Construct a 90​% confidence interval of the population proportion using the given information. x=75 n=150

Below is the proof for the given statement "BC ≅ DA, BC ║ AD ⟹ ΔABC = ΔCDA":

Statements                     Reasons

BC ≅ DA                            Given

BC || AD                             Given

∠ BCA = ∠DAC             Alternate interior angles are known to be  congruent (BC || AD)

AC ≅ CA                           Reflexive Property

∆ ABC = ∆ CDA SAS  (Side-Angle-Side) congruence theorem, by the use of statements 1, 3, and also  4.

In the above text, we are said to be given that line BC is equal to line member DA, and BC . We need to prove that the two triangles ΔABC and ΔCDA are the same.

Therefore, To prove this, we start by using the given information to find harmonious angles in both triangles. Since BC is same to other, we know that alternate interior angles are equal, so ∠ BCA is sane to ∠ DCA.

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See text below

1. Given : BC ≅ DA, BC ║ AD

Prove : ΔABC = ΔCDA

Statements                           Reasons

1. BC  ≅ DA                            ------

2. BC || AD                             ------

2. ∠ BCA = ∠DAC                  ------

4. AC ≅ CA                            ------

5.   -----                                   -------

Answer:

We can use trigonometric identities to rewrite the equation as:

2sin x cos x + cos x = 0

Factoring out cos x, we get:

cos x (2sin x + 1) = 0

This equation has two solutions in the interval [0, 2π):

cos x = 0 when x = π/2 and x = 3π/2

2sin x + 1 = 0 when sin x = -1/2, which occurs at x = 7π/6 and x = 11π/6.

However, we need to find the solutions in the interval [0, 2x). Since the period of both sin x and cos x is 2π, we can add any multiple of 2π to the solutions we found to get all possible solutions in the interval [0, 2x).

For the solutions x = π/2 and x = 3π/2, we have:

π/2, 5π/2 (adding 2π)

3π/2, 7π/2 (adding 2π)

For the solutions x = 7π/6 and x = 11π/6, we have:

7π/6, 19π/6 (adding 2π)

11π/6, 23π/6 (adding 2π)

The smallest solution in the interval [0, 2x) is π/2, and the largest solution is 23π/6.

Therefore, the solutions are:

x = π/2, 3π/2, 7π/6, 11π/6, 19π/6, 23π/6.

John has to deposit $1308.75 every year in order to have the same amount at retirement as Bob

Compound interest is the term used to describe interest that is earned on both the initial principal and the accumulated interest from earlier periods.

It is interest that is calculated on both the initial principal and any accumulated interest, in other words.

If we were to consider an investment of $100 with a 5% compound yearly interest rate as an example.

It would be seen that the total value of the investment would rise to $105 at the end of the first year thanks to interest earnings of $5 (5% of $100).

In the second year, interest would be calculated on both the original $100 and the $5 in accumulated interest if the interest accumulates annually, bringing the total to $110.25 ($105 + 5% of $105).

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give question oh t is so easy

The inequality with the set of solutions (-14, infinity ) can be expressed as follows: x > -14

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Any value of x bigger than -14 will fulfill the inequality, according to this inequality, and the solution set contains all real numbers greater than -14 but excluding -14.

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Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

V = πr^2h

where r is the radius of the cylinder, and h is the height of the cylinder.

The diameter of the pool is 14 feet, so the radius is half of that, or 7 feet. The height is 5 feet. Therefore, the volume of the pool is:

V = π(7)^2(5) ≈ 769.39 cubic feet

We can convert this volume to gallons using the conversion factor given:

1 cubic foot ≈ 7.5 gallons

Therefore:

769.39 cubic feet * 7.5 gallons/cubic foot ≈ 5,770 gallons

So the pool can contain approximately 5,770 gallons of water (rounded to the nearest whole number).

Answer:

270 degrees

Step-by-step explanation:

There are 60 minutes on a clock face, and the minute hand of a clock makes one complete revolution around the clock face in 60 minutes. This means that the minute hand turns through the angle of 360 degrees in 60 minutes.

The time from 3:30 P.M. to 4:15 P.M. is 45 minutes.

So, during this time, the minute hand of the clock turns through a fraction of a circle equal to:

Fraction of a circle = (angle turned by the minute hand) / (angle for a complete circle)

= (45 minutes) / (60 minutes)

= 3/4

Therefore, the minute hand of the clock turned through 3/4 of a circle during this time.

To find the number of degrees turned by the minute hand, we can multiply the fraction of a circle turned by the total number of degrees in a complete circle:

Degrees turned by the minute hand = (Fraction of a circle turned) x (360 degrees)

= (3/4) x (360 degrees)

= 270 degrees

Therefore, the minute hand of the clock turned through 270 degrees during this time.

the probability of event B happening is 0.50 or 50%. This means that the occurrence of event A has no impact on the likelihood of event B happening, and vice versa.

How to solve the question?

If A and B are independent events, then the occurrence of A does not affect the probability of B happening. Mathematically, this can be written as P(B|A) = P(B), where P(B|A) represents the conditional probability of B given that A has occurred.

Using the formula for the probability of the intersection of two events, we have:

P(A AND B) = P(A) * P(B|A)

Since A and B are independent, we can substitute P(B|A) with P(B):

0.30 = 0.60 * P(B)

Solving for P(B), we get:

P(B) = 0.30 / 0.60 = 0.50

Therefore, the probability of event B happening is 0.50 or 50%. This means that the occurrence of event A has no impact on the likelihood of event B happening, and vice versa. It's important to note that independence is a key assumption when using the multiplication rule to calculate the probability of the intersection of two events. If the events are not independent, this rule cannot be used, and other methods such as the addition rule or Bayes' theorem must be used to calculate probabilities.

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The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.2622

The margin of error is:

M = T*s = 2.2622*0.3 = 0.68

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF

The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF.

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Answer:

It would take the company 11.25 days to repave the road.

Step-by-step explanation:

27 miles to repave total

2.4 repavement per day

27 / 2.4 = 11.25

Therefore, it would take the company 11.25 days to repave the road.

[tex]\cfrac{7\times 10^{5}}{2\times 10^{3}}\implies \cfrac{7}{2}\times\cfrac{10^5}{10^3}\implies \cfrac{7}{2}\times 10^5\cdot 10^{-3}\implies \cfrac{7}{2}\times 10^{5-3} \\\\\\ \cfrac{7}{2}\times 10^2\implies 3.5\times 100\implies 350[/tex]

Surface area of the composite figure with cylinder and pentagonal prism is 597 square feet

The surface area of cylinder = 2πrh+2πr²

r is radius and h is height of cylinder

r is 6 ft and h is 4 ft

surface area of cylinder = 2π(6)(4)+2π6²

=48π+2π(36)

=48π + 72π

=128π square feet

=128×3.14

=401.92square feet

Surface area of pentagonal prism = 5ah + 1/2 √5(5+2√5)a²

a is base length and h is height

a=4, h=7

Surface area = 195 square feet

Total surface area = 402+195

=597 square feet

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If triangle XYZ is isosceles, then the two sides (XY and YZ) are congruent in addition to the two base angles.

Angle Y (the one at the top of the triangle) = 42 degrees

Angles X and Z are congruent because of the properties of an isosceles triangle. Let's call both angle measures "x" in our equation.

x + x + 42 = 180

2x + 42 = 180

2x = 138

x = 69

Answer: The measure of Angle Z is 69 degrees.

Hope this helps!

Sasha's next step is to swing arcs on both sides of the segment to intersect the first two arcs created. Option A is correct.

By doing this, she will be creating a two points of intersection on the segment. She can then draw a straight line which is connecting these two points, which will bisect the segment into two equal parts. This method of bisecting a segment is called as the compass-and-straightedge construction, and it is a fundamental technique in Euclidean geometry.

Alternatively, if you want to bisect a segment without using the compass-and-straightedge construction, you can measure the length of the segment and mark its midpoint. Then you can draw a line connecting the two endpoints through the midpoint to bisect the segment.

Hence, A. is the correct option.

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--The given question is incomplete, the complete question is

"Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger than the compass the same width and places it on the other endpoint. What is her next step? A) Swing arcs on both sides to intersect the first two arcs created. B) Swing an arc that intersects the segment. C) Swing arcs that intersect a point that is not on the segment. D) Swing an arc that intersects the opposite endpoint."--

The verbal expression for 0.7x-11 is "seven tenths of x minus eleven."

A scenario expressed using mathematical terms is condensed into a conversational statement. It identifies the connections between and movements made by amounts. Example: The product of a number x and one multiplied by five.

Words are present in verbal utterances. For instance, the phrase "three more than a double a number" is a verb. The algebraic equivalent of the phrase "three more than a double a number" is the expression 2x + 3.

Verbal models are another name for verbal expressiveness. When we communicate ourselves verbally, we describe the mathematical data using language. An expression becomes a verbal expression when it is written in terms or spoken in words. However, compared to verbal expression, an algebraic expression is entirely different.

The verbal expression for 0.7x-11 is "seven tenths of x minus eleven."

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s = 8/T is the required power function if s is inversely proportional to T.

If s varies inversely with T, this is expressed mathematically as;

s α 1/T

s = k/T

Given the following parameters

s = 1/2

t = 16

Substitute to have;

1/2 = k/16

2k = 16

k = 8

The required inverse function will be:

s = 8/T

Hence the required inverse function is s = 8/T

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The data set for which the mean is most appropriate to describe the set instead of the median is; 0, 57, 847, 859, 866, 866, 872.

It follows from the task content that the answer choice for which the dataset is better described by the mean instead of the median is to be identified.

When outliers exist in a dataset, the mean is a better measure of center for the data set.

On this note, it follows that the answer choice for which the mean is a better description of the dataset is; 0, 57, 847, 859, 866, 866, 872.

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you first find the area of the triangle which is A=1/3bh or A=1/3 4.7x5.6 .Then you find the area of the traposiod and add it together

Step-by-step explanation:

To find the equation of the parabola with focus (-3,2) and directrix x-y+1=0, we can use the definition of a parabola: the set of all points that are equidistant to the focus and directrix.

Let P(x, y) be an arbitrary point on the parabola, and let d(P, directrix) be the distance from P to the directrix. The distance from P to the focus is given by the distance formula:

d(P, focus) = √[(x - (-3))^2 + (y - 2)^2] = √[(x + 3)^2 + (y - 2)^2]

Since P is equidistant from the focus and directrix, we have:

d(P, directrix) = |x - y + 1| / √(1^2 + (-1)^2) = |x - y + 1| / √2

Therefore, the equation of the parabola is given by:

d(P, focus) = d(P, directrix)

√[(x + 3)^2 + (y - 2)^2] = |x - y + 1| / √2

Squaring both sides and simplifying, we get:

(x + 3)^2 + (y - 2)^2 = (x - y + 1)^2 / 2

Expanding the right-hand side and simplifying, we get:

2(x + 3)^2 + 2(y - 2)^2 = (x - y + 1)^2

Expanding the right-hand side again and simplifying, we get:

2x^2 + 8xy + 2y^2 - 8x - 12y + 20 = 0

Therefore, the equation of the parabola is:

2x^2 + 8xy + 2y^2 - 8x - 12y + 20 = 0

which is in general form.

The final apportionment of the 103 seats using Jefferson's method is: County A = 84 seats, County B = 119 seats, County C = 136 seats, and County D = 64 seats.

Here are the steps you can follow to apportion the 103 seats to the four counties;

Determine the population of each county; Let's assume the populations of the four counties are as follows;

County A; 250,000

County B; 350,000

County C; 400,000

County D; 200,000

Calculate the geometric mean of the populations; To calculate the geometric mean, we need to multiply the populations of all the counties together and then take the fourth root of the result.

Geometric mean = (250,000 x 350,000 x 400,000 x 200,000)^(1/4)

Geometric mean = 305,541.27

Calculate the ratio of each county's population to the geometric mean; To calculate the ratio for each county, we divide its population by the geometric mean.

County A; 250,000 / 305,541.27 = 0.8171

County B; 350,000 / 305,541.27 = 1.1458

County C; 400,000 / 305,541.27 = 1.3085

County D; 200,000 / 305,541.27 = 0.6542

Calculate the initial apportionment of seats; To calculate the initial apportionment of seats, we assign each county the number of seats equal to its ratio multiplied by the total number of seats.

County A; 0.8171 x 103 = 84.18, rounded down to 84 seats

County B; 1.1458 x 103 = 118.04, rounded up to 118 seats

County C; 1.3085 x 103 = 134.75, rounded up to 135 seats

County D; 0.6542 x 103 = 67.03, rounded down to 67 seats

Check if the initial apportionment is equal to the total number of seats; The initial apportionment gives a total of 404 seats, which is greater than the total number of seats available (103).

Adjust the apportionment to reach the total number of seats; To adjust the apportionment, we assign additional seats to each county based on their fractional remainders.

County C has the largest fractional remainder (0.75), so it gets the first additional seat.

The new apportionment is; A = 84, B = 118, C = 136, D = 65

The total number of seats is 403, so one seat is left unassigned.

We assign the last seat to the county with the largest fractional remainder, which is County B.

Therefore, the final apportionment of the 103 seats will be; County A = 84 seats, County B = 119 seats, County C = 136 seats, and County D = 64 seats.

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The height of the cylinder is approximately 7 twelfths inches.

What is meant by height?

Height generally refers to the measurement of the distance from the base of an object to its top or the highest point, often in a vertical direction. In geometry, height can refer to the perpendicular distance between the base and the top of a two-dimensional shape, such as a triangle or parallelogram.

According to the given information

The volume of a cylinder is given by the formula V = πr²h where V is the volume, r is the radius of the base and h is the height of the cylinder.

Given that the volume of the cylinder is 1 and two ninths cubic inches and the radius of the base is one-third inch, we can calculate the height of the cylinder using the formula above as follows:

V = πr²h

1 and two ninths = π(1/3)²h

1 and two ninths = π/9 * h

h = (1 and two ninths) * 9 / π

h ≈ 7/12 inches 2.

Therefore, the height of the cylinder is approximately 7 twelfths inches.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{5}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +x}{2}~~~ ,~~~ \cfrac{ -10 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE D} }{(11~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ 5 +x }{2}=11\implies 5+x=22\implies \boxed{x=17} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -10 +y }{2}=4\implies -10+y=8\implies \boxed{y=18}[/tex]

The "House Vodka Martini" may sell less when its price is raised since some consumers could prefer the premium brand.

Contribution Margin = Selling Price - Total Cost

Let's start with the "House Vodka Martini":

Czarina Vodka: 2 oz * (Czarina cost per oz)

Dry Vermouth: 0.5 oz * (Dry Vermouth cost per oz)

Olive garnish: 1 * (Olive cost per unit)

Cocktail napkin: 1 * (Napkin cost per unit)

Total Cost (House Vodka Martini) = sum of the costs above

Contribution Margin (House Vodka Martini) = $4.50 - Total Cost (House Vodka Martini)

Let's solve for "Grey Goose Vodka Martini":

Grey Goose Vodka: 2 oz * (Grey Goose cost per oz)

Dry Vermouth: 0.5 oz * (Dry Vermouth cost per oz)

Olive garnish: 1 * (Olive cost per unit)

Cocktail napkin: 1 * (Napkin cost per unit)

Total Cost (Grey Goose Vodka Martini) = sum of the costs above

Contribution Margin (Grey Goose Vodka Martini) = $5.50 - Total Cost (Grey Goose Vodka Martini)

Other considerations, like client preferences and the drinks' perceived value, must also be taken into account. The "House Vodka Martini" may sell less when its price is raised since some consumers could prefer the premium brand.

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a. If a = 5, the value of n will be 17.

(b) A binomial expression for n in general

terms of “a” will be n = 4a - 3.

(a) In the case that a is equal to 5, then the expression transforms into:  

(x^(2a+1))³/(x^(a+3))² = (x^(2(5)+1))³/(x^(5+3))² = (x^11)³/(x^8)² = x^(33-16) = x^17  

Therefore, for a = 5, n = 17.

(b) We can simplify this by making use of the rules of exponents:  

(x^(2a+1))³/(x^(a+3))² = x^(6a+3)/(x^(2a+6)) = x^(6a+3-2a-6) = x^(4a-3)  

Therefore, the binomial expression for n in terms of a equals: n = 4a - 3

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The probability of not getting a number 1 through 18 is b) 10 over 19.

There are a total of 38 slots on the roulette wheel, and 18 of them are numbered 1 through 18. Therefore, there are 20 slots that are not numbered 1 through 18. The probability of not getting a number 1 through 18 on a single spin of the roulette wheel is the same as the probability of getting one of the 20 non-numbered slots.

Thus, the probability of not getting a number 1 through 18 is 20/38 or 10/19.

Therefore, the answer is option b) 10 over 19.

Correct Question :

A roulette wheel has 38 slots total, 36 of which are numbered 1 through 36, and 2 green slots labeled "O" and "00." For any spin of the wheel, what is the probability of NOT getting a number 1 through 18?

a.) 9 over 19

b.) 10 over 19

c.) 1 over 19

d.) 18 over 19

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The equation of the supply function is q = 20000p - 10000

Let's use the point-slope form of a linear equation:

slope = (change in quantity) / (change in price) = (10000 - 5000) / (1.50 - 1.00) = 10000 / 0.50 = 20000

Using the point-slope form with the point (1.50, 10000):

q - 10000 = 20000(p - 1.50)

Simplifying:

q = 20000p - 20000 + 10000

q = 20000p - 10000

So the equation of the supply function is q = 20000p - 10000

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The slope of the given line is -1.

Given is an equation of a line -5x-5y = 10, we need to find its slope,

-5x-5y = 10

It can be written is simpler form,

-5x-5y = 10

-x - y = 2

Now, converting the equation into slope-intercept form,

i.e., y = mx+c, m = slope

So,

-x - y = 2

y = -x-2

Here, m = -1.

Therefore, the slope is -1

Hence, the slope of the given line is -1.

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