What is the value of the underlined digit 5,678.321

Answer: Segment BC of image is parallel to  segment AD of image.

Step-by-step explanation:

Given: Quadrilateral ABCD is the result of a translation of quadrilateral EFGH.

Segment EF is parallel to segment HG in the pre-image.

Since translation is a rigid transformation which preserves the side-lengths and angles of the original figures.

Therefore, all the segments of the image figure are parallel to correspondent segments of the original figure.

Segment AD of image is parallel to segment HG  in the pre-image.

Segment BC of image is parallel to  segment  EF in the pre-image.

Hence, if Segment EF is parallel to segment HG in the pre-image.

⇒ Segment BC of image is parallel to segment AD in image.

To solve for the sum of the lengths of the legs of the larger triangle, we need to know the sum of the legs of the smaller triangle and multiply it by the scaling factor, which is 5. However, we can't find this sum with the given information because we don't have individual leg lengths of the smaller triangle.

To find the sum of the lengths of the legs of the larger triangle, we first need to establish the scale factor between the two similar triangles based on their areas. The area of a triangle scales with the square of the length of its sides. Given that one triangle has an area of 6 square inches and the other has an area of 150 square inches, the scale factor in area is given by the square root of the ratio of the larger area to the smaller area, which is √(150/6), which simplifies to 5. Therefore, if the hypotenuse of the smaller triangle is 5 inches, the hypotenuse of the larger triangle will be 5 times larger, that is 5 * 5 = 25 inches.

Given that the triangles are similar, all corresponding lengths scale by the factor of 5. If we denote the length of the legs of the smaller triangle as a and b, and the legs of the larger triangle as A and B, then A = 5a and B = 5b. Although we don't know the exact lengths of a and b, we can use the Pythagorean Theorem which states that the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b). For the smaller triangle, we have c² = a² + b². But since we only know c (which is 5 inches for the smaller triangle), we cannot directly find the individual lengths of a and b.

Since the question asks for the sum of the legs of the larger triangle (A+B), we only need to find the sum of the legs of the smaller triangle (a+b) and scale it up by the same factor. If a and b were known, we would do (a+b)*5 to get the sum for the larger triangle. However, without those individual lengths, we cannot find the sum based on the given information. To solve this problem, additional information about the lengths of the legs of the smaller triangle would be needed.

The quotient of the expression [tex]\(\frac{a-3}{7} \div \frac{3-a}{21}\)[/tex] is -3.

To find the quotient of the expression [tex]\(\frac{a-3}{7} \div \frac{3-a}{21}\)[/tex], we follow the rules of division for fractions, which involves multiplying the first fraction by the reciprocal of the second fraction.

The expression can be rewritten as:

[tex]\[\frac{a-3}{7} \times \frac{21}{3-a}\][/tex]

Now, we can simplify the expression by canceling out common factors. Notice that [tex]\(a-3\)[/tex] and [tex]\(3-a\)[/tex] are negatives of each other, and [tex]\(7\)[/tex] is a factor of [tex]\(21\)[/tex].

First, we can cancel [tex]\(a-3\)[/tex] with [tex]\(3-a\)[/tex], keeping in mind that a negative sign will be introduced since [tex]\(a-3 = -(3-a)\)[/tex]:

[tex]\[\frac{-1}{7} \times \frac{21}{-1}\][/tex]

Next, we simplify [tex]\(21\)[/tex] divided by [tex]\(7\)[/tex], which is [tex]\(3\)[/tex]:

[tex]\[-1 \times 3\] = -3[/tex]

The next three terms in the geometric sequence are 25, 12.5 and 6.25.

The given geometric sequence is 400, 200, 100, and 50.

We need to find the next three terms in the geometric sequence.

A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term. i.e., To get the next term in the geometric sequence, we have to multiply with a fixed term (known as the common ratio), and to find the preceding term in the sequence, we just have to divide the term by the same common ratio.

In the given geometric sequence the common ratio is 1/2.

5th term=50/2=25

6th term=25/2=12.5

7th term=12.5/2=6.25

Therefore, the next three terms in the geometric sequence are 25, 12.5 and 6.25.

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Using the concept of combinations, there are 10 ways to choose three apples from a basket, where two are rotten and one is not.

The question is asking about the number of ways two rotten apples can be chosen from a basket, given the total apples and the number of rotten ones. This is a problem based on probability and combinations.

The total number of apples in the basket is 12, two of them are rotten. The number of ways of choosing 2 rotten apples from 2 is simply 1 way, because there are only 2 and you're choosing each one of them.

But, the student is asked to select three apples, so the last apple would be one of the other 10 (remaining good ones). The number of ways you can choose that is 10 C 1.

From combinations rules, we know nCr=n!/[r!(n-r)!], where n is the total items, r is the number chosen, and '!' refers to factorial.

So to find the number of ways to choose 1 apple from 10, we find 10! / [1!(10-1)!]. This calculates as 10! / [1!9!] = 10. So, there are 10 ways to choose three apples with two of them being rotten.

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There are 10 different ways to choose a sample of three apples from the basket such that exactly two of them are rotten.

To determine the number of ways to choose two rotten apples from a basket containing 12 apples (2 of which are rotten) when a sample of three apples is selected.

We can use combinatorics.

Step-by-Step Solution:

1. Identify the total number of apples and the rotten apples:

Total apples: [tex]\( 12 \)[/tex]

Rotten apples: [tex]\( 2 \)[/tex]

2. Determine the possible cases for choosing two rotten apples in the sample of three:

We need to choose 2 out of the 2 rotten apples.

We need to choose the remaining 1 out of the 10 good apples.

3. Calculate the number of ways to choose 2 rotten apples out of 2:

[tex]\[ \binom{2}{2} = 1 \][/tex]

4. Calculate the number of ways to choose 1 good apple out of 10:

[tex]\[ \binom{10}{1} = 10 \][/tex]

5. Multiply the results from the above steps to get the total number of ways to choose two rotten apples and one good apple:

[tex]\[ \text{Total ways} = \binom{2}{2} \times \binom{10}{1} = 1 \times 10 = 10 \][/tex].

The Second train will catch up with the first train after 15 hours which is 8a.m the following morning.

First train :

Departure time = 2 pm

Speed = 50 mph

Second train :

Departure time = 2 pm + 3 hours = 5 pm

Speed = 60 mph

Distance = speed × time

Distance already covered by first train before the departure of the second = 50 mph × 3 hpird = 150 miles

The number of hours needed for second train to catch up will be h;

(60 × h) = (50 × h) + 150

60h = 50h + 150

60h - 50h = 150

10h = 150

h = 150/ 10

h = 15

Second train will catch up after 15 hours :

Hence, time will be : (5pm + 15 hours) = 8 a.m the following morning.

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Answer: 8:00 am

Step-by-step explanation:

(5pm + 15 hours) = 8 a.m the following morning.

60h = 50h + 150

60h - 50h = 150

10h = 150

h = 150/ 10

h = 15

Using the least common factor of 15 and 12, it is found that the fewest number of packages that could be bought is of 5.

To find the lcm(least common multiple), we factor the numbers by prime factors, and then multiply these factors.

In this problem, packages of 12 candies will be used to give candies for 9 + 6 = 15 people, hence the least number of candies is lcm(12,15).

Then:

12 - 15|2

6 - 15|2

3 - 15|3

1 - 5|5

1 - 1

Hence lcm(12,15) = 2 x 2 x 3 x 5 = 60.

Since 60 candies are needed, and each package has 12 candies, the number of packages is given by:

n = 60/12 = 5.

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To calculate the total time it takes to run 2 miles uphill at 4 mph and then 3 miles downhill at a speed that takes the same time as running 2 miles uphill, we find that the time for each is 0.5 hours, or 30 minutes, totaling 1 hour

The main question asks how long it would take for the runner to run 2 miles uphill and then 3 miles downhill, knowing that he jogs at a rate of 4 miles per hour uphill, and he can run 3 miles downhill in the same time it takes to run 2 miles uphill

First, let's find the time it takes to run 2 miles uphill. Since he runs at 4 miles per hour uphill, the time for 2 miles uphill is 2 miles divided by 4 miles per hour, which equals 0.5 hours or 30 minutes. Now, since it takes the same time to run 3 miles downhill, we know the downhill time is also 30 minutes

The total time taken for 2 miles uphill and 3 miles downhill is the sum of both, which is 30 minutes + 30 minutes = 60 minutes, or 1 hour. Thus, the answer to the student's question is 1 hour

To express the given ratio as a unit rate, divide the miles by the gallons to obtain 18.8 miles per gallon.

To express the given ratio as a unit rate, divide the miles by the gallons. So, the unit rate would be:

325.4 miles ÷ 17.3 gallons = 18.8 miles per gallon

Therefore, the unit rate for the given ratio is 18.8 miles per gallon.

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Answer:

Question 1)

Option: B

( unpaid balance)

Question 2)

Option: D

( Minimum payment )

Step-by-step explanation:

Question 1)

UNPAID BALANCE:

unpaid balance is the remaining balance of a loan, cash advance or credit that has not been paid.

Hence, The amount left when you subtract last month's payment from last month's balance on a credit card statement is the:

unpaid balance.

Question 2)

Minimum payments are typically calculated as percentage of your outstanding balance plus any fees that have been added to your balance.

Hence, The percentage charged each month on purchases charged to the credit card account is called the:

Minimum payment.

Answer:

The correct option is A.

Step-by-step explanation:

A geometric sequence is defined as

[tex]A(n)=ar^{n-1}[/tex]

Where, a is the first term of the sequence, r is the common ratio and n is number of term. So, n can not be negative or zero.

In option A, the given sequence is

[tex]A(n)=P(1+i)^{n-1}[/tex]

Where, n is positive integers.

Here the first term is P and (1+i) is the common ratio. So, this sequence is geometric sequence.

Therefore the correct option is A.

Answer:

A is correct just took the test

Step-by-step explanation:

Answer:

Value of  [tex]P(Q \cap R)[/tex] is, 0.0081

Step-by-step explanation:

For an independent events A and B is given by:

[tex]P(A \cap B) =P(A) \cdot P(B)[/tex]

As per the statement:

Suppose Q and R are independent events.

P(Q) = 0.27 and P(R) = 0.03.

We have to find [tex]P(Q \cap R)[/tex]

By definition we have;

[tex]P(Q \cap R) =P(Q) \cdot P(R)[/tex]

Substitute the given values we have;

[tex]P(Q \cap R) =0.27 \cdot 0.03[/tex]

⇒[tex]P(Q \cap R)=0.0081[/tex]

therefore, the value of  [tex]P(Q \cap R)[/tex] is, 0.0081

This problem can be solved directly by subtraction.

We are given that there are initially 78 emails in her inbox.

We take out or delete 47 emails therefore we subtract 47 from 78, hence:

                78 – 47 = 31

So there are 31 emails left in her inbox.

Final answer:

The equation 100 cm = 1 m is used to create a conversion factor that allows for conversion between centimeters and meters. This conversion factor is essential when measuring lengths and is part of the metric system, which also includes units like kilometers, millimeters, micrometers, and nanometers.

Explanation:

Understanding Conversion Factors

When considering the statement that 100 cm is equivalent to 1 m, we can create a conversion factor to help us switch from one unit of measurement to another. A conversion factor is a ratio of equivalent measurements used to convert a quantity from one unit to another. In this case, 100 cm/1 m is our conversion factor, and it is equal to 1 because both numerator and denominator represent the same length but in different units.

If we were to divide both sides of the equation by 1 meter, we would get 1 m/1 m on one side and 100 cm/1 m on the other, simplifying to just 1 because any fraction with the same number in the numerator and denominator equals 1. Hence, utilizing this conversion factor allows any given number in meters to be converted into centimeters, and vice versa, without changing the measure's value.

Furthermore, knowing other unit conversions like 1 meter equals 0.001 kilometers, 1.094 yards, or 39.37 inches can be very useful in different contexts. Similarly, we can break down meters into smaller units such as centimeters, millimeters, micrometers, and nanometers, with each having its place in the metric system.

A student is calculating how many additional boxes can be added to an elevator that already has 10 boxes of a certain weight. By using the weight capacity of the elevator and the weights of the boxes, the student determines the number of extra boxes that can be accommodated in the elevator's load.

To solve this problem, we need to first calculate the total weight of the 10 boxes:

You diver begin at -150 feet and then descend at 5 feet/minute for 3.5 minutes, which could be represented by (-5)(3.5). you then go up 122.2 feet. The expression is -150 + (-5)(3.5) + 122.2. You then get that the diver’s depth is 45.3 feet below sea level, or -45.3.