suppose the pharmaceutical company in problem 4.6-21 ran a pilot survey of 20 patients with headache pain and found 14 of them had pain relief within 30 minutes using their product. (a) what is the necessary sample size for future surveys such that a 95% confidence interval for p has an interval width of no more than 6%? is this sample size the same as, or smaller or larger than that from problem 4.6-21 (a)? (b) what is the necessary sample size for future surveys such that a 99% confidence interval for p has an interval width of no more than 6%? is this sample size the same as, or smaller or larger than that from problem 4.6-21 (b)?

Answer:

If I did this right it should be: A)720g flour B)(i) 480g (ii) 2

Step-by-step explanation:

The distance a car travels varies directly with the amount of gasoline it uses. If a car uses 28 gallons of gasoline to travel 924 miles, the car can travel 627 miles with 19 gallons of gasoline.

We can set up a proportion to solve the problem:

distance / gasoline = constant

Let's use x to represent the distance the car can travel with 19 gallons of gasoline:

924 / 28 = x / 19

Simplifying and solving for x:

x = (924 / 28) * 19 = 627 miles

Therefore, the car can travel 627 miles with 19 gallons of gasoline.

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Answer:

x = -4,

y = -1

Step-by-step explanation:

{-3x - 8y = 20,

{-5x + y = 19;

Make x or y the subject from either the 1st or the 2nd equation (I chose to make x the subject from the 2nd equation, because after division, the numbers can be written as a finite decimal fraction):

-5x = 19 - y / : (-5)

x = -3,8 + 0,2y

Replace x in the 1st equation with its value from the 2nd one (the underlined expression):

-3(-3,8 + 0,2y) - 8y = 20

Multiply every term inside the bracket by the term on the outside:

11,4 - 0,6y - 8y = 20

Collect like terms and add them together:

-8,6y = 20 - 11,4

-8,6y = 8,6 / : (-8,6)

y = -1

y = -1x = -3,8 + 0,2 × (-1) = -4

To calculate the volume, you'll need to use the formula V = πr²h, where V represents the volume, r is the radius of the circular base, h is the height of the cylinder,

and π (pi) is a mathematical constant approximately equal to 3.14159.
Hi there! I understand you need help finding the volume of a cylinder
To apply this formula, you'll first need to know the values of the radius and the height of the cylinder. Once you have these values, follow these steps:

1. Square the radius (r²).
2. Multiply the squared radius by the height (r²h).
3. Multiply the result by π (V = πr²h).

Lastly, round the calculated volume to the nearest tenth as requested. Remember that I cannot provide you with the exact volume without the radius and height of the cylinder. Please provide the values, and I'll be glad to assist you with the calculation.

Keep in mind that the answer should be concise, so providing an answer in 180 words is not necessary. The information above should be sufficient to help you understand how to calculate the volume of a cylinder.

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The largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.

what is quadrilateral?

A quadrilateral is a four-sided polygon, which is a two-dimensional closed shape with straight sides. In other words, a quadrilateral is a geometric figure that has four sides, four vertices, and four angles. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.

From the given information, we have:

angle P = 3p

angle Q = 4q

angle R = 5r

Since PQRS is a cyclic quadrilateral, the sum of opposite angles is equal to 180 degrees. Therefore, we have:

angle P + angle R = 180 degrees

3p + 5r = 180 degrees

Similarly, we have:

angle Q + angle S = 180 degrees

4q + S = 180 degrees

S = 180 - 4q

To find the largest angle, we need to find the largest angle measure among angles P, Q, R, and S.

Let's substitute the expression for S in terms of q into the equation for angle Q and simplify:

angle Q = 4q

angle Q + angle S = 180 degrees

4q + (180 - 4q) = 180 degrees

4q - 4q + 180 = 180 degrees

180 = 180 degrees

This equation is true, but it does not provide any information about the largest angle in PQRS.

Let's now substitute the expressions for angles P, Q, and R in terms of p and r into the equation for angle P + angle R = 180 degrees:

3p + 5r = 180 degrees

We want to find the largest angle, so we need to find the largest value of p or r that satisfies this equation. One way to do this is to try different values of p and r that satisfy the equation and see which one yields the largest value for angle P or angle R.

Let's try p = 10 and r = 30:

3p + 5r = 3(10) + 5(30) = 150

This satisfies the equation, so we can calculate angle P and angle R:

angle P = 3p = 30 degrees

angle R = 5r = 150 degrees

Therefore, the largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.

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Answer:93 1/3 yards or 280ft

Step-by-step explanation:Step-by-step explanation: first I converted it all into feet. Giving me L=9ft H=8ft and W= 4ft

Then inserted the values into the formula for surface area SA=2lw+2lh+2hw. Then solved it all out in a calculator

Check the picture below.

The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.

Sample size is defined as the number of observations used to determine

an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.

The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.

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The solution to the system of equations is p = 4 and q = 2

The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.

To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:

p + 2q = 8

p = 8 - 2q

Now we can substitute this expression for p in the first equation:

2p - 3q = 2

2(8 - 2q) - 3q = 2

16 - 4q - 3q = 2

16 - 7q = 2

-7q = -14

q = 2

We can now substitute q = 2 into the expression we found for p:

p = 8 - 2q

p = 8 - 2(2)

p = 4

Therefore, the solution to the system of equations is p = 4 and q = 2.

correct question  Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.

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Answer:15

You multiply 6 and 5. That equals 30 then divide the 30 by 2 and that equals 15

The value that is NOT greater than [-4.2] is D. [-4.5]

The values [-4.2], [3.5], and [4.1] are all greater than [-4.5]. To determine which value is the greatest, we can use a number line or compare the numbers directly. On a number line, we can see that [-4.5] is located to the left of [-4.2], [3.5], and [4.1]. This means that [-4.2], [3.5], and [4.1] are all greater than [-4.5].

Alternatively, we can compare the values directly. We know that -4.5 is less than -4.2 since -4.5 is farther to the left on the number line. We also know that 3.5 and 4.1 are positive values, which are greater than any negative value. Therefore, the answer is [-4.5] is not greater than [-4.2]. Hence, option D is correct.

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Answer:

Step-by-step explanation:

cost of the phone = 150

sale is 35% off

Multiply the original cost $150.00 time the percent off as a decimal.

35% = . 35 (drop the sign and move the decimal two places left.)

150 X .35 = 52.50 off the price

He will save $52.50 off the cell phone during the sale.

Answer: 9 and 1/3

Step-by-step explanation:

First of all, you have to find the unit rate. So 28 divided by 2 = 14.

The bird flies at a unit rate of 14 miles in 1 hour.

Next, we need to find out what fraction of an hour is 40 minutes.

How many minutes in an hour? 60... so 40 would be 40/60 of an hour or 4/6 or 2/3 of an hour.

Next, remember the formula D=rt which is distance= rate multiplied by time

We can use this formula here: 14 times 2/3 = 9 and 1/3

The value of x + y is  (xy -115)/4 .

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

given expression is ,

3x + 2y + xy = 115 + 7x + 6y

so, we have to find the value of x + y

take the value of x and y at one side ,

xy = 7x + 6y - 3x - 2y +115

xy = 4x + 4y + 115

take the integer on other side,

4x + 4y = xy -115

take 4 common from left hand side,

4( x + y) = xy - 115

x + y = (xy -115)/4

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The given measure of ∠ DEC = 80 degrees

We have the following details

m ∠BAC = 46 degrees

m ∠ CBA = 54 degrees

We are to find the measure of angle DEC

This is a question that shows us two similar triangles

We have ∠BAC = DCE

∠ CBA = ∠ EDC

then ∠ DEC  = ∠ BCA

The measure of the angles that are in a triangle is given as 180 degrees

we have ∠BAC + ∠ CBA + ∠ BCA = 180

46 + 54 + ∠ BCA = 180 degrees

∠ BCA = 180 - 100

∠ BCA = 80 degrees

We know that corresponding angles are equal when we have parallel lines

since ∠ DEC  = ∠ BCA

∠ DEC = 80 degrees

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8. The volume of the right cylinder is

9. The height of a slice is h/10

10. The approximate volume of the slice when divided into 10 is

11. The approximate volume of the oblique cylinder by summing up the slices is

12. Cavalieri's principle tells us that if we have two three-dimensional objects that have the same cross-sectional area at every level, then they will have the same volume.

The base of the cylinder is a circle, hence area of the base which is area of a circle is given by the formula

= πr^2

Since the two cylinders, have same cross-sectional area at all points. then the area of the base =  πr^2

With a common height, h we have the volume

= Area of base of the cylinder * height

= πr^2 * h

Cavalieri's principle let us know that if the solid object have equal cross-sectional area at same points then the volume at a particular point is equal

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The coordinates of the image of the triangle and the rules that can be used to transform the triangle are;

1. A' is located at (-3, 3)

B' is located at (-2, -1)

C' is located at (2, 1)

Second part; The rules are;

(x, y) → (x + 5, -y)

(x, y) → (5·x, 5·y)

A transformation of a figure is the reorientation of the figure to change the size and position of the figure.

1. The coordinates of the triangle ABC following the transformation (x, y) → (-x, y) are;

A(3, 3) (x, y) → (-x, y) A'(-3, 3)

B(2, -1) (x, y) → (-x, y) B'(-2, -1)

C(-2, 1) (x, y) → (-x, y) C'(2, 1)

2. The coordinates of the vertices of the triangle are; (1, 1), (4, 1), and (0, 4)

Translating the triangle five units right, we get;

(1 + 5, 1) = (6, 1), (4 + 5, 1) = (9, 1), and (0 + 5, 4) = (5, 4)

The coordinates of the triangle following a translation 5 units right are therefore;  (6, 1), (9, 1), and (5, 4)

The coordinates of the image of the point (x, y) following a reflection across the x-axis is the point (x, -y), therefore;'

The coordinates of the image of the triangle obtained from the previous transformation following a reflection across the x-axis is therefore;

(6, 1) reflection across the x-axis → (6, -1)

(9, 1) reflection across the x-axis → (9, -1)

(5, 4) reflection across the x-axis → (5, -4)

A rule that takes the triangle to a congruent triangle right five units and reflected over the x-axis is therefore;

The transformation of a triangle by a dilation by a scale factor of five, such that the triangle is five times larger can be obtained by the expression for a dilation transformation as follows;

(x, y) → (a·x, a·y)

Therefore, we get;

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Answer:

(x + 1)^2 + (y + 6)^2 = 25.

Step-by-step explanation:

Samantha needs to mix 10 milliliters of the 40% alcohol solution with 90 milliliters of the 60% alcohol solution to create 100 milliliters of a 58% solution.

Let x be the number of milliliters of the 40% alcohol solution that Samantha needs to mix, and let y be the number of milliliters of the 60% alcohol solution. Since Samantha needs to create 100 milliliters of a 58% solution, we can write the following system of equations:

x + y = 100 (equation 1: total volume)

0.4x + 0.6y = 0.58(100) (equation 2: alcohol concentration)

In equation 1, we see that the total volume of the resulting mixture must be 100 milliliters. In equation 2, we convert the concentration of the 58% solution into a decimal and set it equal to the weighted average of the concentrations of the two solutions.

We can solve this system of equations to find the values of x and y:

x + y = 100

0.4x + 0.6y = 58

Multiplying the first equation by 0.4, we get:

0.4x + 0.4y = 40

Subtracting this equation from the second equation, we get:

0.2y = 18

y = 90

Substituting y = 90 into equation 1, we get:

x + 90 = 100

x = 10

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Answer:

Capital One Auto

Step-by-step explanation:

Based on the provided information, Sarah should go for the loan option offered by Capital One Auto with a 6.9% interest rate compounded annually because it is a lower interest rate than that of Chase Auto and compounded annually is more beneficial in the long term as opposed to simple interest rate offered by Chase Auto.

Answer:

The integers you seek are:

759, 761, 763, 765

since

759 + 761 + 763 + 765 = 3048.



Hope this helps!

The five number summary for Mrs. Tinney's class is: 0, 72, 85, 96.5, 100. Tinney's class has a smaller IQR. We would need to look at a histogram or box and whisker plot to confirm these conjectures.

The median is a statistical measure that represents the middle value of a dataset. It is the value that separates the lower half of the dataset from the upper half. To find the median, the data must be arranged in order from smallest to largest, and then the middle value is identified.

If the dataset contains an odd number of values, then the median is the middle value. For example, if the dataset is {2, 4, 6, 7, 9}, then the median is 6, which is the middle value.

If the dataset contains an even number of values, then the median is the average of the two middle values. For example, if the dataset is {2, 4, 6, 7, 9, 10}, then the median is (6+7)/2 = 6.5, which is the average of the two middle values, 6 and 7.

To find the five number summary for Mrs. Tinney's class, we first need to order the scores from least to greatest:

0, 16, 72, 78, 80, 85, 88, 95, 98, 100

The minimum score is 0 and the maximum score is 100.

The median is the middle score, which is 85.

To find the first quartile, we split the scores into two halves at the median and find the median of the lower half:

0, 16, 72, 78, 80

The median of the lower half is 72.

To find the third quartile, we find the median of the upper half:

88, 95, 98, 100

The median of the upper half is 96.5.

Therefore, the five number summary for Mrs. Tinney's class is: 0, 72, 85, 96.5, 100.

To compare the consistency of the two classes, we can look at the interquartile ranges (IQRs), which give the range of scores that contain the middle 50% of the data. The IQR for Mrs. Tinney's class is 96.5 - 72 = 24.5, while the IQR for Mrs. Aguiar's class is 90 - 50 = 40. Mrs. Tinney's class has a smaller IQR, which means that their scores are more consistent.

The means for the two classes suggest that the data may not be symmetric. If the data were symmetric, we would expect the means to be roughly in the middle of the data set. However, the mean for Mrs. Aguiar's class is closer to the upper end of the data set, which suggests that the data may be skewed to the right. The mean for Mrs. Tinney's class is closer to the lower end of the data set, which suggests that the data may be skewed to the left. However, we would need to look at a histogram or box and whisker plot to confirm these conjectures.

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If the number of events is taken as x then the inequality is:

[tex](200*4)+(x*25)\geq 1200[/tex] ( as there are only 4 weeks in a month )

If we further solve this inequality we can get the answer:

[tex]800+(x*25)\geq 1200[/tex]

[tex]x*25\geq 400[/tex]

[tex]x\geq \frac{400}{25}[/tex]

[tex]x\geq 16[/tex]

So, as we saw here, the minimum number of events required for Darlene to complete the goal is 16.

But she is planning to organize 4 events which is insufficient. She needs to organize 12 more events in order to satisfy the inequality.

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Let's first calculate how much Darlene will earn in one week by organizing four recycling events:

$200 (base pay) + $25 (per event) x 4 (number of events) = $300

So, if Darlene organizes four recycling events per week, she will earn $300 per week.

To reach her goal of at least $1,200 in four weeks, we can set up the following inequality:

4 x (number of events) x $25 + $200 x 4 ≥ $1,200

100 x (number of events) + $800 ≥ $1,200

100 x (number of events) ≥ $400

(number of events) ≥ 4

Therefore, the number of events Darlene needs to organize to reach her goal of at least $1,200 is at least 4.

Since Darlene plans to organize four recycling events per week, this means she would need to work four weeks to reach her goal. Therefore, organizing four events each week would be enough to meet her goal, as long as she works all four weeks

The fractions [tex]\frac{-2}{5}[/tex] and the fraction [tex]\frac{-4}{10}[/tex] , both are equal [tex]\frac{-2}{5} =\frac{-4}{10}[/tex], which means the "=" sign makes the statement true.

A mathematical relationship between two expressions is called inequality, and it is expressed using one of the following:

"less than or equal to": [tex]\leq[/tex]

"greater than" :>

"greater than or equal to" : [tex]\geq[/tex]

"less than": <

"not equal to": [tex]\neq[/tex]

To compare the fraction, make the denominator of both fractions the same.

Given:

Fraction 1 = [tex]\frac{-2}{5}[/tex]

Fraction 2 = [tex]\frac{-4}{10}[/tex]

To make the same denominator we can multiply by 2 to the numerator and denominator of the fraction 1.

[tex]\frac{-2}{5} =\frac{-2 * 2}{ 5*2}[/tex]

[tex]\frac{-2}{5} =\frac{-4}{10}[/tex]

Hence from the above calculation, the given fractions are equal.

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Answer: 3.71

Step-by-step explanation:

7. The simplified expression is 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex], 8. The simplified expression is 5(m - 2)/(m - 1),  9. The simplified expression is 3/5,

10. The simplified  expression is -(p + 10)/(p(9 - p)).

What is an expression?

7. To simplify the expression, we can cancel out common factors in the numerator and denominator:

(32x³ * y)/(5x * y²) * (15y)/(8x² *[tex]y^{4}[/tex] )

= (32/5) * (x³/x²) * (1/y²) * (3/2) * (1/x²) * (1/y³)

= 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex]

Therefore, the simplified expression is 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex].

8. The simplified expression is 5(m - 2)/(m - 1).

To simplify the expression, we can factor the numerator:

(m² - 6m + 8)/(2m - 2) = (m - 4)(m - 2)/(2(m - 1))

We can then cancel out common factors:

(m - 4)(m - 2)/(2(m - 1)) * 10/(m - 4)

= 5(m - 2)/(m - 1)

Therefore, the simplified expression is 5(m - 2)/(m - 1).

9. The simplified expression is 3/5.

To simplify the expression, we can first simplify the fractions within the parentheses:

28n + 40/35n + 50 = (4n + 8)/(5n + 10)

12n + 24/8n + 16 = (3n + 6)/(2n + 4)

We can then simplify the expression by multiplying the two fractions:

(4n + 8)/(5n + 10) * (3n + 6)/(2n + 4)

= 2(2n + 4)/(5n + 10) * 3(n + 2)/(2(n + 2))

= 3/5

Therefore, the simplified expression is 3/5.

10. The simplified expression is -(p + 10)/(p(9 - p)).

To simplify the expression, we can factor the second fraction in the numerator and then cancel out common factors:

(p + 10)/(9 - p) * (p² - 5p - 36)/(4p² + 16p)

= (p + 10)/(9 - p) * ((p - 9)(p + 4))/(4p(p + 4))

= -(p + 10)/(p(9 - p))

Therefore, the simplified expression is -(p + 10)/(p(9 - p)).

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Answer: A) Likely

Step-by-step explanation: Without further context, it's hard to tell what 0.999 represents.

Answer: The number 0.999 is a valid number that exists between the values of 0 and 1 on the number line. Therefore, it is possible and not unlikely or impossible. The correct answer is option C, which is "Neither unlikely nor likely".

Step-by-step explanation: The number 0.999 is the decimal representation of a fraction that is very close to 1 but not relatively equal to 1. However, it is still an important number found between 0 and 1 on the number line and is commonly used in math and science.

The statement "0.999 is probable" or "0.999 is unlikely” suggests that the number is somehow unique or rare, which it is not. In fact, 0.999 is a standard number used in many calculations and applications.

So the correct answer is option C, which means that 0.999 is neither particularly probable nor improbable. It only exists as a valid number between 0 and 1.

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Answer:

[tex]y = - \frac{7}{5} x + 59[/tex]

The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588

We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.

The standard error of the mean can be calculated as

SE = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size

Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.

SE = 90 / sqrt(72) = 10.6066

Next, we need to standardize the sample mean using the z-score formula

z = (X - μ) / SE

where X is the sample mean, μ is the population mean.

Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.

z = (1173.8 - 1192) / 10.6066 = -1.7356

We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.

Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.

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