An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the proportion of scanners that can be expected to fail within plus or minus 6 months of the mean. (Enter your answer as a percentage without the percent sign; keep 2 decimal places)

Answer:

81/7 (11.57, 11 4/7)

Step-by-step explanation:

Lets rewrite these mixed fractions

[tex]40\frac{1}{2}=\frac{81}{2}[/tex]

[tex]3\frac{1}{2} =\frac{7}{2}[/tex]

Here we can do divide these two numbers:

[tex]\frac{\frac{81}{2} }{\frac{7}{2} }=\frac{81}{7}[/tex]

The answer therefore is 81/7, or 11.571 (11 4/7)

Answer:

16 to 52

Step-by-step explanation:

Answer:

Step-by-step explanation:

       -(4q+8) + 6q = 12q - 5/6(18q + 6)

Open brackets:

<=>  - 4q - 8 + 6q = 12q - 5/6*18q - 5/6*6

<=>  - 4q - 8 + 6q = 12q - 15q - 5

Put q in one side and non q in one side:

<=> - 4q + 6q - 12q + 15q = 8 - 5

<=> 5q = 3

<=> q = 3/5

Answer:

B

Step-by-step explanation:

No matter how many times you multiply 1 by itself, it will always be 1 which makes A and D incorrect.

x is a power. The question is 1/4 * 1/4 * 1/4 which is 1/64

Answer: B

Step-by-step explanation:

[tex]f(x)=(\frac{1}{4})^x\\f(3)=(\frac{1}{4})^3\\f(3)=(\frac{1}{4})(\frac{1}{4})(\frac{1}{4})\\f(3)=\frac{1}{64}[/tex]

Answer:

58

Step-by-step explanation:

58 because you divide 200 by 100 then getting that answer (3) then divide 175 by 3 which equals one percent and you get 58.333 you round it to the nearest whole and u get 58

Answer:

[tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex]

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

-6x +7y= -62

Rewriting this equation into the slope-intercept form:

7y= 6x -62

[tex]y = \frac{6}{7} x - \frac{62}{7} [/tex]

The product of the slope of 2 perpendicular lines is -1.

Let the slope of the unknown line be m.

[tex]m( \frac{6}{7} ) = - 1[/tex]

[tex]m = - 1 \div \frac{6}{7} [/tex]

[tex]m = - \frac{7}{6} [/tex]

Substitute the value of m into the equation:

[tex]y = - \frac{7}{6} x + c[/tex]

To find the value of c, substitute a pair of coordinates into the equation.

When x= 8, y= -3,

[tex] - 3 = - \frac{ 7}{6} (8) + c[/tex]

[tex] - 3 = - \frac{28}{3} + c[/tex]

[tex]c = \frac{28}{3} - 3[/tex]

[tex]c = \frac{19}{3} [/tex]

[tex]c = 6 \frac{1}{3} [/tex]

Thus, the equation of the line is [tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex].

Answer:

1. What is 0.252525 as a fraction?

0.252525 as a fraction equals 252525/1000000

2. 2.454545 as a fraction equals 2454545/1000000

Step-by-step explanation:

To write 0.252525 as a fraction you have to write 0.252525 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.252525 = 0.252525/1 = 2.52525/10 = 25.2525/100 = 252.525/1000 = 2525.25/10000 = 25252.5/100000 = 252525/1000000

And finally we have:

0.252525 as a fraction equals 252525/1000000

2. What is 2.454545 as a fraction?

To write 2.454545 as a fraction you have to write 2.454545 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

2.454545 = 2.454545/1 = 24.54545/10 = 245.4545/100 = 2454.545/1000 = 24545.45/10000 = 245454.5/100000 = 2454545/1000000

And finally we have:

2.454545 as a fraction equals 2454545/1000000

Thanks

Answer:

A

Step-by-step explanation:

f(-1)=7, f(0)=2, f(1)=-3

Answer:

x=3

Step-by-step explanation:

6(x+5)=4(x+9)

6x+30=4x+36

2x+30=36

2x=6

x=3

Answer:

a) The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.

b) 0.0078.

Step-by-step explanation:

Question a:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting.

At the null hypothesis, it is tested if the mean is of 421, that is:

[tex]H_0: \mu = 421[/tex]

It is believed that the machine is underfilling the bags.

At the alternative hypothesis, it is tested if the mean is of less than 421, that is:

[tex]H_a: \mu < 421[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

421 is tested at the null hypothesis:

This means that [tex]\mu = 421[/tex]

A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.

This means that [tex]n = 43, X = 414, \sigma = 19[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{414 - 421}{\frac{19}{\sqrt{43}}}[/tex]

[tex]z = -2.42[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean below 414, which is the p-value of z = -2.42.

Looking at the z-table, z = -2.42 has a p-value of 0.0078.

The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.

b. Find the P-value of the test statistic.

As found above, the p-value of the test statistic is 0.0078.

Answer:

[tex]\boxed {\boxed {\sf (1.5 , 2.5)}}[/tex]

Step-by-step explanation:

The midpoint is the point that bisects a line segment or divides it into 2 equal halves. The formula is essentially finding the average of the 2 points.

[tex](\frac {x_1+x_2}{2}, \frac {y_1+ y_2}{2})[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 endpoints of the line segment. For this problem, these are (5,4 ) and (-2, 1).

Substitute these values into the formula.

[tex]( \frac {5+ -2}{2}, \frac {4+1}{2})[/tex]

Solve the numerators.

[tex]( \frac {3}{2}, \frac{5}{2})[/tex]

Convert the fractions to decimals.

[tex](1.5, 2.5)[/tex]

The midpoint of the line segment is (1.5 , 2.5)

Answer:

c. 3 1/3

Step-by-step explanation:

8x-2-5x=8

3x=10

x=10/3=3 1/3

Answer:

x=[tex]3\frac{1}{3}[/tex]

Step-by-step explanation:

Hi there!

We want to find the value of x in this expression:

8x-2-5x=8

Our goal is to isolate x on one side

Combine like terms on the left side (add the terms with x together)

3x-2=8

Add 2 to both sides (-2+2=0)

3x-2=8

   +2  +2

__________

3x=10

Divide both sides by 3

x=[tex]\frac{10}{3}[/tex]

Simplify the improper fraction

x=[tex]3\frac{1}{3}[/tex]

Hope this helps!

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{(2x - 1)(5x + 3) = 0}\\\rightarrow\large\textsf{10x}\mathsf{^2}\large\textsf{ + x - 3 = 0}[/tex]

[tex]\huge\text{FACTOR the LEFT SIDE of the equation}[/tex]

[tex]\large\textsf{(5x + 3)(2x - 1) = 0}[/tex]

[tex]\huge\text{SET the FACTORS to equal to 0}[/tex]

[tex]\large\textsf{5x + 3 = 0 or 2x - 1 = 0}[/tex]

[tex]\huge\text{SIMPLIFY \& YOU HAVE YOUR RESULT}\\\\\huge\text{to your question if you solved correctly.}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: \boxed{\mathsf{x = - \dfrac{3}{5}\ or \ x = \dfrac{1}{2}}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: 1/6

Step-by-step explanation:

Given:

4/9 and 11/18

Solve:

STEP ONE: Make the denominators equal by determining the LCM

LCM = Least Common Multiple

First Five multiples of 9 = 9, 18, 27, 36, 45

First FIve multiples of 18 = 18, 36, 54, 72, 90

As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.

STEP TWO: Compare the size and determine the greater one.

4/9 = (4 × 2) / (9 × 2) = 8/18

11/18 = 11/18

Since 11 > 8, therefore, 11/18 is greater than 8/18

STEP THREE: Find the difference between the two fractions.

 11/18 - 4/9

=11/18 - 8/18

=(11 - 8) / 18

= 3 / 18

= 1/6

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Y = 4x - 9

Step-by-step explanation:

Hope this helps! If it’s wrong I’m really sorry.

Pls give brainliest!

Answer:

...

Step-by-step explanation:

Answer:

White

6

Red

9

Green

Total number of balls =5+6+9

=20

(i) Probability =

Total cases

favourable cases

P(Green) =

20

9

(ii) P(White or red) =

20

5+6

=

20

11

(iii) P(neither green nor white) = P(Red)

=

20

6

=

10

3

The probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.

The probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.

(a) Probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls:

Total number of balls = 29

Total number of balls to be pulled = 8

Number of ways to choose 1 green out of 8 = C(8, 1) = 8

Number of ways to choose 1 yellow out of the remaining 7 = C(7, 1) = 7

Number of ways to choose 2 red out of the remaining 6 = C(6, 2) = 15

Total favorable outcomes = 8 x 7 x 15 = 840

Total possible outcomes = C(29, 8) = 2,765,905

Probability

= favorable outcomes / possible outcomes

= 840 / 2,765,905

= 0.000303

Therefore, the probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.

(b) Total number of balls = 29

Total number of balls to be pulled = 6

Number of ways to choose 1 green out of 8 = C(8, 1) = 8

Number of ways to choose another green out of the remaining 7 = C(7, 1) = 7

Number of ways to choose 2 yellow out of the remaining 5 = C(5, 2) = 10

Number of ways to choose 2 red out of the remaining 3 = C(3, 2) = 3

Total favorable outcomes = 8 x 7 x 10 x 3 = 1,680

Total possible outcomes = C(29, 6) = 593,775

Probability

= favorable outcomes / possible outcomes

= 1,680 / 593,775

= 0.00283

Therefore, the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.

(c) Probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls:

Total number of balls = 29

Total number of balls to be pulled = 8

Number of ways to choose the first green = C(8, 1) = 8

Number of ways to choose the last green = C(7, 1) = 7

Number of ways to choose 2 yellow out of the remaining 6 = C(6, 2) = 15

Number of ways to choose 2 red out of the remaining 4 = C(4, 2) = 6

Number of ways to choose the remaining 2 balls (either blue or black) = C(5, 2) = 10

Total favorable outcomes = 8 x 7 x 15 x 6x 10 = 50,400

Total possible outcomes = C(29, 8) = 2,765,905

Probability

= 50,400 / 2,765,905 ≈ 0.0182

Learn more about Probability here:

https://brainly.com/question/31828911

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Answer:

23/16

Step-by-step explanation:

2*4 x x-7 = 16

16x - 7 = 16

16x = 16 + 7

16x = 23

x = 23/16

Give me a rating XD <3

Answer:

f(- 2) = - 9

Step-by-step explanation:

Substitute x = - 2 into f(x) , that is

f(- 2) = (- 2)² + 5(- 2) - 3 = 4 - 10 - 3 = 4 - 13 = - 9

Answer:

Perimeter

[tex]202 = x + x + 26 + 4x + 26 + 4x\\202-26-26=10x\\150=10x\\x=15[/tex]

Therefore, the dimensions are

Answer:

24 bags = 21 kg

1.142 bag = 1 kg

About 139 bags = 122 kg

You start off with 24 bags that equal the same amount as 21 kg. You need to find out how many bags of sugar equal the same amount as 122 kg. The first line is a ratio and to find your answer you need to figure out what is 1 kilogram equal to in the amount of bags. You divide both sides by 21 leaving 1.142 bag equal to 1 kilogram. In order to find 122 kilograms, you have to multiply both sides by 122 kilograms which would give you about 139 bags = 122 kilograms.  

Your final answer: 139 bags

I hope this helped!

Answer:

so 1/3 must be subtracted from the sum of 1/4 and 1/6 to have an average of 1/12 of all the two fractions.

Step-by-step explanation:

let the fraction be x

(1/4 + 1/6)-x =  1/12

or, 10/24 - x = 1/12

or, 5/12-1/12 = x

so, x = 4/12 = 1/3

Answer:

huh

Step-by-step explanation:

that don't make no sense

If a,b,c,d,e are in continued proportion then a/c =  a²/b²

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

It is given that

a,b,c,d,e are in continued proportion

We can write it as

a/b = b/c = c/d = d/e = k

d=ek, c=ek², b=ek³ and a=ek⁴

Here a/c

Substitute the values of a and c

⇒ ek⁴/ek²

⇒ k²    [ k = a/b ]

⇒ a²/b²

Learn more about Ratio here:

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Answer:

The answer is 900 ×6= 5,400 u can use a calculator

[tex]6x+34x -6 = 8(5x+10)\\\\\implies 40x -6 = 40x +10\\\\\implies 40x -40x = 10+6 \\\\\implies 0 =16\\\\\text{Which is not true. So no solution.}[/tex]

Answer:

x=2

Step-by-step explanation:

Expanding, we have 3 - 8-64x=-133.

Combining like terms, we have -5 - 64x=-133

Adding 5 to both sides, we have -64x= -128

Dividing by -64, we have x = 2

Answer:

ushshdbs the 7th century there where the gall bladder and merchants Bank Ltd bank in the 7th

Answer:

(a) [tex]C(x) = 12 + 5x[/tex]

(b) [tex]C(x) = 8x[/tex]

(c) Tables

(d) See attachment for graph

(e) Banner newspaper

(f) Free press newspaper

Free Press

[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]

Banner

[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]

Step-by-step explanation:

Given

Free Press

[tex]Initial = 12[/tex]

[tex]Rate =5[/tex]

Banner

[tex]Initial=0[/tex]

[tex]Rate =8[/tex]

Solving (a): Free Press Equation

This is calculated as:

[tex]C(x) = Initial + Rate * x[/tex]

Where

[tex]x \to[/tex] days

So, we have:

[tex]C(x) = 12 + 5x[/tex]

Solving (b): Banner Equation

This is calculated as:

[tex]C(x) = Initial + Rate * x[/tex]

Where

[tex]x \to[/tex] days

So, we have:

[tex]C(x) = 0 + 8x[/tex]

[tex]C(x) = 8x[/tex]

Solving (c): Table of values

For free press, we have:

[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]

C(x) is calculated as:

[tex]x = 1;\ C(1) = 12 + 5* 1 =17[/tex]

[tex]x = 2;\ C(2) = 12 + 5* 2 =22[/tex]

..

[tex]x = 5;\ C(5) = 12 + 5* 5 =37[/tex]

For banner, we have:

[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]

C(x) is calculated as:

[tex]x = 1;\ C(1) = 8* 1 =8[/tex]

[tex]x = 2;\ C(2) = 8* 2 =16[/tex]

..

[tex]x = 5;\ C(5) = 8* 5 =40[/tex]

Solving (d): Graph of both using rapidtable

See attachment

Solving (e) Newspaper to use for 1 day

From the graph, when [tex]x = 1[/tex]

[tex]Free\ press = 17[/tex]

[tex]Banner = 8[/tex]

So, we use Banner newspaper because it is cheaper

Solving (f) Newspaper to use for 12 days

From the graph, when [tex]x = 12[/tex]

[tex]Free\ press = 72[/tex]

[tex]Banner = 96[/tex]

So, we use free press newspaper because it is cheaper

Answer:

[tex]3x + 6y = 12[/tex]

[tex]3x + 6y - 6y = 12 - 6y[/tex]

[tex]3x = 12 - 6y[/tex]

[tex] \frac{3x}{3} = \frac{12}{3} - \frac{6y}{3} [/tex]

[tex] \frac{3x}{3} = 1 = x[/tex]

[tex] \frac{12}{3} - \frac{6y}{3} [/tex]

[tex] = \frac{12 - 6y}{3} [/tex]

[tex] = \frac{6(2 - y)}{3} [/tex]

[tex] \frac{6}{3} = 2[/tex]

[tex] = 2( - y + 2)[/tex]

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

Answer:

x=2(3-y)

Step-by-step explanation:

3x+6y=12

x+2y=4

x=4-2y

=2(2-y)

9514 1404 393

Answer:

  -1/512

Step-by-step explanation:

The first term is -4, and the common ratio is -2/-4 = 1/2. Then the n-th term is ...

  an = -4·(1/2)^(n-1)

and the 12th term is ...

  a12 = -4(1/2)^(12 -1) = -4/2048

  a12 = -1/512