An equation is shown:
−np − 4 = 2(c − 3)
Which of the following solves for n?
n = the quantity 2 times c plus 2 all over negative p
n = the quantity 2 times c plus 10 all over negative p
n = the quantity 2 times c minus 2 all over p
n = the quantity 2 times c minus 10 all over p

Shape of the distribution of the mean is appropriately normal.

The sampling distribution for a given population is the frequency distribution of the different outcomes that can occur for a population statistic.

In statistics, the population is the entire pool from which statistical samples are drawn. Population can refer to an entire group of people, things, events, visits, or measurements. Populations can therefore be described as aggregated observations from subjects grouped according to common characteristics.

From the given information

X:- impact force produced

X follows normal distribution with mean 30 and standard deviation of 3

n=3

As we know that when random sample is drawn from normal population then sample mean always follows normal distribution irrespective with sample size.

Shape of the distribution of the mean is appropriately normal.

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The differentiated form of 5 - 2x is -2.

Differentiation

Basically, it is a method of finding the derivative of a function.

Given,

Here we have the expression 5 - 2x.

Now, we have to differentiate operation on it.

In this given expression,

By the Sum Rule, the derivative of 5 − 2x with respect to x is written as,

=> d/dx [5] + d/dx [−2x].

Since 5 is constant with respect to x, the derivative of 5 with respect to x is 0.

So, it can be written as,

=> 0 + d/dx [−2x]

Since −2 is constant with respect to x, the derivative of −2x with respect to x is −2 d/dx [x].

Therefore,

=> 0 − 2 d/dx[x]

Differentiate using the Power Rule which states that 

d/dx [xⁿ] = nxⁿ⁻¹ where n=1.

So,

=> 0 − 2⋅1

Multiply −2 by 1.

=> 0 − 2

Therefore, the resulting value is -2.

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Answer:

B )  x = 2 + √2 or x = 2-√2

Step-by-step explanation:

See attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

c

Answer:

D

Step-by-step explanation:

hope it helped:)

The polynomial function with the lowest degree with a leading coefficient of 1 and zeros is 1, -1(multiplicity 3), and 3i is [x³+(2-3i)x²-(3+6i)x+9i].

So, the equation of the curve with a leading coefficient of 1 or the polynomial function with a leading coefficient of 1 f(x) can be expressed as (x-a)* (x-b)* if a, b, and c are the zeros of a polynomial (x-c).

Now, calculate as follows:

Therefore, the polynomial function with the lowest degree with a leading coefficient of 1 and zeros is 1, -1(multiplicity 3), and 3i is [x³+(2-3i)x²-(3+6i)x+9i].

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Answer:

the first, second and last option

Step-by-step explanation:

The machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test using the normal distribution.

What is Normal Distribution?

The Normal Distribution, often known as the Gaussian Distribution, is the most important continuous probability distribution in probability theory and statistics. It is also referred to as a bell curve on occasion. In every physical science and in economics, a huge number of random variables are either closely or precisely described by the normal distribution. Additionally, it may be used to roughly represent various probability distributions, reinforcing the notion that the term "normal" refers to the most common distribution.

Let X denotes the scores.

In the question, It is given that:

Normal distribution with p=400 and 60.

[tex]X \sim N(\mu=400, \sigma=60)\\$$$\frac{X-\mu}{\sigma}(=Z) \sim N(0,1)$\\i.e. $P(Z \leq z)=\Phi(z)$[/tex]

Let 'a' be the score to be in the top 10% of all machinists.

[tex]\begin{aligned}&P(X \leq a)=1-0.10=0.90 \\&\text { or, } P\left(\frac{X-\mu}{\sigma} \leq \frac{a-400}{60}\right)=0.90 \\&\text { or, } \Phi\left(\frac{a-400}{60}\right)=0.90=\Phi(1.282) \\&\text { or, } \frac{a-400}{60}=1.282 \\&\text { or, } \mathbf{a}=\mathbf{4 7 6 . 9 2}\end{aligned}[/tex]

So,

The score a machinist need in order to be in the top 10% is 476.92.  

Hence,

a machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test.

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Here is the proof:

1. Length AB = Length DC

2. Angle BAC = Angle ACD (AB is parallel to CD, so the opposite interior angles are equal)

3. AC length = AC length (2 lines coincide)

Principle of Side - Angle - Side

then the two triangles are said to be congruent

So Length BC = Length DA

Congruence is a condition where two flat shapes have the same size and are said to be congruent.

The characteristics of two triangles that are said to be congruent are:

1. When the pairs of corresponding sides are equal in length. Usually called the side-by-side criterion.

2. Two pairs of corresponding sides are equal in length and the angles between them are equal. Commonly referred to as the side-angle-side criterion.

3. Two pairs of congruent angles and the same side lengths. Also known as angle-side-angle

After doing proportional we will get:
i) Express y in terms of x : y = kx

ii) The value of y when x = 11 is 33

iii)  the value of x when y = 12 is 4

What is proportional?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality as well as proportionality constant, then the two sequences of numbers are proportional as well as directly proportional. If corresponding elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences seem to be inversely proportional. This definition is frequently expanded to include connected variable quantities, also known as variables. Variable has a different meaning in mathematics than it does in everyday language (see variable (mathematics)); such two concepts share the same name due to a shared etymology.

i) y ∝ x

y = kx

when y = 6, x = 2

6 = 2k

k = 3

y = kx

ii) y = 3x

y = 3(11)

y = 33

iii) y = 3x

12 = 3x

x = 4

iv) For the graph:

x  0  1  2

y  0  3 6

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Step-by-step explanation:

The unit rate per carton is 2

A pound of banana has its cost to be (c) $0.59

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

Amount spent on bananas = $3.54 degrees

Number of pounds = 6 pounds

From the above parameter, we can calculate the cost of one pound using the unit rate formula

The unit rate is calculated as

Unit rate = Amount spent on bananas/Number of pounds

Substitute the known values in the above equation

So, we have the following equation

Unit rate = 3.54/6

Evaluate the quotient

Unit rate = 0.59

Hence, the cost of one pound is $0.59

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Step-by-step explanation:

9.

we get the extreme values of y (a function) by finding the zeroes of the first derivative (that gives us the x-positions) and then using these x values in the original function.

a quadratic function has only one extreme value (1 less than the degree of the polynomial). but 2 zeroes (exactly the degree of the polynomial) - don't mix these two things up.

as the leading coefficient is positive (1), we know that the parabola is opening upwards, and the extreme value will be the vertex and therefore the minimum.

y = (x + 4)² + 6

y = x² + 8x + 16 + 6 = x² + 8x + 22

y' = 2x + 8

2x + 8 = 0

2x = -8

x = -4

(-4 + 4)² + 6 = 0² + 6 = 6

the smallest possible value of y = 6 (at x = -4).

10.

the intercept form of a parabola equation is

y = a(x - p)(x - q)

p and q are the x-intercept values.

in our case we see p = -3, q = 3.

also, we see the vertex being (0, 9), which we need to get "a".

y = a(x - -3)(x - 3) = a(x + 3)(x - 3)

using the vertex coordinates to get a :

9 = a(0 + 3)(0 - 3) = -9a

a = 9/-9 = -1

so, the quadratic equation is

y = -(x + 3)(x - 3) = -(x² - 9) = -x² + 9

11.

I assume the thinking here is : the flight curve of every falling object is a parabola.

the vertex of this parabola is (0, 36), as x represents the time in seconds, and y represents the height in ft.

the vertex form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

y = a(x - 0)² + 36 = ax² + 36

a must be negative, as the fall parabola opens downwards.

for typical fall situations on Earth a = -g/2 ≈ -16 (g being the gravity constant of 32.17405... ft/s²).

so, we have

y = -16x² + 36

for what x is y = 0 ?

0 = -16x² + 36

16x² = 36

x² = 36/16 = 9/4

x = 3/2 = 1.5

the coin hits the water after 1.5 seconds.

Answer:

-2<x<3

Step-by-step explanation:

I have attached the work required to solve this problem as well as a pretty good explanation to each step.

(8.1)(8.12 multply by4=263.080

========================================================

Explanation

Use the pythagorean theorem to find b

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

b = sqrt(20^2 - 16^2)

b = sqrt(400 - 256)

b = sqrt(144)

b = 12

The missing leg of this right triangle is 12 feet long. This isn't the final answer, but it does lead to the answer. Choice B is a trick answer, so be careful.

We have a right triangle with sides 12, 16 and 20. The perimeter is therefore 12+16+20 = 28+20 = 48 feet which is the amount of fencing needed. The answer is choice D.

Side note: Your teacher mentions the shortest side is 16 feet, but that's clearly not the case since it should be 12 feet instead. This seems like a typo.

(7x-30) is the expression which you can use that is equivalent to 5x -2(15-x).

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

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Given: [tex]5x-2(15-x)[/tex]

On solving the above equation we get ,

⇒ 5x - 2 (15) + 2 (x)

⇒ 5x - 30 + 2x

⇒ (5x + 2x) - 30

⇒(7x - 30)

Hence, we can say that (7x-30) is the expression which we can use and that is equivalent to 5x -2(15-x).

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The center of the circle is  (3,-3)   and the radius is 6  , the graph is drawn below .

In the question ,

the equation of the circle is given as

(x-3)²+(y+3)² = 36 ,

we know that the general equation of the circle is

(x - h)² + (y - k)² = r²

where , the center is (h,k) and the radius is r .

So , on comparing the given equation with general equation of the circle , we get

h = 3 and k = -3

and r² = 36

So, r = 6 .

the center is (h,k) = (3,-3)

and the radius is 6 .

the graph of the circle (x-3)²+(y+3)² = 36 is shown below .

Therefore , The center of the circle is  (3,-3)   and the radius is 6 .

The given question is incomplete , the complete question is

Graph the circle (x-3)²+(y+3)² = 36 and find the radius and center of the circle ?

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Answer:

∴ a = -4.61 or 2.61 (to 3sf)

Step-by-step explanation:

      (a + 3)(a - 1) = 3(2 + 1)

  a² + 3a - a - 3 = 3(3)

       a² + 2a - 3 = 9

  a² + 2a - 3 - 9 = 0

      a² + 2a - 12 = 0

[(a + 1)² - 1²] - 12 = 0

       (a + 1)² - 13 = 0

              (a + 1)² = 13

∴ a = -4.61 or 2.61 (to 3sf)

Answer:

Step-by-step explanation:

The range is [-4, ∞)

Using a graphing calculator (desmos) we can obtain a graph of the following function.

Explanation:

In the graph, we can see that there is a point a -4 and nothing lower, making it our minimum y-value. However, we cannot see an ending for the function; therefore, it is indeterminable and thus, infinity. As for notation. we use the solid bracket because we know the definite point, though because infinity is not definite we just use a parentheses to enclose it.

The expression is an arithmetic progression and the solution is

aₙ = a + ( n - 1 ) d

where a = 1

d = -1

n = 82

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the number of terms n = 82

Let the first term of the arithmetic progression be a = 1

Now , the common difference is d = -80 - ( -79 )

                                                         = -1

So , the expression for arithmetic progression is :

aₙ = a + ( n - 1 ) d

Substituting the values , we get

a₈₂ = 1 + ( 82 - 1 ) ( -1 )

a₈₂ = 1 + ( -81 )

a₈₂ = -80

And ,

a₈₁ = 1 + ( 81 -1 ) ( -1 )

a₈₁ = 1 + ( - 80 )

a₈₁ = -79

And so on ,

so , the expression is

aₙ = a + ( n - 1 ) d

where n = 82

d = -1

And the first term is a = 1

Hence , The expression is an arithmetic progression and the solution is

aₙ = a + ( n - 1 ) d

where a = 1

d = -1

n = 82

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7x - 3 > 24 can be described as an inequality.

An algebraic expression consists of unknown variables, numbers and arithmetic operators.  It does not contain any equality or inequality symbols.

Variables are number represented with a letter in an expression. Numbers includes 1, 2, 3 etc. Basic operators are addition, subtraction, multiplication and division.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

For example x > y.

Therefore, we can denote 15x -10 as an expression and 7x - 3 > 24 is denoted as an inequality.

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Answer:

1

Step-by-step explanation:

4+1=5

5-4=1

Answer:

you have 1 friend

Step-by-step explanation:

you have 4 then you add another

that's 5

then you lose 4

5-4 is 1

Answer: B

Step-by-step explanation:

2.5/4.5 = x/2.25

x = 1.25 in

The solution of the fractions six and five eighths times negative one and two fifths is  negative 371 over 40

Fractions are numbers written as a quotient, in which a numerator is divided by a denominator

Given: six and five eighths times negative one and two fifths

6 5/8  x -1 2/5

First, convert each fraction to improper fractions:

6 5/8 = (6 x 8)+4/ 8  = 53/8

-1 2/5 = - ( (1 x 5)+2/ 5 ) = - 7/5

Thus,

6 5/8  x -1 2/5  = 53/8  x - 7/5

                       = - (53 x 7) /(8x5)

                       = - 371/40

Therefore, six and five eighths times negative one and two fifths is negative 371 over 40. The 1st option is the answer

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Using the standard z table, a 95% confidence interval for p is (0.5327,0.6173).

In the given question,

A poll is taken in which 302 out of 525 randomly selected voters indicated their preference for a certain candidate.

We have to find a 95% confidence interval for p.

From the question, x=302, n=525

So estimation point,

P=x/n

P=302/525

P=0.575

Now the z value of 95% confidence interval is 1.960 using the standard z table.

Margin of Error (E)=z×√{P(1−P)}/n

Now putting the value

E=1.960×√{0.575(1−0.575)}/525

E=1.960×√(0.575×0.425)/525

E=1.960×√0.244/525

E=1.960×√0.000465

E=1.960×0.0216

E=0.0423

At 95% confidence interval for p is

P−E ≤ p ≤ P+E

Now putting the value

0.575−0.0423≤ p ≤0.575+0.0423

0.5327≤ p ≤0.6173

Hence, a 95% confidence interval for p is (0.5327,0.6173).

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Answer:

39mm=6m52/39= 1 1/31 1/3 times 6 meters4/3 times 6/1 = 24/324/3=8The actual length of the living room is 8 meters

Answer:

6 cats

Step-by-step explanation:

first we can find 2/3 of 18

2/3*18

36/3

12 cats are brown so now since there are 18 cats in total we subtract that from 12 to see how many are not brown

18-12

6 cats are not brown

Hopes this helps please mark brainliest

Answer:

1.) For the first question, the answer is 12

2.) For the second answer, you are correct, the answer is 55

3.) The third answer is 3/2

Step-by-step explanation:

1.) 18x2/3 = 12

2.) 6x8+7 = 55

3.) 1/2 + 1/2 + 1/2 = 3/2 add the numerators (top part of fraction) ONLY and leave the denominators (bottom part of fraction) ALONE.

Hope this helps, please give brainliest!!

Answer:

P=34in

Step-by-step explanation:

just want to help <33333

Answer:34

Step-by-step explanation:34