10 + 5/12c = 20 (deltamath.com Two Step Equations with Fractional Coefficients (L1)

The sample mean for the data is 21.38 and the sample standard deviation for the data is 56.19

To do this, we start by calculating the midpoint of each class using:

Midpoint= (Lower + Upper)/2

Using the above formula, we have:

Age (x)        Frequency (f)

2                   24.8

9.5               422

17                  194

22                 256

29.5             50.7

39.5              35.7

54.5             75.2

70                 54.3

This is calculated using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{2*24.8 + 9.5*422 + 17*194 + 22*256 + 29.5*50.7 + 39.5*35.7 + 54.5*75.2+70*54.3}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3}[/tex]

Evaluate

[tex]\bar x = \frac{23793.8}{1112.7}[/tex]

[tex]\bar x = 21.38[/tex]

Hence, the sample mean for the data is 21.38

This is calculated using:

[tex]\sigma_x = \sqrt{\frac{\sum f(x- \bar x)^2}{\sum f - 1}}[/tex]

So, we have:

[tex]\sigma_x = \sqrt{\frac{2*(24.8-21.38)^2 + .............+70*(54.3-21.38)^2}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3 - 1}}[/tex]

Evaluate

[tex]\sigma_x = \sqrt{\frac{3509508.4556}{1111.7}}[/tex]

[tex]\sigma_x = \sqrt{3156.88446128}[/tex]

[tex]\sigma_x = 56.19[/tex]

Hence, the sample standard deviation for the data is 56.19

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Answer:

62.

Step-by-step explanation:

because I subtract 70 to 8 equal to 62

Answer:

I think

Step-by-step explanation:

I think 62 hope you have a good day

find D which is the discriminant and with D < 0.

therefore the equation has an imaginary root and not a real root.

The annual percent rate(APR) to purchase a living room set for $4,900 at 8% add-on interest for 4 years is 8. 6

Using the formula

APR = ((Interest + Fees / Loan amount) / Number of days in loan term)) x 365 x 100

Note that Interest expense = Original amount / interest rate

Interest amount = $4, 900

Rate = 8% = 0. 08

Interest expense = $4, 900× 0. 08 = $392

Loan amount is also the principal amount ,  P = I / (RT)

where I is Interest Amount, R is Rate of Interest and T is Time Period.

Principal amount = $4, 900 ÷ 0. 08 × 4 = $4, 900 ÷ 0.32 = $ 15,313. 5

Substitute the values into the formula for APR

APR = [tex]\frac{392+ 4900}{15312.5} / 1460 * 365* 100[/tex]

APR = [tex]0.345 / 1460 *365*100[/tex]

APR = [tex]2. 36* 10^-4 *365* 100[/tex]

APR = [tex]8. 625[/tex]

To the nearest tenth is, 8. 6

Therefore, the annual percent rate(APR) is 8. 6

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It is true that the line segment AB equals 26

The given parameters are:

AB = x +16

BC = 4x + 11

AC = 77

The two-column proof is as follows:

AC = AB + BC                     Line segment formula

77 = x + 16 + 4x + 11            Substitution property of equation

77 = 5x + 27                        Addition property of equation

5x = 50                               Subtraction property of equation  

x = 10                                    Division property of equation

AB = 10 +16                          Substitution property of equation

AB = 26

Hence, the line segment AB has been proved to equal 26

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Profit percentage for weaver after selling mat is equals to 140%.

" Percentage is defined as the hundredth part of the whole given quantity. It is represented by symbol %."

Formula used

Profit% = [tex](\frac{Profit }{cost price} )[/tex]×   100

According to the question,

Given,

Cost price of bundle of grass = $50.00

Number of mats made = 8

Selling price of each mat = $15.00

Therefore,

Selling price of 8 mats = 15 × 8

                                     = $120

Selling price > Cost price

Therefore,

Profit = Selling price - Cost price

         = 120 - 50

         = $70

Substitute the value in the formula to get profit percentage we get,

Profit% = [tex]\frac{70}{50}[/tex] ×100

            = 140%

Hence, profit percentage for weaver after selling mat is equals to 140%.

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Answer:

D is the answer hope

Step-by-step explanation:

hope this helped

Step-by-step explanation:

remember, the number of possible combinations to pick m out of n elements is C(n, m) = n!/(m! × (n-m)!)

50,000 transistors.

4% are defective, that means 4/100 = 1/25 of the whole.

so, the probability for one picked transistor to be defective is 1/25.

and the probability for it to work properly is then 1-1/25 = 24/25.

now, 500 picks are done.

to accept the shipment, 9 or less of these 500 picks must be defective.

the probability is then the sum of the probabilities to get

0 defective = (24/25)⁵⁰⁰

1 defective = (24/25)⁴⁹⁹×1/25 × C(500, 1)

= 24⁴⁹⁹/25⁵⁰⁰ × 500

2 defective = (24/25)⁴⁹⁸×1/25² × C(500, 2)

= 24⁴⁹⁸/25⁵⁰⁰ × 250×499

3 defective = 24⁴⁹⁷/25⁵⁰⁰ × C(500, 3) =

= 24⁴⁹⁷/25⁵⁰⁰ × 250×499×166

...

9 defective = 24⁴⁹¹/25⁵⁰⁰ × C(500, 9) =

= 24⁴⁹¹/25⁵⁰⁰ × 500×499×498×497×496×495×494×493×492×491 /

9×8×7×6×5×4×3×2 =

= 24⁴⁹¹/25⁵⁰⁰ × 50×499×166×71×31×55×494×493×41×491

best to use Excel or another form of spreadsheet to calculate all this and add it all up :

the probability that the engineer will accept the shipment is

0.004376634...

which makes sense, when you think about it, because 10 defect units in the 500 is only 2%. and since the whole shipment contains 4% defect units, it is highly unlikely that the random sample of 500 will pick so overwhelmingly the good pieces.

is the acceptance policy good ?

that completely depends on the circumstances.

what was the requirement about max. faulty rate in the first place ? if it was 2%, then the engineer's approach is basically sound.

it then further depends what are the costs resulting from a faulty unit ? that depends again on when the defect is usually found (still in manufacturing, or already out there at the customer site, or somewhere in between) and how critical the product containing such transistors is. e.g. recalls for products are extremely costly, while simply sorting the bad transistors out during the manufacturing process can be rather cheap. if there is a reliable and quick process to do so.

so, depending on repair, outage and even penalty costs it might be even advisable to have a harder limit during the sample test.

in other words - it depends on experience and the found distribution/probability curve, standard deviation, costs involved and other factors to define the best criteria for the sample test.

Answer:

BB

Hope that helps!

Answer:

m = -3

Step-by-step explanation:

The formula to find the slope of the line is :

slope = m = [tex]\frac{y_1 - y_2}{x_1-x_2}[/tex]

Given that the two coordinates of the line are :

( -1 , - 7 ) ⇒ ( x₁ , y₁ )

( 1 , -13 )  ⇒ ( x₂ , y₂ )

Let us solve now.

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

m =  ( -7 - ( -13)) ÷ ( -1 - 1 )

m = ( -7 + 13 ) ÷ ( -2 )

m = 6 ÷ -2

m = -3

Answer:

m = -3

Step-by-step explanation:

Given two points:

To Find:

Solution:

Using slope's formulae,

[tex] \boxed{ \rm{m = \cfrac{y_2 -y_1 }{x_2 - x_1} }}[/tex]

According to the question, on the formula:

Substitute them onto the formulae:

[tex] \rm \: m = \cfrac{ - 13 - ( - 7)}{1 - ( - 1)} [/tex]

Simplify using PEMDAS:

[tex] \rm \: m = \cfrac{ - 13 + 7}{1 \ + 1} [/tex]

[tex] \rm \: m = \cfrac{ - \cancel6}{ \cancel2} = \boxed{ - 3}[/tex]

Hence, the slope of the line that passes through the given points in it's simplest form is -3.

Answer:

Step-by-step explanation:

Comment

The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.

Formula

Sin(A) = Sin(68 = opposite / hypotenuse     Substitute values.

Solution

sin(68) = altitude (side opposite) / 20       multiply both sides by 20

20*sin(68) = 20* altitude / 20                     substitute for sin(68)

20* 0.9272 = altitude

altitude = 18.5

Answer: 18.5 to the nearest tenth

Answer:

4hours

Step-by-step explanation:

1hour =85+85

=170km/h

time= distance÷

speed=170km/h

680÷170=time

=4h

Answer:

Mean = 3.125 ≈ 3.13

Step-by-step explanation:

Mean = Sum of numbers =  1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13

           Amount of number                     8                             8

Answer:

x=5.24-9+180n,174.75+180n

Step-by-step explanation:

Evaluation:

The answe for the function is -1.

Add -5 to each side of the inequality:

-3 ≤ x + 5 ≤ 8

-3 - 5 ≤ x + 5 - 5 ≤ 8 - 5

-8 ≤ x ≤ 3

Since x is an integer, there are 12 possible solutions belonging to {-8, -7, ..., 1, 2, 3}. In the sum of these solutions, the integers -3 to 3 cancel out, and the rest give

-8 - 7 - 6 - 5 - 4 = -30

The expression for the profit is -x^2/30 + 9x - 103 and the percentage profit on 20 bags of rice is 11.1%

The cost and the selling price are given as:

C(x) = 24x + 103

S(x) = 33x - x^2/30

The profit is calculated using:

P(x) = S(x) - C(x)

This gives

P(x) = 33x - x^2/30 - 24x - 103

Evaluate the like terms

P(x) = -x^2/30 + 9x - 103

Hence, the expression for the profit is -x^2/30 + 9x - 103

When x = 20, we have:

Cost: C(20) = 24 * 20 + 103 = 583

Profit: P(20) = -(20)^2/30 + 9(20) - 103 = 64.67

The percentage profit is then calculated as:

Percentage = P(x)/C(x) * 100%

This gives

Percentage = 64.67/583 * 100%

Evaluate

Percentage = 11.1%

Hence, the percentage profit on 20 bags of rice is 11.1%

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Answer:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Step-by-step explanation:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Answer:

3 XD

Step-by-step explanation:

The line that contains an example of assonance is C. He fell asleep under the oak tree, feeling fine.

This refers to the similarity of sounds that can be found in nearby words in a sentence, between their vowels and/or consonants.

Furthermore, alliteration means the occurrence of similar words or sounds in a sentence at the beginning of closely connected words.

With this in mind:

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The table that represents an exponential function of the form y = [tex]b^{x}[/tex] when 0 < b < 1 is Table - 2. See the attached tables.

A function is exponential when its value is a constant that is raised to the power of the argument. This is so especially when the function of the constant is e.

Recall that the exponential function y = [tex]b^{x}[/tex] given that 0 < b < 1. Notice that the table number 2 see to the exponential function that has the following form:

y(x) = (1/3)ˣ

substituting the values of x into the equation, we have:

y(-3) = (1/3) ⁻³ = 27

x = -2; thus

y(-2) =  (1/3) ⁻³ = 9

x = -1; thus

y(-1) =  (1/3) ⁻³ = 3

x = 0; thus

y(0) =  (1/3) ⁻⁰ = 1

x = 1; thus

y(1) =  (1/3) ¹ = 1/3

x = 2; thus

y(2) =  (1/3) ⁻² = 1/9

x = 3; thus

y(3) =  (1/3) ⁻³ = 1/27

Therefore, according to the obtained values, one can summarize that the table that depicts the exponential function y  = bˣ is table 2.

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[tex]3(x - 8) - 13x(x - 8) + 3 = 0 \\ 3x - 24 - 13 {x}^{2} + 104x + 3 = 0 \\ - 13 {x}^{2} + 107x - 21 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ a = - 13 \\ b = 107 \\ c = - 21 \\ x = \frac{ - 107 + - \sqrt{ {107}^{2} - 4(13)( - 21)} }{2( - 13)} \\ x1 = \frac{107 - \sqrt{10357} }{26} \\ x2 = \frac{107 + \sqrt{10357} }{26} [/tex]

Hope it helps

Please give brainliest

Answer:

[tex]\huge\boxed{\sf R. 16.75}[/tex]

Step-by-step explanation:

*Assuming commas are used for decimals.

2.6 kg potatoes = R 13.20

Divide 2.6 to both sides

1 kg potatoes = R 13.20/2.6

1 kg potatoes = R 5.1

Multiply 3.3 to both sides

3.3 kg potatoes = R 5.1 × 3.3

3.3 kg potatoes = R 16.75

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

Answer:

79.8

Step-by-step explanation:

Explanation:

Given f(x) : (2, -3)

f(x) + 2 then graph translates up by 2 units up =  [tex]\boxed{\sf (2, -1)}[/tex]

f(x) - 3 then graph translates down 3 units down = [tex]\boxed{\sf (2, -6)}[/tex]

f(x + 5) then graph translates left 5 units = [tex]\boxed{\sf (-3, -3)}[/tex]

-f(x) then graph reflects over x axis = [tex]\sf \boxed{\sf (2, 3)}[/tex]

f(-x)  then graph reflects over y axis = [tex]\sf \boxed{\sf (-2,-3)}[/tex]

f(2x) then graph has horizontal compression = (2/2, -3) = [tex]\boxed{\sf (1, -3)}[/tex]

2f(x) then graph has vertical compression = (2, (-3)2) = [tex]\boxed{\sf (2, -6)}[/tex]

-f(x - 4) then graph reflects over x axis, moves 4 units to right = [tex]\sf \boxed{\sf (6, 3)}[/tex]

Parent function: y = x²

Graph function: f(x) = (x + 8)² - 4

After Identification:

D. The graph has a translation of 8 units left and 4 units down.

Answer:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Given:  [tex]f(x)=(2,-3)[/tex]

[tex]f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)[/tex]

[tex]f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)[/tex]

[tex]f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)[/tex]

[tex]-f(x) \implies (x,-y)=(2,-(-3))=(2,3)[/tex]

[tex]f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)[/tex]

[tex]f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)[/tex]

[tex]2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)[/tex]

[tex]-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)[/tex]

[tex]\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}[/tex]

Parent function:  [tex]y=x^2[/tex]

Given function:  [tex]f(x)=(x+8)^2-4[/tex]

[tex]f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}[/tex]

[tex]f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}[/tex]

Therefore, a translation 8 units to the left and 4 units down.

Answer:

its C ^^ makes more sense :D

Step-by-step explanation:

hope this helps

Answer:

6 inches

Step-by-step explanation:

Formula for surface area of a cylinder:

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

Plug in values and solve for the radius:

[tex]180\pi =2\pi r^{2} +2\pi r(9)\\[/tex]

Divide both sides by [tex]2\pi[/tex]

[tex]90=r^{2} +r(9)[/tex]

Subtract 90 from both sides

[tex]0=r^{2} +9r-90[/tex]

Use the quadratic equation to find the roots

[tex]x=(-b[/tex]±[tex]\sqrt{b^2-4ac})*\frac{1}{2a}[/tex] (sorry for formatting, Brainly doesn't

                                           allow equations with ± in them)

[tex]x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}[/tex]        and          [tex]x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}[/tex]

[tex]x=\frac{(-9+\sqrt{81+360})}{2}[/tex]          and          [tex]x=\frac{(-9-\sqrt{81+360})}{2}[/tex]

[tex]x=\frac{(-9+\sqrt{441})}{2}[/tex]               and          [tex]x=\frac{(-9-\sqrt{441})}{2}[/tex]

[tex]x=\frac{(-9+21)}{2}[/tex]                   and          [tex]x=\frac{(-9-21)}{2}[/tex]

[tex]x=\frac{12}{2}[/tex]                           and          [tex]x=\frac{-30}{2}[/tex]

[tex]x=6[/tex]                             and          [tex]x=-15[/tex]  

We can't have a negative radius, so that leaves us with r=6 in.

The domain of the function is all real numbers, the range of a function is y ≤ 4

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = –(x + 6)(x + 2)

If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.

Here the no other details are given.

But we can say:

Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4

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Answer:

Solution = (2,1)

Step-by-step explanation:

Make them equal each other and solve for x.

2x - 3 = 1

2x = 4

x = 2

2 * 2 - 3 = 1

Solution = (2,1)