How do you prove SSS similarity theorem?.

The result for simplifying;

[tex] {( \frac{2a²b×b⁴}{2a²b×9 {a}^{2} } )}^{ \frac{1}{2} } [/tex]

is;

[tex] \frac{ {b}^{2} }{3b} [/tex]

Simplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.

The greatest common factor the numerator and denominator is 2a²b and so we divide through with it to give;

[tex] {( \frac{b⁴}{9 {a}^{2} } )}^{ \frac{1}{2} } [/tex]

evaluate the square root, we have;

[tex] {( \frac{2a²b⁵}{18 {a}^{4}b } )}^{ \frac{1}{2} } = {( \frac{b²}{3a})} [/tex]

Therefore,

[tex] {( \frac{b²}{3a})} [/tex]

is the result after simplifying the algebraic expression

[tex] {( \frac{2a²b⁵}{18 {a}^{4}b } )}^{ \frac{1}{2} } [/tex]

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I don't know so like ya I don't know

The expressions are written as

(a) The expression from east side of ski trail to reach skier's current position is θ = π/2 + 3.1 × t

(b) The expression for skier's distance to east of  ski trail is 1.9 × cos(π/2 + 3.1 × t)  km .

(c) The expression for skier's distance to north of ski trail  is 1.9 × sin(π/2 + 3.1 × t)  km  .

In the question ,

it is given that ,

the radius of the circular ski trail is = 1.9 km

The Skier starts from the Northern most point

the radians that is sweeped in per hour is = 3.1 radians per hour

that means the angular speed is = 3.1 radians per hour ,

Part(a)

From the above data the expression in terms for t that represents number of radians swept out from each side of ski trail to reach skier's current position is written as ,

θ = π/2 + 3.1 × t

Part(b)

From the above data , expression in terms of t to represent skier's distance to the east of ski trail is written as ,

we know that , x = rcosθ

Substituting the value of θ from part(a) ,

we get ,

= 1.9 × cos(π/2 + 3.1 × t)  km

Part(c)

From the above data , expression in terms of t to represent skier's distance to the north of ski trail is written as ,

we know that , y = rsinθ

Substituting the value of θ from part(a) ,

= 1.9 × sin(π/2 + 3.1 × t)  km

Therefore , The expressions are (a) for radians is θ = π/2 + 3.1 × t

(b) the distance to the east is 1.9 × cos(π/2 + 3.1 × t)  km  ,

(c) the distance to the north is 1.9 × sin(π/2 + 3.1 × t)  km  .

The given question is incomplete , the complete question is

A skier skis ccw along a circular ski trail that has a radius of 1.9 km. she starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. let t represent the number of hours since she started skiing.

(a) write an expression in terms of t to represent the number of radians that would need to be swept out from the east side of the ski trail to reach the skier's current position.

(b) write an expression in terms of t to represent the skier's distance to the east of the ski trail (in km).

(c) write an expression in terms of t to represent the skier's distance to the north of the ski trail (in km).

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The probability that no more than three are enrolled in college or university is P(x≤3)=(C⁵ₓ(0.63)ˣ(0.37)⁵⁻ˣ

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.

When we are confused about the outcome of an event, we might discuss the probabilities of certain outcomes—how likely they are. Statistics is the study of events that are guided by probability.

Probability (P) = 0.63

n= 5

By using binomial distribution,

We know that,

P(x=x)= Cⁿₓ(p)ˣ(1-p)ⁿ⁻ˣ

P(x≤3)=(C⁵ₓ(0.63)ˣ(0.37)⁵⁻ˣ

The probability that no more than three are enrolled in college or university is P(x≤3)=(C⁵ₓ(0.63)ˣ(0.37)⁵⁻ˣ

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The matching vocabularies are;

1.  Factor

2. Algebraic

3. Denominator

4.  Improper fraction

5. Coefficient

Given,

1. A number that divides evenly into a given number

2. Expressions, equations, and operations involving variables

3. The bottom part of a fraction, represents the whole

4. A fraction with a numerator that is larger than or equal to the denominator

5. The number in an algebraic term improper fraction

We have to match the vocabulary to the proper definition;

Here,

1. A number that divides evenly into a given number  - Factor

2. Expressions, equations, and operations involving variables  -Algebraic

3. The bottom part of a fraction, represents the whole - Denominator

4. A fraction with a numerator that is larger than or equal to the denominator - Improper fraction

5. The number in an algebraic term  - Coefficient

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The equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

What is a parabola?

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

The given equation is x² + y² = 25 ; (4, 3)

Now when we put x = 4 and y = 3

then LHS = RHS.

Now find the slope:

      2x + yy' = 0

       ⇒ y' = -x/y

Now at (4, 3) slope would be y' = -4/3.

The equation of the tangent would be

      y - y1 = m(x - x1)

      y - 3 = (-4/3)(x-4)

     3y - 9 = -4x + 16

     4x + 3y = 25

     y = -4x/3 - 25/3

Now equation of the normal is:

  y - y1 = (-1/m)(x - x1)

  y - 3 = 3/4(x - 4)

  y = 3x/4

Hence, the equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

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Answer:

A and E

Step-by-step explanation:

The geometric series which has the common ratio 2 is 0.0625, 0.125, 0.25, 0.5, 1, … thus option (C) is correct.

A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.

As per the given,

Common ratio r = 2

Common ratio = next term / previous term

In the series 0.0625, 0.125, 0.25, 0.5, 1, … the common ratio is 2.

In the series [tex]a_{n}[/tex] = (1/2) × [tex]a_{n-1}[/tex]

a₁ = 2 so

a₂ = (1/2)a₁ 1

The ratio is 1/2, not 2.

Hence "The geometric series which has the common ratio 2 is 0.0625, 0.125, 0.25, 0.5, 1, …".

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The steps of the analytical problem-solving model include: identifying the problem, exploring alternatives, building an implementation plan, implementing a solution, and evaluating the situation.

Analytical problem solving, as we've defined it above, refers to the approaches and methods you use rather than the particular issue you're trying to resolve.

Analytical issue solving is a crucial prerequisite for problem resolution; the problem itself does not determine whether you need it.

Analytical problem solving involves recognising a problem, investigating it, and then creating ideas (such as causes and solutions) around it.

Solving analytical problems calls for inquiry, examination, and analysis that encourages additional study of the subject (including causality, symptoms, and solution).

According to the steps involved in analytical problem solving model:

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The variable that is used to predict the volume of timber in this tree using a simple linear regression model is Diameter .

In the question ,

a scatter plot is given ,

the scatter plot shows the relationship between height , diameter and the volume .

and diameter of tree is measured 4.5 feet above the ground .

it is given that suppose , we have height and diameter measurements for another black cherry tree ,

we have to find the variable that help in predicting the volume of the timber .

So , from the scatter plot given below ,

we can say that , the relationship between diameter and volume of these trees is strong  than height .

So , diameter is used to predict the volume of timber in this tree using a linear regression model.

Therefore , the variable that help in predicting the volume of the timber is Diameter .

The given question is incomplete , the complete question is

The scatterplots below show the relationship between height, diameter, and volume of timber in 31 felled black cherry trees. The diameter of the tree is measured 4.5 feet above the ground .

Suppose you have height and diameter measurements for another black cherry tree. Which of these variables would be preferable to use to predict the volume of timber in this tree using a simple linear regression model ? Explain your reasoning.

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The population of the city grew most rapidly in the year 1988.

Given, the population of a city is modeled by a function

P(t) = 250/(1 + 480e^-0.8t)

we have to find that when the population is growing most rapidly.

On differentiating, we get

P'(t) = 250/(1 + 480e^-0.8t)²×(-384e^-0.8t)

Again differentiating we get

P''(t) = 96000(e^-1.6t)(-0.8e^-0.8 + 384)

Putting P''(t) = 0, we get

e^0.8t = 0

t = 8

So, the population of the city grew most rapidly in the year (1980 + 8) = 1988.

Hence, the population of the city grew most rapidly in the year 1988.

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The answer of two iterations of newton's method to approximate a zero of the function using the given initial guess is 1.5262!

Iteration refers to doing a procedure repeatedly. Starting with an initial value, enter it into the iteration formula to get a new value. Next, use the new value for the next substitution, and so on, to solve an equation using iteration.

By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1,

and by using the previous guess, xn, like so-

xn+1 = xn - f(xn)/f'(xn)

and herethe case is f(x) = cos(x), and so f'(x) = -sin(x).

Also, furthermore, cos(x)/(-sin(x)) = -cot(x).

here, we have to simplify the formula to get a better guess for a zero to:

xn+1 = xn + cot(xn)

x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...

And x3 = 2.06170... + cot(2.06170...) = 1.52615...

Ans =  1.5262!

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The probability that Chuck will shop for k hours be,

C(n , k).p^k.q^(n - k)

Given, Chuck will go shopping for probability books for K hours.

K is a random variable and is equally likely to be 1, 2, 3, or 4.

The number of books N that he buys is random and depends on how long he shops.

The probability that chuck will shop for k hours be,

P(X = k) = C(n , k).p^k.q^(n - k)

So, we can find the probability that chuck will shop for k hours by,

C(n , k).p^k.q^(n - k)

Hence, the probability that Chuck will shop for k hours be,

C(n , k).p^k.q^(n - k)

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Probability is simply how likely something is to happen, so the probability of landing heads up on the next flip is 1/2.

The probability is obtained by dividing the total number of outcomes by the entire number of potential ways an event may occur. Odds are a separate concept from probability. The probability of an event happening is divided by the probability that it won't, and the result is the odds.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value among 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

P(H)= Probability of getting  head while flipping a coin is 1/2

and,

P(T)= Probability of getting  tail while flipping a coin is 1/2

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Answer:

Step-by-step explanation:

1/4 if you multiplying

1 1 /12 if you adding

Answer:

perimeter: [tex]2\frac{1}{6}[/tex] yards

Area: [tex]\frac{1}{4}[/tex] [tex]yards^{2}[/tex]

Step-by-step explanation:

perimeter is 2(l)+2(w)

And area is (l)(w)

So to find perimeter we fill in the formula

2(3/4)+2(1/3)

6/4+2/3

Find common denominator

6*3/4*3+2*4/3*4

18/12+8/12

26/12

2 2/12

2 1/6 is the perimeter

Now for the area we multiply width by length

3/4x1/3

3/12

1/4 is the area

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The Submarine is 7.74 Km away from its base .

In the question ,

it is given that ,

the distance travelled by Submarine from base in East direction = 4.2 Km let the distance from base to east direction be denoted by AB ,that means AB = 4.2 Km

the distance travelled by Submarine from East to North direction = 6.5 Km let the distance from east to north direction be denoted by BC . that means BC = 6.5 Km

the given situation form a right triangle ,

So , the distance from submarine to its base is the hypotenuse of the right triangle , that is AC .

So By Pythagoras Theorem ,

AC² = AB² + BC²

Substituting the values , we get

AC² = 4.2² + 6.5²

AC² = 17.64 + 42.25

AC² = 59.89

AC = √59.89

AC = 7.7388

AC = 7.74

Therefore , The Submarine is 7.74 Km away from its base .

The given question is incomplete , the complete question is

A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?

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Answer:

x=2

y=5

Step-by-step explanation:

fill in x

5y+(y-3)=27

6y-3=27

  +3.  +3

6y=30

/6.  /6

y=5

now fill in y to find x

x=5-3

x=2

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Answer:

Step-by-step explanation:

54=t

The dollar duration of the given bond is $3.71

Dollar duration:

Dollar duration means a linear approximation of how a bond's value will change in response to changes in interest rates.

Given,

Here we have to assume that a bond sells at $92.10 and its modified duration is 4.03.

And we need to compute dollar duration. answer with two decimal digits accuracy and the correct sign.

As per the formula of dollar duration, the values of

bond price = $92.10

duration = 4.03

interest rate = 0.01

So, the dollar duration is calculated as follows,

=> dollar duration = 0.01 x 92.10 x 4.03

=> dollar duration = 3.71

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By using the concept of bell shaped curve of normal distribution, it can be concluded that

The histogram would not look like a bell shaped curve because occurance of fire may not be constant in  all the case.

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is given by

f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^-{\frac{z^2}{2}[/tex]

Where z = [tex]\frac{x - \mu}{\sigma}}[/tex] where [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

A fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem.

Here, in this case it is not confident that the histogram would not look like a bell shaped curve because occurance of fire may not be constant in  all the case.

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A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2. The new graph will have moved right.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function. The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.

Given,

A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2.

The new graph will have moved right.

For periodic functions, phase shift refers to a horizontal shift to the left or the right. The sine wave is moved to the left if c = 2. if, the sine wave is then three degrees to the right. Despite going in the opposite way from what you may anticipate, this follows the general transformational principles for all functions.

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Some of the real life examples of parallel lines cut by transversal are: chessboard, graph paper,railway tracks,net on the tennis court etc.

When two lines don't intersect, they are said to be parallel. Parallel lines are two lines that run parallel to each other and meet at infinity.

A transversal is formed when a line intersects two lines at distinct points.

Real life examples of parallel lines cut by transversal line are:

Thus, in real life situations parallel lines cut by transversal can be observed very frequently.

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The null and alternative hypothesis test using μ as mean hours of sleep for LMC students is [tex]H_0[/tex] : μ = 6.9 and ([tex]H_a[/tex] : μ ≠ 6.9).

Given:

Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.

here

μ = 6.9

σ = 1.45

Null hypothesis:

[tex]H_0[/tex] : μ = 6.9

Alternative hypothesis:

([tex]H_a[/tex] : μ ≠ 6.9)

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Full question:

Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.

what are the null and alternative hypothesis?(use  μ = mean hours of sleep for LMC students).

Number of hours taken by Mike and Sabrina to wash a car when they work together is equal to (6/ 5) hours .

As given in the question,

Number of hours taken by Mike to wash a car = 3 hours

Work done by Mike in 1 hour = 1/3

Number of hours taken by Sabrina to wash a car = 2 hours

Work done by Sabrina in 1 hour = 1/2

Amount of work done by Mike and Sabrina together in 1 hour

= (1/3) + (1/2)

= ( 2 + 3 ) / 6

= 5/6

Now,

1 work done by Mike and Sabrina together = 6/5 hours

Therefore, number of hours taken them together to wash a car is

(6/5) hours.

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The line containing the slope -1/5 and coordinates (1,-4) can be graphed by moving one unit negative of y and running 5 towards of x axis

Slope is defined as the rate of change of y to rate of change of x

How to graph the slope of a line?

To graph an equation in point slope form,  

The first step is to extract the known point and slope from the equation.

The equation of the line is given by:   y−yₐ=m(x−xₐ)

From the parameter; M=[tex]\frac{Y-Y_{1} }{X-X_{1} }[/tex]

The given parameters are

[tex]-\frac{1}{5} =\frac{y+4}{x-1}[/tex]

Solving the equation,

x+1=-y+20

x+y=20-1

x+y=19

The slope -1/5 is used  to find which way the line extends.

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A scatter plot allows a researcher to visually inspect the plotted points and possibly to spot a systematic nonlinear relationship.

The scatter plot is defined as the graph that shows the set of points plotted on a horizontal and vertical axes. The scatter plot is used to shows the extend of correlation therefore it is important in the statistics. It also used to show how much one variable is affected by another variable. In scatterplot usually the dots are used to represents the numeric variables

Hence, a scatter plot allows a researcher to visually inspect the plotted points and possibly to spot a systematic nonlinear relationship.

The complete question is

a _____ allows a researcher to visually inspect the plotted points and possibly to spot a systematic nonlinear relationship.

a) Multiple line graph b) Scatter plot c) Stacked bar chart d) Line graph

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Answer:

40min per day

Step-by-step explanation:

Answer: 40 minutes

Step-by-step explanation: All you have to do is subtract 55 and 15, which equals 40 minutes.

hope this helps!

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The person is making money more than the half of the population of the teachers.

Given, a person is making the median salary for a construction worker.

we have to find that more than how many teachers the person is making money

as, we know that the median is more than the half of the population.

So, the person is making money more than the half of the population of the teachers.

Hence, the person is making money more than the half of the population of the teachers.

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A. The bacteria that had a smaller initial population is of:

Sample A: 100 bacteria.

B. The correct option regarding which sample was larger in the 5th week is of:

Sample A; 8,300.

An exponential function is defined as follows:

[tex]y = ab^x[/tex]

In which the meaning of each parameter is given by:

For Sample A, the values of these parameters are given as follows:

Hence the function is:

f(x) = 100(3)^x.

In the 5th week, the population was of:

f(5) = 100 x 3^5 = 24,300.

For Sample B, the function is:

g(x) = 500(2)^x.

Hence, from the parameters, we have that:

In the 5th week, the population was of:

g(5) = 500 x 2^5 = 16,000.

Hence the difference of the larger population in Sample A by the smaller population in Sample B is of:

24,300 - 16,000 = 8,300.

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The population be in 2024 , to the nearest tenth of a million is 397.5

Population after n years equals P x (1+R/100)n if growth is constant at R% per year. 3. If the population is declining at a constant rate of R% annually, the population after n years will be equal to P x (1-R/100)n.

Population after n years equals

P x (1+R/100)n

48.2 * (1 - 49.9)7

397.5

The population be in 2024 , to the nearest tenth of a million is 397.5

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