An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $20.5 for a random sample of 1190 people. Assume the population standard deviation is known to be $11. Construct the 85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.

Answer:

Pull terms out from under the radical, assuming positive real numbers.

0

Step-by-step explanation:

Answer:

bottom graph of left picture

Step-by-step explanation:

For each day he makes his bed, he earns $0.50

In 1 day he earns $0.50

In 2 days he earns $1.00

In 3 days, he earns $1.50

...

In 8 days, he earns $4.00

Look in the 4 graphs.

Which graph has the following points, (1, 0.5), (2, 1), 3, 1.5), ... , (8, 4)?

It is the second graph (bottom graph of left picture.)

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

\(a = 20\) --- tree distance from north gate

\(b =14\) --- movement from south gate

\(c = 1775\) --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

\(\triangle ADE \sim \triangle ACB\) --- similar triangles

So, we have the following equivalent ratios

\(AE:DE = AB:CB\)

Where:

\(AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775\)

Substitute these in the above equation

\(20:x/2 = 20 + x + 14: 1775\)

\(20:x/2 = x + 34: 1775\)

Express as fraction

\(\frac{20}{x/2} = \frac{x + 34}{1775}\)

\(\frac{40}{x} = \frac{x + 34}{1775}\)

Cross multiply

\(x *(x + 34) = 1775 * 40\)

Open bracket

\(x^2 + 34x = 71000\)

Rewrite as:

\(x^2 + 34x - 71000 = 0\)

Expand

\(x^2 + 284x -250x - 71000 = 0\)

Factorize

\(x(x + 284) -250(x + 284)= 0\)

Factor out x + 284

\((x - 250)(x + 284)= 0\)

Split

\(x - 250 = 0 \ or\ x + 284= 0\)

Solve for x

\(x = 250 \ or\ x =- 284\)

x can't be negative;

So:

\(x = 250\)

Step-by-step explanation:

values of d, g, and n :

d = 118°

g = 62°

n = 96°

Answer:

5 days

Step-by-step explanation:

Answer:

It will take 5 days for 4 people to do the job.

How to do it :

2 is half of 4.

5 is half of 10.

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Based on this estimate, the insurance company's projected value of this probability insurance policy is negative, implying that the insurance company will lose money on this policy.

Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.

The total of the potential payouts multiplied by the odds of each payout occurring equals the anticipated value of the insurance policy. In this scenario, the possible compensation is the $1500 insurance payout, and the likelihood of the client being involved in an accident is 3.3%, or 0.033.

Expected value = (Payout if event happens) x (Probability of event happening) - (Annual premium)

($1500) x (0.033) - ($120) = expected value

Value expected = $49.50 - $120

-$70.50 is the expected value.

Based on this estimate, the insurance company's projected value of this insurance policy is negative, implying that the insurance company will lose money on this policy.

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Set of data:

a. The mean of the set is 3.6.

b. The middle number is 3.

c. The mode of the set is 1.

d. The standard deviation of the set is 2.94.

The mean, we add up all the numbers in the set and divide by the total number of numbers:

mean = (3 + 1 + 1 + 4 + 9) / 5

mean = 18 / 5

mean = 3.6

The mean of the set is 3.6.

The median, we need to first arrange the numbers in order from smallest to largest:

1, 1, 3, 4, 9

Since there are an odd number of numbers in the set, the median is simply the middle number.

The middle number is 3.

The median of the set is 3.

The mode, we need to identify the number(s) that occur(s) most frequently in the set. In this case, the number 1 occurs twice, and all the other numbers occur only once.

The mode of the set is 1.

The standard deviation, we first need to find the deviation of each number from the mean.

The deviation of a number is simply the difference between the number and the mean.

The deviation of the first number (3) is:

deviation = 3 - 3.6

deviation = -0.6

Each number in the set and get the following deviations:

-0.6, -2.6, -2.6, 0.4, 5.4

Square each deviation:

\((-0.6)^2\) = 0.36

\((-2.6)^2\) = 6.76

\((-2.6)^2\) = 6.76

\((0.4)^2\) = 0.16

\((5.4)^2\) = 29.16

Squared deviations and divide by the total number of numbers in the set, and then take the square root of the result to get the standard deviation:

standard deviation = \(\sqrt{((0.36 + 6.76 + 6.76 + 0.16 + 29.16) / 5)\)

standard deviation = \(\sqrt{(43.2 / 5)\)

standard deviation = \(\sqrt{(8.64)\)

standard deviation = 2.94 (rounded to two decimal places)

The standard deviation of the set is 2.94.

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Answer:

22 meters/23.98 yards= 1 meter/ 1.09 yards

Step-by-step explanation:

You would multiply 22 by 1.09 and that is 23.98. Then you divided that from 1 and get 23.98 or you can round it to 24.

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

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Answer:

y = -3/2x-6

Step-by-step explanation:

y-intercept = - 6

Slope = - 3/2

Answer:

7 i think

Step-by-step explanation:

Answer:

8 square units I believe!

Step-by-step explanation:

Hope that helps!

Answer:

25.5

Step-by-step explanation:

1530 divided by 60 is 25.5 and 25.5 multiplied by 60 is 1530.

Answer:

t - 7/8 is the answer

hope it helps

The perimeter of PQRS would depend on the lengths of the tangent segments and the lengths of the intercepted arcs. Without specific measurements, we cannot determine the precise perimeter.

To determine the perimeter of quadrilateral PQRS, we need more information about the lengths of the sides or the relationship between the sides and angles. Without specific measurements or additional details, we cannot calculate the exact perimeter of the quadrilateral.

However, we can provide some general information.Since PQ¯ is tangent to circle R at point Q, it is perpendicular to the radius drawn from the center of the circle to point Q. Similarly, PS¯ is tangent to circle R at point S, so it is perpendicular to the radius drawn to point S.

The quadrilateral PQRS is formed by the tangents PQ¯ and PS¯ along with the two arcs intercepted by these tangents on the circle R.

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Answer:

We conclude that the slope of line 'n' is: m₂ = 10

Step-by-step explanation:

Given

The slope of line m is: m₁ = 10

Let m₂ be the slope of the 'n' line.

We know that when two lines are parallel, they have equal slopes.

i.e.  m₁ = m₂

as

The slope of line m is: m₁ = 10

and

The lines are parallel

so

The slope of line 'n' is: m₂ = 10

Therefore, we conclude that the slope of line 'n' is: m₂ = 10

Answer:

7.5 cm

Step-by-step explanation:

Since it's a right triangle, apply pythegorean theorem

Let the missing side be x

\( {7.8}^{2} = 2.1 { }^{2} + x {}^{2} \)

\(60.84 = 4.41 + {x}^{2} \)

\( {x}^{2} = 60.84 - 4.41\)

\( {x}^{2} = 56.43\)

\( \sqrt{ {x}^{2} } = \sqrt{56.43} \)

\(x = 7.5\)

Therefore, the length of the missing side is 7.5 cm

Answer:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

In this case, (x1, y1) = (4.25, 6.25) and (x2, y2) = (22, 6.25).

Plugging these values into the distance formula, we get:

distance = sqrt((22 - 4.25)^2 + (6.25 - 6.25)^2)

= sqrt(17.75^2 + 0^2)

= sqrt(315.0625)

= 17.75

Therefore, the length of the line segment is 17.75 units.

The expressions that describe the wingspan of the bat are Wingspan = 19.438 inches, Wingspan = 1.620 feet and Wingspan = 1.22 meters

The wingspan of the bat is given as

Wingspan = 19.438 inches

Convert the length from inches to feet.

So, we have:

Wingspan = 19.438 * 1/12 feet

Evaluate the product

Wingspan = 1.620 feet

Next, convert the length from feet to meters.

So, we have:

Wingspan = 1.620/1.33 meters

Evaluate the quotient

Wingspan = 1.22 meters

Hence, the expressions that describe the wingspan of the bat are Wingspan = 19.438 inches, Wingspan = 1.620 feet and Wingspan = 1.22 meters

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The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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Answer:

1/2 is 1 example

Step-by-step explanation:

what

A fraction that is less than 5/8 is 4/8

The fraction is given as:

Fraction = 5/8

A fraction less than 5/8 will have the same denominator but a smaller numerator compared to 5/8

Take for instance, the numerator can be

1 to 4

So, we have;

Smaller fraction = 4/8

Hence, a fraction that is less than 5/8 is 4/8

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The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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The absolve value function that models the ditch's vertical depth below ground level, is B. f(x) = -|x − 5| − 5

From the information given, it was stated that the ditch will be 5 feet deep at its lowest point. Also, x is the horizontal distance from the left edge of the ditch.

Now, the absolve value function that models the ditch's vertical depth below ground level will start with a (-) sign since it's below ground level. The appropriate function will be f(x) = = -|x − 5| − 5

In conclusion, the correct option is B.

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Answer:

Step-by-step explanation:

We know that:

Let's first solve for y by choosing any equation.

Now, let's substitute the value of y into the second equation.

Now, let's substitute the value of x into the equation of y.

Hence, the value of x and y are 2.5 and 4 respectively.

Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

Given this pair of probabilities, the probability that Mary is the first is  n(A) = n-1!, while the probability that Betty is last is  n(A) = n-1!

There are n! ways of making this arrangement

We have probability of A: Betty is the first person in this line

Probability of B: Mary is the last person

A U B = p(A) + p(B) - p(A ∩ B)

n(A) = n-1 that is given that Betty is the first person on the line.

then n(A) = n-1!

As the last person on the line P(B) = n-1!

Probability of (A∩B) =( n-2)!  this has Mary as the first and Betty as the last person.

Remaining students that would have to be on this line are n-2

Prob(A∪B) = n(A ∪ B)/n!

= 2(n-2)/n(n-1)

This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.

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We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

Answer:

The answer is $2.00 per ounce of soda.

Step-by-step explanation:

Hope this helps!

Answer:

$2.00 per ounce of soda. please mark me brainliest :)

Step-by-step explanation: