Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard from, given that the point-slope form is y+1=2/3(x-8)

____x+____y=____

Answer:

535,095 different samples of size six that contain exactly 2 defective parts.

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

As the order of the parts is not important, the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

How many different samples are there of size six that contain exactly 2 defective parts?

2 defective from a set of 3, and 4 non-defective from a set of 47. So

[tex]D = C_{3,2}*C_{47,4} = \frac{3!}{2!1!}*\frac{47!}{4!43!} = 535095[/tex]

535,095 different samples of size six that contain exactly 2 defective parts.

What is the probability that a sample contains exactly 2 defective parts?

The total number of samples is:

[tex]T = C_{50,6} = \frac{50!}{6!44!} = 15890700[/tex]

Then...

[tex]p = \frac{D}{T} = \frac{535095}{15890700} = 0.0337[/tex]

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Answer:

[tex]Mean = 100[/tex]

[tex]Median = 96[/tex]

Step-by-step explanation:

Given

[tex]C_v = 30\%[/tex] --- coefficient of variation

[tex]mode = 88[/tex]

[tex]Skp = 0.4[/tex]

Required

The mean and the median

The coefficient of variation is calculated using:

[tex]C_v = \frac{\sigma}{\mu}[/tex]

Where:

[tex]\mu \to[/tex] mean

So:

[tex]30\% = \frac{\sigma}{\mu}[/tex]

Express percentage as decimal

[tex]0.30 = \frac{\sigma}{\mu}[/tex]

Make [tex]\sigma[/tex] the subject

[tex]\sigma = 0.30\mu[/tex]

The coefficient of skewness is calculated using:

[tex]Skp = \frac{\mu - Mode}{\sigma}[/tex]

This gives:

[tex]0.4 = \frac{\mu - 88}{\sigma}[/tex]

Make [tex]\sigma[/tex] the subject

[tex]\sigma = \frac{\mu - 88}{0.4 }[/tex]

Equate both expressions for [tex]\sigma[/tex]

[tex]0.30\mu = \frac{\mu - 88}{0.4 }[/tex]

Cross multiply

[tex]0.4*0.30\mu = \mu - 88[/tex]

[tex]0.12\mu = \mu - 88[/tex]

Collect like terms

[tex]0.12\mu - \mu = - 88[/tex]

[tex]-0.88\mu = - 88[/tex]

Divide both sides by -0.88

[tex]\mu = 100[/tex]

Hence:

[tex]Mean = 100[/tex]

Calculate [tex]\sigma[/tex]

[tex]\sigma = 0.30\mu[/tex]

[tex]\sigma = 0.30 * 100[/tex]

[tex]\sigma = 30[/tex]

So:

Also, the coefficient of skewness is calculated using:

[tex]Skp = \frac{3 * (Mean - Median)}{\sigma}[/tex]

[tex]0.4= \frac{3 * (100 - Median)}{30}[/tex]

Multiply both sides by 30

[tex]0.4*30= 3 * (100 - Median)[/tex]

Divide both sides by 3

[tex]0.4*10= 100 - Median[/tex]

[tex]4= 100 - Median[/tex]

Collect like terms

[tex]Median = 100 - 4[/tex]

[tex]Median = 96[/tex]

Answer: hello your question has some missing data attached below is the missing data

answer :

∑ Volume variance = $55272

∑ Sales price variance = $41944 ( F )

Step-by-step explanation:

First step : prepare a flexible budget data for the current year using the formulae below

flexible budget = Actual units * Budgeted rate

and

Sales price variance = Actual - Budgeted data

Attached below is the Table showing the evaluation of sales price variance and volume variance

Answer:

D

Step-by-step explanation:

We have the quadratic function:

[tex]f(x)=-x^2-4x+5[/tex]

First, the domain of all quadratics is always all real numbers unless otherwise specified. You can let x be any number and the function will be defined.

So, we can eliminate choices A and B.

Note that since the leading coefficient is negative, the parabola will be curved downwards. Therefore, it will have a maximum value. This maximum value is determined by its vertex, which is (-2, 9).

Since it is curving downwards, the maximum value of the parabola is y = 9. It will never exceed this value. Therefore, the range or the set of y-value possible is always equal to or less than 9.

So, the range of the function is all real numbers less than or equal to 9.

Our answer is D.

It is not C because the maximum value is dependent on y and not x.

Answer:

5.313 ft (about 5'3.75")

Answer:

[tex]{ \tt{12 {y}^{2} + 12y - 3 {y}^{3} = 124 - (y + 5)}} \\ 3 {y}^{3} - 12 {y}^{2} - 12y = - 124 + (y + 5) \\ {3y}^{3} - 12 {y}^{2} - 12y = - 124 + y + 5 \\ { \tt{3 {y}^{3} - {12y}^{2} - 11y + 119 = 0 }}[/tex]

Answer:

the answer should be B, because I think the collection of fruits is right

Answer:

i think its b

Step-by-step explanation:

Answer:

yes, this forms a right angle

Answer:

Step-by-step explanation:

Answer:

x≤-8

Step-by-step explanation:

-1/2x ≥ 4

Multiply each side by -2, remembering to flip the inequality

-2*-1/2x≤ 4*-2

x≤-8

Answer:

Step-by-step explanation:

Note: by the rule of order of operations, -1/2x == -1/2*x = -x/2

-x/2 >= 4

-x >= 4*2 = 8

x <= -8

The number line looks like this:

<============================O--------------------------------------

where the circle should be filled and at x= -8

The valid part of the number line is to the left of the circle but INCLUDING the circle (solid dot).

9514 1404 393

Answer:

  B.  relative maximum of 8.25 at x=2.5

Step-by-step explanation:

A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...

  x = -5/(2(-1)) = 5/2

The value of the extreme is ...

  f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25

The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.

The function has a relative maximum of 8.25 at x = 2.5.

__

A graphing calculator can show this easily.

Answer:

Due to the lower price per kilogram, purchasing the regular size at 720 grams for 60c is more economical.

Step-by-step explanation:

Which is more economical?

Whichever situation has the lowest price per kilogram.

3 kilograms for $3.15

3.15/3 = $1.05 per kilogram.

720 grams for 60c

0.6/0.72 = $0.83 per kilogram.

Due to the lower price per kilogram, purchasing the regular size at 720 grams for 60c is more economical.

Answer:

The answer is "(0.727, 1.573)".

Step-by-step explanation:

The confidence interval of 98 percent is C.I = (0.727, 1.573). You might disregard the statement of the experts that the genuine average duration in California of earthquakes is 0.5 minutes.

[tex]C.I = \bar{x}\pm t_{\frac{\alpha }{2}}\times \frac{s }{\sqrt{n}}\\\\[/tex]

      [tex]= 1.15 + 3.365 \times 0.12574\\\\= 1.15 + 0.4231\\\\= (0.7269, 1.5731)[/tex]

Answer:

Answer:

Since i m not sure of the equation i have dont both possible ways :)

Step-by-step explanation:

b)

(5/9) ÷ 5

    [tex]= \frac{5}{9} \div 5\\\\=\frac{\frac{5}{9}}{5}\\\\=\frac{5}{9 \times 5}\\\\=\frac{1}{9}[/tex]

5/(9÷5)

   [tex]=\frac{5}{9 \div5}\\\\= \frac{5}{\frac{9}{5}}\\\\=\frac{5 \times 5}{9}\\\\=\frac{25}{9}[/tex]

A. Definition = (the third meaning.)

B. Postulate (axiom) = (the first meaning.)

C. Common notion = (the last meaning.)

D. Theorem = (The second meaning.)

E. Corollary = (the fourth meaning.)

Proof is evidence or an argument that helps to establish a fact or the truth of a statement. For example, most people won't accept new concepts or ideas without proof of its existence.

Hello,

Part A:

[tex]f(x)=4x^2+8x-5\\=4(x^2+2x)-5\\=4(x^2+2x+1-1)-5\\=4(x+1)^2-9\\=(2(x+1)-3)(2(x+1)+3)\\=(2x-1)(2x+5)\\x-intercepts\ are\ x=\frac{1}{2} \ and\ x=-\frac{5}{2} \\[/tex]

Part B:

x² coefficient is 4 >0 thus a minimun

as y=4(x+1)²-9 : vertex is (-1,-9)

Proof: see picture

Sorry for Part c: I don't know

In France, we make an array of (x,f(x)) and then plot the severals points.

Answer:

C. 3/8

Step-by-step explanation:

[tex] - 3x + 8y = 12 \\ \therefore 8y =3x + 12 \\ \therefore \: y = \frac{3}{8} x + 12 \\ equating \: it \: with \\ y = mx + b \: we \: find: \\ m = \frac{3}{8} \\ \therefore \: slope = \frac{3}{8} [/tex]

The answer above is wrong I took the test. It's in the picture below!

You can solve for the velocity and position functions by integrating using the fundamental theorem of calculus:

a(t) = 40 ft/s²

v(t) = v (0) + ∫₀ᵗ a(u) du

v(t) = -20 ft/s + ∫₀ᵗ (40 ft/s²) du

v(t) = -20 ft/s + (40 ft/s²) t

s(t) = s (0) + ∫₀ᵗ v(u) du

s(t) = 10 ft + ∫₀ᵗ (-20 ft/s + (40 ft/s²) u ) du

s(t) = 10 ft + (-20 ft/s) t + 1/2 (40 ft/s²) t ²

s(t) = 10 ft - (20 ft/s) t + (20 ft/s²) t ²

If you folded the figure up, you would have a prism where the parallel bases are right triangles. Each lateral face is a rectangle.

It might help to imagine a room where the floor and ceiling are triangles (they are identical or congruent triangles). Each wall of this room is one of the rectangles shown.

Answer:

2.3 =x

Step-by-step explanation:

We know the opposite and adjacent sides.

Since this is a right triangle, we can use trig functions

tan 38 = opp/ adj

tan 38 = x/3

3 tan 38 = x

2.34385688= x

To the nearest tenth

2.3 =x

Answer:

x ≈ 3.9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 38°

Opposite Leg = x

Adjacent Leg = 5

Step 2: Solve for x

Answer:

47

Step-by-step explanation:

1. #2 and #3 reveal that it must be between 31 to 89

2. #4 and #5 reveals that the answer is one of these numbers:

44, 45, 46, 47, 48, 49

64, 65, 66, 67, 68, 69

84, 85, 86, 87, 88, 89

This is because only 4, 6, and 8 are divisible by 2

3. You must add up all the numbers to see which ones add up to either 11 or 12.

4 + 7 = 11

4 + 8 = 12

6 + 5 = 11

6 + 6 = 12

8 + 4 = 12

This means that these are the following numbers: 47, 48, 65, 66, 84

4. #7 says that you must find the smallest number. The smallest number left is 47.

Answer:  r = 5

Step-by-step explanation:

I hope it's helpful for u but I am not sure my answer is right !

Rate of change = RΔ = (y2-y1)/(x2-x1) = Δy/Δx

(X1,Y1)(X2,Y2)

(1, 2) (2, 4)

RΔ = Δy/Δx

= (4-2)/(2-1)

RΔ = 2

(2, 4) (3, 8)

RΔ = (8-4)/(3-2)

RΔ = 4

(3, 8) (4, 16)

RΔ = (16-8)/(4-3)

RΔ = 8

Step-by-step explanation:

Using an online calculator, I was able to find that one pattern is

[tex]a_{n} = a_{n-1} + 14 * 3^{n-1}[/tex] . Finding a recursive sequence is generally based on guess and check, so there isn't much explanation to obtaining one

Answer:

[tex]336m^2[/tex]

Step-by-step explanation:

[tex]6*8=48[/tex]

[tex]10*12=120[/tex]

[tex]8*12=96[/tex]

[tex]6*12=72[/tex]

Add all these up

[tex]48+120+96+72=336[/tex]

Hope this helps