QUESTION 4
You and a friend want to create a confidence interval for the proportion of undergraduates at a college who favor eliminating evening exams.
Your friend will choose a simple random sample of 250 students for their confidence interval.
If you choose a simple random sample of 1000 students, your interval will have
A. approximately the same estimate but a smaller margin of error.
OB. approximately the same estimate but a larger margin of error.
C. a smaller estimate and a smaller margin of error.
D. a larger estimate but a smaller margin of error.
E. a larger estimate but a larger margin of error.

Answer:

\(12 = n - 0.25(12 + 8n) \\ 12 = n - \frac{1}{4} (12 + 8n) \\ 12 = n - 3 - 2n \\ 12 + 3= n -2n \\ n = -15 \)

Answer:

k < - 11

Step-by-step explanation:

- 3k - 12 > - k + 10 ( add k to both sides )

- 2k - 12 > 10 ( add 12 to both sides )

- 2k > 22

Divide both sides by - 2 , reversing the symbol as a result of dividing by a negative quantity.

k < - 11

Hi!

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

-3k-12>-k+10

-3k+k>10+12

-2k>22

-k>11

Now, when we divide by a negative variable, we change the sign of our inequality:

k<-11

Hope it helps!

~SparklingFlower

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Answer:

(x+3)² + (y+2)² = 49

Step-by-step explanation:

To graph the circle that has centre of (-3,-2) with a point (-3, -9) on it.

First, let us write the equation of the circle

The equation is expressed as;

(x-a)² + (y-b)² = r²

(a, b) is the centre

r is the radius

r = √(-9-(-2))² +(-3-(-3))²

r = √(-9+2)² +(-3-(-3))²

r = √(-7)²

r = √47

r = 7

Get the equaton

(x-(-3))² + (y-(-2))² = 7²

(x+3)² + (y+2)² = 49

This gives the required equation

The points jada score is 159.25.

Given that james scored 182 points while playing a video game and he scored 7 times as many points as jada scored.

Let x be the points scored by james and y be the points scored by jada.

The total points scored by james and jada is 182 points.

x+y=182    .....(1)

James scored 7 times many points as jada scored.

y=7x         .....(2)

So, there are two equations and two unkowns.

Firstly, we will substitute equation (2) in equation (1), we get

x+7x=182

8x=182

Divide both sides by 8, we get

8x/8=182/8

x=22.75

Further, we will substitute the value of x in equation (2), we get

y=7×22.75

y=159.25

Hence, the jada score 159.25 when james scored 182 points while playing a video game and ahe scored 7 times as many points as jada scored.

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Answer: x <- -8

x is less than negative eight.

Step-by-step explanation:

First, subtract 11 from both sides. Then divide both sides by 11. The arrow should be open and pointing to the left.

Answer:

x <- -8

Step-by-step explanation:

Answer:

7, -10, -2

Step-by-step explanation:

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

f/373 = 294

Step-by-step explanation:

Answer:

$1600

Step-by-step explanation:

just multiply$8 by 200 and I think $1600 is the answer

The maximum amount, in dollars, of profit Michelle, can earn from the sale of her necklaces is $1,450.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The rent that Michelle pays for the booth at the craft fair is $150. Also, it is mentioned that the selling price of a single necklace is $8, while the number of necklaces that Michelle sells is 200.

The total revenue that Michelle will be able to make from 200 necklaces will be,

The total revenue = $8 × 200 = $1,600

Since profit is the difference between the total revenue and the expenses, therefore, the total profit of the organization can be written as,

Total Profit = $1,600 - $150 = $1,450

Hence, the maximum amount, in dollars, of profit Michelle can earn from the sale of her necklaces is $1,450.

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-5/-8

Step-by-step explanation:

I think the question is asking about the gradient so to find the gradient, you need to minus the first y coordinate form the second y coordinate

-4 - 1 = -5

then the first X from the second X

-6 - 2 = -8

The equation for the perpendicular bisector will pass through the midpoint of the segment and will have the slope

Answer:

use the y=mx + b method

rise over fun

Answer:

-4/3

Step-by-step explanation:

Like the other person said, rise up 4 and 3 to the left. Line is going from left to right so it's negative.

Steve spent 2/3 of $15, to find how much this 2/3 of $15 is, we have to multiply $15 by 2/3, as follows:

Therefore, we have found that Steve already spent $10 .

To simplify the given rational expression, proceed as follows:

According to this:

The numerator is 6z-4y

The denominator is (y^2)z

Answer:

proportional

Step-by-step explanation:

Answer:

Proportional

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

point 01 (-3, 3)

point 02 (2 , -32)

Step 02:

equation of the line (y = mx + b)

slope = m

(y - y1) = m (x - x1)

(y - 3) = -7 (x - (-3))

y - 3 = -7 (x + 3)

y = -7x - 21 + 3

y = -7x - 18

The answer is:

y = -7x - 18

The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

What is amount and example?

amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.

To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:

wood (m) = (wood (ft) x 0.3048) / 6

Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:

wood (m) = (6 ft x 0.3048) / 6

wood (m) = 1.8288 m      

Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

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The derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹ * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

To find the derivative of the given function g(x), we can apply the product rule and the chain rule. Let's break down the function into its constituent parts: f(x) = (x² - x + 1\()^1^0\) and h(x) = (tan(x))³.

Using the product rule, the derivative of g(x) can be calculated as g'(x) = f'(x) * h(x) + f(x) * h'(x).

First, let's find f'(x). We have f(x) = (x² - x + 1\()^1^0\), which is a composite function. Applying the chain rule, f'(x) = 10(x² - x + 1\()^9\) * (2x - 1).

Next, let's determine h'(x). We have h(x) = (tan(x))³. Applying the chain rule, h'(x) = 3(tan(x))² * sec²(x).

Now, we substitute these derivatives back into the product rule formula:

g'(x) = f'(x) * h(x) + f(x) * h'(x)

       = 10(x² - x + 1)² * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\)* (tan(x))² * sec²(x).

In summary, the derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹  * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

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The alternative and hull hypotheses is H₀: P=0.03, H₁: P≠0.03.

Given that,

According to a representative of the Ohio Department of Education, 3% of graduating high school seniors in Ohio have dropped out in recent years. Out of the 600 pupils enrolled, 30 students from Podunk High School dropped out of school last year.

We have to find is there enough data to say that this school's dropout rate is higher than the state average. Using symbols and words, state the alternative and hull hypotheses.

We know that,

n is 600,

3% Ohio high school seniors dropout.

30 dropout out of 600 in Podunk high school.

Here,

H₀: μ₁=μ₂  vs   H₁:μ₁≠μ₂

In coordinates,

H₀⇒ dropout number is equal for both schools.

H₁⇒ dropout number not equal for both schools.

H₀: P=0.03, H₁: P≠0.03.

Therefore, The alternative and hull hypotheses is H₀: P=0.03, H₁: P≠0.03.

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If we have a regular five-pointed start as follows:

If we draw a line from each of the vertices of the regular five-pointed star, we can say that we have 5 lines of symmetry, in this case, that is, each of the lines divides the figure into two identical parts.

Therefore, in summary, we can say that we 5 lines of symmetry in a regular five-pointed star.

Answer:

180

Step-by-step explanation:

The definition of angles that are supplementary is that their measures add to 180°.

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The percentage of the guests ordered food is 40%

"Information available from the question"

In the question:

There were 425 guests at a hotel. 170 guests ordered food.

To find the what percentage of the guests ordered food?

Now, According to the question:

Total guests in hotel is 425

and, 170 guests ordered food

=> Divide 170 by 425

= 170/ 425 = 0.4

The percentage of the guests ordered food:

=> 0.4 x 100 = 40%

Hence, The percentage of the guests ordered food is 40%

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The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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The probability of both events occurring is 1/20.

What are examples and probability?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                                   The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

Events X and Y are independent.

The probability of X occurring is 1/4

The probability of Y occurring is 1/5

Since both events are independent, then we have

P(X and Y ) = P(X) * P(Y)

                  = 1/4 * 1/5

                 = 1/20

 P( X and Y ) = 1/20

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Based on the provided information, the Type 1 error is that you conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. (Option C)

In statistical hypothesis testing, a Type I error refers to the rejection of null hypothesis when it's actually true while a type II error is the failure to reject a null hypothesis that is actually false. Type I error means to conclude that results are statistically significant when, in actuality they are caused purely by chance or because of unrelated factors. The risk of committing this error is the significance level (alpha or α) chosen. As the null hypothesis states that weightlifting bar can withstand weights of 800 pounds or less while alternative hypothesis states that weightlifting bar can withstand weights of over 800 pounds, the type I error would be to conclude that weightlifting bar can withstand weights of greater than 800 pounds when, in fact, it cannot.

Note: The question is incomplete. The complete question probably is: Suppose the null hypothesis, H0, is a weightlifting bar that can withstand weights of 800 pounds and less. The alternative hypothesis, Ha, is a weightlifting bar can withstand weights greater than 800 pounds. What is the Type 1 error in this scenario? Select the correct answer below: A) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of greater than 200 pounds B) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. C) You conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. D) You conclude the weightlifting bar can withstand weights of greater than 100 pounds when, in fact, the weightlifting bar can withstand weights of greater than 800 pounds.

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Answer:

m=-4/3

Step-by-step explanation:

0-8/5-(-1)

-8/5+1

-8/6

-4/3