Write an equation for 51 divided by 3 is k

Answer:

2nd option

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference × fraction of circle

     = 2πr × \(\frac{120}{360}\) ( r is the radius )

    = 2π × 10 × \(\frac{1}{3}\)

    = 20π × \(\frac{1}{3}\)

   = \(\frac{20\pi }{3}\) in

Answer:

please this search in Google

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

4/mx

Answer:

4.46% probability that the pressure will exceed this value.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi.

Gaussian distribution = normal.

This means that \(\mu = 69, \sigma = 10\)

If it is important that the pressure stays below 86 psi, what is the probability (in percent) that the pressure will exceed this value?

As a proportion, this probability is 1 subtracted by the pvalue of Z when X = 86. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{86 - 69}{10}\)

\(Z = 1.7\)

\(Z = 1.7\) has a pvalue of 0.9554

1 - 0.9554 = 0.0446

0.0446*100 = 4.46%

4.46% probability that the pressure will exceed this value.

Answer:

Step-by-step explanation:

1 is 60 2 i 60 and 3 is 61 ;)

Answer: 1200 dollars

Step-by-step explanation:For this question we use the formula:

principal amount x interest rate/100 x time

4000 x 6/100 x 5

4000 x 0.06 x 5

1200

Answer:

$5,387.42

Step-by-step explanation:

Use the formula:

\(A = P\left(1 + \dfrac{r}{n}\right)^{nt}\\\)

where A = amount accrued (principal + interest)
P = initial deposit

r = annual interest rate as a decimal

n = number of times compounded annually

t = number of years

Given
P = 4000
r = 6/100 = 0.06
n = 4 times a year
t = 5 years

\(A = 4000\left( 1 + \dfrac{0.06}{4}\right)^{4\cdot 5}\\\\A = 4000 ( 1+ 0.015)^{20}\\\\A = 4000 (1.015)^{20}\\\\A = \$5,387.42\)

The functions of the coefficients of the quadratic equation indicates that the correct statements are;

a. The y-intercept of the function is (0, c)

c. The coefficient b determines the horizontal shift of the parabola compared to the parent function

d. If a is negative, the parabola opens upwards

The quadratic equation is; y = a·x² + b·x + c

The functions of the coefficients of the above quadratic function are;

a = The scale factor, and the coefficient that determines the direction the projectile faces.

a < 1; Indicates that the graph is wider than the parent function

a > 1; Indicates that the graph is narrower than the parent function

a < 0; Indicates that the parabola opens downward

a > 0; Indicates that the parabola opens upwards

b = The coefficient b together with coefficients a and c determines the coordinate of the vertex of the graph of the quadratic function, which is; (-b/(2·a), -D/(4·a))

Where;

D = The discriminant

Therefore, b determines the x-value, and therefore, the horizontal shift of the parabola compared to the parent function

c = The y-coordinate of the y-intercept of the quadratic function, which is (0, c)

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Answer:

(-3, -1)

Step-by-step explanation:

Moving left 2 units is an example of horizontal translation. This means that the x value will be affected. When it comes to coordinate pairs, 2 left can be represented as -2 because moving left subtracts 2 units from the x-value. However, the question asks what the original coordinate pair is. So, you have to work backward. Thus, instead of subtracting 2, add 2 to find the starting place.

So, the final answer is (-3, -1) because -5 + 2 is -3. We can prove this is the correct answer because (-3, -1) shifted 2 left is (-5, -1).

Answer:

x=1

Step-by-step explanation:

(2(x+4))/5=2

Multiply both sides by 5

2(x+4)=10

Divide both sides by 2

x+4=5

subtract 4 from both sides

x=1

\(\frac{3x^{2} }{y}\)

The value of the given division 469.4 ÷ 62 will be 7.57.

In mathematics, the arithmetic operation has four main operators such as addition, subtraction, multiplication, and division.

The symbol of + represents addition.

The symbol of - represents subtraction

The symbol of × represents multiplication

The symbol of ÷  represents division.

Given the division,

469.4 ÷ 62

⇒ 7.570967742

Rounded to the nearest tenth decimal place

⇒7.57

Hence "The resultant of the 469.4 ÷ 62 is 7.57 ".

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The unit rate of the relationship will be 10/3. The correct option is C.

The given equation is,

y = 10/3x + 8

The general form of an equation of the line is,

y = mx +  c

here, the slope will be 10/3

Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.

The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.

A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.

The unit relationship will be 10/3.

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The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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Answer:

1) 13.9

2) 96. 0

3) 667.2

Step-by-step explanation:

Edge

Hope this helps!!

Answer:

There would be 104 rooms on 4 floors in total.

Step-by-step explanation:

If there were 26 rooms on 2 floors, then you multiply 26 x 4, the result would be 104 rooms on 4 floors in total.

Answer:

52 rooms

Step-by-step explanation:

you could set up a proportion to solve this

26 rooms/ 2 floors = ?/4 floors

to find the answer for the question mark you can divide the amount of rooms by floors and get 13.

With the 13 you can multiply that by 4 to get 52 rooms. You basically used the 13 as the amount of increase

i hope this helped

if you have anymore questions feel free to ask again:3

The measure of angle A in the triangle is 78° ( option A)

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc.The law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side.

then a/sinA= b/sinB = c/sinB

in the triangle a = 37cm, c= 29cm , C = 50 therefore a/sinA= c/sinC

37/sinA= 29/sin50

sinA= sin50×37/29

sinA= 0.766×37/29

sinA = 0.977

A = sin^-1(0.977 )

A = 78°( nearest degree)

Therefore angle A is measured as 78°

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Answer:

9x

Step-by-step explanation:

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

The time taken for 3 machines to pack 5000 articles is 8 hours.

It is given that,

A machine can pack 5000 articles in 24 hours. I.e,

1 machine → 5000 articles → 24 hours

3 machines → 5000 articles → 24/3 hours

Thus, 3 of such machines can pack the same number of articles in

24 ÷ 3 = 8 hours.

Therefore, 3 of such machines take 8 hours to pack 5000 articles.

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Answer:

1. 18

2. 13.5

3. 3rd choice

4. 2nd choice

5. 18.6

6.3m + 8

7. 5x2 + y

i hope this work for you

Answer:

\(\displaystyle h'(s) = 64s + 20\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                                  \(\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)

Step-by-step explanation:

Step 1: Define

\(\displaystyle h(s) = (-8s - 9)(-4s + 2)\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Step-by-step explanation:

-5/8 + 3/4

= -5/8 + 6/8

=1/8

the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.

What is rotational symmetry?

Rotational symmetry is a type of symmetry where a shape or object can be rotated by a certain angle and still appear exactly the same as it did before the rotation. The smallest angle of rotation for which the shape or object appears the same is called the angle of rotational symmetry or the order of the rotational symmetry.

In light of the posed query

There is rotational symmetry in the image.

This picture can be seen as a circle. A whole circle has 360 degrees.

Six wings cover the figure.

360/6

=60°

Hence, the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.

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The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8