Triangle CAT is transformed by a sequence of rigid motions that maps onto triangle DOG. Which three congruency statements would show ASA congruency for these triangles? (select all that apply)

A.∠ A ≅ ∠ T

B.CA ≅ DO

C.AT ≅ OG

D.CT ≅ DG

E.∠ A ≅ ∠ O

F.∠ C ≅ ∠ D

Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.

Given that,

If and only if, two events, a and b, are independent. Remember that rearranging the multiplication rule will result in. Consider some events a and b.

We have to find which of the following claims about a and b is true.

We know that,

We have if the occurrence of event A has no bearing on the probability that event B will also occur, then the two events A and B are said to be independent.

P(A and B) = P(A) P(B) can be used to numerically describe the probability of two separate events.

As a result, we can draw the conclusion that two events, a and b, are independent if and only if they are.

Therefore, Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.

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Answer:

  2268π ft³ ≈ 7125 ft³

Step-by-step explanation:

You want the volume of a 22 ft long cylinder capped by a hemisphere 9 ft in radius.

The formula for the volume of a cylinder of radius r and height h is ...

  V = πr²h

The formula for the volume of a hemisphere of radius r is ...

  V = 2/3πr³

The sum of the volumes of the two figures is ...

  Vtotal = πr²h +2/3πr³ = πr²(h +2/3r)

Using the given values for height and radius, we find the volume to be ...

  Vtotal = π(9 ft)²(22 ft + 2/3(9 ft)) = π(9 ft)²(28 ft)

  Vtotal = 2268π ft³ ≈ 7125 ft³

The volume of the composite is about 7125 cubic feet.

The derivative of the following are:

(a) 36x³ + 72x² + 32x

(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)

(c) -1/2√x(x+3)² + 2(x+3)(2+√x)

(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³

What is a derivative?

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

Here, we have

Given

(a) y = x²(3x + 4)²

Derivative with respect to x and we get

dy/dx = 2x(3x + 4)² + x²(18x + 24)

dy/dx = 36x³ + 72x² + 32x

(b) y = (1+x²) (2 - x²³)³

Derivative with respect to x and we get

dy/dx = 2x(2 - x²³)³ + (1+x²)(-23x²²)3(2 - x²³)²

dy/dx = 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)

(c) y = (2+√x)(x+3)²

Derivative with respect to x and we get

dy/dx = -1/2√x(x+3)² + (2+√x)2(x+3)

dy/dx = -1/2√x(x+3)² + 2(x+3)(2+√x)

(d) y = (2x² + 1)(x⁵ +3)⁴

Derivative with respect to x and we get

dy/dx = 4x(x⁵ +3)⁴ +  (2x² + 1)4(x⁵ +3)³(5x⁴)

dy/dx = 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³

Hence, the derivative of the following are:

(a) 36x³ + 72x² + 32x

(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)

(c) -1/2√x(x+3)² + 2(x+3)(2+√x)

(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³

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The sample variance is 2.976 , which means it's lesser than 6.25. We calculate this using the standard method.

Given:

Sample data is 0.05

The sample size is 20.

And ,

The hypotheses are:

H0: sigma^2 = 6.25 (>=)

Ha: sigma^2 < 6.25

The critical value is 10.117. If the test statistic is less than this value, we'll reject the null hypothesis. We Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go.

The test statistic is:

2.976 * 19 / 6.25 = 9.047.

So we reject the null hypothesis. The variance is not 6.25, which means it is lesser then 6.25

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The length of DE is 6.3

Similar triangles are triangles that have a similar appearance but differ in size.

Two triangles are similar if their angles are the same (corresponding angles) and their sides have the same ratio or proportion (corresponding sides)

The " ~ " symbol is used to represent similarity.

According to the question,

In ΔABC and ΔDBE,

(1) ∠B = ∠B (common)

(2) ∠ACB = ∠DEB (opposite sides are equal)

(2) ∠CAB = ∠ECB

Therefore , ΔABC ~ ΔDBE

By using similar triangle property

The ratio of correspond sides are equal ,

AB/BD = BC/BE = AC/DE

=> 2/1 = AC/DE

=> 12.6 / DE = 2/1

=> DE =  12.6/2

=> DE = 6.3

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As per question and the information provided we can compute the solution for both exercises as follows:

Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate additional revenue or to make money on the investment over a certain amount of time.

Exercise (a)

The sequence "an "'s" first five terms are:

[tex]a1 = 6000(1.04) = 6240 [/tex]

[tex]a2 = 6000(1.04) ^2 = 6489.6 [/tex]

[tex]a3 = 6000(1.04)^3 = 6749.184 [/tex]

[tex]a4 = 6000(1.04) ^4 = 7019.151 [/tex]

[tex]a5 = 6000(1.04)^5 = 7299.197[/tex]

Exercise (b)

Because infinity, which is not a finite number, serves as the series's limit as n approaches infinity, the sequence is divergent.

[tex]an = 6000(1.04)^n [/tex]

that is the formula for the nth term of the sequence. As n rises, the value of

[tex](1.04)^n[/tex]

it grows steadily larger, which causes a to grow steadily larger until it approaches infinity. The sequence "an" diverges as a result.

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Answer:

5.2%

Step-by-step explanation:

Receiving $4.88 dividend out of the closing stock price of $59.95, means that the stock yield is 8.1%

Dividend is defined as a distribution of payment by a company to its shareholders that is originated from the company's profit and is payable to the shareholders every quarter in a given year, while stock yield is defined as an income generated by the stock being held by the shareholders.

To determine the percentage of stock yield, we will need to divide the closing price of the stock which is $59.95 with the amount of dividend distributed for each stock held which is $4.88, and the calculation is as follows:

59.95/4.88×100%=8.1%

Therefore the stock yield is 8.1%

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Answer:

HA:A hypotenuse and an acute angle define congruence

HL:A hypotenuse and a leg define congruence

LL: Two legs define congruence

LA:A leg and an acute angle define congruence

Step-by-step explanation:

HA theorem:

                     When hypotenuse and one acute angle of a triangle is congruent to hypotenuse and one acute angle of a other triangle, then the triangles are congruent

HL theorem:

                     When hypotenuse and one leg of a triangle is congruent to hypotenuse and one leg of other triangle, then the triangles are congruent

LL theorem:

                    When two legs of a triangle is congruent to the two legs of other triangle, then the triangles are congruent

LA theorem:

                    When one leg and one acute angle of a triangle is congruent to one leg and one acute angle of other triangle, then the triangle are congruent

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By using the properties of angle, it can be concluded that

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

What is angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

[tex]\angle QPS[/tex] and [tex]\angle TSU[/tex] are not consecutive interior angle as [tex]\angle PST[/tex] falls in between

[tex]\angle QPS[/tex] and [tex]\angle RSU[/tex] are not consecutive interior angle as [tex]\angle RSU[/tex] is an exterior angle

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

[tex]\angle QPS[/tex] and [tex]\angle OPN[/tex] are not consecutive interior angle as [tex]\angle OPN[/tex] is an exterior angle

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If Diana averages 6 mph walking to school. The distance from  the school to her home is 5.4 miles.

Distance can be defined as how far an object is from another object.

Formula for Distance

Distance = Speed × Time

Solving for t (time) to walk to school

6t = 35 (t-.75)              

6t = 35t - 26.25

Collect like terms

29t= 26.25

Divide both side by  29t

t = 26.25/29

t=  .9

t=54 minutes

Solving for Distance (d)

d = 6× .9

d = 5.4 miles

Therefore the distance is 5.4 miles.

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The complete question is:

Diane averages 6 mph walking to school. Averaging 35 mph on the way back home by car, she takes 3/4 hour less time. How far is the school from her home?

The contrapositive is true

Proving a contraposition involves proving that the contrapositive of a statement is true. The opposite of "if m n is even then m is even or n is even" is "if m is not even and n is not even then m n is not even".

To prove this statement by a proof by contrast, first assume that m is not even and neither is n. This means that both m and n are odd.

Since m and n are odd, m n is also odd. This can be expressed as:

If m and n are odd, we can write m as;

2k + 1 and n as 2l + 1 for integers k and l.

Then mn = (2k + 1)(2l + 1) = 4kl + 2k + 2l + 1 = 2(2kl + k + l) + 1,

which is odd. Therefore, m n is not even if m is not even and n is not even.

It turns out that the opposite of the original statement is true, so the original statement must also be true. Therefore, if m n is even, then we can say that   that m is even or n is even using a proof by contrast.

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In the following first scenario the conditions for the t-test is not met for the difference in populations mean so the hypothesis test cannot be done.

1)The distribution of time spent at university recreational facilities is considerably skewed to the right in a random sample of 100 university students.

The variable is X, which stands for time spent at the university's leisure facilities.

Because the variable "time" is at least ordinal, this criterion is satisfied.

The sample was drawn at random, hence this requirement is met.

The data is heavily skewed to the right, the normal distribution is symmetrical, and this data set is highly unlikely to have a normal distribution.

2)The distribution of time spent at university recreational facilities is highly skewed to the right for females but not strongly skewed for males in a random sample of 50 university students (37 females and 13 males).

In this scenario, you have two groups of interest, and the variable X: Time spent at the university recreational facilities will be measured for each group.

Because the variable "time" is at least ordinal, this criterion is satisfied.

The samples "male students" and "female students" were randomly taken so this condition tests.

You have two populations of interest in this case. Male university students and female university students are divided into two groups. To use the t-test, both populations must be normal.

The distribution for the females has strongly skewed to the males have a somewhat skewed distribution.

If the distribution of females is substantially skewed, it is impossible for it to be normal.

In this case, a t-test is not appropriate.

3)Because the experimental units are dependent, this is a "paired sample" situation. (Consider the sibling pair's relationship; if they get along well, it is more likely that they will spend time together in the recreational facilities; if their relationship is not so good, it is more likely that the presence of one of the siblings in the facilities will cause the other to spend less time there.)

X will be the variable measured for each member of the "sibling pair": Time spent at university recreational facilities, and the research variable in this case, will be defined by the difference in times measured for both siblings.

The normality condition checks.

so the t-test in this scenario can be applied.

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The exact expression for the cosine function is given as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

The definition of the cosine function is given as follows:

h(x) = acos(b(x - c)) + d.

The parameters of the function are given as follows:

The difference between the maximum value and the minimum value is of 6 - (-9) = 15, hence the amplitude is obtained as follows:

a = 15/2 = 7.5.

From the graph given at the end of the answer, the period is of 7 units, hence:

2π/b = 7

7b = 2π

b = 2π/7.

The minimum value should be at x = 0, however it is at x = -0.5, hence the phase shift is given as follows:

c = -0.5.

Considering the amplitude of 7.5, without vertical shift the function would oscillate between -7.5 and 7.5, however is oscillates between -9 and 6, hence the vertical shift is given as follows:

d = -1.5.

Thus the function is defined as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

The graph of the function is given by the image shown at the end of the answer.

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They collected $134.45 and we can find this using percentage.

Travis = $43

Jessica = 43 - (43 × 20%) = $34.4

Robin = 43 + (43 × 35%) = $58.05

Percentage (%):

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Answer:

OptionB)

Step-by-step explanation:

→→When you are talking about sample proportion You are considering a Single ,set of same kind of Data,Like body weight of  Students in a class, from which you are taking out samples for Observation.

For example, A colony is being studied whether each human in that colony is healthy or not by checking their body mass index.

→→When we are investigating or considering Sampling Distribution we consider two different sets or kinds of Data set Possessing Similar Characteristics because we have to compare these two sets of Data.

For example , Take two colonies A and B , Check their honesty by observing how many floors they have made in their Plot.Whether they care or don't care about their Surrounding or Mother Earth by looking, if number of floors exceeds than 2 i.e ground floor and first floor , it means Dishonest , if maximum number of floor =2 ,it means honest.

Answer:

it's 0.25 for the first one

Step-by-step explanation:

27w - 18 - 5w = 4w - 24 - 8

22w - 18 = 4w - 32

18w = -14

w = -14/18

w = -7/9

The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)

In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:

y = b · aˣ

Where:

By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.

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Answer:

average rate of change = 19

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

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

here [ a, b ] = [ 3, 7 ] and y = f(x) , then

f(b) = f(7) = 7² + 9(7) = 49 + 63 = 112

f(a) = f(3) = 3² + 9(3) = 9 + 27 = 36

then

average rate of change = [tex]\frac{112-36}{7-3}[/tex] = [tex]\frac{76}{4}[/tex] = 19

The hypotheses that can be used to test for a significant difference between the population proportions for the two years is H0 :- P1 = P2

How to calculate the hypotheses?

In math, the process of calculating the hypotheses is to select a statistic based on a sample of fixed size, calculate the value of the statistic for the sample and then reject the null hypothesis if and only if the statistic falls in the critical region.

Here we know that certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.

And we need to find the hypotheses that can be used to test for a significant difference between the population proportions for the two years.

Here let us consider P1 refers population proportion saying financial security more than fair in 2012 and P2 refers population proportion saying financial security more than fair in 2010.

As per the definition of the hypotheses, the resulting hypotheses is written as,

=> H0 :- P1 = P2

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The appropriate test to perform is one sample t test

The rejection reason is t statistic less than -2.012 or t statistic more than -2.012

The p value of the test is 0.0292

Firstly,

       As the population standard deviation is unknown and the sample size is more than 30, it is appropriate to use one sample t test for this hypothesis testing

Testing if the mean is changed from 700 levels or not

Null and alternate hypothesis are 700

Degree of freedom,

                       n-1

                      = 48-1

                      = 47

Using alpha level 0.05 and t critical table, we found the following two critical values

t critical values= -2.012 and 2.012

So, the rejection reason is t statistic less than -2.012 or t statistic more than -2.012

Now,

        Population means = 700 hours

        Sample mean = 675 hours

        n = 48

So,

Test statistic= (mean-alternate hypothesis)/(s/√n)

                     = (675-700)/ (77/√48)

                     =-25/11.1140

                     = -2.249

Degree of freedom = n-1

                                  = 48-1  

                                  = 47

With t distribution table for -2.249 and 47 degrees of freedom obtain p value of 0.0292

So, pvalue= 0.0292

Reject null hypothesis since the p value is less than alpha level

So, we conclude that the mean has changed from 700 hours

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Answer: [tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]

Step-by-step explanation:

     We will use the distance formula to help us solve (see attached). Let (6, -2) be point one and (1, 2) be point two.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]\displaystyle d=\sqrt{(1-6)^2 +(2--2)^2}[/tex]

[tex]\displaystyle d=\sqrt{(-5)^2 +(4)^2}[/tex]

[tex]\displaystyle d=\sqrt{25 +16}[/tex]

[tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]

41 is a prime number, so this is the simplest radical form.

C. H2 1,96

To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values ​​in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).

Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.

Hence, the correct answer in this case is c. H2 1,96

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The range of 90% confidence will be: (0.5305,0.5695)

What is percentage?

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Given,

Sample percentage equals 0.55

z = 1.645 for 90% confidence.

Therefore, the range of 90% confidence will be:

(0.5305,0.5695)

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The volume of the figure can be calculated by adding the volumes of the two rectangular prisms. The first rectangular prism has dimensions 12 in x 10 in x 2 in, so its volume is 12102 = 240 in^3. The second rectangular prism has dimensions 10 in x 7 in x 21 in, so its volume is 10721 = 1540 in^3. The total volume of the figure is 240 in^3 + 1540 in^3 = 1780 in^3.

Answer: the function is nonlinear

Step-by-step explanation:

y = x2 + 1 is a nonlinear equation because for it to be an linear question it must be the following

Linear:

2x-1=y 

y=2x-1

nonlinear

y = x2 + 1 

Answer:

[tex]2x + y \leq 8[/tex]

Step-by-step explanation:

since potatoes cost $2 they are represented as 2x

Carrots cost $1 and are simply y

According to the question asked the number of digits with all digits even can be found as:

aₙ = 6ⁿ + 2.3ⁿ + 1(n≥0)

Given:

let the number be aₙ.

The number aₙ equals the number of n permutations at the multiset S

where S = { ∞ 2, ∞ 4, ∞ 6, ∞, 8, ∞ 10} on which 2 and 4 occurs

a non zero even number at times.

The exponential generating function have a₀, a₁, a₂,....aₙ

f'(x) = (1+x²/2! + x⁴/4!+...)ⁿ

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