Solve the inequality. Graph your solution. $$ - 5.3 x > 21 |

For a perfectly symmetrical Distribution, the perfect relationship is

Mean = Median.

A symmetric distribution is when the values ​​of a variable occur with regular frequency, often the mean, median, and mode all occurring at the same point. A line in the middle of the chart indicates that the two planes are mirror images of each other. In graphical form, symmetric distributions are displayed as normal (that is, bell-shaped) distributions. Symmetric distribution is a central concept in technical trading as it assumes that the price movements of an asset over time follow a symmetric distribution curve.

A symmetric distribution can be contrasted with an asymmetric distribution. Asymmetric distributions are probability distributions that are skewed or otherwise irregular in shape.

The Properties of Symmetrical distribution is :

Mean:

In mathematics, especially statistics, there are several kinds of instruments. Each average is used to summarize a particular group of data in order to better understand the overall values ​​(magnitude and sign) of a particular data set.

For datasets, the arithmetic mean, also called the "arithmetic mean", is a measure of the central tendency of a finite set of numbers. More specifically, the sum of the values ​​divided by the number of values. The arithmetic mean of a series of numbers x₁, x₂, ..., xₙ is usually given by the overhead bar. The dataset was based on a series of observations obtained by sampling from a statistical population. The arithmetic mean is the population mean is denoted by μ.

Median:

The median is the number in the middle of a sorted ascending or descending list of numbers that better describes the data set than the mean. This is the point above and below which half (50%) of the observed data lies, representing the midpoint of the data. Often compared to descriptive statistics.

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The graph of the function is attached below:

The asymptote of the function is:

(-3 log(-x-4)/log2)-8  →∞ as x→ -4

Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. The sets X and Y are referred to together as the function's codomain and domain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known approach to the concept of function. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically with the infinitesimal calculus towards the end of the 17th century, and until the 19th century, the functions that were taken into consideration were differentiable.

Given function is,

f(x)= -3 log₂ (-x-4) - 8

The graph of the function is attached below:

The asymptote of the function is:

(-3 log(-x-4)/log2)-8  →∞ as x→ -4

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Answer:

the height of the goalpost is approximately 10.48 meters.

Step-by-step explanation:

To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.

Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.

The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.

In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:

1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)

Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.

Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:

sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.

In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:

sin(52.22) / 13.25 = sin(37.78) / h

Solving for h, we find that the height of the goalpost is approximately 10.48 meters.

Therefore, the height of the goalpost is approximately 10.48 meters.

Answer:

On attached woksheet

Step-by-step explanation:

The graph has units of time (sec) on the x axis and distance (meters) on the y.  The lines in the graph represent a change in distance from the origin as a function of time.  The slopes of these lines represent the speed, in m/sec., for that line.  Since they are straight lines, the speed is not changing for that time period.  A flat, horizonal, line represent a stationary object.  Distance does not change with time.  Steeper lines represnt faster speeds - the distance changes more quickly for the same time period.

See attached worksheet.

The standard deviation of the team members' heights is 2.35.

A z-score is a number that indicates how far an observation deviates from the mean and in which direction.

A z-score is a common name for a standardized number.

The standardized value of x is: If x is an observation from a distribution with known mean and standard deviation :

z = (x - mean) / Standard Deviation

Given in question,

z = -0.85

x = 74

mean = 76

Let the Standard deviation be s.

By putting the values in the equation,

-0.85 = (74 - 76)/s

s = -2/-0.85

  = 2/0.85

  = 2.35

Hence, the standard deviation of the team members' heights is 2.35.

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Programming or the process of writing algorithms both involve pseudocode. A technique that aids the programmer in defining an algorithm's implementation is pseudocode.

The algorithms are described using pseudocodes in pseudocode algorithms because it is simpler for everyone to understand the pseudo-codes, regardless of programming experience or familiarity with a different programming language.

do{

input=take input

}

While(input not equal to -1)

{

Store in an array for every input

Like append the new input to an array

}

After loop terminates  

Take the average of the array  

By traversing through all elements of an array and store in a variable  

The sum divided by the length of the array gives the average  

IN C language:

#include<stdio.h>

Int main(){

Int input,i=0,sum,avg,are[1000];

Do{

Scanf(“%d”,&input);

}

While(input !=0)

{

arre[i]=input;

i=i+1;

}

Sum=sum(arre[]);

Avg=sum/len(arre);

Printf(“%d”,Avg);

Return 0;

}

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Answer:

B. 123

Step-by-step explanation:

⭐What does "divisible" mean?

Thus, we can find which number is divisible by 3 by dividing each number by 3 and seeing if the remainder is 0.

However, that process may be too long.

You can do it if you'd like, but there's a rule you can use:

⭐"If the sum of the digits is divisible by 3, the number is also."

Let's apply this rule:

A.

76

⇒ 7 + 6

⇒ = 13

13 is NOT divisible by 3. Therefore, 76 is NOT divisible by 3.

B.

123

⇒ 1 + 2 + 3

⇒ = 6

6 IS divisible by 3. Therefore, 123 IS divisible by 3.

C.

457

⇒ 4 + 5 + 7

⇒ = 16

16 is NOT divisible by 3. Therefore, 457 is NOT divisible by 3.

B.

9082

⇒ 9 + 0 + 8 + 2

⇒ = 19

19 is NOT divisible by 3. Therefore, 9082 is NOT divisible by 3.

⭐if this response helped you, please mark it the "brainliest"!⭐

Therefore, Gracie will earn $61600 if she waits until December 21. However, she will earn bank discount $61132.87 on November 12.

A bank discount is interest that the bank deducts beforehand in the basic discount note. The maturity value less the bank discount equals the amount owed. The total of the principle and interest due at the conclusion of the time period is the maturity value.

Date of note = 14th July

Face value = $60000

Length of note = 160 days,

Interest rate = 6%

Calculating the interest and maturity value:

Interest  = Principal × interest × time

= 60000 × 0.06 × 160/360

= 1600

So the maturity value MV = Face value + interest

= 60000 + 1600

= 61600

2. Calculating discount period:

Note discounted on 12th November

Time till 12th November = 315 days

Time till 14th July = 194 days

So days before note is discount = 315 - 194= 121 days

Length of note = 160 days,

So the discount period = 160 - 121 = 39 days

3 - Bank discount:

Bank discount = MV × Bank discount rate × number of days bank waits till due date

= 61600 × 0.07 × 39/360

= 467.133

4 - Proceeds from bank: Proceeds = MV - Bank discount

= 61600 - 467.133

= 61132.87

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Multiply the numerator and denominator by the conjugate of the denominator to simplify (2+i/(2-i)).

To determine, multiply the denominator's conjugate by the numerator and denominator.

[tex]\frac{2+i}{1-i} = \frac{1}{2} +\frac{3}{2}i[/tex]

The complex number a + bi has the conjugate a-bi. A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.

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

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In the given formula we have variables:

If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.

If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.

Since n is the power of a number we need logarithm to solve it for n.

Answer:

"Principal (loan amount)"

"Term of the loan (in months)" or "Number of monthly payments"

Logarithms

Step-by-step explanation:

Monthly Payment Formula

[tex]M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}[/tex]

where:

If we solve for P, the name of the formula is "Principal (loan amount)".

If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".

When solving for n, we need to use logarithms:

[tex]\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}[/tex]

You would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.

What is a line graph?

An informational shift over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments.

Michael starts with 40 bags of cucumbers and gives out 8 bags per hour until there are none left.

Michael starts giving them away until he has no bags left.

To create the graph we need coordinate points to locate on the graph.

So initially he has 40 bags and gives away 8 bags for every 1 hour.

The number of bags will be represented on the y-axis, and the number of hours will be represented on the x-axis.

The coordinates are:

x-axis           y-axis

  0                 40

  1                  32

  2                 24

  3                  16

  4                   8

  5                   0

Hence, you would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.

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Answer:

I just know one of them but I think it's "step one:distributive property"

Step-by-step explanation:

im sorry I wasn't able to get the third one

Therefore , the probability of at least two born on the same day of the week is  0.143

Probability is the possibility that an event will happen.This could mean that something is definitely going to happen, that it has a chance of happening, or that it is impossible. Mathematically, probability is quantified on a scale from 0 to 1.

Given:

group of 5 people at random.

We used the formula for the conditional probability

The conditional probability is,

P(A|B)=P(AUB)/P(A)

The complement rule of probability, which is the second, is

P(E) = 1 - P(e)

Calculate one by one

a) Since a week has seven days and the first person has seven possible birth dates, the likelihood of that person is:

P(1st person) = 7/7 = 1

The second person now gets the same possibilities as person 1, but he or she must match that person's day, therefore there is only one option out of seven that fits that criteria, as follows:

P(A|B) = 1/7

Then the probability is

P = 1 * 1/7 = 1/7 or 0.143

Therefore , the probability of at least two born on the same day of the week is  0.143

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We can conclude that there is a statistically significant correlation between the two variables, a and b. The correlation coefficient is .10, which indicates a weak positive relationship.

A correlation coefficient of .10 indicates that there is a weak positive relationship between the two variables, a and b. A p-value of .01 indicates that the correlation between the two variables is statistically significant, meaning that it is unlikely to be due to chance. This suggests that there is a real relationship between the two variables, even though it is weak.

To calculate the correlation coefficient, you can use the formula  where x and y are the two variables in question. In this case, the correlation coefficient is .10. This can be determined by plugging in the values for x and y and doing the necessary calculations.

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Solution of 8^x=1000 is x ≈ 3.322 .

Use the

law of logarithms

[tex]log x^{n} = nlogx[/tex]

The word algorithm does not appear in data protection law. But an algorithm often results in an automated decision (or algorithmic decision making). It is code that decides something. There is a law that deals with automated individual decision-making and this is very relevant to algorithms.

An algorithm is a set of rules or a computational procedure that is typically used to solve a specific problem.

Applies to logarithms to any base.

Take the ln ( natural log) of both sides.

log 8^x = log 1000

An algorithm is a procedure used for solving a problem or performing a computation. Algorithms act as an exact list of instructions that conduct specified actions step by step in either hardware- or software-based routines. Algorithms are widely used throughout all areas of IT.

Using the above law

x log 8 = log 1000

dividing both side by log 8

[tex]\frac{xlog8}{log8} = \frac{log1000}{log8}[/tex]

x = ㏒8 (1000)

[tex]log_{a} b = \frac{log_{c}b }{log_{c}a }[/tex]

[tex]x = log_{10} 1000/log_{10} 8[/tex]

x ≈ 3.322  to 3 decimal places

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The exponential equation may be solved using log base x and log base 10 logarithm bases. The right answer is D.

Finding the base of the logarithm that may be used to determine the value of x is necessary in order to solve an exponential equation with the form log base x (y) = z.

The equation log base x (y) = z applies here. Let's explore each possible logarithm base:

Log base x: The problem may be solved directly using this logarithm base. The value of x that the equation requires may be discovered using the logarithm base x.

Log base 25: The problem cannot be properly solved using this logarithm base. It does not work with the provided equation.

Log base 4: The equation cannot be properly solved using this logarithm base. It does not work with the provided equation.

Log base 10: The problem may be readily solved using this logarithm basis. To determine the value of x that the equation requires, use the logarithm base 10 function.

The logarithm bases that may be utilised to solve the exponential equation based on the provided parameters are log base x and log base 10.

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Fron the given question, we can say that systematic sample because not all sample are possible.

Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.

[tex]Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.[/tex]

Further,

Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.

If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.

If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.

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The required choice for inequality is Option 2.

What is inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

Given, 3(8 – 4x) < 6(x – 5)

or, 24 - 12x < 6x - 30

or, 24 + 30 < 6x + 12x

or, 54 < 18x

or, 18x > 54

or, x > 3 means x is greater than positive 3 and pointing to the right.

Hence, the required choice for inequality is Option 2.

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Answer: b

Step-by-step explanation:

Nothing further can be done with simplifying the given expression.

Answer:

x=4.321928

Here’s your explanation

Let's solve your equation step-by-step.

2^x=20

Solve Exponent.

2^x=20

log(2^x)=log(20) (Take log of both sides)

x*(log(2))=log(20)
x=log(20)

log(2)

Then you get your answer x=4.321928

Step-by-step explanation:

Take the log of both sides:

log2(2^x) = log2(20)

xlog2(2) = log2(20)

x(1) = log2(20)

x = log2(20) ≈ 4.322

Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+160}x\stackrel{\stackrel{c}{\downarrow }}{+20} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 160}{2(-16)}~~~~ ,~~~~ 20-\cfrac{ (160)^2}{4(-16)}\right) \implies \left( - \cfrac{ 160 }{ -32 }~~,~~20 - \cfrac{ 25600 }{ -64 } \right) \\\\\\ \left( 5 ~~~~ ,~~~~ 20 +400 \right)\implies (\stackrel{seconds}{5}~~,~~\stackrel{feet}{420})[/tex]

The monthly cost for 66 minutes of calls will be $15.84.

Monthly cost is the payment or the bill amount that needs to be paid at the end of the month.

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes)

The monthly cost for 45 minutes of calls = $14.40

The monthly cost for 102 minutes = $19.53

The above values can be paired in groups so as to satisfies the coordinates of a linear function

(45,14.40)  and (102,19.53)

Finding the slope of the graph using these points

slope, m=Δy/Δx

m=Δy=19.53 - 14.40 = 5.13

Δx=102 - 45 = 57

m = 5.13/57 =0.09

Finding the equation of the linear function using m = 0.09, and point (45,14.40)

m=Δy/Δx

0.09=y-14.40/x-45

0.09(x-45)=y-14.40

0.09x-4.05=y-14.40

0.09x-4.5+14.40=y

y=0.09x + 9.9

So for 66 minutes, the cost will be;

x = 66, y = ?

y=0.09*66 + 9.9

y=5.94+9.9 = $15.84

The monthly cost for 66 minutes of calls is $15.84.

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A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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The following equation √ 3x² - 2x + 1/2 = 0 is quadratic

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.

Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."

As the expression √ 3x² - 2x + 1/2 = 0 has square root so it is  a quadratic equation.

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Answer: lines j and k are perpendicular

Step-by-step explanation:

Let's find the equations of lines j and k

                       [tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

Line j: (8,2)  (-2,-2)

x₁= 8     x₂=-2    y₁=2     y₂=-2

[tex]\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\[/tex]

 Multiply both parts of the equation by -4:

[tex]\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2[/tex]

Line k: (-4,3)   (-6,8)

x₁=-4    x₂=-6    y₁=3    y₂=8

[tex]\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}[/tex]

Multiply both parts of the equation by 5:

[tex]\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7[/tex]

Hence, lines j and k are perpendicular

If there are 60 apples in total, then green are 15 .

Given:

in a basket of red and green apples, green apples are only 1/3 as common as red apples.

if there are 60 apples in total, how many are green = ?

x is the number of red apples

y is the number of green apples

x/3= y;

x=3y

x+y= 60

3y+y=60;

4y=60;

that means y=60/4

y = 15

Hence there are 15 green apples.

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The no. of ways or Probability can a student select 2 from each set of books = 13860

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

By multiplying the number of possibilities there are to choose books from each kind, separately, one can determine the maximum number of ways a student can choose two books from each subject.

Rule for Multiplication:

If an event A can be performed in m different ways and another event B in n different ways, then the two events together can be performed in (mn) different ways.

A combination problem is created by the various ways that math, science, and literature books might be chosen.

As a result, the total number of choices can be calculated as follows: (Number of math books chosen) x (Number of scientific books chosen) x (Number of literature books selection)

= C ( 7,2) * (12,2) * (5,2)

= C (7*6/2!) * (12*11/2!) * (5*4/2!)

= 21 * 66* 10

= 13860

The no. of ways or Probability can a student select 2 from each set of books = 13860

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