11. If 4 < x < 14, what is the range for -x - 4?

Answer:

Add 1.2 fluid ounces of oil

Revised statement and question:

You've come across a Puch Maxi Moped from the mid-Eighties, and the pleasant spring weather has inspired you to take it for a spin. It doesn't run solely on gasoline; you must combine oil and gas at a specific ratio, which is 2.4 fluid ounces of oil for every gallon of gasoline. Given that you possess 2 quarts of gas, how much oil is necessary to add?

Step-by-step explanation:

1. Let's examine the provided information to accurately answer the question:

Ratio = 2.4 fluid ounces of oil per gallon of gasoline

Gas amount on hand = 2 quarts

2. Determine the required amount of oil:

Since 1 liquid gallon equals 4 liquid quarts, we can reformulate the ratio:

Ratio = 2.4 ounces of oil for 4 quarts of gasoline

By substituting our actual gas amount:

Ratio = 1.2 ounces of oil for 2 quarts of gasoline (this is derived from halving both the oil and gas quantities)

Therefore, we should add 1.2 fluid ounces of oil

Answer:

Step-by-step explanation:

Hello!

To determine whether boys excel in math classes compared to girls, two random samples were collected:

Sample 1

X₁: score achieved by a boy in calculus

n₁= 15

X[bar]₁= 82.3%

S₁= 5.6%

Sample 2

X₂: score obtained by a girl in calculus

n₂= 12

X[bar]₂= 81.2%

S₂= 6.7%

To estimate a confidence interval for the difference between the average percentages of boys and girls in calculus, it's essential that both variables come from normally distributed populations.

For utilizing a pooled variance t-test, it is also required that the population variances, though unknown, are assumed to be equal.

The confidence interval can then be calculated with:

[(X[bar]_1 - X[bar]₂) ± * ]

[(82.3 - 81.2) ± 1.708 * (6.11 * ]

[-2.94; 5.14]

Using a 90% confidence level, the interval [-2.94; 5.14] is expected to encompass the true difference between the average percentages achieved by boys and girls in calculus.

I hope this is of assistance!

There are 0.015 kilograms in 15 grams. Since each can weighs 0.015 kg and the payment rate is 50p per kilogram, 0.015 multiplied by 66 amounts to 1 kilogram! Therefore, 66 cans are needed to generate one kilogram. As a result, earning £15 would mean that with 2 kg equating to one dollar, then 15 multiplied by 2 equals 30. Consequently, 66 times 30 gives 1980!

66 relates to each kilogram, and 30 indicates how many 50p are required for one dollar!

Thus, to obtain £15, Adam has to recycle a total of 1980 cans!

Answer: The correct choice is (C) A = {1, 2, 3, 4, 5, 7, 8}.

Step-by-step explanation: We have eight identical slips of paper, each numbered from one to eight, which have been mixed inside a bag.

The sample space, S is as follows:

S = {1, 2, 3, 4, 5, 6, 7, 8}.

Subset A consists of the complement of the event where the number 6 is drawn.

Let 'B' denote the event of drawing the number 6.

Thus, B = {6}.

Since 'A' represents the complement of 'B', it will include all elements in the sample space 'S' that are not part of set 'B'.

Therefore,

A = B' = {1, 2, 3, 4, 5, 7, 8}

So, A = {1, 2, 3, 4, 5, 7, 8}.

Consequently, (C) is the correct choice.

Assuming arcs are measured in degrees, let S represent the following sum:

S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°


By rearranging, S can be reformulated as

S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°

S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360°          (i)


However, for any real k,

sin(360° – k) = – sin k


Thus,

S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°

S results in 0 + 0 +... + 0 + 0 + 0        (... since sine of 180° and 360° are both equal to 0)

Therefore, S equals 0.


Each pair within the brackets negates itself, leading the sum to total zero.

∴   sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0.          ✔


I hope this clarifies things. =)


Tags:  sum summatory trigonometric trig function sine sin trigonometry