Suppose 3% of students drink more than 3 cups of coffee each day. To check this claim, a researcher randomly selected a sample of 133 students and found that 5 drink more than 3 cups of coffee each day. What is the sampling distribution of the sample proportion? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.) The distribution of the sample proportion of students drinking more than 3 cups of coffee each day is approximately normal $ with a mean of and a standard deviation of Check

The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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Answer:

[tex]4\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

DE's length is 1/2 of BC's length, due to it being a mid segment (13)((You can tell it is a mid segment due to the congruency lines)). AD's length is 12, due to there being a midpoint. EC's length is 10, also due to the congruency lines.

Emely gοt 35% οf her math hοmewοrk questiοns wrοng.

A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.

Emely gοt 13 questiοns cοrrect fοr every 7 questiοns she gοt wrοng.

We can start by finding the fractiοn οf questiοns Emely gοt wrοng, which is 7/(7+13) = 7/20. Tο cοnvert this tο a percentage, we can multiply by 100 tο get 35%.

Therefore, Emely got 35% of her math homework questions wrong.

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Answer: x = π - π/4 = 3π/4

Step-by-step explanation:

If sec(x) = -√2 and x is in the second quadrant (between π/2 and π), we can use the identity:

sec^2(x) - 1 = tan^2(x)

to find the value of tan(x):

sec^2(x) - 1 = tan^2(x)

(-√2)^2 - 1 = tan^2(x)

2 - 1 = tan^2(x)

1 = tan^2(x)

Taking the square root of both sides, we get:

tan(x) = ±1

Since x is in the second quadrant, the angle that satisfies tan(x) = 1 is π/4. Therefore, we have:

x = π - π/4 = 3π/4

Note that the angle that satisfies tan(x) = -1 is in the fourth quadrant, so it is not relevant to this problem.

To simplify the given expression, we can first evaluate each term inside the square root, and then add them up. Using basic algebraic operations, we get:

T = √(2023^2)(4046) + (2023^2) + 0

T = √(2023^2)(4046 + 1)

T = √(2023^2)(4047)

T = 2023√4047

Therefore, the simplified expression for T is 2023√4047.

The slope of the line that passes through the pair of points (7/20,5/19) and (5/9,11/16) is 3/5.

To find the slope of a line passing through two points, we need to use the slope formula. The slope formula is m = (y2 - y1) / (x2 - x1). To calculate the slope, we need to first calculate the x and y values of the two points, (7/20,5/19) and (5/9,11/16). The x values are 7/20 and 5/9 and the y values are 5/19 and 11/16. We can then plug these values into the slope formula to get the slope. The slope is (11/16 - 5/19) / (5/9 - 7/20) = 3/5. Therefore, the slope of the line that passes through the two points (7/20,5/19) and (5/9,11/16) is 3/5.

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The integer that satisfies all of these conditions is -4.

Exponentiating -4 gives 16, which is less than -1.

The y-coordinate of -4 on the coordinate plane is above 2.

The x-coordinate of -4 on the coordinate plane is greater than -3.

And, the sum of the absolute values of the coordinates of -4 is 7, which is equal to five.

The power consumed by resistor R3 is 0.79 watts.

The rate at which energy is transferred or converted is known as Power. It is a measure of how much work can be done in a given amount of time. Power is typically measured in watts and is a key factor in determining the efficiency of machines and systems.

To determine the power consumed by resistor R3, we need to first find the current flowing through it.

E₁ = I(R₁ + R₂ + R3 + R4)

I = E₁ / (R₁ + R₂ + R3 + R4)

= 30 / (152 + 202 + 252 + 102)

= 0.056 A

Now that we know the current flowing through R3, we can use Ohm's Law again to find the power consumed by it:

P = I²R3

= (0.056)² x 252

= 0.79 W

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Answer:

[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find an \underline{equivalent expression}.}[/tex]

[tex]\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}[/tex]

[tex]\Large\textsf{What is the Distributive Property?}[/tex]

[tex]\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}[/tex]

[tex]\large\underline{\textsf{For this problem;}}[/tex]

[tex]\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}[/tex]

[tex]\large\underline{\textsf{Distribute:}}[/tex]

[tex]\mathtt{8(2y+\frac{1}{4} )}[/tex]

[tex]\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}[/tex]

[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]

Answer:

16y + 2

Step-by-step explanation:

Now we have to,

→ Find the equivalent expression.

The expression is,

→ 8(2y + (1/4))

Let's simplify the expression,

→ 8(2y + (1/4))

→ 8(2y) + 8(1/4)

→ 16y + (8/4)

→ 16y + 2

Hence, the answer is 16y + 2.

Answer:

The sum of a number and 9 can be written as:

x + 9

where "x" represents the number being referred to.

Alternatively, if we want to use a different variable, we can write it as:

n + 9

where "n" represents the number being referred to.

Hope this helped, if not I'm sorry! If you need more help, feel free to ask! :]

The equation correctly relates the total cost y to rent the washer for x days is option (B) Y = 40 + 20x

The rental fee of $40 is charged regardless of the number of days the power washer is rented. In addition to this fee, there is a daily charge of $20 per day.

Therefore, the total cost of renting the power washer for x days can be calculated by multiplying the daily charge by the number of days rented and adding the rental fee:

Total cost = (daily charge) x (number of days rented) + rental fee

Total cost = $20x + $40

This linear equation can be rearranged to the form:

Y = 40 + 20x

Therefore, the correct option is (B) Y = 40 + 20x

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Answer:

D. 1/4

Step-by-step explanation:

The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.

1/2 x 1/2 = 1/4

Answer: Here we will learn how to find the probability of tossing two coins.

Let us take the experiment of tossing two coins simultaneously:

When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of outcome are 22 = 4

The above explanation will help us to solve the problems on finding the probability of tossing two coins.

Step-by-step explanation:

THE ANSWER MUST BE AT LEAST 1/4 OR 1/8

IF THAT IS WRONG LET ME KNOW!

AND IF YOU NEED A TUTOR I AM OPEN FOR HELP JUST CONTACT ME IF YOU HAVE ANY QUESTIONS!

Answer:

1 . x(x+1)
2.(3a-1)(5a+8)
3.(4x + 3y) ( 3x - 3y)
4.(a+b)

Using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.

What is meant by an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Given,

The initial amount of caffeine in the beverage = 120 mg

The rate at which the caffeine decreases = 12% per hour w

We are asked to find the time taken for the caffeine amount to become 10mg.

Now let the initial amount be 100 per cent.

After one hour, the amount becomes (100-12)  = 88% of 120 = 0.88 * 120

So after every one hour, there is 88% caffeine left.

Now after two hours,

the amount of caffeine = 88% of (0.88*120) = 0.88*0.88*120 = 120(0.88)²

So after x hours, we can write the equation as:

Amount of caffeine left C(x) = 120(0.88)ˣ

Now for 10mg to be left, the time taken is:

10 = 120(0.88)ˣ

1/12 = (0.88)ˣ

log (1/12) = x log(0.88)

-1.079 = x (-0.056)

x = 19.27 hours

Therefore using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.

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The missing coefficients in the equation y = mx + b are m = 0.841 and b = 18.813. The final equation that fits the given data is y = 0.841x + 18.813

To find the missing coefficients in the equation y = mx + b, we need to use the given data in the table to determine the values of m and b.

We can start by using two of the data points to set up a system of equations:

Using (5, 23.018) and (6, 23.859):

m(5) + b = 23.018

m(6) + b = 23.859

Subtracting the first equation from the second equation gives:

m(6) - m(5) = 0.841

Simplifying this expression:

m = 0.841 / (6 - 5) = 0.841

Now we can substitute the value of m into one of the original equations to solve for b:

m(5) + b = 23.018

0.841(5) + b = 23.018

b = 23.018 - 4.205

b = 18.813

Therefore, the missing coefficients are:

m = 0.841

b = 18.813

The equation y = 0.841x + 18.813 fits the given data.

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The given question is incomplete, the complete question is:

Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y 5 23.018 5.5 23.438 6 23.859 6.5 24.035 7 25.449 7.5 24.868 8 26.058 I Enter an integer or decimal number [more..] y = I+

Probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.

The probability of Harry, Jason, and Sarah getting admission to their desired schools is the probability that Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670. The scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115.So, let's first standardize Harry's score:Z = (650 - 550) / 115 = 0.87Similarly, for Jason's score:Z = (630 - 550) / 115 = 0.70And for Sarah's score:Z = (670 - 550) / 115 = 1.04Now we need to find the probabilities of getting each of these Z-values. We can do that using the standard normal distribution table. The table gives the probability that a standard normal random variable is less than or equal to a certain Z-value.To find the probability that Harry's score is above 650, we need to find the probability that Z > 0.87. This can be found by subtracting the probability of Z ≤ 0.87 from 1:P(Z > 0.87) = 1 - P(Z ≤ 0.87) = 1 - 0.8078 = 0.1922Similarly, the probability that Jason's score is above 630 is:P(Z > 0.70) = 1 - P(Z ≤ 0.70) = 1 - 0.7580 = 0.2420And the probability that Sarah's score is above 670 is:P(Z > 1.04) = 1 - P(Z ≤ 1.04) = 1 - 0.8508 = 0.1492The probability that all three events occur (Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670) is the product of their probabilities:P(Harry, Jason, and Sarah) = P(Z > 0.87) × P(Z > 0.70) × P(Z > 1.04) = 0.1922 × 0.2420 × 0.1492 = 0.0088Therefore, the probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.

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Answer:

D.) 3.14/2

Step-by-step explanation:

The scenariο that wοuld mοst likely be biased against nοn-vοters is a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences

A cοgnitive bias clοuds οur critical thinking and may result in the spread οf false infοrmatiοn that may be harmful tο οther peοple. Biases cause us tο avοid infοrmatiοn that might be uncοmfοrtable οr unwelcοme rather than lοοking intο the infοrmatiοn that might help us reach a mοre accurate cοnclusiοn.

A cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences is nοt a biased sample. Since the nοn-vοters are nοt

A vοlunteer sample cοllected at a pοlitical rally was used tο determine candidate preferences. It prefers a particular member. This is a biased survey.

A simple randοm sample οf all nοn-vοters was used tο determine why they dοn’t vοte. It is biased. Because a grοup οf peοple decides nοt tο give a vοte.

A simple randοm sample οf all eligible vοters, sοme οf whοm didn’t have time tο vοte. It is a sample.

A vοlunteer sample was cοllected at a large department stοre tο determine whο they vοted fοr. It is a nοn-biased survery. The peοple dο nοt prefer a particular team.

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probability-=0.3419

The probability that the number of defective bulbs in a sample of 550 light bulbs is greater than 15 is 0.3419. To calculate this probability, you need to use the binomial probability formula: P(x) = nCx * p^x * q^(n-x), where n is the sample size (550), p is the probability of a defective bulb (0.035), x is the number of defective bulbs you want to calculate (15) and q is the probability of a non-defective bulb (1-0.035). Plugging in the values, we get P(x) = 550C15 * 0.035^15 * 0.965^(550-15) = 0.3419

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Step-by-step explanation:

94 - 50% * 94   =

             94 - .50 * 94  =

                              94 - 47 =  47  

Answer:

47

Step-by-step explanation:

50 × 94 ÷ 100 =

47,00 ÷ 100=

47

Answer:

1\2

Step-by-step explanation:

As a result, the answer to the following question, As a result, the supplied radius arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).

In more modern use, the length of a sphere or sphere is equal to its radius in standard geometric, so it has several line segments from its centre to its circumference. The phrase is derived from the Latin word for radius, which also referred to the spokes of a waggon wheel. The radius of a circle is the distance between the centre and any point on its periphery. Often, "R" or "r" is used to signify it. A radius is a boundary line with one terminus in the centre and a second around the perimeter of a circle. Vide letter diameter equals radius The dimension of a circle is the segment that passes its centre and has extremities that are on the circle.

The formula for calculating the arc length of a circle is:

Arc length = radius x central angle in radians,

In order to use this formula, we must first convert the centre angle from degrees to radians. We are aware of the following:

2 radians Equals 360 degrees

360 degrees divided by 2 radians equals x degrees divided by y radians

(x degrees * 2 radians) / 360 degrees = y

y = (22 deg * 2 radians) / 360 deg = 0.38397 deg (rounded to five decimal places)

arc length Equals radius multiplied by Centre angle in radians

With r = 18 inches and = 0.38397 radians, we get:

arc length = 18 inches multiplied by 0.38397 equals 6.9115 inches (rounded to four decimal places)

As a result, the supplied arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).

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Answer:

5^x+x

Step-by-step explanation:

5^x+1+5^x-1

First of all 1- 1 = 0

so we are here with 5^x +5^x

Answer:

The answer you're looking for is x = 6, and the missing angle is 30º

Step-by-step explanation:

In order to find the answer we need to find out what the angle amount actually is. We can use the equation 180º = 110+ 40 + (8x-18).

Now there are two ways to solve this equation you could solve it by starting with the equation actually is or you can find out the missing angle using another equation.

First Method:

Using 180º = 110+ 40 + (8x-18), you first need to do is to combine like terms such as combining 110, 40, and -18, giving you 132.

Now you have 180 = 132 + 8x.

Then you will have to make sure that 8x is left by itself so do the opposite operation and to keep the equation balanced you do it on both sides giving you 48 = 8x. The only step left to do is to do the opposite operation on both sides which is dividing by 8, giving you 6 = x

Now with that, you replace x, with 6, and go from there.
(8x-18) = (8×6-18) = (48 - 18) = 30.

With that, we are finished with the equation.

However, the other method you could use, which is easier in my opinion, can be found below.

Second Method:

The first thing we do is find out immediately what the missing angle (m) is using the equation 180 = 110 + 40 + m.

You combine like terms 110 and 40, giving 150 and then get,
180 = 150 + m.

You then do the inverse of operations, which is subtracting 150 from both sides and you get 30 = m.

Now that we complete that we start with our other equation which is:
30 = 8x-18. You then do inverse of -18, which adds 18 to both sides giving: 48 = 8x.

Finally doing the inverse operation of multiplying is dividing 8 by both sides giving 6 = x as the correct answer.

Dot plots are useful for visualizing the distribution of data and identifying patterns, trends, and outliers. They are often used in data analysis, quality control, and scientific research to help draw conclusions and make informed decisions based on data.

A dot plot is a graphical representation of statistics that presents character information factors through the use of dots. From a dot plot, possible decide several conclusions, depending on the data being displayed.

For instance, if the dot plot presents information on the height of a collection of people, you can still determine the range of heights inside the organization, the most common top, and any outliers (i.e., individuals with severe heights).

If the dot plot displays facts at the ratings of a collection of students on a test, you can still determine the range of rankings, the median score, and the distribution of rankings (i.e., whether or not the ratings are evenly distributed or clustered round sure values).

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What conclusion can be determined by the dot plot? Explain in detail about the dot plot.

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Answer:

$150

Step-by-step explanation:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan.

In this case, the Principal is $1,000, the Rate is 10%, and the Time is 18 months (which we'll convert to a fraction of a year).

First, we need to convert 18 months to a fraction of a year. Since there are 12 months in a year, 18 months is equal to 18/12 = 1.5 years.

Using the formula:

Interest = Principal x Rate x Time

Interest = $1,000 x 0.10 x 1.5

Interest = $150

So the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.

Answer:

The formula for simple interest is I = Prt, where I is the interest, P is the principal or amount borrowed, r is the interest rate, and t is the time in years.

In this case, P = $1,000, r = 10% or 0.10 as a decimal, and t = 1.5 years (since 18 months is equivalent to 1.5 years).

I = Prt

I = $1,000 * 0.10 * 1.5

I = $150

Therefore, the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.