Consider the recursively defined set S: Basis Step: The unit circle is in S. Recursive Step: if x is in S, then x with a line through any diameter is in S. (a) (4 points) Prove that: is in S. (b) ( 6 points) For an element x ∈ S, define V (x) be the number of vertices (i.e. the number of intersections of lines and arcs and lines with lines), let E(x) to be the number of edges (line segments or arcs between vertices), and let F(x) be the number of faces. Prove that for any x ∈ S that F + V = E + 1. (Please use structural induction.)

Answer:

The amount of white fabric to coloured fabric as a ratio is 20:11

Step-by-step explanation:

We are given that For each 11 mm of colored fabric Nick uses to make his curtains, he also uses 2 cm of white fabric.

Length of colored fabric = 11 mm

Length of White fabric = 2 cm

1 cm = 10 mm

2 cm = 20 mm

So, length of white fabric = 20 mm

So, Ratio of the amount of white fabric to coloured fabric = [tex]\frac{20}{11}[/tex]

Hence the amount of white fabric to coloured fabric as a ratio is 20:11

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

Where

σ = population standard Deviation

n = number of samples

From the information given

1) x = 17.5

σ = 5

n = 50

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645

Margin of error = 1.645 × 5/√50 = 1.16

Confidence interval = 17.5 ± 1.16

Answer:

3 would be the initial value so B

Step-by-step explanation:

Answer:

The answer is There were initially 3 bacteria in the culture.

Step-by-step explanation:

Answer:

d) The t-distribution with 18 degrees of freedom

Step-by-step explanation:

If we have the population standard deviation, we use the standard normal distribution.

Otherwise, if we only have the standard deviation for the sample, we use the t-distribution.

The number of degrees of freedom is the sample size subtracted by 1.

In this problem:

Sample size of 19, we have the standard deviation for the sample.

So the t-distribution will be used to solve this question, with 19-1 = 18 degrees of freedom.

So the correct answer is:

d) The t-distribution with 18 degrees of freedom

In a hypothesis test where the population standard deviation is unknown and estimated by the sample standard deviation, we use the t-distribution with degrees of freedom equal to the sample size minus one. In this case, the distribution of the test statistic would follow a t-distribution with 18 degrees of freedom.

In this particular case, the sample size is 19, and the population standard deviation is unknown and estimated by the sample standard deviation. Because of these conditions, the t-distribution would be used to determine the test statistic. Specifically, we would use the t-distribution with degrees of freedom equaling the sample size minus one, i.e., 18. Therefore, the correct answer among the options given is 'The t-distribution with 18 degrees of freedom'.

For example, suppose we have a set of samples from an unknown population, we compute the sample standard deviation and use it as an estimator of the actual unknown population standard deviation. In such cases, we use the t-distribution with (n-1) degrees of freedom, where n is our sample size. Here, it would be the t-distribution with 18 degrees of freedom because our sample size is 19.

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Answer:

A

Step-by-step explanation:

The simplified expression is x+5.

To simplify the expression x^2 +3x−10 /x−2, you can use polynomial long division or factorization.

Here's how to do it by factorization:

Factor the numerator

x^2 +3x−10:

x^2 +3x−10=(x+5)(x−2)

Rewrite the expression with the factored form of the numerator:

(x+5)(x−2)/ x−2

​Cancel out the common factor of x−2:

(x−2) /(x+5) /x−2

The simplified expression is x+5.

So, x^2 +3x−10/ x−2​ =x+5.

The volume of a spherical boulder with a diameter of 18 ft can be calculated using the formula V = 4/3πr³, with 'r' being the radius of the sphere. By substituting the radius of 9 ft (half of 18 ft), we find that the volume is approximately 3053.62 cubic feet.

To find the volume of a sphere, we use the formula: V = 4/3πr³, where 'r' is the radius of the sphere. The radius can be found from the diameter by dividing it by 2; therefore, for this boulder, the radius will be 18 ft/2 = 9 ft. Substituting 'r' into the volume equation: V = 4/3 * 3.14 * (9ft)³ = 3053.62 cubic feet. Therefore, the spherical boulder has a volume of approximately 3053.62 cubic feet.

To find the volume of a spherical boulder, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the boulder is 18 ft, we can find the radius by dividing the diameter by 2, which gives us a radius of 9 ft. Plugging this value into the formula, we get V = (4/3)π(9 ft)³. Using the value of π as 3.14, we can calculate the volume:

V = (4/3)(3.14)(9 ft)³ = (4/3)(3.14)(729 ft³) = 3053.96 ft³

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Answer:

1: 20

2: 2020

Step-by-step explanation:

just got it man so ima go yeet

The group will have  290 members in the year 2020

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here, the equation is  y = 14x + 10 and we are required to have 290 members  thus,                     290=14x + 10

                                                 x= 280/14

                                                 x = 20 years

Hence the number of years required to achieve 290 members is equal to 20 years.

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The theoretical probability of landing on orange when spinning a spinner with five colors is 1/5.

Since there are five colors on the spinner, each color has an equal chance of landing, so the theoretical probability of landing on orange is 1 out of 5, or 1/5.

Answer:

The United states is rich in resources

Step-by-step explanation:

Got it right on study island:))

Final answer:

The opening sentence that best fits the paragraph's context is 'The United States is rich in resources,' as it introduces the theme of resource consumption and sustainability within the U.S.

Explanation:

The best opening sentence that goes with the details in the paragraph provided is option D: The United States is rich in resources. This opening sentence sets the context for discussing how the people in the United States have historically acted as if their resources were unlimited. It leads into the realization that there must be a more prudent approach to using resources going forward, as indicated in the paragraph. The passage indicates a shift in understanding within the United States regarding resource consumption and the necessity for wiser use, aligning well with the recognition of resource richness and the implication of historical abundance.

Answer:

  -4, 2

Step-by-step explanation:

The equation can be factored as ...

  (x +4)(x -2) = 0

This has solutions that make the factors zero:

  x = -4, x = 2

The solution set is {-4, 2}.

Answer:

7.95.

Step-by-step explanation:

Absolute value is the positive version of that number.

The student's question involves a statistical hypothesis test to compare the mean response times between drug-injected and control rats. The calculation of beta, representing the risk of Type II error, requires more information not provided in the question.

The given scenario involves setting up a hypothesis test to determine if the mean response time for drug-injected rats is significantly different from the control group (rats not injected with the drug) with a known mean response time of 1.2 seconds. The null hypothesis would state that the mean response time for drug-injected rats (μ) is equal to 1.2 seconds (H0: μ = 1.2), while the alternative hypothesis would state that the mean response time is greater than 1.2 seconds (Ha: μ > 1.2).

Given that the sample mean response time for drug-injected rats is 1.05 seconds, which is actually lower than the control mean, this initially suggests that the drug does not increase the response time but rather decreases it or has no effect. However, as the question indicates a confusion with the typo in sample mean, we will proceed with testing the hypothesis based on the provided assumption that the drug-injected rats have a mean response time of 1.1 seconds.

To calculate the value of beta (the probability of a Type II error, which occurs when the null hypothesis is not rejected even though it is false), we would need to define the rejection regions for our test. The rejection region is typically defined based on the significance level (alpha) and the distribution of the test statistic under the null hypothesis. Without specifics such as the sample size, standard deviation, and significance level for defining the rejection regions, we cannot calculate beta directly.

Answer:

don't bother commenting im a bot

Step-by-step explanation:

Answer:

5/18 I believe

Step-by-step explanation:

Answer:

Is there any picture ?

Step-by-step explanation:

Answer:

its 2,21

Step-by-step explanation:

The only point that is in the circle of radius 5 is option A: (2, √21).

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

The distance between a point (x, y) and the origin is:

d = √(x² + y²).

Of the given options, the only one that meets this condition is the one in option A. (2, √21).

If we find the distance to the origin, we get:

d = √(2² + √21²) = √(4 + 21) = 5.

So that is the correct option.

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Complete question:

Which point is on the circle centered at the origin with a radius of 5 units?

Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

A. (2, StartRoot 21 EndRoot)

B. (2, StartRoot 23 EndRoot)

C. (2, 1)

D. (2, 3)

Answer:26.6 miles

Step-by-step explanation:

Given

Charlie distance to his destination  is a linear function of total driving time

suppose distance d is related to time t as

[tex]d=mt+c\quad \ldots(i)[/tex]

at [tex]d=49\ miles[/tex] after [tex]t=15\ min[/tex]

Substitute in (i)

[tex]49=m(15)+c\quad \ldots(ii)[/tex]

at [tex]d=32.2\ miles[/tex] after [tex]t=39\ min[/tex]

[tex]32.2=m(39)+c\quad \ldots(iii)[/tex]

Solving (ii) and (iii) we get

[tex]m=-0.7[/tex]

substitute in eq (ii) we get

[tex]c=59.5[/tex]

so after [tex]t=47\ min[/tex]  

[tex]d=(-0.7)47+59.5[/tex]

[tex]d=59.5-32.9=26.6\ miles[/tex]

So 26.6 miles is left to travel after 47 minutes

Answer:

9.

Step-by-step explanation:

[tex]f(x) = -(x - 3)^2 + 9[/tex] is a parabola in its vertex form. For clarity, let [tex]f(x) = a (x - h)^2 + k[/tex] represent this function.

Note that [tex]a[/tex], the leading coefficient, is negative. Therefore, this parabola opens downwards. The vertex of the parabola would be [tex](h,\, k)[/tex], which in this question is the point [tex](3,\, 9)[/tex]. Since the parabola opens downwards, that vertex would be a local maximum (a crest) on its graph.

Before concluding that the maximum area of this rectangle is [tex]9[/tex], make sure that [tex](3,\, 9)[/tex] is indeed on the graph of [tex]y = f(x)[/tex].

The length of a rectangle should be positive. Since [tex]x[/tex] represents the length of this rectangle, [tex]x > 0[/tex]. Also, since the perimeter should be less than [tex]12[/tex], the length of one side should be less than [tex]12 / 2 = 6[/tex]. Therefore, the domain of [tex]f[/tex] should be the open interval [tex](0,\, 6)[/tex]. (Endpoints not included.)

Indeed, [tex]x = 3[/tex] is in that interval. [tex](3,\, 9)[/tex] would be on the graph [tex]y = f(x)[/tex]. Therefore, [tex]9[/tex] is indeed the maximum area of this rectangle.

Side note: if the domain is a closed interval (i.e., endpoints included,) then consider checking the endpoints, as well.

Answer:

Step-by-step explanation:

9

Answer:

Jada can do 48 loads of laundry.

Step-by-step explanation:

There are 6 cups of detergent in the bottle. If Jada uses 1/8 cup of detergent each load you would have to find out how many 1/8 cups are in 6 cups. There are 8, 1/8 cups in 1 cup. So you would do 6 time 8, which equals 48 loads.

Answer: I literally gust took the the test and the answer is 112.

Your welcome!!

Answer:

We conclude that the proportion of adults who totally abstain from alcohol​ has changed.

Step-by-step explanation:

We are given that in 1943​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?"

Of the 1100 adults​ surveyed, 429 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 352 in

Let p = proportion of adults who totally abstain from alcohol.

where, p = [tex]\frac{429}{1100}[/tex] = 0.39

So, Null Hypothesis, [tex]H_0[/tex] : p = 39%      {means that the proportion of adults who totally abstain from alcohol​ has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 39%      {means that the proportion of adults who totally abstain from alcohol​ has changed}

The test statistics that would be used here One-sample z proportion statistics;

                    T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adults who totally abstain from alcohol = [tex]\frac{352}{1100}[/tex] = 0.32

           n = sample of adults surveyed = 1100

So, test statistics  =  [tex]\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }[/tex]  

                              =  -4.976

The value of z test statistics is -4.976.

Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Since our test statistics doesn't lie within the range of  critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of adults who totally abstain from alcohol​ has changed.

The expected number of days until the prisoner reaches freedom is 2.8 days.

To find the expected number of days until the prisoner reaches freedom, we can use the concept of expected value. We'll multiply the number of days it takes to reach freedom through each door by the probability of choosing that door, and then sum up these values.

Let's denote:

[tex]- \( X_1 \)[/tex] as the number of days it takes to reach freedom through door 1 (returns to the cell after 2 days).

[tex]- \( X_2 \)[/tex] as the number of days it takes to reach freedom through door 2 (returns to the cell after 4 days).

[tex]- \( X_3 \)[/tex] as the number of days it takes to reach freedom through door 3 (direct freedom after 1 day).

Given the probabilities:

- Probability of choosing door 1: [tex]\( P(X_1) = 0.3 \)[/tex]

- Probability of choosing door 2: [tex]\( P(X_2) = 0.5 \)[/tex]

- Probability of choosing door 3: [tex]\( P(X_3) = 0.2 \)[/tex]

Now, we calculate the expected value:

[tex]\[ E[X] = P(X_1) \times X_1 + P(X_2) \times X_2 + P(X_3) \times X_3 \][/tex]

[tex]\[ E[X] = 0.3 \times 2 + 0.5 \times 4 + 0.2 \times 1 \][/tex]

[tex]\[ E[X] = 0.6 + 2 + 0.2 \][/tex]

[tex]\[ E[X] = 2.8 \][/tex]

So, the expected number of days until the prisoner reaches freedom is 2.8 days.

Answer:

22 millimetres

Step-by-step explanation:

[tex]width \: of \: rectangle \\ = \frac{area}{length} \\ = \frac{198}{9} \\ = 22 \: millimeters \\ [/tex]

Answer:

2/10 or simplified, 1/5

Step-by-step explanation:

5 are purple out of 10 flowers so 5/10. 3 are pink so 3/10. That leaves 2/10 left, and depending on what your teacher prefers, the simplified answer is 1/5. I hope this helps.

Answer:

Car: Exponential Function

Train: Exponential Function

Step-by-step explanation:

The consecutive differences are quite far from being constant. However, the consecutive ratios are quite close to being constant, being approximately 0.49 for every increase in 2 seconds.Therefore, the speed of the car is best modeled by an exponential function. The consecutive ratios for the trains are quite close to being constant, being approximately 0.56 for every increase in 2 seconds. Therefore, the speed of the train is best modeled by an exponential function.

The data of car is exponential function.

The data of truck is exponential function.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

As, the difference between two consecutive terms is not constant.

but the ratios are quite close to being constant,  approximately 0.49 for every increase in 2 seconds.

The consecutive ratios for the trains are 0.56 for every increase in 2 seconds.

Thus, the speed of the car and truck is an exponential function.

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Answer:

[tex]a_n = a_o +(n-1) d[/tex]

[tex] 22.5 = 15 +(2-1) d[/tex]

[tex] d = 22.5-15 =7.5[/tex]

The general expression is:

[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]

Step-by-step explanation:

For this case we have the following arithmetic sequence given:

15, 22.5, 30,37.5

In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:

[tex]a_n = a_o +(n-1) d[/tex]

Where [tex]a_n[/tex] is the nth term [tex]a_o[/tex] the initial value for the sequence and d the common difference. For this case we have that [tex]a_o =15[/tex]

And for the first term we have:

[tex] 15= 15 +(1-1)d[/tex]

For the second term we have this:

[tex] 22.5 = 15 +(2-1) d[/tex]

And solving for the value of d we got:

[tex] d = 22.5-15 =7.5[/tex]

And for the 3th term we have:

[tex] a_3= 15 +(3-1)*7.5 =30[/tex]

And for the 4th term

[tex]a_4 =15 +(4-1)*7.5 =37.5[/tex]

So then our expression is correct and would be given by:

[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Answer:

7 boys

Step-by-step explanation:

252525=3*5²*7*13*37

353535=3*5*7²*13*37

(252525; 353535)= 3 * 5 * 7 * 13 * 37 = 50505

The greatest number of teams possible=50505

252525=5*50505

353535=7*50505

So, are 50505 teams, each containing 5 girls and 7 boys.

7 boys

Answer:

r =45.5 units

Step-by-step explanation:

The diameter is twice the radius, or the radius is 1/2 the diameter

r = d/2

r = 91/2

r =45.5 units

Answer: 45.5

Step-by-step explanation: 91/2 because to find the diameter you have to multiply the radius by 2 and now we need to reverse it