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uppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.2 and a standard deviation of 1.49. Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

Answers

Answer 1

Answer:

Answer:

99.85% of American women have shoe sizes that are less than 12.67

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 8.2

Standard deviation = 1.49

Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

12.67 = 8.2 + 3*1.49

12.67 is 3 standard deviations above the mean.

Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above. Of those 50% above, 99.7% are between the mean and 12.67. So

0.5 + 0.997*0.5 = 0.9985

99.85% of American women have shoe sizes that are less than 12.67

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Arrange the four expressions in ascending order of their values when x = -2.

Answers

Answer:

3-1 2-4 1-3 4-2

Step-by-step explanation:

If h(x) = -2x+5/4, find h(x) = 3/4

Answers

Answer:

$x=(1)/(4)$

Step-by-step explanation:

So we have the function:

$h(x)=-2x+(5)/(4)$

And we want to find h(x)=3/4.

So, we want to find the value of x such that h(x) equates to 3/4.

So, substitute 3/4 for h(x):

$(3)/(4)=-2x+(5)/(4)$

First, subtract both sides by 5/4. The right will cancel.

$(3)/(4)-(5)/(4)=-2x+(5)/(4)-(5)/(4)$

Subtract on the left:

$-(2)/(4)=-2x$

Reduce on the left:

$-(1)/(2)=-2x$

Now, multiply both sides by -1/2. The right will again cancel:

$-(1)/(2)(-(1)/(2))=-(1)/(2)(-2x)$

Multiply on the left:

$x=(1)/(4)$

So, for h(x) to be 3/4, the value of x is 1/4.

And we're done!

Answer:

x = 1/4

Step-by-step explanation:

We are given the function as h(x) = - 2x + 5/4. If we have to determine h(x) = 3/4 given this function, let's substitute this value into our function and solve for 'x.' This will be our solution -

3/4 = - 2x + 5/4,

If we subtract 5/4 from either side : - 2x = - 1/2

Now divide either side by - 2 : x = 1/4

Therefore our solution is x = 1/4

(1 point) For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt . A) Let r(t)=(cos4t,sin4t)Let r(t)=(cos⁡4t,sin⁡4t). Then r′(π4)r′(π4)= ( , )? B) Let r(t)=(t2,t3)Let r(t)=(t2,t3). Then r′(5)r′(5)= ( , )? C) Let r(t)=e4ti+e−5tj+tkLet r(t)=e4ti+e−5tj+tk. Then r′(−5)r′(−5)= i+i+ j+j+ kk ?

Answers

Answer:

(a)

$r'(\frac \pi 4) =(0.-4)$

(b)

r'(5)= (10,75)

(c)

$r'(-5) =4 e^(-20)\hat i-5e^(25)\hat j+\hat k$

Step-by-step explanation:

(a)

Give that,the position vector is

r(t) = (cos 4t, sin 4t)

Differentiating with respect to t

r'(t) = (-4sin 4t, 4 cos 4t) [ $(d)/(dt) cos mt = -m \ sin \ mt$ and $(d)/(dt) sin mt = m \ cos \ mt$ ]

To find the $r'(\frac\pi 4)$ , we put $t=\frac \pi4$

$r'(\frac\pi 4) = (-4sin (4.\frac \pi 4), 4 cos (4.\frac \pi 4))$

=(0, -4)

(b)

Give that,the position vector is

r(t) = (t²,t³)

Differentiating with respect to t

r'(t) = (2t, 3t²)

To find r'(5) , we put t=5

r'(5) = (2.5,3.5²)

= (10,75)

(c)

Given position vector is

$r(t) = e^(4t)\hat i+e^(-5t)\hat j+t\hat k$

Differentiating with respect to t

$r'(t) =4 e^(4t)\hat i+(-5)e^(-5t)\hat j+\hat k$

$\Rightarrow r'(t) =4 e^(4t)\hat i-5e^(-5t)\hat j+\hat k$

To find r'(-5) , we put t= - 5 in the above equation

$r'(-5) =4 e^(4.(-5))\hat i-5e^(-5.(-5))\hat j+\hat k$

$\Rightarrow r'(-5) =4 e^(-20)\hat i-5e^(25)\hat j+\hat k$

For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt are:

$A) r' (\pi /4) = (0, -4) \nB) r'(5) = (10, 75)\nC) r'(-5) = (4e^(-20), -5e^(25), 1)$

To compute the velocity vector, we need to find the derivative of the position vector with respect to time (t). This will give us the tangent velocity vector.

A) Let r(t) = (cos⁡4t, sin⁡4t).

To find r'(t), we take the derivative of each component with respect to t:

r'(t) = (d/dt (cos⁡4t), d/dt (sin⁡4t))

r'(t) = (-4sin⁡4t, 4cos⁡4t)

To find r'(π/4), we substitute t = π/4 into r'(t):

r'(π/4) = (-4sin⁡(4(π/4)), 4cos⁡(4(π/4)))

r'(π/4) = (-4sin⁡π, 4cos⁡π)

r'(π/4) = (0, -4)

B) $Let \ r(t) = (t^2, t^3).$

To find r'(t), we take the derivative of each component with respect to t:

$r'(t) = (d/dt (t^2), d/dt (t^3))\nr'(t) = (2t, 3t^2)$

To find r'(5), we substitute t = 5 into r'(t):

$r'(5) = (2(5), 3(5)^2)\nr'(5) = (10, 75)$

C) Let $r(t) = e^(4t)i + e^(-5t)j + tk.$

To find r'(t), we take the derivative of each component with respect to t:

$r'(t) = (d/dt (e^(4t)), d/dt (e^(-5t)), d/dt (t))]\n\nr'(t) = (4e^(4t)), -5e^(-5t), 1)$

To find r'(-5), we substitute t = -5 into r'(t):

$r'(-5) = (4e^(4{-5}), -5e^(-5(-5)), 1) \n\nr'(-5) = (4e^(-20), -5e^(25), 1)$

So, the answers are:

$A) r' (\pi /4) = (0, -4) \nB) r'(5) = (10, 75)\nC) r'(-5) = (4e^(-20), -5e^(25), 1)$

To know more about vectors:

brainly.com/question/33923402

#SPJ3

22 - x/2 =14 ........

Answers

Answer:

x=16

Step-by-step explanation:

PLEASE QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Which number completes the system of linear inequalities represented by the graph? y > 2x – 2 and x + 4y > -12 -3 4 6

Answers

Answer:

-12

Step-by-step explanation:

Edge 2021

1/2 minus 2/3
I have trouble with fractions

Answers

Answer:

-1/6

Step-by-step explanation:

Hope this helps down below! Pls mark brainliest

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(12×33)−(23×22)=?

Complete the multiplication and the equation becomes

36−46=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

3−46=−16

This fraction cannot be reduced.

Therefore:

12−23=−16

Solution by Formulas

Apply the fractions formula for subtraction, to

12−23