a careless university student leaves her iclicker device behind with probability 1/4 each time she attends a class. she sets out with her iclicker device to attend 5 different classes (each class is in a different lecture theatre). part 1) if she arrives home without her iclicker device and she is sure she has the iclicker device after leaving the first class, what is the probability (to 3 significant figures) that she left it in the 5th class? probability

Answers

Answer 1

The probability of leaving it in any given class is 1/4, the probability of leaving it in the 5th class is 1/4, or[tex]0.250 (25.0%).[/tex]

The probability that the student left her iClicker device in the 5th class is 0.250 (25.0%). This is because the probability of leaving it in any given class is 1/4, and as she attends 5 different classes,

there is 5/4 or 1.25 chances of her leaving it in the 5th class.

To explain further, the probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. In this case, the event is leaving the iClicker device in the 5th class, and the total number of possible outcomes is 5 (for the 5 classes).

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Related Questions

The position vectors of points C and D are 2i + 37 and 7i + 5i respectively. Find the position vector of a point H which divides the line PQ in the ratio of 2: 3.​

Answers

Answer:

Step-by-step explanation:

Let P be the point C with position vector 2i + 3j and Q be the point D with position vector 7i + 5j. We want to find the position vector of point H which divides PQ in the ratio 2:3.

Let the position vector of point H be r. Then we have:

PH/PQ = 2/3

(P - r)/(Q - r) = 2/3

Multiplying both sides by (Q - r), we get:

P - r = (2/3)(Q - r)

Expanding the brackets and rearranging, we get:

r = (2Q + 3P)/5

Substituting the position vectors of P and Q, we get:

r = (2(7i + 5j) + 3(2i + 3j))/5

= (14i + 10j + 6i + 9j)/5

= (20i + 19j)/5

= 4i + 3.8j

Therefore, the position vector of point H is 4i + 3.8j.

Aubrey used
4
7
liter
7
4

literstart fraction, 4, divided by, 7, end fraction, start text, space, l, i, t, e, r, end text of paint for a mural in her room and
2
10
liter
10
2

literstart fraction, 2, divided by, 10, end fraction, start text, space, l, i, t, e, r, end text for a wall in her bathroom.

Answers

The total amount of paint Aubrey used is more than 1/2 liter but less than 1 liter

Estimating the total amount of paint Aubrey used

To estimate the total amount of paint that Aubrey used for both the mural and the wall, we can add the fractions of paint used

So, we have

Total = 4/7 + 2/10

Evaluate the sum in decimals

This gives

Total = 0.77 (approximated)

This value is between 0.5 liters and 1 liter

Hence, the estimate is between 0.5 liters and 1 liter

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Complete question

Aubrey used 4/7 liter of paint for a mural in her room and 2/10 for a wall in her bathroom.

Determine a reasonable estimate for the total amount of paint Aubrey used

Answer: B or the one that is more than 1/2 but it is less than 1

Step-by-step explanation: Took quiz on khan

A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard correct to 2 places.

Answers

The maximum area of the surfboard correct to 2 places is 0.67 m².

Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.

Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)

Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)

We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)

Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.

To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),

we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.

Area of surfboard =

[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]

[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]

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Help me with this question please

Answers

Answer:

x= 2√ 7

Step-by-step explanation:

We can solve it with applying the sin of 30°

Sin 30° = opposite leg / hypotenuse

Sin 30° = √ 7 / x

Being x unknown.

Now, being 30°  a notable angle, we know that its sin is 1/2.

Sin 30° = 1/2

Replacing,

Sin 30° = √ 7 / x.           (we clear x)

1/2 = √ 7 / x

x/2 = √ 7

x= 2√ 7

In triangle ABC, AB = (x + 2) cm, AC = (x + 1) cm and BC = x cm.
Given that cos BAC=3/4 , find the value of x.

Answers

Answer:

the value of x is approximately 0.382 cm.

Step-by-step explanation:

A random sample of 100 freshman showed 9 had satisfed the university mathematics requirement and a second random sample of 50 sophomores showed that 10 had satisfied the university mathematics requirement.
A) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is: 2.222
b) The increased risk of having satisfied the university mathematics requirement for sophomores as compard to freshmen is:

Answers

a) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 2.222.


b) The increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 122.2%.

Relative Risk is defined as the ratio of the risk of an event in the exposed group and the risk of the event in the unexposed group. The formula for relative risk is

RR = [a / (a + b)] / [c / (c + d)].

where, a = the number of individuals in the exposed group with the event,

b = the number of individuals in the exposed group without the event,

c = the number of individuals in the unexposed group with the event, and

d = the number of individuals in the unexposed group without the event.

Now, in this question, we have to calculate the relative risk and the increased risk for sophomores as compared to freshmen.

Given that,

Sample size of freshman = 100

Number of freshman who have satisfied the mathematics requirement = 9

Sample size of sophomores = 50

Number of sophomores who have satisfied the mathematics requirement = 10

a = 10, b = 40, c = 9, and d = 91

Relative risk for sophomores as compared to freshmen = (10 / (10 + 40)) / (9 / (9 + 91)) = 2.222

Therefore, the relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 2.222.

Increased risk = (RR - 1) × 100% = (2.222 - 1) × 100% = 122.2%

Therefore, the increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 122.2%.

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A farmer has 20 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in two boxes to the total number of eggs. Give your answer in its simplest form. ​

Answers

Answer:

Step-by-step explanation:

number of eggs in 2 boxes = 12

Total number of eggs = 20 x 6 = 120


12:120

Simplify

2:20

Simplify

1:10


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Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to
0.008.
0.02.
0.03.
0.04.
0.208.

Answers

The proportion of students who can roll their tongues will be estimated and the margin of error for a 95 percent confidence interval for the true proportion of tongue rollers among students will be determined. There were 317 tongue rollers out of a sample of 400 students.

      As a result, the sample proportion is 317/400 = 0.7925.

      We'll compute the margin of error next. The margin of error (E) for a 95 percent confidence interval is:

                E = zα/2 * sqrt[p(1 - p) / n]

                              where zα/2 is the z-score that corresponds to the level of confidence α/2, p is the sample proportion, and n is the sample size.

               E = 1.96 * sqrt[0.7925 * (1 - 0.7925) / 400]E

                  = 1.96 * sqrt[0.7925 * 0.2075 / 400]E

                  = 1.96 * sqrt(0.00040875)E

                  = 1.96 * 0.0202E

                  = 0.0395

    The margin of error is approximately 0.04 or 4 percent. Hence, the correct option is 0.04.

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to 0.04

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In order for the parallelogram to be a
rectangle, x = [?].
Diagonal AC = 4x+68
Diagonal BD = 6x + 8

Answers

30 is the value of x in parallelogram .

What is a parallelogram?

With sides that are parallel to one another, a parallelogram is a two-dimensional geometric shape. The pair of parallel sides in this sort of polygon with four sides, also known as a quadrilateral, are of equal length. In a parallelogram, the sum of the adjacent angles equals 180 degrees.

4x+68 = 6x + 8

 6x - 4x = 68 - 8

     2x = 60

        x = 30

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how much does a typical water bed weigh? useful data: 1 cubic foot of water weighs 64.2 pounds and a typical water bed holds 28 cubic feet of water.

Answers

A typical water bed weighs around 1797.6 pounds. It depends upon the volume of water bed and the unit conversion of the weight and volume units.

What is the typical water bed weigh?

A typical water bed holds 28 cubic feet of water.

The volume of the typical water bed and its weight can be calculated with the help of the quantities:

Identify the volume of water held by the water bed, which is 28 cubic feet.
Multiply the volume by the weight of 1 cubic foot of water, which is 64.2 pounds.
Perform the calculation: 28 cubic feet × 64.2 pounds per cubic foot = 1797.6 pounds.

Therefore, a typical water bed weighs approximately 1797.6 pounds when filled with water.

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50 POINTS!! Scientists measure a bacteria population and find that it is 10,000. Five days later,

they find that the population has doubled. Which function f could describe the

bacteria population d days after the scientists first measured it, assuming it grows

exponentially?

Answers

According to the solving  function f could describe the bacteria population d days after the scientists first measured it, assuming it grows exponentially F(d) = 10000 - a[tex]^\frac{d}{5}[/tex].

What is function, exactly?

A mathematical expression, rule, or law known as a function defines the relationship between two independent variables and a dependent variable (the dependent variable). In mathematics, functions are often utilised, and they are essential for creating physical connections in the sciences.

According to the given information:

Substituting d = 5 and f(d)

Solution: fid) = 10000⋅ ad

{substitute d=5 and fid)=20000 into fid=10000. ady

10000- a⁵ =20000

a⁵ =2[tex]^\frac{1}{5}[/tex]

a = 2

F(d) = 10000 - a[tex]^\frac{d}{5}[/tex]

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Christina’s car used 14 gallons of gas to travel 546 miles. How many miles did her car travel per gallon of gas.

Answers

Step-by-step explanation:

You are given miles ( 546) and gallons (14)  and you

   want miles / gal     this is just     546 miles / 14 gallons  = 39  mpg

Answer:

39

Step-by-step explanation:

14 is the main number here.

assuming 1 tank = 14gallons. / 546 miles

a = gallons

b = miles

b / a = mpg (miles per gallon)

so: 546 / 14 = 39

Please help quick with this question.

Answers

Answer:

b = [tex]\frac{S-2la}{h+l}[/tex]

Step-by-step explanation:

S = bh + lb + 2la ( reversing the equation )

bh + lb + 2la = S ( subtract 2la from both sides )

bh + lb = S - 2la ← factor out b from each term on the left side

b(h + l) = S - 2la ← divide both sides by (h + l)

b = [tex]\frac{S-2la}{h+l}[/tex]

What would be the best first step in solving this system?

Answers

Answer:

D

Step-by-step explanation:

sub y into the 2nd equation and find x

A triangle has area 100 square inches. It's dilated by a factor of k= 0.25.
Mai says, "The dilated triangle's area is 25 square inches."
Lin says, "The dilated triangle's area is 6.25 square inches."

1. For each student, decide whether you agree with their statement. If you
agree, explain why. If you disagree, explain what the student may have done to arrive at their answer.

2. Calculate the area of the image if the original triangle is dilated by each of these scale factors:
a. K = 9
b. K = 3/4

Answers

Lin's statement is correct. The incorrect answer is obtained due to inaccurate calculations of the new area of triangle.

What is dilation?

A geometric modification called a dilation alters a figure's size. Each coordinate in the graphic is multiplied by a preset scale factor k to obtain it. The same element causes the figure to be stretched or contracted in all directions, creating a new figure that resembles the original but is smaller. Both two-dimensional (2D) and three-dimensional (3D) dilations are possible (3D). They are frequently employed in geometry to generate analogous figures and compute scale factors.

Mai's statement is incorrect. When a triangle is dilated by a factor of k, its area is multiplied by k².

When the given area of 100 square inches is dilated by a factor of 0.25 the new area is 6.25.

Hence, Lin's statement is correct. The incorrect answer is obtained due to inaccurate calculations of the new area.

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There are 9 out of 25 students in science class who passed the test and 4 out of 16 in history. What is the percentages of students in each class that passed the test?

Answers

Answer: 36% passed the science test, while 25% passed the history test.

In order to find a percentage we divide our two know numbers

Science Class- 9/25 is a fraction with / standing for divided by. 9 divided by 25 is .36   This means 36% of the class passed the science test.

History Class- 4/16 is a fraction with / standing for divided by. 4 divided by 16 is .25   This means 25% of the class passed the science test.

I hope this helped & Good Luck <3!!!!

the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses.true or false

Answers

The statement "the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses" is TRUE.

What are the equations of motion?

The equations of motion refer to a set of mathematical equations that describe the behavior of a physical system over time. These equations define how the position, velocity, and acceleration of an object are related. The equations of motion are applicable to both single and multi-degree-of-freedom systems.

What is a two-degree-of-freedom system?

A two-degree-of-freedom system is a physical system with two independent modes of motion or two degrees of freedom. It is defined by two generalized coordinates that completely define the system's state.

A two-degree-of-freedom system can be either linear or nonlinear, depending on the nature of the force. It is used in the study of structural dynamics, mechanical vibrations, and control engineering.

In a two-degree-of-freedom system, the equations of motion can be expressed in terms of the displacement of either of the two masses. The equations of motion are usually derived using Lagrange's equations, which are a set of equations that describe the dynamics of a mechanical system in terms of its energy. They are given as follows:

Where q₁ and q₂ are the generalized coordinates, m₁ and m₂ are the masses, k₁ and k₂ are the spring constants, and c₁ and c₂ are the damping coefficients.

These equations of motion are nonlinear and can be solved analytically or numerically using various techniques.

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The exponential 12 (3) 2x-12 has been converted to 12(k)*-6, what is the value of k?

Answers

Answer:

The solution set is (13,− 32). A quadratic equation of the form x 2= k can be solved by factoring with the following sequence of equivalent equations.

Step-by-step explanation:

can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10​

Answers

Answer:

can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10​

Step-by-step explanation:

To solve sin y - cos (y + 20) = 0, we can rearrange it as sin y = cos (y + 20).

Then, we can use the identity sin (90 - x) = cos x to rewrite the right side as cos (y + 20) = sin (70 - y).

Substituting this into the equation, we get sin y = sin (70 - y).

Now, there are two possibilities:

y = 70 - y, which gives y = 35 degrees.

y = 180 - (70 - y), which gives y = 105 degrees.

To solve cos theta = sin theta - 10, we can rearrange it as cos theta - sin theta = -10 and then use the identity cos (x - 90) = sin x to rewrite it as -sin (theta - 90) = -10.

Taking the inverse sine of both

PLEASE HELP I DONT HAVE TIME

Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?

The answer is 48 but I need step by step explanation

Answers

The number of toy soldiers Leo has is 48.

How to calculate the number of toy soldiers Leo has?

To solve this problem, we need to find a number that satisfies the three given conditions:

The number is between 27 and 54.

When the number is divided by 4, there is no remainder.

When the number is divided by 7, the remainder is 6.

When the number is divided by 5, the remainder is 3.

Let's start by finding a number that satisfies the first two conditions. We can do this by listing the multiples of 4 between 27 and 54:

28, 32, 36, 40, 44, 48, 52

Next, we need to find which of these numbers also satisfies the third condition, that is, leaves a remainder of 6 when divided by 7. We can go through each of these numbers and check:

28 divided by 7 leaves a remainder of 0.

32 divided by 7 leaves a remainder of 4.

36 divided by 7 leaves a remainder of 1.

40 divided by 7 leaves a remainder of 5.

44 divided by 7 leaves a remainder of 2.

48 divided by 7 leaves a remainder of 6.

52 divided by 7 leaves a remainder of 3.

So, the only number that satisfies the first three conditions is 48.

Finally, we need to check if 48 also satisfies the fourth condition, that is, leaves a remainder of 3 when divided by 5. Indeed, 48 divided by 5 leaves a remainder of 3.

Therefore, the number of toy soldiers Leo has is 48.

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If a police officer wants to find out whether the average speed of motorists on a highway with a speed limit of 55 mph is greater than 55 mph, then the null hypothesis is 55.
True or False?

Answers

The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.Given statement is false.

What is hypothesis test?

A statistical hypothesis test is a technique for determining whether the available data are adequate to support a specific hypothesis. We can make probabilistic claims about demographic parameters through hypothesis testing.

According to question:

The null hypothesis should be a statement of no difference or no effect. In this case, the null hypothesis would be that the average speed of motorists on the highway is equal to 55 mph.

So the correct statement would be:

The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.

Thus, Given statement is false.

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Solve the triangle MNO (find the measure of ∠O and the lengths of sides MO and NO).
(I need help finding both side measures and angle measure please and thank you

Answers

Answer:

Step-by-step explanation:

m∠O = 90° - 34° = 56°

cos M = [tex]\frac{MN}{MO}[/tex]  ⇒  MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm

tan M = [tex]\frac{ON}{MN}[/tex]  ⇒  ON = 12 × tan 34° ≈ 8.1 cm  

kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
a. 1
b. x.x’
c. 1+ x.x’
d. (1+ x.x’)^2
e. exp (x+x’), for x.x’ ER
f. min (x.x’) for x.x’ E Z

Answers

Answer:

Step-by-step explanation:

kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )

An amusement park opened at 10:00 a.m. In the first hour,
480 people purchased admission tickets. In the second hour,
40% more people purchased admission tickets than in the
first hour. Each admission ticket cost $24.50.
What was the total amount of money paid for all the tickets
purchased in the first two hours?

A) $16,464.00
B) $4,704.00
C) $18,816.00
D) $28,224.00

Answers

Answer:

D) $28,224.00

Step-by-step explanation:

1st hour: 480 ticket sales

2nd hour: 480 + 40% of 480 = 480 + 0.4 × 480 = 480 + 192 = 672

Total ticket sales in first 2 hours: 480 + 672 = 1152

Ticket price: $24.50

Total sales: 1152 × $24.50 = $28,224

A movie theater is attracting customers with searchlights. One circular searchlight has a
radius of 2 feet. What is the searchlight's circumference?
Use 3.14 for л. If necessary, round your answer to the nearest hundredth.

Answers

The nearest hundredth, we get:

C ≈ 12.56 feet.

What is the value of 2r of a circle?

Circle circumference (or perimeter) = 2R

where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.

The circumference of a circle is calculated as follows:

C = 2πr

where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.

When the given values are substituted, the following results are obtained:

C = 2(3.14)(2) \s= 12.56

We get the following when we round to the nearest hundredth:

C ≈ 12.56 feet.

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9. Jess spins a pointer 25 times and finds an
experimental probability of the pointer landing
on 3 to be 25, or 16%. The theoretical probability
of the spinner landing on 3 is à, or 25%. Why
might there be a significant difference between
the theoretical and experimental probabilities?

Answers

The number of times the experiment is run affects the experimental probability.

What is Probability?

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

According to our question-

multiply that percentage by 25 to get the experimental probability percentage.

16%25

Hence, The number of times the experiment is run affects the experimental probability.

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One of the legs of a right triangle measures 4 cm and its hypotenuse measures 11 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Answer: 10.2 cm

Step-by-step explanation:

We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's call the unknown length of the other leg "x". Then we can set up the following equation:

4^2 + x^2 = 11^2

Simplifying this equation, we get:

16 + x^2 = 121

Subtracting 16 from both sides, we get:

x^2 = 105

Taking the square root of both sides, we get:

x = sqrt(105)

x ≈ 10.2 cm (rounded to the nearest tenth)

Therefore, the measure of the other leg is approximately 10.2 cm.

Complete the proof that △STU∼△WVU

Answers

So,To prove that △STU∼△WVU, we need to show that the two triangles are similar, which means that their corresponding angles are equal, and their corresponding sides are proportional.

What is triangle?

A polygon with three sides and three angles is termed as triangle.

Triangles can be classified based on the length of their sides and the size of their angles, and they have a variety of properties and theorems associated with them in mathematics.

Angles: Since line VS is the bisecting line on line WT, angles VST and TSU are equal. Similarly, angles UVW and WVU are equal since U is the bisecting point on the line. Therefore, angle VUS is equal to angle WUV since they are vertically opposite angles.

Sides: We need to show that the corresponding sides are proportional.

Using the angle bisector theorem, we know that US/UT = VS/VT, which can be written as:

9/6 = VS/VT

Simplifying this, we get:

3/2 = VS/VT

Using the segment bisector theorem, we know that UW/WV = UT/TV, which can be written as:

6/4 = UT/TV

Simplifying this, we get:

3/2 = UT/TV

Since both ratios are equal to 3/2, we can say that:

VS/VT = UW/WV

Therefore, we can conclude that △STU∼△WVU by the angle-angle similarity theorem.

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Consider all four-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0. What is the probability of choosing a random number that starts with 2 from this group? Enter a fraction or round your answer to 4 decimal places, if necessary

Answers

Answer:

Step-by-step explanation:

To find the probability of choosing a random number that starts with 2, we need to find two things:

1. The total number of valid four-digit numbers that can be created from the digits 0-9 where the first and last digits are even and no digit can repeat.

2. The number of valid four-digit numbers that start with 2 and meet the other criteria.

Let's begin by calculating the total number of valid four-digit numbers.

There are 5 even digits (0, 2, 4, 6, 8) to choose from for the first and last digits. For the second digit, there are 9 digits to choose from (since 0 cannot be repeated), for the third digit there are 8 digits to choose from (since we used one digit already and neither the first nor last digit can be repeated), and for the last digit there are only 4 choices left (since we used 5 for the first digit, and one more can’t be repeated). Therefore, the total number of valid four-digit numbers is:

5 * 9 * 8 * 4 = 1,440

Now we need to calculate the number of valid four-digit numbers that start with 2.

We already determined that there are 5 even digits to choose from for the last digit, leaving 8 digits for the second and 7 for the third digit (since the first digit is fixed). So the number of valid four-digit numbers that start with 2 is:

5 * 8 * 7 * 1 = 280

Therefore, the probability of choosing a random number that starts with 2 is:

280 / 1,440 = 0.1944 rounded to 4 decimal places.

So the answer to the problem is 97/500, which simplifies to 0.1940 when rounded to 4 decimal places.

For what value of x is the figure a rectangle? Please help

Answers

Answer:

x = 8

Hope this helps!

Step-by-step explanation:

( 2x + 42 )° + ( 4x )° = 90°  ( right angle )

6x + 42 = 90

6x = 90 - 42

6x = 48

x = 8

X=8


(2x + 42) + 4x = 90 degrees

Add 4x + 2x to get 6x + 42 = 90

Then, subtract 42 from both sides to get, 6x = 48

Lastly, divide both sides by 6 to get your final answer of X = 8.
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