a college student organization wants to start a nightclub for students under the age of 21. to assess support for this proposal, they will select an srs of students and ask each respondent if he or she would patronize this type of establishment. what sample size is required to obtain a 90% confidence interval with a margin of error of at most 0.04?

Answer:

x = 4

Step-by-step explanation:

2x(x) + 28 = (2x + 2)(x + 2) ← expand factors using FOIL

2x² + 28 = 2x² + 6x + 4 ( subtract 2x² from both sides )

28 = 6x + 4 ( subtract 4 from both sides )

24 = 6x ( divide both sides by 6 )

4 = x

The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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The wooden artifact was made approximately 3,183 years ago. The amount of carbon-14 present in an artifact can be used to determine how long ago the organism that the artifact came from died.

The half-life of carbon-14 is 5730 years, which means that every 5730 years, half of the carbon-14 in a sample will decay. Let's call the amount of carbon-14 in the living tree sample 100%. Since the artifact contains 35% of that amount, we can write:

0.35 x 100% = 100% x (1/2)^(t/5730)

where t is the number of years since the artifact was made.

Simplifying this equation, we get the following:

0.35 = 0.5^(t/5730)

Taking the logarithm of both sides, we get:

log(0.35) = (t/5730) x log(0.5)

Solving for t, we get:

t = (5730 x log(0.35)) / log(0.5)

Using a calculator, we get:

t ≈ 3,183 years

Therefore, the wooden artifact was made approximately 3,183 years ago.

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Answer: the initial points is 30.
and per pair of shoes is 15.

Step-by-step explanation:

The measure of <E= 60, <F= 95 and <G= 25 degree.

In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.

Given:

The two triangles are similar.

In triangle JKL using Angle Sum Property

<J + <K + <L = 180

95 + 60 + <K = 180

155 + <K = 180

<K = 180- 155

<K = 25 degree

Thus, the measure <E= 60

and, the measure <F= 95

and, the measure of <G= 25.

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An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.

To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:

$200/$12 = $150/$9

We can simplify this proportion by dividing both sides by 3:

$200/$4 = $150/$3

Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:

$200 x $3 = $150 x $4

$600 = $600

This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.

In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.

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Answer:

The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:

2.65

2.68

2.82

Step-by-step explanation:

Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:

Start by finding an approximate square root by making an educated guess or by using a calculator.

Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.

Refine the estimate by averaging the guess and the number divided by the guess.

Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.

Here's an example for 7.07:

An educated guess for the square root of 7.07 could be 2.7

Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.

To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.

Repeat steps 2 and 3 until the desired level of accuracy is achieved.

After several iterations, the square root of 7.07 is approximately equal to 2.65.

Similarly, you can find the approximate square roots of 7.21 and 7.93.

Answer:

C) E = 118°; T = 118°

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

The given figure is a kite since it has two pairs of congruent sides as marked.

Its one pair of opposite angles are congruent. That is:

Sum of all interior angles of a quadrilateral is 360°:

Both the missing angles are 118°.

Last month 26 of the 280 students won a free lunch. The experimental probability of winning will be 13/140

Probability is the occurence of the events. Some of the events cannot be predicted with certainty. Probability of any event can be defined as P(A) , and there are many types of probability density functions.

Once a month, the cafeteria has each student pick a card from a standard deck of cards. From the deck of cards, each student has to pick a card for every one month.

Students who pick an ace get a free lunch

Given that,

Last month 26 of the 280 students won a free lunch and the percentage of winning is near to 9.2% approximately and it is very near to the 10%.

The experimental probability of winning is the ratio of number of possible outcomes to the total number of outcomes.

So, the experimental probability of winning is 26/280 = 13/140

Therefore, the  experimental probability of winning is 13/140

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Answer: -1/3

Step-by-step explanation:

Slope = Rise/Run

Answer:

Step-by-step explanation:

The equation connects m and n.

Suppose n=1,

m=3/1=3.

If n=2,

m=3/2=1.5

If n=3,

m=3/3=1. This shows that as n increases, m decreases.

If m was equal to 1,

1=3/n

Thus n=3.

If m=2,

2=3/n

n=1.5

If m=3,

3=3/n

n=1.

This also shows that as m increases, n decreases.

Hope this helps :)

Answer:

When I increased n, m decreased.

When I increase m, n decreases

Step-by-step explanation:

Let's say that m is one and n is 3

1 = [tex]\frac{3}{3}[/tex]  Us this as our base to compare increasing m and n.

Increase n to 6

[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]

When I increased n, m decreased.

Increase m to 3

3 = [tex]\frac{3}{1}[/tex]

When I increase m, n decreases

a) Since Todd and Amani started with the same initial deposit, they will never have the same amount in their accounts if they keep to their weekly savings plans because Todd's weekly savings are two times that of Amani.

b) An equation to represent the total amount in each of their accounts at any given time or weeks is as follows:

An equation is a statement of equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine values, variables, and numbers or constants without the equation symbol (=), which differentiates them from equations.

                                        Todd     Amani

Initial deposit in account  $10       $10

Weekly deposits               $4         $2

Let the number of weeks of deposits = w

Let the total deposit in Todd's account in w weeks = t

t = 10 + 4w

Let the total deposit in Amani's account in w weeks = a

a = 10 + 2w

For Todd's and Amani's account to be equal, 10 + 4w = 10 + 2w

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Answer:

Let's call the length of side 1 "x". Then, the length of side 2 is 2x, and the length of side 3 is x + 4. So, the expression for the three sides of the triangle can be represented as:

x + 2x + (x + 4) = 3x + 4

This expression represents the sum of the lengths of all three sides of the triangle.

Step-by-step explanation:

Answer: x+2x+(4+x)

Step-by-step explanation:

since side one is unknown, we can substitute it with variable x, and side two is twice as much as side one so we do 2x, and side three is four cm longer than side one so we do 4+x at the end

Answer:

256

Step-by-step explanation:

65% is 208

15% is 48

15% + 65% is 80%

So, just add 48 and 208 together:

48 + 208 = 256

Therefore, 80% of that number is 256.

Answer:

256

Step-by-step explanation:

We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.

The length of the garden which is in the shape of a rectangle with a perimeter of 18 meters and whose length is 3 meters more than twice the width, is 7 metres.

Let's name the width "w" and the length "l" of the rectangle.

We know from the problem description that the rectangle's perimeter is 18 metres, thus we can formulate an equation:

2l + 2w = 18

We also know that the length is 3 metres longer than the breadth, thus we can solve the following equation:

l = 2w + 3

We may plug the second equation into the first to remove the letter "l" and get an equation with only one variable:

2(2w + 3) + 2w = 18

When we simplify this equation, we get:

6w + 6 = 18

When we subtract 6 from both sides, we get:

6w = 12

When we divide both sides by 6, we get:

w = 2

We can use the second equation to get the length now that we know the width is 2 metres:

l = 2w + 3 = 2(2) + 3 = 7

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Answer:

In 6 seconds: 180 m

20 m: in 2 seconds

Step-by-step explanation:

y = distance

x = time

y is proportional to x:

y = kx

y is proportional to the square of x:

y = kx²

We are given: (3, 45)

45 = k × 3²

45 = 9k

k = 5

The equation is:

y = 5x²

When x = 6,

y = 5(6²)

y = 180

180 m in 6 seconds

When y = 20,

20 = 5x²

x² = 4

x = 2

2 seconds for 20 m

Answer:

(x-1)(x+1)(x+3)

Step-by-step explanation:

[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]

10:40 am

63 mile distance and 27 mph. starting from 8 am

63/27 => 2 (2/3) hours. 2/3 of an hour is also, 40 minutes.

so 8 am plus 2 hours and 40 minutes means 10:40 am

A triangular fence having dimensions 2x + 3, y − 6, and 4x − 3, has a perimeter of Option D: 6x + y - 6 feet.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangular fence has measurements -

a = (2x + 3) feet

b = (y - 6) feet

c = (4x - 3) feet

The formula for perimeter of a triangle is -

Perimeter = sum of all three sides

So the equation will be -

Perimeter = a + b + c

Substitute the values in the equation -

Perimeter = (2x + 3) + (y - 6) + (4x - 3)

Perimeter = 2x + 3 + y - 6 + 4x - 3

Perimeter = 6x + y - 6

Therefore, the value for perimeter is 6x + y - 6 feet.

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The account would contain 10,230.00 after 1 year.the amount in the account after 1 year, we can use the formula: [tex]P (1 + r/n)^nt[/tex]

To find the amount in the account after 1 year, we can use the formula:[tex]P (1 + r/n)^nt[/tex]

Where,

P = Principal Amount

r = Rate of Interest

n = Number of times the interest is compounded per year

t = Time in years

For this question,

P = 10,000

r = 2.3%

n = 1

t = 1

Therefore,

[tex]10,000 (1 + 0.023/1)^1*1\\10,000 (1.023)^1[/tex]

10,000 x 1.023

= 10,230.00

The complete question is:

If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account contain after 1 year?

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The minimum number of hours life guarding that Daniel must work to meet his requirements = 12 hours

To the nearest whole number approximately:

If the digit following the decimal is less than 5, only the number preceding the decimal should remain unchanged.

Add one to the number before the decimal and eliminate the decimal part if the digit following the decimal is five or greater.

Given the information,

Babysitting pays Daniel $8 per hour, and life guarding pays him $15 per hour.

Daniel can only work a total of 18 hours per week and must make at least $200.

Daniel has been babysitting for three hours.

Daniel thus makes 3 x 8 = 24 dollars.

He has earned $200 - 24 = 176 dollars from the original $200.

Let's say Daniel was a lifeguard for m hours.

He therefore made m x 15 = 176.

15 × m = 176

m = 11.73

m ≈ 12 hours

So, the minimum number of whole hours = 12

This means, Daniel must work 12 hours lifeguarding to meet his requirements.

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Answer:

The graph of the function will shift vertically up by $5.

Step-by-step explanation:

The original function is m(x) = 2x + 15, where x is the number of people in the car. If the per car charge is changed to $20 per car, the new function becomes m(x) = 2x + 20, because the charge per car has increased by $5.

This means that the y-intercept of the new function is 20 instead of 15, which represents the minimum cost for a car, regardless of the number of people inside. So the graph of the new function will be shifted vertically up by $5 from the graph of the original function.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11

From the question, we have the following parameters that can be used in our computation:

The graphs

The lines are absolute function graphs, and they can be represented as

y = a|x - h| + k

Where

Vertex = (h, k)

For the blue line, we have

(h, k) = (2, -5) and (x, y) = (0, -4)

So, we have

-4 = a|0 - 2| - 5

2a = 1

a = 1/2

So, the equation is y = 1/2|x - 2| + 5

For the red line, we have

(h, k) = (-2, 3) and (x, y) = (0, -11)

So, we have

-11 = a|0 + 2| + 3

2a = -14

a = -7

So, the equation is y = -7|x + 2| - 11

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Answer:  His average is 85 now.

Step-by-step explanation:

Average is the sum of all his math tests divided by the number of the math tests he took, so we get:

[tex]\frac{sum }{11}=80[/tex]

sum = 11 x 80

sum = 880

880 - 30, we get 850, which becomes the new sum of the 10 math test scores, because he eliminated one test score.

[tex]\frac{850}{10} =85[/tex]

His average is 85 now.

The formula to calculate the new value after an increase is to multiply the original value by the percentage of the increase.

The formula to calculate the new value after an increase is to multiply the original value by the percent of the increase. For example, if the original value is $100 and the increase is 10%, the new value would be $100 x 1.10 = $110. This formula can be applied to any original value and any percentage increase. It is useful for calculating the new value after applying a percentage increase, such as when calculating a pay raise or the cost of goods after a price increase. The formula can also be applied to calculate the new value after a percentage decrease, by multiplying the original value by 1 minus the percentage of the decrease.

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The complete question is

the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase  by multiplying the original value by the percent for a new value?

Answer:

50 kg of green tea leaves and 50 kg of assam black tea leaves.

Step-by-step explanation:

Let x kg be the amount of green tea and y kg be the amount of Assam tea.

x+y=100 (1) [mass]

price for 1 kg of assam tea= 7.20/600×1000g

= $12/kg

total cost= 100×10

= $1000

8x+12y= 1000 (2) [cost]

(1)×8: 8x+8y= 800 (3)

(2)-(3): (8x+12y)-(8x+8y)= 1000-800

4y= 200

y= 50 (4)

sub (4) into (1):

x+50= 100

x= 50

If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

From the given choices, we get:

No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.

The correct option is D.

A computer experiment in which you can select a random sample from the given probability distributions is called a simulation.

Given:

A student wants to simulate 28 birthdays,

but she does not have a calculator or software program available,

so she makes up 28 numbers between 1 and 365.

By comparing with the definition:

From the given choices, we get,

D. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.

Hence, D is the correct option.

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