Work out the first seven digits after the
decimal point when 0.50 is written out in
full.
0.50 = 0.

The reasoning for the third step of the proof is the SAS Triangle Congruence Theorem, which establishes the congruence of the two triangles involved.

In the given proof, we are trying to prove that AC is equal to ED in a rectangle ABCD. The reasoning for the third step of the proof can be explained as follows:

Statement 3: ZBAD = ZCDA

Reason: SAS Triangle Congruence Theorem

Explanation: The SAS (Side-Angle-Side) Triangle Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

In this case, we are considering triangles ZBA and ZDA. We know that AB is congruent to AD (statement 2, "AB & CD") and that the angles ZBA and ZDA are right angles since ABCD is a rectangle (statement 1, "Quadrilateral ABCD is a rectangle").

Therefore, by the SAS Triangle Congruence Theorem, we can conclude that triangle ZBA is congruent to triangle ZDA. And since corresponding parts of congruent triangles are congruent (CPCTC), we can say that angle ZBAD is congruent to angle ZCDA.

For more such questions on congruent

https://brainly.com/question/3999145

#SPJ8

Answer:

Step-by-step explanation:

Range: what the numbers range from the smallest to largest.   Subtract the largest number and smallest.

Range =  9 - 1

Range = 8

Median:  Middle number.  If you listed numbers in order from smallest to largest, it is the middle number

Median = 5

Answer:

To calculate the total dividends received over 6 years, we can use the formula:

Total dividends = Annual dividend per share x Number of shares x Number of years

In this case, the annual dividend per share is $0.29, the number of shares is 125, and the number of years is 6.

Total dividends = $0.29 x 125 x 6 = $217.50

Therefore, the answer is (B) $217.50.

Step-by-step explanation:

Answer:

y = 4.71 and y = -8.71

Step-by-step explanation:

Step 1:  Subtract 5 from both sides:

((y + 2)^2 + 5 = 50) - 5

(y + 2)^2 = 45

Step 2:  Take the square root of both sides, subtract 2 from both sides, and round to the nearest hundredth to solve for y.  

Positive answer:

√(y + 2)^2 = √45

(y + 2 = √45) - 2

y = √45 - 2

y = 4.708203932

y = 4.71

Thus, one answer for y (rounded to the nearest hundredth) is approximately 4.71.

Negative answer:

√(y + 2)^2 = -√45

(y + 2 = -√45) - 2

y = -√45 - 2

y = -8.708203932

y ≈ - 8.71

Thus, the other answer for y (rounded to the nearest hundredth) approximately. -8.71

Optional Step 3:  We can check our work by plugging in 4.71 and -8.71 for y and seeing whether we get 50.  Because they're rounded, you won't get exactly 50, but the answer should be close enough for us to trust our approximations:

Plugging in 4.71 for y:

(4.71 + 2)^2 + 5 = 50

(6.71)^2 + 5 = 50

45.0241 + 5 = 50

50.0241 > 50

Our answer is close enough to 50 that we can trust our approximation.

Plugging in -8.71 for y:

(-8.71 + 2)^2 + 5 = 50

(-6.71)^2 + 5 = 50

45.0241 + 5 = 50

50.0241 > 50

Again, our answer is close enough to 50 that we can trust our approximation.

The coordinates of the vertices after a dilation with a scale factor of 1/3 considered at the origin include:

Q' (-3, -3).

R' (1, -3).

S' (3, 3).

T' (-1, 3).

In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.

In this scenario and exercise, we would dilate the coordinates of the vertices by applying a scale factor of 1/3 that is centered at the origin as follows:

Coordinate Q (-9, -9) → Q' (-9 × 1/3, -9 × 1/3) = Coordinate Q' (-3, -3).

Coordinate R (3, -9) → R' (3 × 1/3, -9 × 1/3) = Coordinate R' (1, -3).

Coordinate S (9, 9) → S' (9 × 1/3, 9 × 1/3) = Coordinate S' (3, 3).

Coordinate T (-3, 9) → T' (-3 × 1/3, 9 × 1/3) = Coordinate T' (-1, 3).

Read more on dilation and scale factor here: brainly.com/question/4421026

#SPJ1

Sure! Here are the solutions for the long division problems:

3 561 ÷ 7 = 509

2 308 ÷ 4 = 577

8 288 ÷ 9 = 920

7 616 ÷ 8 = 952

5 365 ÷ 5 = 1 073

9 990 ÷ 3 = 3 330

6 294 ÷ 7 = 899

6 180 ÷ 6 = 1 030

5 205 ÷ 9 = 578

Please note that the results are rounded down to the nearest whole number since you specified "no remainder" in the problem statement.

Answer:

The unit price is $.25 per ounce.

Step-by-step explanation:

To find the unit price per ounce, take the total cost and divide by the number of ounces

12 dollars/ 48 ounces

.25

The unit price is $.25 per ounce.

Answer:

The area of a parallelogram is given by the formula:

Area = base * height

We are given that the area is 36 square meters and the height is 4 meters. Substituting these values into the formula, we get:

36 = base * 4

36 / 4 = base

9 = base

Therefore, the length of the base is 9 meters.

Answer: No

To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.

If the equation is true, then the ordered pair is a solution to the equation.

If we put (-5,6) into y=-7, we get 6=-7, which is not true.

So, (-5,6) is not a solution to the equation y=-7.

Answer:

2y² + 3

Step-by-step explanation:

width of one side is 4y² - y + 6.

two equal sides of rectangle = 2(4y² - y +6) = 8y² - 2y + 12.

perimeter = 2 lengths + 2 widths

12y² - 2y + 18 = 2 lengths + 8y² - 2y + 12

2 lengths = (12y² - 2y + 18) - (8y² - 2y + 12)

= 4y² +6

length = 1/2 (4y² +6)

= 2y² + 3

Answer:

a. 2

Step-by-step explanation:

We Know

Side AB = 7

Side XY = 14

7 → 14, we time 2. So, the scale factor is 2.

Using the function f(x) = 1/2 x and the inverse of the function f⁻¹(x) = 2x, the solutions of the given are :

f(2) = 1, f⁻¹(1) = 2, f⁻¹(f(2)) = 2

f⁻¹(-2) = -4, f(-4) = -2, f(f⁻¹(-2)) = -2

Given a function,

f(x) = 1/2 x

And an inverse function,

f⁻¹(x) = 2x

We have to find the values of the following.

f(2) = 1/2 × 2 = 1

f⁻¹(1) = 2 × 1 = 2

f⁻¹(f(2)) = f⁻¹(1) = 2 × 1 = 2

f⁻¹(-2) = 2 × -2 = -4

f(-4) = 1/2 × 4 = -2

f(f⁻¹(-2)) = f (-4) = 1/2 × 4 = -2

So, in general, f⁻¹(f(x)) = f(f⁻¹(x))

Learn more about Inverse Functions here :

https://brainly.com/question/29141206

#SPJ1

Answer:

Step-by-step explanation:

Ukraine wants to join the european union.Due to this Russia realize that if ukraine join the european union then if war started between Ukraine and any other country like Russia it means Ukraine and european union both attack on this country.

Answer:

B and C

Step-by-step explanation:

Answer:  B and C

Step-by-step explanation:

Pythagorean Theorem:

c²=a²+b²              >where a and be are the shorter legs and c is the

                                longer/hypotenuse

Let's plug each into the pythagorean theorem

A)   Not a right triangle

33² = 5² + (√8)²

1089 = 25 +8

1089 = 33             >Not equal,  The statement is not true, so this is not a

                                 right triangle.

B)  Yes, it is a right triangle

17²=8²+15²

289=64+225

289=289       They are equal, true statement, so yes it is a right triangle

C) No, it is not a right triangle

2² = (√2)²+(√2)²

4 = 2+2

4=4              They are equal, true statement, so yes it is a right triangle

Whitney needs 5/4 cup of sugar in total to bake all the brownies.

To calculate the total amount of sugar needed to bake all the brownies, we need to add the quantities of sugar required for each type of brownie.

According to the information given, one type of brownie requires 1/2 cup of sugar and the other type requires 3/4 cup of sugar.

To find the total amount of sugar needed, we add these two quantities:

1/2 cup + 3/4 cup

To add fractions, we need to have a common denominator.

The common denominator is 4:

(1/2) x (2/2) cup + (3/4) x (4/4) cup

This simplifies to:

2/4 cup + 12/16 cup

Now, we can add the fractions:

(2/4) cup + (12/16) cup = (4/8) cup + (12/16) cup

Next, we find a common denominator, which is 16:

(4/8) x (2/2) cup + (12/16) x (1/1) cup

This simplifies to:

8/16 cup + 12/16 cup

Finally, we add the fractions:

8/16 cup + 12/16 cup = 20/16 cup

Since 20/16 is an improper fraction, we can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(20/4)/(16/4) cup = 5/4 cup

For similar questions on Whitney

https://brainly.com/question/21939808

#SPJ11

To find the probability that two distinct numbers chosen randomly from the set {-2, -6/5, -1/3, 0, 1/2, 5/6, 3} will be the slopes of two perpendicular lines, we need to determine the total number of possible pairs of distinct numbers and the number of pairs that result in perpendicular slopes.

Total number of possible pairs:

Since we are choosing two distinct numbers from a set of seven, the total number of possible pairs is given by the combination formula:

C(7, 2) = 7! / (2!(7 - 2)!) = 7! / (2! * 5!) = 21

Pairs resulting in perpendicular slopes:

For two lines to be perpendicular, the product of their slopes must be -1. So, we need to count the number of pairs whose product is -1.

The set contains two negative numbers {-2, -6/5} and one positive number {3}. None of these numbers have a reciprocal within the set that gives a product of -1. Therefore, no pairs can be formed from these numbers that result in perpendicular slopes.

Hence, the number of pairs resulting in perpendicular slopes is 0.

Therefore, the probability of randomly choosing two distinct numbers from the set {-2, -6/5, -1/3, 0, 1/2, 5/6, 3} that will be the slopes of two perpendicular lines is 0/21, which simplifies to 0.

The repetitions that result in no magenta marbles will be 62.5.

The expected value is the predicted average outcome of a random variable, calculated by multiplying each outcome by its probability.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The number of magenta turquoise and black marbles is equal. Thus, the probability will be equal. Then the probability of not selecting a magenta marble is calculated as,

P = (1/2) x (1/2)

P = 1/4

The expected value is calculated as,

E = 1/4 x 250

E = 62.5

More about the expected value link is given below.

https://brainly.com/question/13945225

#SPJ1

The result obtained by adding the three digits is 17.

Let's denote the three-digit number as XYZ, where X, Y, and Z represent the individual digits.

Given that the product of the three digits is 135, we have the equation

X × Y × Z = 135.

To find the result obtained by adding the three digits (X + Y + Z), we need to determine the individual values of X, Y, and Z that satisfy the given equation.

We can start by listing all possible combinations of three digits that multiply to 135:

1 × 3 × 45

1 × 5 × 27

1 × 9 × 15

3 × 5 × 9

Out of these combinations, we can observe that the sum of the digits in each combination is:

1 + 3 + 45 = 49

1 + 5 + 27 = 33

1 + 9 + 15 = 25

3 + 5 + 9 = 17

Therefore, the result obtained by adding the three digits is 17.

In conclusion, by adding the three digits of the three-digit number, we get the result of 17.

for such more question on three-digit numbers

https://brainly.com/question/20118982

#SPJ11

Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.

The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.

The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.

Step-by-step explanation:

Therefore, the expected value can be calculated as follows:

(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)

= $0.073

The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.

Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.

References:

Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.

"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.

To simplify the given expression: 4x + 8 + (6x - 7) - (8x + 9), we can follow the order of operations (parentheses, exponents, multiplication and division, and addition and subtraction) to simplify it step by step.

First, let's simplify the expression inside the parentheses:

6x - 7 becomes 6x - 7

8x + 9 becomes 8x + 9

Now, let's simplify the entire expression:

4x + 8 + 6x - 7 - 8x - 9

Combining like terms:

(4x + 6x - 8x) + (8 - 7 - 9)

2x - 8

Therefore, the simplified form of the expression 4x + 8 + (6x - 7) - (8x + 9) is 2x - 8.

The area of the base of the cylinder is A = 16π units²

Given data ,

Let the area of the base of the cylinder be A

Now , the radius of the cylinder is r = 4 units

And , the height of the cylinder is h = 6 units

where A = πr²

The base of the cylinder is a circular disk of radius r units

On simplifying , we get

A = π ( 4 )²

A = 16π units²

So , the value of A is 16π units²

Hence , the area of the base is A = 16π units²

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ1

The Simplified form of the expression (x+2)(x-2) - (x+3)² is -13 - 6x.

The expression (x+2)(x-2) - (x+3)², we'll follow the distributive property and simplify each term.

First, let's expand (x+2)(x-2):

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

          = x² - 2x + 2x - 4

          = x² - 4

Next, let's expand (x+3)²:

(x+3)² = (x+3)(x+3)

      = x(x) + x(3) + 3(x) + 3(3)

      = x² + 3x + 3x + 9

      = x² + 6x + 9

Now, we can substitute these expansions into the original expression:

(x+2)(x-2) - (x+3)² = (x² - 4) - (x² + 6x + 9)

To simplify further, let's distribute the negative sign to every term inside the parentheses:

(x² - 4) - (x² + 6x + 9) = x² - 4 - x² - 6x - 9

Now, we can combine like terms:

(x² - x²) + (-4 - 9) - 6x = -13 - 6x

Therefore, the simplified form of the expression (x+2)(x-2) - (x+3)² is -13 - 6x.

To know more about Simplified form.

https://brainly.com/question/29029030

#SPJ11

(3,1)

Ordered pairs are always ordered as (x,y).  Point B has an x-value of 3 and a y-value of 1.

Step-by-step explanation:

y = 1/3 x +4  

       is the equation of a line in the form  

                 y = mx+b      where m =slope   and    b = the y-axis intercept

                           so  m = slope = 1/3   for this line

Answer:

[tex]\huge\boxed{\sf Slope = 1/3}[/tex]

Step-by-step explanation:

[tex]\displaystyle y=\frac{1}{3} x + 4[/tex]

y = mx + c

Where m is slope and c is y-intercept.

So,

By comparing both the equations, we get:

m = 1/3

[tex]\rule[225]{225}{2}[/tex]

The steps to create a bar graph are explained below.

To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.

Here is how we can match the two-way table to the segmented bar graph:

By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.

Learn more about graphs here:

https://brainly.com/question/17267403

#SPJ1

To determine the best model for fitting the given data, we can analyze the trend and pattern in the population values over time. One common approach is to perform linear regression to find the equation of the line that best represents the data.

To find the regression equation, we'll use the given data points (t, P) as follows:

t: 0, 1, 2, 3, 4

P: 22.8, 25, 26.5, 27.1, 27.8

Using a calculator or statistical software, we can perform linear regression to find the equation of the line that best fits the data. The equation will have the form:

P = mt + b

where m represents the slope of the line and b represents the y-intercept.

Performing the regression calculation, we find that the equation of the line that best fits the data is approximately:

P = 1.155t + 22.625

To determine the year when the population will be less than 24,000, we can substitute P = 24 into the equation and solve for t:

24 = 1.155t + 22.625

1.155t = 24 - 22.625

1.155t = 1.375

t ≈ 1.19

Rounding to the nearest whole number, we find that the year when the population will be less than 24,000 is 1 (1997).

To find the population in 2008, we substitute t = 12 into the equation:

P = 1.155(12) + 22.625

P ≈ 36.18

Rounding to the nearest whole number, the estimated population in 2008 is 36,000.

In summary:

6) The linear regression equation that best fits the data is P = 1.155t + 22.625.

The population will be less than 24,000 in the year 1997.

The estimated population in 2008 is 36,000.

<33

I apologize, but it seems that the table and graph you mentioned did not come through in your message. Could you please provide the table and graph or describe the information in more detail? That way, I can assist you with your question.