the academy of orthopedic surgeons states that 80% of women wear shoes that are too small for their feet. a researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. how large a sample is necessary?

Answer:

  4.05 pounds

Step-by-step explanation:

You want to know the weight that can be added to 2.65 pounds and 10.8 pounds if the total is to be 17.5 pounds.

The available capacity is the difference between the capacity and the weight already in the container:

  17.5 lb -2.65 lb -10.8 lb = 4.05 lb

The container can hold up to 4.05 more pounds.

Answer:

a) 8.8 square centimetres

b) 31.8 square centimetres

c) (3a + 12) square centimetres

d) Area = (2b + 2c + 4) square centimetres

Step-by-step explanation:

a) We have to split the diagram into three separate rectangles as shown below.

The area of A:

Area = 5.3 * 1 = 5.3 square centimetres

The area of B:

Area = 3.3 * 1 = 3.3 square centimetres

The area of C:

Area = 2 * 1 = 2 square centimetres

The area of the shape is the sum of the areas of the three shapes:

Area = 5.3 + 3.3 + 2 = 8.8 square centimetres

b) We have to split the diagram into two separate rectangles as shown below.

Note:(The diagram has conflicting values for 2.6 and 2.1 but I went with 2.6 as it seems more feasible in the diagram)

The area of A:

Area = 3 * 2.6 = 7.8 square centimetres

The area of B:

Area = 6 * 4 = 24 square centimetres

The area of the shape is the sum of the areas of the two shapes:

Area = 7.8 + 24 = 31.8 square centimetres

c) The shape is a rectangle and so its area is:

Area = 3 * (a + 4) = (3a + 12) square centimetres

d) The shape is a trapezium and so its area is:

Area = 0.5(A + B)H

where A =  c cm

B = b + 2 cm

H = 4 cm

The area of the shape is therefore:

Area = 0.5 * (c + b + 2) * 4

Area = 2 * (b + c + 2)

Area = (2b + 2c + 4) square centimetres

Answer:

Step-by-step explanation:

A correlation coefficient of 0.55 implies a weak positive correlation, because it's close to 0.50. Remember that strong correlations are 1 or -1, positive or negative, and the middle of the interval represents no correlation.

Having said that, 0.55 indicates some correlation, but weak. Therefore, the right answer is C.

Her prediction will be somewhat likely to be close to the actual value.

We have given that,

Madelina wants to make a prediction using a linear model with a correlation coefficient of 0.55.

We have to determine the correct statement.

The correlation coefficient is a statistical measure of the strength of the relationship between the relative movements of two variables.

A correlation coefficient of 0.55 implies a weak positive correlation because it's close to 0.50. Remember that strong correlations are 1 or -1, positive or negative, and the middle of the interval represents no correlation.

Having said that, 0.55 indicates some correlation, but weak.

Therefore, the right answer is C.

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The fewest number of days over which the tournament can take place is 5 days.

As each team plays with other team Once and we have total 5 teams so number of matches will be (4+3+2+1)

Counted as team 1 plays with all other teams = 4 matches

Team 2 plays with team 3,4,5 =3 matches

Team 3 play with team 4,5=2 match

And the last match is between team 4 and team5

Total match = 10 and can be played two matches per day:

Number of days = 10/2

= 5 days.

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c) You travel about 50 miles per hour.

d) You were 15 miles from home when you started.

e) After 7 hours, you will be 365 miles away from home.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

When x = 0, y = 15, hence the intercept b is given as follows:

b = 15.

In six hours, the distance increased by 300 miles, hence the slope m is given as follows:

m = 300/6 = 50.

Hence the equation is:

y = 50x + 15.

After seven hours, the predicted distance is given as follows:

y = 50(7) + 15 = 365 miles.

The points on the line are:

(0,15) and (6, 315).

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Answer:

Linda makes 3 more cards than Paul.

Step-by-step explanation:

Let's express the affirmations into equations:

Paul (P) can make 1 card for every 3 cards Linda (L) makes:

\(  \frac{P}{L} = \frac{1}{3} \)

\( 3P = 1L \)            (1)

Linda can make 3 cards for every 2 cards that Aaron (A) makes:

\( \frac{L}{A} = \frac{3}{2} \)  

\( 2L = 3A \)          (2)        

During a week, Aaron makes 72 cards, hence the number of cards of Linda and Paul can be calculated as follows:

From equation (2):

\( L = \frac{3}{2}A = \frac{3}{2}72 = 108 \)

Now, from equation (1):

\( P = \frac{1}{3}L = \frac{1}{3}108 = 36 \)

Finally, the number of cards that Linda makes more than Paul is:

\( \frac{L}{P} = \frac{108}{36} = 3 \)

Therefore, Linda makes 3 more cards than Paul.

I hope it helps you!    

Number of more cards Linda made than Paul for the week is; she made 72 more cards than Paul for the week.

We are told that;

Paul can make 1 card for every 3 cards Linda makes. Let number of card Paul makes be p and let number of cards Linda makes be L. Thus, we have;

p/l = 1/3

Thus;

l = 3p

Linda can make 3 cards for every 2 cards that Aaron makes. If number of cards that Aaron makes is a, then;

l/a = 3/2

l = 3a/2

Now, we are told that Aaron made 72 cards in a week. Thus, a = 72 and so we have;

l = (3 × 72)/2

l = 108 cards for the week

Since l = 3p, then;

p = l/3

p = 108/3

p = 36 cards for the week.

Thus;

Difference between number of Linda's cards and Paul's cards = 108 - 36 = 72

Thus,linda made 72 more cards than Paul for the week.

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Answer:

Choice D:

Step-by-step explanation:

If we check them one by one...

Choice A is all correct, so we leave that there for now

Choice B's 3x12 is equal to 36, so therefore it's wrong

Choice C has the same mistake as Choice B - 3x12 is not equal to 32

Choice D is all correct, so therefore it is the answer

Though Choice A is also correct, the question asked for all of the different ways you can arrange the cars

So, therefore... the answer is A!

Hope this helped!

The end of the long hand of the clock travels about 78.54 inches (25π) in 2 1/2 hours.

Clock can be defined as a machine in which a device that performs regular movements in equal intervals of time is linked to a counting mechanism that records the number of movements

The long hand of the clock completes one full revolution in 12 hours. Therefore, in one hour, it travels a distance equal to the circumference of a circle with a radius of 5 inches, which is given by 2πr = 2π(5) = 10π inches.

In 2 1/2 hours, the long hand of the clock travels a distance equal to (2 1/2) x 10π = 25π inches.

So, the end of the long hand of the clock travels about 78.54 inches (25π) in 2 1/2 hours.

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Let's call the cost of the dryer "x".

We know from the problem that the washer costs $68 less than the dryer, so the cost of the washer would be "x - 68".

The problem also tells us that the combined cost of the washer and dryer is $782. So we can set up an equation:

x + (x - 68) = 782

Simplifying this equation, we get:

2x - 68 = 782

Adding 68 to both sides, we get:

2x = 850

Dividing both sides by 2, we get:

x = 425

So the dryer costs $425.

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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The solution to the differential equation y' + 3y = f(t), y(0) = α using Laplace transforms is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

We use the Laplace transform on both sides of the problem in order to solve the given differential equation. Let Y(s) and F(s) represent the Laplace transforms of y(t) and f(t), respectively. Taking the Laplace transform of both sides of the equation, we have:

sY(s) - y(0) + 3Y(s) = F(s)

Substituting y(0) = α, we get,

sY(s) - α + 3Y(s) = F(s)

Rearranging the equation and solving for Y(s), we have,

Y(s) = (F(s) + α)/(s + 3)

Now, we need to find the inverse Laplace transform of Y(s) to obtain y(t). Using the properties of Laplace transforms, we know that the inverse Laplace transform of Y(s) is y(t) = L⁻¹{Y(s)}. Applying the inverse Laplace transform, we find,

y(t) = αe⁻³ᵗ + L⁻¹{F(s)/(s+3)}

The term αe⁻³ᵗ corresponds to the initial condition y(0) = α. The remaining term L⁻¹{F(s)/(s+3)} represents the inverse Laplace transform of F(s)/(s+3), which depends on the specific function f(t) and its Laplace transform.

Therefore, the solution to the differential equation is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

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The correct answer is 3780 bolts

Explanation:

In one hour the machine can make either 500 nuts or 840. Now, if the machine first made 750 nuts, this means the machine worked 1.5 hours. You can know this using the rule of three:

500 nuts  (a)  = 1 hour (b)

750 nuts  (c) = x (time spent to make 750 nuts)

x = 750 x 1 / 500

x = 1.5

Note: In a rule of three you find the fourth unknown value if you multiply value b by c and divide it by the value a.

According to this, the machine worked 1.5 hours making nuts, and if the machine started at 2 pm, this means the machine ended making nuts at 3.30 pm as 2 pm + 1.5 hours = 3:30 pm (2 + 1.5 = 3.5 ). Now you know the machine made bolts from 3: 30 pm to 8:00 p.m. This means the time the machine made bolts was 4 and a half hours or 4.5 hours (8 - 3.5 = 4.5). At this point, the only missing step is to multiply the time 4.5 hours by the number of bolts the machine makes each hour 840 and this is equivalent to 3780 bolts (840 x 4.5 = 3780).

Answer:

Step-by-step explanation:

\(5\frac{1}{6}=\frac{(5*6)+1}{6}=\frac{31}{6}\)

Answer:

31/6 (improper fraction).

Step-by-step explanation:

5 1/6 = (6 × 5) + 1/6 = 31/6

31/6 is the improper fraction.

Answer:

2 triangles and 3 rectangles

Step-by-step explanation:

Because all triangular prisms have 2 triangle faces and 3 rectangle faces

1,692,489,445 expression is equivalent to 22^3 squared 15 - 9^3 squared 15.

To simplify this expression, we can first evaluate the exponents:

22^3 = 22 x 22 x 22 = 10,648

9^3 = 9 x 9 x 9 = 729

Substituting these values back into the expression, we get:

10,648^2 x 15 - 729^2 x 15

Simplifying further, we can calculate the values of the squares:

10,648^2 = 113,360,704

729^2 = 531,441

Substituting these values back into the expression, we get:

113,360,704 x 15 - 531,441 x 15

Which simplifies to:

1,700,461,560 - 7,972,115

Therefore, the final answer is:

1,692,489,445.

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Answer:

C. A set of objects chosen from a larger set in which the order of the objects doesn't matter.

Step-by-step explanation:

That is the definition of a combination. Order does not matter

For example, selecting 3 students from a total of 10 students. The set selected is a smaller set from a larger set

Answer:

The sequence is Arithmetic because it uses subtraction.

The first term is a(1) = 65 since it comes first in the formula.

Step-by-step explanation:

We are given the equation 65-100n. 65 is the first term since it comes first in the arithmetic formula and 100n is the common difference. So the correct answer should be an arithmetic sequence and 65 as the first term.

I also got it right when i took the test :)

Answer:

s=6.2

Step-by-step explanation:

-3.1s=-19.22

divide -19.22 by -3.1 to get s

s=6.2

Answer:

When calculating startup costs, it's essential to consider both the market and the product you want to produce. In our infographic analysis, the startup cost of a lemonade stand in today's world would range from under $10 to almost $400 for a pre-fab stand ordered from the Internet and a fancy Breville juice extractor.

Step-by-step explanation:

We have coordinates (-2, -3) and (1, 1)

To find: Slope of a line that passes through these two coordinates

Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)

We will use the formula of Slope :

m = y₂ - y₁ / x₂ - x₁

Where 'm' stands for slope

m = 1 - (-3) / 1 - (-2)

m = 1 + 3 /  1 + 2

m = 4 / 3

The slope of the line is  4/3

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In correlational and experimental study designs, a key requirement for a sample is that population whom the researchers are investigation

A sample is a portion of a larger population that is selected to represent the entire group. In both correlational and experimental study designs, a key requirement for a sample is that it should be representative of the population it is meant to represent.

In a correlational study design, the goal is to examine the relationship between two or more variables. The sample must be representative of the population to ensure that the correlation calculated from the sample is representative of the correlation that exists in the population.

If the sample is not representative, the correlation calculated from the sample may be different from the correlation that exists in the population, leading to incorrect conclusions.

In an experimental study design, the goal is to test a causal relationship between two or more variables.

The sample must be representative of the population to ensure that the results of the experiment are generalizable to the population.

If the sample is not representative, the results of the experiment may not be generalizable to the population, leading to incorrect conclusions.

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Therefore, the coordinates of point B are approximately (3.8, 6.8) that is option A.

To find the coordinates of point B, we can use the concept of a ratio and the formula for finding a point along a line segment.

Let's assume the coordinates of point B are (x, y).

The ratio of AB to BC is given as 2:3. This means that the distance from point A to point B is two-fifths of the total distance from point A to point C.

We can calculate the distance between points A and C using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the given values:

d = √((5 - 3)² + (11 - 4)²)

d = √(2² + 7²)

d = √(4 + 49)

d = √53

Now, we can set up the ratio equation based on the distances:

AB / BC = 2/3

(√53 - AB) / (BC - √53) = 2/3

Next, we substitute the coordinates of points A and C into the ratio equation:

(√53 - 4) / (5 - √53) = 2/3

To solve this equation, we can cross-multiply and solve for (√53 - 4):

3(√53 - 4) = 2(5 - √53)

3√53 - 12 = 10 - 2√53

5√53 = 22

√53 = 22/5

Now, we substitute this value back into the equation to find B:

x = 3 + 2√53/5 ≈ 3.8

y = 4 + 7√53/5 ≈ 6.8

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Step-by-step explanation:

f(x) = y = 64x³ - 1

y + 1 = 64x³

(y + 1)/64 = x³

\(x = \sqrt[3]{(y + 1) \div 64} \)

\(x = \sqrt[3]{y + 1} \div 4\)

that is the actual inverse function to calculate the original x value for a given y value of the original function.

but to make it a "normal" function, we need to rename the variables (x to y, y to x) :

\(y = \sqrt[3]{x + 1} \div 4\)

this is now f^-1(x)

but careful, don't get confused, if dealing together with the original function, this "x" is actually standing for the "y" of the original function ...

By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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The researcher will Eliminate the nonsignificant independence variable and rerun the regression.  

Meaning of multiple regression analysis: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables. The objective of multiple regression analysis is to use the independent variables whose values are known to predict the value of the single dependent value.

When modeling the relationship between a single response variable and multiple regressor variables, multiple regression analysis is used.

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Answer:it might be (F)

Step-by-step explanation:

Tell me if I’m right or wrong

The area of the rectangular park is equal to 0.233 sq miles.

The measurements of the park that are given in the question are given as 7/10 mile by 2/6 mile.

The length of the rectangle park is 7/10 and the width of the park is 2/6 mile. We know that the area of the rectangle park is given as the:

= length * width of the park.

= L * W

= (7/10) * (2/6)

we can reduce the fraction even further to make the calculation easy

= (7/10) * (1/3)

Multiplying the denominators we get

= 7/30

To make the answer even simpler it can be converted into a decimal form which will be:

= 0.233 sq miles.

Therefore, The area of the rectangular park is equal to 0.233 sq miles.

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Answer: The numbers are 4 and 6.

Step-by-step explanation:

Let one number be represented as

x

and the other as

y

.

According to the problem:

x

=

2

3

y

and

x

+

y

=

10

From the second equation we get:

x

+

y

=

10

∴

y

=

10

−

x

(subtracting

x

from both sides)

Replacing the value of

y

in the first equation we get:

x

=

2

3

y

x

=

2

3

(

10

−

x

)

Multiplying both sides by

3

we get:

3

x

=

2

(

10

−

x

)

Opening the brackets and simplifying we get:

3

x

=

20

−

2

x

Add

2

x

to both sides.

5

x

=

20

Divide both sides by

5

.

x

=

4

Since from the second equation we have:

x

+

y

=

10

substituting

x

with

4

we get:

4

+

y

=

10

Subtract

4

from both sides.

y

=

6

Answer: The smaller number is 12.

Step-by-step explanation:

Just took the test

Answer:

The slope of the line is m=−1.

The equation of the line in the slope-intercept form is y=−x+5.

The equation of the line in the point-slope form is y−3=−(x−2).

The equation of the line in the point-slope form is y−5=−x.

The general equation of the line is x+y−5=0.