Similar polygons
State if the polygons are similar

Answer:

7.4

Step-by-step explanation:

Use Pythagorean Theorem: [tex]a^2+b^2+c^2[/tex]

In this case we have a and c. So let's plug those into the equation:

[tex](6.7)^2+b^2=10^2[/tex]

[tex]44.9+b^2=100[/tex]

[tex]b=\sqrt{55.1}[/tex]

[tex]b=7.4[/tex]

All other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median. The given statement is true.

What is the mean and median?

Outliers are values that are significantly different from the other values in a data set, and their presence can greatly affect the value of measures of central tendency, such as the mean and the median.

The mean is a measure of central tendency that is calculated as the sum of all the values in a data set divided by the number of values. The presence of outliers can greatly affect the mean because outliers can have a large impact on the sum of the values in the data set. For example, if a data set has a few very large outliers, the mean will be pulled up to be much higher than the median, which represents the midpoint of the data set.

On the other hand, the median is a measure of central tendency that is calculated as the middle value of a data set when the values are arranged in order. The median is not as sensitive to outliers as the mean because outliers do not affect the median unless the number of outliers is so large that it changes the value of the middle value.

Hence, all other things being equal, outliers tend to have a greater effect on the value of the mean than on the value of the median.

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The probabilities of all the events related to drawing two marbles without replacement are discussed below.

What is meant by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

  Number of blue marbles B = 2

 Number of red marbles R = 3

Number of marbles drawn = 2

a) Sample points are different possible combinations.

  { R,R} , {R,B}, {B, R}, {B,B}

b) Probablitiy of  { R,R} = 3/5 * 2/4 = 6/20 = 3/10 = 0.3

    Probablitiy of {R,B} = 3/5 * 2/4 = 0.3

    Probablitiy of {B,R} = 2/5* 3/4 = 0.3

     Probablitiy of {B,B} = 2/5 * 1/4 = 0.1

c) A: { Two blue marbles are drawn. }

    Probability = 2/5 * 1/4 = 0.1

  B:{ A red and a blue marble are drawn. }

 Probability = 0.3 ( from above)

C:{ Two red marbles are drawn. }

 Probability = 0.3 (from above)

Therefore the different sample points are found and probabilities of different events are also found.

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Answer:

im pretty sure ia 31,61

Step-by-step explanation:

Answer: 10⁰

Step-by-step explanation:

We know that,

 the summation of 3 angles of a triangle is 180⁰.

now, (6x-5)⁰+(5x-5)⁰+8x⁰=180

 or, 19x-10=180⁰

 or, 19x=190⁰

 or, x= (190/19)⁰

 or, x= 10⁰

Answer:

First option: 4.9 in

Step-by-step explanation:

The area of a circle, given radius = r is computed using the formula
A = πr²

Here we are given the area and asked to find the radius r

A = 75.43 in² = πr²

So
πr² = 75.43
r² = 75.43/π
   = 24.01
   = 24 rounded to nearest integer

r = √24
  = 4.9

The optimum sampling strategy is (iii), which is listed below.

By selecting a student's initial name from each page of the cam pus phone book, you may measure the heights of the chosen pupils.

Sampling is a technique for selecting a small group of people or a subset of the population in order to make generalizations and estimate the features of the population. In order to acquire relevant information without studying the entire society, researchers commonly use a variety of sampling approaches in market research.

To ascertain the average height of all students at a certain institution and guarantee that the result is statistically reliable, the sampling process must be applied.

a. Measure the heights of 50 students found in the gym during basketball intramurals.

This approach is not ideal since you would only sample basketball players while leaving all other university students out; hence, your sample would not be representative of all students, simply those who play basketball.

b. Measure the heights of all engineering majors.

This approach is flawed since the sample exclusively includes engineering majors, leaving out students studying other courses.

c. Measure the heights of the students selected by choosing the first name on each page of the campus phone book.

This strategy, which is the finest of the three, allows you to select students independent of the sport or subject they are pursuing. It is more representative of the university student population.

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Answer:

21 miles per hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cost of goods available for sale:

Starting inventory: 150 units * $6/unit = $900

Purchase on June 1: 450 units * $7/unit = $3150

Purchase on June 23: 400 units * $8/unit = $3200

Total cost: $900 + $3150 + $3200 = $7450

Moving Average Unit Cost:

June 1: $7450 / (150 + 450) = $7/unit (rounded to 3 decimal places)

June 12: $7450 / (150 + 450 + 400) = $7.36/unit (rounded to 3 decimal places)

June 15: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)

June 23: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)

June 27: $7450 / (150 + 450 + 400 + 500 + 420) = $7.43/unit (rounded to 3 decimal places)

Cost of ending inventory using perpetual inventory system:

FIFO: $7.51/unit * 80 units = $604 (rounded to 3 decimal places)

LIFO: $7/unit * 80 units = $560 (rounded to 3 decimal places)

Average Cost: $7.43/unit * 80 units = $594.4 (rounded to 3 decimal places)

The required domain of the function If g(x) = f(-2x) is [-16, 8] in interval notation.

The domain of g(x) is the set of all x for which the function g(x) is defined. If g(x) = f(-2x), then the domain of g(x) is the same as the domain of -2x, subject to the restriction that f(x) is defined for the corresponding values of x.

In interval notation, the domain of -2x is (-∞, ∞).

However, since f(x) is defined only on the interval [-8, 4], the domain of g(x) must be restricted to values of x that correspond to values of -2x within the interval [-8, 4].

To find the corresponding values of x, we need to solve the equation -2x = t for x, where t is a number in the interval [-8, 4].

Solving for x, we get x = -t/2. So, the domain of g(x) is the set of all x such that -t/2 is in the interval [-8, 4], or equivalently, t is in the interval [-16, 8]. In interval notation, this is [-16, 8].

So, the domain of g(x) is [-16, 8] in interval notation.

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A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

An even degree  must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.

Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.

Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

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The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.

A type of data hypothesis known as both a null hypothesis claims that a certain collection of data has no statistically significant results. The viability of hypotheses be evaluated using sample. Sometimes refers to as "zero," and symbolized as H0. The premise made by the researchers is that there is a correlation between the variables. The h0, on the other hand, says that such an association doesn't quite exist. Despite its inability to seem significant, the null hypothesis is a crucial component of a study.

given

Calculating the p-value requires knowledge of the distribution of your test statistic under the assumption that the null hypothesis is true.

Cdf as the p-value for the left-tailed test (x).

Right-tail test: p-value = 1 - cdf (x).

The two-tailed test's p-value is 2 mincdf(x), 1 - cdf (x).

The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.

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Answer:

2

Step-by-step explanation:

10-5=5.....the ones she ate

5-2=3 .... the 2 she gave to Mary

3-1 =2.....the one she threw away

2 mangoes!

10 - 5 = 5

5 - 2 = 3

3 - 1 = 2

The regression equation is Y = 95.0 + 0.84X.The regression line is a mathematical model that is used to predict the value of a dependent variable (Y) based on the value of an independent variable (X).

In this case, the regression line is used to predict Y from X using the following data: X = 10, 20, 30, 40, 50, 60 and Y = 111, 109, 110, 94, 92, 93. By using a regression analysis tool such as StatKey, we can calculate the regression equation that best fits this data. The regression equation is Y = 95.0 + 0.84X, where 95.0 is the intercept and 0.84 is the slope. This equation can be used to make predictions about the value of Y for a given value of X. The rounded answer for the intercept is 95.0 and the rounded answer for the slope is 0.84.

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Answer:

pop'n = 358000*(1-0.25%)^t

Step-by-step explanation:

pop'n = 358000

decreasing rate = 0.25%

after t years

pop'n = 358000*(1-0.25%)^t

The length of the triangle is given by the equation L = 15.9 yards

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the length of the triangle be represented as L

Now , the equation will be

Let the base of the triangle be represented as W

Now , the value of W = 8 yards

The area of the triangle = 63.6 yards²

Now , Area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

Area of the triangle A = ( 1/2 ) x 8 x L

4L = 63.6

Divide by 4 on both sides of the equation , we get

L = 15.9 yards

Hence , the length of the triangle is 15.9 yards

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The average rate of change for the given function is -72.

What Is the Average Rate of Change?

To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change. To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.

The rate of the change for the interval [a,b] is given by

[tex]\frac{f(b)-f(a)}{b-a} \\[/tex]

For the given interval [3,11],

[tex]= \frac{f(11)-f(3)}{11-3} \\\\= \frac{-623+47}{8} \\\\= -72[/tex]

So, the required average rate of change is -72.

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Answer: To find the height of the roof, we need to find the point where the ball reaches the maximum height, i.e., the point where the velocity of the ball is equal to 0.

The velocity of the ball can be found by taking the derivative of the function s. The derivative of the function s = −t^2 + 3t + 4 is given by v = ds/dt = 3 − 2t, and the derivative of the function s = −2t^2 + t + 7 is given by v = ds/dt = 1 − 4t.

Setting v = 0, we get 3 − 2t = 0 and t = 3/2 seconds.

Plugging t = 3/2 seconds into the first equation, s = −t^2 + 3t + 4, we get s = −(3/2)^2 + 3(3/2) + 4 = 9/4 + 9/2 + 4 = 7 metres.

Therefore, the height of the roof from the ground is 7 metres.

Step-by-step explanation:

The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is  log₃{(x⁶z⁴)/y⁷}.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

The simplification of the provided logarithmic expression can be done as follows:-

6 log₃x - 7 log₃y + 4 log₃z,

= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}

= log₃x⁶ + log₃z⁴ - log₃y⁷

= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}

= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.

Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is  log₃{(x⁶z⁴)/y⁷}.

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How the ffffffffffffffffffffffffffffffffffffffffff

Answer:

$60

50×3=150

182-150=32

so Sally made 3 $50 so 20+20+20=60

The value of the side lengths x and y are 29.4 units and 17 units

From the information given, we have that;

Using the cosine identity'

sin 30 = y/34

find the value

0. 5000 (34) = y

Multiply

y = 17 units

Using the cosine identity

cos 30 = x/34

multiply

x = 34(0.8660)

x = 29. 4 units

Hence, the values are  17 units and 29. 4 units

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Answer:

15.81 ft

Step-by-step explanation:

Basically it's giving your 2 sides of the right angle triangle & ask you for the long side length.

15²+5²=250

√250 =15.81

Answer:

60%

Step-by-step explanation:

12/20 = 3/5 = 0.6 = 60%

Hey there! To find out how much of her homework Jewel completed, all we need to do is a little math. First, let's divide the number of questions she did by the total number of questions. That's 12 divided by 20 which equals 0.6.

Now, we just need to turn that decimal into a percentage. To do that, we simply multiply 0.6 by 100, which gives us 60. And voila! Jewel completed 60% of her homework.

Answer: The annual percentage yield for Rahela's account can be calculated by finding the effective annual interest rate, which takes into account the frequency of compounding. The effective annual interest rate is calculated as follows:

Effective annual interest rate = (1 + (6.5/2))^2 - 1 = 6.6725%

So, the annual percentage yield for Rahela's account is 6.6725%.

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

my boy its 52 she said times it means multiply

Angelique needs 3 8/15 hours to completely build the fence.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Angelique builds a fence and she can build 5/8 of the fence in 2 5/6 = 17/6 hours.

We know a number multiplied to its reciprocal is 1.

Therefore, The amount of time Angelique needs to complete the fence is,

(5/8)×(8/5) the complete fence in (17/6)×(8/5) hours.

= 136/30 hours.

= 3 16/30 hours.

= 3 8/15 hours.

Q. Angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence, how much time she needs to complete the fence?

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The equations that represent the balance A after m months are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, we have that each month, the balance increases by 100, hence the slope m is given as follows:

m = 100.

Hence:

y = 100x + b.

When x = 5, y = 1200, hence the intercept b is given as follows:

1200 = 500 + b

b = 700.

Hence these following two equations are correct:

Taking the fifth month as the initial month, we consider an intercept of 1200, hence the final equation is given as follows:

A = 1200 + 100(m - 5).

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The center of dilation is (1, -4).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

From the given graph,

Vertices of RSTV are R(1, -4), S(2, 0), T(1, 2) and V(-2, 1).

Vertices of R'S'T'V' are R'(1, -4), S'(4.5, 2), T'(2, 5) and V'(-2.5, 3.5).

Here, the center of dilation is (1, -4).

The transformation is enlargement by scale factor 1.5

Therefore, the center of dilation is (1, -4).

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