MATHEMATICS COLLEGE

Please help me with this real quick

Answers

Answer 1

Answer:

Answer: 7.5 miles

Step-by-step explanation:

think of it as a triangle; the bold line is the hypotenuse, or x.

8 |\ x

|_\ it's not a good triangle but you get the point

and then get out pythagorean theorem: a^2+b^2=c^2

put the numbers in: 8^2 + 6^2 = x^2

do some math:

64+36=x^2

100=x^2 (and then find square root)

10=x

BUT, it said each unit was 3/4 of a mile, so we must multiply 10 by 3/4 to get the actual distance, which is 7.5

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A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat

Answers

Answer:

2 servings of salad and 1 serving of soup

Step-by-step explanation:

In the given scenario the aim is to minimise the fat content of the food combination.

Fat content of soup is 3mg while fat content of salad is 2 mg.

Using Soup as 0 and Salad as 2 will not give the required vitamin content

The logical step will be to keep servings of soup to the minimum.

Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1

1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.

This will not work because amount of vitamin B complex is not up to 10 mg

2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat

This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.

Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving

Patients come into a medical clinic have a mean weight of 207.6 pounds with a standard deviation of 22.6 pounds. the distribution of weight is not assumed to be symmetric. between what two ways does Chebyshev's Theorem guarantee that we will find at least 95% of the patients? Round your answers to the nearest 10th

Answers

I know the answer it is 98.2

Answer: 105.9 lbs and 309.3 lbs

Step-by-step explanation:

By Chebyshev's Theorem, the proportion of patients with weights within 4.5 standard deviations of the mean is at least 95%. Therefore k=4.5.

The weight that is 4.5 standard deviations less than the mean is 207.6−4.5(22.6)=105.9 pounds.

The weight that is 4.5 standard deviations greater than the mean is 207.6+4.5(22.6)=309.3 pounds.

So at least 95% of the patients have weights between 105.9 and 309.3 pounds.

Renya plans to make a down payment plus monthlypayments in order to buy a motorcycle. At one dealer
she would pay $2,450 down and $175 each month. At another dealer, she would pay $3,050 down and
$150 each month. After how many months would the total amount paid be the same for both dealers?
What would that amount be?
After months Kenya will have paid $ for the bike at elther dealer. PLS HELP ASAP

Answers

Answer:

For the first, it would take 6 months to reach $3,500. For the second dealer, it would take 3 months to reach $3,500.

Explanation:

I hope this helps!

How many inches are in 3 feet 8 inches

Answers

Answer:

Step-by-step explanation:

3 x 12 = 36 + 8 = 44

Please answer both of them questions please no links or you will be reported

Answers

if ur a u r so good but bot a good

Find the length of the curve. R(t) = 2 i + t2 j + t3 k, 0 ≤ t ≤ 1

Answers

Length of a curve is the length of its plot its curve. The length of the given curve for given range of t is: L = 1.44 units approx.

How to find the length of a curve?

If the curve has position vector p(x) for value of x ranging from x = a to x = b,

then, the curve's length is calculated as:

$L = \int_a^b ||p'(x)||dx\n$ units.

For the given case, we have:

Position vector = $R(t) = 2\hat i + t^2 \hat j + t^3 \hat k$

Its differentiation gives:

$R'(t) = 2t\hat j + 3t^2\hat k$

Its non negative magnitude is: ||R'(t)|| = $√((2t)^2 + (3t^2)^2) = t√(4+9t^2)$

Thus, as t ranges from a = 0 to b = 1, thus, length of the curve is:

$L = \int_0^1 (t√(4+9t^2))dt\n\n\text{Let v = 4+9}t^2, \text{then dv = 18tdt}\nand\nt=0\implies v = 4\nt=1 \implies v = 13\nThus,\nL = \int_4^(13)((√(v))/(18))dv = (1)/(18) [(2(v)^(3/2))/(3)]^(13)_4 \approx (38.87)/(27) \approx 1.44 \: \rm units$