Determine if there enough information to prove that each pair of triangles is congruent by SSS,SAS, or ASA. write the congruence statements represented by the markers in each diagram.ΔPRT ≅ ΔTVP

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Die:

$9 ===> 6

$3 ===> 5

$1 ===> 4

expected winnings = ?

Step 02:

Expected winnings

probability (6) = favorable outcomes / total outcomes

= 1/6

probability (5) = 1/6

probability (4) = 1/6

E (die winnings) = $13 / 6 = $2.17

The answer is:

The expected winnings are $2.17

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2



:11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)



:3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

Okay, here we have this:

Considering the provided confidence interval, we are going to express it in interval form, so we obtain the following:

So we will first convert the given confidence interval from percent to decimal:

Confidence interval=50.8% ± 6.2%

Confidence interval=50.8/100 ± 6.2/100

Confidence interval=0.508 ± 0.062

Now let's convert it to interval form, where the smaller endpoint will be the result of taking the minus operation, and the larger endpoint will be the result of taking the plus operation:

Confidence interval= (0.508 - 0.062, 0.508 + 0.062)

Confidence interval= (0.446, 0.57)

Finally we obtain that the confidence interval in interval form is (0.446, 0.57).

the distance between two points is found:

answer: distance = 12.8

Answer:

Decimal Fraction.

Explanation:

If we have 25%, we can write it as:

A percent can also be written as a Decimal Fraction.

1. Possible inputs:

The values of the dice. Can be 1,2,3,4,5,6

2. Outputs

Values in which you don't move on the map. 2,5,6,11,14,15...

On the others, there will be a move operation. So you will have to move until you fall on a dot in which there is no move command.

Given:

Sales in 2013 = 36.44 billions of dollars

Sales in 2019 = 38.16 billions of dollars

(a) Change of annual sales between 2013 and 2019

The change of annual sales between 2013 and 2019 is the difference between the annual sales in 2019 and the annual sales in 2013:

Substituting the given values:

Hence, the change of annual sales is 1.72 billions dollars

(b) The average rate of change in sales for the 2019 year begining in 2013:

The average rate of change can be calculated using the formula:

Hence, the average rate of change in sales for the 2019 year begining in 2013 is 0.287 billion dollars per year

Solution:

Speed, s, can be calculated using the formula;

Thus;

ANSWER: Her speed is 25 miles per hour.

sweater: $43

sale 20% off

final price ?

the final price is 34.4

Total cost T of bikes production

5x^2 - 15x = 0

then

5x^2 = 15x

divide by 5

x^2 = 3x

now divide by x, -x

x = 3, -3

Then answer is

OPTION D) 3, -3

Answer:

A, D, and E.

Explanation:

Definitions:

• Two angles are said to be ,supplementary, if they ,add up to 180 degrees.

• Two angles are said to be ,congruent if their measures are equal.

•

If lines m and n are parallel lines, the following statements are true:

0. 1 and 2 are supplementary angles

1. 4 and 6 are consecutive interior angles

2. 5 and 8 are congruent angles

The given information is:

- A washer and a dryer cost $731 combined.

- The washer costs $81 more than the dryer.

We need to find the cost of the dryer.

We can call the cost of the washer x and the cost of the dryer y, then:

And also:

Replace equation 2 into equation 1 and solve for y:

As we said y is the cost of the dryer, then the dryer costs $325.

The given figure is form by a semi circle and a rectangle

In the given figure, the diamter of the semi circle is 7 ft, Radius = 3.5 cm

The general expression for the perimeter of the circle is :

then for the semi circle :

Substitute the value of r = 3.5 cm

Now, for the rectangle

The perimeter of rectangle = 2(Length + Breadth)

In the given figure, we have Length = 14 ft and breadth = 7ft

We have the following system of equations:

To see if (5,4) is a solution, we must substitute x=5 or y=4 into the two equations:

Therefore (5,4) is NOT a solution to this system of linear equations.

We have that we can represent the total sales with the following expression:

Now, we have that the sales person earns 5% comission on the first $5000, this is equivalent to:

then, if the salesperson earns $1375 in comissions, we have the following equations:

we have that the sales with 7.5% comissions got the salesperson $1125, then, we have the following:

therefore, the salesperson had 15000+5000=$20000 in sales to earn $1375 in comissions

Notice that both graphs have the same shape, but the blue curve is the red one after a translation to the right.

In general, given a function h(x), a translation in the x-axis direction is given by the formula

In our case, notice that the vertex of the parabola (0,0) transforms into (5,0)

Then,

The answer is g(x)=(x-5)^2

Here we have the expression:

We want to find its value when x = -2 and y = 5. For this, we could replace the value of each variable:

Remember that:

Replacing these values:

Which is the same that:

So the correct option is A.

Explanation:

First, we need to graph the equality y = x² + 2x - 3

So, to graph the parabola, we need to identify the vertex and 2 points in the parabola.

The vertex can be calculated as:

Where b is the number beside the x and a is the number beside the x². Then the value of y is equal to:

So, the vertex (- 1, - 4)

Then, to find 2 points in the parabola we can replace x by 0 and x by -2 as:

For x = 0

For x = -2

Therefore, we have the vertex (-1, -4) and the points (0, -3) and (-2, -3)

Then, the inequality is y less or equal than the parabola so, the zone for the inequality is:

So, the graph of the inequality is the region below the graph of the parabola.

Answer:

5.625 miles per hour

Explanation:

The distance that can be covered by Jason = 23 3/4 miles

The time that is taken to cover the distance = 2/3 of an hour

Therefore:

His speed in miles per hour is 35.625 miles per hour.

Since the dice is a fair one we know that we have the same probability for each side to come up. That means that each number has a probability of 1/15 to appear.

Now we need to find the probability of finding a number that is divisible by 5. The numbers in the dice are 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. The numbers that are divisible by 5 are 5,10 and 15. Then the probability we are looking for is the sum of each probability, then we have:

Therefore the probability is 0.2.

There are 52 cards in a standard deck, from which there are 4 aces and 4 tens.

The probability of picking a ten or an ace in the first turn, is:

Either if a ten or an ace is taken out of the deck, there is a probability of 4/51 of picking the missing card. Then, the probability of picking a ten and an ace is:

Answer

The absolute difference between the sum of the multiples of two from 1 and 100, inclusive, and the sum of the multiples of three from 1 and 100, inclusive = 867

Explanation

To solve this, we need to first find the sum of multiples of 2 from 1 to 100 inclusive and find the sum of multiples of 3 from 1 to 100 inclusive. These set of numbers, form an arithmetic progression because all the terms have the same common difference

To do that, we need to note that the sum of an arithmetic progression is given as

a = First term

n = number of terms

d = common difference

For the multiples of 2

a = 2

n = 50

d = 2

For the multiples of 3

a = 3

n = 33

d = 3

So,

The absolute difference = |(Sum of multiples of two from 1 to 100 incusive) - (Sum of multiples of three from 1 to 100 incusive)

= |2550 - 1683|

= 867

Hope this Helps!!!

First we have to find how much is the 120% of a dollar so we can made a rue of 3

and the equation will be:

So to have 1.20 dollars we can have:

option 1: 1 coin of 1 dollar and two dimes

option 2: 1 coin of a dollar and 4 coins of 5 cents.

We are asked to write the equation for the circle in standard form based on the information below.

center = (-4, 1)

radius = 3

Recall that the equation of the circle in standard form is given by

Where (h, k) are the coordinates of the center and r is the radius.

Substituting the coordinates of the center and value of the radius we get

Therefore, the equation of the given circle is

An arithmetic sequence has a common difference.

Let's try if the given sequence has a common difference.

From the problem, we have :

The differences are :

Since the differences are the same, the sequence is arithmetic.

The answer is Arithmetic Sequence

In order to find the solution of this system of inequations, let's isolate the variable x in each inequation:

We have that x > -9 and x < 9, so the solution is the interval -9 < x < 9.

Other notations for this answer are:

To find the total time that Mary will spend correcting the tests,we have to multiply 27 by 1/9 using the general rule for the product of fractions:

then, in this case we have the following:

therefore, Mary will spend 3 hours correcting the 27 tests