In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points is 50, what is the least possible positive difference between n and m?

a. 1

b. 3

c. 5

d. 7

e. 9

Please show work!

Answers

Answer 1

Answer:

b. 3

Step-by-step explanation:

Here, n players score 2 points and m players score 5 points,

So, total scores = 2n + 5m,

According to the question,

The total number of points is 50,

2n + 5m = 50

Since, n and m can be any positive integers including 0 ( because number of players can not be negative or in fraction )

Also, for the positive integer value of m, n must be the multiple of 5 less than or equal to 25,

Thus, the possible values of m and n are,

(5,8), (10, 6), (15, 4), (25,0),

Since, 8-5 < 10-6 < 15-4 < 25-0

Hence, the least possible positive difference between n and m is 3.

Option 'b' is correct.

Answer 2

Final answer:

The least possible positive difference between the number of players scoring 2 points and 5 points to reach a total of 50 points is 3. This is determined by finding pairs of values (n, m) that satisfy the equation 2n + 5m = 50 and choosing the pair with the smallest difference. The correct option is b.

Explanation:

The question given is a linear Diophantine equation mathematics problem where we need to find the least possible positive difference between the number of players scoring 2 points (n) and the number of players scoring 5 points (m), given that the total points scored is 50.

To solve this, we start with the equation 2n + 5m = 50 and find pairs of values (n, m) that satisfy this equation. We're looking for the pair with the smallest positive difference |n - m|.

Let's look at the possibilities for m and calculate corresponding n values, remembering that both m and n must be non-negative integers:

If m = 0, then 2n = 50, so n = 25 (difference is 25).

If m = 2, then 2n = 40, so n = 20 (difference is 18).

If m = 4, then 2n = 30, so n = 15 (difference is 11).

If m = 6, then 2n = 20, so n = 10 (difference is 4).

If m = 8, then 2n = 10, so n = 5 (difference is 3).

If m = 10, then 2n = 0, so n = 0 (difference is 10, but not a smaller difference).

From these calculations we can see that the smallest positive difference is when m = 8 and n = 5, which is 3. Therefore, the answer is b. 3.1


Related Questions

If you drive 5 miles​ south, then make a left turn and drive 12 miles​ east, how far are​ you, in a straight​ line, from your starting​ point? Use the Pythagorean Theorem to solve the problem. Use a calculator to find square​ roots, rounding to the nearest tenth as needed.

Answers

Answer: Hence, the distance covered in a straight line from the starting point is 13 miles.

Step-by-step explanation:

Since we have given that

Distance between AB = 5 miles

Distance between BC = 12 miles

We need to find the distance covered from the starting point.

We will use "Pythagorean Theorem":

[tex]H^2=P^2+B^2\\\\AC^2=AB^2+BC^2\\\\AC^2=5^2+12^2\\\\AC^2=25+144\\\\AC^2=169\\\\AC=\sqrt{169}\\\\AC=13\ miles[/tex]

Hence, the distance covered in a straight line from the starting point is 13 miles.

The unemployment rate in a city is 13%. If 6 people from the city are sampled at random, find the probability that at least 3 of them are unemployed. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

Answers

The answer would be 20 % if it was on Plato

Please need help on 2 math questions

13. Divide the rational expressions.


(7y-1)/(y2-36)÷(1-7y)/(y+6)


2. Add or subtract as indicated. Write the answer in descending order.

(3n^4 + 1) + (–8n^4 + 3) – (–8n^4 + 2)


A. –13n^4 + 6


B. 3n^4 + 6


C. 3n^4 + 2


D. 19n^4 – 4



Answers

Question 1:

For this case we have the following expression:

[tex]\frac {\frac {y-1} {y ^ 2-36}} {\frac {1-7y} {y + 6}} =\\\frac {(7y-1) (y + 6)} {(y ^ 2-36) (1-7y)} =[/tex]

We have to:

[tex]y ^ 2-36 = (y + 6) (y-6)[/tex]

Rewriting:

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

We take common factor "-" in the denominator:

[tex]\frac {7y-1} {(y-6) * - (- 1 + 7y)} =\\\frac {7y-1} {- (y-6) * (7y-1)} =\\- \frac {1} {(y-6)}[/tex]

ANswer:

[tex]- \frac {1} {(y-6)}[/tex]

Question 2:

For this case we must simplify the following expression:

[tex](3n ^ 4 + 1) + (- 8n ^ 4 + 3) - (- 8n ^ 4 + 2) =[/tex]

We eliminate parentheses keeping in mind that:

[tex]+ * - = -\\- * - = +\\3n ^ 4 + 1-8n ^ 4 + 3 + 8n ^ 4-2 =[/tex]

We add similar terms:

[tex]3n ^ 4-8n ^ 4 + 8n ^ 4 + 1 + 3-2 =\\3n ^ 4 + 2[/tex]

Answer:

[tex]3n ^ 4 + 2[/tex]

The Length of a rectangle is 3x+7 .The Width is x-4 . Express the Area of the Rectangle in terms of the Variable x. A) 3x^2 -5x-28 B) 3x^2 +5x +28 C) 2x^2 +4 x-28 D ) 3x^2 -5x +28 ​

Answers

A) 3x²-5x-28. The area of the rectangle  with length 3x+7 and width x-4 can be represented as 3x²-5x-28.

The equation to find the area of ​​the rectangle is simply A = l * w. This means that the area of ​​a rectangle is equal to the product of its length (l) by its width (w), or of its length by its width.

A = w*l

A = (3x + 7)(x -4) = (3x)(x) + (3x)(-4) + (7)(x) + (7)(-4)

A = 3x² - 12x + 7x - 28

A = 3x² -5x - 28

This​ year, Druehl,​ Inc., will produce 57,600 hot water heaters at its plant in​ Delaware, in order to meet expected global demand. To accomplish​ this, each laborer at the plant will work 160 hours per month. If the labor productivity at the plant is 0.15 hot water heaters per labor​ hour, how many laborers are employed at the​ plant?

Answers

Answer:

200

Step-by-step explanation:

Goal 57600 heaters per year

160 hr per 1 month

so 160(12)hr per 1 year

that is 1920 hr per 1 year

We also have that .15 heaters are produced every 1 hour

so multiply 1920 by .15 and you have your answer

160(12)(.15)=288 heaters are produced per one person per year

so we need to figure how many people we need by dividing year goal by what one person can do

57600/288=200 people needed

200 laborers are employed at the plant.

First find out the number of hours each worker will have to work in a year:

= Number of hours per month x 12 months

= 160 * 12

= 1,920 hours

Find out the number of units each worker will produce in those hours:

= Annual number of hours x Units per hour

= 1,920 * 0.15

= 288 heaters

The number of laborers employed is:

= Yearly demand of heaters / Number of heaters produced per worker

= 57,600 / 288

= 200 laborers

The plant employs 200 laborers.

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The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. If a soccer team of 11 players were to make the next batch of orders, what would be the standard error of the mean? 1.64 0.82 2.71 3.67

Answers

Answer: 2.71

Step-by-step explanation:

We know that the formula to calculate the standard error is given by :-

[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex], where [tex]\sigma[/tex] is the standard deviation and 'n' is the sample size.

Given : Standard deviation : [tex]\sigma=\$9[/tex]

Sample size : [tex]n=11[/tex]

Then , the standard error of the mean is given by :-

[tex]S.E.=\dfrac{9}{\sqrt{11}}=2.7136021012\approx2.71[/tex]

Hence, the standard error of the mean = 2.71

Final answer:

The standard error of the mean for the size of individual customer orders with a standard deviation of $9 and a sample size of 11 is approximately $2.71.

Explanation:

The Ransin Sports Company is looking to calculate the standard error of the mean for the size of individual customer orders. The standard error of the mean (SEM) is found by dividing the standard deviation by the square root of the sample size. Given a standard deviation of $9 and a sample size of 11 players (the soccer team), the standard error of the mean can be calculated using the formula SEM = σ / √n, where σ is the standard deviation and n is the sample size.

SEM = $9 / √11
SEM = $9 / 3.316...
SEM = approximately $2.71.

Therefore, the standard error of the mean is $2.71.

Find the geometric means in the following sequence.

Answers

Answer:

Choice A

Step-by-step explanation:

a=-6           (1st term)

ar=             (2nd term)

ar^2=         (3rd term)

ar^3           (4th term)

ar^4=         (5th term)

ar^5=-1458 (6th term)

a=-6 so -6r^5=-1458

divide both sides by -6 giving r^5=243 so to obtain r you do the fifth root of 243 which is 3.

The common ratio is 3.

so ar=6(-3)=-18 (2nd term)

Only choice A fits this.

If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500? Round to the nearest month.

Answers

Final answer:

To calculate the time required for an investment of $1000 at 3% interest compounded monthly to grow to $1500, use the compound interest formula. Solve for 't' using natural logarithms and rounding to the nearest month.

Explanation:

To determine how long it takes for $1000 invested at 3% interest compounded monthly to grow to $1500, we use the formula for compound interest:

Final Amount = Principal (1 + (Interest Rate / Number of Compounding Periods in a Year))^(Total Number of Compounding Periods)

Plugging in the values we have:

$1500 = $1000 (1 + 0.03/12)^(12t)

Where 't' is in years. To find 't', we need to isolate it in the equation:

1.5 = (1 + 0.03/12)^(12t)

Take the natural logarithm of both sides:

ln(1.5) = 12t * ln(1 + 0.03/12)

Then, solve for 't' by dividing both sides by 12 * ln(1 + 0.03/12), and round to the nearest month:

t = ln(1.5) / (12 * ln(1 + 0.03/12))

If random samples of size 525 were taken from a very large population whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

Answers

Answer: 0.02

Step-by-step explanation:

Given: Sample size : [tex]n= 525[/tex]

The population proportion [tex]P=0.3[/tex]

Then, [tex]Q=1-P=1-0.3=0.7[/tex]

The formula to calculate the standard error is given by :-

[tex]S.E.\sqrt{\dfrac{PQ}{n}}[/tex]

[tex]\Rightarrow\ S.E.=\sqrt{\dfrac{0.3\times0.7}{525}}=0.02[/tex]

Hence, the standard deviation of the sample proportions (i.e., the standard error of the proportion) is 0.02.

What is the area of a square that measures 3.1 m on each side?

Answers

The area of a square that measures 3.1 m on each side will be 9.61 m².

How to find the area of the square?

The area of the square is found as the square of the length of its side. If the length of a side is a;

Area of a square = side²

Given data;

S is the length of the side= 3.1 m

Area of a square = a²

A=a²

A= (3.1 m)²

A = 9.61 m²

Hence, the area of a square will be 9.61 m².

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Final answer:

The area of a square With each side measuring 3.1 m is 9.61 m², and this answer is provided with three significant figures.

Explanation:

The area of a square is calculated as the product of its side lengths. Since all sides of a square are equal, if a square measures 3.1 m on each side, the area will be:

Area = side × side = 3.1 m × 3.1 m

To find this product, you multiply 3.1 by itself:

3.1 m × 3.1 m = 9.61 m²

To report this area, we express it in square meters (m²) and use the correct number of significant figures, which in this case is three, based on the given measurements of the sides of the square.

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At The Car rental Company , You must play a rate of $ 130 and then a daily fee of $ 17 Per day . Wrote a Linear Equation to describe the total Cost , y, of renting the car for x days . What is the Cost of renting a Car for 9 days With this Company... ​

Answers

Answer:

y = 17x + 130

For 9 days, you would pay $283.

Step-by-step explanation:

y = 17x + 130

Total cost = 17$ a day, plus the 130$ fee.

x = 9

y = (17)(9) + 130

y = 153 + 130

y = 283

The required cost of renting a car for 9d days with the company is $283.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
At The Car rental Company, You must pay a rate of $ 130 and then a daily fee of $ 17 Per day.
Let the number of days be x for renting a car,
According to the question,
Total cost(y) = 130 + 17x
Put x = 9

Total cost = 130 + 17×9
               = $283

Thus, the required cost of renting a car for 9d days with the company is $283.

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15, Evaluate 6 choose 4.

Answers

Answer:  The required result is 15.

Step-by-step explanation:  We are given to evaluate the following :

"6 choose 4".

Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.

We know that

the formula for the combination of n different things chosen r at a time is given by

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}.[/tex]

For the given situation, n = 6  and  r = 4.

Therefore, we get

[tex]^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6!}{4!2!}=\dfrac{6\times5\times4!}{4!\times2\times1}=15.[/tex]

Thus, the required result is 15.

math problem The number of incarcerated adults N​ (measured in​ thousands) in a certain country can be approximated by the equation N = -2.7 x^2 + 72.4x + 1911​, where x is the number of years since 2000. In 2013​, the number of incarcerated adults peaked. How many adults were incarcerated in that​ year?

Answers

Answer:

Step-by-step explanation:

-2.7(13)^2 + 72.4(13) + 1911

1,232.01 + 941.2 + 1911 = 4084.21

Compute the face value of a 90-day promissory note dated October 22, 2018 that has a maturity value of $76,386.99 and an interest rate of 7.5% p.a.

Answers

Answer:

The face value would be $75,000

Step-by-step explanation:

Maturity value = $76,386.99

Time = 90 days

Rate of interest = 7.5%

Let face value be 'x'

By using the formula [tex]A=P(1+\frac{RT}{100})[/tex]

                      $76,386.99 = [tex]x(1+\frac{7.5\times \frac{90}{365}}{100})[/tex]

Time in years = [tex]\frac{90}{365}[/tex]

⇒ $76,386.99 = x( 1 + 0.01849315 )

⇒ x = [tex]\frac{76,386.99}{1.01849315}[/tex]

x = $75,000

The face value would be $75,000

What is the GCF of the expression a2b2c2 + a2bc2 - a2b2c

Answers

Answer:

a^2bc

Step-by-step explanation:

The GCF of the expression a2b2c2 + a2bc2 - a2b2c is a2bc.

The greatest common factor (GCF) of an algebraic expression is the largest polynomial that divides each of the terms without leaving a remainder. To find the GCF of the expression a2b2c2 + a2bc2 - a2b2c, first identify the common factors in each term.

Inspecting each term we see that a2 is a common factor for all of them, and the smallest power of b and c present in all terms is b and c, respectively. Therefore, the GCF is a2bc.

Translate the phrase "" Nine times the difference of a number and 8"" into a algebraic expression . Simplify your result​

Answers

click on picture, sorry if it's hard to read, but my phone messed up the typing

The phrase 'Nine times the difference of a number and 8' is translated into the algebraic expression 9(n - 8) and simplified to 9n - 72.

The phrase 'Nine times the difference of a number and 8' translates to an algebraic expression by following specific mathematical operations. To represent an unknown number, we use a variable, such as 'n', and the phrase 'the difference of a number and 8' would be written as 'n - 8'. To adhere to the phrase 'nine times', we multiply the difference by 9, leading to the expression 9(n - 8).

When we simplify the expression, we need to distribute the 9 to both terms within the parentheses: 9 × n and 9 × (-8), which gives us 9n - 72. Thus, the simplified algebraic expression for the phrase 'Nine times the difference of a number and 8' is 9n - 72.

Solve the following system of equations.

9x + 4y = 4

-5x + 7y = 7

Answers

Answer:

this is the answer with steps

hope it helps!

Answer:

The solution is:

[tex](0, 1)[/tex]

Step-by-step explanation:

We have the following equations

[tex]9x + 4y = 4[/tex]

[tex]-5x + 7y = 7[/tex]

To solve the system multiply by [tex]\frac{9}{5}[/tex] the second equation and add it to the first equation

[tex]-5*\frac{9}{5}x + 7\frac{9}{5}y = 7\frac{9}{5}[/tex]

[tex]-9x + \frac{63}{5}y = \frac{63}{5}[/tex]

[tex]9x + 4y = 4[/tex]

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

[tex]\frac{83}{5}y=\frac{83}{5}[/tex]

[tex]y=1[/tex]

Now substitute the value of y in any of the two equations and solve for x

[tex]9x + 4(1) = 4[/tex]

[tex]9x +4 = 4[/tex]

[tex]9x = 4-4[/tex]

[tex]9x = 0[/tex]

[tex]x=0[/tex]

The solution is:

[tex](0, 1)[/tex]

.....Help Please......

Answers

Answer:

i cant see the picture

Step-by-step explanation:

Out of 25 attempts, a basketball player scored 17 times. One-half of the missed shots are what % of the total shots?

Answers

Answer:

16%

Step-by-step explanation:

Eight shots were missed. Take half of eight; 4. You now have 4\25, which is 160‰ [16%].

Answer:

%16

Step-by-step explanation:

Step 1:  Find the shots missed

25 - 17 = 8

Step 2:  Find half of the shots missed

8 / 2 = 4

Step 3:  Divide 4 by 25

4/25 = 0.16

Step 4:  Convert to Percent

0.16 * 100 = %16

Answer:  %16

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The probability that an adult possesses a credit card is .70. A researcher selects two adults at random. By assuming the independence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is:

Answers

Answer: 0.21

Step-by-step explanation:

We know that if two events A and B are independent , then the probability of A and B is given by :-

[tex]\text{P and B}=P(A)\times P(B)[/tex]

Given: The probability that an adult possesses a credit card P(A)= 0 .70

The probability that an adult  does not possess a credit card[tex]P(B)= 1-P(A)=0 .30[/tex]

By assuming the independence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is given by :-

[tex]0.70\times0.30=0.21[/tex]

Hence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is 0.21.

Final answer:

To find the probability that the first adult selected at random has a credit card and the second does not, multiply the probability of the first event (0.70) by the probability of the second event (0.30), which yields 0.21 or 21%.

Explanation:

The subject of this question is Mathematics, specifically dealing with probability. The question is at a High School level, focusing on the concept of independent events in probability. To calculate the probability that the first adult possesses a credit card and the second adult does not possess a credit card, we use the rule of independent events:

The probability of the first adult having a credit card is 0.70 (given).

The probability of the second adult not having a credit card is 1 - 0.70 = 0.30.

Since these two events are independent, we multiply the probabilities of each event occurring:

P(First has a credit card AND Second does not have a credit card) = P(First has a credit card) * P(Second does not have a credit card) = 0.70 * 0.30

The answer is therefore 0.21 or 21%

The Beardstown Bearcats baseball team plays 60 percent of its games at night and 40 percent in the daytime. It wins 55 percent of its night games but only 35 percent of its day games. You read in the paper that the Bearcats won their last game against the Manteno Maulers. What is the probability that it was played at night?

Answers

Answer: 0.7021

Step-by-step explanation:

Let D be the event that team plays in day , N be the event that the team plays in night and W be the event when team wins.

Then , [tex]P(D)=0.40\ \ \ P(N)=0.60[/tex]

[tex]P(W|D})=0.35\ \ \ \ P(W|N)=0.55[/tex]

Using the law of total probability , we have

[tex]P(W)=P(D)\timesP(W|D)+P(N)\timesP(W|N)\\\\\Rightarrow\ P(W)=0.40\times0.35+0.60\times0.55=0.47[/tex]

Using Bayes theorem ,

The required probability :[tex]P(N|W)=\dfrac{P(N)P(W|N)}{P(W)}[/tex]

[tex]=\dfrac{0.60\times0.55}{0.47}=0.702127659574\approx0.7021[/tex]

Choose the property used to rewrite the expression. log base 4, 7 + log base 4, 2 = log base 4, 14

Answers

Answer:

[tex] log_{a}(x) + log_{a}(y) = log_{a}(xy) [/tex]

In this high school level mathematics problem, the Product Rule of Logarithms is applied to rewrite the given expression using the appropriate property.

The property used to rewrite the expression is the Product Rule of Logarithms. According to this property, when adding two logarithms with the same base, it is equivalent to multiplying the values inside the logarithms.

So, log base 4 of 7 + log base 4 of 2 can be rewritten as log base 4 of (7*2), which simplifies to log base 4 of 14.

Find the volume of the solid whose base is the circle x2+y2=25 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=4.

Answers

Triangles with height [tex]h[/tex] and base [tex]b[/tex], with [tex]b=h[/tex] have area [tex]\dfrac{b^2}2[/tex].

Such cross sections with the base of the triangle in the disk [tex]x^2+y^2\le25[/tex] (a disk with radius 5) have base with length

[tex]b(x)=\sqrt{25-x^2}-\left(-\sqrt{25-x^2}\right)=2\sqrt{25-x^2}[/tex]

i.e. the vertical (in the [tex]x,y[/tex] plane) distance between the top and bottom curves describing the circle [tex]x^2+y^2=25[/tex].

So when [tex]x=4[/tex], the cross section at that point has base

[tex]2\sqrt{25-16}=6[/tex]

so that the area of the cross section would be 6^2/2 = 18.

In case it's relevant, the entire solid would have volume given by the integral

[tex]\displaystyle\int_{-5}^5\frac{b(x)^2}2\,\mathrm dx=4\int_0^5(25-x^2)\,\mathrm dx=\frac{1000}3[/tex]

Final answer:

The question is about finding the volume of a solid with a circular base and equilateral triangular cross-sections, and the area of a cross section at x = 4. The base is defined by the circle equation x2 + y2 = 25 and the height and base of triangles are equal.

Explanation:

The question relates to the calculation of the volume of a solid object and the area of its cross section. The base of the solid is a circle defined by x2 + y2 = 25, which is a circle of radius 5. As the cross sections perpendicular to the x-axis are equal in height and base, they form equilateral triangles.

So the area A of the triangle at x = 4 is given by A = 1/2 * Base * Height. But in an equilateral triangle, the base and height are equal, so A = 1/2 * b2. From the equation of circle, the value of 'b' at x = 4 can be calculated as √(25 - 42) = 3. To get the volume we integrate the area A over the x domain of [-5,5].

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find the solutions of the system

y=x^2+3x-4

y=2x+2


a. (-3,6) and (2,-4)

b. (-3,-4) and (2,6)

c. (-3,-4) and (-2,-2)

d. no solution

Answers

Answer:

b. (-3, -4) and (2, 6)

Step-by-step explanation:

By the transitive property of equality, if y equals thing 1 and y also equals thing 2, then thing1 and thing 2 are also equal.  So we will set them equal to each other and factor to solve for the 2 values of x:

[tex]2x+2=x^2+3x-4[/tex]

Get everything on one side of the equals sign, set the whole mess equal to 0, and combine like terms to get:

[tex]0=x^2+x-6[/tex]

Because this is a second degree polynomial, a quadratic to be precise, it has 2 solutions.  We need to find those 2 values of x and then use them in either one of the original equations to solve for the y values that go with each x.  

Factoring that polynomial above gives you the x values of x = -3 and 2.  Sub in -3 first:

y = 2(-3) + 2 and

y = -6 + 2 so

y = -4

Therefore, the coordinate is (-3, -4).

Onto the next x value of 2:

y = 2(2) + 2 and

y = 4 + 2 so

y = 6

Therefore, the coordinate is (2, 6)

If f (x) =1/9x-2 what is f1(x)?

Answers

Answer:

[tex]\large\boxed{f^{-1}(x)=9x+18}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{9}x-2\to y=\dfrac{1}{9}x-2\\\\\text{Exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y-2\\\\\text{solve for}\ y:\\\\\dfrac{1}{9}y-2=x\qquad\text{add 2 to both sides}\\\\\dfrac{1}{9}y=x+2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x+(9)(2)\\\\y=9x+18[/tex]

A family has four children. If the genders of these children are listed in the order they are born, there are sixteen possible outcomes: BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG. Assume these outcomes are equally likely. Let represent the number of children that are girls. Find the probability distribution of .

Answers

Final answer:

The probability distribution of the number of female children in a family with 4 children, assuming male and female children are equally likely, is calculated by enumerating combinations for each possible number of girls and dividing by the total number of outcomes.

Explanation:

This problem involves understanding the concept of probability distribution. Let's denote 'G' for girl and 'B' for boy. In a family with 4 children, every child can be either a boy or a girl which gives us 2*2*2*2 = 16 possible combinations which we see listed in the problem.

Let's represent 'X' as the number of girls in the family. X could be 0, 1, 2, 3 or 4. For each of these values of X, we need to calculate the probability, i.e., the number of combinations which satisfy each X, divided by 16 (the total possibilities).

For X=0(genders: BBBB), there is only 1 combination. Therefore, P(X=0) = 1/16.For X=1 (genders: BBBG, BBGB, BGBB, GBBB), there are 4 combinations. Therefore, P(X=1) = 4/16 = 1/4.For X=2 (genders: BGBG, BBGG, GBGB, GBBG, BGGB, GGBB), there are 6 combinations. Therefore, P(X=2) = 6/16 = 3/8.For X=3 (genders: BGGG, GBGG, GGBG, GGGB), there are 4 combinations. Therefore, P(X=3) = 4/16 = 1/4.For X=4 (gender: GGGG), there is 1 combination. Therefore, P(X=4) = 1/16.

So the probability distribution of X is: P(X=0) = 1/16, P(X=1) = 1/4, P(X=2) = 3/8, P(X=3) = 1/4, P(X=4) = 1/16.

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Final answer:

The probability distribution of the number of girls in a family with four children is as follows: P(X = 0) = 1/16, P(X = 1) = 4/16, P(X = 2) = 6/16, P(X = 3) = 4/16, P(X = 4) = 1/16.

Explanation:

The probability distribution of the number of girls in a family with four children can be determined by analyzing the possible outcomes. There are 16 possible outcomes, ranging from all boys (BBBB) to all girls (GGGG) and various combinations in between. To find the probability distribution, we need to calculate the probability of each outcome. Since all outcomes are equally likely, the probability of each outcome is 1/16. Therefore, the probability distribution is as follows:

P(X = 0) = 1/16P(X = 1) = 4/16P(X = 2) = 6/16P(X = 3) = 4/16P(X = 4) = 1/16

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Evaluate the Expression B^2-4 ac given by that a = -2 ,, b= -2 and c =2​

Answers

F* you B*!!!!!! Your so S*! That's the easiest thing in the world!!

Explain why f(x) = x^2+4x+3/x^2-x-2 is not continuous at x = -1.

Answers

Answer:

The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)

Step-by-step explanation:

We have the following expression

[tex]f(x) = \frac{x^2+4x+3}{x^2-x-2}[/tex]

Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.

Now we search that values of x make 0 the denominator factoring the polynomial [tex]x^2-x-2[/tex]

We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.

These numbers are -2 and 1

Then the factors are:

[tex](x-2) (x + 1)[/tex]

We do the same with the numerator

[tex]x^2+4x+3[/tex]

We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.

These numbers are 3 and 1

Then the factors are:

[tex](x+3)(x + 1)[/tex]

Therefore

[tex]f(x) = \frac{(x+3)(x+1)}{(x-2)(x+1)}[/tex]

Note that [tex]\frac{(x+1)}{(x+1)}=1[/tex] only if [tex]x \neq -1[/tex]

So since [tex]x = -1[/tex] is not included in the domain the function has a discontinuity in [tex]x = -1[/tex]

Final answer:

The function f(x) = (x²+4x+3)/(x²-x-2) is not continuous at x = -1 because the denominator becomes zero at that point, rendering the function undefined.

Explanation:

The function f(x) = (x²+4x+3)/(x²-x-2) is not continuous at x = -1 primarily because the denominator of the function becomes zero at x = -1.

Specifically, the denominator factors as (x-2)(x+1), and when x equals -1, the denominator equals zero, which makes the function undefined at that point.

Therefore, the function has a discontinuity at x = -1, and by definition, a function is not continuous at points where it is not defined.

In 1987, the General Social Survey asked, "Have you ever been active in a veteran's group? " For this question, 52 people said that they did out of 98 randomly selected people. The General Social survey randomly selects adults living in the US. Someone wanted to compute a 95% confidence interval for p. What is parameter?

Answers

Final answer:

The parameter in this question refers to the population proportion. To compute a 95% confidence interval for the proportion, you can use the formula: p ± z × √(p × (1-p) / n). The sample proportion is 0.53 and the sample size is 98. By plugging these values into the formula, you can calculate the confidence interval.

Explanation:

The parameter in this question refers to the population proportion. In statistics, a parameter is a measure that describes a characteristic of a population. In this case, the parameter is the proportion of all adults living in the US who have been active in a veteran's group. To compute a 95% confidence interval for this proportion, you can use the formula:  p ± z × √(p × (1-p) / n), where p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

Using the provided information, the sample proportion is 52/98 = 0.53. To find the z-score for a 95% confidence level, you can use a standard normal distribution table or a calculator with the function invNorm(0.975). The z-score for a 95% confidence level is approximately 1.96. The sample size is 98. Plugging these values into the formula, you can calculate the confidence interval for the population proportion.

Confidence interval = 0.53 ± 1.96 × √(0.53 × (1-0.53) / 98) = 0.53 ± 0.0907

The parameter p is the true proportion of adults in the US who have ever been active in a veteran's group, and the 95% confidence interval for this parameter is (0.4317, 0.6295).

The formula for a 95% confidence interval for a proportion is given by:

[tex]\[ \hat{p} \pm z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \][/tex]

where z is the z-score corresponding to the desired confidence level. For a 95% confidence interval, the z-score is approximately 1.96.

Let's calculate the confidence interval:

 1. Calculate the sample proportion [tex]\( \hat{p} \)[/tex]:

[tex]\[ \hat{p} = \frac{52}{98} \approx 0.5306 \][/tex]

2. Calculate the standard error of the proportion:

[tex]\[ SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = \sqrt{\frac{0.5306(1 - 0.5306)}{98}} \approx \sqrt{\frac{0.2503}{98}} \approx \sqrt{0.002554} \approx 0.0505 \][/tex]

3. Find the z-score for a 95% confidence interval, which is approximately 1.96.

4. Calculate the margin of error:

[tex]\[ ME = z \times SE \approx 1.96 \times 0.0505 \approx 0.0989 \][/tex]

5. Calculate the confidence interval:

[tex]\[ \text{Lower bound} = \hat{p} - ME \approx 0.5306 - 0.0989 \approx 0.4317 \] \[ \text{Upper bound} = \hat{p} + ME \approx 0.5306 + 0.0989 \approx 0.6295 \][/tex]

Therefore, the 95% confidence interval for the proportion p of all adults living in the US who have ever been active in a veteran's group is approximately (0.4317, 0.6295).

2x - 20 = 32

20 - 3x = 8

6x - 8 = 16

-13 - 3x = -10

Answers

Answer:

Step-by-step explanation:

1st one is x=26

2nd one is x=4

3rd is x=4

4th is x=-1

Hope that helps!

Answer:

so the answers are 26, 4, 4, and -1

Step-by-step explanation:

If you want me to solve all of them it is: Your getting x by itself

so do the opposite of each problem i'll do the first one

2x - 20 = 32

     + 20   +20

2x = 52 divide the 2

2       2

x  = 26

Hope my answer has helped you if not i'm sorry.

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