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3 years ago

Evaluate 3/5 - 3/10 and explanation thanks

Mathematics

1 answer:

Setler [38]3 years ago

4 0

It would be 3/10 because you have to create a common denominator. That would be 10. 3x2=6 and 5x2=10, so 3/5 would become 6/10, which is equivalent. If you kept the denominators the same and subtracted the numerators, you would get 3/10.

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Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

3 years ago

People tend to evaluate the quality of their lives relative to others around them (Frieswijk et al., 2004). In one study, resear

Alborosie

Answer:

Step-by-step explanation:

Hello!

Research.

n=9 frail elderly were interview and compared to a fictitious person who was worse off then the interviewee, a life-satisfaction score was determined for each person.

18, 23, 24, 22, 19, 27, 23, 26, 25

Assuming that the population average score is μ= 20, the researchers think that the elderly in the sample are more or less satisfied than others in the general population.

a. You have the information of one sample, assuming this sample has a normal distribution and each elderly interviewed is independent, then the t-test of choice is a one-sample t-test.

b. and c. If you say that the elderly are "more or less" satisfied than the others, this means that they are either as satisfied as to the general population or not satisfied as to the general population. Symbolically:

H₀: μ = 20

H₁: μ ≠ 20

This is a two-tailed test, meaning, you will have two critical regions.

α: 0.05

Left critical value: $t_{n-1;/\alpha 2} = t_{8; 0.025}= -2.306$

Right critical value: $t_{n-1;1-\alpha /2} = t_{8;0.975} = 2.306$

$t_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}$

X[bar]= 23

S= 3

$t_{H_0}= \frac{23-20}{\frac{3}{\sqrt{9} } }= 3$

Considering that the calculated t-value is greater than the right critical value, the decision is to reject the null hypothesis, so using a significance level of 5% you can conclude that the average life-satisfaction score of the elderly is different than 20.

I hope it helps!

7 0

3 years ago

Use distributive property to simplify <br> -(x+3y-z)

UkoKoshka [18]

Answer:

-x - 3y + z

Step-by-step explanation:

Think of a imaginary 1(-1 because of the sign) in front of the parenthesis and distribute it to the other number and so x will become -x, 3y will become -3y and -z will become z because two negatives make a positive.

4 0

3 years ago

7. John, Paul, and George are having a disagreement over interest rates. John

gayaneshka [121]

John Paul is correct

7 0

3 years ago

A gallon of water weighs 8.345 pounds. Simon uses 11.81 gallons of water while taking a shower. About how many pounds of water d

stealth61 [152]

1 gallon= 8.345 pounds

11.81 gallons= ? Ibs

11.81*8.345= 98.5 Ibs (99)

5 0

3 years ago