From the tree diagram find the following.
(a) P(An E)
0
(b) P(A)
(c) P(A|E)
X
0.1
0.9
A A
0.3
0.3
0.4
0.4
0.4
0.2

31 people chose Petra as leader in the student council elections.

Percentage is used to represent a fraction of 100.

Percent is represented by the sign "%".

Mathematically, we can write the percentage as -

A% of B

(A/100) x B

AB/100

Given is that in the student council elections, 39% of the 80 voters chose Petra.

We can find the total number people who chose Petra as leader as -

{x} = 39% of 80

{x} = (39/100) x 80

{x} = 31.2

{x} = 31

Therefore, 31 people chose Petra as leader in the student council elections.

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{Question in English -

In the student council elections, 39% of the 80 voters chose Petra. How many optical votes Petra?}

The kilograms of compost in the barrel is 5.6 kg

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

Amount filled on day 1 = 1/4

Remaining space = 4200 grams

The number of kilograms in the barrel is calculated as

Remaining space = (1 - 1/4) * Original space

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

(1 - 1/4) * Original space = 4200 grams

Convert to kg

(1 - 1/4) * Original space = 4.2 kg

So, we have

Original space = 4.2 kg/(1 - 1/4)

Evaluate

Original space = 5.6 kg

Hence, the original space is 5.6 kg

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The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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The length of the two sides of the given right triangle is 5√2

A triangle with an angle right angle is called a right triangle.

Given that, a right triangle, with an acute angle of 45° and the length of hypotenuse is 10 units,

We need to find the length of two sides u and v,

The sum of a triangle is 180°, and if one angle is 90° and the other is 45° therefore, the third is also 45°

Now, we know that, sides opposite to equal angles are equal,

Therefore, v = u,

Now, using the Pythagoras theorem,

10² = v²+u²

v² + v² = 100

2v² = 100

v² = 50

v = 5√2

u = 5√2

Hence, the length of the two sides of the given right triangle is 5√2

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There are 180 different starting lineups that can be created for the college team.To find the number of different starting lineups that can be created for the college team, we need to use the combination formula.

The number of ways to choose k items from a set of n distinct items is given by the formula:

nCk = n! / (k! * (n-k)!)

where "!" denotes the factorial function, which means the product of all positive integers up to that number.

In this case, we want to choose 2 guards out of 5, 2 forwards out of 4, and 1 center out of 3. So the total number of different starting lineups that can be created is:

(5C2) * (4C2) * (3C1)

= (5! / (2! * 3!)) * (4! / (2! * 2!)) * (3! / (1! * 2!))

= (10) * (6) * (3)

= 180

Therefore, there are 180 different starting lineups that can be created for the college team.

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The trees will be the same height in 2 years and the height of these trees will be 22 ft.

A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+10. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=1 and b=10.

For solving the question you should convert the given text into an algebraic expression.

Tree01= 18+2*y

Tree02= 20.5+0.75*y (Note that  3/4=0.75)

y= number of years

Therefore,

18+2*y=20.5+0.75*y

2y-0.75*y=20.5-18

1.25y=2,5

y=2

Thus, at 2 years the trees will be the same height.

When y=2, you have:

Tree01= 18+2*y= 18+2*2=18+4=22

Tree02= 20.5+0.75*y =20.5+1.5=22

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The percent of change is the change in value in percent from 90 to 18 that is an 80% decrease.

To calculate the percent change from 90 to 18, we first need to find the difference between the two values:

Change = Final Value - Initial Value

Change = 18 - 90

Change = -72

The negative sign indicates that there has been a decrease in value.

To find the percent change, we can use the following formula:

Percent Change = (Change / Initial Value) x 100%

Percent Change = (-72 / 90) x 100%

Percent Change = -80%

So there is decrease in percent from 90 to 18 that is by 80%.

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540° is your answer!

Answer:

A = 648π cm²

Step-by-step explanation:

the area (A) of a semicircle is half the area of a circle , then

A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then

A = [tex]\frac{1}{2}[/tex] × π × 36² = [tex]\frac{1}{2}[/tex] × π × 1296 = 648π cm²

A Colorado blue spruce's first ten years have an average diameter of 0.62 inches.

Measure the diameter of the tree in its first ten years and divide it by 10 to determine the average diameter of a Colorado blue spruce in its first ten years. The outcome is the tree's average diameter during its first ten years. Measure the diameter of the tree in its first ten years and divide it by 10 to determine the average diameter of a Colorado blue spruce in its first ten years. The outcome is the tree's average diameter during its first ten years. For instance, if a Colorado blue spruce is five years old, you would calculate its diameter and multiply it by 10. You will then know the tree's typical diameter for the first ten years. Any age of Colorado blue spruce tree can use the same calculation. Depending on the age of the tree, a Colorado blue spruce's first ten years' average diameter will vary. The average diameter will be greater if the tree is older than ten years. The average diameter will be less, however, if the tree is less than 10 years old. In general, a Colorado blue spruce's first ten years have an average diameter of 0.62 inches.

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Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.

Therefore, factors which vary systematically with the given independent variable is called  confounds variables or extraneous variable.

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The equations that are true of the values x, y, and z are :

The line that x degrees and 65 degrees is on, is a straight line which means that they will both add up to 180 degrees :

x degrees + 65 degrees = 180 degrees

x and z are congruent angles which means they are both the same angle measure.

y would be equal to 65 degrees because, just like x and z, y and 65 degrees are congruent.

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Options include:

To solve a direct proportion problem with decimal numbers, you can follow the same steps as with whole numbers.

A direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable.

To solve a direct proportion problem with decimal numbers:

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By factorizing the polynomials, the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy) is 3.

HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

To obtain the HCF of algebraic expression, take the common of all the prime factors of two polynomials.

We first factorize the given algebraic expressions:

3(x - y)^2 = 3 × (x - y) × (x - y)

12x^2(x^2+y^2+2xy) = 12x^2(x + y)^2

12x^2(x + y)^2 = 2 × 2 × 3 × x × x ×  (x + y) × (x + y)

so, the highest common factor between the both expressions is 3.

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The solution to the given system of equation is (-2,7) and (2, -1).

A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.

The graph denotes the two equations in which one is line and another one is parabola.

These system equation has two solutions.

That is, the point where the curve and line intersect is the solution for the system.

In this graph, the line and the curve intersects at two points,

i.e., (-2,7) and (2, -1).

Hence, the solution to the given system of equation is (-2,7) and (2, -1).

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The area of the picture is 144 square inches.

The area is a measurement of the extent of a two-dimensional surface or region. It is expressed in square units, such as square inches, square meters, or square feet. The area of a shape is the amount of space it occupies in a plane or on a flat surface. The calculation of area depends on the shape of the object. For example, the area of a circle is calculated by using the formula A = πr², where r is the radius of the circle.

The area of a square with side length s is given by the formula A = s². If the side length of the picture is 12 inches, then we can substitute s = 12 into the formula to get:

A = s² = 12² = 144

Therefore, the area of the picture is 144 square inches.

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Answer:

the sum of 2rude 5 is 4.47-(answer)and the sum of 3 rude 7 is 7.79-(answer).

Hi there, here's your answer:

Given the question [tex]2\sqrt{5} + 3\sqrt{7}[/tex]

Since these two roots have no common factors, we can either leave the expression as it is, or simplify using the values of the roots.

In which case, [tex]\sqrt{5} = 2.236[/tex] and [tex]\sqrt{7} = 2.645[/tex]

On simplifying, we get

[tex]2\sqrt{5}[/tex] = 2 × 2.236 = 4.472

And

[tex]3\sqrt{7}[/tex] = 3 × 2.645 = 7.935

Thus, the sum will be 4.472 + 7.935 = 12.407

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The straight line distance from the front seat to the back is approximately 69.7 feet.

Straight line distance refers to the shortest distance between two points in a straight line, as opposed to the distance that would be traveled along a curved path or following the contours of the terrain.

Let the distance from the front row to the back row be x.

Then, we can use the tangent function to find the height difference between the front and back rows:

tan(12°) = (height difference) / x

Solving for the height difference:

height difference = x * tan(12°)

The problem tells us that the height difference is 15 feet, so we can set up an equation:

15 = x * tan(12°)

Solving for x:

x = 15 / tan(12°) ≈ 69.7 feet

Therefore, the straight line distance from the front seat to the back is approximately 69.7 feet.

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To construct a line segment that is half the length of segment AB, follow the steps below.

What is the intersection points of the circle?

The intersections of two circles determine a line known as the radical line. If three circles mutually intersect in a single point, their point of intersection is the intersection of their pairwise radical lines, known as the radical center.

Draw a straight line passing through points A and B.

Bisect the line segment AB at point C.

Draw a circle centered at point C with a radius equal to AC or BC.

The intersection points of the circle and the line passing through A and B will be points D and E.

The line segment DE will be half the length of segment AB.

Therefore, To construct a line segment that is half the length of segment AB, follow the steps above.

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Multiplying the total number of children by the fraction that like chocolate yields [tex]32(3/8)=12[/tex]

Answer:

Area A, is x times y

Step-by-step explanation:

To find the area you must multiply the light x width of a rectangle or square

um.... kauser is this u

The angle m∠B of the quadrilateral has a measure of 72°

The complete question is added as an attachment

For any quadrilateral, the sum of its four interior angles is equal to 360°,

Using the above as a guide, we have the following:

17x + 5 + 13x + 7 + 118° + 80° = 360°

Evaluate the like terms

So, we have

30x + 210° = 360°

Subtract 210° from both sides

30x = 150°

So, we have

x = 5

Given that

B = 13x + 7

We have

B = 13 * 5 + 7

Evaluate

B = 72

Therefore, the measure for the angle m∠B is 72°

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Answer:

55

Step-by-step explanation:

Since 1 rectangle is 10 and there are 5, that means the whole length is 50.

Which means with can set the equation equal to 50

[tex]x - 5 = 50[/tex]

Adding 5 gets us

[tex]x = 55[/tex]

Answer:

Tje answer is 36

Step-by-step explanation:

16-30=14

24+14=-36

The cost per student for the app is $3, and can be found by dividing the total cost of $96 by the number of students, 32, which equals $3 per student.

Let x be the cost of the almonds Sophia bought and y be the cost of the app per student. Then, we have the subsequent two equations:

x + $5 = $15

32y = $96

To find the cost of the app per student, we can solve for y in the second equation:

y = $96 / 32 = $3

So the app costs $3 per student.

To find the cost of the app per student, we need to find the total cost of the app and then divide it by the number of students. Mr. Boone spent $96 on the app for 32 students, so the cost per student would be $96 / 32 = $3. This means that each student paid $3 for the app.

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Answer:

Step-by-step explanation:

An expression to display a loss of 42 yards on the football field would be: -42 yards.

The negative sign in front of the number 42 indicates a loss or a decrease in the yards, which represents a loss of 42 yards on the football field.

The standard deviation of the data set is  0.7.

First, calculate the mean of the data set:

(mean) = (2+1+1+2+2+3)/6 = 11/6 ≈ 1.8

Next, calculate the deviation of each data point from the mean:

2 - 1.8 = 0.2

1 - 1.8 = -0.8

1 - 1.8 = -0.8

2 - 1.8 = 0.2

2 - 1.8 = 0.2

3 - 1.8 = 1.2

Now square each deviation:

0.2² = 0.04

(-0.8)² = 0.64

(-0.8)² = 0.64

0.2² = 0.04

0.2² = 0.04

1.2² = 1.44

The sum of the squared deviations is:

0.04 + 0.64 + 0.64 + 0.04 + 0.04 + 1.44 = 2.84

To find the variance, we divide by the number of data points:

variance = 2.84/6 ≈ 0.4733

Finally, take the square root of the variance to get the standard deviation:

standard deviation = √(0.4733) ≈ 0.69

Therefore, the standard deviation of the data set {2,1,1,2,2,3} is approximately 0.7 (rounded to the nearest tenth).

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The value of the equation 8x² - 8x + 2 -( 6x² - 10x + 4) is 2x² + 2x - 2.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that

two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The equation can be illustrated thus:

8x² - 8x + 2 -( 6x² - 10x + 4)

8x² - 8x + 2 - 6x² + 10x - 4

= 2x² + 2x - 2

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