Polygon ABCDE will be dilated by a scale factor of 5.2 with the origin as the center of dilation to produce polygon A′B′C′D′E′. What will the length of A'E' be?
Select one:
a. 10.4 units
b. 3 units
c. 15.6 units
d. 8.2 units

Answer:

vertex is 2 and -4

Step-by-step explanation:

Thus, Bao age is 27.

acc to our question-

hence,Thus, Bao age is 27.

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Answer:

2.294117647

Step-by-step explanation:

3/17  =  u/13

Cross multiply:

3 * 13 = 17 * u

Simplifying

3 * 13 = 17 * u

Multiply 3 * 13

39 = 17 * u

Solving

39 = 17u

Move all terms containing u to the left, all other terms to the right.

Add '-17u' to each side of the equation.

39 + -17u = 17u + -17u

Combine like terms: 17u + -17u = 0

39 + -17u = 0

Add '-39' to each side of the equation.

39 + -39 + -17u = 0 + -39

Combine like terms: 39 + -39 = 0

0 + -17u = 0 + -39

-17u = 0 + -39

Combine like terms: 0 + -39 = -39

-17u = -39

Divide each side by '-17'.

u = 2

Simplifying

u = 2.294117647

The transformation of the graph f(x) = x² to the graph g(x) = -3(x+5)² + 12 involves a horizontal shift, a vertical stretch, and a vertical translation.

The graphs of f(x) = x² and g(x) = -3(x+5)² + 12 are the parabola.

The transformation of the graph is following as:

Firstly, the parabola has been shifted horizontally by 5 units to the left, which is reflected in the expression (x+5)².

Secondly, the parabola has been stretched vertically by a factor of -3, which is reflected in the coefficient in front of (x+5)².

Finally, the parabola has been raised up to 12 units. This means that the vertex of the parabola has been shifted upwards from the origin to the point (−5,12).

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Answer:

The equation has only one solution, x = -9

Step-by-step explanation:

We want to find how many solutions the equation:

8x = -9 + 7x

has.

To find it, let's simplify the equation.

First, let's move all the terms with x to the left side, and the terms without x to the right side:

8x - 7x = -9

(8 - 7)*x = -9

1*x = -9

x = -9

So we can see that we have only one solution, x = -9

The ^ symbol means exponent. We have 2 as the base and 5 as the exponent. You might write it like this \(2^5\) though 2^5 is more common with computers and keyboards.

Using your calculator, you should find that 2^5 = 2*2*2*2*2 = 32. We have five copies of the base 2 multiplied together.

You can use logs to determine how to write 32 as a base 2. You would do so like this

log(32)/log(2) = 5

it doesn't matter which base log you use. This is through the change of base formula.

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The statement "If U is invariant under every linear operator on V, then U = {0} or U = V" is false.

To disprove the statement, we need to provide a counterexample where U is invariant under every linear operator on V, but U is neither the zero subspace nor the entire vector space V.

Consider a finite dimensional vector space V with dimension greater than 1. Let U be a proper non-zero subspace of V. Since U is a proper subspace, it does not equal V.

Now, consider a linear operator T on V such that T maps any vector in V outside of U to zero, and T maps any vector in U to itself. In other words, T is the identity operator on U and the zero operator on V\U.

Since U is a proper subspace, there exist vectors in V\U, and under the linear operator T, these vectors will be mapped to zero. Hence, U is invariant under this linear operator T.

However, U is not equal to V, as it is a proper subspace. Therefore, the statement "If U is invariant under every linear operator on V, then U = {0} or U = V" is false.

The statement "If U is invariant under every linear operator on V, then U = {0} or U = V" is disproved by providing a counterexample where U is a proper non-zero subspace of V that is invariant under a specific linear operator on V.

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The vectors are linearly dependent when h = -61/18, because this will cause the third variable to be a linear combination of the first two variables.

For the given vectors to be linearly dependent, there must exist some non-zero scalars k1, k2, and k3 such that:

k1[3, -3, 9] + k2[9, -12, 26] + k3[-2, 2, h] = [0, 0, 0]

Expanding this equation gives us the system of equations:

3k1 + 9k2 - 2k3 = 0

-3k1 - 12k2 + 2k3 = 0

9k1 + 26k2 + hk3 = 0

We can solve this system of equations using row reduction or elimination, but it is easier to use the fact that the determinant of the matrix of coefficients must be zero for there to exist non-zero solutions for k1, k2, and k3. Therefore:

| 3 9 -2 |

|-3 -12 2 | = 0

| 9 26 h |

Expanding the determinant, we get:

3(-12h - 52) - 9(2h + 27) - 2(-36) = 0

Simplifying, we get:

-12h - 52 - 6h - 81 + 72 = 0

-18h - 61 = 0

h = -61/18

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Answer:

1555.61 birrs

Step-by-step explanation:

Perform this operation:

83.5 liters      18.63 birr

---------------- * ----------------- = 1555.61 birrs             This was the total amount

         1               1 liter                                              of the bill.

Answer:

1,555.605

Step-by-step explanation:

per liter is 18.63 and the driver got 83.5 liters

the bill is 18.63 × 83.5 = 1,555.605 if you are asked to approximate

it will give you 1,556

Answer:

35 as a fraction is 7/20

Step-by-step explanation:

Answer:

11/35

Step-by-step explanation:

The probability of ml1 is 0.890, or 89.0% the specificity or probability of ml2 is 0.993, or 99.3% to three significant digits

To find the sensitivity of ml1, we need to look at the true positive rate, which is the probability of the machine learner predicting an intrusion given that an intrusion actually occurred. This can be found from the table as:

sensitivity = P(ml1 predicts intrusion | intrusion) = 0.0129/(0.0129 + 0.0016) = 0.890

Therefore, the probability of ml1 is 0.890, or 89.0% (to three significant digits).

To find the probability of ml2, we need to look at the true negative rate, which is the probability of the machine learner predicting a valid user given that a valid user is actually using the system. This can be found from the table as:

specificity = P(ml2 predicts valid user | valid user) = 0.985/(0.985 + 0.007) = 0.993

Therefore, the specificity of ml2 is 0.993, or 99.3% (to three significant digits).

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Answer:

\(4.\\\text{E. }x=5, x=-6,\\\\5.\\\text{A. }x=7, x=-3\\\\\text{18.}\\\text{D. No mistakes.}\)

Step-by-step explanation:

For \(a=|b|\), there are two cases:

\(\begin{cases}a=b,\\a=-b\end{cases}\)

Question 4:

Given \(5|2x+1|=55\),

Divide both sides by 5:

\(|2x+1|=11\)

Divide into two cases and solve:

\(\begin{cases}2x+1=11,2x=10, x=\boxed{5}\\-(2x+1)=11,2x+1=-11, 2x=-12, x=\boxed{-6}\end{cases}\)

Therefore, the solutions to this equation are \(\boxed{\text{E. }x=5, x=-6}\).

Question 5:

Given \(\frac{1}{2}|4x-8|-7=3\),

Add 7 to both sides:

\(\frac{1}{2}|4x-8|=10\)

Multiply both sides by 2:

\(|4x-8|=20\)

Divide into two cases and solve:

\(\begin{cases}4x-8=20,4x=28, x=\boxed{7}\\-(4x-8)=20, 4x-8=-20, 4x=-12, x=\boxed{-3}\end{cases}\)

Therefore, the solutions to this equation are \(\boxed{\text{A. }x=7, x=-3}\)

Question 18:

There are no mistakes in the solution shown. The answer properly isolates the term with absolute value with no algebraic mistakes. Following that, the answer divides the equation into both absolute value cases and solves algebraically correctly. Therefore, the correct answer is \(\boxed{\text{D. No mistakes.}}\)

Answer:

2

Step-by-step explanation:

|x| + |x-2| =

Let x= 1

|1| + |1-2| =

|1| + |-1| =

The absolute value means take the non negative value

1 + 1 = 2

P(all 4 are seniors) = (10/49) * (9/48) * (8/47) * (7/46), P(1 each: freshman, sophomore, junior, senior) = (17/49) * (17/48) * (12/47) * (10/46),  P(2 sophomores and 2 freshmen) = P(selecting 2 sophomores) * P(selecting 2 freshmen) and  P(at least 1 senior) = 1 - P(none of the students is a senior)

To find the probabilities, we'll calculate the desired outcomes divided by the total number of possible outcomes.

a) All 4 are seniors:

There are 10 seniors in the team, so the probability of selecting a senior as the first captain is 10/49. After selecting the first captain, there are 9 seniors remaining out of 48 players, so the probability of selecting a senior as the second captain is 9/48. Similarly, the probabilities for the third and fourth captains are 8/47 and 7/46, respectively. Since these events are independent, we multiply the probabilities together:

P(all 4 are seniors) = (10/49) * (9/48) * (8/47) * (7/46)

b) There is 1 each: freshman, sophomore, junior, and senior:

We'll calculate the probabilities for each class individually and then multiply them together.

P(selecting a freshman) = 17/49

P(selecting a sophomore) = 17/48

P(selecting a junior) = 12/47

P(selecting a senior) = 10/46

P(1 each: freshman, sophomore, junior, senior) = (17/49) * (17/48) * (12/47) * (10/46)

c) There are 2 sophomores and 2 freshmen:

We'll calculate the probabilities for selecting 2 sophomores and 2 freshmen.

P(selecting 2 sophomores) = (17/49) * (16/48)

P(selecting 2 freshmen) = (17/47) * (16/46)

P(2 sophomores and 2 freshmen) = P(selecting 2 sophomores) * P(selecting 2 freshmen)

d) At least 1 of the students is a senior:

We'll calculate the probability of the complement event (none of the students is a senior) and subtract it from 1.

P(none of the students is a senior) = (39/49) * (38/48) * (37/47) * (36/46)

P(at least 1 senior) = 1 - P(none of the students is a senior)

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Step-by-step explanation:

when you get a decimal like 0.02 and you want to express it in fraction,this is a simple trick.

first,put your pen at the point and move it forward till you end at the last number.

While you move the pen over each value, you will count the number of jumps and record the number of jumps in zeros i. e

2÷100 and it means that,the last 1or 3or 3whole numbers will become the numerator

The solution of the equation y = (2/3)x + 3 is 5/3

The given equation is

y = (2/3)x + 3

The slope of the line is the change in y coordinates with respect to the change in x coordinates.

This is the linear equation in the the slope intercept form

y = mx + b

Where m is the slope of the line

b is the y intercept

y is the y coordinates

x is the x coordinates

The value of x = -2

Substitute the value of x in the equation

y = (2/3) × -2 + 3

Do the arithmetic operations

= -4/3 + 3

Add the numbers

= 5/3

Therefore, the solution is 5/3

I have solved the question in general, as the given question is incomplete

The complete question is:

What is the solution of the equation y = (2/3)x + 3x, when x = -2?

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The new value after the original value is increased by 30% is 1.3 times the original value.

Percentage is used to express a fraction number or decimal in fraction of hundred. It is given by:

Percentage = [(new value - original value) / original value] * 100%

Let x represent the new value and y represent the original value, hence:

30% = [(x - y)/y] * 100%

0.3 = (x - y)/y

x - y = 0.3y

x = 1.3y

The new value after the original value is increased by 30% is 1.3 times the original value.

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There are 90 different ways in which the four scholarships can be distributed such that at least two are awarded to freshman students.

We first need to determine the number of ways in which we can choose two of the six freshman students to receive scholarships. This can be done using the binomial coefficient formula: \(${6 \choose 2} = 15$\).

Next, we need to determine the number of ways in which we can choose two of the four sophomore students to receive scholarships. This can also be done using the binomial coefficient formula: \(${4 \choose 2} = 6$\)

Finally, we need to multiply these two values together to get the total number of ways in which the scholarships can be distributed: 15 * 6 = 90. Therefore, there are 90 different ways in which the four scholarships can be distributed such that at least two are awarded to freshman students.

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Step-by-step explanation:

(f o g)(x)

= f(x² - 5)

= 4(x² - 5) + 1

= 4x² - 19.

Therefore (f o g)(4) = 4(4)² - 19 = 64 - 19 = 45.

Answer:

\(\boxed {\boxed {\sf 45}}\)

Step-by-step explanation:

When solving a composition of function composition, work from the inside to the outside.

We have the composition:

We must start on the inside, and find g(4) first.

1. g(4)

The function for g is:

\(g(x)=x^2-5\)

Since we want to find g(4), we have to substitute 4 in for x.

\(g(4)=(4)^2-5\)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction. First we should solve the exponent.

\(g(4)=16-5\)

Subtract 5 from 16.

\(g(4)= 11\)

Now, since g(4) equals 11, we have:

2. f(11)

The function for f is:

\(f(x)= 4x+1\)

We want to find f(11), so substitute 11 in for x.

\(f(11)= 4(11)+1\)

Solve according to PEMDAS and multiply first.

\(f(11)= 44+1\)

Add.

\(f(11)= 45\)

(f o g)(4) is equal to 45.

The type of statistical study that the researchers used is a randomized controlled trial (RCT). In a randomized controlled trial, participants are randomly assigned to two or more groups.

One group is the treatment group, which receives the intervention being studied. The other group is the control group, which does not receive the intervention.

The researchers in this study randomly assigned 200 full-time employees to two groups: a treatment group and a control group. The treatment group was instructed to meditate 10-20 minutes twice per day, and to participate in weekly 1-hour sessions. The control group was not given any special instructions.

After a period of 8 weeks, all participants were required to fill out the psychological strain questionnaire (PSQ). The PSQ is an accepted measure of work stress.

The researchers calculated the difference in questionnaire scores for all participants, where a positive change corresponds to a reduction in work stress. Then, they compared the average differences of each group.

The researchers found that the treatment group had a significantly lower average difference in PSQ scores than the control group. This suggests that meditation may be an effective way to reduce work stress.

Here are some other details about randomized controlled trials:

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The 99% confidence interval for the mean score of all students is constructed as (85.497, 96.5026).

Given,

Sample size, n = 30

Sample mean, x = 91

Standard deviation, s = 11.7

The 99% confidence interval for the mean score of all students can be calculated as,

x ± z \(\frac{s}{\sqrt{n} }\)

z value for 99% confidence interval = 2.576

Confidence interval = (91 ± (2.576 × 11.7/√30)

                                 = (91 ± 5.5026)

                                 = (85.497, 96.5026)

Hence the confidence interval is (85.497, 96.5026).

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A radical equation is an equation that contains a variable within a radical expression.

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A. The cost of 2 hamburgers is $2.75 x 2 = $5.50.

The cost of 1 bag of chips is $1.50.

The cost of 1 soda is $1.25.

Therefore, the total cost of 2 hamburgers, 1 bag of chips, and 1 soda is:

$5.50 + $1.50 + $1.25 = $8.25.

B. If the student pays with a $10 bill, the amount of change he will receive is the difference between $10 and the total cost of the food:

$10 - $8.25 = $1.75.

Therefore, the student will receive $1.75 in change.

Answer:100 mph

Step-by-step explanation: it’s always distance divided by time. lol

The train travels to a distance of 75 miles in 0.75 hours, then the speed of the train will be equal to 100 miles per hour.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Distance (d) traveled by train = 75 miles

Time (t) taken by train to travel the distance = 0.75 hours

Then, use the equation of speed (s),

\(Speed =\frac{Distance}{Time}\)

s = 75/0.75

s = 100 miles per hour.

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sin(4π3) = sin(240 degrees) = -√3/2 found using the trigonometric ratios of right-angled triangle.

Sine of a positive acute angle: sin(4π3)

The sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse of a right-angled triangle.

Consider a right-angled triangle ABC, with an acute angle α, opposite side length O and hypotenuse length H. We can express the sine of angle α as sin(α) = O/H.

For a positive acute angle, the sine is always positive since the opposite side is positive and the hypotenuse is positive. In the case of sin(4π3), we can determine the exact value by first converting it to degrees. Recall that 2π radians is equivalent to 360 degrees.

Therefore, 4π3 radians is equivalent to 240 degrees. We can then use the unit circle to find the sine of 240 degrees.

The unit circle is a circle of radius 1 with its center at the origin of the coordinate plane. Any point on the circle can be expressed as (cos θ, sin θ) where θ is the angle formed between the x-axis and the terminal side of the angle in standard position.

In the case of 240 degrees, the terminal side is in the third quadrant and forms a 60-degree angle with the x-axis.

This means that the point on the unit circle corresponding to 240 degrees is (-1/2, -√3/2).

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When the water flows through the sprinkler nozzle, it speeds up, creating a low-pressure area that sucks water up from the supply pipe and distributes it over the lawn.

Archimedes' principle, Pascal, and Bernoulli's principle have been proved to be the most fundamental principles of physics. Here is a detailed explanation of the similarities and differences between the three and three examples of daily life for each of the principles:

Archimedes' principle: This principle of physics refers to an object’s buoyancy. It states that the upward buoyant force that is exerted on an object that is submerged in a liquid is equal to the weight of the liquid that is displaced by the object.
It is used to determine the buoyancy of an object in a fluid.
It is applicable in a fluid or liquid medium.
Differences:
It concerns only fluids and not gases.
It only concerns the buoyancy of objects.

Examples of daily life for Archimedes' principle:

Swimming: Swimming is an excellent example of this principle in action. When you swim, you’re supported by the water, which applies a buoyant force to keep you afloat.
Balloons: Balloons are another example. The helium gas in the balloon is lighter than the air outside the balloon, so the balloon is lifted up and away from the ground.
Ships: When a ship is afloat, it displaces a volume of water that weighs the same as the weight of the ship.

Pascal's principle:
Pascal's principle states that when there is a pressure change in a confined fluid, that change is transmitted uniformly throughout the fluid and in all directions.
It deals with the change in pressure in a confined fluid.
It is applicable to both liquids and gases.
Differences:
It doesn’t deal with the change of pressure in the open atmosphere or a vacuum.
It applies to all fluids, including liquids and gases.

Examples of daily life for Pascal's principle:

Hydraulic lifts: Hydraulic lifts are used to lift heavy loads, such as vehicles, and are an excellent example of Pascal's principle in action. The force applied to the small piston is transmitted through the fluid to the larger piston, which produces a greater force.
Syringes: Syringes are used to administer medicines to patients and are also an example of Pascal's principle in action.
Brakes: The braking system of a vehicle is another example of Pascal's principle in action. When the brake pedal is depressed, it applies pressure to the fluid, which is transmitted to the brake calipers and pads.

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Answer i believe the rule is y= x/2 so n=6

Step-by-step explanation:

Answer:

let the number be n :

\(3 \times n = k \\ { \underline{ \: \: 3n = k \: \: }}\)