠C

Now, in △DSJ, we can write -

m ∠D + m ∠S + m ∠J = 180

m ∠S = 180 - 156

m ∠S = 24 = m ∠C

Therefore, the measure of angle m ∠C is 24°.

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The independent variable of the study is texting.

Independent variables are what we determine will influence dependent variables. A Dependent variable is what occurs as a result of the independent variable. In short, an independent variable is the cause and a dependent variable is the effect.

For example, if we are measuring how the amount of sunlight influences the growth of a plant, the independent variable is the amount of sunlight. We can control how much sunlight each plant gets. The growth is the dependent variable, which is the effect of the amount of sunlight.

In this study, the independent variable is texting, because the researcher can control how many texts need to be responded to and how many texts have to be sent.

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Answer: If Zendaya invests $70 in an account paying a simple interest of 7.3% per year, and no money will be added or removed from the investment, she will have $75.11 in one year.

To calculate the amount of interest earned, you can use the formula:

Interest = Principal x Rate x Time

where

Principal = $70

Rate = 7.3/100 (expressed as a decimal)

Time = 1 year

So the interest earned is:

$70 x 0.073 x 1 = $5.11

To find the total amount at the end of the year, you add the interest to the original principal:

$70 + $5.11 = $75.11

Step-by-step explanation:

Answer:

Step-by-step explanation:

The conditional probability that a randomly chosen student is left-handed, given that the student is a boy, can be represented as:

P(left-handed|boy) = P(left-handed and boy)/P(boy) = 3/16

The conditional probability that a randomly chosen student is left-handed, given that the student is a girl, can be represented as:

P(left-handed|girl) = P(left-handed and girl)/P(girl) = 2/14

Both expressions are examples of conditional probability, as they show the probability of one event (left-handed) given that another event (boy or girl) has occurred.