Give a recursive definition of each of these sets of ordered pairs of positive integers. (Hint: plot the points in the set in the plane and look for lines containing points in the set. 1. S={(a, b) I a E Z+, b Ñ Z+ , and a | b}2. S={(a, b) I a E Z+, b Ñ Z+ , and 3 | a + b} 3. S={(a, b) | a Ñ Z+ , b Ñ Z+ , and a + b is odd) a) (1,2) S, (2, 1) E S and if (a, b) S then (a + 2, b) E S, (a, b + 2) E S and (a + 1, b + 1) E S b) (1,2) es, (2, 1) Ñ Sand if (a, b) Ñ S then (a + 3, b) Ñ s, (a, b + 3) Ñ s, (a+1, b + 2) ES and (a + 2, b + 1) Ñ s c) (1,1) Ñ Sand if (a, a) Ñ Sthen (a + 1, a + 1) Ñ S and if (a, b) Ñ S, then (a, b + a) Ñ s

Answer:

39

Step-by-step explanation:

g(5) = 3(5) + 5 = 20

f(20) = 2(20) - 1 = 39

Answer:

f ( 2 x + 1 ) = 6 x − 2

Step-by-step explanation:

Set up the composite result function.

f ( g ( x ) )

Evaluate  f ( g ( x ) )

by substituting in the value of  g  into  f

. f ( 2 x + 1 ) = 3 ( 2 x + 1 ) − 5

Simplify each term.

Apply the distributive property.

f ( 2 x + 1 ) = 3 ( 2 x )+ 3 ⋅ 1 − 5

Multiply  2  by  3 .

f ( 2 x + 1 ) = 6 x + 3 ⋅ 1 − 5

Multiply  3  by  1  .

f ( 2 x + 1 ) = 6 x + 3 − 5

Subtract  5  from  3 . f ( 2 x +1 ) = 6 x− 2

Answer:

1. 3:25

2. 60:7

Step-by-step explanation:

To express the ratio in the lowest terms:

1. 360 metres to 3 kilometres

First of all, we need to convert both the terms in same unit.

Let us convert kilometres to metres for simplicity.

We know that 1 km = 1000 m

So, 3 km = 3000 m

Hence, the ratio can be represented as:

[tex]360\ m: 3000\ m\\\Rightarrow \dfrac{360}{3000}\\ \\\text{Dividing by 10:}\\\Rightarrow \dfrac{36}{300}\\\\\text{Dividing by 12:}\\\Rightarrow \dfrac{3}{25}\\\Rightarrow 3:25[/tex]

So, the simplest ratio is 3:25.

2. 2 minutes to 14 seconds​

Converting minutes to seconds.

1 minute = 60 seconds

2 minutes = 120 seconds

So, the ratio can be written as:

120 seconds : 14 seconds

Dividing by 2:

60:7

So, the simplest form is 60:7.

The answers are:

1. 3:25

2. 60:7

Answer:

84.13% probability a particular tire of this brand will last longer than 57,100 miles

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 60000, \sigma = 2900[/tex]

What is the probability a particular tire of this brand will last longer than 57,100 miles

This is 1 subtracted by the pvalue of Z when X = 57100. So

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

[tex]Z = \frac{57100 - 60000}{2900}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

1 - 0.1587 = 0.8413

84.13% probability a particular tire of this brand will last longer than 57,100 miles

Answer:

Step-by-step explanation:

a^2+b^2=c^2

assuming that 11 and 10 are the shorter sides of the triangle

11^2+10^2=c^2

121+100=c^2

221=c^2

[tex]\sqrt{221}=\sqrt{c^2}[/tex]

this will equal 14.87 approximately

The missing side of the triangle is √221 yd .

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Let recall the Pythagorean theorem formula:

a² + b² = c²

Replacing by the values we have;

11² + 10² = c²

c² = 121 + 100

c² = 221

c = √221 yd

Therefore, the correct answer is √221 yd .

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Answer:

The 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}[/tex]

The sample selected is of size, n = 50.

The critical value of t for 95% confidence level and (n - 1) = 49 degrees of freedom is:

[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 49}=2.000[/tex]

*Use a t-table.

Compute the sample mean and sample standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum {x}=\frac{1}{50}\times [6+4+6+...+9+6]=6.34\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{50-1}\times 229.22}=2.163[/tex]

Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}[/tex]

     [tex]=6.34\pm 2.00\times\frac{2.163}{\sqrt{50}}\\\\=6.34\pm 0.612\\\\=(5.728, 6.952)\\\\\approx(5.7, 7.0)[/tex]

Thus, the 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

Answer:

c) 0.0871

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d is given by the following formula.

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

On a single day:

24 hours, so [tex]a = 0, b = 24[/tex]

8:25 P.M. is 8:25 = 8.4167h

3:30 P. M. is the equivalent to 12 + 3:30 = 15:30 = 15.5h

Probability of rain between these times:

[tex]P(8.4167 \leq X \leq 15.5) = \frac{15.5 - 8.4167}{24 - 0} = 0.2951[/tex]

On both days:

Two days, each with a 0.2951 probability

0.2951*0.2951 = 0.0871

The correct answer is:

c) 0.0871

Answer:

None of the above

Step-by-step explanation:

Answer:

None of the Above

Step-by-step explanation:

I got it right on Khan Academy :) Have a Great Day!

Answer:

(6,-3)

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

Susan can pick 4 pounds of coffee beans in an hour.  Tom can pick 2 pounds of coffee beans in an hour.  Together, they can pick 6 pounds of coffee an hour.

4 + 2 = 6

There are 24 hours in a day.  Multiply the time by the amount that can be picked to find the answer.

24 × 6 = 144

Together, the maximum number of pounds of coffee beans the can pick in a day is 144 pounds.

Together they can pick a maximum of 36 pounds of coffee

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

given:

Susan can pick 4 pounds of coffee or 2 pounds of nuts.

Tom can pick 2 pounds of coffee or 4 pounds of nuts.

So, In 6 hours

Susan will pick

= 4 * 6

= 24 pounds of coffee.

In 6 hours,

Tom will pick

=2 * 6

= 12 pounds of coffee.

Hence, together they can pick a maximum of 36 pounds of coffee

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Answer:

20160 ways

Probability = 0.0556

Step-by-step explanation:

We have 9 different letters, so the total number of words we can make is:

[tex]Total = 9! = 362880\ words[/tex]

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

[tex]N = 4 * 7! = 4*7*6*5*4*3*2 = 20160\ words[/tex]

The probability is calculated by the division of the number of words we want over the total number of words:

[tex]P = N / Total = 20160 / 362880 = 0.0556[/tex]

Answer:

39

Step-by-step explanation:

factors of 18= 1, 2, 3, 6, 9, 18

1+2+3+6+9+18=39

Answer:

  39

Step-by-step explanation:

The divisors of 18 are ...

  1, 2, 3, 6, 9, 18

Their sum is ...

  1 + 2 + 3 + 6 + 9 + 18 = 39

Answer:

M = 90 for a sample of n = 100

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance or M = 90 with s sample of n = 100. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Let n = total boxes (5)

Probability (p) = 1 out of 4 = 1/4 = 0.25

Probability she wins at most 1 out of 5 is p(x <=1) Which is also = p (x =0) + p(x=1)

Probability of not winning would be 0.75 ( 1-0.25)

No prizes in 5 boxes = 0.75^5

1 prize in 5 boxes = 5 x 0.25 x 0.75^4

Total probability = 0.75^5 + 5 x 0.25 x 0.75^4 = 0.63

Answer: 0.63

Step-by-step explanation:

Answer:

solution,

Similar Right triangles:

[tex] \frac{c}{h} = \frac{h}{d} \\ {h}^{2} = cd \\ {y}^{2} = 4 \times 9 \\ {y = 36 }^{2} \\ y = \sqrt{ {(6)}^{2} } \\ y = 6[/tex]

Hope this helps..

Good luck on your assignment..

Answer:whats the measure of x i really need help

Step-by-step explanation:

Answer:

Step-by-step explanation:

If x is increased by 50%, it means that the amount by which x is increased is

50/100 × x = 0.5 × x = 0.5x

The new value of x would be

x + 0.5x = 1.5x

If the new value is further decreased by 30%, it means that the amount by which it was decreased is

30/100 × 1.5x = 0.3 × 1.5x = 0.45x

The new value of x would be

1.5x - 0.45x = 1.05x

Therefore, the result is 1.05x

Answer:

y= -2/3 x - 9

Step-by-step explanation:

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = -2/3 x+b

We have a point to substitute into the equation

-5 = -2/3(-6) +b

-5 = 4 +b

Subtract 4 from each side

-5-4 = 4-4+b

-9 = b

y= -2/3 x - 9

Answer:

[tex]b.\ cos 70 =\dfrac{4}x[/tex] is the correct answer.

Step-by-step explanation:

First of all, let us label the diagram as shown in the attached figure.

OR = 20'

QS = 16'

[tex]\triangle OPQ[/tex] is the right angled triangle that we get.

[tex]\angle P=90^\circ[/tex]

[tex]\angle O =70^\circ[/tex]

From the given figure symmetry, we can clearly see that:

Side OP = OR - QS

OP = 20 - 16 = 4'

Now, let us use trigonometric identity of cosine in [tex]\triangle OPQ[/tex].

[tex]cos\theta = \dfrac{Base}{Hypotenuse}[/tex]

[tex]cosO= \dfrac{OP}{OQ}\\\Rightarrow cos70^\circ= \dfrac{4}{OQ}[/tex]

Let the distance of ramp, OQ = x'

So, the above ratio becomes:

[tex]cos70^\circ= \dfrac{4}{x}[/tex]

So, the correct answer is:

[tex]b.\ cos 70 =\dfrac{4}x[/tex]

Answer:

[tex]n \geq 42[/tex]

Step-by-step explanation:

Data provided

P = 0.6

The calculation of sample size is shown below:-

Here the sampling distribution of proportion will be approximately normal, then follow the rule which is here below:-

[tex]np\geq 10\ and\ np (1 - p)\geq 10[/tex]

Now we will consider condition 2

[tex]np(1 - p)\geq \ 10[/tex]

[tex]n(0.6) (1 - 0.6) \geq \ 10[/tex]

[tex]n(0.6) (0.4) \geq\ 10[/tex]

[tex]n\geq \frac{10}{0.24}[/tex]

[tex]n \geq 41.66667[/tex]

or

[tex]n \geq 42[/tex]

Therefore for computing the required sample size we simply solve the above equation.

Answer:

66.992%

Step-by-step explanation:

[tex]Sales, S(t)=7-6\sqrt[3]{t}[/tex]

Since we want to maximize revenue for the government

Government's Revenue= Sales X Tax Rate

[tex]R(t)=t \cdot S(t)\\R(t)=t(7-6\sqrt[3]{t})\\=7t-6t^{1+1/3}\\R(t)=7t-6t^{4/3}[/tex]

To maximize revenue, we differentiate R(t) and equate it to zero to solve for its critical points. Then we test that this critical point is a relative maximum for R(t) using the second derivative test.

Now:

[tex]R'(t)=7-6*\frac{4}{3} t^{4/3-1}\\=7-8t^{1/3}[/tex]

Setting the derivative equal to zero

[tex]7-8t^{1/3}=0\\7=8t^{1/3}\\t^{1/3}=\dfrac{7}{8} \\t=(\frac{7}{8})^3\\t=0.66992[/tex]

Next, we determine that t=0.6692 is a relative maximum for R(t) using the second derivative test.

[tex]R''(t)=-8*\frac{1}{3} t^{1/3-1}\\R''(t)=-\frac{8}{3} t^{-2/3}[/tex]

R''(0.6692)=-3.48 (which is negative)

Therefore, t=0.66992 is a relative maximum for R(t).

The tax rate, t that maximizes revenue for the government is:

=0.66992 X 100

t=66.992% (correct to 3 decimal places)

Answer:

  34°

Step-by-step explanation:

Because AB and CB are tangents, the measure of angle B is the supplement of the measure of arc AC:

  180° -146° = 34°

Answer:

False

Step-by-step explanation:

2 + 3x = 5

Put x as 1.1.

2 + 3(1.1) = 5

2 + 3.3 = 5

5.3 = 5

False.

Answer:

Solution,

X=1.1

[tex]2 + 3x = 5 \\ 2 + 3 \times 1.1 = 5 \\ 2 + 3.3 = 5 \\ 5.3 = 5 \: \: \\ hence \: it \: is \: false[/tex]

Answer:

10 stickers.

Step-by-step explanation:

Let's say that Mandy has m stickers, and Priscilla has p stickers.

m = 1/4p

6/5(m + 28) = p + 28

6/5(1/4p + 28) = p + 28

1/4p + 28 = 5/6p + 23 and 1/3

5/6p - 1/4p = 28 - 23 and 1/3

10/12p - 3/12p = 84/3 - 70/3

7/12p = 14/3

p = (14/3)(12/7)

p = 8

At the beginning, Priscilla had 8 stickers. That means that Mandy had 1/4 * 8 = 8 / 4 = 2 stickers.

So, in the packet, there were 8 + 2 = 10 stickers.

Hope this helps!

Answer:

5 ways

Step-by-step explanation:

We have to name the cases.

1. 4 - 0 - 0 - 0

2. 3 - 1 - 0 - 0

3. 2 - 2 - 0 - 0

4. 2 - 1 - 1 - 0

5. 1 - 1 - 1 - 1

We don't name 0 - 0 - 1 - 3 or 0 - 1 - 1 - 2 etc. because it is the same thing.

There are 35 ways to distribute 4 identical balls among 4 identical boxes

The given parameters are:

Balls, n = 4

Boxes, r = 4

The number of ways is then calculated as:

(n + r - 1)C(r - 1)

This gives

(4 + 4 - 1)C(4 - 1)

Evaluate

7C3

Apply the combination formula

7C3 = 7!/((7 - 3)! * 3!)

Evaluate the difference

7C3 = 7!/(4! * 3!)

Evaluate the expression

7C3 = 35

Hence, the number of ways is 35

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Answer:

0.001

Step-by-step explanation:

Here, the aim is to support the null hypothesis, Ha. Where Ha: p > 0.5. Which means we are to reject null hypothesis H0. Where H0: p = 0.5.

The higher the pvalue, the higher the evidence of success. We know If the pvalue is less than level of significance, the null hypothesis H0 is rejected.

Hence the smallest possible value 0.001 is preferred as the pvalue because it corresponds to the sample evidence that most strongly supports the alternative hypothesis that the method is effective

Answer:

amount 291 I'm not sure abt the others

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 3

For the alternative hypothesis,

H1: µ > 3

This is a right tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 3.1

µ = population mean = 3

s = samples standard deviation = 0.5

n = number of samples = 100

t = (3.1 - 3)/(0.5/√100) = 2

We would determine the p value using the t test calculator. It becomes

p = 0.024

Alpha = 1 - confidence level = 1 - 0.95 = 0.05

Since alpha, 0.05 > than the p value, 0.024, then we would reject the null hypothesis. Therefore, at 95% confidence level, it can be concluded that the mean of the population is significantly greater than 3.

Answer:54

volume:side*side*side

side:1 cm*1 cm *1 cm      

answer=icm

Answer:

[tex] \frac{1}{2} {r}^{2} ( \frac{1}{2}\pi - 1)[/tex]

option D is the right option.

solution,

Area of shaded region:

Area of sector-Area of ∆

[tex] = \frac{90}{360} \times \pi {r}^{2} - \frac{1}{2} \times r \times r \\ = \frac{1}{4} \pi {r}^{2} - \frac{1}{2} {r}^{2} \\ = \frac{1}{2} {r}^{2} ( \frac{1}{2} \pi - 1)[/tex]

Hope this helps...

Good luck on your assignment..

The  expression in square units that represents the area of the shaded segment of C. Geometry is [tex]\frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]

Since we know that

The area of the shaded region = Area of the sector - an area of a triangle

So,

[tex]= \frac{90}{360} \times \pi r^2 - \frac{1}{2} \times r\times r\\\\ = \frac{1}{4}\pi r^2 - \frac{1}{2}r^2 \\\\= \frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]

hence, The  expression in square units that represents the area of the shaded segment of C. Geometry is [tex]\frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]

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Answer:

the answer is: 9.25

Step-by-step explanation:

the cube root of 792 is approximately 9.252.

To find the cube root of 792, we can use the relationship between cube roots and cube numbers.

If the cube root of 99 is approximately 4.626, we can use this information to find the cube root of 792.

Let's calculate the cube root of 792 using the relationship:

(cube root of 792) = (cube root of 99) * (cube root of 8)

Since 792 is equal to 99 multiplied by 8 (792 = 99 * 8), we can rewrite the equation as:

(cube root of 792) = (4.626) * (cube root of 8)

Now, we need to find the cube root of 8:

(cube root of 8) = 2

Substituting this value back into the equation, we get:

(cube root of 792) = (4.626) * (2) = 9.252

Therefore, the cube root of 792 is approximately 9.252.

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Answer:

3 GB

Step-by-step explanation:

Since the family has used 1 GB in 10 days. With the same rate in 30 days they would have 3 GB