Given the equation k over 22.8 equals 6.9, determine the value of k.

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

We are given that the scores are normally distributed.

The mean of the data is 573.

The standard deviation of this data is 72.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

So,

We can write,

μ = 573

σ = 72

Then, the given expression is,

( μ - 3σ < x < μ +3σ ) = 99.7%

So,

μ - 3σ = 573 - 3*72

μ - 3σ = 573-216

μ - 3σ = 357

μ +3σ = 573 + 3*72

μ + 3σ = 573+216

μ + 3σ = 789

Hence, the mean is halfway between these two integers are = 357 and 789

Empirical rule states that for a normally distributed data that

about 68% data lies between μ + 1σ that is one standard deviation from mean.

about 95% data lies between μ + 2σ that is one standard deviation from mean.

about 99.7% data lies between μ + 3σ that is one standard deviation from mean.

Therefore,

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

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From the data provided, we can consider the following function as a good approximation:

Therefore:

The answer is:

a quadratic function with a negative value of a

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.

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The  five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).

Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.

A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.

Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.

Let the value of

x = 0,

then,

0 + y = 3

⇒

y = 3

One of the solutions

for x + y =3, is =(0,3)

Similarly, If x = 1,

then,

1 + y =3 ⇒ y = 3 - 1 = 2

One of the solutions for x + y =3, is

(1,2)

If x = 2,

then,

2 + y = 3

⇒ y = 3 - 2 = 1

One of the solutions for x + y =3, is

(2,1)

If x = 3, then,

3 + y = 3

⇒ y = 3 - 3 = 0

One of the solutions for x + y =3, is

(3,0)

If x = 4,

then,

4 + y = 3

⇒ y = 3 - 4 = -1

One of the solutions for x + y =3, is

(4, -1)

Hence,

five

solutions of the equation x + y = 3, are:

(0,3), (1,2), (2,1), (3,0) and (4, -1).

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The circle that has the larger circumference is circle B. The difference in the circumference is  9.42 cm.

A circle is a bounded object in which points from the center is equidistant to the circumference. The circumference of a circle is the perimeter of the circle. The diameter of a circle is a straight line that touches two opposite points on the circumference of a circle and also passes through the center. Radius is half the diameter of a circle.

The circumference of a circle = 2πr

Where:

Circumference of Circle A = 22/7 x 2 x (9/2) = 28.29 cm

Circumference of Circle B = 22/7 x 2 x 6 = 37.71 cm

Difference in circumference = 37.71 - 28.29 = 9.42 cm

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The equation is:

If x grows then y is going to reduce, and if y gets smaller, then t grows. this means that is an inverse variation

A ribbon is 3 4/5 feet long. Each hair tie needs 2/5 feet. Number of hair ties is 6

No of hair ties = 6

How to find number of hair ties :

Length of the ribbon = 3 4/5 feet

Length of each hair tie needed = 2/5 feet

To find how many ties , divide the total length of ribbon by 2/5

That is  = [tex]\frac{3 (4/5)}{2/5}[/tex]

= 6 You can make 6 no.  of hair tie from 3 4/5 feet ribbon.

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Answer:

-49.

Step-by-step explanation:

Convert to vertex form:

f(x) = -7x^2 - 14x - 56

     = -7(x^2 + 2x + 8)

     = -7 [(x + 1)^2 - 1 + 8)

      = 7(x + 1)^2  - 49

- so the maximum value is -49.

The solution to the quadratic equation -3 = 4x² + 9x using quadratic formula is; x = (-9 + √33)/8 or (-9 - √33)/8

The general form of any quadratic equation is written as;

ax² + bx + c = 0

The quadratic formula that is used to solve this is given by;

x = [-b ± √(b² - 4ac)]/(2a)

Now, we are given the quadratic equation as;

-3 = 4x² + 9x

It can be written as;

4x² + 9x + 3 = 0

Thus, using quadratic formula we have;

x = [-9 ± √(9² - (4 * 4 * 3))]/(2 * 4)

x =  [-9 ± √(81 - 48)]/8

x = (-9 ± √33)/8

x = (-9 + √33)/8 or (-9 - √33)/8

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The most appropriate choice for trigonometry will be given by -

AB = 32

AC = [tex]16\sqrt{3}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta,[/tex] [tex]cos\theta[/tex], [tex]tan\theta[/tex], [tex]cot\theta[/tex], [tex]sec\theta[/tex], [tex]cosec\theta[/tex]

[tex]sin\theta=\frac{perpendicular}{hypotenuse}\\\\cos\theta=\frac{base}{hypotenuse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here,

The figure has been attached here.

Since this is a right angled triangle, trigonometry can be applied here,

Since ∠C = 90°, AB is the hypotenuse of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex] as the side opposite to 90° angle is the hypotenuse.

Let BC be the base of  [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex]

BC = 16

m∠B = 180 - (90 + 30)

        = 180 - 120

        = 60°

cos 60 = [tex]\frac{BC}{AB}[/tex]

[tex]\frac{1}{2} = \frac{16}{AB}\\AB = 16\times 2\\AB = 32[/tex]

sin 60 = [tex]\frac{AC}{AB}[/tex]

[tex]\frac{\sqrt{3}}{2} = \frac{AC}{32}\\\\AC = 32 \times \frac{\sqrt{3}}{2}\\\\AC = 16\sqrt{3}[/tex]

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Answer:

.0025 inches

Step-by-step explanation:

[tex] \frac{.15}{150} = \frac{x}{2.5} [/tex]

[tex]150x = 3.75[/tex]

[tex]x = .0025[/tex]

Answer:

x= -2, y= 3

Step-by-step explanation:

5. Solve the system using substitution.

4x + 5y = 7

y= 3x + 9

What variable in the top equation will you substitute the bottom equation into? y

6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation?

4x + 5(3x+9) = 7

7. Using the equation you came up with for question 6, what does it look like simplified?

4x+5(3x+9) = 7, distribute 5 over the sum in parenthesis

4x+15x+45 = 7, subtract 45 from both sides of the equation

4x+15x+45-45 = 7-45, combine like terms

19x = -38, divide both sides by 19

x = -2

8. What is the solution to the equations from question 5?

y= 3x+9, substitute x for -2

y = 3(-2) +9

y = -6+9

y = 3

The solution for the system of equations

4x + 5y = 7

y= 3x + 9

is x= -2, y= 3

This means that the point (-2, 3) is the intersection of line 4x+5y=7 and line y=3x+9 and that point belongs to both lines.

Answer:

Below in bold.

Step-by-step explanation:

5. 4x + 5y = 7

y= 3x + 9

Substitute for y from the top equation.

5y = -4x + 7

y = (-4x + 7)/5

Substituting:

(-4x + 7)/5 = 3x + 9

6. Substituting from bottom equation, we get:

4x + 5(3x + 9) = 7

7. Simplifying the above:

4x + 15x + 45= 7

19x = -38

8. Solving equations from part 5:

(-4x + 7)/5 = 3x + 9

-4x + 7 = 15x + 45

-38 = 19x

x = -2.

Now substitute x = -2 into y = 3x + 9

y = 3(-2) + 9

= 3.

Solution is x = -2, y = 33

The answer to the question is A-

16.6

Answer:

A. 16.6

Step-by-step explanation:

d = sqrt{(x2 - x1)^2 + (y2-y1)^2}

so this is our distance formula

now we need the two points

(-6, -6) and (3, 8)

lets plug these into our formula

d = sqrt{(3 - (-6))^2 + (8 - (-6))^2}

lets simplify

d = sqrt{(9)^2 + (14) ^2}

d = sqrt{277}

d = 16.64 or 16.6

Answer:

6 oranges

Step-by-step explanation:

1) I know that 5 oranges equals to $2.85

2)I need to find the cost of 1 orange

3)Divide the 3.42 to the cost of 1 orange

MY WORK:

2.85 / 5=  $0.57 ( the cost per orange )

3.42 / 0.57= 6 oranges

Hope this helps!

Answer:

its A

Step-by-step explanation

i took this test

Answer:

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11

Answer:

r ≤ -24.32

Step-by-step explanation:

r/-3.2 > 7.6

r /-3.2 × 3.2 > 7.6 × -3.2

r ≤ -24.32

Answer: r ≤ −24.32

Step-by-step explanation:

The inequality you provided is:

r/-3.2 >= 7.6

To solve for r, we can multiply both sides of the inequality by -3.2 to get:

r <= -24.32

Therefore, r is less than or equal to -24.32.

I hope this helps! Let me know if you have any other questions.

The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match.  A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies

The classification of various types of functions can be done using four primary categories. depending on a factor Onto function, one-to-one relationship, many-to-one relationship, and into function are all examples of relationships between function.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.

Equations' true strength is in their ability to explain numerous aspects of the world in a highly accurate manner. (This is why, if one can be found, an equation's solution can be helpful.)

Hence, A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies

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The value of variable x in the equation is 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Therefore, let's solve for variable x in the equation below.

2x - 8 + 3x - 10 = 10x - 43

A variable is number represented with a letter in an equation.

Hence,

2x - 8 + 3x - 10 = 10x - 43

2x + 3x - 8 - 10 = 10x - 43

5x - 18 = 10x - 43

5x - 10x = - 43 + 18

-5x = - 25

divide both sides of the equation by -5

-5x / - 5= - 25 / -5

Therefore,

x = 5

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Answer:

1.056

Step-by-step explanation:

Answer:2000 will be the nearest thousand.

Step-by-step explanation:

Given the expression:

2.5x

Let's determine the situation which best represents the expression.

Let's start from the first statement:

• A. The total amount of change received to pay for an item that cost $2.50:

The best representation for this is: C = A - 2.50

Where A is the amount paid, C is the amount of change.

• B. The area of a rectangle with side lengths 2.5 and x:

The best representation for this situation is:

2.5x

• C. The total cost of an item that is 2.50 more than x dollars:

T = 2.50 + x

• D. The total square footage of a yard when 2.50 yards is divided into equal parts:

This expression cannot be represented by 2.5x

Therefore, the situation which can be represented by the expression 2.5 is:

The area of a rectangle with side lengths 2.5 and x

ANSWER:

B. The area of a rectangle with side lengths 2.5 and x

By definition, Scientific notation has the following form:

Where the coefficient "a" is a number from 1 to 10, but not including 10 and the exponent "n" is an Integer. The base will be always 10.

When you write a number in Scientific notation, the decimal point must be after the first digit of the coefficient.

In this case, you have:

So, in order to write that product in Scientific notation, you must move the decimal point one space to the left. This must be represented in the exponent. If you move it just one space, to the left, then the exponent will be 1 and will be positive.

Therefore, you get that this is:

Therefore, you can determine that the answer is:

1 ) Let's solve this Linear System with the elimination method

Choose the x, as the first variable to be eliminated

2x + 5y = 8 Multiply by 5 the whole equation

-10x – 9y = -72

Adding both equations:

10x +25y=40

-10x -9y=-72

----------------------

0 16y=-32 Dividing both equations by 16

y=-2

2) Plugging into the simplest equation within that Linear System:

2x +5(-2) = 8

2x -10 = 8 Adding 10 to both sides

2x = 18 Dividing both sides by 2

x=9

3) So the answer is the pair (9,-2)

The formula for calculating the volume of a sphere is expressed as

Volume = 4/3 x pi x radius^3

From the information given,

pi = 3.14

radius = 6.2

By substituting these values into the formula, we have

Volume = 4/3 x 3.14 x 6.2^3

Volume = 997.7999

Rounding to the nearest tenth,

Volume = 997.8 m^3

The ordered pair is [4k , 3k]

In first equation, 3x - 4y = 0

∴ 3x = 4y

  x = 4y/3.   ----1

Placing the value of x in second equation:

 4x - 5y = k

 4[4y/3] - 5y = k

16y/3 - 5y = k

[tex]\frac{16y - 15y}{3}[/tex] = k

16y - 15y = 3k

y = 3k

Replacing the value of y in eq. 1, we get

x = 4k

∴ The ordered pair is [4k , 3k]

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Answer:

Slope = 2

Step-by-step explanation:

See attached graph/worksheet.

Applying the transitive property of congruency and other postulates, lines l and m are proven to be parallel as explained below.

The transitive property of congruency states that when two angles are sides are congruent to another third angle or side, then the three sides or angles are all congruent to each other.

For example, if <A = <C, and <B = <C, then <A = <B.

The proof that shows that lines l and m are congruent is explained below:

Statement                                      Reason                                        

1. r║s, <5 is congruent to <6    1. Given

2. <5 is supplementary to <4    2. Same-side interior angles theorem

3. <4 is supplementary to <6    3. Transitive property of congruency

4. l║m                                         4. Converse of same-side interior <s theorem

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Answer: 16 inches

Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.

Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents