the radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60, how many centimeters does it move? express your answer in terms of pand then round to two decimal places.

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: 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]

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.

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 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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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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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 total number of games did they played is 80

The term total in math is also known as sum is defined as the result of arithmetically adding numbers or quantities.

Here we have given that the team wins 20 games.

And the number of games won by the team is 80% of the number of games played.

Then the calculation is done as follows:

Here let us consider that the total number of games played be 100 units.

As we can say that the number of games won by the team will be 80 units.

Then according to the question it can be written as

=> 50 units = 40

Then for 100 units (40 x 100)/80 = 80

Therefore the total number of games played by the team is 80.

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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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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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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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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 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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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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On solving the provided question we can say that By the help of the Trigonometry [tex]dθ/dt = (1/0.866) [-4/(82)] (-0.30) rad/sec = 0.0217 rad/sec\\[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

By the help of the Trigonometry -

θ = angle between hypotenuse and water

r = length of hypotenuse

[tex]sinθ = 4 / r\\cosθ dθ/dt = (-4/r2) dr/dt\\dθ/dt = (1/cosθ)(-4/r2) dr/dt\\dr/dt = -0.30 m/s \\[/tex]

When the line is 8m out,

r = 8m

[tex]cosθ = √(1 - sin2θ) = √[1 - (4/r)2] = √[1 - (4/8)2] ≅ 0.866\\dθ/dt = (1/0.866) [-4/(82)] (-0.30) rad/sec = 0.0217 rad/sec\\[/tex]

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This statistic is misleading because Howard surveys only his department and not members of all the departments that the company has.

When studying anything from a population, it is usual practice in statistics to identify a sample of that group.

However, the sample has to be representative.

For example: I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, let's say, 1000 randomly selected Buffalo residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

Howard wants to know the proportion of employees of a company who use the company's healthcare. He asks only his department. However, a company as multiple departments, which leads to the statistics found in Howard's survey being misleading.

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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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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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The number of ways to arrange the pets such that at least one pair of cats are next to each other is:
(n+m)!/(n!m!) - (m+n-1)!/(m!(n-1)!). Considering n as catcats and m as dogs

There are a few different ways to approach this problem, but one possible method is to use the complement principle, which states that the total number of ways to arrange the pets minus the number of ways to arrange them such that no cats are next to each other will give the number of ways to arrange them such that at least one pair of cats are next to each other.

Let n be the number of cats and m be the number of dogs. The total number of ways to arrange the pets in a row of chairs is (n+m)!/(n!m!), which is the number of ways to arrange n identical cats and m identical dogs. To arrange the pets such that no cats are next to each other, we can first arrange the cats in n! ways and then place the dogs between the cats in (m+n-1)!/(m!(n-1)!) ways, since there are m+n-1 spaces to place the m dogs and n-1 dividers between the n cats.

Therefore, the number of ways to arrange the pets such that at least one pair of cats are next to each other is:
(n+m)!/(n!m!) - (m+n-1)!/(m!(n-1)!)

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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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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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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 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:

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.

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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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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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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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.

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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