A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s = 17.7 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?

Click the picture to view a partial table of critical values.

A.) 99% confidence level requires _____ subjects. (Round up to the nearest subject.)

B.) 95% confidence level requires _____ subjects. (Round up to the nearest subject.)

C. How does the decrease in confidence affect the sample size required?

A. The sample size is the same for all levels or confidence .
B. Decreasing the confidence level decreases the sample size needed*
C. Decreasing the confidence level increases the sample size needed

Answer:

m = 7/6

Step-by-step explanation:

Find coordinates of two points:

(-2,3)

(-8,-4)

Slope formula =

y1 - y2 / x1 - x2

So...

-4-3 / -8 -- 2

-7 / -6

7/6

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George needs to fix the expression because if you did the equation as is, it wouldn't subtract the added value from 15.

George always requires $1.48.

The order of operations exists as a law that tells the correct sequence of measures for considering a math expression. We can determine the mandate utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).

Given: George tries to purchase a movie ticket ($9.00), a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each)

9 + 2.65 + 1.35 + 1.74 + 1.74 = 16.48

Subtract 15 to 16.48

15 - 16.48 = 1.48

George always needs $1.48.

Therefore, the proper answer is $1.48.

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The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

Rs. 4200

Step-by-step explanation:

If Ramesh buys 10 containers, each for 150, we can add 150 + 150 + 150 + 150 + 150 + 150 + 150 + 150 + 150 + 150 (there's ten 150's).

Or, instead of doing a lot of adding, we can use multiplication (repetitive addition is the same thing as multiplication; but instead of adding over and over again, we multiply by how many "groups" of the number that we have. For example, let's say that our group size is 150. If we buy 10 containers, we have bought 10 x 150 containers.)

So, we can use 10 x 150 for the first ten containers. However, we can solve this problem in a slightly more practical way. We can first add the total amount of containers (the total amount of "groups" of 150), 10 + 18 = 28.

So, to solve this equation, we are finding 28 x 150.

150 x 28 = 4200

(150 = size of "group"/price of container)

(28 = amount of "groups"/containers)

So, the total amount of money spent by Ramesh is Rs. 4200

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

108 cube

Step-by-step explanation:

the volume of one cube is (1/3)^3 = 1 / 27

1/27X = 4

X = 108

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Orbital period of the planet is 2√2 earth years

According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its semi major axis.  

T² α a³

where, T is orbital period and a is length of semi-major axis.

Given,

Distance between the sun and the planet

= twice the distance of sun and earth

Let distance between sun and earth a₁ = d

then distance between planet and sun a₂= 2d

Orbital period of earth T₁ = 1 earth year

By Kepler's third law

T² α a³

(T₁/T₂)² = (a₁/a₂)³

(1/T₂)² = (D/2D)³

1/T₂² = 1/8

T₂ = 2√2 earth years

Hence, 2√2 earth years is the orbital period of other planet.

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Answer:

Step-by-step explanation:

The center is halfway between vertices, at (4, -6).

It is also halfway between foci.

:::::

The vertices are vertically aligned, so the parabola is vertical.

General equation for a vertical ellipse:

 (y-k)²/a² + (x-h)²/b² = 1

with

 center (h,k)

 vertices (h,k±a)

 co-vertices (h±b,k)

 foci (h,k±c), c² = a²-b²

Apply your data and solve for h, k, a, and b.

center (h,k) = (4, -6)

h = 4

k = -6

vertices (4,-6±a) = (4,-6±9)

a = 9

foci (4,-6±c) = (4,-6±5√2)

b² = a² - c² = 9² - (5√2)² = 31

b = √31

The equation becomes

 (y+6)²/81 + (x-4)²/31 = 1

:::::

length of major axis = 2a = 18

length of minor axis = 2b = 2√31

The various parts of the question needs to be answered.

Center: (4,-6)

Standard equation: \(\dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1\)

Length of major axis: 18 units

Length of minor axis: \(2\sqrt{31}\ \text{units}\)

Graph is attached.

The Vertices are of the form

\((h,k\pm a)=(4,-6\pm 9)\)

This means that the ellipse is symmetrical to the y axis.

The center of an ellipse is given by \((h,k)\)

So, here the center is \((4,-6)\)

\(a=\pm 9\)

The foci are of the form

\((h,k\pm c)=(4,-6\pm 5\sqrt{2})\)

So, \(c=\pm 5\sqrt{2}\)

\(b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{9^2-(5\sqrt{2})^2}\\\Rightarrow b=\pm\sqrt{31}\)

The standard equation for major axis being parallel to y axis is given by

\(\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1\)

Length of major axis is

\(2a=2\times 9\\ =18\ \text{units}\)

Length of minor axis is

\(2b=2\sqrt{31}\ \text{units}\)

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Answer: V≈56.55

Step-by-step explanation:

V=πr2h

3 = radius

2=height

Fill in the formula = V=πr2h=π·32·2≈56.54867

V≈56.55

Answer:

22.5 degrees.

Step-by-step explanation: Just change the half to 0.5 so then times 4.5 times 5.

Answer:

22 1/2

Step-by-step explanation:

I did the quiz

Answer: The numbers are 25 and 68.

Step-by-step explanation:

Answer:

x = 68

y = 25

Step-by-step explanation:

Let the larger number be x and smaller number be y.

x = 18 + 2y ----------------(1)

x + y = 93 -----------------(2)

Put Eq. (1) in Eq. (2)

18 + 2y + y = 93

18 + 3y = 93

Subtract 18 to both sides

3y = 93 - 18

3y = 75

Divide 3 to both sides

y = 72/3

Put y = 24 in Eq. (1)

x = 18 + 2(25)

x = 18 + 50

\(\rule[225]{225}{2}\)

Answer:

4 1/3

Step-by-step explanation:

Subtract to find the difference.

Answer:

4 1/3

Step-by-step explanation:

7 - 2 2/3 = 4 1/3

The point on the line closest to the given point is (71/21, 20/21). The solution has been obtained by using the concept of slope of line.

What is a slope?

In mathematics, the slope of a line is calculated by dividing the change in y coordinate by the change in x coordinate.

We are given equation of line as 2x + 5y - 2 = 0

On simplifying it, we get

⇒2x + 5y = 2

⇒5y = -2x + 2

⇒y = -2x/5 + 2/5

Slope of the line is -2/5.

Now, slope of the line perpendicular to this will be 5/2.

So, equation of the line which passes through (-5,-5) and has a slope of 5/2 is as follows

⇒y + 5 = 5/2 (x + 5)

⇒2y + 10 = 5x + 25

⇒5x - 2y + 15 = 0

Now, the point of intersection of the two lines is

⇒(5x + 15)/2 = (2x - 2)/5

⇒25x + 75 = 4x - 4

⇒21x = 71

⇒x = 71/21

On substituting this, we get

y = 20/21

Hence, the point on the line closest to the given point is (71/21, 20/21).

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Answer:

The brightest star in the night sky is Sirius, located 500,000 times further away than the sun. Sirius is also 20 times brighter than the sun, which is why it is so easy to see at night. Our sun is a medium star of average size and brightness.

We can use polynomial long division to find the remainder of the expression (5x^3 + 7x + 5) divided by (x + 2). The steps are as follows:

5x^2 - 3x + 19

       ____________

x + 2 | 5x^3 + 7x + 5

      - (5x^2 + 10x)

      ______________

              -3x + 5

              -(-3x - 6)

              ________

                    11

Therefore, the remainder of (5x^3 + 7x + 5) divided by (x + 2) is 11.

Answer:

The remainder of the polynomial equation is -49

Step-by-step explanation:

The area, in square inches, of the painted face of the brick is; 144 in²

The area of a square is given by;

A = L²

where;

L is the length of the side of the square

The sides of a square all have the same length, and as such we just need to find the length of one side.

The length of the side of the square here is the distance between two vertices, which can be calculated as

L = √[(x₂ - x₁)² + (y₂ - y₁)²]

However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;

Horizontal length = (6 + 6) = 12

Thus;

Area = L² = 12² = 144 in²

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Answer:

Step-by-step explanation:

66

Answer:

.

Step-by-step explanation:

Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Answer:

he would be able to ride 4 miles

Step-by-step explanation:

20/5=4

The biker ride 4 miles in one hour.

The slope of a line can be calculated using the formula:

Slope = (change in y-coordinates) / (change in x-coordinates)

We can take two point from the graph as (0, 0) and (2, 8)

So, Slope = (change in y)/ (change in x)

Now, putting the values as

Slope= (8-0)/ (2-0)

Slope= 8/2

slope= 4

Thus, the biker ride 4 miles in one hour.

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Answer:

the anwer is 1/2

Step-by-step explanation:

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

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To solve for 1/x(x-3) = 2/(x-3) + 3/x, we can simplify and rearrange the terms on the right side:

1/x(x-3) = 2/(x-3) + 3/x

Multiplying both sides by x(x-3):

1 = 2x + 3x(x-3)/x

Expanding the right side:

1 = 2x + 3x^2 - 9x/x

Cancelling x from the right side:

1 = 2x + 3x^2 - 9

Dividing both sides by x^2:

1/x^2 = 2/x + 3 - 9/x^2

Rearranging the terms:

1/x^2 - 9/x^2 = 2/x + 3

Isolating the x terms:

-8/x^2 = 2/x + 3

Multiplying both sides by x^2:

-8 = 2x + 3x^2

Expanding the right side:

-8 = 2x + 3x^2

Rearranging the terms:

3x^2 + 2x + 8 = 0

This is a quadratic equation and can be solved using the quadratic formula or factoring. The solutions are the values of x that make the equation equal to zero.

Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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