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3 years ago

Please help. My son and I don't get it

Mathematics

2 answers:

vfiekz [6]3 years ago

6 0

So you have 3 and you want to get rid of 2 2/5. 3-2 is 1 1-2/5 is equal to three fifths, which is the answer.

Vikki [24]3 years ago

3 0

Which answer would you like me to help you on. I can help you on any of them

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What is the GCF of 20, 10 and 30?

Deffense [45]

Answer:

10 is the GCF

Step-by-step explanation:

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3 years ago

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The population of Bridgetown triples every decade. If the population

Afina-wow [57]

Between 2000 and 2030 three decades will have gone by, which means the population will triple three times.

$2000-25,000 \\ 2010-25,000*3=75,000 \\ 2020-75,000*3=225,000 \\ 2030-225,000*3=675,000$

Therefore, the population of Bridgetown will be 675,000 people in 2030.

4 0

3 years ago

Harold uses the binomial theorem to expand the binomial (3x^5 - 1/9y^3)^4

riadik2000 [5.3K]

<h3>The complete question:</h3>

Harold uses the binomial theorem to expand the binomial $(3x^5 -\dfrac{1}{9}y^3)^4$

(a) What is the sum in summation notation that he uses to express the expansion?

(b) Write the simplified terms of the expansion.

Answer:

(a). $(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}( -\dfrac{1}{9}y^3)^k $$$

(b). $(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561}$

Step-by-step explanation:

(a).

The binomial theorem says

$(x+y)^n=$$\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k $$$

For our binomial this gives

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}x^{4-k}y^k $$}$

(b).

We simplify the terms of the expansion and get:

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}y^k $$= \binom{4}{0}(3x^5)^{4-0}(-\dfrac{1}{9}y^3 )^0+\binom{4}{1}(3x^5)^{4-1}(-\dfrac{1}{9}y^3 )^1+\\\\\binom{4}{2}(3x^5)^{4-2}(-\dfrac{1}{9}y^3 )^2+\binom{4}{3}(3x^5)^{4-3}(-\dfrac{1}{9}y^3 )^3+\binom{4}{4}(3x^5)^{4-4}(-\dfrac{1}{9}y^3 )^4$

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}(-\frac{1}{9}y^3 )^k $$= (3x^5)^{4}+4(3x^5)^{3}(-\frac{1}{9}y^3 )+6(3x^5)^{2}(-\frac{1}{9}y^3 )^2+\\\\4(3x^5)(-\frac{1}{9}y^3 )^3+(-\frac{1}{9}y^3 )^4$

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561} }$

3 0

3 years ago

the names of 11 boys and 6 girls from your class are put into a hat. what is the probability that the first two names chosen wil

zloy xaker [14]

Answer:

25%

is that what you were looking for?

6 0

3 years ago

A wedge of cheese in the shape of a triangular prism has lengths of 10 cm, 13 cm, and 13 cm for its triangular sides. The perpen

Rina8888 [55]

Answer:

480 cubic cm.

Step-by-step explanation:

We have been given that a wedge of cheese in he shape of a triangular prism has lengths of 10 cm, 13 cm, and 13 cm for its triangular sides. The perpendicular distance from the 10 cm side to the point of the wedge is 12 cm. The height of the wedge is 8 cm.

$\text{Volume of triangular prism}=\text{Base area*Height of the wedge}$

We can see from our attachment that base of our triangular face is 10 cm and height of the triangular face is 12 cm and height of wedge is 8 cm.

Substituting these values in volume formula we will get,

$\text{Volume of cheese wedge}=\frac{1}{2}*\text{10 cm*12 cm*8 cm}$

$\text{Volume of cheese wedge}=\text{5 cm*12 cm*8 cm}$

$\text{Volume of cheese wedge}=480\text{cm}^3$

Therefore, the volume of cheese wedge will be 480 cubic cm.

4 0

3 years ago