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3 years ago

I need help with this perimeter

Mathematics

2 answers:

spin [16.1K]3 years ago

5 0

The length of that semi circle is 6pi. So the perimeter should be 6pi + 24

Tasya [4]3 years ago

4 0

Answer:

42.85 cm

Step-by-step explanation:

Step 1: Find the perimeter of the semicircle

Perimeter of a semi circle: 1/2π * d

1/2π * 12

18.85

Step 2: Find the total perimeter

6 + 10 + 8 + 18.85

42.85

Answer: 42.85 cm

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How many juice glasses, each having a capacity of

sashaice [31]

Answer: 16 Juice Glasses

Step-by-step explanation:

2 Liters of Juice = 2000 Milliliters of Juice

2000 mL/125 mL = 16 Juice Glasses

3 0

3 years ago

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:

C. $(5-\frac{1}{2})^6$

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]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

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

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 $^6C_4$

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

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

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

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

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

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

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

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

Check the list of options for the expression on the left hand side

The correct answer is $(5-\frac{1}{2})^6$

3 0

3 years ago

Mr. snorkel drove 169 miles in 3 h 30 min. find the rate in feet per minute

AVprozaik [17]

169 miles * 5280 ft/ mile = 892320 ft

3 hours * 60 minutes/1 hr = 180 minutes

3 hrs 30 minutes = 180 minutes + 30 minutes = 210 minutes

169 miles/ 3 hrs 30 minutes = 892320 ft/ 210 minutes = 4249.1 ft/ minutes

3 0

3 years ago

The probability that a certain kind of component will survive a shock test is 3/4. Find the probability that exactly 2 of the ne

Marina86 [1]

Answer:

Therefore the required probability is $=\frac{27}{128}$

Step-by-step explanation:

The probability of success is $\frac{3}{4}$

The number of trial = 4

X= the items survive out of 4

$P(x=r)=^nC_rq^{n-r}p^r$ p =the probability of success and q = the probability failure.

p= $\frac{3}{4}$ and $q=(1-\frac{3}{4})=\frac{1}{4}$

$\therefore P(X=2)=^4C_2(\frac{1}{4} )^2(\frac{3}{4} )^2$

$=\frac{4!}{2!2!} (\frac{1}{16} )(\frac{9}{16} )$

$=\frac{27}{128}$

Therefore the required probability is $=\frac{27}{128}$

3 0

3 years ago

Help! ASAP!

Goshia [24]

9514 1404 393

Answer:

A- Cai are used an invalid reason to justify the congruence of a pair of sides or angles.

Step-by-step explanation:

In step 4, Cai referred to the angles as "alternate interior." In fact, they are "corresponding." The reason used to justify congruence of the angles was invalid.

7 0

2 years ago