Determine the sample size required to estimate the mean score on a standardized test within 5 points of the true mean with 99% confidence. assume that s=17 based on earlier studies.

Answer:

y = sin(4x) + 3

Step-by-step explanation:

y = Asin(Bx + C) + D

A is amplitude = 1

B = 2pi/period = 2pi / (pi/2) = 4

C does not mention.

D: shift up or down = 3

=> y = sin(4x) + 3

The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.

Let's denote:

- [tex]\( x \)[/tex] as the length of one side of the square (in feet).

- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.

1. Area of the Square [tex](\( A_s \))[/tex]:

The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].

2. Area of the Circle [tex](\( A_c \))[/tex]:

The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:

[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]

Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]

The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].

Substituting the value of [tex]\( r \)[/tex], we get:

[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]

[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]

Answer:

The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Step-by-step explanation:

Given  : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

To find : The four angles of the quadrilateral are °, °, °, and °, respectively.

Solution : We have given that  The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

Let the angle of the quadrilateral is x

Then all the  angles are  x  , 2x , 5x ,4x

Complete angle formed by circle is 360 °

Sum of all the angle are 360

x + 2x + 5x + 4x = 360 .

12 x = 360 .

On dividing both sids by 12.

x = 30 .

Then

2x =  60

5x = 5 * 30 = 150 .

4x = 4 *30 = 120 .

Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Answer:

for plato users the answers are 45,75,135,105

Step-by-step explanation:

i = [tex]p(0) = \frac {3} {8} x \frac {2} {7} = \frac {3} {28} ; p (1) = \frac {3} {8} x \frac {5} {7} + \frac {5} {8} x \frac {3} {7} = \frac {15} {28}; p (2) = \frac {5} {8} x \frac {4} {7} = \frac {5} {14} [/tex]

(a)  i. The probability mass function of X is 5 / 14

Hypergeometric Distribution is the probability distribution of a hypergeometric random variable.

The hypergeometric distribution is used to calculate the statistical importance of having drawn a specific k successes (out of n total draws) from the aforementioned population in the hypergeometric test uses.

ii. Please see attached image for the answer.

To find the probability distribution for x, consider the possible values of x and calculate the probability of each value. When 2 marbles are drawn without replacement, there are two possible outcomes. The probability distribution for x is P(x = 0) = 3/28, P(x = 1) = 15/56, and P(x = 2) = 5/14.

To find the probability distribution for x, we need to consider the possible values of x and calculate the probability of each value.

Since there are 5 white marbles and 3 black marbles in the urn, the total number of marbles is 8.

When 2 marbles are drawn without replacement, there are two possible outcomes: (1) both marbles are white and (2) one marble is white and one marble is black.

Let's calculate the probabilities:

P(x = 0) = P(both marbles are black) = (3/8) * (2/7) = 6/56 = 3/28

P(x = 1) = P(one marble is white and one marble is black) = (5/8) * (3/7) = 15/56

P(x = 2) = P(both marbles are white) = (5/8) * (4/7) = 20/56 = 5/14

Therefore, the probability distribution for x is:

P(x = 0) = 3/28

P(x = 1) = 15/56

P(x = 2) = 5/14

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)

15-3 =12

16-7=9

12^2 = 144

9^2 = 81

144+81 = 225

square root of 225 = 15

 the distance is 15

Answer:

Money that Martin make is $ 275.9

Step-by-step explanation:

Number of shares Martin Bought = 30

Cost Price of a share = $ 24.53

Total Cost price of all share = 30 × 24.53 = $ 735.9

Selling Price of a share = $ 33.71

Total Selling Price of all shares = 30 × 33.71 = $ 1011.3

Profit money that Martin make = 1011.3 - 735.9 = $ 275.9

Therefore, Money that Martin make is $ 275.9

The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:

C = 2 π r

We can see that in the formula, what is multiplied by 2 π is the radius (r).

Therefore the answer to this is

B. Radius

Downpayment is the percent amount paid from a sum  of money. The amount left after the downpayment is  $904.80

Downpayment is the percent amount paid from a sum  of money. If Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price, the amount he have left is;

Amount left = (100 - 13)% * 1040

Amount left .= 87% of 1040

Amount left = 0.87 * 1040

Amount left =  $904.80

Hence the amount left after the downpayment is  $904.80

Learn more on downpayment here: https://brainly.com/question/26173748

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Answer: The total loss incurred by the store owner is 100$.

At first look, the answer might seem to be 200$ or 130$, but that's not the correct one. The explanation is below:

The lady stole 100$ from the owner therefore loss incurred is 100$.

The lady went back to the store  and:

Step 1 - The lady hands back the 100$ to the store owner. Loss incurred is back to 0$.

Step 2 - The store owner hands over merchandise worth 70$. Loss Incurred is now 70$.

Step 3 - The store owner hands over 30$ worth of change. Loss Incurred is (70 + 30)$ = 100$

The given problem is very confusing since it was copy pasted directly from the source so the equations look scrambled and plus it was one words. After my own translation, I believe the given numbers are:

4 ⋅ 10^6

and

1 ⋅ 10^4

The symbol ⋅ means that the two numbers are multiplied while the symbol ^ means an exponent of. Now we are asked to find how much the 1st number is larger than the 2nd number. To solve this, we simply have to divide the bigger number by the smaller number. Since 4 ⋅ 10^6 has bigger exponent than 1 ⋅ 10^4 then it is the bigger number.

Ratio = 4 ⋅ 10^6 / 1 ⋅ 10^4

Ratio = 4 ⋅ 10^2 = 400

Therefore 4 ⋅ 10^6 is 400 times bigger than 1 ⋅ 10^4.

Answer:

400 times

Having knowledge about potencies we will find that the final value will be greater than 400 times.

Recalling the properties of powers we find:

Then we can write the two given powers as:

[tex]4 *10^6\\1 * 10^4[/tex]

We know that we have a multiplication and a power, so solving for each of them, we find:

[tex]Ratio = 4 *10^6 / 1 * 10^4\\Ratio = 4 * 10^2 = 400[/tex]

See more about power at brainly.com/question/1618040

Answer: The speed of the plane with no wind is 440 miles per hour.

Step-by-step explanation:

Let the maximum speed of the plane be 'x'.

Let the maximum speed of the wind be 'y'.

Since we have given that an airplane travels 2400 miles against the wind in 6 hours.

As we know that

Downstream is given by

[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]

Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.

As we know tha t

Upstream is given by

[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]

We just need to find the speed of the plane with no wind.

Using the elimination method,

[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]

Hence, the speed of the plane with no wind is 440 miles per hour.

This question is based on the mental math. Therefore, the total amount of bill is  $16.25.

Given:

Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15.

We need to determined the  total amount of the bill.

Let  start with the price of the dessert and the sales tax $3.85+ $1.15= $5.  

Now,  added 2.75  to $5 .

We get,  

$2.75 + $5 = $ 7.75

Then, add 7.75 + 8.50.

We get,

= $16.25

Therefore, the total amount of bill is  $16.25.

For further details, please prefer this link:

https://brainly.com/question/2017990

The probability of choosing a blue marble from the bag is 1/3.

The probability of choosing a blue marble can be calculated by dividing the number of blue marbles by the total number of marbles in the bag. In this case, there are 8 blue marbles out of a total of 7 + 8 + 9 = 24 marbles.

So, the probability of choosing a blue marble is:

P(Blue Marble) = Number of Blue Marbles / Total Number of Marbles = 8 / 24 = 1/3

Final answer:

The probability of choosing a blue marble when one marble is drawn from the bag is 1/3 or approximately 0.333.

Explanation:

To find the probability of choosing a blue marble when one marble is drawn from a bag, we need to determine the number of favorable outcomes (blue marbles) and divide it by the total number of possible outcomes (all the marbles).

In this case, there are 8 blue marbles out of a total of 7 red + 8 blue + 9 green = 24 marbles. So the probability of choosing a blue marble is 8/24, which simplifies to 1/3 or approximately 0.333.

Therefore, the probability of choosing a blue marble when one marble is drawn is 1/3 or approximately 0.333.

In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.

Together, the x and y coordinates specify the precise location of a point in the xy-plane.