Proba
Find the probability that a randomly
selected point within the circle falls in the
red-shaded square.
7
U
7
7
P = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter

The length of the side EF = 22.5 Units

The properties of the triangle are:

The sum of all the angles of a triangle (of all types) is equal to 180°.

The sum of the length of the two sides of a triangle is greater than the length of the third side.

In the same way, the difference between the two sides of a triangle is less than the length of the third side.

From the property of the similar triangle,

The ratio of the sides is always equal

So,

DE/EF = GH/EH

12/EF = 8/15

Cross multiply to get

(12*15)/8 = EF

180/ = 22.5

EF= 22.5 units

Therefore, the length of the EF is 22.5 Units.

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The roots of equation are 2 , -2, 3i, 1/5 and -5.

We have,

([tex]x^4[/tex] + 5x² -36)(2x² + 9x-5)=0

Now, factories each equation as

([tex]x^4[/tex] + 5x² -36)

= ([tex]x^4[/tex] + 9x² - 4x² -36)

= x²(x² + 9) - 4(x² + 9)

= (x² - 4)(x² + 9)

= (x-2)(x+2)(x²+9)

and, 2x² + 9x-5

= 2x² + 10x - x -5

= 2x(x+5)- (x+5)

= (2x -1)(x+5)

So, the factored form is (x-2)(x+2)(x²+9) (2x -1)(x+5)

and, the roots of equation are 2 , -2, 3i, 1/5 and -5.

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Answer:

  C)  a = b  ⇒  b = a

Step-by-step explanation:

You want to identify the statement that represents the symmetric property of equality.

If a = b and b = c, then a = c. This is the transitive property of equality.

If a = b, then ac = bc. This is the multiplication property of equality.

If a = b, then b = a. This is the symmetric property of equality.

a(b +c) = ab +ac. This is the distributive property of multiplication over addition.

The value of x in the heptagon is 38.6 degrees.

An heptagon is a polygon with 7 sides. A regular heptagon is an heptagon with all sides equal to each other.

Therefore,  sum of angles in an heptagon is equal to 900 degrees.

Let's find each angle of the heptagon.

each angle in the regular heptagon = 900 / 7

each angle in the regular heptagon = 128.57 degrees

Therefore, each angle of a square is 90 degrees.

Hence,

x = 128.57 - 90

x = 38.5714285714

Finally,

x = 38.6 degrees

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The ratio of apple oranges and bananas cannot be calculated with the given information

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

Fruits = Orange, Bananas and Apple

Total number of fruits = 48

The available parameters is not enough to determine the ratio

Assuming that we have

Banana = 10

Orange =  20

Apple = 18

Then the ratio would be:

Apple : oranges : bananas = 18 : 20 : 10

Simplify

Apple : oranges : bananas = 9 : 10 : 5

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The answer to the given energy is  5096327.2 J

Remember that Joule is a derived unit of energy which is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of its motion through a distance of one meter

m = 1 tonelada = 1000 kg

h = 500 m

v = 50 km / hr = 13.88 m / s

9 = 10 m / s²

Ep = ?

Ec = ?

The given formula Formula

Ep = m g h = 1000 kg X 10 m / s² X 500 m =  5000000 Joule

Ec = m V² / 2 = 1000 kg X (13.88 m / s)² / 2 = 96327.2 Joule

Et = Ep  +   Ec  =  5000000 J    +   96327.2 J = 5096327.2 J

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Answer:

55

70

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

55 and 70

Step-by-step explanation:

5÷2=2.5

20÷8=2.5

45÷18=2.5

so

22×2.5=55

and

28×2.5=70

The expected number of education majors in the sample is 20.

Since 80 out of 200 freshmen are education majors, the probability of randomly selecting an education major from the population is:

P(edu major) = 80/200 = 0.4

To find the expected number of education majors in a sample of 50 freshmen, we can use the formula for the expected value of a discrete random variable:

E(X) = n x p

Substituting the given values, we get:

E(X) = 50 x 0.4 = 20

Therefore, the expected number of education majors in a sample of 50 freshmen is 20.

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Based on the conditions, the correct statements are,

⇒  Bracelet B has 8 more letter beads than Bracelet A.

We have to given that;

Donovahn made two bracelets for a friend.

And, Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads.

Hence, We have;

Based on the information provided, we can say that Bracelet B contains more letter beads than Bracelet A.

Specifically, Bracelet B has 8 more letter beads than Bracelet A.

Thus, Based on the conditions, the correct statements are,

⇒  Bracelet B has 8 more letter beads than Bracelet A.

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Answer:

23 apple pies and 13 cherry pies were sold.

Step-by-step explanation:

Let's use the variables a and c to represent the number of apple and cherry pies sold, respectively.

From the problem, we know that:

The total number of pies sold is 36: a + c = 36

The total revenue from pie sales is $304.00: 7a + 11c = 304

We now have two equations with two unknowns. We can use substitution or elimination to solve for a and c. Here's one way to use substitution:

Solve the first equation for a: a = 36 - c

Substitute a = 36 - c into the second equation: 7(36 - c) + 11c = 304

Simplify: 252 - 7c + 11c = 304

Simplify further: 4c = 52

Solve for c: c = 13

Substitute c = 13 into the first equation to solve for a: a + 13 = 36

Simplify: a = 23

Therefore, 23 apple pies and 13 cherry pies were sold.

The statement that is not true is (c) The measure of ∠R is the same as ∠N.

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

Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)

This is a rigid transformation

And so, the side lengths and the corresponding angle measures are equal

However, angles R and N are not corresponding angles

So, the false statement is (c) The measure of ∠R is the same as ∠N.

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the y intercept of the linear function in the table is

A linear function is represented using the equation

y = mx + c

the parameters are defined as

y = out put values

m  = slope

x = input variable

c = y - intercept

Solving for slope using values in the table

m = (y2 - y1) / (x2 - x1)

m = (10 - 13) / (4 - 5)

m = -3 / -1

m = 3

Using point slope formula

y - y1 = m(x - x1)

y - 13 = 3(x - 5)

y = 3x - 15 + 13

y = 3x - 2

hence the y intercept is -2

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On solving the "equation" written as "5x² - 8x + 12 = 3x + 10" by using "factoring-method" , the "solutions" are x = 1/5 and x = 2.

To solve "5x² - 8x + 12 = 3x + 10" by using the "factoring-method", it should first be rearranged in "standard-form", where one side of the equation is = 0,

First, we combine the constant terms on the right side of the quadratic:

⇒ 5x² - 8x + 2 = 3x,

⇒ 5x² - 11x + 2 = 0,  Now, we factor the quadratic expression on the left side of the equation as :

⇒ 5x² - 10x -x + 2 = 0,

⇒ 5x(x - 2) -1(x - 2) = 0,

⇒ (5x - 1)×(x - 2) = 0

By applying the zero product property, we know that either "5x - 1 = 0" or "x - 2 = 0";

⇒ 5x - 1 = 0 , We get x = 1/5,

⇒ x - 2 = 0, We get x = 2;

Therefore, the solution are x = 2, and x = 1/5.

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The given question is incomplete, the complete question is

Solve the quadratic-equation "5x² - 8x + 12 = 3x + 10" by factoring.

Answer:

Step-by-step explanation:

To create a magic square with -6,-5,-4,-3,-2,-1,1,2, we need to arrange these numbers in a 3x3 grid such that each row, column, and diagonal add up to the same sum.

Here's one possible solution:

diff

Copy code

-6 1 2

-4 -5 9

8 -3 -2

To check if this is a magic square, we can calculate the sum of each row, column, and diagonal:

Rows:

(-6 + 1 + 2) = -3

(-4 - 5 + 9) = 0

(8 - 3 - 2) = 3

Columns:

(-6 - 4 + 8) = -2

(1 - 5 - 3) = -7

(2 + 9 - 2) = 9

Diagonals:

(-6 - 5 - 2) = -13

(2 - 5 + 8) = 5

All of these sums are equal to 0, so this is indeed a magic square.

According to the information, the least number of committees that need to be formed to meet all of the conditions is 8.

To minimize the number of committees, we can try to use each student in as many committees as possible. Since each student must be in exactly 2 committees, and there are 12 students, we need a total of 24 "student committee slots".

Now we need to figure out how to assign the students to committees so that no two committees have more than one student in common. One way to do this is to use a "round-robin" approach:

Assign the first student to committees 1, 2, and 3.

For the next student, assign them to committees 1, 4, and 5.

For the third student, assign them to committees 2, 4, and 6.

Continue in this way, cycling through the remaining students and assigning them to three committees at a time, making sure to avoid any duplicates.

After assigning all 12 students to committees in this way, we will have a total of 8 committees. We can check that each committee contains exactly 3 students, and that no two committees have more than one student in common.

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When 6 is divided by 1/2 the result is 12 because the expression to multiply by the reciprocal is 6 × 2.

The reciprocal of a number is the multiplicative inverse of that number. In other words, if you multiply a number by its reciprocal, the result is always 1.

In division by a fraction, the reciprocal of that fraction is the fraction that you multiply by to obtain the quotient hence for 6 divided by 1/2 the expression becomes;

6 ÷ 1/2 = 6 × 2/1

6 ÷ 1/2 = 12.

Therefore, when 6 is divided by 1/2 the result is 12 because the expression to multiply by the reciprocal is 6 × 2.

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The profession that would earn that amount more than a bank teller is Office Clerk.

The profession that would earn $1,151,700 in 30 years is Bookkeeper.

The profession that will earn  $828,600 over a 20-year career is Truck Driver.

The profession that earns $136,200 more than a fire fighter over a period of 30 years is Electrician

The 15 year difference between bank teller and office clerk is:

= ( 30, 850 x 15 ) - ( 27, 260 x 15 )

= $ 53, 850

The earnings of a Bookkeeper in 30 years is:

= 38, 390 x 30

= $ 1, 151, 700

The earnings of a Truck driver in 20 years is :

= 41, 430 x 20

= $ 828, 600

The difference between earnings of Fire fighter and Electrician over 30 years is:

= ( 52, 570 x 30 ) - ( 48, 030 x 30 )

= $ 136, 200

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Answer:

x = 8

Step-by-step explanation:

[tex]5|x-8|+2=2 \\ −5∣x−8∣=0 \\ ∣x−8∣=0 \\ x = 8[/tex]

First, you need to cancel out the 2 by subtracting 2 from both sides. Then, we divide both sides by -5. And finally, we remove the absolute value.

The perimeter of the parallelogram is 90 ft while it's area is calculated to be 900 square feet.

The sum of the boundary length of the parallelogram is it's perimeter so;

perimeter of the parallelogram = 15ft + 15ft + 30ft + 30ft

perimeter of the parallelogram = 90 ft

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

height of the parallelogram = 30ft × tan 45°

height of the parallelogram = 30ft {recall tan 45° = 1}

area of the parallelogram = 30ft × 30ft

area of the parallelogram = 900 ft²

Therefore, the perimeter of the parallelogram is 90 ft while it's area is calculated to be 900 square feet.

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By translation, the image of the vertices of the figure A'B'C' are A''(x, y) = (1, - 3), B''(x, y) = (- 2, - 1) and C''(x, y) = (- 3, - 5), respectively.

In this problem we must determine the image of the figure A'B'C', whose vertices are A'(x, y) = (4, - 1), B'(x, y) = (1, 1), C'(x, y) = (0, - 3), by translation, whose definition is shown below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that T(x, y) = (- 3, - 2), then the image of the vertices of the figure A'B'C' are:

A''(x, y) = (4, - 1) + (- 3, - 2)

A''(x, y) = (1, - 3)

B''(x, y) = (1, 1) + (- 3, - 2)

B''(x, y) = (- 2, - 1)

C''(x, y) = (0, - 3) + (- 3, - 2)

C''(x, y) = (- 3, - 5)

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(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Applying the inscribed angle theorem, the measure of angle STU in the circle is: 29°.

When an inscribed angle intercepts an arc in a circle, the measure of the inscribed angle is always half of the measure of the arc it intercepts, based on the inscribed angle theorem.

Angle STU is an inscribed angle that intercepts arc SU in the given circle, therefore:

(5x - 16) = 1/2(12x - 50)

Solve for x:

2(5x - 16) = 12x - 50

10x - 32 = 12x - 50

10x - 12x = 32 - 50

-2x = -18

x = 9

m∡STU = (5x - 16) = 5(9) - 16

m∡STU = 29°

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There are a total of 4 + 3 + 2 + 1 = 10 marbles in the bag. The probability of picking a red marble is the number of red marbles divided by the total number of marbles:

Probability of picking a red marble = 4/10 = 2/5

Therefore, the probability Aisha picks a red marble is 2/5 or 0.4 when written as a decimal.

Answer:

8 ft

Step-by-step explanation:

Area of a triangle=1/2*base*height

You know the area of the triangle and the height, so you can set up an expression to solve for the base

48=1/2*base*12

4=1/2*base

base=8ft

Check: A=1/2*8*12, A=48 ft²

The measure of angle TDC in the triangle is 32 degrees.

The tangent CD forms a right angle with the radius CT of the circle. This forms a right angle triangle.

Therefore, the sum of angles in the triangle is 180 degrees.

Hence,

∠C = 90 degrees

Therefore,

3x + 14 + 8x + 10 + 90 = 180

11x + 114 = 180

11x = 180 - 114

11x = 66

divide both sides by 11

x = 66 / 11

x = 6

Therefore,

∠TDC = 3x + 14 = 3(6) + 14 = 18 + 14 = 32 degrees.

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The amount of money is 4000 was invested at 3%.

Let x be the amount of money invested at 3%.

Then, the amount of money invested at 5% is 6000 - x.

The interest earned on the amount invested at 3% is 0.03x.

The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.

The total interest earned is given as $220.

So, we can write the equation:

0.03x + (300 - 0.05x) = 220

Simplifying and solving for x, we get:

0.03x + 300 - 0.05x = 220

-0.02x + 300 = 220

-0.02x = -80

x = 4000

Therefore, $4000 was invested at 3%.

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Answer:

  34.8°

Step-by-step explanation:

You want the angle opposite a side of length 8 cm in a right triangle with hypotenuse 14 cm.

The sine relation is the one of interest in this geometry:

  Sin = Opposite/Hypotenuse

  sin(x°) = (8 cm)/(14 cm)

The angle can be found using the inverse sine function:

  x° = arcsin(8/14) ≈ 34.8°

The size of the angle x° is 34.8°.

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The y-intercept for the function g(x) is 4.

The y-intercept of a function is a point where the line crosses the y-axis. The linear function can be given as below.

f(x) = mx+n

Where m is the slope of the line and n is a real number and y-intercept of the line.

The given function is f(x)=-4x—2.

The function is vertically translated 6 units up to g(x).

The y-intercept of the function f(x) is -2. Then the y-intercept for the function g(x) can be given as below.

y-intercept g(x) = -2+6

y-intercept g(x) = 4

Hence,  the y-intercept for the function g(x) is 4.

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