The triangles are congruent by the SSS congruence theorem.

Triangles B C D and W X Y are shown. Triangle B C D is shifted up and to the right and then rotates about point D to form triangle W X Y.

Which transformation(s) can map TriangleBCD onto TriangleWXY?

rotation only
reflection only
translation, then rotation
translation, then reflection

The complete table as determined from the given probabilities is given below:

         X    Y   Total

A       40   28   68

B      38   54    92

Total 78   82   160

P(A|X) means the conditional probability of A given X has occurred. In this case, 40/92 means out of 92 times X occurred, A occurred 40 times.

P(B) means the marginal probability of B, which is the total probability of B occurring regardless of whether A occurred or not. In this case, 78/160 means out of 160 trials, B occurred 78 times.

The row and column totals are calculated by adding up the corresponding values.

The grand total is the sum of all the values in the table.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the attached image.

Answer:

8x^6-27y^6

Step-by-step explanation:

simplify the expression

Answer:

20,000 feet

Step-by-step explanation:

Based on the initial altitude and the rate that the plane is descending, the relevant equation is = 30,000 - 2,000x. The altitude after 5 minutes is 20,000 feet above sea level.

The plane begins at 30,000 feet above ground and is descending at 2,000 feet per minute. The relevant equation after x minutes is:

= Initial altitude - (Descent in feet per minute x Number of minutes)

Plugging in the values gives:

= 30,000 - (2,000 × x)

= 30,000 - 2,000x

creds to Parrain

Answer:

Step-by-step explanation:

Assuming that the motion of the hanging mass is only in the vertical direction, we can use the following equation of motion:

y = A*cos(ωt + φ)

where y is the position of the mass as a function of time, A is the amplitude of the motion (i.e., the maximum displacement from the equilibrium position), ω is the angular frequency of the motion (related to the period T by ω = 2π/T), t is the time elapsed since the motion started, and φ is the initial phase angle (which we can set to zero since the mass starts at the equilibrium position with zero velocity).

We can find the amplitude A from the initial condition given in the problem. The spring is stretched 0.13 m by the hanging mass, which means that the weight of the mass is balanced by the force of the spring when the spring has stretched by 0.13 m. This corresponds to the maximum displacement of the mass from the equilibrium position, so we have:

A = 0.13 m

We can find the angular frequency ω from the properties of the spring-mass system. The force exerted by a spring is given by:

F = -kx

where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position. For small displacements, the force is proportional to the displacement, so we have:

F = -kA*cos(ωt)

At the equilibrium position, the force is zero, so we have:

0 = -kAcos(ω0)

which means that cos(0) = 1 and k = mg/A, where m is the mass of the hanging object and g is the acceleration due to gravity. Substituting these expressions into the equation for the force, we get:

F = -mg*cos(ωt)

Comparing this to the equation for the force exerted by the spring, we see that:

-kAcos(ωt) = -mgcos(ωt)

which means that:

k = mg/A = ω^2

Solving for ω, we get:

ω = sqrt(g/A)

Substituting the given values, we have:

ω = sqrt(9.81 m/s^2 / 0.13 m) = 8.01 rad/s

Now we can use the equation for the position of the mass to find its position after 4.6 s:

y = Acos(ωt) = 0.13cos(8.01*4.6) = -0.092 m

Since the upward direction is defined as positive in this problem, the negative sign indicates that the mass is below the equilibrium position. Therefore, the position of the mass after 4.6 s is 0.092 m below the equilibrium position.

Answer:

\(um \: where \: the \: \\ triangles \: are ???\)

Answer:

y=5x-11

Step-by-step explanation:

parallel lines have the same slope 5

y-4=5(x-3)

y-4=5x-15

y=5x-15+4

y=5x-11

Answer:

B. h=S/πr²

Step-by-step explanation:

The question lacks options. Here is the complete question.

Which of the following equations is equivalent to S = πr²h

a. h=S-πr^2

b. h=S/πR^2

C. h= πr^2/S

D. h=S+ πr^2

To know the equation equivalent to πr²h, we will make h the subject of the formula as shown from the one given in equation.

S = πr²h

To get h, we will divide both sides by the coefficient of h (i.e πr²)

S/πr² = πr²h/πr²

S/πr² = h

h = S/πr²

This shows that h = S/πr² is equivalent to S = πr²h

Answer:

1.) We don't reject the null

2.) We reject the Null

3.) We do not reject the null

Step-by-step explanation:

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0

A.)

Left tail , Z = - 1.32 ; α = 0.10

We can use the Pvalue calculator from Z score :

Pvalue = 0.934

Pvalue > α ; Hence, we fail to reject the null, H0

B.)

Right-tailed test, z = 2.46, α = 0.01

Pvalue from Zscore calculator ;

Pvalue = 0.0069

Pvalue < α ; Hence, we reject the null, H0

C.)

Two-tailed test, z = -1.68, α = 0.05

Pvalue from Zscore calculator ;

Pvalue = 0.093

Pvalue > α ; Hence, we fail to reject the null, H0

The grams of cocoa does it contains is 36.57 grams

From the question, we have the following parameters that can be used in our computation:

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

Substitute the known values in the above equation, so, we have the following representation

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer: 30  i took a test with that question

Step-by-step explanation:

The requried, probability that both the first digit in the last digit of the three-digit number is even numbers is 20%.

To count the number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9, we can use the permutation formula:

P(n, r) = n! / (n-r)!

In this case, we have n = 6 (since we have 6 digits to choose from) and r = 3 (since we want to form three-digit numbers). Using the formula, we get:

P(6, 3) = 120

We can choose the first digit in two ways (2 or 8), and we can choose the last digit in three ways (2, 8, or 6). For the middle digit, we have four digits left to choose from (1, 3, 5, or 9), since we cannot repeat digits. Therefore, the number of three-digit numbers with distinct digits that have an even first and last digit is:

2 x 4 x 3 = 24

The total number of three-digit numbers with distinct digits is 120, so the probability that a randomly chosen three-digit number with distinct digits has an even first and last digit is:

24/120 = 0.2 or 20%

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By calculating the median of the data, the meteorologist can claim that Portland tends to receive more rainfall than Seattle.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The ordered data-sets for each city are given as follows:

The median is the middle element for each data-set, hence it is given as follows:

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

The student made the first error in Step 2. The correct expression for Step 2 should be: 5/6m - 2/3m + 6.

In this step, the student incorrectly combined the constant terms of 12 and -6 to get 12-6=6, instead of 12-6=6m.

To see why this is the case, simplify the original expression step by step:

5/6m + 12 - 2/3m - 6

= (5/6m - 2/3m) + (12 - 6) (group like terms)

= (5/6 * 2/3)m + 6 (simplify fractions and simplify constants)

= 10/18m + 6 (multiply fractions and simplify)

The expression in Step 4 is correct, but it was obtained using an incorrect expression in Step 2.

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The cost of Sneakers, pair of pants, Jacket and T-shirt are $95, $50, $100 and $290 respectively.

This can be solved by forming linear equations. A linear equation is the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Let us assume the cost of Sneakers be 's', cost of Pants be 'p', cost of Jacket be 'j' and cost of t-shirt be 't'.

The cost of all the items is equal to $535

s + p + j + t = $535                 ......(1)

Sneakers cost $5 less than the jacket

s = j - $5                                 ......(2)

Pants cost $50 less than the jacket

p = j - $50                              ......(3)

T-shirt cost $10 less than three times the jacket

t = 3j - $10                              ......(4)

Putting the values of equation (2), (3) and (4) in equation (1)

j - $5 + j - $50 + j + 3j - $10 = $535

6j = $535 + $65

=> 6j = $600

=> j = $100 which is the cost Jacket.

Now, s = $100 - $5 = $95 which is the cost of Sneakers.

p = $100 - $50 = $50 which is the cost of pair of pants.

t = $300 - $10 = $290 which is the cost of t-shirt.

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Answer:

sorry

Step-by-step explanation:

The value of (f∘g)(x) is 3x² - 2.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: f(x) = √x²-4 and g(x) = 3x²

We have to find the value of (f∘g)(x).

(f∘g)(x) = f(g(x))

(f∘g)(x) = f(3x²)

f(3x²) = √9x⁴- 4

f(3x²) = 3x² - 2

Hence, the value of (f∘g)(x) is 3x² - 2.

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Answer:

A cylinder has parallel discs bases that are congruent in size.

Step-by-step explanation:

Answer:

A, C, D

Step-by-step explanation:

Answer:

2,975

Step-by-step explanation:

First you have to convert the percentage into a decimal which is>>>0.35

Then, you have to multiply the employee’s current pay rate by that decimal which is>> 0.35 x 8.50= 2,975

there you got your answer hope this was helpful!  

The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

\(P(t) = \frac{K}{1 + Ae^{-kt} }\)

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)

\(1 + 9e^{-k} = 4\)

\(9e^{-k} = 3\)

\(e^{-k} = \frac{1}{3}\)

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)

\(1.9178 = 1 + 9e^{-1.0986t}\)

\(0.9178 = 9e^{-1.0986t}\)

\(\frac{0.9178 }{9} = e^{-1.0986t}\)

\(t = \frac{ln \: 0.10198}{-1.0986}\)

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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A quadrilateral is a shape with four sides

The indicated measures are A = 56, B = 128, C = 100 and D = 76

The angles in a quadrilateral add up to 360 degrees.

So, we have:

4n + 5n + 6 + 9n + 2 + 8n - 12 = 360

Collect like terms

4n + 5n + 9n + 8n = 360 - 6 - 2 + 12

Evaluate the like terms

26n = 364

Divide through by 26

n = 14

From the figure, we have:

A = 4n

B = 9n + 2

C = 8n - 12

D = 5n + 6

So, we have:

A = 4 * 14 = 56

B = 9*14 + 2 = 128

C = 8*14 - 12 = 100

D = 5*14 + 6 = 76

Hence, the indicated measures are

A = 56, B = 128, C = 100 and D = 76

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Answer:

8 = 34 + (n * 2) / 8 = (n * 2) + 34 ; n = -13

Step-by-step explanation:

In this question we have 2 numbers and a variable. The variable is "a number," which I have represented as "n" in my answer. As long as there is a letter in the spot of n, that is the correct answer- your assignment might have represented the variable differently.

When the question says "8 is" it is saying "8 is equal to." "Is" represents an equals sign in this equation. "More than" represents addition, or the sum of. "The product of" represents multiplication. "The product of a number and 2" means that we are multiplying n and 2 BEFORE adding it to 34, so we want to make sure to include those in parenthesis to signify that we do indeed solve that part of the equation first. As long as you know PEMDAS you should be fine here, but I prefer to add what the equation wants me to do first in parenthesis so that it's more readable. Since the order of numbers doesn't matter in addition, 34 can go both before and after "the product of n and 2."  

This gives us the equation "8 = 34 + (n * 2)," or the alternate "8 = (n * 2) + 34."

If you want to solve for N, you would need to subtract 34 from 8 and 34 itself, leaving -26 = (n * 2) or -26 = n(2). Then, since we're multiplying n by 2, we want to divide 2 by 2 to cancel it out, doing the same thing to -26. We are left with -13 = n, or n = -13.

Answer:

4+x>13

x>9

Step-by-step explanation:

This statement represents an inequality. To solve for the missing number first write out the inequality algebrically.

"Four more" implies that 4 is being added to the number. Another way to "a number" is to use the variable, x. So, the left side of the inequality is 4+x. Then, it says that this is "more than" 13. Thus, the greater than sign, >, should be used. This means that the final inequality is 4+x>13.

Next, you can solve the inequality by subtracting 4 from both sides. This gives  x>9.

Answer:

  (-√8, -√6] ∪ [-√2, 0) ∪ (0, √2] ∪ [√6, √8)

Step-by-step explanation:

The inequality resolves into 4 inequalities. There are 4 intervals in the solution.

Starting at the left, for the absolute value argument less than 0:

  2 ≤ -(x^2 -4) . . . . . . . for x^2 -4 ≤ 0

  2 ≤ -x^2 +4

  -2 ≤ -x^2

  2 ≥ x^2 . . . . . . . . . . consistent with the above 4 ≥ x^2

  -√2 ≤ x ≤ √2 . . . . . square root; may be limited by other constraints

For the absolute value argument greater than 0:

  2 ≤ x^2 -4 . . . . . . . for x^2 -4 ≥ 0

  6 ≤ x^2 . . . . . . . . . .consistent with x^2 ≥ 4

  -√6 ≥ x ∪ x ≤ √6 . . . . take the square root

__

The inequality on the right can be written as the compound inequality ...

  -4 < x^2 -4 < 4

  0 < x^2 < 8 . . . . . add 4

  0 < |x| < √8 . . . . take the square root

This resolves to ...

  -√8 < x < 0 ∪ 0 < x < √8

__

So, the solution set is the set of values of x that satisfy these restrictions on x:

  -√2 ≤ x ≤ √2

  x ≤ -√6 ∪ x ≤ √6

  -√8 < x < 0 ∪ 0 < x < √8

That is a collection of 4 intervals:

  (-√8, -√6] ∪ [-√2, 0) ∪ (0, √2] ∪ [√6, √8)

_____

You may be expected to write √8 as 2√2.

__

These intervals are the portions of the red curve that lie between the two horizontal lines. The points on the upper (dashed) line are not part of the solution set. The points on the lower (solid) line are part of the solution set.

Answer:

16%

Step-by-step explanation:

First we start by solving for the z score

We have the following information

x = 3.25

Standard deviation = sd = 2.25

Mean = 5.50

Z = (x - mean)/sd

z = 3.25 - 5.50/2 25

z = -1.00

If we look this up in the standard normal distribution table,

P(z<-1.00) = 0.1587

Which when approximated gives us

16%

Therefore approximately 16% of lobsters will have to be returned back to the sea.

Answer:

Step-by-step explanation:

Probability is the possibility for an event to occur or not to occur.

The formula for a combination is:

n choose r = n! / (r! x (n-r)!)

Given

n=14

r= 11 to 13

Hence, we shall add up the cases for 11 through 13.

nCr

14C11 + 14C12 + 14C13

14!/11!(14-11)! + 14!/12(14-12)! + 14!/13(14-13)!

= 14!/11!•3! + 14!/12!•2! + 14!/13!•1!

= 14*13*12*11!/11!•(3*2*1) + 14*13*12!/12!•(2*1) + 14*13!/13!•(1*1)

= 2184/6+182/2+14/1

= 364+91+14

= 469 ways

Step-by-step explanation:

469 ways are the ways to I think so if the answer is correct plz make ma the brainliest