Briana has 1 red, 1 green, and 1 blue mechanical pencil in her
backpack. All of the pencils are the same size and shape. She
also has 1 red, 1 green, 1 blue, and 1 yellow eraser cap in the
backpack. All of the caps are the same size and shape. Briana
will randomly select 1 pencil and 1 cap. What is the probability
that she will select a pencil and a cap that are the same color?

Answer:

10

Step-by-step explanation:

Answer:

-10

Step-by-step explanation

By substituting -2 in for all the X's you have (-2)^2+2(-2)-10. After ths is simplified you have 4+(-4)-10. -4+4 =0 and 0-10= -10

Answer: add 4 on both sides

Step-by-step explanation:

Answer:

Isolate the constant

Step-by-step explanation:

i just took it on edge A

Answer:

Probability that at least 1 of those sampled have access to on-line services at home is 0.9648.

Step-by-step explanation:

We are given that current estimates suggest that 20% of people with home-based computers have access to on-line services.

Suppose that 15 people with home-based computers were randomly and independently sampled.

The above situation can be represented through binomial distribution;

[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 15 people

            r = number of success = at least one

            p = probability of success which in our question is % of people

                   who have access to on-line services at home, i.e.; p = 20%

Let X = Number of people who have access to on-line services at home

So, X ~ Binom(n = 15, p = 0.20)

Now, probability that at least 1 of those sampled have access to on-line services at home is given by = P(X [tex]\geq[/tex] 1)

           P(X [tex]\geq[/tex] 1) =  1 - P(X = 0)

                        =  [tex]1- \binom{15}{0}\times 0.20^{0} \times (1-0.20)^{15-0}[/tex]

                        =  [tex]1- (1\times 1 \times 0.80^{15})[/tex]

                        =  1 - 0.0352 = 0.9648

Hence, the required probability is 0.9648.

The following problem can be solved using the binomial distribution.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

There is 96.481% chance that at least 1 of those sampled have access to online services at home.

Substituting the values in a binomial distribution,

[tex]P(x\geq 1) = 1- P(0)[/tex]

[tex]P(x\geq 1) = 1-\ ^{15}C_0\times [0.20^0]\times [0.80^{(15-10)}]\\\\ P(x\geq 1)=1-\ 0.032\\\\ P(x\geq 1) = 0.96481\\\\ [/tex]

Hence, there is 96.481% chance that at least 1 of those sampled have access to online services at home.

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Answer:

B graph 2

Step-by-step explanation:

The future value of Michael's investment after 5 years is $44,038.01.

The future value of an annuity can be determined using the following formula:

[tex]FV=PV(1+r/n)^{n}[/tex]

FV = future value

PV = present value

r = annual interest rate

n = number of periods interest held

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 20 quarters (5 years x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $2,440.38

Total Interest = $440.38

Thus, the value of Michael's investment after 5 years is $2,440.38.

Answer:

The total number of ways of assignment is 314,790,828,599,338,321,972,833,000.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]

In this case we need to determine the number of ways in which the drugs are assigned to each mouse.

It is provided that new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes.

Drug A is to be given to 22 mice.

Compute the number of ways to assign drug A to 22 mice as follows:

[tex]{60\choose 22}=\frac{60!}{22!(60-22)!}\\\\=\frac{60!}{22!\times 38!}\\\\=14154280149473100[/tex]

Now the remaining number if mice are: 60 - 22 = 38.

Compute the number of ways to assign drug B to 22 mice as follows:

[tex]{38\choose 22}=\frac{38!}{38!(38-22)!}\\\\=\frac{38!}{22!\times 16!}\\\\=22239974430[/tex]

Now the remaining number if mice are: 38 - 22 = 16.

Compute the number of ways to assign no drug to 16 mice as follows:

[tex]{16\choose 16}=\frac{16!}{16!(16-16)!}\\\\=1[/tex]

The total number of ways of assignment is:

[tex]N = {60\choose 22}\times {38\choose 22}\times {16\choose 16}\\\\=14154280149473100\times 22239974430\times 1\\\\=314,790,828,599,338,321,972,833,000[/tex]

Thus, the total number of ways of assignment is 314,790,828,599,338,321,972,833,000.

Final answer:

The number of ways to assign treatments to the mice can be found using combinations. The calculation involves selecting a certain number of mice from the total pool and dividing it by the number of ways to arrange those mice within the group. The total number of ways to assign treatments to the mice is approximately 10,682,514,784,300.

Explanation:

When assigning treatments to the mice, we have 22 mice for drug A, 22 mice for drug B, and 16 mice for the control group. The assignment of treatments can be thought of as distributing the mice among these three groups.

To find the number of ways this can be done, we can use the concept of combinations. We can think of selecting 22 mice for drug A from the total pool of 60 mice, and then selecting 22 mice for drug B from the remaining pool. The remaining 16 mice automatically go to the control group.

The number of ways to select 22 mice out of 60 is denoted as C(60,22) and is calculated using the formula C(n, r) = n! / (r!(n-r)!). Therefore, the number of ways to assign treatments to the mice is C(60,22) multiplied by the number of ways to assign the remaining 22 mice to drug B, which is C(38,22).

Using a calculator or software, we can calculate C(60,22) as approximately 95,023,780 and C(38,22) as approximately 112,385.

Therefore, the total number of ways to assign treatments to the mice is approximately 95,023,780 * 112,385 = 10,682,514,784,300.

Answer:

800

Step-by-step explanation:

1.35x = 1080 -->

x = 1080/1.35 -->

800

Answer:

18 inches

OQ2 + PQ2 = OP2

PQ2 = OP2 - OQ2

= (OR + PR) SQUARE - OQ2

= (24/2 + 10 ) SQUARE - 24/12Square

= 22square - 12square

PQ = Root 340

= 18 inches...

The answer is 18 inches.

OQ2 + PQ2 = OP2

PQ2 = OP2 - OQ2

= (OR + PR) SQUARE - OQ2

= (24/2 + 10 ) SQUARE - 24/12Square

= 22² - 12²

PQ = √ 340

= 18 inches.

Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.

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Answer:

8

Step-by-step explanation:

0.2:2.5*100 =

( 0.2*100):2.5 =

20:2.5 = 8

Answer:

Callie's comparison of two options for college education

The true statement is:

She would save $11,300 by choosing option A.

Step-by-step explanation:

Cost Analyses:

Option A:            Community College  + University               Total Expenses

Tuition & Fees    $5,800 ($2,900 x 2) + $19,000 ($9,500 x 2)    = $24,800

Scholarships       ($1,600) ($800 x 2)   + ($20,000) ($10,000 x 2)=($21,600)

Room & Board    $2,500 ($1,250 x 2)  + $23,000 ($11,500 x 2) =   $25,500

Work-Study                                            + ($4,000)  ($2,000 x 2)  = ($4,000)

Total Cost           $6,700                       + $18,000      =                    $24,700

Option B:            4 years' University

Tuition & Fees    $38,000 ($9,500 x 4)

Scholarships       ($40,000) ($10,000 x 4)

Room & Board    $46,000 ($11,500 x 4)

Work-Study         ($8,000)  ($2,000 x 4)

Total Cost          $36,000

Difference between the two options = $11,300 ($36,000 - $24,700

Answer: She would save $11,300 by choosing option A

Step-by-step explanation:

Community College Financial Analysis:

Tuition and fees = 2900

Scholarship and grant = 800

Rooms and board = 1250

University Financial Analysis:

Tuition and fees = 9500

Scholarship and grant = 10000

Rooms and board = 11500

Work study - 2000

Option A :

First two years at college :2 × (2900 + 1250 - 800)

2 × (3350) = $6700

2 years at university : 2 × (9500 +11500 - 2000 - 10000)

2 × 9000 = 18000

Option A total = $(18,000 + 6700) = $24,700

Option B :

4 years at university : 4 × (9500 +11500 - 2000 - 10000)

4 × 9000 = $ 36000

She would be saving $(36,000 - 24,700) = $11,300 by choosing option A

Answer:

a3 = 45

Step-by-step explanation:

a1 = 20

an = a(n-1) *3/2  where n is the term number

a2 = a(2-1) *3/2

     a1 *3/2

We know a1 = 20

a2 = 20*3/2 = 30

a3 = a(3-1) *3/2

    = a2 *3/2

We know a2 = 30

    = 30*3/2 = 45

Answer: 4.067units.

Step-by-step explanation:

(a) The highlighted arc is the major arc. That is , it covers from G to I.

(b) The length of the major arc will be

πr0°/180 where the angle substended at the center by the highlighted arc is

360° - 127° ( the angles if the arc not highlighted)

= 233°

Though this radius of the circle was not given so we are going to find the arc length without necessarily defining the radius.

Arc length = π × r × 233°

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

180

= 3.142 × r × 233°

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

180

= 4.067runits.

The arc that is highlighted is the major arc

The measure of the highlighted arc is 4.067runits.

The formula for the length of major arc

πr0°/180

Without highlioghts the angles are

360° - 127°

= 233 degrees

Formula for lenght of arc Arc length = π × r × 233° / 180

= = 3.142 × r × 233° / 180

= 4.067runits.

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Answer:

  5.7 meters

Step-by-step explanation:

The Pythagorean theorem can be used to find the second leg (b) of a triangle with diagonal (c) 6 meters and first leg (a) 2 meters.

  c^2 = a^2 + b^2

  6^2 = 2^2 +b^2

  b^2 = 36 -4 = 32

  b = √32 ≈ 5.7 . . . . meters

The kitchen is about 5.7 meters long.

The length of the kitchen, where a mouse has made holes in opposite corners with a diagonal distance of 6 meters across a width of 2 meters, is approximately 5.7 meters.

To find the length of the kitchen where a mouse has made holes in opposite corners, forming a diagonal of 6 meters across a width of 2 meters, we can use the Pythagorean theorem.

1. Understanding the problem:

  - The width of the kitchen (distance between the holes along one side) is w = 2 meters.

  - The diagonal distance (distance between the holes) is d = 6 meters.

2. Applying the Pythagorean theorem:

  - In a rectangle, the diagonal d , the width w, and the length l form a right triangle.

  - The Pythagorean theorem states [tex]\( d^2 = w^2 + l^2 \)[/tex].

3. Substitute the given values:

  [tex]\[ 6^2 = 2^2 + l^2 \][/tex]

  [tex]\[ 36 = 4 + l^2 \][/tex]

4. Solve for [tex]\( l^2 \)[/tex] :

  [tex]\[ l^2 = 36 - 4 \][/tex]

  [tex]\[ l^2 = 32 \][/tex]

5. Find l (length of the kitchen):

  [tex]\[ l = \sqrt{32} \][/tex]

  [tex]\[ l \approx 5.7 \text{ meters (rounded to the nearest tenth)} \][/tex]

Therefore, the length of the kitchen is approximately [tex]\( \boxed{5.7} \)[/tex]meters.

The length of the kitchen, rounded to the nearest tenth, where a mouse has made holes in opposite corners with a diagonal distance of 6 meters across a width of 2 meters, is [tex]\( \boxed{5.7} \)[/tex] meters. This solution utilizes the Pythagorean theorem to determine the missing dimension of the rectangle based on given measurements.

Question:

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.44 . Complete parts​ (a) through​ (c) below.

​(a) Describe the sampling distribution of ModifyingAbove p with caret.

A.)Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002

B.)Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005

C.)Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157

​(b) What is the probability of obtaining xequals480 or more individuals with the​ characteristic?

​P(xgreater than or equals480​)equals

nothing ​(Round to four decimal places as​ needed.)

​(c) What is the probability of obtaining xequals410 or fewer individuals with the​ characteristic?

​P(xless than or equals410​)equals

nothing ​(Round to four decimal places as​ needed.)

Answer:

a) Option C.

b) 0.1021

c) 0.0280

Step-by-step explanation:

Given:

Sample size, n = 1000

p' = 0.44

a) up' = p' = 0.44

The sampling distribution will be:

[tex] \sigma _p' = \sqrt{\frac{p' (1 - p')}{n}}[/tex]

[tex] = \sqrt{\frac{0.44 (1 - 0.44)}{1000}}[/tex]

[tex] = \sqrt{\frac{0.44*0.56}{1000}} = 0.0157 [/tex]

Option C is correct.

b) The probability when x ≥ 460

[tex] P' = \frac{x}{n} = \frac{460}{1000} = 0.46[/tex]

p'(P ≥ 0.46)

[tex] 1 - P = \frac{(p' - up')}{\sigma _p'} < \frac{0.46 - 0.44}{0.0157} [/tex]

[tex] = 1-P( Z < 1.27) [/tex]

From the normal distribution table

NORMSDIST(1.27) = 0.898

1-0.8979 = 0.1021

Therefore, the probability = 0.102

c) x ≤ 410

[tex] P' = \frac{x}{n} = \frac{410}{1000} = 0.41[/tex]

p'(P ≤ 0.41)

[tex] P = \frac{(p' - up')}{\sigma _p'} < \frac{0.41 - 0.44}{0.0157} [/tex]

[tex] = P( Z < - 1.9108) [/tex]

From the normal distribution table

NORMSDIST(-1.9108) = 0.0280

Probability = 0.0280

Answer:

He has to save his clients $75,000.

Step-by-step explanation:

$2,000 per month is 2*2,000 = $24,000

He eanrs a fixed rate of $18,000 per year. So in bonuses, he has to earn 24,000 - 18,000 = $6,000.

His bonuses are 8% of the money he saves his clients.

So this 8% must be $6,000. How much his 100%?

0.08 - $6,000

1 - $x

[tex]0.08x = 6000[/tex]

[tex]x = \frac{6000}{0.08}[/tex]

[tex]x = 75000[/tex]

He has to save his clients $75,000.

Answer:

x= -7    x=3

Step-by-step explanation:

(x-2)(x+5)=18

FOIL

x^2 +5x -2x-10 = 18

Subtract 18 from each side

x^2 +5x -2x-10-18 = 18-18

x^2 +3x -28 =0

Factor

What 2 numbers multiply to -28 and add to 3

7*-4 = -28

7-4 =3

(x+7) (x-3) =0

Using the zero product property

x+7 =0    x-3 =0

x= -7    x=3

Answer:D

Step-by-step explanation:

Answer:

The growth rates at t = 0 is 8⁵.

The growth rates at t = 4 is 0.

The growth rates at t = 8 is -8⁵.

Step-by-step explanation:

The expression representing the size of the population at time t​ hours is:

[tex]b(t)=8^{6}+8^{5}t-8^{4}t^{2}[/tex]

Differentiate b (t) with respect to t to determine the growth rate as follows:

[tex]\frac{db(t)}{dt}=\frac{d}{dt} (8^{6}+8^{5}t-8^{4}t^{2})[/tex]

       [tex]=0+8^{5} (1)-8^{4}(2t)\\=8^{4}(8-2t)[/tex]

The growth rate is:

R (t) = 8⁴ (8 - 2t)

Compute the growth rates at t = 0 as follows:

[tex]R (0) = 8^{4} (8 - 2\times 0)\\=8^{4}\times 8\\=8^{5}[/tex]

Thus, the growth rates at t = 0 is 8⁵.

Compute the growth rates at t = 4 as follows:

[tex]R (4) = 8^{4} (8 - 2\times 4)\\=8^{4}\times 0\\=0[/tex]

Thus, the growth rates at t = 4 is 0.

Compute the growth rates at t = 8 as follows:

[tex]R (4) = 8^{4} (8 - 2\times 8)\\=8^{4}\times (-8)\\=-8^{5}[/tex]

Thus, the growth rates at t = 8 is -8⁵.

The growth rates at t=0 hours, t=4 hours, and t=8 hours can be calculated using the given equation.

When a bactericide is added to a nutrient broth in which bacteria are​ growing, the bacterium Population Growth in Bacteria continues to grow for a​ while, but then stops growing and begins to decline.

The size of the population at time t​ (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2.

Find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.t=8 hours.

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The probable question may be:

When a bactericide is added to a nutrient broth in which bacteria are​ growing, the bacterium population continues to grow for a​ while, but then stops growing and begins to decline. The size of the population at time t​ (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2. Find the growth rates when

t equals 0 hours commat=0 hours,

t equals 4 hours commat=4 hours,

t equals 8 hours.t=8 hours.

Answer:1

Step-by-step explanation:

(x+2)(x+3)

x^2+3x+2x+6

x^2+5x+6

Therefore the coefficient of x^2 is 1

Answer:

1

Step-by-step explanation:

(x+2) (x+3)

FOIL

x^2 + 3x+2x+6

x^2 +5x+6

The coefficient of x^2 is 1

Answer: jon & jim painted 8/12 of the fence

Step-by-step explanation: first, convert. one quarter is equal to 1/4, & 1/4 of 12 (since Jim painted 5/12) is 3/12. now we know that Jon painted 3/12 of the fence & that Jim painted 5/12 of the fence (we already knew this, didn't we?). all you have to do now is add: 3/12 + 5/12 = 8/12. so, jon & jim painted 8/12 of the fence.

- hope this helps

:)

Jon and Jim painted a total of two thirds of the fence together. We found this by converting 1/4 to 3/12 and then adding it to 5/12, which gave us 8/12, or 2/3.

The question involves understanding the addition of fractions. Jon painted a quarter of the fence which is equal to 1/4 and Jim painted five twelfths of the fence which is equal to 5/12.

To find out how much of the fence they painted together, we simply add these fractions. The lowest common multiple of 4 and 12 is 12. So, we convert 1/4 to 3/12 to make the denominators the same. Now, we have 3/12 (Jon's part) and 5/12 (Jim's part). The total part of the fence they painted together is 3/12 + 5/12 = 8/12 = 2/3.

So, Jon and Jim painted two thirds of the fence together.

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Answer:

3.3

Step-by-step explanation:

[tex] = > \frac{4 \frac{2}{5} }{1 \frac{1}{3} } \\ \\ = > \frac{ \frac{20 + 2}{5} }{ \frac{3 + 1}{3} } \\ \\ = > \frac{ \frac{22}{5} }{ \frac{4}{3} } \\ \\ = > \frac{22}{5} \times \frac{3}{4} \\ \\ = > \frac{11}{5} \times \frac{3}{2} \\ \\ = > \frac{33}{10} \\ \\ = > 3.3[/tex]

Answer:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ... No; The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ANSWER: No; 9.

Answer:

1728 cubic in

Step-by-step explanation:

24 in x 8 in x 9 in = 1728 cubic in

Final answer:

The volume of water in Sam's aquarium is 1,728 cubic inches, calculated by multiplying the length (24 inches), width (8 inches), and height (9 inches) of the aquarium.

Explanation:

The volume of Sam's aquarium can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. The dimensions given are 24 inches long, 8 inches wide, and 9 inches tall.

To find out how many cubic inches of water the aquarium can hold, we multiply these dimensions:

× 24 inches (length)
× 8 inches (width)
× 9 inches (height)

Thus, the volume of the aquarium is:

24 inches × 8 inches × 9 inches = 1,728 cubic inches

Answer: Carl paid $25.98 for this DVD in dollars and cents.

Step-by-step explanation:

The original cost of the DVD was $24.00. If a sales tax of 8.25% was charged, it means that the original cost of the DVD would increase by 8.25%.

The value in dollar and cents of an 8.25% increment(sales tax) would be

8.25/100 × 24 = 0.0825 × 24

= $1.98

Therefore, the amount that Carl would pay for this DVD in dollars and cents is

24 + 1.98 = $25.98

Answer:it’s ACD=ECB

Step-by-step explanation:

The correct option is Segment Addition Postulate.

Similarity of triangles. The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Here, we have,

The segment addition postulate states that where there are two points on a line A and C and a third point B can only be located on the line segment AB if and only if the the distances between point A and point B as well as the distance between point B and point C satisfy the equation AB + BC = AC

Therefore, given that in the figure,  the point B is in between point A and point C on segment AC then AB + BC

Similarly, AD = AE + ED.

The correct option is Segment Addition Postulate.

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complete question:

BE || CD 1. Given 2. ∠A ≅ ∠A 2. Reflexive Property 3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅. 4. ∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅. 5. ΔABE ∼ ΔACD 5. AA Similarity Postulate 6. AC AB = AD AE 6. Definition of Similar Triangles 7. AC = AB + BC, AD = AE + ED 7. ??? 8. AB + BC AB = AE + ED AE 8. Substitution 9. AB AB + BC AB = AE AE + ED AE 9. Addition 10. BC AB = ED AE 10. Subtraction Fill in the missing reason for the proof. A) Transitive Property B) Subtraction Property C) SSS Similarity Theorem D) Segment Addition Postulate

Answer:

Sarah spent $15.75 at the movies on a ticket and snacks.

She earned $40 babysitting.

She bought a book for $9.50.

She has $34.75 left.

=> The amount of money she started with:

A = 34.75 + 9.5 - 40 + 15.75 = 20$

Hope this helps!

:)

Answer:

95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].

Step-by-step explanation:

We are given that the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16.

They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                      P.Q. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average half-life = 7.4 hours

            [tex]\sigma[/tex] = population standard deviation = [tex]\sqrt{0.16}[/tex] = 0.4 hour

            n = sample of people = 50

            [tex]\mu[/tex] = population mean

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                     of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] <

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                            = [ [tex]7.4-1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] , [tex]7.4+1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] ]

                                            = [7.29 , 7.51]

Therefore, 95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].

The length of this interval is = 7.51 - 7.29 = 0.22

Answer:

A

Step-by-step explanation:

We know that each machine makes x fixtures and we have 5 machines. So we need to use multiplication:

5 * x = 5x

The above expression indicates how many fixtures the 5 machines can make. We want the total to be more than 20, so we need to use the greater than sign: >.

5x > 20

The answer is A.

Answer:

A. 5x > 20

Step-by-step explanation:

Total production by 5 machines: 5x

5x > 20