Which of the following measurements for triangle ABC will result in no solution and which will result in two solutions for angle B? Justify your answer. Triangle 1: A = 25°, a = 14 m, b = 18 m Tri

Answer:

Step-by-step explanation:

2

What?

joshuasalazar697 avatar

A because u should have gotten a 3x after adding them together since u do what is inside the () before anything

fionaferlich1 avatar

3+x does not equal 3x

joshuasalazar697 avatar

y not

fionaferlich1 avatar

because 3x equals x times x times x not 3+x

joshuasalazar697 avatar

but why is it d

joshuasalazar697 avatar

they did it right u have to divide it from the right to the left

fionaferlich1 avatar

a rule of inequalities is when you divide by a negative the sign switches. so because u had to divide the entire thing by -6 it should be x is greater than -1

joshuasalazar697 avatar

no u have to divide it by positive 6 cause u are taking it the 6 from the right and moving it under the 6 from the left wich u would divide

fionaferlich1 avatar

u always divide by the coefficient of x and that's -6

joshuasalazar697 avatar

no cause since u moved all the letters to the right and all the lone numbers to the left u have to take that last one and divide it from the one with the x

fionaferlich1 avatar

the one with the x is the coefficient of x which is -6

joshuasalazar697 avatar

yeah i know that ut u don't divide the 6 from the -6x like u gonna divide -6x by 6

joshuasalazar697 avatar

also if i am wrong what happened to the 3 and why did it turn to an 18

fionaferlich1 avatar

so say that's what you're supposed to do (which it is ) but then u would get -x>1 and x must be positive

joshuasalazar697 avatar

i should have paid attention in algebra no wonder I don't get geometry but geometry is way easier

joshuasalazar697 avatar

i see what u are getting to now

joshuasalazar697 avatar

still don't see how 3 turned into 18

joshuasalazar697 avatar

i just say this hole thing is written wrong from the start and made it all wrong

there is ur explanation

Answer:

d

Step-by-step explanation:

since when u divide by a negative it switches signs

Answer:

Let ten's place digit =x and unit place digit =y

Number=10x+y

x+y=5 ...(i)

10x+y−9=10y+x

9x−9y=9x−y=1 ...(ii)

from (i) and (ii) we get,

x=3,y=2

∴Number=10×3+2=32.

Step-by-step explanation:

Hope it helps!

Exponents represent how many times a number is multiplied by itself. In this case, we have a negative exponent of -1/15625. To simplify this, we can rewrite it as 1 over the base number raised to the positive exponent 1/15625.

So, if the base number is x, then the expression can be written as:
x^(-1/15625) = 1/x^(1/15625)
This means that we take the reciprocal of the base number and raise it to the positive exponent 1/15625. Note that since the exponent is very small, the value of x^(1/15625) will be very close to 1. Therefore, the reciprocal will also be very close to 1, but slightly smaller.
The given value is -1/15625. To express this as an exponent with a base, you can rewrite it as a fraction with a negative exponent:
-1/15625 = (-1)(1/15625)
Now, let's find the exponent for the denominator. Since 15625 is equal to 5^6, we can rewrite the fraction as:
(-1)(1/5^6)
Finally, express the fraction as a single exponent:
(-1)(5^-6)
So, -1/15625 can be written as (-1)(5^-6) in terms of exponents.

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Answer:

Mean = 43.969

Standard deviation = 12.341

Step-by-step explanation:

Given the data :

36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, 50.06

The sample mean :

Σx / n = 351.75 / 8 = 43.969

Sample standard deviation :

√Σ(x - mean)²/n-1

√[(36.45-43.969)² + (67.90-43.969)² + (38.77-43.969)² + (42.18-43.969)² + (26.72-43.969)² + (50.77-43.969)² + (38.9-43.969)² + (50.06-43.969)² ] / ((8 - 1)

Standard deviation = 12.341

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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Answer:

2x + 3x^2 (4x - 5)

2x + 12x^3 - 15x^2

12x^3 - 15x^2 + 2x

Degree - 3

Terms - 3 (Trinomial)

12x³-15x²+2x is simplified equation of 2x+3x²(4x-5) and degree is 3 with three terms.

An expression is a combination of numbers, variables and operators.

The given expression is two x plus three x square times of four x minus five.

2x+3x²(4x-5)

Use distributive law and simplify

2x+3x²(4x)+3x²(-5)

2x+12x³-15x²

12x³-15x²+2x

The degree of a polynomial is the highest power of its variable. The degree of the polynomial is three.

There are three terms in 12x³-15x²+2x.

Hence 12x³-15x²+2x is simplified equation and degree is 3 with three terms.

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The estimate value of the standard deviation of the population ( manufacturing process) is 0.125..

The standard deviations is estimated to be one fourth of the sample range (as most of data values are within two standard deviations of the mean).

We have given that,

A sample of manufacturing process.

Sample size, n = 5

Mean of sample ranges = 0.50

we have to calculate the estimate of standard deviations of population.

thus , we estimate the standard deviations as fourth of the mean of the sample ranges is

S = Mean of sample ranges/4

=> S = 0.50/4

=> S = 0.125

Hence, the standard deviation of the population is estimated as 0.125..

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To prove that if O is an optimal solution to a linear program, then O is a vertex of the feasible region, we can use the following argument:

Assume that O is an optimal solution to a linear program.

By definition, an optimal solution maximizes or minimizes the objective function while satisfying all the constraints.

Suppose O is not a vertex of the feasible region.

If O is not a vertex, it must lie on an edge or in the interior of a line segment connecting two vertices.

Consider two neighboring feasible solutions, A and B, that define the line segment containing O.

Since O is not a vertex, there exists a feasible solution on the line segment between A and B that has a higher objective function value (if maximizing) or a lower objective function value (if minimizing) than O.

This contradicts our assumption that O is an optimal solution since there exists a feasible solution with a better objective function value.

Therefore, our initial assumption that O is not a vertex must be false.

Thus, O must be a vertex of the feasible region.

By contradiction, we have shown that if O is an optimal solution to a linear program, then O must be a vertex of the feasible region.

The publisher should produce and sell 2356 books so that the production costs will equal the money from sales.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $24,149. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $21.75 per book.

Assume the number of books to be printed be [x].

Then, we can write -

24149 + 11.50x = 21.75x

21.75x - 11.5x = 24149

10.25x = 24149

x = 2356 books

Therefore, the publisher should produce and sell 2356 books so that the production costs will equal the money from sales.

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Answer:

18 miles.

Step-by-step explanation:

You start with 12 miles and then you first need to figure out what 5% of that is by doing the equation x/12 = 5/100 and you will then get .6. Then you multiply that number by 10 (one for each week) getting 6. Then you add the 6 to your starting total to get 18.

See the attached picture:

A construction company is designing a new playground. They plan to use a combination of rectangular and circular areas. The rectangular area will be used for a basketball court, while the circular area will be used for a play area.

The rectangular area will have a length of x + 5 meters and a width of x meters, while the circular area will have a radius of x meters. The combined area of the rectangular and circular areas will be 400 square meters.

The construction company needs to determine the value of x that will minimize the cost of constructing the playground. The cost of constructing the basketball court is $50 per square meter, while the cost of constructing the play area is $75 per square meter.

To solve this problem, we need to find the minimum cost of constructing the playground, which is given by a degree 3 polynomial equation.

Let C(x) be the cost of constructing the playground, then we have:

C(x) = 50(x + 5)x + 75πx^2

We need to find the value of x that minimizes C(x). To do this, we take the derivative of C(x) with respect to x and set it equal to 0:

C'(x) = 50(2x + 5) + 150πx = 0

Simplifying, we get:

4x + 10 + 3πx = 0

Rearranging and factoring out x, we get:

x(4 + 3π) = -10

Therefore, the value of x that minimizes the cost of constructing the playground is:

x = -10 / (4 + 3π)

This is the solution to the degree 3 polynomial equation. However, since x represents a length, it must be positive. Therefore, we reject the negative value and the final answer is:

x ≈ 2.9 meters

This means that the rectangular area will have a length of approximately 7.9 meters and a width of approximately 2.9 meters, while the circular area will have a radius of approximately 2.9 meters.

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Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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Answer:

E 60+60+60=180 sum of triangle's angels must be 180

Answer:

(p/3)-3=114

114 plus 3 = 117 (one-third of the novel)

117 x 3 = p = 351 (entire novel)

Step-by-step explanation:

(p/3)-3=114

114 plus 3 = 117 (one-third of the novel)

117 x 3 = p = 351 (entire novel)

The following statements are proved using mathematical induction:

(b) Prove that for any positive integer n,6 evenly divides \(7^n -1\).

(c) Prove that for any positive integer n,4 evenly divides \(11^n-7^n\).

(e) Prove that for any positive integer n,2 evenly divides \(n^2-5n+2\).

(b) Prove that for any positive integer n, 6 evenly divides \(7^n - 1.\)

Step 1: Base case

Let's check if the statement holds true for the base case, n = 1.

For n = 1, we have  \(7^1 - 1 = 6\), which is divisible by 6. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 6 evenly divides  \(7^k - 1\).

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \(7^{(k + 1)} - 1.\)

We can rewrite it as  \(7 * 7^k - 1.\)

Using the assumption from the inductive hypothesis, we know that \(7^k - 1\)is divisible by 6.

Since 7 is congruent to 1 (mod 6), we have \(7 * 7^k\) ≡ \(1 * 1^k\) ≡ 1 (mod 6).

Therefore,  \(7^{(k + 1)} - 1\) ≡ 1 - 1 ≡ 0 (mod 6), which means 6 evenly divides \(7^{(k + 1)} - 1.\)

By the principle of mathematical induction, we can conclude that for any positive integer n, 6 evenly divides  \(7^n - 1\).

(c) Prove that for any positive integer n, 4 evenly divides  \(11^n - 7^n.\)

Step 1: Base case

For n = 1, we have \(11^1 - 7^1 = 11 - 7 = 4\), which is divisible by 4. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 4 evenly divides  \(11^k - 7^k.\)

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \(11^{(k + 1)} - 7^{(k + 1)}.\)

We can rewrite it as  \(11 * 11^k - 7 * 7^k.\)

Using the assumption from the inductive hypothesis, we know that \(11^k - 7^k\) is divisible by 4.

Since 11 is congruent to 3 (mod 4) and 7 is congruent to 3 (mod 4), we have  \(11 * 11^k\) ≡ \(3 * 3^k\) ≡ \(3^{(k+1)}\) (mod 4) and  \(7 * 7^k\) ≡ \(3 * 3^k\) ≡ \(3^{(k+1)}\) (mod 4).

Therefore,  \(11^{(k + 1)} - 7^{(k + 1)}\) ≡ \(3^{(k+1)} - 3^{(k+1)}\) ≡ 0 (mod 4), which means 4 evenly divides  \(11^{(k + 1)} - 7^{(k + 1)}.\)

By the principle of mathematical induction, we can conclude that for any positive integer n, 4 evenly divides \(11^n - 7^n.\)

(e) Prove that for any positive integer n, 2 evenly divides \(n^2 - 5n + 2.\)

Step 1: Base case

For n = 1, we have  \(1^2 - 5(1) + 2 = 1 - 5 + 2 = -2,\)  which is divisible by 2. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 2 evenly divides  \(k^2 - 5k + 2.\)

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \((k + 1)^2 - 5(k + 1) + 2.\)

Expanding and simplifying, we get  \(k^2 + 2k + 1 - 5k - 5 + 2 = k^2 - 3k - 2.\)

Using the assumption from the inductive hypothesis, we know that 2 evenly divides  \(k^2 - 5k + 2\).

Since 2 evenly divides -3k, and 2 evenly divides -2, we can conclude that 2 evenly divides  \(k^2 - 3k - 2\).

By the principle of mathematical induction, we can conclude that for any positive integer n, 2 evenly divides  \(n^2 - 5n + 2\).

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Total ways can occur is 19,653,800.

What is Combination?

Combinations are ways to choose elements from a larger set in mathematics where the order of the elements is irrelevant. Repetition is prohibited and the order of the elements does not matter in a combination, which is a subset of items.

The number of combinations of 51 things chosen 10 at a time, represented as C, determines the number of possibilities to choose 10 finalists from 51 contestants (51, 10).

Combinations are calculated as follows: C (n, k)=\(n! / (k! (n-k)!).\)

Consequently, there are three options to choose 10 finalists from the pool of 51 applicants:\(C(51, 10) = 51! / (10! (51-10)!) = 51! / (10! 41!) = 19,653,800.\\\)

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in the miss America pageant, 51 contestants must be narrowed down into 10 finalists. The total number of ways that can occur is 19,653,800.

What is Combination?

In mathematics, combinations are strategies to select components from a bigger set where the order of the elements is unimportant. In a combination, which is a subset of items, repetition is not permitted and the position of the parts is irrelevant.

The possibility of selecting 10 finalists from 51 contenders is determined by the number of combinations of 51 things picked 10 at a time, denoted as C. (51, 10).

Combinations are calculated as follows: C (n, k)= \(\frac{n!}{k!(n-k)!}\)

Consequently, there are three options to choose 10 finalists from the pool of 51 applicants: 19653800

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The 98% confidence interval to estimate the average number of hours studying for the exam is approximately 6.61 to 7.99.

Hence option D is correct.

Given that,

Number of students in the statistics class: 115

Sample size: 41 students

Average number of hours studied by the sample: 7.3 hours

Standard deviation of the sample: 1.9 hours

Desired confidence level: 98%

To accurately the problem and calculate the 98% confidence interval,

Use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

Where:

Sample Mean is the average number of hours studied by the sample (7.3 hours).

Z is the critical value corresponding to the desired confidence level (98%). For a 98% confidence level, the Z-value is approximately 2.326.

Standard Error is calculated by dividing the standard deviation of the sample (1.9 hours) by the square root of the sample size (41 students).

Calculate the confidence interval: Standard Error = 1.9 / √41 ≈ 0.2965

Confidence Interval = 7.3 ± (2.326 x 0.2965)

Now, Calculate the upper and lower bounds of the confidence interval:

Upper Bound = 7.3 + (2.326 * 0.2965) ≈ 7.3 + 0.6895 ≈ 7.9895

Lower Bound = 7.3 - (2.326 * 0.2965) ≈ 7.3 - 0.6895 ≈ 6.6105

Therefore, the 98% confidence interval to estimate the average number of hours studying for the exam is approximately 6.61 to 7.99.

Based on the given options, the correct answer would be:

d- 6.11 and 8.49

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The probability that the Yankees scored fewer than 5 runs is 0.805.

It is the chance of an event occurring from a total number of outcomes.

The formula for probability is:

Probability = Number of required events / Total number of outcomes.

We have,

We will use conditional probability.

P(A/B) = P(A∩B) / P(B)

The probability that the Yankees won a game.
= 0.59

This means,

The probability that the Yankees lost a game.
P(A) = 1 - 0.59 = 0.41

The probability that the Yankees scored 5 or more runs.

= 0.45

P(B) = The probability that the Yankees scored fewer than 5 runs.

So,

The probability that the Yankees lose and score fewer than 5 runs.

P(A ∩ B) = 0.33

Now,

The probability that the Yankees scored fewer than 5 runs.

P(B/A) =P(A∩B) / P(A)

So,

= 0.33 / 0.41

= 0.8048

= 0.805

Thus,

The probability that the Yankees scored fewer than 5 runs is 0.805.

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The amount credited from the partial payment made during the discount period is $1,470. The balance on the invoice after the partial payment was made is $1,530.

The payment terms "4/10n/45" indicate that a 4% discount is applicable if the payment is made within 10 days, and the full amount is due within 45 days. Marcus made a partial payment of $1,500 during the discount period.

To calculate the amount credited, we first determine the discount amount by multiplying the invoice amount ($3,000) by the discount percentage (4%). This gives us a discount of $120. Since Marcus made a partial payment of $1,500, we subtract the discount amount from the partial payment to find the credited amount. Therefore, $1,500 - $120 = $1,380. Rounded to the nearest cent, the amount credited is $1,380.

To calculate the balance on the invoice after the partial payment was made, we subtract the credited amount from the remaining balance. The remaining balance is the invoice amount ($3,000) minus the partial payment ($1,500), which equals $1,500. Subtracting the credited amount of $1,380 from this balance, we get $1,500 - $1,380 = $120. Rounded to the nearest cent, the balance on the invoice after the partial payment is $120.

In summary, the amount credited from the partial payment made during the discount period is $1,380, and the balance on the invoice after the partial payment was made is $120.

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The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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Answer:

6

Step-by-step explanation:

5*6 is 30 - 7 is 23

work backwards

A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.

= 2 1/5% / 100

= (2 + (1/5)) / 100

= 0.022

A value that is less than 0.022 from the given data is 0. 0215.

Therefore, a value less than 2 1/5% is 0. 0215.

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Use a 0.01 significance level, it can be concluded the proportion of students smoking is not the same at all four colleges.

The null and alternative hypotheses in this case are:

Null hypothesis: H0: The proportion of students smoking is the same at all four colleges.

Alternative hypothesis: Ha: The proportion of students smoking is not the same at all four colleges.

We have observed number of smokers and non-smokers in all four colleges, which is shown below:

Name of College A B C D

Number of Smokers 17 26 11 34

Number of non-smokers 83 74 89 66

To test this hypothesis, we calculate the expected number of smokers and non-smokers under the null hypothesis. If the null hypothesis is true, the expected number of smokers and non-smokers would be equal in all four colleges.

The expected number of smokers in each college can be found by multiplying the total number of students in that college with the overall proportion of students who smoke. Since we don't have the overall proportion of students who smoke, we can calculate it from the data. The total number of students in all four colleges is 100*4=400.

The total number of smokers is 17+26+11+34=88.

So, the overall proportion of students who smoke is 88/400=0.22.

The expected number of smokers in each college is:

Expected number of smokers in A = 100*0.22 = 22

Expected number of smokers in B = 100*0.22 = 22

Expected number of smokers in C = 100*0.22 = 22

Expected number of smokers in D = 100*0.22 = 22

The expected number of non-smokers in each college can be found by subtracting the expected number of smokers from the total number of students in each college.

Expected number of non-smokers in A = 100 - 22 = 78

Expected number of non-smokers in B = 100 - 22 = 78

Expected number of non-smokers in C = 100 - 22 = 78

Expected number of non-smokers in D = 100 - 22 = 78

To test the hypothesis, we calculate the test statistic X², which is given by:

X² = Σ(observed - expected)²/expected

where Σ is taken over all four colleges.

The observed and expected values are shown below:

Name of College A B C D

Number of Smokers 17 26 11 34

Number of non-smokers 83 74 89 66

Expected number of smokers 22 22 22 22

Expected number of non-smokers 78 78 78 78

The test statistic X² is given to be 17.832. The degrees of freedom for the test is (4-1) = 3, since we are estimating one parameter (the overall proportion of students who smoke) from the data.

Using the chi-square distribution with 3 degrees of freedom and a 0.01 significance level, we can find the critical value. The critical value is the value of X² such that the area to the right of X² is 0.01. We can find this value using a chi-square distribution table or a calculator.

The critical value of X² with 3 degrees of freedom and a 0.01 significance level is 11.345.

We can see that the test statistic X² = 17.832 is greater than the critical value X²₀.₀₁ = 11.345. This means that the null hypothesis is rejected at the 0.01 significance level.

We can conclude that the proportion of students smoking is not the same at all four colleges, and there is evidence to suggest that the proportion of students smoking differs among the colleges.

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The angle subtended by the women voters are 100° more than the angle subtended by the men voters.

Reasons:

The angle subtended by the men on the pie chart = 130°

The number of women = 2800 + The number of men

Therefore;

Angle subtended by the women voters on the pie chart = 360° - 130° = 230°

The difference between the angle representing women and the angle

representing men = 230° - 130° = 100°

Therefore;

100° = 2800

Which by common ratios gives;

\(\dfrac{100^{\circ}}{360^{\circ}} = \dfrac{2800}{Total \ number \ of \ voters }\)

100 × Total number of voters = 2800 × 360

\(The \ total \ number \ of \ voters = \dfrac{2800 \times 360}{100} = 10080\)

The total number of voters = 10080

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Answer:

The angle subtended by the women voters are 100° more than the angle subtended by the men voters.

The total number of voters are 10080 voters

Reasons:

The angle subtended by the men on the pie chart = 130°

The number of women = 2800 + The number of men

Therefore;

Angle subtended by the women voters on the pie chart = 360° - 130° = 230°

The difference between the angle representing women and the angle

representing men = 230° - 130° = 100°

Therefore;

100° = 2800

Which by common ratios gives;

100 × Total number of voters = 2800 × 360

The total number of voters = 10080

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.