In a normal distribution curve, the mean is equal to what?​

Answer:

Step-by-step explanation:

[tex]2(3x-2) = 2\times3x-2\times2[/tex]     (multiply each term in the parenthesis by 2)

               [tex]=6x-4[/tex]

Answer:

6x - 4

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 2(3x - 2)

Let's simplify the expression,

→ 2(3x - 2)

→ 2(3x) + 2(-2)

→ 6x + (-4)

→ 6x - 4

Hence, the answer is 6x - 4.

The area of the sector is 37.7 ft.

A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.

The formula for the area of a sector is given by

Where θ is the central angle in degrees, and r is the radius of the circle

Here we have

A circle has a radius of 4 ft.  

The central angle of sector formed = 270°

Using the formula, Area of sector = (θ/360°) × π r²

Area of the given sector = [ 270/360] × 3.14 × (4)²

= [0.75 ] × [50.24]

= 37.68 ft

= 37.7 ft

Therefore,

The area of the sector is 37.7 ft.

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In response to the query, we have that The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

This trigonometric identity is valid for all theta values. Because it is connected to the geometry-related Pythagorean theorem, it is known as the Pythagorean identity.

According to Pythagorean theory,

[tex]Cos(theta)^2 + Sin(theta^)2 = 1[/tex]

So, you can easily include that value into the equation and simplify it if you need to assess sin(theta) + cos(theta) for a certain value of theta:

[tex]Cos(theta)2 + Sin(theta)2 = 1\\Sin(2) + Cos(30)\\If theta = 30, then 2(30) = 1.\\(1/2)\\c^2 + (√3/2)\\c^2 = 1 \s1/4 + 3/4 = 1 \s1 = 1[/tex]

The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

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Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.

Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:

=> s =√((h²) + ((w/2)²))

We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.

The following formula can be used to determine how much steel tubing is required:

=>  L = 3s + 3h

where h is the height of the frame and s is the length of each edge of the triangle.

Using the method instead of s, we obtain:

=> L = 3(√(h²) + ((w/2²))) + 3h

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Answer:

The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:

V = (2)(7/3)(2)

V = 28/3

V = 9.33 (rounded to two decimal places)

So the volume of the rectangular prism is approximately 9.33 cubic units.

Using linear equations, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.

Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. In the elimination procedure, any coefficient is first made equal, then deleted. After elimination, the equations are solved to provide the other equation.

Given that, the car wash charges $5.25 to use its facilities, plus an additional $0.69 for each minute.

C = 5.25 + 0.69x

For 8 minutes:

C = 5.25 + 0.69(8)

C = $10.77

Hence, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.

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The shape οf the graph is similar tο the letter W; hοwever, the regiοn οf interest will lie οn the right οf the οrigin, which means οnly the right half οf the W(a negative number οf cans cannοt be prοduced).

The prοfit prοduced will be maximized if the number οf cans prοduced is greater than 3. The cοmpany will be at a lοss if the number οf cans prοduced is near 2.5. The break even situatiοns are present if the cοmpany prοduces 2 οr 3 cans.

A pοlynοmial functiοn is a functiοn that can be expressed as a sum οf pοwer functiοns in οne variable, where each term has a cοnstant cοefficient and a nοn-negative integer expοnent.Tο sketch the graph οf the functiοn [tex]P(x) = x^4-x^3-11x^2+9x+18[/tex], we can start by analyzing the end behaviοrs οf the functiοn and identifying where the functiοn crοsses the x-axis (i.e., where P(x) = 0).

Tο find the x-intercepts, we need tο sοlve fοr the rοοts οf the equatiοn P(x) = 0. This can be dοne by factοring the expressiοn οr by using numerical methοds. After sοme algebraic manipulatiοn, we can factοr the expressiοn as fοllοws:

[tex]P(x) = (x-3)(x+1)(x^2-8x-6)[/tex]

Therefοre, the rοοts οf the equatiοn P(x) = 0 are x = 3, x = -1, and x = 4 + √(7) οr x = 4 - √(7). The first twο rοοts indicate that the cοmpany breaks even when x = 3 οr x = -1, which means that the cοmpany needs tο prοduce and sell at least 3 οr -1 cans οf sοda tο make a prοfit οf zerο.

With this infοrmatiοn, we can sketch the graph οf the functiοn by plοtting the x-intercepts and the end behaviοrs. The graph will be symmetric abοut the vertical line x = 1.5 (the average οf 3 and -1) and will have a glοbal minimum at the pοint (1.5, -19.5). The graph will alsο have twο additiοnal rοοts at x = 4 + 2√(7) and x = 4 - 2²(7).

In summary, the graph οf the functiοn [tex]P(x) = x^4-x^3-11x^2+9x+18[/tex] has a "U" shape with a glοbal minimum at (1.5, -19.5). The cοmpany will break even when it prοduces and sells at least 3 οr -1 cans οf sοda. By analyzing the end behaviοrs and the x-intercepts, we can sketch the graph withοut using technοlοgy.

Hence, the graph of the function would be given below:

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The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

A ratio is a mathematical comparison of two quantities or values. It is expressed as the quotient or fraction of one value to another value.

Ratios are often written in the form of a:b or a/b, where a and b are the two quantities being compared.

To complete the following table determine the ratio of the table using the values in the table and calculate the remaining values

Here we have

The ratio table -1

Pages   50                        

Hours    1      3      5      10

Here, the ratio of page/ hours = 50/1 = 50

Let the x, y, and z be the values

According to ratio

=> x/3 = y/5 = z/10 = 50

=> x/3 = 50 => x = 150

=> y/5 = 50 => y = 250

=> z/10 = 50 => z = 500

The ratio table - 2

Feet    100

Hours   1       2     4     6  

The ratio of feet/ second = 100/1 = 100

Let a, b, and c be the values

=> a/2 = b/4 = c/6 = 100

=> a/2 = 100 => a = 200

=> b/4 = 100 => b = 400

=> c/6 = 100 => c = 600

Therefore,

The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

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110 is the value of x in function .

What exactly are function and example?

A function is a type of rule that produces one output from one input.   This is illustrated by the equation y=x2. You only get one output for y if you enter anything for x.

                        Considering that x is the input value, we would state that y is a function of x.

f(x) = {  5;  x< 1 }

        { -1/2x + 4 ; x≥ 1 }

 f(4) =  { -1/2  * 4 + 4 }

         =  { -2 + 4 }

         = { 2 }

f( -2) =  { -1/2 * -2 + 4 }

         =  { 1 + 4 }

          = 5

3f(0) = { -1/2 * 0 + 4 }

       = { 0 + 4}

        = 4 * 3 = 12

10f(14) = ( -1/2 * - 14 + 4 )

        =  7 + 4

         = 10 * 11  = 110

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It will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

A lοgarithm is an inverse οperatiοn tο expοnentiatiοn. It is a mathematical functiοn that helps tο sοlve equatiοns where the variable is in the expοnent. The lοgarithm οf a number tο a certain base is the expοnent tο which the base must be raised tο get that number.

Accοrding tο given infοrmatiοn :

In the given expressiοn, 1,000 • e0.034t, the variable "t" represents the time in years, and "e" is a mathematical cοnstant called Euler's number (apprοximately 2.71828).

The entire expressiοn represents the amοunt οf mοney in an accοunt after "t" years, assuming an initial investment οf $1,000 and a cοntinuοus interest rate οf 3.4% per year (0.034 in decimal fοrm).

Tο find the number οf years it will take fοr the accοunt tο reach $15,000, we can set the expressiοn equal tο 15,000 and sοlve fοr "t".

1,000 • e0.034t = 15,000

Dividing bοth sides by 1,000 gives:

e0.034t = 15

Tο sοlve fοr "t", we can take the natural lοgarithm (ln) οf bοth sides:

ln(e0.034t) = ln(15)

0.034t • ln(e) = ln(15)

Since ln(e) = 1, we can simplify tο:

0.034t = ln(15)

Dividing bοth sides by 0.034 gives:

t = ln(15) / 0.034

Using a calculatοr, we get:

t ≈ 23.29

Therefοre, it will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

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Answer:

Step-by-step explanation:

We can use the Pythagorean theorem to find the distance from second base to home plate, which is the diagonal of a right triangle with legs of 60 feet each:

d = sqrt(60^2 + 60^2) = sqrt(7200) ≈ 84.85 feet

So the total distance that you ran is:

60 + 60 + 84.85 ≈ 204.9 feet

Rounded to the nearest tenth, the answer is:

204.9 feet ≈ 204.9 feet

Answer:

x=3

x=-7

Step-by-step explanation:

The way we can find the pencil Dan has in total is 16+5

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equations.

San has 16 pencils with him before,

Quentin gives him more 5 pencils

then the total pencil Dan will have is obtained by adding all the pencils together,

= 16+5

= 21 pencils

therefore the total number of pencil is found by 16+5 = 21

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Answer:

$36,500 per employee

Step-by-step explanation:

$730,000/20 employees

Answer:

it should be DCE

Step-by-step explanation:

Since both ABE and DCE are similar because because they are both corresponding angels that are congruent.  I'm sorry i couldn't think of another triangle but I'm hoping that at least helped a  bit

We can see that there are 9 possible outcomes for spinning the spinner two times.

By pairing each potential result for the first spin with each potential result for the second spin, we can list all the outcomes and establish the sample space for spinning the spinner twice. Since there are three possible results for each spin, spinning the spinner twice has a total of 3 x 3 = 9 outcomes.

Making a table that displays every scenario is one technique to list the sample space:

Spin 1 Spin 2

Blue  Blue

Blue Orange

Blue  Red

Red          Blue

Red   Orange

Red          Red

Orange  Blue

Orange  Orange

Orange   Red

Listing all the potential pairs of outcomes is another way to list the sample space:

Blue, Blue, Blue, Orange, Blue, Red, Red, Blue, Orange, Red, and Orange, Red; Blue, Blue, Blue, Orange, Blue, Red; and Orange, Blue, Orange, Orange, Red

In either case, we can see that spinning the spinner twice can result in 9 different results.

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Answer: .654 not rounded

Step-by-step explanation:

5.232 divided by 8 is 0.654

So, the simplified form of the given expression is cosxsinx(3cosx - sinx).

A statement, at least two parameters or integers, and one or more calculations make up a mathematical expression. It is possible to multiply, divide, add, or subtract quantities using this mathematical operation. The following is the expression's structure: An expression is (total count, numerical operator, number, or variable).

We can simplify the given expression using the product-to-sum identities:

sin2x × cosx + cos2x × sinx

= 2sinx × cosx × cosx + (cos²x - sin² x) × sinx [using the identity sin2x

= 2sinx × cosx and cos²x = cos² x - sin² x]

= 2sinx × cos² x + cos²x × sinx - sin² x × sinx [expanding the brackets]

= cosx × sinx(2cosx + cosx - sinx)

= cosx × sinx(3cosx - sinx)

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The monthly payment for a 30-year mortgage in this scenario is $1,713.78.

What are Percentages?

Percentages are a way of expressing a proportion or ratio in terms of a fraction of 100.

To solve this problem, we can use the formula for calculating the monthly payment for a mortgage:

[tex]M = P[r(1+r)^n/((1+r)^n)-1][/tex]

where M is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments (the term of the loan in months).

First, we need to calculate the down payment, which is 10% of the purchase price:

Down payment = 0.1 x $340,000 = $34,000

The principal is the purchase price minus the down payment:

Principal = $340,000 - $34,000 = $306,000

Next, we need to calculate the monthly interest rate. The annual interest rate is 5.3%, so the monthly interest rate is:

r = 0.053/12 = 0.00441667

Finally, we need to calculate the number of monthly payments. A 30-year mortgage has 360 monthly payments (30 years x 12 months per year).

n = 360

Now we can plug in these values into the formula and solve for M:

[tex]M = \$306,000[0.00441667(1+0.00441667)^360/((1+0.00441667)^360)-1][/tex]

M = $1,713.78

Therefore, the monthly payment for a 30-year mortgage in this scenario is $1,713.78.

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According to given conditions, I will earn $913,441.60.

What is interest ?

Interest is the cost of borrowing money, usually expressed as a percentage of the amount borrowed. It is also the amount earned on an investment, usually expressed as a percentage of the amount invested. The rate of interest is determined by factors such as the level of risk involved, the term of the loan or investment, and prevailing market conditions.

To calculate the monthly deposit required, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/n)[tex]^{(n*t)}[/tex]- 1) / (r/n))

where FV is the future value, P is the monthly deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we want to solve for P, so we can rearrange the formula:

P = FV * (r/n) / (((1 + r/n)[tex]^{(n*t)}[/tex]- 1))

Substituting the given values, we get:

P = 600000 * 0.04/12 / (((1 + 0.04/12)[tex]^{(12*25)}[/tex]- 1))

Simplifying and solving for P, we get:

P ≈ $1,518.14 per month

To calculate the interest earned, we can use the formula:

I = FV - P * t

where I is the interest earned, FV is the future value, P is the monthly deposit, and t is the number of years.

Substituting the given values, we get:

I = 600000 - 1518.14 * 12 * 25

Simplifying, we get:

I ≈ $913,441.60

Therefore, according to given conditions, I will earn $913,441.60.

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The zeros ( roots ) of the function y = (x + 2)^2 - 25 are x = 3 and x = -7.

Given the function in the question;

y = ( x + 2 )² - 25

To find the zeros of the function, simply means find the values of  x in the function y = ( x + 2 )² - 25, when y equals zero.

Equat the function to 0

(x + 2)^2 - 25 = 0

Adding 25 to both sides, we get:

(x + 2)^2 - 25 + 25  = 0 + 25

(x + 2)^2  = 25

Taking the square root of both sides, we get:

x + 2 = ±√25

x + 2 = +5

Solving for x, we get:

x = -2 + 5 = 3

or x = -2 - 5 = -7

Therefore, the zeros of the function are 3 and -7.

Option 4) -7 and 3 is the correct answer.

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Answer:

8,192

Step-by-step explanation:

20/100*80 =16 apply tjis in every step as they asked 4 times

the answer is 42 will be 42 because i answer that before

The distance between points A and B is: A. 4√5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-4))² + (-2 - 2)²]

Distance = √[(8)² + (-4)²]

Distance = √(64 + 16)

Distance = √80

Distance = √16 × √5

Distance = 4√5 units.

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Answer:

none of them are right it is 4 to the 10

Step-by-step explanation:

The domain of the function y = 3Inx graphed below is: A. x greater than 0.

A domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:

Domain = {1, ∞} or x > 0.

In conclusion, ln(0) is undefined and there is no negative natural logarithm, ln.

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It will take {log(1 - r/n)/n} years to exactly double your investment.

The formula for compound interest is -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

Given is that an investment of $2800 made at an APR of 5% compounded monthly.

The formula for compound interest is -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

For A = 2P, we can write -

Substituting 2P = A, we get -

2P = P(1 + r/n)^nt

2 = (1 + r/n)^nt

log 2 = log {(1 + r/n)^nt}

log 2 = (nt) log(1 + r/n)

(log 2)/log(1 + r/n) = nt

{t} = log{2 - 1 - r/n}/n

{t} = log{1 - r/n}/n

Therefore, it will take {log(1 - r/n)/n} years to exactly double your investment.

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The equation for number of miles is 14/7 = x and she ran 2 miles each day.

Simplify the equation to bring all the variable terms to one side and the constant value to the other in order to solve linear equations with a single variable. Find the LCM (least common multiple) if there are any fractional terms, then simplify them so that the variable values are on one line and the steady terms are on the other.

Let us suppose the number of miles she ran each day = x.

Given that, Aroline ran 14 miles in 7 days.

Thus,

Total distance / Number of days = x

14/7 = x

x = 2

Hence, the equation is 14/7 = x and she ran 2 miles each day.

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Answer:

We can simplify the given expression using the rules of exponents and radicals:

4xy³√ 27x^2y^5

= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)

= 4xy * ³√(3^3 * x^2 * y^3 * y^2)

= 4xy * 3xy * ³√y^2

= 12x^2y^2 * ³√y^2

Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.

Step-by-step explanation:

9x^3 + 4x^2 + 5

Explanation:

Let's simplify step-by-step.

6x^2−3−5x^3−(4x^3+2x^2−8)

Distribute the Negative Sign:

=6x^2−3−5x^3+−1(4x^3+2x^2−8)

=6x^2+−3+−5x^3+−1(4x^3)+−1(2x^2)+(−1)(−8)

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

Combine Like Terms:

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

=(−5x^3+−4x^3)+(6x^2+−2x^2)+(−3+8)

=−9x^3+4x^2+5