Which of the following is a rational number?

Answers

Answer 1

Answer:

Answer:

A, B, D are the answers

Step-by-step explanation:

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Insert four arithmetic means between -1 and 14

Answers

Answer:

Step-by-step explanation:

d = 7%2F2

-2, -2+7%2F2, -2+2%287%2F2%29, -2+3%287%2F2%29, 12

-2, -4%2F2+7%2F2, -4%2F2+14%2F2, --4%2F2+21%2F2, 12

-2, 3%2F2, 10%2F2, 17%2F2, 12

-2, 3%2F2, 5, 17%2F2, 12

Is the sum of two rational number is 5/18 if one of the number is 1/8 find the other

Answers

Answer: 4/8

Step-by-step explanation:

Equation: 1/8+x=5/18

-1/8 -1/8

x=4/8

Double Check: 4/8+1/8=5/8

Cos3x+cosx=2cos2xcosx

Answers

$cos(3x)+cos(x)=2\cdot cos\left((3x+x)/(2)\right)\cdot cos\left((3x-x)/(2)\right)=2\cdot cos(2x)\cdot cos(x).$

Green eyes.

Grandma Gertrude's Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. In order to determine the mean percentage of cacao in its dark chocolate products, quality inspectors sample 36 pieces. They find a sample mean of 60% with a standard deviation of 8%. What is the correct value of t to construct a 90% confidence interval for the true mean percentage of cacao? (Round to the nearest thousandth.)Select Answer:
A. (0.577, 0.623)
B. (0.539, 0.561)
C. (0.527, 0.573)
D. (0.589, 0.611)

Answers

Answer with explanation:

Given : Sample size : n = 36

Significance level for 90% confidence : $\alpha: 1-0.9=0.1$

Sample mean : $\overline{x}=0.60$

Standard deviation : $\sigma=0.08$

By using standard normal table for t-values,

Critical t-value : $t_((n-1, \alpha/2))=t_((35,\ 0.05))=1.690$

Thus, the correct value of t to construct a 90% confidence interval for the true mean percentage of cacao : $t_((35,\ 0.05))=1.690$

Confidence interval for population mean :

$\overline{x}\pm t_((n-1, \alpha/2))(\sigma)/(√(n))\n\n=0.60\pm(1.69)(0.08)/(√(36))\n\n=0.60\pm0.0225333333333\n\n\approx0.60\pm0.023\n\n=(0.60-0.023,\ 0.60+0.023)=(0.577,\ 0.623)$

Hence, A is the correct answer .

In order to keep a boat from drifting away, the boat is tied to a pier with a 60-foot rope. When the boat drifts as far from the pier as the rope will allow, the rope forms a 15° angle relative to the horizontal water line.To the nearest foot, find the maximum horizontal distance, d, that the tied-up boat can drift from the pier.

Answers

A right triangle will be formed upon sketching the given scenario with the rope as the hypotenuse. So, using the cosine function:

cos 15 = d/60
d = 60 cos 15
d= 57.96 ft

Therefore, the maximum horizontal distance that the tied-up boat can drift from the pier is 58 ft.

Answer:

58 feet

Step-by-step explanation:

Just finished this lesson and checked the answer key.

A circle has an area of 36π in2. What is the area of a sector of the circle that has a central angle ofπ 6?

A)3 in2
B)6 in2
C)12 in2
D)196 in2

Answers

A central angle : π / 6 = 30 °
30 ° = 360 ° / 12
The area of the sector is 1/12 of the area of a circle.
Therefore area of the sector is:
A = 36 π / 12 = 3 π
Answer: A ) 3 π in²

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Area of a circle = 36π in²

As we know the formula for "Area of circle ":

$Area=\pi r^2\n\n36\pi=\pi r^2$

Now, we need to calculate the area of sector.

As we know the formula for "Area of sector":

$Area\ of\ sector=(\theta)/(360\textdegree)\pi r^2\n\nArea\ of\ sector=(30)/(360)* 36\pi \n\nArea\ of\ sector=(1)/(12)* 36\pi\n\nArea\ of\ sector=3\pi\ in^2$

Hence, Option 'A' is correct.

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