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3 years ago

The 100th term of the pattern : 5 , 9 ,13 , 17.

Mathematics

2 answers:

qaws [65]3 years ago

8 0

Answer:

Tn=4n+1

4(100)+1

400+1

=401

tensa zangetsu [6.8K]3 years ago

5 0

Answer:

Step-by-step explanation:

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Help now. a storage tank in the shape of a cuboid of base 2.5 m by 2 m can hold up to 7500 litres of water. Calculate the height

Minchanka [31]

Answer:

Height of the tank is 1.5m

Step-by-step explanation:

Given

Shape: Cuboid

Base Dimension = 2.5m by 2m

Volume = 7500 litres

Required

Determine the height of the tank

First, the area of the base has to be calculated;

$Area = 2.5m * 2m$

$Area = 5.0m^2$

Next is to calculate the height using volume formula;

$Volume = Area * Height$

Recall that Volume = 7500L [Convert to m³]

$1 L = 0.001m^3$

So;

$7500L = 7500 * 0.001m^3$

$7500L = 7.5m^3$

Hence;

$Volume = 7.5m^3$

Substitute 7.5m³ for Volume and 5.0m² for Area in the following formula

$Volume = Area * Height$

$7.5m\³ = 5.0m\² * Height$

Divide both sides by 5.0m²

$\frac{7.5m\³}{5.0m\²} = \frac{5.0m\² * Height}{5.0m\²}$

$\frac{7.5m\³}{5.0m\²} = Height$

$1.5m = Height$

$Height = 1.5m$

<em>Hence, the height of the tank is 1.5m</em>

5 0

3 years ago

63% of US adults opposed to taxes on junk food and soda. You randomly select 10 US adults. Find the probability that the number

WARRIOR [948]

Answer:

a) 0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.

b) 0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.

c) 0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they are opposed to taxes on junk food and soda, or they are not. Each adult is independent of other adults, which means that the binomial probability distribution is used to solve the question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

63% of US adults opposed to taxes on junk food and soda.

This means that $p = 0.63$

You randomly select 10 US adults.

This means that $n = 10$

(a) exactly one

This is $P(X = 1)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008$

0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.

(b) at least four

This is

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.63)^{0}.(0.37)^{10} \approx 0$

$P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008$

$P(X = 2) = C_{10,2}.(0.63)^{2}.(0.37)^{8} = 0.0063$

$P(X = 3) = C_{10,3}.(0.63)^{3}.(0.37)^{7} = 0.0285$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0008 + 0.0063 + 0.0285 = 0.0356$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0356 = 0.9644$

0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.

(c) less than eight

This is

$P(X < 8) = 1 - P(X \geq 8)$

In which

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.63)^{8}.(0.37)^{2} = 0.1529$

$P(X = 9) = C_{10,1}.(0.63)^{9}.(0.37)^{1} = 0.0578$

$P(X = 10) = C_{10,2}.(0.63)^{10}.(0.37)^{0} = 0.0098$

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1529 + 0.0578 + 0.0098 = 0.2205$

$P(X < 8) = 1 - P(X \geq 8) = 1 - 0.2205 = 0.7795$

0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.

5 0

3 years ago

1. Fill in the blanks with the proper vocabulary.<br> |5y - 8 = 7v+22

Virty [35]

Answer:

12x+4x-7y+45b+78a-44b+1a+1z+0d+1.1a+1.1a+2+2+2

7 0

3 years ago

2 The point C ( − 3 , − 1 ) C(−3, −1) is rotated 18 0 ∘ 180 ∘ clockwise about the origin. What are the coordinates of the res

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

If we have the coordinate (x,y), if this coordinate is rotated by 180 degrees clockwise, the resulting coordinate will be expressed as (-x, -y) i.e the original coordinate axis are both negated.

Given the coordinate C(-3, -1), if this coordinate is rotated clockwise about the origin, the coordinate of the resulting point will be at C' (-(-3), -(-1))

C' (-(-3), -(-1))

C' = (3, 1)

Hence option A is correct

8 0

3 years ago

NO SILLY ANSWERS PLEASE <br> Can someone help me with this?

marusya05 [52]

Keep in mind that, when the logarithm base is not explicitly written, base 10 is assumed, therefore,

$\bf \textit{Logarithm Cancellation Rules}\\\\
log_a a^x\implies x\qquad \qquad a^{log_ax}=x\\\\
-------------------------------\\\\
10^{log(3)}+log(100)\implies 10^{log_{10}(3)}+log_{10}(100)\implies 3+log_{10}(10^2)
\\\\\\
3+2\implies 5$

7 0

4 years ago