A survey was sent out to compare the proportion of adults who use their car horns when driving for two age populations (1=younger adults, defined as between 20 and 39 years old and 2 =older adults, defined as over 60 years old). The following data was obtained from those who responded.

Calculate the 90% confidence interval using the standard normal distribution. Note that 1 =0.52. P2= 0.35, and s.e.(P1-P2) =0.0338. Round to the fourth decimal point. Please enter you answer in the following format: (lower value, upper value)

Use the horn Use the horn
Group Yes No Total
1= younger adults 261 240 501
2= older adults 123 229 352

c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

Janet ran 100 meters in 15 seconds. How long did she take to run 2 meters?

Solution:

100/15 = y/2

Solve for y.

y = (15/100)(2)

y = 0.3

Answer: She took 0.3 seconds.

Answer:

\(Probability = \frac{27}{80}\)

Step-by-step explanation:

Given

\(Blue =9\)

\(Yellow = 7\)

Required

Determine the probability that one of the balls is blue while others is yellow

The order of selection may be any of these three:

Yellow, Yellow, Blue or Yellow, Blue, Yellow or Blue, Yellow, Yellow

Solving Yellow, Yellow, Blue

\(Probability = P(Y_1) * P(Y_2) * P(B)\)

\(Probability = \frac{7}{16} * \frac{6}{15} * \frac{9}{14}\)

\(Probability = \frac{1}{8} * \frac{1}{5} * \frac{9}{2}\)

\(Probability = \frac{9}{80}\)

Solving Yellow, Blue, Yellow

\(Probability = P(Y_1) * P(B) * P(Y_2)\)

\(Probability = \frac{7}{16} * \frac{9}{15} * \frac{6}{14}\)

\(Probability = \frac{9}{80}\)

Solving Blue, Yellow, Yellow

\(Probability = P(B) *P(Y_1) * P(Y_2)\)

\(Probability = \frac{9}{16} * \frac{7}{15} * \frac{6}{14}\)

\(Probability = \frac{9}{80}\)

Hence:

The required probability is:

\(Probability = \frac{9}{80} + \frac{9}{80} + \frac{9}{80}\)

\(Probability = \frac{27}{80}\)

Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation is 9.5 for a population.

This means that \(\sigma = 9.5\)

Sample of 60:

This means that \(n = 60\)

What is the standard deviation of the distribution of sample means for samples of size 60?

\(s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264\)

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Answer:

Step-by-step explanation:

Given data

mass of rock, m= 200 kg

height/distance = 3 m

Now we know that the expression for work done is

w= force* distance

and also we need to find the force exerted by mass of rock

F= mg

Substituting our data and solving for force we have (assuming g= 9.81 m/s^2)

Force= 200*9.81

Force= 1962 N

Now we can find the work done

work done= 1962*3

work done= 5880 joules

The work done should be 5880 joules

Since there is the mass of the rock is 200 kg

And, the height is 3 m

Now we know that

work done = force (distance)

Also,

F= mg

= 200(9.81)

=  1962 N

Now the work done is

= 1962(3)

= 5880 joules

Hence, The work done should be 5880 joules

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Answer:

40

Step-by-step explanation:

We are using sigma notation to solve for a sum of arithmetic sequences:

The 10 stands for stop at i = 10 (inclusive)

The i = 6 stands for start at i = 6

The i stands for expression of each term in the sum

Answer:

its 10w-3t+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The original one is false, with the answer being 84.

Answer: \(x-0.1x=27\)

Step-by-step explanation:

Let x be the number that gets decreased by 10% of itself.

x decreased by 10% of x is 27.

x is 100%, so 100%-10%=90%

So, 90% of x equals 27.

90% = 0.9

0.9x = 27

x = 30

Using the knowledge of proportion, the number of quarter-acre lots that will be made out of 6½ acres of land is: 26 lots.

Proportion is a form of equation whereby two ratios are equal to each other.

A land = 6½ acres

1 lot = ¼ acre

Number of quarter-acre lots in 6½ acres = 6½ ÷ ¼

13/2 ÷ ¼

13/2 × 4/1

52/2

= 26 lots.

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Note that the roots of the equation Unequal and rational (Option D)

The roots of the equation   (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.

x - 3 = ±√4

⇒ x - 3 = ±2

Solve for x

For the positive square root.

x - 3 = 2

x = 2 + 3

x = 5

For the negative square root.

x - 3 = -2

x = -2 + 3

x = 1

Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The roots of the equation (x - 3)² = 4 are

A.Unequal and irrational.

B.Equal and rational.

C.  Equal and irrational.

D.  Unequal and rational.

Answer:4.5

Step-by-step explanation:

39929292902902

Answer:

52=2.5,and,2

Step-by-step explanation:

Suppose that xandy are the reqd. nos.

Then, by what is given, we have,

(1):x+y=4.5=92,and,(2):xy=5.

From (1),y=92−x.

Subst.ing this y in (2), we have, x(92−x)=5,or,

x(9−2x)=10,i.e.,2x2−9x+10=0.

∴2x2−5x−−−−−−−−−4x+10−−−−−−−=0.

∴x(2x−5)−2(2x−5)=0.

∴(2x−5)(x−2

The differential equation dy/dt = y(3-y) smug all of the given conditions.

One possible autonomous differential equation with equilibrium solutions at y=0 and y=3, and with y' > 0 for 0 < y < 3 and y' < 0 for -∞ < y < 0 and 3 < y < ∞, is:

dy/dt = y(3-y)

We can see that y=0 and y=3 are equilibrium solutions by setting dy/dt = 0 and solving for y:

dy/dt = y(3-y) = 0

y = 0 or y = 3

To check the sign of y', we can use the derivative of y(3-y) with respect to y:  d/dy (y(3-y)) = 3 - 2y

For y < 0, we have y(3-y) < 0, so d/dy (y(3-y)) < 0, which says that y' < 0.

For 0 < y < 3, we have y(3-y) > 0, so d/dy (y(3-y)) > 0, which implies that y' > 0.

For y > 3, we have y(3-y) < 0, so d/dy (y(3-y)) < 0, which implies that y' < 0.

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Answer:

$20

Step-by-step explanation:

Since the discount was 10%, that means she paid 90% of the original price.

90% of x = 18

0.9x = 18

x = 18/0.9

x = 20

Answer: $20

Answer:

Step-by-step explanation:

\(10/18 = 1 R8, 1 + 8 = 9\)

Answer:

Area = 100 ft^2

Step-by-step explanation:

To calculate the area of this composite shape, you need to find the area of all shapes and add them together.

1. Break the composite shape into different shapes.

Shapes: one rectangle, one square,  and one triangle.

2. Find the area of each of them.

Rectangle

L= 8ft    

W= 10ft

A= L x W

A= 8ft x 10ft

A= 80ft^2

Square

L= 4ft

W=10ft - 6ft = 4ft

A= L x W

A= 4ft x 4ft

A= 16ft^2

Triangle

A= 1/2 x base x height

b= 14ft -8ft-4ft = 2ft

h= 10ft - 6ft =4ft

A= 1/2 (2ft x 4ft)

A= 1/2 (8 ft^2)

A= 4ft^2

3. Add all the areas.

Area = Rectangle Area+ Square Area+ Triangle Area

A = 80ft^2 + 16ft^2 + 4ft^2

A= 100ft^2

Hope this helps!

Answer:

1 hour

Step-by-step explanation:

Equation: 6 hours × 1/6 hours = 1 hour

If there are 6 hours and Tamela missed 1/6, that means she missed 1 hour of school.

Answer:

true

Step-by-step explanation: I hope this helps pls follow me, mark me as a brainiest, and like my post-bye have a good day!

Answer:

yes

Step-by-step explanation:

4/6 is 2/3 doubled

The two other positive angles of rotation that take Point A to Point B on the unit circle is (5π/6) and (5π/6) + 2π .

Given data ,

To find two other positive angles of rotation that take Point A to Point B, we need to consider the angle values that yield the same coordinates as (1, 0) after rotating counterclockwise.

The position of Point A is (1, 0) on the unit circle.

Now, let's find the coordinates of Point B after rotating (7π/6) radians counterclockwise.

To rotate counterclockwise by (7π/6) radians, we can subtract (7π/6) from the angle of Point A. So, the angle for Point B would be:

Angle of Point B = 0 - (7π/6) = - (7π/6)

Now , for positive angles of rotation, we can add multiples of 2π to the angle of Point B while keeping the same coordinates. Adding 2π to the angle gives us:

Angle of Point B = - (7π/6) + 2π = (5π/6)

Hence , two other positive angles of rotation that take Point A to Point B are (5π/6) and (5π/6) + 2π. Both of these angles yield the same coordinates as Point B, which is (1, 0) on the unit circle.

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A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).

In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;

f(x) = −x² + 2x - 15

f(x) = −2x + 2

0 = −2x + 2

2x = 2

x = 2/2

x = 1

For the maximum value of function 2, we have:

f(1) = −(1)² + 2(1) - 15

f(1) = -14

For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.

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Answer:

The slope is 5

the y-intercept is (0,7)

Step-by-step explanation:

The multiplier that will give the value of this house after 2 years is 2.22

What is multiplier?

The multiplier in this case means the extent to which the price of the house increases over the two-year period rather than the increase in individual years in years 1 and 2 which are denoted as 10% and 12%, in essence, we need to add 1 to the growth rate in the year in both years 1 and 2 respectively, then multiply the results together to arrive at the multiplier of the housing price

multiplier=(1+% increase in year 1)+(1+% increase in year 2)

% increase in year 1=10%

% increase in year 2=12%

multiplier=(1+10%)+(1+12%)

multiplier= 2.22

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Both angles 1 and 2 are supplementary and linear angles.

So, options (1) and (3) are the correct options.

If consider, ∠1 and ∠2 are supplementary. If two angles form a linear pair, the angles are supplementary. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.  

If consider complementary angles. They are equals if the two intersected lines by the transversal are parallel. In the figure, angles 1 and 2 are corresponding. The 1 is external and the 2 is internal. Angles that are on opposite sides of the transversal of two other lines.

If consider linear pair angles. The sum of angles of a linear pair is always 180 degrees. Consider the image as shown. Here angle 2 and angle 1 are said to be a linear pair because they are formed on the same line with a standard arm S and common vertex point Q. Also, the sum of angles 1 and 2 is equal to 180 degrees.

Two angles are said to be adjacent angles, if, they share a common vertex, a common side and they do not overlap. Observe the following figure to understand what adjacent angles look like. Angle 1 and 2 are adjacent because they have a common side BD and a common vertex B.

A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.

We can see all images.

So, that

When two lines intersect each other at a point, angles formed on the point are called as linear pair.

Since pair of linear angles is supplementary, sum of linear angles will be 180°.

m∠1 + m∠2 = 180°

Therefore, both angles 1 and 2 are supplementary and linear angles.

Options (1) and (3) are the correct options.

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The amount of interest due on the account is $8.36.

The interest on a loan or deposit can be calculated using simple interest. In order to calculate it, multiply the principal amount by the interest rate and then by the number of time periods (usually in years).

We must first determine the number of days for which the interest will accrue in order to calculate the amount of interest owed on the account. Since the charge was made on the 28th day after the payment was made on the 9th day, the interest will accrue for 19 days instead of the 28 since the payment was made.

We then use the formula for simple interest: Interest = Principal x Rate x Time

In this instance, the Principal is the initial balance of $660, the Rate is the annual percentage rate (APR), which needs to be converted to decimal form by dividing by 100, and the Time is the total number of days over which interest will accrue (19 days).

The Interest = $660 × 0.26 × (19/365) = $8.36

Thus, the total amount of interest due on the account is $8.36.

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Given:

The function is,

The graph of the above function is dilated by x. It is given as,

The points on h(x) is (-3,0),(0,-3),(1,-4),(2,-5).

Now, dilate the graph by multiplying x values.

The graph is given as,

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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