A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 116.4-cm and a standard deviation of 0.8-cm. For shipment, 29 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 116-cm.

Answer:

a) 23 and b) 13

Step-by-step explanation:

I. If f(g(x)) is composit function

Find fog and gof

     fog = 3(g) - 1

           = 3(x+5) -1

           = 3x + 15 -1

           = 3x + 14

    gof = (f) + 5

          = (3x - 1) +5

          = 3x + 4

II. Fill in a) and b) question

            lim x -> 3 fog

           = 3(x) + 14

           = 3(3) + 14

          = 9 + 14

       a)  = 23

            lim x-> 3 gof

           = 3x + 4

           = 3(3) + 4

           = 9 + 4

        b)  = 13

Got more question or something to discuss, leave comment below

Answer:

[tex]2.21 \times {10}^{ - 10} [/tex]

Step-by-step explanation:

When we shift (.) from left to right in scientific notarion, the power of 10 varies in negative numbers according to how many numbers we shift.

Answer:

7

Step-by-step explanation:

The equation of direction variation is

y = kx where k is the constant of variation

y = 7x  so 7 is the constant of variation

Answer:

7

Step-by-step explanation:

The equation of direction variation:-  

y = kx where k is the constant of variation -> Eq 1  

y = 7x  -> Eq 2

Comparing Eq 1 and Eq 2,

k=7

Number lines are used to represent numbers on a line at regular intervals. The coordinate of point H is -2.2

From the number line, we have:

[tex]C = -4[/tex]

[tex]F = 5[/tex]

First, we calculate the distance between C and F using absolute functions

[tex]CF = |C - F|[/tex]

[tex]CF = |-4- 5|[/tex]

[tex]CF = |-9|[/tex]

Remove absolute bracket

[tex]CF = 9[/tex]

Point H is [tex]\frac 15[/tex] of the distance so, we have:

[tex]H = \frac 15 CF[/tex]

[tex]H = \frac 15 \times 9[/tex]

[tex]H = 1.8[/tex]

This means that point H is 1.8 from the right of C.

So, the coordinate of H is:

[tex]H = C + 1.8[/tex]

[tex]H = -4 + 1.8[/tex]

[tex]H = -2.2[/tex]

Hence, the coordinate of point H is -2.2

Read more about number lines at:

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Answer:

1.08 = m

Step-by-step explanation:

2= 2.27- m/4

Subtract 2.27 from each side

2-2.27= 2.27-2.27- m/4

-.27 = -m/4

Multiply each side by -4

-.27 * -4 = -m/4 *-4

1.08 = m

Answer:

2 1/10 miles.

Step-by-step explanation:

She has already jogged 2 1/2 + 3 2/5 miles.  This is 2 5/10 + 3 4/10 or 5 9/10.  8 miles is also equal to 7 10/10 miles.  So, to find the remaining amount of miles, we can do 7 10/10 - 5 9/10 = 2 1/10.

Amaya still needs 2.1 miles to jog to meet her goal​.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Operators who let do basic mathematical calculations.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given that this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday

She has already jogged 2 1/2 + 3 2/5 miles.  

⇒ [tex]2\dfrac{1}{2} + 3\dfrac{2}{5} = \dfrac{5}{2} + \dfrac{17}{5}[/tex]

Convert fractions into decimals,

⇒ 2.5+3.4

Apply the arithmetic operation,

⇒ 5.9

So, to find the remaining amount of miles,

⇒ 8 -5.9 = 2.1

Hence, Amaya still needs 2.1 miles to jog to meet her goal​.

Learn more about Arithmetic operations here:

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[tex]4 {p}^{3} q + 12 {p}^{2} {q}^{2} + 8p {q}^{3} \\ = 4pq(p + q)(p + 2q)[/tex]

I hope I helped you^_^

Step-by-step explanation:

Use the distance formula:

(x2, y2) with (x1, y1)

[tex] d \: = \sqrt{( x2 \: - \: x1) {}^{2} \: + \: (y2 \: - \: y1) {}^{2} } [/tex]

Find the lengths of each segment one at a time.

For AC:

A(-3,8) C(0,2)

[tex]d = \sqrt{( - 3 - 0) {}^{2} + (8 - 2) {}^{2} } [/tex]

[tex]d \: = \sqrt{9 + 36} [/tex]

[tex]d \: = \sqrt{45} = 3 \sqrt{5} [/tex]

For BC:

B(6,5) C(0,2)

[tex]d \: = \sqrt{(6 - 0) ^{2} + (5 - 2) {}^{2} } [/tex]

[tex]d \: = \sqrt{36 + 9} [/tex]

[tex]d \: = \sqrt{45} = 3 \sqrt{5} [/tex]

For CD:

C(0,2) D(2,-4)

[tex]d \: = \sqrt{(0 - 2) {}^{2} + (2 - ( - 4)) {}^{2} } [/tex]

[tex]d \: = \sqrt{4 + 36} [/tex]

[tex]d \: = \sqrt{40} = 2 \sqrt{10} [/tex]

With all the segment lengths found, we can conclude that segments AC and BC have the same lengths.

Answer:

[tex](3x + 5)(2 {x}^{2} - 3x + 2) \\ \\ (3x)(2 {x}^{2} - 3x + 2) + (5)(2 {x}^{2} - 3x + 2) \\ \\ 6 {x}^{3} - 9 {x}^{2} + 6x + 10 {x}^{2} - 15x + 10 \\ \\ = 6 {x}^{3} + {x}^{2} - 9x + 10[/tex]

I hope I helped you^_^

Answer:

[tex]6x^3+x^2-9x+10[/tex]

Step-by-step explanation:

[tex](3x+5)(2x^2 - 3x+2)[/tex]

Distribute

[tex]3x(2x^2-3x+2)+5(2x^2-3x+2)[/tex]

Distribute

[tex]6x^3-9x^2+6x+5(2x^2-3x+2)[/tex]

Distribute again

[tex]6x^3-9x^2+6x+10x^2-15x+10[/tex]

Combine like terms

[tex]6x^3+1x^2+6x-15x+10[/tex]

Multiply by 1

[tex]6x^3+x^2+6x-15x+10[/tex]

Combine like terms

[tex]6x^3+x^2-9x+10[/tex]

the answer is 37%

: 16500*37%= 6150

6150+16500=22605 :correct

Answer:

Step-by-step explanation:

[tex]\dfrac{3}{6}=\dfrac{9}{18}=\dfrac{27}{54}[/tex]

[tex]\dfrac{3*3}{6*3}=\dfrac{9}{18}\\\\\\\dfrac{3*9}{6*9}=\dfrac{27}{54}[/tex]

B. The cost of orange juice is $3 per jug

A unit rate, in terms of mathematics, is a rate per unit.

Examples of unit rates are:

The car travels 25 km per hour

The cost of bags of apples is $6.00 per bag of apples.

The unit rate in these choices is Choice B:

The cost of orange juice is $3 per jug

The other choices are rates, not unit rates.

Answer:

SEE THE IMAGE FOR SOLUTION .

HAVE A GREAT DAY

Answer:

11. D

12. C

13. D

14. B

15. E

Step-by-step explanation:

11.

1/3 + 1/2 = 2/6 + 3/6 = 5/6

A is 3/4

B is 2/3

C is 9/10

D is 4/5

E is 2/5

the closest to 5/6 is 4/5.

12.

this is totally easy. just simply additions and one subtraction (to see what is left).

8+10+9 = 27

so, he has

60 - 27 = 33 hours left

13.

the mean value of a series of equal weighted numbers is simply their sum divided by the amount of numbers.

so,

(2+5+3+6+4)/5 = 20/5 = 4

14.

a scale factor is always applied to all dimensions, otherwise the result will be distorted. and that would be especially bad for a map.

so, clearly the width of the larger map is 3 times the width of the smaller map. therefore, the length of the larger map has to be also 3 fine the length of the smaller map.

3×6 = 18

15.

3t - 10 = 8

3t = 18

t = 6

Answer:

[tex]y = -4x + 5[/tex]

Step-by-step explanation:

We want to find the equation of the line that is perpendicular to:

[tex]\displaystyle y = \frac{1}{4} x - 5[/tex]

And which passes through the point (2, -3).

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

In other words, since the slope of the original line is 1/4, the slope of the perpendicular line will be -4.

We are also given that it passes through the point (2, -3). Hence, we can consider using the point-slope form:

[tex]\displaystyle y - y_1 = m(x- x_1)[/tex]

Substitute:

[tex]\displaystyle y - (-3) = -4 (x - (2))[/tex]

Simplify:

[tex]y + 3 = -4(x - 2)[/tex][tex]y = -4x + 5[/tex]

Distribute:

[tex]y + 3 = -4x +8[/tex]

And subtract:

[tex]y = -4x + 5[/tex]

In conclusion, our equation is:

[tex]y = -4x + 5[/tex]

Answer:

And

Step-by-step explanation:

Noted Sir. Thanks A Lot 2 U

Answer:

Looks like it's 1.

Step-by-step explanation:

Since it is a positive slope and it goes up 1 unit, the slope is 1.

Answer:

1. [tex]2(16 {y}^{4} - 81)[/tex]

2. [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex]

Step-by-step explanation:

1. [tex] a^{8} - {b}^{8} [/tex]

➡️ [tex]( {a}^{4} - {b}^{4} ) \times ( {a}^{4} + {b}^{4} )[/tex]

➡️ [tex]( {a}^{2} - {b}^{2} ) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]

➡️ [tex](a - b) \times (a + b) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]

➡️ [tex]2(16 {y}^{4} - 81)[/tex] ✅

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

2. [tex] 32 {y}^{4} - 162[/tex]

➡️ [tex] 2(16y^{4} - 81)[/tex]

➡️ [tex]2(4 {y}^{2} - 9) \times (4 {y}^{2} + 9)[/tex]

➡️ [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex] ✅

Answer:

r = -4

Step-by-step explanation:

4r + 13 = -15 -3r

7r = -28

r = -28/7

r = -4

Answer:

r = -4

Step-by-step explanation:

4r + 13 = -15 -3r

Add 3r to each side

4r + 13+3r = -15 -3r+3r

7r +13 = -15

Subtract 13 from each side

7r+13-13 = -15-13

7r = -28

Divide each side by 7

7r/7 = -28/7

r = -4

Answer:

sum 14, difference -8, product 33, quotient 3/11

Step-by-step explanation:

Sum: add

3 + 11 = 14

Difference: subtract

3 - 11 = -8

Product: multiply

3 * 11 = 33

and quotient: divide

3 / 11

(we can leave it like this as a fraction)

Answer:

age of boy = 12

age of mother = 4 times age of boy = 4*12 = 48

let x = years time

3(12+x) = 48+x

36+3x = 48+x

3x-x = 48-36

2x = 12

x = 6

In 6 years time the mother will be three times as old as the son.

pleasexmark me as brainlist

The slope (m) will be "279.33". A further solution to the question is provided below.

At one moment this same instantaneous modification rate would be the same with the functionality derivative assessed somewhere at the time. In certain other terms, the pitch of such tangent line towards the curvature is somewhere at a level equivalent to that as well.

According to the question,

As we know,

⇒  [tex]Slope (m) = \frac{y_2-y_1}{x_2-x_1}[/tex]

By substituting the values, we get

⇒                  [tex]=\frac{838-0}{6-3}[/tex]

⇒                  [tex]=\frac{838}{3}[/tex]

⇒                  [tex]=279.33[/tex]

Learn more:

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The instantaneous rate of change is the rate of change at a particular point or instant in the graph. The instantaneous rate of change of P at [tex]t=4[/tex] is 250

I've added as an attachment, the graph that represents the population of the fish.

To determine the instantaneous rate of change at [tex]t=4[/tex], we simply calculate the slope (m) of the tangent line using:

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

Because of the scale of the graph, I will use the following estimated points from the tangent line

[tex](x_1,y_1) = (3,0)[/tex]

[tex](x_2,y_2) = (4,250)[/tex]

So, the slope is:

[tex]m = \frac{250 - 0}{4 - 3}[/tex]

[tex]m = \frac{250}{1}[/tex]

[tex]m = 250[/tex]

Hence, the instantaneous rate of change of P at [tex]t=4[/tex] is 250

Read more about instantaneous rate of change at:

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Answer:

y = 39

Step-by-step explanation:

550 x [tex]\pi[/tex] = [tex]\pi[/tex] [tex]r^{2}[/tex] x 11 + y

550 x [tex]\frac{7}{22}[/tex] = [tex]\frac{7}{22}[/tex] x 11 x 11 + y

550 x [tex]\frac{7}{22}[/tex] x [tex]\frac{22}{7}[/tex] = 11 x 11 + y

550 = 11 x 11 + y

[tex]\frac{550}{11}[/tex] = [tex]\frac{11}{11}[/tex] x 11 + y

50 = 11 + y

50 - 11 = y

39 = y

Answer:

$150

Step-by-step explanation:

CP = 100/(100 - L%) × SP

CP = 100/(100 - 20) × 120

CP = 100/80 × 120

CP = 5/4 × 120

CP = 5 × 30

CP = $150

Answer:

8,000 - (-400)

Step-by-step explanation:

Answer: 8,000 - (-400) =

Step-by-step explanation:

Answer:

-7j + 3

Step-by-step explanation:

Combine like terms:

-5j + (-2j) = -7j

-7j + 3

Answer and Step-by-step explanation:

Simply combine the values together.

-5j - 2j + 3

-7j + 3 is the answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

 and seven is equal to six times a number.

Word problems can be tricky no matter what level of math or science you are in.

First look at the question for words that indicate mathematical symbols.

"times" indicates multiplication

"and" indicates addition

"a number" means we have a variable, x, to solve for

Now we can go from left to right and write it in a mathematical equation

7x + 7 = 6x

Then, solve for x

7x + 7 = 6x

7 = 6x - 7x

7 = -1x

7/-1 = x

x = -7

Finally, we check our work.

7x + 7 = 6x

7(-7) + 7 = 6(-7)

-49 + 7 = -42

-42 = -42 √

The answer is x = -7

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Parviz F. answered • 02/11/14

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Mathematics professor at Community Colleges

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 First thing you do in word problems : choose a variable for unknown, what problem is asked you to find.

       n    the number

       7n     7 times the number

        7n + 7       7 times the number and 7

      Then the problem says it is equal  6n , make the equation

       7n + 7 = 6n

       and solve:

        7n - 6n = -7

         n = -7  / is the answer

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KERITHA C. answered • 02/25/18

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If 1 is added to seven times a number, the result is equal to 2 more than six times the number. Find the number.

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Rodney S. answered • 02/16/14

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Seven times a number and seven is equal to six times a number.

Step 1:  Translate the verbal to Algebra.

7x + 7 = 6x.  ("And" means addition if no other operation is present.)

Step 2:  Solve for x.

7x - 6x + 7 = 6x - 6x.      (subtract 6x from both sides)

1x + 7 = 0.             (Simplify)

1x + 7 - 7 = 0 - 7.      (subtract 7 from both sides)

1x = -7.             (Simplify)

1x/1 = -7/1.        (Divide both sides by 1)

x = -7.              (Simplify)

Step 3:  Check 7 times the number -7 and 7 is equal to six times the number -7.

7(-7) + 7 = 6(-7)

-49 + 7 = -42

-42 = -42.   (Both sides are equal!)

The number again is -7.

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Vivian L. answered • 02/10/14

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Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH

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Hi Alyson;

7x+7=6x

Let's subtract 7x from both sides...

7x+7-7x=6x-7x

7=-x

Let's multiply both sides by -1...

(-1)(7)=(-1)(-x)

-7=x

Let's check our work...

7x+7=6x

[(7)(-7)]+7=(6)(-7)

-49+7=-42

-42=-42

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Answer:

width=7 cm

Step-by-step explanation:

perimeter=2(lengths+width)

        56   =2(21+x)

         56  =42+2x

   56-42  =2x

        2x    = 14

            x   =7    

therefore the width=7 cm

Answer: Well 100g is 100 grams so 100 grams?

Step-by-step explanation: