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murzikaleks [220]
3 years ago
15

Find the product of 3 1/5 and 5/8. Express your answer in simplest form.

Mathematics
2 answers:
____ [38]3 years ago
8 0
3 \frac{1}{5}= \frac{3.5+1}{5}= \frac{15+1}{5}= \frac{16}{5}

\frac{16}{5}. \frac{5}{8}=> \frac{16.5}{8.5}= \frac{80}{40} simplify this   

=2 \\  \\\framebox[1.1\width]{Good Luck!} \par

Serggg [28]3 years ago
7 0
First convert 3 1/5 into an improper fraction.

We do that by multiplying the denominator to the whole number and adding it to the numerator and we keep the denominator.

5 * 3 + 1 = 16

So 3 1/5 is equal to 16/5

16/5 * 5/8

Multiply the numerators together and the denominators together:

16/5 * 5/8 = 80/40 = 2

So the product of 3 1/5 and 5/8 is 2.
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For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
Elina [12.6K]

Answer:

<em>C.</em> (5-\frac{1}{2})^6

Step-by-step explanation:

Given

15(5)^2(-\frac{1}{2})^4

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

Sum = 2 + 4

Sum = 6

Each term of a binomial expansion are always of the form:

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

Where n = the sum above

n = 6

Compare 15(5)^2(-\frac{1}{2})^4 to the above general form of binomial expansion

(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......

Substitute 6 for n

(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

By direct comparison of

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

and

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

We have;

^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4

Further comparison gives

^nC_r = 15

a^{n-r} =(5)^{6-4}

b^r= (-\frac{1}{2})^4

[Solving for a]

By direct comparison of a^{n-r} =(5)^{6-4}

a = 5

n = 6

r = 4

[Solving for b]

By direct comparison of b^r= (-\frac{1}{2})^4

r = 4

b = \frac{-1}{2}

Substitute values for a, b, n and r in

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

Solve for ^6C_4

(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em>(5-\frac{1}{2})^6<em />

3 0
3 years ago
A varsity boy's basketball team has ratio of seniors to juniors that is 7:4. The varsity girl's basketball team has a ratio of s
valentina_108 [34]

Answer:

Girl's basketball team has more seniors

Step-by-step explanation:

A varsity boy's basketball team has ratio of seniors to juniors that is 7:4.

Let there are 7x seniors and 4x juniors in boy's basketball team.

ATQ,

7x+4x = 12

11x = 12

x = 12/11

Seniors = 7\times \dfrac{12}{11}=7.63

The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2.

Let there are 7x seniors and 4x juniors in girl's basketball team.

3x+2x = 12

5x = 12

x = 12/5

Seniors = 7\times \dfrac{12}{5}=16.8

As we can see that girl's basketball team has more seniors as compared to the boy's team.

4 0
3 years ago
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stepladder [879]

Answer:

This is pogers

Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
The differance of six times a number and 7 is -49
Neko [114]
6x - 7 = -49
6x = -49 + 7
6x = -42
x = -42/6
x = -7
8 0
3 years ago
There are 30 major league baseball teams and 32 national football league teams. The expanded roster for major league baseball te
Helga [31]

Answer:

Step-by-step explanation:

32(53) - 30(40) = 1696 - 1200 = 496 <==

5 0
3 years ago
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