eight times the sum of 5 and some number is 104. What is the number

You just put the expression in a calculator! We have

[tex]\dfrac{7}{2^6} = \dfrac{7}{64}=0.109375[/tex]

Answer:

For any value of x

Step-by-step explanation:

Solve by using system of equations!

3x+12

3(x+4)=3x+12

3x+12=3x+12

x=x

This means that any value of x would create the same answer for both equations.

Answer:

Always.

Step-by-step explanation:

Always.  This is true by distributive property.

Answer: 0.8186

Step-by-step explanation:

Given: Mean : [tex]\mu=1.01\text{ inch}[/tex]

Standard deviation :  [tex]\sigma=0.003\text{ inch}[/tex]

Sample size :  [tex]n=9[/tex]

The formula to calculate z-score :-

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

For x=1.009 inch

[tex]z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1[/tex]

For x=1.012 inch

[tex]z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2[/tex]

Now, The p-value =[tex]P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186[/tex]

Hence, the required probability = 0.8186

Answer: The first number is 2000 times greater than second number.

Step-by-step explanation:

Let the first number be 'x' and second number be 'y'

We are given:

x = [tex]8\times 10^{-3}[/tex]

y = [tex]4\times 10^{-6}[/tex]

To calculate the times, number 'x' is greater than number 'y', we divide the two numbers:

[tex]\frac{x}{y}=\frac{8\times 10^{-3}}{4\times 10^{-6}}\\\\\frac{x}{y}=2\times 10^3\\\\x=2000y[/tex]

Hence, the first number is 2000 times greater than second number.

The number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times grater than the number [tex]4\times 10^{-6}[/tex].

Given information:

The number [tex]8 \times 10^{-3}[/tex]

And number [tex]4\times 10^{-6}[/tex]

Now , consider the first number as [tex]x[/tex] and number second as [tex]y[/tex].

So, according to the information given in the question we can write as:

[tex]\frac{x}{y} =\frac{8\times 10^{-3}}{4\times 10^{-6}}[/tex]

[tex]\frac{x}{y} = 2\times 10^3\\x=2000y[/tex]

Hence, We can conclude that the number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times the number [tex]4\times 10^{-6}[/tex].

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Answer:

Step-by-step explanation:

n^2 is less than 2^n for n < 2 and for n > 4. The smallest size of n that is of interest is n=1. For that, n^2 = 1^1 = 1.

The n^2 algorithm will outperform the 2^n algorithm for n = 1. That problem size will take 1 day to solve.

_____

Please note that there are no algebraic methods for solving an inequality of the form x^2 < 2^x. We have solved it using a graphing calculator.

Final answer:

The smallest instance size where the n² days algorithm outperforms the 2n seconds algorithm is n=43200. However, it's not practical, as this size leads to a computation time of approximately 1.86496 × 10⁹ days for the first algorithm, showing that for any realistic value of n, the second algorithm is more efficient.

Explanation:

The student's question is about the comparison of the performance of two different algorithms. Specifically, the question asks at what size the algorithm, which takes n² days to solve an instance of size n, will outperform the 2n seconds algorithm.

To determine the smallest instance size at which the first algorithm outperforms the second, we must set the two times equal and solve for n. Let's denote the time taken by the first algorithm as T1 and the second algorithm as T2, where T1 = n² days and T2 = 2n seconds. We should convert both times to a common unit, which typically is seconds, as follows:

1 day = 24 hours = 86400 seconds

T1 in seconds: n²  times 86400 seconds/day

T2 is already in seconds: 2n seconds

Now equate the two to find the smallest n:

n²  times 86400 = 2n

n²  times 86400 / 2 = n

n = 86400 / 2 = 43200

Thus, the smallest instance size n is 43200. To find how long this instance takes to solve by the first algorithm:

T1 = 43200² days

T1 ≈ 1.86496 × 109 days

This is impractically large, indicating that for any realistic value of n, the second algorithm is more efficient.

Answer: (a)  [tex]\dfrac{1}{7}[/tex]    (b)  [tex]\dfrac{12}{35}[/tex]

Step-by-step explanation:

Given: Number of white balls : 6

Number of red balls = 9

Total balls = 15

(a)  The probability that both balls are white is given by :-

[tex]\dfrac{^6C_2}{^{15}{C_2}}\\\\=\dfrac{\dfrac{6!}{2!(6-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{1}{7}[/tex]

∴ The probability that both balls are white is  [tex]\dfrac{1}{7}[/tex] .

(b)  The probability that both balls are red is given by :-

[tex]\dfrac{^9C_2}{^{15}C_2}\\\\=\dfrac{\dfrac{9!}{2!(9-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{12}{35}[/tex]

∴ The probability that both balls are red is [tex]\dfrac{12}{35}[/tex] .

Answer:

We need to find how many number of equivalence relations are on the set {1,2,3}

A relation is an equivalence relation if it is reflexive, transitive and symmetric.

equivalence relation R on {1,2,3}

1.For reflexive, it must contain (1,1),(2,2),(3,3)

2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R

3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R

Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,

we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.

This is because if (1,2) is in the relation then (2,1) must be there in the relation.

the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}

we can have three possible equivalence relations:

{(1,1),(2,2),(3,3),(1,2),(2,1)}

{(1,1),(2,2),(3,3),(1,3),(3,1)}

{(1,1),(2,2),(3,3),(2,3),(3,2)}

Equivalence relations on a set satisfy conditions of reflexivity, symmetry, and transitivity. The Bell number counts the number of partitions, or equivalence relations, on a set. Hence, for the set {1, 2, 3}, there are five equivalence relations.

The subject of this question relates to equivalence relations on a set which is an important topic in discrete mathematics and set theory. In simple terms, an equivalence relation is a relation on a set that equates certain pair of elements. In your set {1, 2, 3}, an equivalence relation must meet three conditions: reflexivity (each number is equal to itself), symmetry (if 1 is related to 2, then 2 is related to 1), and transitivity (if 1 is related to 2 and 2 is related to 3, then 1 is related to 3).

To find the number of equivalence relations on a set, we refer to the Bell number. Bell numbers count the number of partitions of a set. For a set with 3 elements like yours, the third Bell number gives the number of equivalence relations, which is 5. Therefore, there are 5 equivalence relations on the set {1, 2, 3}.

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Answer:

  28 mi

Step-by-step explanation:

The cars are separating at the rate of 52 mi/h - 45 mi/h = 7 mi/h. Then after 4 hours, their separation distance will be ...

  (7 mi/h)(4 h) = 28 mi

The two cars will be 28 miles apart after 4 hours.

To find the distance between the two cars after 4 hours, we need to calculate the distance traveled by each car. The formula to find distance is speed multiplied by time. The first car travels at an average speed of 45 mph for 4 hours, so its distance traveled is 45 mph * 4 hours = 180 miles.

The second car travels at an average speed of 52 mph for 4 hours, so its distance traveled is 52 mph * 4 hours = 208 miles. Therefore, the two cars will be 208 miles - 180 miles = 28 miles apart after 4 hours.

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Answer: 0.9032

Step-by-step explanation:

Given: Mean : [tex]\mu = 20,000\text{ hours}[/tex]

Standard deviation : [tex]\sigma = 1800 \text{ hours}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 17659

[tex]z=\dfrac{17659-20000}{1800}=−1.30055555556\approx-1.3[/tex]

The P Value =[tex]P(z>-1.5)=1-P(z<1.3)=1- 0.0968005\approx0.9031995\approx 0.9032[/tex]

Hence, the probability that the life span of the monitor will be more than 17,659 hours = 0.9032

To find the probability that the life span of the monitor will be more than 17,659 hours, use the z-score formula and the standard normal distribution table. The probability is approximately 0.0968.

To find the probability that the life span of the monitor will be more than 17,659 hours, we need to calculate the z-score and use the standard normal distribution table. The z-score is calculated as:

z = (x - μ) / σ

Where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = 17,659, μ = 20,000, and σ = 1800. Plugging these values into the formula, we get:

z = (17659 - 20000) / 1800 = -1.3

Now, we can look up the probability corresponding to the z-score -1.3 in the standard normal distribution table. The probability is approximately 0.0968. Therefore, the probability that the life span of the monitor will be more than 17,659 hours is approximately 0.0968.

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Answer:

Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)

Step-by-step explanation:

Given:

Weights of Broilers are normally distributed.

Mean = 1387 g

Standard Deviation = 161 g

To find: Probability that a randomly selected broiler weighs more than 1454 g.

we have ,

[tex]Mean,\,\mu=1387[/tex]

[tex]Standard\,deviation,\,\sigma=161[/tex]

X = 1454

We use z-score to find this probability.

we know that

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

[tex]z=\frac{1454-1387}{161}=0.416=0.42[/tex]

P( z = 0.42 ) = 0.6628   (from z-score table)

Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 =  0.3372

Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)

Answer:

Part a) The amount of hardwood floor is [tex]480\ ft^{2}[/tex]

Part b) The amount of trim to buy is [tex]78\ ft[/tex]

Part c) The amount of paintable space is [tex]1,297\ ft^{2}[/tex]

Part d) The amount of paint needed is [tex]7.41\ gallons[/tex]

Step-by-step explanation:

Part a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?

Find the area of the floor

[tex]A=(10+5+3)(10+5+10)+(2+6+2)(3)[/tex]

[tex]A=(18)(25)+(10)(3)[/tex]    

[tex]A=480\ ft^{2}[/tex]

Part b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?  

step 1

Find the perimeter of the  master bedroom

[tex]P=2(25)+2(18)+2(3)[/tex]

[tex]P=50+36+6[/tex]

[tex]P=92\ ft[/tex]

step 2

Subtract the front of the french doors, sliding doors and hallway from the perimeter

[tex]92-(5+6+3)=78\ ft[/tex]

Part c) You want to paint your new bedroom. How much paintable space is there in the room?

step 1

Find the area of the ceiling

we know that

The area of the floor is equal to the area of the ceiling

so

The area of the ceiling is equal to [tex]A=480\ ft^{2}[/tex]

step 2

Find the area of the walls

Multiply the perimeter by the height

[tex]92*10=920\ ft^{2}[/tex]  

step 3

Subtract 73 square feet of surface that does not get painted (windows and sliding doors ) and the area of the hallway

The amount of paintable space is equal to

[tex]A=480+920-73-3(10)=1,297\ ft^{2}[/tex]

Part d) How many gallons of paint would you need to buy?

we know that

One gallon of paint covers 350 square feet

Multiply the area by two (because You want to put on two coats of paint on every paintable surface)

so

[tex]1,297*(2)=2,594\ ft^{2}[/tex]

using proportion

[tex]1/350=x/2,594[/tex]

[tex]x=2,594/350[/tex]

[tex]x=7.41\ gallons[/tex]

Answer:

The correct answer option is C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex].

Step-by-step explanation:

We are given that two line segments AB and CD are formed from the points A ([tex](x_1, y_1)[/tex], B ([tex](x_2, y_2)[/tex], C ([tex](x_3, y_3)[/tex] and D ([tex](x_4, y_4)[/tex].

We are to determine which condition needs to be met in order to prove that AB is perpendicular to CD.

When slopes of two perpendicular lines are multiplied, they give a product of -1.

Hence option C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex] is the correct answer.

Answer: 0.0668

Step-by-step explanation:

Given: Mean : [tex]\mu = 5\text{ minutes}[/tex]

Standard deviation : [tex]\sigma = 2\text{ minutes}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

To check the probability it takes at least 8 minutes (X≥ 8) to find a parking space.

Put X= 8 minutes

[tex]z=\dfrac{8-5}{2}=1.5[/tex]

The P Value =[tex]P(z\geq1.5)=1-P(z\leq1.5)=1- 0.9331927=0.0668073\approx0.0668[/tex]

Hence, the probability that it takes at least 8 minutes to find a parking space = 0.0668

The probability that it takes atleast 8 minutes to find a parking space is 0.0668

Given the Parameters :

First we find the Zscore :

Zscore = (8 - 5) / 2 = 1.5

The probability of taking atleast 8 minutes can be expressed thus and calculated using the normal distribution table :

P(Z ≥ 1.5) = 1 - P(Z ≤ 1.5)

P(Z ≥ 1.5) = 1 - 0.9332

P(Z ≥ 1.5) = 0.0668

Therefore, the probability, P(Z ≥ 1.5) is 0.0668

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Answer:

It diverges to positive infinity  

Step-by-step explanation:

I see it was 4/(x-6)^3 not 4(x-6)^3... but still can't make out everything else.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

The integrand does not exist at x=6.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} } \int_z^8 4(x-6)^{-3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }\frac{4(x-6)^{-2}}{-2} |_z^8dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }[\frac{4(8-6)^{-2}}{-2} -\frac{4(z-6)^{-2}}{-2} ] [/tex]

[tex] \frac{1}{-2} - -\infty [/tex]

[tex] \infty [/tex]

So it diverges

Answer:

I could not properly read this but here was what I could make out

Step-by-step explanation:

Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)

home this helped ;)

Answer:

The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]

Step-by-step explanation:

Let

x----> amount in sales this month

we know that

[tex]7\%=7/100=0.07[/tex]

The inequality that represent this situation is equal to

[tex]2,500+0.07x\geq2,900[/tex]

Solve for x

Subtract 2,500 both sides

[tex]0.07x\geq2,900-2,500[/tex]

[tex]0.07x\geq400[/tex]

Divide by 0.07 both sides

[tex]x\geq400/0.07[/tex]

[tex]x\geq \$5,714.29[/tex]

therefore

The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]

Step-by-step explanation:

The square root of 17 is 4.12. Minus one equals 3.12

The square root of 5 is 2.23.

pi+7 equals 10.142. Divided by five equals around 2.

so you end up with, 3.12, 2.23, and 2.1

Answer:

Graph A

Basically a graph of a function will have no turns if linear, 1 turn if quadratic, 2 turns if cubic, and 3 terms if quartic.

Graph A has a small turn on its right side.

Step-by-step explanation:

I love the way this other guy explained it, basically you count the turns that it says. i.e quartic = 4, so 4 turns, so A in this case

This was so confusing and I've been learning it for over a week and never understood it but literally took me 2 seconds to read his answer and understand it perfectly

Step-by-step explanation:

Well it is simple.If he was able to solve 400 problems in just 25 ' then how long would it take him to solve 100(1/4 of 400)?It would take him 6.25' to solve 100 problems(1/4 of 25).So if he had to do another 500 (because 1000 -500=500) it would take him 31.25' (5*6.25) to complete them.If you have any further questions please contact me.

Yours sincerely,

Manos

Answer:

the number to be expected is 1,000

Step-by-step explanation:

you multiply 100,000 by 1% which give you 1,000

Answer:   1000

Step-by-step explanation:

Given : The proportion of the defective widgets manufactured by XYZ corp= 1%

= 0.01   [we divide a percent by 100 to convert it into decimal to perform further calculations]

If the total number of widgets manufactured by XYZ = 100000

Then, the number of defective widgets is expected to be

(proportion of defective widgets) x (number of widgets manufactured by XYZ)

= 0.01 x 100000

= 1000

Hence, the number of defective widgets is expected to be 1000 .

The total tax comes to $5,173.50, with a monthly withholding of approximately $431.13.

To calculate Mr. Profit's federal income tax based on a taxable income of $35,000 in 2007, we need to find the correct tax bracket and perform a series of calculations:

Therefore, Mr. Profit's federal income tax for 2007 would be $5,173.50, and his monthly withholding would be approximately $431.13.

Mr. Profit's earned income level is $35,000. The base tax is $4,386, with an additional tax of $787.50 for amounts over $31,850. Monthly withholding comes to approximately $431.13.

To calculate Mr. Profit's tax liability based on his taxable income, we need to identify which tax bracket his income falls into and then compute the tax accordingly.

Given that Mr. Profit has a taxable income of $35,000, he falls into the 25% tax bracket, where the taxable income is over $31,850 but not over $77,100.

The tax table for this bracket is:

Base tax for incomes from $7,825 to $31,850: $788

The marginal tax rate for income over $31,850: 25%

Let's compute the tax following the provided steps.

Earned Income Level

Mr. Profit's earned income level is his taxable income:

Earned Income Level = $35,000

Base Amount

The base tax amount for his tax bracket:

Base Amount = $4,386

Amount Over

The amount over the lower bound of his tax bracket:

Amount Over = $35,000 - $31,850 = $3,150

Multiply by Percentage

Multiply the amount over by the tax rate for his bracket (25%):

Multiply Line 3 by 25% = $3,150 \times 0.25 = $787.50

Add Base and Multiplication Result

Add the base amount and the calculated tax from step 4:

Add Lines 2 and 4 = $4,386 + $787.50 = $5,173.50

Compute Monthly Withholding

Given that there are 12 months in a year, compute the monthly withholding:

Compute monthly withholding [tex]= $5,173.50 \div 12 \approx $431.13[/tex]

Thus, rounding to two decimal places, we have :

Earned Income Level: $35,000

Base Amount: $4,386

Amount Over: $3,150

Multiply Line 3 by Percentage: $787.50

Add Lines 2 and 4: $5,173.50

Compute monthly withholding: $431.13

The complete question is : 2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Mr. Profit had a taxable income of $35,000. He figured his tax from the table above. 1. Find his earned income level. 2. Enter the base amount. = $ 3. Find the amount over $ = $ 4. Multiply line 3 by % = $ 5. Add Lines 2 and 4 = $ 6. Compute his monthly withholding would be = $

Answer:

a.   Single-sample Z-Test

b.   Single-sample t-test

c.   Independent-measures t-test

d.   Repeated-measures t-test (Paired-samples t-test)

e.   Independent-measures ANOVA

Answer: 0.0668

Step-by-step explanation:

Given: Mean : [tex]\mu=\text{4 min. 3 sec.=4.05 minutes}[/tex]

Standard deviation : [tex]\sigma = \text{2 seconds=0.033333 minutes }[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 4 minutes  , we have

[tex]z=\dfrac{4-4.05}{0.03333}\approx-1.5[/tex]

The P-value = [tex]P(z\leq-1.5)=0.0668072\approx0.0668[/tex]

Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668

The probability that on a given run, the time will be 4 minutes or less is approximately 6.68%.

To find the probability that on a given run, the time will be 4 minutes or less, we need to calculate the z-score for 4 minutes and then use the standard normal distribution table to find the probability. The z-score can be calculated using the formula (x - mean) / standard deviation. In this case, the z-score is (4 - 4.05) / 0.0333333⋯ = -1.50. Looking up the z-score in the standard normal distribution table, we find that the probability is approximately 0.0668 or 6.68%.

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Answer:

  sales are increasing at the rate of 6000 units per week

Step-by-step explanation:

Your demand equation appears to be ...

  4p³ +x² =38400

Then differentiation gives ...

  12p²·p' +2x·x' = 0

Solving for x', we get ...

  x' = -6p²·p'/x

Filling in the given values, we find the rate of change of sales to be ...

  x' = -6(20²)(-0.20/wk)/80 = 6/wk . . . . . in thousands of units/wk

Sales are increasing at the rate of 6000 units per week.

[tex]|\Omega|={_{16}C_5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{120}=4368\\|A|={_{12}C_5}=\dfrac{12!}{5!7!}=\dfrac{8\cdot9\cdot10\cdot11\cdot12}{120}=792\\\\P(A)=\dfrac{792}{4368}=\dfrac{33}{182}\approx18\%[/tex]

The probability of the event is defined as the ratio of the number of cases favourable to an occurrence, and the further calculation can be defined as follows:

4 of the 16 modems are defective, while the remaining 12 are not.

P(accepting shipment) = P (all 5 modems work)

[tex]\bold{^{12}C_{5}}[/tex] methods could be used to choose 5 non-defective modems from a pool of 12 non-defective modems.

[tex]\to \bold{^{12}C_{5} = \frac{12!}{ (12 -5)! \times 5! }}[/tex]

             [tex]\bold{ = \frac{12!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}}\\\\\bold{ =11 \times 9 \times 8}\\\\\bold{=792}[/tex]

The total number of methods to choose 5 modems from a pool of 16 modems is [tex]\bold{^{16}C_{5}}[/tex].

[tex]\to \bold{^{16}C_{5} = \frac{16!}{ (16 -5)! \times 5! }}[/tex]

             [tex]\bold{ = \frac{16!}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11 !}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5\times 4\times 3 \times 2 \times 1}}\\\\\bold{ = 8 \times 3 \times 14 \times 13 }\\\\\bold{ = 4368 }\\\\[/tex]

P(accepting shipment) = P(all 5 modems work):

[tex]= \bold{\frac{^{12}C_5}{ ^{16}C_{5}}}[/tex]

[tex]\bold{=\frac{792}{4368}}\\\\\bold{=0.18131}\\\\\bold{=0.18131 \times 100= 18.131 \approx 18.131\%}\\\\[/tex]

Therefore, the final answer is "18.131%".

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Answer:

[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Let's define irrational by stating what rational means first, and the use the process of elimination.

A rational number is one that can be expressed as a ratio.  When dividing the numerator of this ratio by the denominator, we will either get a whole number, a decimal that repeats a pattern, or we will get a decimal that terminates.

.14 terminates, so it is rational

1/3 divides to .333333333333333333333333333333333333333 indefinitely, so it is rational

square root of 4 is 2, a whole number, so it is rational

the square root of 6, to 9 decimal places, is 2.449489743... and it goes on without ending and without repeating.  So this is the only irrational number of the bunch.

Answer:

D

Step-by-step explanation:

Answer: [tex]P = \$\ 52[/tex]

Step-by-step explanation:

We have the equation [tex]P = 31 + 1.75w[/tex] where P represents the payment and w represents the amount of water used.

To calculate the monthly payment that corresponds to 12 units of water you must do [tex]w = 12[/tex] in the main equation and solve for the variable P.

[tex]P = 31 + 1.75w[/tex]

[tex]P = 31 + 1.75(12)[/tex]

[tex]P = 31 + 21[/tex]

[tex]P = 52[/tex]

Tuyet's payment for a month when 12 units of water are used is $52.

To find Tuyet's payment for a month when 12 units of water are used, we can substitute 12 for 'w' in the equation P = 31 + 1.75w and solve for P.

P = 31 + 1.75(12)

P = 31 + 21

P = 52

Therefore, Tuyet's payment for a month when 12 units of water are used is $52.

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Let's first consider converting to polar coordinates.

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\begin{cases}x^2+y^2=1\iff r=1\\x^2+(y-1)^2=1\iff r=2\sin\theta\end{cases}[/tex]

We have

[tex]1=2\sin\theta\implies\sin\theta=\dfrac12\implies\theta=\dfrac\pi6\text{ or }\theta=\dfrac{5\pi}6[/tex]

Then [tex]\mathrm dA=r\,\mathrm dr\,\mathrm d\theta[/tex] and the integral is

[tex]\displaystyle\iint_Ry\,\mathrm dA=\int_{\pi/6}^{5\pi/6}\int_{2\sin\theta}^1r^2\sin\theta\,\mathrm dr\,\mathrm d\theta=\boxed{-\frac{\sqrt3}4-\frac{2\pi}3}[/tex]

Answer: $ 18681.45

Step-by-step explanation:

Given: Future value : [tex]FV=\$25,000[/tex]

The rate of interest : [tex]r=0.06[/tex]

The number of time period : [tex]t=5[/tex]

The formula to calculate the future value is given by :-

[tex]\text{Future value}=P(1+i)^n[/tex], where P is the initial amount deposited.

[tex]\Rightarrow\ 25000=P(1+0.06)^5\\\\\Rightarrow\ P=\dfrac{25000}{(1.06)^5}\\\\\Rightarrow\ P=18681.4543217\approx=18681.45[/tex]

Hence, the lump that must be deposit today : $ 18681.45

Try this suggested solution, note, 'D' means the region bounded by the triangle according to the condition. It consists of 6 steps.

Answers are underlined with red colour.

Answer with explanation:

It is given that,  for all real numbers x, if 2 x+1 is rational .

      When you will look at the expression ,2 x +1

⇒1 is rational

⇒2 x will be rational, because the expression , 2 x+1, is rational.

⇒2 x is rational, it means , x will be rational,because 2 is rational.

Some important rules considering rational and irrational

1.⇒Product of rational and rational is Rational.

2.⇒Product of Irrational and Rational is Irrational.

3.⇒Product of Irrational and Irrational may be irrational or rational.

≡2 x →is rational, 2 is rational number ,so x will be rational also.

If 2x+1 is rational, hence 2x is rational subtracting 1 which is also rational. Assuming 2x is expressible as a/b, then x is a/2b, again showing x is rational.

To prove that if 2x+1 is rational, then x must also be rational, we must understand the definition of rational numbers and basic properties of arithmetic operations involving rational numbers. A number is considered rational if it can be written as the quotient of two integers (where the denominator is not zero). Given that the sum of two rational numbers is also rational, if 2x+1 is rational, and we know that 1 is rational (since 1 can be written as 1/1), then 2x must be rational because rational minus rational yields a rational result.

Now, assuming 2x is rational, we can express it as a fraction [tex]\frac{a}{b}[/tex], with a and b being integers and b non-zero. Since the multiplication of a rational number by an integer is also rational, and knowing that 2 is an integer, we can then say that x, which is  [tex]\frac{a}{2b}[/tex], is also rational. This is because we can express the result of  [tex]\frac{a}{2b}[/tex] with integers in the numerator and the denominator.