Compute $\frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16}\cdot \frac{24}{25}\cdot \frac{35}{36}\cdot \frac{48}{49}\cdot \frac{63}{64}\cdot \frac{80}{81}\cdot \frac{99}{100}$. Express your answer in the simplest way possible.


(Suggestion: First, try computing $\frac{3}{4}\cdot \frac{8}{9},$ then $\frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16},$ and so on. Look for patterns.)

Answers

Answer 1

Answer:

[tex] \sf\frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16}\cdot \frac{24}{25}\cdot \frac{35}{36}\cdot \frac{48}{49}\cdot \frac{63}{64}\cdot \frac{80}{81}\cdot \frac{99}{100} \\ \implies \sf \frac{3 \times 8 \times 15 \times 24 \times 35 \times 48 \times 63 \times 80 \times 99}{4 \times 9 \times 16 \times 25 \times 49 \times 64 \times 81 \times 100} \\ \implies \sf \frac{7333035494400}{11732856791040} \ \sf \\ \implies \sf \: 0.625[/tex]


Related Questions

Use the quadratic formula to solve x2 – 5x - 2 = 0.

Answers

Answer:

• The quadratic formular is as below:

[tex]{ \boxed{ \rm{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}}[/tex]

• Basing on our equation given, x² - 5x - 2 = 0;

a → 1b → -5c → -2

[tex]{ \rm{x = \frac{ - ( - 5) \pm \sqrt{ {( - 5)}^{2} - (4 \times 1 \times - 2) } }{(2 \times 1)} }} \\ \\ { \rm{x = \frac{5 \pm \sqrt{33} }{2} }} [/tex]

• Therefore;

[tex]{ \boxed{ \rm{x = \frac{5 + \sqrt{33} }{2} }}}{ \rm{ \: \: or \: \: }}{ \boxed{ \rm{x = \frac{5 - \sqrt{33} }{2} }}} \\ \\ { \boxed{ \boxed{ \rm{x = 5.37 \: \: or \: \: - 0.37}}}}[/tex]

HELPPPPP PLEASE!! ;)

Answers

Answer:

its 2 8/11

Step-by-step explanation:

i hope this helps have a good day

Amy has $70.00 and Alice has $9.52. How much money do they have
together?

Answers

Answer:

Together they have $79.52

Which of these is a good conductor?
wood
silver
paper
air

Answers

Silver is an excellent conductor for heat.
the answer is silver

A little help? A set of numbers is given below. √72, 9.25, √83, 2, 8.7 Which list correctly orders the numbers from least to greatest?​

Answers

Answer:

2, √72, 8.7, √83, 9.25

Step-by-step explanation:

First, you need to find the integers of each number that is not already a integer.

Square root of 72: 8.48528137424

9.25

Square root of 83: 9.11043357914

2

8.7

Now, list the numbers by their whole number (in the ones place). If they have the same whole number, look at their tenths place and see which one is greater.

Overall, the answer would be 2, √72, 8.7, √83, 9.25.

If Haley earns $12 for each hour babysitting how many hours will it take Katie to earn a total of $48?

Answers

Answer:

4 hours

Step-by-step explanation:

12 x 4 = 48

[tex]\sqrt{4x-5}-\sqrt{16-5x}[/tex]

Answers

Answer:

[5/4,16/5]

Step-by-step explanation:

Which two triangles are congruent by the SSS Theorem? Complete the congruence
statement.

Answers

Triangle CED and YZX are congruent


Hilary put 5 items on his birthday wish list. He received 3 of the items for his birthday. What percent of the
items did Hilary receive ?

Answers

Answer:

60%

Step-by-step explanation:

100 ÷ 5 = 20

20 × 3 = 60

60 = 60%

I hope this helps

willie's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 10 adult tickets and 4 student tickets for a total of $194. The school took in $182 on the second day selling 7 adult tickets and 7 student tickets. What is the price each one adult ticket and one student ticket? ​

Answers

Adult tickets - $15

Student tickets - $11

First day:

10 tickets * $15 = $150

4 tickets * $11 = $44

Total: $194

Second day:

7 tickets * $15 = $105

7 tickets * $11 = $77

Total: $182

5) John Tavares needed some new plants for his apartment. Each tree he purchased was
21.99. If John bought 4 trees and left a 34% tip, how much did he pay in total for the
plants including the tip?

Answers

Answer:

$117.87

Step-by-step explanation:

4 trees x $21.99 = $87.96

34% x $87.96 = $29.91 tip

Total = $87.96 + $29.91 = $117.87

I’m giving the right
Answer brainlyest and 5 star rating

Answers

Answer:

the first one i think sorry it im wrong

Step-by-step explanation:

the answer is the third one

Mrs. Snow divided thirty-six books equally
and placed them on nine desks. How many
books did she place on each desk?

Answers

Mrs. Snow divided thirty-six books equallyMrs. Snow divided thirty-six books equallyand placed them on nine desks. How many books did she place on each desk?

every desk have a 4 books

if you're going to divide 36 into 9 then you'll have the answer

hope it helps

Each desk has 4 books

if you need 3/4 cups of beans for 7 servings. How many do you need if you want to make 35 servings

Answers

Answer:

3 3/4 cups

Step-by-step explanation:

We need 3/4 cups of beans for 7 servings, and we need to figure out how many cups we need for 35 servings. You'll notice that 7 times 5 is 35. We can multiply 3/4 by 5 to find the answer to our problem. This thought process looks somewhat like this:

[tex]\frac{\frac{3}{4} }{7} = \frac{x}{35}[/tex]

Notice that we can multiply 5 by 3/4 to find the value of x.

So, 3/4 times 5 is equal to 15/4, or 3 3/4. So, you need 3 3/4 cups of beans for 35 servings.

Hopefully this was helpful! If you have any more questions, let me know.

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.
AB = RS
AB = 2RS
ABC ~ RST
ABC = RST
m<BAC = m<SRT
m<BAC = 2m<SRT​

Answers

The reflection transformation in the question is a rigid transformation,

therefore, the image and the preimage are congruent.

The statements that are true are;

AB = RS∠ABC ~ ∠RSTΔABC = ΔRSTm∠BAC = m∠SRT

Reasons:

The given parameter are;

Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST

Required:

To select the true statements

Solution:

A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.

Therefore;

AB = RS

BC = ST

AC = RT

Given that the image formed by a reflection is congruent to the preimage, we have;

ΔABC ≅ ΔRST

∠ABC ≅ ∠RST

m∠ABC = m∠RST by the definition of congruency

∠BCA ≅ ∠STR

m∠BCA = m∠STR by the definition of congruency

∠BAC ≅ ∠SRT

m∠BAC = m∠SRT by the definition of congruency

Therefore, the true statements are;

AB = RS; Image formed by rigid transformation∠ABC ~ ∠RST; Definition of similarityΔABC = ΔRST; By definition of congruencym∠BAC = m∠SRT; by the definition of congruency

Learn more here:

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Solve for n
n - 17=3

Answers

Answer:

N=20

Step by Step:

First you add 17 to both of the sides:

N−17+17=3+17

Second, you simplify;

N=20

Brainiest please?

Answer:D

Step-by-step explanation:

/Which of the following pairs consists of equivalent fractions? 8/16 and 3/4 5/3 and 3/5 12/18 and 10/15 12/20 and 10/25

Answers

Answer:

12/18 and 10/15

Step-by-step explanation:

12/18 = 2/3 (when the numerator and denominator are divided by 6)

10/15 = 2/3 (when the numerator and denominator are divided by 5)

∴ 12/18 and 10/15 are equivalent

what is the perimeter of 10cm length and 8cm width of a rectangle ?

Answers

Answer:

36 cm

Step-by-step explanation:

rectangle perimeter = sum of all the side

10+8+10+8=36 cm

Answer:

Step-by-step explanation:

Perimeter =2(10+8)=36 cm.

Is the list of numbers an arithmetic sequence?
22,25,27,30,33,…

Answers

Answer:

No

Step-by-step explanation:

The jump from each of the numbers is 3 but from 25 to 27 is 2 therefore it is not an arithmetic  sequence.

What is absolute of -0.9

Answers

Answer:

0.9

Step-by-step explanation:

absolute is the positive number

Answer:

0.9

Step-by-step explanation:

The absolute value is the distance of a number from zero, and 0.9 is 0.9 steps away from zero.

Rittle - Mary didn't know how to pronounce the name but she knew that she had to go inside to impress her parents, where was she? (giving out the answer in 5 mins. SO HURRY)

Answers

at school i think because i’m so confused

Please help due in 2 hours and I’m clueless.

Identify the domain and range of each graph.


Answers

So all u have to do is say all the x values that have a point (the domain) and all the y values that have a point (the range). If it is continuous, like a line, then u say all the points between two points. For example the range of the bottom right is [-1,5]. If it goes to infinity or negative infinity, you say something like (-infinity,infinity). With the sideways 8 of course. Btw, (-infinity, infinity) is the domain of the bottom right ;D

a is a negative odd number
choose two words from the list which describe a^2
Negative
Positive
Odd
Even

Answers

Answer:

even

Step-by-step explanation:

because a is not and odd number its even

The requried two words that describe A² are "Odd" and "Positive".

What are odd numbers?

Odd numbers are integers that cannot be divided evenly by 2, which means they have a remainder of 1 when divided by 2. They can be represented as 2n + 1, where n is an integer. Examples of odd numbers include 1, 3, 5, 7, 9, and so on. The opposite of odd numbers are even numbers, which can be divided evenly by 2.

The square of any negative or positive number is always positive. Thus, the first two options "Negative" and "Positive" do not apply to A². As for "Even", it describes a number that is divisible by 2, while "Odd" describes a number that is not divisible by 2. Since A is an odd number, A² will also be odd, as it is the product of an odd number multiplied by itself.

Therefore, the two words that describe A² are "Odd" and "Positive".

Learn more about odd numbers here:

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HURRY PHOENIX! Hey Phoenix It's worth 100 points!
What should the following equation be multiplied by to eliminate the decimals? -200k – 3.01 = 3.3
100
10
2
20

Answers

10

3.3×10= 33

Hope this helped you- have a good day bro cya)

Juan is paid a salary of $302 biweekly find Juan’s earnings per year

Answers

Answer:

7852

Step-by-step explanation:

There are 52 weeks in a year

Divide by 2 to determine bi-weekly

52/2 = 26

You will be paid 26 times in a year if you are paid bi-weekly

302 * 26

7852

Choose the correct answer​

Answers

Answer:

b) 50 degrees

Step-by-step explanation:

I'm not sure if it 100% correct but this is what i remember:

BCE is a straight line and a straight line is equal to 180 degrees.

If AB=AC then the angle of both those corners will be 180-115

which equals to 65 degrees (both angles)

Now because all corners of a triangle add up to 180

you can do 180-65-65 which is 180-130

this equals to the angle BAC which is 50 degrees

HELP ME PLEASE im begging!!

Answers

Answer:

[tex]x = 40[/tex]

Step-by-step explanation:

As the Corresponding angles are equal

[tex]4x - 50 = 2x + 30 \\ 4x - 2x = 50 + 30 \\ 2x = 80 \\ \frac{2x}{2} = \frac{80}{2} \\ x = 40 \degree[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

[tex]x = 40 [/tex]

Step-by-step explanation:

that's the answer

If you have swimming every 5 days and diving every 3 days and today you have both in how many days will u have bit classes again

Answers

Answer:

In 15 days

Step-by-step explanation:

So you have to find the smallest common factor(a number they both share in the multiplication table) which in this case is 15.

I think you meant to say both not bit lol

Have a nice day! :-)

Which statement is true about the relationship between the height of the plant and the number of days?

A. This relationship is a function because the plant can be more than one height at a time.
B. This relationship is not a function because the plant can be more than one height at a time.
C. This relationship is not a function because the plant can only be one height at a time.
D. This relationship is a function because the plant can only be one height at a time.

Answers

This relationship is a function because the plant body can be of only one particular height at a time.

A function can be defined as a relationship between a set of inputs having only one output each. In other words, a function is basically a relationship between inputs and outputs; where each input is related to only one output at a time. Functions are said to occur when the recorded value of x is varied each time. Since we know that the height of the plant (the x-value) varies by each day, Therefore it is a function.

thus we can conclude that the correct option for the relationship between the height of the plant and the number of days is option D, which tells that this relationship is a function because the plant body can only be of one particular height at a time.

To learn more about functions

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Directions: Find the specified term of the geometric sequences given the first term and the common ratio.​

Answers

Step-by-step explanation:

As you know

[tex] a_{n} = a_{1} \times {r}^{n - 1} [/tex]

1.

[tex]3 \times {3}^{4} = {3}^{5} \\ 3 \times {3}^{6} = {3}^{7} \\ 3 \times {3}^{8} = {3}^{9}[/tex]

2.

[tex]2 \times {2}^{4} = {2}^{5} \\ 2 \times {2}^{6} = {2}^{7} \\ 2 \times {2}^{8} = {2}^{9}[/tex]

3.

[tex] - \frac{1}{2} \times {( - 6)}^{4} = { \frac{ - 1}{2} } \times {6}^{4} \\ - \frac{1}{2} \times {( - 6)}^{6} = { \frac{ - 1}{2} } \times {6}^{6} \\ - \frac{ 1}{2} \times {( - 6)}^{8} = { \frac{ - 1}{2} } \times {6}^{8} [/tex]

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