What method is used to find the prime factors of a number *?.

Using the given information, we can calculate the z-score as z = (56.4 - 67.6) / 3.5, which gives us a z-score of -2.3. This means that 2.3 standard deviations below the mean of adult men's heights is the doorway height of 56.4 inches. Since the area under the normal curve from -∞ to -2.3 is 16%, this means that 84% of adult men can fit through the door without bending.

Using the given information and the desired percentage, we can calculate the z-score as z = (x - 67.6) / 3.5, where x is the doorway height. Solving for x, we get x = 57.6 inches. Therefore, a doorway height of 57.6 inches would allow 40% of adult men to fit through without bending.

Learn more about probability:

https://brainly.com/question/25870256

#SPJ4

Answer:

x=83

Step-by-step explanation:

All angles of a triangle add up to 180 so:

53+44=97

180-97=83

Answer:

[tex]\huge\boxed{\sf x = 83\°}[/tex]

Step-by-step explanation:

So,

x + 53 + 44 = 180

x + 97 = 180

x = 180 - 97

[tex]\rule[225]{225}{2}[/tex]

The following triangles are congurent

Yes SAS

A 90-degree tan is referred to as infinity. Thus, 90 degrees is the value for tan-1.

It is given that, tan⁻¹∞

We have to find the value of tan⁻¹∞.

Now,

The value of tan⁻¹∞ is π/2.

By using the trigonometric concepts, we can find the value of tan⁻¹∞

we already know that, tan π/2 = ∞

we have to apply tan⁻¹ on both sides

we get,

              tan⁻¹ tan π/2 = tan ∞

                             π/2 = tan⁻¹∞

Hence, the value of tan⁻¹∞ is  π/2.

The trigonometric function "tangent" is represented by the inverse function "inverse tan." The opposing side of the right triangle is divided by the adjacent side, and this relationship is utilized to compute the angle by using the tangent ratio of the angle. All inverse trigonometric functions must be named with the prefix "arc," so inverse tangent is abbreviated as "arctan."

To learn more about inverse: https://brainly.com/question/3831584

#SPJ4

For a quadratic of the form px^2 + 40x + 16 to be a perfect square, it must be able to be written in the form (mx + n)^2 for some real numbers m and n.

Expanding (mx + n)^2 gives:

(mx + n)^2 = m^2x^2 + 2mnx + n^2

Comparing this to the given quadratic, we can see that:

m^2 = p

2mn = 40

n^2 = 16

Solving for m and n, we find that:

m = ±√p

n = ±4

Therefore, in order for the quadratic to be a perfect square, the square root of p must be rational, and the value of p must be one of the following:

p = 0, 1, 16

So the possible values of p that make the quadratic a perfect square are 0, 1, 16.

A shape that has all sides equal and all angles right angles is called a square.

In a square, all four sides are congruent (equal in length) and all four angles are right angles (90 degrees).

A square is also a special case of a rectangle, which is a four-sided polygon with opposite sides parallel and equal in length. In rectangle, all angles are right angles (90 degrees).

A square is also special case of a rhombus, which is a four-sided polygon with opposite sides parallel and equal in length, but all angles are not necessarily right angles.

A square is also special case of a parallelogram, which is a four-sided polygon with opposite sides parallel and equal in length, but all angles are not necessarily right angles.

To learn more about squares visit: brainly.com/question/28776767

#SPJ4

The value of the acute angle theta is 59.99 degrees

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

tan theta equals1.73205

Express teh equation properly

So, we have the following representation

tan theta = 1.73205

Take the arc tan of both sides

theta = tan^-1(1.73205)

Evaluate

theta = 59.99

HEnce, the acute angle is 59.99

Read more about trigonometry at

https://brainly.com/question/24349828

#SPJ1

Order of addends has no bearing on the amount according to the commutative property of addition. 6 added value.

The machine below produces a different number when a number is entered. 9 is produced if 3 is inserted. If 6 is put in, 12 will come out. If 7 is put in, 13 will come out. ​

Order of addends has no bearing on the amount according to the commutative property of addition.

Changing the addends' order does not alter the amount, according to the commutative property of addition.

Every output number, as we can see, adds a value of 6 to the corresponding input number.

3 + 6 = 9.

6 + 6 = 12.

7 + 6 = 13.

The Complete Question.

To Learn more About addition Refer To:

https://brainly.com/question/25421984

#SPJ1

Answer:

Where is the statement?

Step-by-step explanation:

For least integer function,

domain :  set of all real numbers

range : set of all integers

We know that the least integer function of any real number p is the least integer which is greater than or equal to the given number p.

The mathematical definition of ceiling function is :

f(x) = minimum { a ∈ Z ; a ≥ x }

where Z is the set of integers.

A least integer function is also known as the ceiling function.

The symbol to represent least integer function is ⌈ ⌉.

We can write least integer function for x as:

⌈x⌉ or ceil (x)

From above definition of ceiling function we can say that the domain of least integer function is the set of all real numbers whereas the range of  is the set of all integers.

Learn more about the domain and range here:

https://brainly.com/question/28135761

#SPJ4

The 2 equations will have infinitely many solutions if k equals 10.

Here we have

10x + 5y − (k−5) = 0 and 20x + 10y − k = 0

Since these 2 are already in the standard form

a₁x + b₁y + c₁ = 0

and

a₂x + b₂y + c₂ = 0

we don't have to make any changes to them

According to the law, an equation has infinitely many solutions if

a₁/a₂ = b₁/b₂ = c₁/c₂

here,

a₁ = 10,  b₁ = 5, and c₁ = - k + 5

and,

a₂ = 20, b₂ = 10, and c₂ = - k

Hence, we get

10/20 = 5/10 = ( - k + 5)/(-k)

or, (k - 5)/k = 1/2

or, 2k - 10 = k

or, k = 10

Hence the 2 equations will have infinitely many solutions if k is equal to 10.

To learn more about Simultaneous Equations visit

https://brainly.com/question/29093214

#SPJ4

Complete Question

For what value of k does the following pair of linear equations have infinitely many solutions?

10x + 5y − (k−5) = 0 and 20x + 10y − k = 0

Answer:

115

Step-by-step explanation:

The example of a linear equation in two variables in standard form is 3x + 2y = 6

A linear equation in two variables in standard form is of the form:

Ax + By = C

where A, B, and C are constants and x and y are variables.

An example of a linear equation in two variables in standard form is:

3x + 2y = 6

This equation can be written in standard form by first subtracting 6 from both sides,

3x + 2y -6 = 0

and then dividing both sides by the greatest common factor of the coefficients,

(3/1)x + (2/1)y = 6/1

This gives the standard form of the equation:

3x + 2y = 6.

To learn more about linear equations visit: brainly.com/question/29739212

#SPJ4

Answer:50

Step-by-step explanation:

Answer:

x=2.3

Step-by-step explanation:

Isosceles triangle means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem ([tex]a^2+b^2=c^2[/tex])

[tex]x^2+x^2=\sqrt{11}^2 \\2x^2=11\\x=\sqrt{\frac{11}{2} } \\x=2.345...\\x=2.3[/tex]

Assuming all my math is right, this is your answer

The given expression x² + 2x + 3 is a polynomial.

In the math term expression is defined as an expression that is made up of variables and constants, along with algebraic operations

Here we have given the expression that can be written as x² + 2x + 3 and here we need to identify the given expression is polynomial or not.

AS we all know that the term polynomial means  an expression that consists of variables (or indeterminate), terms, exponents and constants

And we have also know that the polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

And the non-polynomial expressions will be the expressions which contain other operations.

Based on these rule we have identified that the given expression is an polynomial.

Complete Question:

Is the expression x² + 2x + 3 is polynomial or not?

To know more about Expression here.

https://brainly.com/question/14083225

#SPJ4

The space between the 1/3 and 1/6 is 3.83.

Division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to determine the quotient. Division can be used to solve problems involving fractions, decimals, and percentages. It is also used to simplify complex equations and to break down large numbers into smaller, more manageable parts. Division is one of the four basic operations of arithmetic, along with addition, subtraction, and multiplication.

To calculate this, first add 3/4 and 1/3 to get 1.08, then add 1/6 to get 1.14, then subtract 1/2 to get the final answer of 3.83.

To know more about division click-
https://brainly.com/question/25289437
#SPJ1

The element will be gone in approximately 10.9 minutes.

We can calculate this by using the formula:

Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))

Time = (log(300 / 110)) / (log(1 - 0.054))

Time = 10.9 (rounded to the nearest tenth of a minute)

Therefore, The element will be gone in approximately 10.9 minutes.

A logarithmic function is a mathematical function that relates the logarithm of a number to its argument. The logarithm of a number (base 10) is represented by the log symbol (log 10) and the number being used as the argument. The inverse of this function is an exponential function, which relates the exponential of a number to its argument. Logarithmic functions are often used in mathematics and science to simplify and solve equations involving large exponents. They are also commonly used in finance, engineering, and other fields that involve large numbers.

To learn more about logarithmic functions,

Visit; brainly.com/question/30284289

#SPJ4

Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))

Time = (log(300 / 110)) / (log(1 - 0.054))

Time = 10.9 (rounded to the nearest tenth of a minute)

Un equipo de cuatro personas participó en una carrera de relevo de 400 yardas, lo que significa que cada miembro del equipo corrió una distancia de 400 yardas. El equipo completo completó la carrera en 53.2 segundos. Para calcular el tiempo promedio que cada persona corrió, debemos dividir el tiempo total de la carrera entre el número de personas en el equipo. En este caso, se divide 53.2 segundos entre 4 personas, lo que da un tiempo promedio de 13.3 segundos por persona.

Set up a ratio: 150/100 = 210/x, or your investment gave you a return of 36% of the 150 you invested.

The investment's initial value is subtracted from its current value, which is then divided by the investment's original value to determine a simple rate of return.

The calculation is as follows in light of the facts above:

The entire sum should be

30 × 15

= $450

= 210 - 6

= $204

The total amount should be because it was sold for $210 plus a $6 commission.

Right now, rate of return is

= (204 - 450) ÷ 204×100

= 16.58%

You spent $150 to purchase 10 shares at a price of 15%, or 36%. You made 54$ after subtracting the commission of $6 and selling it for 210$.

Set up a ratio: 150/100 = 210/x, or your investment gave you a return of 36% of the 150 you invested.

To learn more about sale refer to:

https://brainly.com/question/29857652

#SPJ1

Answer:

How do you calculate grams per 100mL concentration?

The concentration is the amount divided by the volume it is dissolved in. For example you might dissolve 0.9g of sodium chloride in 100mL of water. Sometimes this is referred to as 0.9% w/v since it is 0.9g weight divided by 100mL volume and “w/v” stands for weight per volume.”

Solubility≡62.5⋅g⋅100⋅mL−1..

Explanation:

☯We want Concentration=Mass of solute100 mL volume of solvent.

We make the reasonable assumption that the volume of solution is equal to 40⋅mL.

And so we set up the quotient.

25⋅g(40100)⋅mL=

☯In order to answer this question, you'll want to make use of the fact that pure water under standard conditions has a density of 1 g/ml. This means that 50 ml of pure water would have a mass of 50 grams. Therefore, we know that our sample has a 25 grams of sugar, in order for the total mass to be 75 grams.

☯The question doesn't specify what unit of concentration they prefer, so you can use the easiest, which is (mass of solute)/(volume of solvent) which in this case is 25g/50ml or .5 g/ml. If you need to write this in terms of molarity, you can use the molar mass of sugar to convert the 25g into moles and divide by .05 L, as molarity is given by (moles of solute)/(volume of solvent in liters).

☯Sugar solutions or "syrups" are used extensively in canning, and sometimes referred to as "heavy" or "light" syrups.

The terms heavy and light are commonly used in two different ways. We refer to weight when we say that an adult is heavier than a child. On the other hand, something else is alluded to when we say that one syrup is heavier than another. A teaspoon of heavy syrup would obviously weigh less than a gallon of light syrup, but heavy syrup is heavier in the sense that a given volume weighs more than the same volume of light syrup. It's interesting that a given volume of "heavy cream" actually weighs less than "light cream" (in this case, "heavy" refers to the thickness, or percent milk fat).

In "Molecular Gastronomy", Herve This (pronounced Thees) points out[2] that more precision is needed in canning recipes. Some call a heavy syrup 1 cup sugar to 2 cups water (a ratio of 0.5:1) while others refer to a medium syrup as 3-1/4 c sugar to 5 c water (a ratio of 0.65:1). The latter is actually heavier, or denser. Which is better for canning?

Step-by-step explanation:

You can solve 2 equations with 2 variables using calculator in equation mode.

To solve a system of two equations with two variables using a scientific calculator, you can use the following steps (based on CASIO fx-991ES PLUS):

First press the 'mode' button and then press '5' corresponding to equations.

Now press '1' corresponding to a linear equation in two variables of format anX + bnY = cn. Now a matrix appears, each row correspond to each equation. The first column represent the coefficient of X, second column represent the coefficient of Y and third column, the coefficient. Note that the equation should be of the format mentioned before.

Now press '=' to get the solution. On the first press you get X and on second press, you get the value of 'Y'.

To know more on two variable linear equation

https://brainly.com/question/29167509

#SPJ4

Answer:

Step-by-step explanation:

Answer:

A fruit bouquet artist charges $1.50 for each piece of fruit in a bouquet, x, plus an additional $17 for the basket and decorations. Customers receive free delivery when their order is over $40.

Step-by-step explanation:

$1.50 represents the cost of each piece of fruit, but we don't know how many fruits are included in the basket, so let x be the number of fruit. That total must be added to the cost of the basket.

If consumers receive free delivery for orders over $40, then 17+1.50x must be greater than $40.

Answer:

[tex]\left(x+5\right)^2- 33=0[/tex]

See explanation below for steps

Step-by-step explanation:

We are given the quadratic equation

[tex]x^2+10x-8 = 0[/tex]

and asked to rewrite it in the form
[tex]\left(x+a\right)^2=b[/tex]

Move 8 to the right side:
[tex]x^2+10x=8[/tex]

[tex]\mathrm{Rewrite\:in\:the\:form}\:x^2+2ax+a^2[/tex]
[tex]\mathrm{Solve\:for\:}a,\:2ax=10x:\quad a=5[/tex]

[tex]\mathrm{Add\:}a^2=5^2\mathrm{\:to\:both\:sides}[/tex]

[tex]x^2+10x+5^2=8+5^2[/tex]

So we get the original equation as:
[tex]\left(x+5\right)^2=33[/tex]

which can be rewritten as
[tex]\left(x+5\right)^2- 33=0[/tex]

Here a = 5, b = -33

The range in the following question is the set of all real numbers from 0 to 200.

To learn more about range from the given link:

https://brainly.com/question/28135761

#SPJ1

The difference between the largest 8-digit number and the smallest 7-digit number is 98999999.

The aim is to find the smallest 7-digit and largest 8-digit numbers, and then we need to determine the difference between these two values.

Let's start by finding the smallest 7-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 therefore it  can be used in the highest place value.

Thus, we can create the required 7-digit smallest number with 0 and 1.

Hence, the smallest 7-digit number is 1000000.

Now, we will discover the largest 8-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 8-digit number with the digit 9.

Thus, the largest 8-digit number is 99999999.

Now, find the difference between these two values.

So, we can determine the difference between the smallest 7-digit and the largest 8-digit numbers by subtracting the smallest from the largest.

Thus, we get,

⇒99999999−1000000

⇒98999999

Hence, 98999999 is the difference between the smallest 7-digit and the largest 8-digit numbers.

To know more about place value, here

brainly.com/question/843056

#SPJ4

The value for a in quadratic function a(x-1)²+3 is obtained as a = 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The vertex of the quadratic function is (1,3).

The line passes through the points (3,5).

The equation is in the form - a(x-1)²+3

It is known that the vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola.

So it can be written -

f(x) = a(x-1)² + 3

Substitute the value of (1,3).

f(1) = a(1-1)² + 3 = 3

And for the point (3,5) the equation will be -

f(3) = a(3-1)² + 3 = 5

Set up a system of equations -

a(1-1)² + 3 = 3

a(3-1)² + 3 = 5

Solving for a in these equations -

a = 2

Therefore, the value of a is obtained as 2.

To learn more about quadratic function from the given link

https://brainly.com/question/25841119

#SPJ1