How many four-letter words can be formed by using the letters in facetious? There are nine letters
available, and each one can be used at most once per word.

Answer:

3_0

Step-by-step explanation:

on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.

What is the number line?

The number line is a visual representation of the set of all real numbers, which are the numbers that can represent any value on the continuous number scale, including fractions and decimals. On the number line, each point corresponds to a specific real number.

The number 2 is represented by a point on the number line, as is the number 2.0. These two numbers are different because 2.0 is a decimal number, while 2 is a whole number.

2 is 10 times the value of 2.0 if you multiply 2.0 by 10. This is because multiplying a number by 10 shifts its decimal point one place to the left, which increases its value by a factor of 10. For example, if you multiply 2.0 by 10, you get 20.0, which is 10 times the value of 2.0.

Hence, on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.

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The critical values and shecht the rejection reglues for a theo-tall tent, in a Z procedure with significance level isterse is (-1.812,1.812).

[tex]$\alpha=0.07$[/tex] This is two tailed lest

critical values are [tex]$\pm 1.812$[/tex]

What is critical values ?

A critical value is a value used as a cut-off to indicate the beginning of a zone where the test statistic from a hypothesis test is unlikely to decrease. In hypothesis testing, the crucial value and the resulting test statistic are compared to decide whether or not the null hypothesis has to be rejected.

For hypothesis testing, the crucial value graphically separates the graph into the acceptance region and the rejection zone. A test statistic's statistical significance should be verified. We will learn more about the critical value in this article, including its types, formula, and calculation method.

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The solution to the first and the second equation are 28.648 and 183.5 respectively.

A radical expression is an expression consisting of a square root or nth root.

(1) The given equation is [tex]-5\sqrt[4]{x-1}=12[/tex].

Solve the equation as follows:

[tex]-5\sqrt[4]{x-1}=12\\\\\sqrt[4]{x-1}= -\frac{12}{5}\\\\(x-1) = (-\frac{12}{5})^4\\x-1 = 27.648\\x = 28.648[/tex]

(2) The given equation is [tex]-2\sqrt[6]{4x-5}+9 =3[/tex].

Solve the equation as follows:

[tex]-2\sqrt[6]{4x-5}+9 =3\\ \\2\sqrt[6]{4x-5}= 9-3\\\\\sqrt[6]{4x-5}=3\\\\4x-5=3^6\\\\4x=729+5\\\\x=734/4\\\\x=183.5[/tex]

The third equation is the same as the first equation.

Hence, the solution to the first and the second equation are 28.648 and 183.5 respectively.

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He spend 0.48 per pounds

What is division ?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A group is divided into equal portions. Division can be used to divide a class into equal groups for a game or activity, or even to divide a pizza among a group of friends in equal quantities. Partitive division and quotative division are the two types of division.

As it is $5.76 for 12 pounds

∴ for one pound

5.76 / 12

= 0.48 pounds

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The quadratic equation 3 / x - [x / x + 6] = 18 / (x² + 6) have roots at 0 and 3

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is given as ax² + bx + c = 0

In the given equation, we are to solve for the value of x

3 / x - [x / x + 6] = 18 / (x² + 6)

On the left hand side of the equation, we can find the LCM and simplify

3(x + 6) - x² = 18

3x + 18 - x² = 18

x = 3 or x = 0

The solutions to the equation are 0 and 3

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Services provided by public service companies are also known as utilities.

What are public utilities, housing expenses, cost of living and bills?

The term "public utilities" describes a group of particular services offered by entities and organisations that are both public and private and make up the public services sector.

The sum of a homeowner's monthly mortgage principal and interest payments and any additional costs related to their home constitutes their total housing expense.

The cost of living is the sum of money required in a certain location and time frame to meet necessities including housing, food, taxes, and medical care.

A declaration of money owed for products or services provided is referred to as a bill.

Based on the above definition,

Hence, services provided by public service companies are also known as utilities.

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Options F and A=[tex]y=\frac{1}{2}^{x}[/tex] match the fourth graph (exponential decay.)

Options G and B=[tex]y=\log_{10}x[/tex] match the second graph (logarithmic growth).

Options E and C=[tex]y=e^{x}[/tex] match the first graph (exponential growth).

Options H and D=[tex]y=\log_{0.5}x[/tex] matches the third graph (logarithmic decay).

What are growth curves?

An illustration of changes in similar circumstances is referred to as a growth curve. It exemplifies how things vary through time, including population, consumer preferences, demand or supply, etc.

What are decay curves?

The decay curve, basically, is a way to depict the rate or specifically exponential rate at which disintegration occurs in a radioactive sample

If we equate the curves and the graphs, we see that both options A and F merge up to the exponential decay model.

Similarly, both options B and G merge up to the logarithmic growth graph model.

Options C and E merge up to the exponential growth model.

Options D and H merge up to the logarithmic decay model.

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Answer:

W/O insurance: 235.50

with insurance: 1597.94

Step-by-step explanation:

Weighted Average:

annual premium 1      $1,580.00 $0

single doctor visit 0.3      $7.50        $105

two doctor visits 0.18      $9.00        $126

medication        0.06      $1.44         $5

                             $1,597.94 $235.50

Answer:

pls mark as brainliest

Step-by-step explanation:

If A = {3, 5, 7, 8, 9, 10} and B= {1,4,7,9,11,12}

a) ANB= { 7 , 9 }

b.)AUB= { 1 , 3 , 4 , 5 , 7 , 8 , 9 , 10 , 11 , 12 }

The value of A is -28 according to arithmetic

What is BODMAS?

BODMAS is associate descriptor and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In sure regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is employed, that is that the word of BODMAS.

Main body:

According to question:

2-[(8×2)+(8×2)]+2=A ​

to find:    value of A

firstly we need to remove brackets according to rule

⇒2-[(8×2)+(8×2)]+2

⇒2-[16+16]+2

⇒2- 32 +2

⇒-28

hence value of A is -28

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Value of the expression 4n - 5r when n = -2 and r = 3 is -23.

The surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given expression:

4n - 5r

When n = -2 and r = 3

The value of the expression become,

4(-2) - 5(3)

= -8 - 15

= -23

Hence, option D is correct.

Now, it is given that the surface area for a rectangular prism with a square base is given by the expression 2s²+4sh, where s is the side length of the square h is the height of the prism.

The surface area in square feet rectangular prism when s=4 feet and h=6feet is

2[tex](4)^{2}[/tex] + 4(4)(6)

= 2(16) + 96

= 32 + 96

= 128 square feet

therefore, the surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.

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The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]

What is Inverse of a Function ?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

For instance, f(x) = 2x + 5 = y

Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.

A function is said to be an inverse function if its own inverse is represented by the symbol f-1.

[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex]  is the inverse of y=-x²+9

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Justyne is frequently moved around the company to wherever she is needed as it is likely that she has high generalised self-efficacy.

Justyne is valued by her organization as a high-utility employee who can answer the phones, greet customers, handle billing questions, operate the manufacturing equipment, and be a quality checker. This proves her capacity that she can act in the ways necessary to reach specific goals that she is meant to achieve.

As she is competent in so many areas, she is frequently moved around the company wherever needed.

Hence, it is likely that Justyne has high generalized self-efficacy.

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Check the picture below, so the hyperbola looks more or less like so.

the center of the hyperbola is half-way between the foci, so namely at (-2 , -1) as you see there, since we know the covertices, half that distance is the "b" component, so all we're really missing is the "a" component, but we know what "c", since it's just the distance from a foci to the center, so

[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-2\\ k=-1\\ b=15 \end{cases}\implies \cfrac{( ~~ x- (-2) ~~ )^2}{ a^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1[/tex]

[tex]\stackrel{\textit{we know that}}{c=17}\qquad 17=\sqrt{a^2+15^2}\implies 17^2=a^2+15^2\implies 17^2-15^2=a^2 \\\\\\ \sqrt{17^2-15^2}=a\implies \sqrt{64}=a\implies 8=a \\\\[-0.35em] ~\dotfill\\\\ \cfrac{( ~~ x- (-2) ~~ )^2}{ 8^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+2)^2}{64}-\cfrac{(y+1)^2}{225}=1 \end{array}}[/tex]

Use quadratic regression  a model for the following data set is [tex]y=1.96 x^2-5.2 x+5.33[/tex].

What is quadratic regression?

A statistical method called quadratic regression is used to identify the parabola equation that best fits a given collection of data. Finding the equation of the straight line that most closely fits a collection of data is the goal of this sort of regression, which is an extension of simple linear regression.

The equation of the parabola that best fits a collection of data is the process of a quadratic regression. As a consequence, we arrive at the equation y=ax2+bx+c where a≠0. The least squares approach is the most effective way to manually locate this equation.

[tex]$$\begin{aligned}& x=1, f(x)=2.1 \\& x=3 \quad f(x)=7.4 \\& x=5 \quad f(x)=20 \cdot 4 \\& y=a x^2+b x+c \\& \text { Print (1) } \\& 2 \cdot 1=a(1)^2+b \times 1+c \\& 2.1=a+b+c \\& \text { Point(2) } \\& 7.4=a(3)^2+b \times 3+c \\& 7.4=9 a+3 b+c \\& \text { Poin (3) } \\& 28.4=a(5)^2+b \times 5+c \\& 28 \cdot 4=25 a+5 b+c \\& \text { by solving (4) (5) (6) } \\& a=1.96 \\& b=-5.2 \\& c=5.33 \\&\end{aligned}$$[/tex]

so, quadratic equation -

[tex]y=1.96 x^2-5.2 x+5.33[/tex]

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Answer:

x = -2

Step-by-step explanation:

Isolate the variable by dividing each side b factors that don't contain the variable.

The value of x and y is x = -5 and y = 2

x - y = -7

What is an equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Solving the equation

4x + 4y = -12 ⇒(1)

3x - 4y = -23 ⇒(2)

eq (1)*3 eq (2)*4

12x + 12y = -36  ⇒ (3)

12x - 16y = -92  ⇒ (4)

Solving eq (3) and eq (4)

    28 y = 56

       y = 2

substituting the value of y in eq (1)

4x + 4(2) = -12

4x + 8 = -12

4x = -12 - 8

4x = -20

 x = -5

x - y = -5 -2

       = -7

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{doubled}{\$9000}\\ P=\textit{original amount deposited}\dotfill &\$4500\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases}[/tex]

[tex]9000=4500\left(1+\frac{0.0725}{4}\right)^{4\cdot t} \implies \cfrac{9000}{4500}=\left(1+\frac{0.0725}{4}\right)^{4\cdot t} \\\\\\ 2=1.018125^{4t}\implies \log(2)=\log(1.018125^{4t})\implies \log(2)=t\log(1.018125^{4}) \\\\\\ \cfrac{\log(2)}{\log(1.018125^{4})}=t\implies 9.65\approx t\qquad \textit{about 9 years and 8 months}[/tex]

I'm sorry i don't know :(

The equation of the required parabola is  y = [tex]6x^2+6x+ 8[/tex]

What is a parabola?

Parabola is a curve where all the point on the curve maintains a fixed distance from a point called the focus and a line called the directrix.

Let the equation of the parabola be y = [tex]ax^2+bx+c[/tex]

Here, a = 6

So equation of parabola is y = [tex]6x^2+bx+c[/tex]

The parabola passes through (0, 8) and (-1, 8)

Putting x = 0 and y = 8 in the equation

c = 8

y = [tex]6x^2+bx+8[/tex]

Putting x = -1 and y = 8

[tex]8 = 6(-1)^2 + b(-1) + 8\\ b = 6[/tex]

So equation of the parabola is y = [tex]6x^2+6x+ 8[/tex]

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Answer:

2x³ + 3x² - x + 10

Step-by-step explanation:

2x³ - 2x² + 4x + 5x² - 5x + 10

2x³ + 3x² - x + 10

the correct answer is a=(2,3)

The evaluated expression the quantity of 6 less than y, raised to the power of x is - 8. Therefore, the correct option is D.

The quantity of 6 less than y, raised to the power of x can be expressed as follows:

The verbal expression can be converted to a mathematical expression as follows:

(y - 6)ˣ

when

y = 4

x = 3

Therefore,

(y - 6)ˣ = (4 - 6)³

Therefore,

(4 - 6)³ = (-2)³

(-2)³ = -8

Therefore, the evaluated expression is -8.

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Answer:

The probability of guessing this password is 1 in 62^7, or approximately 1 in 5.4 trillion.

Step-by-step explanation:

Based on the information you provided, your friend's password is a randomly generated 7-character password that contains both upper- and lower-case letters and numbers. This means that the password could be any combination of the 62 possible characters (26 upper-case letters, 26 lower-case letters, and 10 digits).The probability of guessing this password is 1 in 62^7, or approximately 1 in 5.4 trillion. This means that, in theory, it would take someone a very long time to guess your friend's password by randomly trying different combinations of characters.However, it's important to note that there are other factors that can affect the security of a password, such as whether the password is easy to guess or has been used before by the user or someone else. It's generally recommended to use a long, complex password that is unique and not easily guessable to maximize security.

Answer:  1/(3,521,614,606,208)

Explanation:

There are 26 letters in the English alphabet. This doubles to 52 when considering upper and lowercase letters. Then add on 10 more because of the digits 0 through 9.

In total, there are 2*26+10 = 52+10 = 62 different characters to pick from for any given slot of the 7-character password.

Assuming repeated characters are allowed, this then gives us

62^7 = 3,521,614,606,208

different passwords possible. This massive number is a little over 3.5 trillion. In scientific notation, it is approximately equal to 3.522 * 10^12

The probability of randomly guessing the correct password is 1 over that massive number, since there's only one way to get the correct password. We get the fraction 1/(3,521,614,606,208)

We can say the odds of guessing the correct password are roughly 1 in 3.5 trillion.

The amount that was invested in each account is:

Maricopa Success invested $47,858 in stocks.

Maricopa Success invested $63,571 in bonds.

Maricopa Success invested $47,571 in CDs.

Let c represent Cds

Let b represent bonds

Let s represent stocks

Equations:

b = c + 15000

s = 160000 - b - c = 160000 - c - 15000 - c = -2c + 145,000

0.08(-2c + 145000) + 0.036(c + 15000) + 0.04c = 7520

-0.16c + 11600 + 0.036c + 540 + 0.04c = 7520

-0.084c = -4,080

Divide both side by -0.084

c = -4,080 / 0.084

c= $48,571 (CDs)

b = 48,571+ 15000

b=$63,571 (bonds)

s = 160,000 - $63,571- 48,571

s= $47,858 (stock)

Therefore Maricopa Success invested $47,858  in stocks,Maricopa Success invested $63,571 in bonds and Maricopa Success invested $47,571 in CDs.

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Using the concept of ratio, the percentage Emily saved is 40%

Percentage can be defined as a ratio or a number which can be expressed as a fraction of 100. When we need  to calculate percent of a number, divide the number by the whole and multiply by 100. The percentage in this can be said to be a part per hundred.

Data;

The percentage saved = (amount saved / total amount earned) * 100

Substituting the values into the equation above;

The percentage saved = (18 / 45) * 100

The percentage saved = 0.4 * 100

The percentage saved = 40%

The percentage saved is 40%

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1. To convert 0.00526 into scientific notation, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 5.26, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 5.26 × 10-3

Therefore, the decimal number 0.00526 written in scientific notation is 5.26 × 10-3 and it has 3 significant figures.

2. To convert 0.00639 into scientific notation also known as standard form, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 6.39, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 6.39 × 10-3

Therefore, 0.00639 in scientific notation is 6.39 × 10-3 and It has 3 significant figures. In scientific e-notation it is written as 6.39e-3.

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The percentage of companies with revenue between 73 million and 87 million dollars is; 0.30

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

Population mean; μ = 80 million

Population standard deviation; σ = 18 million

The percentage of companies with revenue between 73 million and 87 million dollars is expressed as;

P(73 < X < 87)

z₁ = (73 - 80)/18

z₁  = -0.389

z₂ = (87 - 80)/18

z₂ = 0.389

Using probability between two z-scores, we have;

P(-0.389 < Z < 0.389) ≈ 0.30

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