An article on the relation of cholesterol levels in human blood to aging reports that average cholesterol level for women aged 70-74 was found to be 230m/dl. If the standard deviation was 20mg/dl and the distribution normal, what is the probability that a given woman in this age group would have a cholesterol level
a) Less than 200mg/dl
b) More than 200mg/dl
c) Between 190mg/dl and 210mg/dl
d) Write a brief report on the guidance you would give a woman having high cholesterol level in this age group

Answer:

a.14

Step-by-step explanation:

2+2 =4

7+7= 14

I hope it helpful

Answer:

5⁷

Step-by-step explanation:

5³×5⁴

when bases are same powers are added

so..

5(³+⁴)

5⁷

Answer:

5^7

Step-by-step explanation:

Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)

You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!

Answer:

Okay that would be A) -3/5.

Answer:

Step-by-step explanation:

5

The tangent point and a second tangent point of a line with the same slope as the given line are (2.67, 6) and (2.57, 6.1).

The slope of the given line is -0.75.

The radius of the circle is |6 - 1.25| / -0.75 = 7.

The equation of the tangent line is y = -0.75x + c.

Substituting the coordinates of the center of the circle into this equation, we get 6 = -0.75 * 2 + c

Solving for c, we get c = 8.

The equation of the tangent line is y = -0.75x + 8.

The point of tangency is the point where the tangent line intersects the circle. To find the point of tangency, we need to solve the equation of the tangent line for x.

y = -0.75x + 8

6 = -0.75x + 8

-2 = -0.75x

x = 2.67

The point of tangency is (2.67, 6).

The second tangent point is the point where the tangent line intersects the circle at a different location. The direction of the tangent line is the same as the direction of the vector (-0.75, 1).

We can move the point of tangency a small distance in the direction of the tangent line by adding a small multiple of the vector (-0.75, 1) to the point of tangency.

Let's add a multiple of 0.1 to the point of tangency.

(2.67, 6) + 0.1 * (-0.75, 1)

= (2.57, 6.1)

The second tangent point is (2.57, 6.1).

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The line y = - 0.75x + 1.25 is tangent to a circle whose center is located at (2, 6) Find the tangent point and a second tangent point of a line with the same slope as the given line

Answer:

yes

Step-by-step explanation:

Answer:

trueeeeeeee

Step-by-step explanation:

hope this helps

The maximizing value of x is approximately 2.

What is the maximum value of x that maximizes the utility function \(U(x, y) = \sqrt{x} y,\) given the budget constraint 10x + 9y ≤ 35?

The maximum value of x, rounded to one decimal place, that maximizes the utility function is approximately 2.0. This value is obtained by solving the optimization problem using Lagrange multipliers and considering the budget constraint.

To maximize the utility function subject to the budget constraint 10x + 9y ≤ 35, we can use the method of Lagrange multipliers. We want to maximize the function U(x, y) subject to the constraint 10x + 9y ≤ 35.

The Lagrange function is defined as \(U(x, y,\lambda) = \sqrt{x} y+\lambda(35-10x-9y),\), where λ is the Lagrange multiplier.

To find the maximum, we need to find the values of x, y, and λ that satisfy the following equations:

\(1.\frac{\delta L}{\delta x }= 0\\\\2.\frac{\delta L}{\delta y}= 0\\\)

3.Constraint equation: 10x + 9y = 35

Taking partial derivatives and setting them equal to zero:

\(1.\frac{\delta L}{\delta x }= \frac{1}{2}\sqrt{y}+ \lambda(-10) = 0\\\\2.\frac{\delta L}{\delta y }= \frac{1}{2}\sqrt{x} +\lambda(-9) = 0\)

Solving these equations, we get:

\(\sqrt{y }= 5\lambda\\\\\sqrt{x} = 4.5\lambda\)

Squaring both equations:

\(y = 25\lambda^2\\\\x = 20.25\lambda^2\)

Substituting these values into the constraint equation:

\(10x + 9y = 10(20.25\lambda^2) + 9(25\lambda^2)\\ = 350\lambda^2\)

Setting this equal to 35:

\(350\lambda^2 = 35\)

Simplifying, we find:

\(\lambda^2 = 0.1\)

Taking the square root of both sides:

\(\lambda = \pm\sqrt{0.1}\)

Since λ must be positive, we take \(\lambda= \sqrt{0.1 }= 0.3162.\)

Substituting this value into\(x = 20.25{\lambda}^2\), we get:

\(x = 20.25(0.3162)^2= 2.03\)

Therefore, rounding to one decimal place, the maximizing value of x is approximately 2.

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Answer:

It is 2/15

Step-by-step explanation:

\( = \sqrt{ \frac{1}{ {6}^{2} } - \frac{1}{ {10}^{2} } } \\ \\ = \sqrt{ \frac{4}{225} } \\ \\ = \frac{ \sqrt{4} }{ \sqrt{225} } \\ \\ = \frac{2}{15} \)

The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.

Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:

Diameter in kilometers = Diameter in miles × Conversion factor

Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile

Diameter in kilometers = 12,681.6 kilometers

Rounding this value to the nearest whole number, we get 12,682 kilometers.

Therefore, the correct answer is option D: 12,682 km.

Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.

Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.

Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.

In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

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Answer:

(7, 0) The pool will be Empty

Step-by-step explanation:

It's leaking 5 liter each minute, by the time it gets to 7 minutes, it'll be empty

I think

Answer:

A. (7, 0); The time it takes to empty the water in the pool.

Step-by-step explanation:

2.5 pounds per square foot

Examples: 16 ga CRS is 2.5 pounds per square foot.

So, 40.035

Answer:

y= P(0.87)^t

Step-by-step explanation:

Given data

Price P=  $24,000

Rate of decay in price= 13%

The expression in terms of y, p and t  is

y=P(1-r)^t

y= P(1-0.13)t

y= P(0.87)^t

Answer:

A= 2,2

B= 0,0

C= -2,2

here is your answer

Answer:

5.6

Step-by-step explanation:

....................

Answer:

3x+1 = 5y+9=61

Step-by-step explanation:

All three of these angles are equal to each other as the figure is a pair of parallel lines with a line through the middle. This means that the angles opposite to each other are equal, thus 61 = 3x + 1. 5y+9 = 61 from the same definition as the lines are parallel. We can also find that it's equal to 61 as 180=119+5y+9.

Thus, x = 20 and y = 52/5

Answer:

-3x + 7

Step-by-step explanation:

Divide -8x + 6    into   the product   to find the other is -3x+7

Answer:

I believe ... yes

Step-by-step explanation:

Answer:

fraction form- 372/100

decimal- 3.72

Step-by-step explanation:

Answer:

Step-by-step explanation:

dddfykb

Answer:1,050

Step-by-step explanation:

Answer:

the next terms are 2.8 , 2.5 and 2.2

Answer:

a

Step-by-step explanation:

Answer:

Check to see if each input value is paired with only one output value. If so, the table represents a function.

Yes. It is a function.

Step-by-step explanation:

Answer:

graph C

Step-by-step explanation:

Well I lik it spread out cause you get more information and you can tell how the data is aligned and not scrunched up. Since the example said that the explanatory variable (indepdent variable) is best on the X axis, only C and A are left. A is all scrunch’s up and data could be read worng, but C is nice and spread and it shows all the data and rating clearly

The probability that the random variable with a normal distribution with μ = 30 and σ = 5 will take on a value less than 32 is approximately 0.6554.

To find the probability that the random variable will take on a value less than 32, we need to use the standard normal distribution. We can first standardize the value of 32 using the formula:

z = (x - μ) / σ

where x is the value we're interested in, μ is the mean, and σ is the standard deviation. Plugging in the values we have:

z = (32 - 30) / 5 = 0.4

Now we can use a standard normal distribution table or calculator to find the probability that a standard normal variable is less than 0.4. From the table, we find that this probability is approximately 0.6554.

The probability that the random variable with a normal distribution with μ = 30 and σ = 5 will take on a value less than 32 is approximately 0.6554.

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The task is to find the convolution of the marginal distributions of two independent random variables x and y with identical geometric distributions.

To find the convolution of the marginal distributions of x and y, we need to calculate the probability distribution function of the sum of x and y. Since x and y have identical geometric distributions, we know that the probability of x=k and y=m is given by p(x=k, y=m) = (1-p)^k * p * (1-p)^m * p = p^2 * (1-p)^(k+m), where p is the probability of success in each trial of the geometric distribution.

To find the probability distribution function of the sum Z=x+y, we need to compute the probability of each possible value of Z. That is, P(Z=k) = Σ P(X=i, Y=k-i) for all i from 0 to k. Plugging in the probability distribution function of x and y, we get P(Z=k) = Σ p^2 * (1-p)^(i+k-i) = p^2 * (1-p)^k * Σ 1. The summation is over all i from 0 to k, and is equal to k+1. Therefore, we have P(Z=k) = (k+1) * p^2 * (1-p)^k. This is the probability distribution function of the sum of two independent random variables x and y with identical geometric distributions, and is the convolution of the marginal distributions of x and y.

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9514 1404 393

Answer:

  3, 4

Step-by-step explanation:

If x represents the integer, then the relationship required is represented by the equation ...

  x^2 = 7x -12

  x^2 -7x +12 = 0 . . . . put in standard form

  (x -3)(x -4) = 0 . . . . . factor

The values of x that make this relation true are x=3 and x=4.

The two integers are 3 and 4.

Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

Note that: one has to derive b using the law of sine.

\(\frac{b}{sin (15)} = \frac{40}{sin 90}\)

b  = [40  x  Sin (15)] / sin (90)

So:

Sin (15) = √3−1)/(2√2

= 0.2588190451

Then: Sin (90)  = 1

So,  b  = (0.2588190451 *40)/1

= 10.35/1

= 10.35

So one has to also derive for h

= \(\frac{b}{sin (15)} = \frac{h}{sin 75}\)

Note that b = 10.35

Hence : h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]

h  = 10.35 * 3.73

h = 38.62

Using  simple trigonometric analysis, we can say that:

∠ GJH = 90°; and

∠ GHJ = 10°

Therefore, to obtain Z

Z/ Sin (90) = h/Sin (10)

(Then make Z the subject of the formula)

Thus Z = h * Sin (90)/ Sin (10)

Z = 38.62 * 1/ 0.1736

Z = 222.47m

Therefore, Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

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Answer:

$0.24

Step-by-step explanation:

7.68/32=0.24

There are 32 cups per 2 gallons. The total cost for 2 gallons is 7.68