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2 months ago

15

One can convert temperature from Fahrenheit into Newton using the formula N=11/60(F-32) . What is the temperature in Fahrenheit

corresponding to N degrees Newton?

1 answer:

babunello [11.8K]2 months ago

5 0

N=11/60*(F-32). To isolate F, first multiply both sides by 60/11, leading to 60/11*N=F-32. Then, add 32 to both sides, resulting in F=60/11*N+32.

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1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms? Round your answer t

AnnZ [12381]

The weight of an orangutan is 64.5 kilograms

Solution:

It is stated that the orangutan's weight is 142 pounds

Additionally,

1 kilogram is approximately 2.2 pounds

We will now convert 142 pounds into kilograms

1 kilogram = 2.2 pounds

$\text{1 pound } = \frac{1}{2.2} \text{ kilograms }$

As a result, 142 pounds translates to

$142 \text{ pound } = \frac{1}{2.2} \times 142 \text{ kilogrmas }$

$\rightarrow \frac{1}{2.2} \times 142 = 64.545 \text{ kilograms }$

When rounding to the nearest tenth, we obtain 64.5 kilograms

Therefore the mass of the orangutan is 64.5 kilograms

3 0

2 months ago

105,159 rounded to the nearest ten thousand

Svet_ta [12734]

In this problem the number we are working with is:

105,159

By definition we note:

thousand place: a five-digit quantity greater than zero.

Moreover, the rounding rule is:

if the digit being removed is 5 or more, increase the kept digit by one.

Therefore, rounding to the nearest ten thousand yields:

105,159 = 110,000

Answer:

105,159 rounded to the nearest ten thousand is:

105,159 = 110,000

6 0

3 months ago

Read 2 more answers

Calculating conditional probabilities - random permutations. About The letters (a, b, c, d, e, f, g) are put in a random order.

AnnZ [12381]

A="b is situated in the center"

B="c lies to the right of b"

C="The letters def occur sequentially in that arrangement"

a) b can occupy 7 positions; however, only one of these is the center. Therefore, P(A)=1/7

b) Let X=i; "b holds the i-th position"

Y=j; "c occupies the j-th position"

$P(B)=\displaystyle\sum_{i=1}^{6}(P(X=i)\displaystyle\sum_{j=i+1}^{7}P(Y=j))=\displaystyle\sum_{i=1}^{6}\frac{1}{7}(\displaystyle\sum_{j=i+1}^{7}\frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}$

P(B)=1/2

c) Let X=i; "d holds the i-th position"

Y=j; "e occupies the j-th position"

Let Z=k; "f is in the i-th position"

$P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}$

P(C)=1/42

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

$P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)=\displaystyle\sum_{i=1}^{3}\frac{1}{6}\frac{1}{7}\frac{1}{5}(\displaystyle\sum_{j=1+3}^{6}\frac{1}{4}\frac{1}{3})=1/420$

P(B∩A)=3*(1/7*1/6)=1/14

P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7

P(A∩B)=1/14

P(A)P(B)=(1/7)*(1/2)=1/14

Events A and B are independent

P(A∩C)=1/420

P(A)P(C)=(1/7)*(1/42)=1/294

Events A and C are not independent

P(B∩C)=1/420

P(B)P(C)=(1/2)*(1/42)=1/84

Events B and C are not independent

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2 months ago

Alejandro surveyed his classmates to determine who has ever gone surfing and who has ever gone snowboarding. Let A be the event

tester [12383]

Answer:

$\text{A and B are independent events}, P(A|B)=P(A)=0.16$

Step-by-step explanation:

To establish independence between two events, we must understand the concept of independence:

Events are deemed independent if $P(A|B)=P(A)$ , which means that the occurrence of one does not influence the probability of the other event.

In this situation, the only selection that aligns with the independence criterion is $P(A|B)=P(A)=0.16$ . Other options do not comply with the independent events definition.

4 0

2 months ago

Read 3 more answers