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]
what is five divided by 2835
Suppose Q and R are independent events. Find P(Q and R) if P(Q) = 0.27 and P(R) = 0.03.
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
given : 100cm= 1 m .01 = 1cm
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.
select the function that represents a geometric sequence?
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:
Sasha donated 9/100 of her class’s entire can collection for the food drive. What decimal is equivalent to 9/100?
how many pairs of feet are needed to have at least 76, toes
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Table tennis the path of a table-tennis ball after being hit and hitting the surface of the table can be modeled by the function h=-4.9t(t-0.42) where h is the height in meters above the table and t is the time in seconds. how long does it take the ball to hit the table?
What does the y intercept represent in distance vs time squared?
A diver begins at 150 feet below sea level, descends at a steady rate of 5 feet per minute for 3.5 minutes, and then ascends 122.2 feet. What is the diver’s current depth? Explain how to write a numerical expression to find the answer.
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.
find the next three terms in the geometric sequence: 400, 200, 100, 50
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.
What is 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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How many integers between 100 and 999 have all distinct digits (i.e., no two digits the same)?
Final answer:
To determine how many integers between 100 and 999 have distinct digits, we calculate the possibilities for each position, giving us 9 options for the first digit, 9 for the second, and 8 for the third, resulting in a total of 648 integers.
Explanation:
The question is about finding the number of integers between 100 and 999 with distinct digits. To find this, we calculate the possibilities for each digit separately. The first digit can be anything from 1 to 9 (excluding 0 because the number cannot be less than 100), so there are 9 possibilities for the first digit. For the second digit, since it cannot be the same as the first, there are 9 possibilities (0 can now be included). Finally, for the third digit, we subtract the choices we've already used, so there are 8 possible digits left.
Calculating the total, we multiply the possibilities for each digit: 9 (first digit) × 9 (second digit) × 8 (third digit) = 648. Therefore, there are 648 integers between 100 and 999 that have all distinct digits.
Quadrilateral ABCD is the result of a translation of quadrilateral EFGH. Segment EF is parallel to segment HG in the pre-image.
Select from the drop-down menus to correctly complete the statement.
Segment EF is parallel to segment HG in the pre-image.
The corresponding segments are what
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.
Alexandra has 78 emails in her inbox. She deletes 47 emails. How many emails are left in her inbox? Draw jumps and label the number line to show your thinking. —————————————78
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.
The packaging lists a model airplane’s length as 10.5 in. It also gives the scale as 1:83. What is the length of the actual airplane to the nearest foot?
a.87ft
b.104ft
c.127ft
d.73ft
A runner can jog at a rate of 4 miles per hour uphill. Downhill, he can run 3 miles in the same time it takes him to run 2 miles uphill. How long would it take to run 2 miles uphill and then 3 miles downhill?
what is the most important variable?
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
stacey has 18 bracelets after she organizes the bracelets by color she has 3 equal groups how many bracelets are in each group
A basket contains 12 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen
Using the concept of combinations, there are 10 ways to choose three apples from a basket, where two are rotten and one is not.
Explanation: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].
A sea lion dove from the water's surface at sea level to an altitude of −216.12 meters in 2.4 minutes. What is the average change in the sea lion's altitude per minute? Enter the your answer in the box as a decimal.
1.Parallelogram ACFD is split in two parts so that ABED and FEBC are congruent isosceles trapezoids. What are the measures of all the angles of trapezoid FEBC if angle D is 48°?
I know that Angle C is 48 degrees
I know that Angle F is 132 degrees
What is < CBE equal to and why?
What is < FEB equal to and why?
If there were to be 9 boys and 6 girls at a party and the host wanted each to be given the same number of candies that could be bought in packages containing 12 candies, what is the fewest number of packages that could be bought? I got 36. But i'm not sure.
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.
How to find the least common factor of two amounts?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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Can you plz solve 336.752 divided by 31 in long division form. This would help a whole bunch:)
how many 1/4 cup servings of oatmeal are in 3/5 of a cup of oatmeal?
Fuaad solved an absolute value inequality and expressed the solution as -12
A sign in an elevator says the elevator can lift up to 450 kg. John has 10 boxes that weigh 13.75 kg each, and a number of additional boxes that weigh 15.5 kgs each. If he puts the 10 boxes on the elevator, how many of the additional boxes can be lifted in the same load?
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:
Weight of 10 boxes = 10 boxes x 13.75 kg/box = 137.5 kgSubtract this weight from the maximum capacity of the elevator: 450 kg - 137.5 kg = 312.5 kgDivide the remaining weight by the weight of each additional box to find out how many more boxes can be lifted: 312.5 kg ÷ 15.5 kg/box ≈ 20 boxesDetermine which numbers could not be used to represent the probability of an event. select all that apply.
a. minus−1.5, because probability values cannot be less than 0.
b. 0.0002, because probability values must be rounded to two decimal places.
c. startfraction 64 over 25 endfraction 64 25, because probability values cannot be greater than 1.
d. 33.3%, this is because probability values cannot be greater than 1.
e. startfraction 320 over 1058 endfraction 320 1058, because probability values cannot be in fraction form. f. 0, because probability values must be greater than 0.
The amount left when you subtract last month's payment from last month's balance on a credit card statement is the
A. APR.
B. unpaid balance.
C new balance.
D. minimum payment.
The percentage charged each month on purchases charged to the credit card account is called the
A. periodic rate
B. new balance
C. unpaid balance
D. minimum payment
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.
What is the value of the underlined digit 5,678.321
The value of the underlined digit is 600.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
We must determine the values of each integer in order to calculate the value of the underlined digit (6) in the equation.
In 5,678.321, the first digit, 5, is 1,000 in the thousands of places.
The second digit, 6, is in the hundreds (100) place.
So the value is 600.
Hence, the value of the underlined digit is 600.
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Your question is incomplete, probably the complete question is:
What is the value of the underlined digit 5,678.321, the underlined digit (6)
Two similar right triangles have areas of 6 square inches and 150 square inches. The length of the hypotenuse of the smaller triangle is 5 inches. What is the sum of the lengths of the legs of the larger triangle?
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.
Explanation: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.
A train leaves Los Angeles at 2 p.m. heading north at 50 mph. If the next train leaves three hours later and also heads north at 60 mph, at what time will the second train catch up with the first?
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