a team of medical researchers sample 30 subjects from a population with replacement, and find that 8 of them have high bone mineral density (bmd). unbeknownst to the researchers, the population consists of 622 patients, of whom 147 have high bmd. what is the standard error of the sample proportion of patients with high bmd?

Answer:

The answer is B. One solution

Answer:

-4+2x-3

Step-by-step explanation:

The experimental probability of dealing a black cards on the basis of given dealt cards is 10/19.

The dealt cards are,

Spades: 3, 4, 6, J, Q, K that is six spade cards

Clubs: A, 2, 5, 7, J, K that is six clubs cards

Hearts: A, 2, 5 that is three hearts cards

Diamonds: A, 2, 3, 6, K that is four cards

So total number of dealt cards = 6 + 6 + 3 + 4 = 19 cards

Here number of black cards = Spade cards + Diamond Cards = 6 + 4 = 10 cards.

The probability of dealing a black card = Number of dealt black cards/ Total number of dealt cards = 10/19

Hence the experimental probability of dealing a black card is 10/19.

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The minimum sample size required to ensure that the estimate has an error of at most 0.15 at the 99% level of confidence = 426

Here, the population variance is σ² = 1.44

The mean is \(\bar{x}\) = 6

And the margin of error is  E = 0.15

The standard deviation is given by,

⇒ σ = \(\sqrt{1.44}\)

⇒ σ = 1.2

Here, the confidence level is 99%

So, the level of signoficance would be,

⇒ α = (100 - 99)%

⇒ α = 0.01

From the normal distribution table the critical value would be,

\(z_{\alpha /2}\) = 2.58

Now we find the sample size :

\(n=(\frac{z_{\alpha /2}\times \sigma}{E} )^2\\\\n=(\frac{2.58 \times 1.2}{0.15} )^2\)

n = 426

Therefore, the sample size is 426

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The z or t score to be used is  (0.422,0.978)

How to find the critical value ?

Critical probability (p*) = 1 - (Alpha / 2), where Alpha is equal to 1 - (the confidence level / 100), is the unit statisticians use to determine the margin of error within a set of data in statistics.

The critical value for α = 0.13 is \(z_{c} = \frac{z_{1} - \alpha }{2}\)

The corresponding confidence interval is computed as shown below

\(CI = (X1_{1} - X_{2}- z_{c} \sqrt{\frac{a_{1}^{2}}{n_{1} } + \frac{a_{2}^{2}}{n_{2} }} , X1_{1} - X_{2}+z_{c} \sqrt{\frac{a_{1}^{2}}{n_{1} } + \frac{a_{2}^{2}}{n_{2} }} )\)

\(CI = (2.1 - 1.4- 1.514\sqrt{\frac{1^{2}}{37 } + \frac{0.5_{2}^{2}}{38 }} , 2.1 - 1.4 + 1.514 \sqrt{\frac{1^{2}}{37 } + \frac{0.5^{2}}{38 }} )\)

CI = (0.422, 0.978)

0.422< mu1 - mu 2 < 0.978

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Step-by-step explanation:

\(→ \frac{8 {a}^{( - 5) } {b}^{(4)} }{12 {a}^{( - 6)} {b}^{( - 2)} } = \frac{2 {a}^{(6 - 5)}{b}^{(4 + 2)} }{3} = \boxed{ \frac{2}{3}a {b}^{6} }✓ \\ \)

Answer:

16

Step-by-step explanation:

substitute the values into the equation

9(4)+4(-5)

solve...

36-20=16

Answer:

16

Step-by-step explanation:

9x + 4y

Let x =4 and y = -5

9(4)+ 4(-5)

36 -20

16

To illustrate the budget constraints, let's consider the two proposals for a representative individual and the original budget constraint with no policy.

Proposal 1: Income Guarantee of $3000 per year ($15 per day)

In this proposal, the individual receives an income guarantee of $3000 per year, which is equivalent to $15 per day. We can plot the budget constraint with leisure on the x-axis and income on the y-axis.

The slope of the budget constraint represents the wage rate, which is $5 per hour. Assuming an individual works an average of 200 days per year, the maximum income can be calculated as follows:

Max Income = Wage Rate * Hours per Day * Days per Year

          = $5/hour * 8 hours/day * 200 days/year

          = $8000

Therefore, the budget constraint with the income guarantee of $3000 per year would be a straight line passing through the point (0, $3000) and (160, $5000) since $5000 is the income level when all days are worked (200 days * $25 per day).

Proposal 2: Original Budget Constraint with No Policy

In this proposal, we consider the original budget constraint with no policy. Assuming the wage rate is $5 per hour and the individual works an average of 200 days per year, the maximum income is still $8000. The budget constraint without any policy would also be a straight line passing through the point (0, $0) and (160, $8000).

To illustrate both proposals and the original budget constraint on the same graph, we can plot the budget constraints as straight lines with leisure on the x-axis and income on the y-axis. The budget constraints would intersect at different points representing the different policies.

Note: Without specific information about the leisure-income trade-off or any additional policies, it is difficult to provide precise coordinates for the intersection points or the slopes of the budget constraints. The graph provided is a general representation to illustrate the concepts.

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a = 12 (cos(π/3) + i sin(π/3))

b = 3 (cos(π/4) + i sin(π/4))

a • b = 36 (cos(π/3) cos(π/4) + i cos(π/3) sin(π/4) + i cos(π/4) sin(π/3) + i ² sin(π/3) sin(π/4))

… = 36 (cos(π/3 + π/4) + i sin(π/3 + π/4))

… = 36 (cos(7π/12) + i sin(7π/12))

… ≈ -9.32 + i 34.8

The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.

To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.

In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:

ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)

Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:

ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134

Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.

Therefore, the value of the error for Z, with one decimal place, is 4.

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Add the measurements to the drawing. Angle JEF and angle JFE both measure x degrees, while angle JED measures 180 - x degrees.

To find the measure of the base angles JEF and JFE in a trapezoid, we need to consider the fact that the opposite angles of a trapezoid are supplementary, meaning they add up to 180 degrees.

Since the trapezoid has two pairs of opposite angles, we can apply this property to solve for the base angles. Let's assume angle JEF measures x degrees. Since angle JEF is opposite to angle JFE, the measure of angle JFE is also x degrees.

Now, let's consider the other pair of opposite angles. Since the sum of the measures of the opposite angles is 180 degrees, the measure of angle JEF plus the measure of angle JED equals 180 degrees. Since angle JEF measures x degrees, we can set up the equation: x + JED = 180.

The given question is half of part , the full answer for the question is below.

To find the measure of JED, we subtract x from both sides: JED = 180 - x. Finally, we can add the measurements to the drawing. Angle JEF and angle JFE both measure x degrees, while angle JED measures 180 - x degrees.

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Answer: 18x + 12

Step-by-step explanation:

Step #1: Determine the length of each side.

The polygon is regular, so all the sides are equal. Thus, all sides measure 3x+2.

Step #2: Determine the number of sides in the polygon.

This polygon is identified as a hexagon meaning it consists of 6 sides.

Step #3: Set up an expression and distribute.

       (Number of sides) x (Length of each side)

       (6)(3x+2)

So, the answer is 18x + 12.

Answer:

B. 3x + 2

Step-by-step explanation:

The polygon has 6 equal sides.

1 side has a side length of 3x + 2

Therefore, all sides of the polygon measure 3x + 2

Hope this helps!

The quotient of 1065 ÷ 33 is \(32\ \frac{3}{11}\) .

1065 ÷ 33 = 32.2727272727

Dividend = 1065

divisor = 33

quotient = 32

balance = 9

answer as a mixed number  \(32\ \frac{9}{33} = 32\ \frac{3}{11}\)

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Jim ran for approximately 4 minutes before dropping out of the 1600-meter race.

Jim ran 4/5 of a mile before dropping out of the 1600-meter race. To calculate how many minutes he ran, we first need to determine the distance he covered in meters, as the given pace is in miles per hour. Since 1 mile is approximately 1609.34 meters, Jim ran (4/5) * 1609.34 ≈ 1287.47 meters.

His pace was 12 miles per hour, which is equivalent to 12 * 1609.34 ≈ 19312.08 meters per hour. To convert this to meters per minute, we divide by 60: 19312.08/60 ≈ 321.87 meters per minute.

Now, we can determine the number of minutes Jim ran by dividing the distance he covered (1287.47 meters) by his pace in meters per minute (321.87 meters per minute):

1287.47 meters / 321.87 meters per minute ≈ 4 minutes

So, Jim ran for approximately 4 minutes before dropping out of the 1600-meter race.

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Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

Answer:

351cm³

step by step explanation:

Volume of the prism:

=[1/2×(a+b)×h]×l

=[1/2×(5+8)×6]×9

=(1/2×13×6)×9

=(6.5×6)×9

=39×9

=351cm³

The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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Answer: x <-3 (use the less than sign with the line under I don’t know how to put it on there through my phone.)

Step-by-step explanation: 2x-10< -16

2x<-6

x<-3

Answer:

x ≤ -3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

2(x - 5) ≤ -16

Step 2: Solve for x

Here we see that any value x smaller than or equal to -3 would work as a solution.

Step-by-step explanation:

x+77=126 (vertical opposite angles are equal)

x=126-77

x= 49

Answer:

k =-2

Step-by-step explanation:

Using the slope formula

( y2-y1)/(x2-x1) = m

( k- -1)/( -10 - -8) = 1/2

( k+1)/ ( -10+8) = 1/2

( k+1) /-2 = 1/2

Multiply each side by -2

( k+1) /-2 * -2 = 1/2 * -2

k+1 = -1

Subtract 1 from each side

k+1-1 = -1-1

k = -2

Answer:

K= -5 because -10 divided by -5 which is K gives u 2

Answer:

2.5 OR 2 1/2

Step-by-step explanation:

PEMDAS

P: PARENTHESES

E: EXPONENT

M: MULTIPLICATION

D: DIVISION

A: ADD

S: SUBTRACT

3X4 15

12÷5= 2.5

ANSWER:2.5

Answer: See step-by-step

Step-by-step explanation:

first plot a point at (5,0), then plot a point at (0,3) and draw a straight line between them and beyond.

Answer:

Measuring Spoon

Step-by-step explanation:

The tool you would use is a measuring spoon.

Answer:

Measuring spoon

Step-by-step explanation:

To convert the masses of copper and chlorine to moles, Avogadro's unit relationships can be utilized.

Avogadro's number (6.022 x 10^23) represents the number of particles (atoms, molecules, ions) in one mole of a substance. Using this concept, the relationship between mass and moles can be established by utilizing the molar mass of the respective elements.

To convert the mass of copper to moles, the molar mass of copper (Cu) is required. The molar mass of copper is determined by adding up the atomic masses of its constituent atoms, which can be found on the periodic table. By dividing the mass of copper by its molar mass, the number of moles of copper can be obtained. Similarly, to convert the mass of chlorine to moles, the molar mass of chlorine (Cl) is used. By dividing the mass of chlorine by its molar mass, the number of moles of chlorine can be determined.

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Answer:

Adult Admission: 215 Tickets $1,290

Child Admission: 385 Tickets $3,870

Step-by-step explanation:

Child:

5,160÷4=1,290

1,290÷6=215

Adult:

500-215=385

5,160-1,290=3,870

Answer:

1. x = 54, y = 114,

missing angles => 66° and 114°

2. x = 42, y = 14,

Missing angles => 84°, 86°

3. x = 40, y = 50

Missing angles => 105°, 75°

Step-by-step explanation:

1. y° = 114° (corresponding angles are congruent)

(x + 12)° + y° = 180° (linear pair angles)

Substitute

x + 12 + 114 = 180

x + 126 = 180

Subtract 126 from each side

x = 180 - 126

x = 54

✔️Find the missing angles by plugging in the values of x and y in each case

(x + 12)° = 54 + 12 = 66°

y = 114°

2. ✔️Find x:

(2x)° + 96° = 180° (consecutive interior angles are supplementary)

Subtract 96 from each side

2x = 180 - 96

2x = 84

x = 84/2

x = 42

✔️Find y:

(3y + 44)° + 94° = 180° (consecutive interior angles are supplementary)

3y + 44 + 94 = 180

3y + 138 = 180

3y = 180 - 138

3y = 42

y = 42/3

y = 14

✔️Missing angles:

(2x)°

Plug in the value of x

= 2(42) = 84°

(3y + 44)°

Plug in the value of y

3(14) + 44 = 86°

3.

✔️Find x:

3x - 15 = 105 (corresponding angles are congruent)

3x = 105 + 15

3x = 120

x = 120/3

x = 40

✔️Find y:

(3x - 15)° + (y + 25)° = 180° (linear pair angles are supplementary)

Plug in the value of x to solve for y

3(40) - 15 + y + 25 = 180

120 - 15 + y + 25 = 180

Add like terms

130 + y = 180

y = 180 - 130

y = 50

✔️Missing angles:

(3x - 15)°

Plug in the value of x

3(40) - 15 = 105°

(y + 25)°

Plug in the value of y

50 + 25 = 75°

Answer: 2,342 people wear glasses or contacts.

Step-by-step explanation:

1): You take 40% of 5,855 which is 2,342

We might predict that around 2,342 people wear glasses or contacts in Gabriela's town with a population of 5,855.

We have,

If 2 out of 5 people wear glasses or contacts in Gabriela's class, we can use this proportion to predict how many people might wear glasses or contacts in her town with a population of 5,855:

The proportion of people wearing glasses or contacts in Gabriela's class: 2/5

Now, apply this proportion to the town's population:

Number of people wearing glasses or contacts

= Proportion * Total population

= (2/5) x 5,855

Calculating this:

Number of people wearing glasses or contacts ≈ 2,342

Thus,

We might predict that around 2,342 people wear glasses or contacts in Gabriela's town with a population of 5,855.

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If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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Step-by-step explanation:

she sell 5piece out of 6 per hour

for 36 hour, she sell:

5 × 36 = 180piece of pie

one pie is cut to 6 piece

180/6 = 30pie