A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 500 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.47. The polling agency will take another sample from a different region, Region B, of the city. The agency plans to select a random sample of 400 voters. Assume that the population proportion of voters who would support the ballot measure in Region B is 0.51.
b. What is the probability that the two sample proportions will differ by more than 0.05?

The Formula is p(A and B) = p(A) * p(B|A)

1) In general, the formula for finding the probability of the intersection of two events, A and B, is:

p(A and B) = p(A) * p(B|A)

This is also known as the conditional probability formula, where p(B|A) is the probability of event B occurring given that event A has already occurred.

2) The addition rule for disjoint events is:

p(A or B) = p(A) + p(B)

This rule applies when events A and B are disjoint, meaning they cannot occur at the same time. In other words, the two events have no common outcomes.

The general addition rule, on the other hand, is:

p(A or B) = p(A) + p(B) - p(A and B)

This rule applies when events A and B are not disjoint, meaning they can occur at the same time. In this case, we need to subtract the probability of the intersection of A and B, as we have double-counted the outcomes that are common to both events.

3) Joint probability refers to the probability of two or more events occurring together, also known as the probability of the intersection of the events. It is the probability of multiple events occurring at the same time.

4) Conditional probability refers to the probability of an event occurring, given that another event has already occurred. It is the probability of an event A happening, given that event B has already happened. The conditional probability of A given B is represented as P(A|B).

5) Conditional probability is the probability of an event occurring given that another event has already occurred. It is a way to express how likely an event is given that another event has already occurred. It is represented as P(A|B) where A and B are events, it is the probability of event A happening given that event B has already happened.

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If the expression [tex]r(x) = 3x - 1[/tex] and the expression [tex]s(x) = 2x + 1[/tex] , then the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is (a) [tex]\frac{3(6)-1}{2(6) +1}[/tex] .

What are Algebraic Expression ?

The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : [tex]3x+7[/tex] .

Here the two expressions are given as [tex]r(x) = 3x - 1[/tex] and [tex]s(x) = 2x + 1[/tex] ;

we have to find equivalent expression for [tex]\frac{r}{s} (6)[/tex] ;

By the Division Property of Algebraic Expression ;

it can be written as : [tex]\frac{r(6)}{s(6)}[/tex] ;

So , Substituting [tex]x=6[/tex] , in r(x) ,

we get ; [tex]r(6) = 3(6) - 1[/tex] , ......equation(1)

On Substituting [tex]x=6[/tex] , in s(x) ,

we get ; [tex]s(6) = 2(6)+1[/tex] ,  ....equation(2) ;

Substituting the values of r(6) and s(6) from equation(1) and equation(2) in [tex]\frac{r(6)}{s(6)}[/tex] ;

we get ;

⇒ [tex]\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}[/tex] ;

Therefore , the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is [tex]\frac{3(6)-1}{2(6) +1}[/tex] .

The given question is incomplete , the complete question is

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?

(a) [tex]\frac{3(6)-1}{2(6) +1}[/tex]

(b) [tex]\frac{(6)}{2(6)+1}[/tex]

(c) [tex]\frac{36-1}{26+1}[/tex]

(d) [tex]\frac{(6)-1}{(6)+1}[/tex]

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a) To find the 5-number summary for these data, we need to find the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values.

Minimum: the smallest value in the data set
Q1: the value that separates the lowest 25% of the data from the rest
Median: the middle value of the data set (when the data is arranged in numerical order)
Q3: the value that separates the highest 25% of the data from the rest
Maximum: the largest value in the data set
b) To sketch a boxplot, we can represent the data using a box that goes from the Q1 to Q3, with a line (the median) in the middle. Whiskers extend from either end of the box to the minimum and maximum values, with any observations outside of the whiskers represented as dots (outliers).

c) The shape of the data is not specified in the problem statement. However, it can be described as skewed, symmetric or normal. The center of the data can be described as the mean or median, and the spread can be described as the range or interquartile range.

d) It is not possible to determine if there are any outliers without the data set.

Please note that the data is not provided, so the above steps are theoretical.

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Answer: 67 degrees

Step-by-step explanation: If you add two angles together, this is actually equal to the second angle because it has to be if you pay attention to the complementary angles.

Answer:

  43.5 square units

Step-by-step explanation:

You want to know the area of shading in a 12 by 7 rectangle with a white right triangle of side length 9 removed.

The area of the white triangle is ...

  A = 1/2bh

  A = 1/2(9)(9) = 40.5 . . . . square units

The area of the rectangle is ...

  A = LW

  A = (12)(7) = 84 . . . . square units

The shaded area is the area of the rectangle that is not included in the triangle.

  Shaded area = 84 -40.5 = 43.5 . . . . square units

__

Additional comment

The given figure cannot actually be constructed. The triangle is too large to be inscribed in the rectangle. An inscribed right triangle can have a side length between 7 and √74 ≈ 8.6.

Marcella is correct. A square is a type of rectangle.

A rectangle is a four-sided plane figure with four right angles. A trapezoid is a four-sided plane figure with one pair of parallel sides. Thus, it is not possible to draw a trapezoid that is also a rectangle. However, a square is a four-sided plane figure with four equal sides and all four right angles, making it a type of rectangle. Therefore, it is possible to draw a square that is a rectangle.

A rectangle is a four-sided plane figure with four right angles. A trapezoid is a four-sided plane figure with one pair of parallel sides.

Marcella is correct. A square is a type of rectangle.

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According to the given information the line integral is 8(1+125[tex]\sqrt{110}[/tex]) / 15 .

What distinguishes a line integral from a definite integral?

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

[tex]\int\limits_c {xy} \, ds[/tex],  C : x = t^2 , y = 2t,  0 ≤ t ≤ 3

x' = 2t , y' = 2

ds = [tex]\sqrt{(x')^2 + (y')^2}[/tex]

[tex]\sqrt{4(t)^2 + 4}[/tex]

[tex]\int\limits C {xy} \, ds[/tex] = [tex]\int\limits^3_0 {2.2t.2\sqrt{1+t^2}} \, dt[/tex]

t = tanθ

dt = (1+[tex]tan^{2}[/tex]θ)dθ = ([tex]sec^{2}[/tex]θ)dθ

= [tex]\int\limits^3_0 {4t^3\sqrt{1+t^2} } \, dt[/tex]

= 8(1+125[tex]\sqrt{110}[/tex]) / 15

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The ratio of 2 or more integers is known as fraction. The answer to the given expression is 10

Fractions are written as a ratio of two integers. Fractions are written in the form a/b

The expression in question is given as 5/8 * 16

Simplified form of the expression

On solving, we will have;

5/8 * 16

5 * 16/8

Since the ratio of 18 to 8 is 2, hence the expression will be further simplified as;

5 * 16/8 = 5 * 2

5 * 16/8 = 10

Hence the answer to the given expression is 10

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The z-score for this amount of advertising time will be -5.217.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

A TV slot guarantees how much promotion each hour of transmission time has a normal of 17 minutes and a standard deviation equivalent to 2.3 minutes.

The amount of advertising time is equal to 5 minutes. Then the z-score is calculated as,

z = (5 - 17) / 2.3

z = -12/ 2.3

z = -5.217

The z-score for this amount of advertising time will be -5.217.

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The value of the size of angle PSQ of the given triangle is; 61°

From the given triangle ΔPQR, we see that;

m∠QPS = 65°

m∠PRQ = 43°

Now, it is clear that Line PSR is a straight line divided in the ratio;

size of angle PQS : size of angle SQR = 3:1

m∠PQS : m∠SQR = 3:1

Thus, since sum of angles in a triangle is 180°, then we say that;

∠PQR = 180° - (∠QPS + ∠PRQ)

Plugging in the relevant values;

∠PQR = 180° - (65° + 43°)

∠PQR = 72°

Using the concept of angle addition postulate, we have that;

∠PQR = m∠PQS + m∠SQR

Since m∠PQS : m∠SQR = 3:1, then we have;

m∠PQS = 3 × m∠SQR

Thus;

∠PQR =  (3 × m∠SQR) + m∠SQR

∠PQR = 4 × m∠SQR

4 × m∠SQR = ∠PQR

4 × m∠SQR  = 72°

m∠SQR = 72°/4

m∠SQR  = 18°

m∠PQS = 3 × m∠SQR

m∠PQS = 3 × 18°

m∠PQS  = 54°

Finally;

∠PSQ = 180° - (65° + 54°)

∠PSQ  = 61°

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Answer:

To find the volume of the cereal box, we multiply the length, width, and height:

12 inches * 7 and 3/4 inches * 2 inches = 96 inches * 7.75 inches * 2 inches = 1458 cubic inches

To find the volume of the pastry box, we multiply the length, width, and height:

3 and 2/3 inches * 3 and 1/2 inches * 2 and 1/3 inches = 3.666 inches * 3.5 inches * 2.333 inches = 25.158 cubic inches

To find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:

1458 cubic inches - 25.158 cubic inches = 1432.842 cubic inches

So the difference in volume between the two boxes is 1432.842 cubic inches.

Answer:1432.842 cubic inches

Step-by-step explanation:

On solving the provided question we can say that at confidence Level  = 90%, we have  sample size = 423

The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.

Confidence Level  = 90%

E = 0.04

Corresponding to 90%

confidence level role=="1654454884514"  Z = 1.645

formula

n= p(1 - p)(0Z/E)

n = 0.50(1 - 0.50)(1.645/0.04)

= 422.816 = 423

so, sample size = 423

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Orthocenter is the best term to describes point R in the triangle UVW.

What is orthocenter?

" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."

According to the given figure,

In triangle UVW,

Ray VR perpendicular to UW

Ray UR perpendicular to VW

Ray WR perpendicular to UV

Altitudes of side  ( UV , VW, and WU) of triangle UVW intersect at

point R.

As per the definition of orthocenter , point R represents orthocenter.

Hence, orthocenter is the best term to describes point R in the triangle UVW.

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Answer:

To prove that the measure of angle RST is greater than the measure of angle R, we can use the following steps:

By the definition of a triangle, angle RST is supplementary to angles R, S and T.

Since RT > ST, we can conclude that angle R is less than angle S.

Since angle RST is supplementary to angles R and S, the measure of angle RST is greater than the measure of angle R.

This can be written as measure of angle RST = measure of angle R + measure of angle S > measure of angle R

So, we've proven that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.

Proof by contradiction could also be used to prove that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.

Assume that the measure of angle RST <= measure of angle R. By the triangle inequality theorem, we know that RT + ST > R. But we are given that RT > ST, so RT + ST > RT > R which is a contradiction. Therefore, measure of angle RST must be greater than measure of angle R.

The correct answer is option D , which states that , both estimators are unbiased, and var() < var().

The efficiency pf an unbiased estimator, is known as the estimator's precision when divided by the precision's upper bound . It's the lower bound on the variance which is when  divided by the estimator's variance.

The ratio of the precisions of two unbiased estimators represents their relative efficiency . In case of a biased estimators, relative efficiency is defined as the MSE ratio.

If we want to compare the efficiency of two estimators it can be done by  simply comparing the variance of the estimators. The one having a lower variance is said to be more efficient. It should satisfy certain conditions like,

The two estimators are used to predict the same parameter of the population.

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Answer:

8.5

Step-by-step explanation:

850/100

Answer:

[tex]8.5l[/tex]

Step-by-step explanation:

1cl = 10ml

850cl = 8500ml

1000ml= 1l

8500ml= 8.5l

The sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) is 1440°

A polygon having ten sides (or a ten-sided polygon) is called a decagon or ten-gon, in geometry. Also, it has ten vertices and ten angles.

The summation of the interior angles of a polygon is ( n - 2 ) x 180 where n is the number of sides.

The sum of interior angles = (10 - 2) x 180

The sum of interior angles = 1440º

Therefore the measure of each angle is

10 angles = 1440

1 angle = 1440 ÷ 10 = 144º

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Work Shown:

y - y1 = m(x - x1)

y - (-3) = -3(x - 5)

y + 3 = -3(x - 5)

Explanation:

The variable m refers to the slope. The point (x1,y1) is on the line. We do not distribute the -3 through to the terms in (x-5), nor do we isolate y, since your teacher wants this in point-slope form.

Answer: 26

Step-by-step explanation:

Simplify
2x-6y
Plug in numbers
2(4)-6(-3)

Answer:

26

Step-by-step explanation:

We want to find the value of the following expression:

[tex](x-3y)2[/tex]

We are given the following variable values:

[tex]x=4[/tex]

[tex]y=-3[/tex]

Start by simplifying the given expression with the distributive property:

[tex]2x-6y[/tex]

Now, plug in the provided variable values:

[tex]2(4)-6(-3)[/tex]

Simplify:

[tex]8+18[/tex]

Finally, add to get the simplified expression:

[tex]26[/tex]

a carnival game offers a 100 cash prize for anyone whjo can break a balloon by throwing a dart at it. then The expected number of darts you'll throw is 3.44 darts .

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Expected = ∑ value * probability

= $1*0.01 + 2.(0.09) + 3(0.081) + 4(0.0729)

= 3.44

Thus, 3.44 darts .

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A graph of this system of equations with the data points is shown in the image attached below.

In this scenario, we would use an online graphing calculator to plot the given system of equations by using five (5) points and three (3) points respectively;

y = 2(x - 7)^2 - 3   ........equation 1.

y = -(x + 5)(x + 1)        ........equation 2.

Generally speaking, the solution to any system of equations is the point of intersection of the lines on the graph representing each of them.

In this scenario, the points that are located on the line of the graph of this equation y = 2(x - 7)^2 - 3 include the following:

Ordered pair (5, 5).

Ordered pair (10, 15).

Ordered pair (7, -3).

Ordered pair (5.775, 0).

Ordered pair (8.225, 0).

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So, the base of the triangle is decreasing at the rate of 1.6 cm/min.

Given that:

The altitude of is increasing at a rate of 1 centimeters/minute, which means;

dh/dt = 1 cm/min

The area of the triangle is increasing at a rate of 4 square centimeters/minute;

dA/dt = 4 cm2/min

When A = 100 cm2, h = 10 cm

We know that, area of a triangle is given by:

A = 1/2 × b × h

b = 20 cm

Let us differentiate both sides with respect to time:

dA/dt = 1/2 [b dh/dt + h db/dt]

Substituting the values

2 = 1/2 [20 × 1 + 10 × db/dt]

By further simplification, we get

4 = 20 + 10 db/dt

db/dt = -1.6 cm/min

Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.

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In order to be in the 85th percentile Eli would need to score 26.62.

In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.

Given that act math scores are approximately normally distributed,

mean (μ) = 21 and a standard deviation (σ) = 5.4

percentile P(X>x) = 85 =0.85

P(z<x) = 0.85

z = 1.04

y the formula

z = (x - μ)/ σ

⇒ 1.04 = (x - 21)/5.4

⇒ 1.04*5.4 = x - 21

⇒ 5.616 = x - 21

⇒ x = 5.616 + 21

⇒ x = 26.62

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Isabelle concluded that the sample maximum is an unbiased estimator of the population maximum.

Value is a term used to describe the worth of something. It can refer to monetary value, but it can also be used to describe the worth of intangible things such as relationships, ideas, and experiences. Value creates an understanding between two parties, as each may have a different opinion on what something is worth. It can be seen as an exchange or trade of something that both parties consider to be of equal or greater value.

This conclusion is supported by the high number of samples that had a maximum value of 999999. The dotplot shows that the sample maximum was 999999 in over 95% of the trials. The other samples had maximum values that were lower, but still close to the true maximum of 999999. This indicates that the sample maximum did not systematically overestimate or underestimate the population maximum.
The sample maximum was also consistent across the different trials, with the majority of the samples having a maximum value near 999999. This consistency indicates that the sample maximum is a reliable estimator of the population maximum. While there is always a chance that the sample maximum may deviate from the population maximum, the results suggest that the sample maximum is unbiased and reliable for estimating the population maximum.

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The answers are  46/35 ,5/4, 5/4, 7/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: 3/5 + 5/7 = 46/35

6/12 + 9/12=5/4

1/4 + 4/4 = 5/4

2/3 + 5/3 = 7/3

Hence, The answers are  46/35 ,5/4, 5/4, 7/3

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Using Elimination method the simultaneous equations is -16/3.

Elimination is a mathematical technique that can be used to solve a system of three equations with three variables.

In standard form, without any fractions or decimals, write all the equations. Decide which one of the three variables you want to eliminate, then pick any two of the equations to do so.

The term "simultaneous equations" refers to two or more algebraic equations that share the same unknown variables and have the same answer. This suggests that the simultaneous equations have a single, solvable problem. For instance, 2x - 4y = 4, 5x + 8y = 3, are instances of simultaneous equations.

    10m-7n=26

  - 7m+7n=42​

    3m = -16

m = -16/3

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The main difference between X1 and x1 is that X1 is a random variable and x1 is a specific numerical value.

In mathematics, variables are often used to represent different values, and the difference between uppercase and lowercase letters is often used to distinguish between different types of variables. X1 is a random variable, which represents a value that can take on different values depending on the outcome of an experiment or a probability distribution. x1, on the other hand, is a specific numerical value, which represents a fixed value that is known or can be determined. In short, X1 refers to a variable whose value is uncertain and x1 refers to a specific value of that variable.

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Answer:

Pete is 5

Step-by-step explanation:

Let Pete's age be x

Therefore Masha is 3x

since their age difference is 10,

3x - x = 10

2x = 10

x = 5

check:

3x = 15

x = 5

15 - 5 = 10

The area of the resulting two-dimensional cross-section of the pyramid geometry will be 5 square inches.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

What is an area in math definition

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares

A slice is made parallel to the base of a right rectangular pyramid, as shown.

Then the area of the resulting two-dimensional cross-section will be

Area = 2 in × 2.5 in

Area = 5 in²

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To find the number of distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, we need to look at the values in each of the five squares that make up the diagonal.

In the first column, there are 5 possible values (1-15), in the second column, there are 4 possible values (16-30), in the third column there are no possible values because the middle square is WILD, in the fourth column there are 4 possible values (46-60) and in the fifth column there are 5 possible values (61-75).

We need to find the total number of possible combinations of these values. To find the total number of combinations, we can use the formula for combination:

C(n, k) = n! / (k! (n-k)!)

where n is the number of items to choose from and k is the number of items to choose.

In this case, we have 5 items to choose from in the first column, 4 items in the second column, 0 items in the third column, 4 items in the fourth column and 5 items in the fifth column. So we have:

C(5, 1) * C(4, 1) * C(0, 0) * C(4, 1) * C(5, 1) = 5 * 4 * 1 * 4 * 5 = 400

There are 400 distinct possibilities for the values in the diagonal going from top left to the bottom right of a BINGO card.

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