I am a two digit number. My tens place is 8 more than my ones place.

A boat travels N 31° E for 65 miles and then N 59° W for 102 miles. Find the distance of the boat from its starting point.

ra1l [238]

The directions of travel are at right angles to each other, so the Pythagorean theorem can be used to find the straight-line distance to the starting point. That distance (d) satisfies ...

d² = 65² +102²

d = √(4225 +10404) = √14629 ≈ 120.95

The appropriate choice is ...

... c. 121 miles

4 0

2 years ago

Read 2 more answers

Suppose y = 2x + 1 , where x and y are functions of t. (a) if dx/dt = 3, find dy/dt when x = 4. dy dt = (b) if dy/dt = 2, find d

qwelly [4]

Answer:

Step-by-step explanation:

If y = 2x + 1, then dy/dt = 2(dx/dt).

If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x. y = 81.

(a) if dx/dt = 3, find dy/dt when x = 4:

Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.

(b) if dy/dt = 2, find dx/dt when x = 40:

Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.

3 0

2 years ago

3. Nutrition labels. The nutrition label on a bag of potato chips says that a one ounce (28 gram) serving of potato chips has 13

svetoff [14.1K]

Answer:

The 95% confidence interval of for this random sample is between 128.16 calories and 139.84 calories. This means that we are 95% that the mean number of calories for all bags of potato chips is in this interval.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 35 - 1 = 34

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 34 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.0322

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.0322\frac{17}{\sqrt{35}} = 5.84$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 134 - 5.84 = 128.16 calories

The upper end of the interval is the sample mean added to M. So it is 134 + 5.84 = 139.84 calories

The 95% confidence interval of for this random sample is between 128.16 calories and 139.84 calories. This means that we are 95% that the mean number of calories for all bags of potato chips is in this interval.

3 0

3 years ago

The weight of an object on a particular scale is 175.2 lbs. The measured weight may vary from the actual weight by at most 0.1 l

snow_lady [41]

Either 175.25 ( 175.2 + 0.1/2) or 175.15 ( 175.2 - 0.1/2) ----------> Range. 175.15 < weight < 175.25

5 0

3 years ago

Read 2 more answers

Each year, Kipp raises money by participating in the Walk for Breast Cancer. Last year, Mr. Madrid walked at a pace of 12 miles

Ilia_Sergeevich [38]

A.

The rate is 12:2

B.

Set up a proportion:

12/2 = x/5

Multiply 5 to both sides:

60/2 = x

Divide:

30 = x

So he will walk 30 miles in 5 hours.

C.

To find out, we can divide 12 / 2.

12 / 2 = 6 miles per hour

8 0

3 years ago