The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:



thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth



According to this data, what is the experimental probability that a team will consist of two girls and a boy?

0.33
0.375
0.23
0.46

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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Answer:

1.25

Step-by-step explanation:

you have to take the 9 pages and divide by 7 and then divide that by 60 and u get 1.25

The bearing angle exists 53.49°.

A bearing of 36° corresponds to the corresponding angle of

θ = 90 -36 = 54°

The (x, y) values for the position of the ship after achieving its first heading exist:

\(x_1\) = 12.1 Cos 54° = 7.11 m

\(y_1\) = 12.1 Sin 54° = 9.78 m

Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore

\(x_2\) = 6.1 mi

\(y_2\) = 0 mi

To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:

Δx \(= x_1+x_2\)

= 7.11 mi + 6.1 mi = 13.21 mi

Δy \(=y_1+y_2\)

= 9.78 mi + 0 mi = 9.78 mi

\($r=\sqrt{(x_{total})^2+(y_{total})^2}\)

\(=\sqrt{(13.21mi)^2+(9.78mi)^2}\)

= 16.43 mi

The direction of the displacement vector exists given by

tan θ = Δy/Δx

θ = arc tan (Δy/Δx)

= arc tan (9.78/13.21)

= 36.51°

The question requested for the bearing angle, which exists just this angle subtracted from 90°:

90° - 36.51° = 53.49°.

Therefore, the bearing angle exists 53.49°.

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Answer:

\( \frac{9 - 15}{2 - 0} = \frac{3 - 9}{4 - 2} = - \frac{6}{2} = - 3\)

Answer:

Culture has a significant impact on heroes. For starters, it influences how a person or character perceives a particular situation or idea, as well as their point of view on a variety of ideas and topics. Next, it has an impact on how the hero is portrayed in the story. Third, it influences how a character reacts to an idea or situation.

Culture has an impact on heroes. We see an example of this in 'Black Ships Before Troy,' where in Achilles' culture, to be a hero, you must be brave and fight. This is also evident in 'Heart of a Samurai,' where Manjiro's culture dictates that in order to be a hero, you must provide for your family.

Answer:

there aren't boys who have the numbers of marbles .

Step-by-step explanation:

Therefore, the number of minutes of talk time used each month is 581.

In terms of time measurement, a minute is a unit of time equal to 60 seconds. It is one-sixtieth of an hour and one-third of an hour. The word "minute" comes from the Latin word "minutes," meaning "small" or "minute."

Minutes are commonly used in everyday life to measure short durations of time, such as the length of a phone call or the time it takes to boil an egg. They are also used in scientific fields to measure very small-time intervals, such as in nuclear physics or astronomy. Additionally, minutes are often used in meetings and official proceedings to record the details of what was discussed and decided.

Let's first calculate the cost of 500 minutes of talk time, which is $23.70.

To get email access, it costs 10% of the price for 500 minutes of talk time, which is 0.1 x $23.70 = $2.37.

So the total cost per month is $23.70 + $2.37 = $26.07 for 500 minutes of talk time and email access.

For each additional minute over 500, it costs $0.07. Let's say you use x minutes of talk time per month, where x is greater than 500.

Then the cost for talk time would be\($23.70 + ($0.07)(x - 500).\)

The total cost per month, including email access, would be \($2.37 + $23.70 + ($0.07)(x - 500) = $26.07 + ($0.07)(x - 500).\)

Since the bill is the same each month for 8 months, the total cost for 8 months is\($26.07(8) + ($0.07)(x - 500)(8) = $208.56 + ($0.07)(x - 500)(8) = $253.92.\)

Simplifying, we get:

\(($0.07)(x - 500)(8) = $253.92 - $208.56\)

\(($0.07)(x - 500)(8) = $45.36\)

Dividing both sides by 0.56:

\((x - 500)(8) = 648\)

\(x - 500 = 81\)

\(x = 581\)

Therefore, the number of minutes of talk time used each month is 581.

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Answer:

\(\frac{1}{256}\)

Step-by-step explanation:

Given

\(\left(4^4\right)^{-1}\)

We can use the power rule to multiply the exponents.

The power rule for exponents states

\(\left(a^b\right)^{c}=a^{bc}\)

\(4^{4*-1}\)

Multiply 4 by −1.

\(4^{-4}\)

Rewrite the expression using the negative exponent rule.

The negative exponent rule states

\(a^{-b}=\frac{1}{a^b}\)

\(\frac{1}{4^4}\)

Raise 4 to the power of 4.

\(\frac{1}{256}\)

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Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

The expression is equivalent to 2 , Option C is the correct answer.

An expression is a mathematical statement consisting of variables , constants and mathematical operators.

The expression given in the question is

\(\rm( {\dfrac{4^{5/4} * 4^{1/4}}{4^{1/2}}})^{1/2}\)

By exponent rule

\(\rm a^m * a^n = a^{m+n}\\\\a^m \div a^n = a^{m-n}\)

Here so ,

\(\rm 4^{(\dfrac{5}{4} +\dfrac{1}{4} -\dfrac{1}{2})^{1/2}\)

\(\rm 4^{(\dfrac{6}{4} -\dfrac{1}{2})^{1/2}\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\)

\(4^{(\dfrac{6-2}{4} )^{1/2}\\\)

\(4^{1/2}\\\\(2^2)^{1/2}\\\\2\)

Therefore the expression is equivalent to 2 , Option C is the correct answer.

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Answer:

X=32, Y=148

Step-by-step explanation:

X is 32 degrees because it is parallel to that 32 between f and b.

Y is 148 degrees because x and y together make a straight line and a straight line is 180 degrees therefore, 180-32 = 148.

Answer:

1,664 fluid ounces = 13 gallons

Step-by-step explanation:

\(\\ \sf\longmapsto {\displaystyle{\int}}(sinx.cosx.tanx) dx\)

\(\\ \sf\longmapsto {\displaystyle{\int}}sinx.\cancel{cosx}.\dfrac{sinx}{\cancel{cosx}}dx\)

\(\\ \sf\longmapsto {\displaystyle{\int}}sinx.sinx \:dx\)

\(\\ \sf\longmapsto {\displaystyle{\int}}sin^2x\:dx\)

\(\\ \sf\longmapsto {\displaystyle{\int}}\dfrac{1-cos2x}{2}dx\)

\(\\ \sf\longmapsto \dfrac{1}{2}{\displaystyle{\int}}1-cos2x\)

\(\\ \sf\longmapsto \dfrac{1}{2}{\displaystyle{\int}}dx-\dfrac{1}{2}{\displaystyle{\int}}cos2x\)

\(\\ \sf\longmapsto \dfrac{1}{2}x-\dfrac{1}{2}{\displaystyle{\int}}cos2xdx\)

Here Taking

Then

Now put values

\(\\ \sf\longmapsto \dfrac{1}{2}du=dx\)

Then

\(\\ \sf\longmapsto \dfrac{1}{2}x-\dfrac{1}{2}{\displaystyle{\int}}cos2xdx\)

\(\\ \sf\longmapsto \dfrac{1}{2}x-\dfrac{1}{2}\times \dfrac{1}{2}{\displaystyle{\int}}cosudu\)

\(\\ \sf\longmapsto \dfrac{1}{2}x-\dfrac{1}{4}{\displaystyle{\int}}cosudu\)

\(\\ \sf\longmapsto \dfrac{1}{2}x-\dfrac{1}{4}sin u\)

\(\\ \sf\longmapsto\underline{\boxed{\bf{\dfrac{1}{2}x-\dfrac{1}{4}sin 2x+C}}}\)

Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

Answer:

A.

The first 5 terms:

B.

The first 5 terms:

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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b'

Let the given points be A(3,-5) and B(5,-1).

AB= sqrt of (5−3) ² +(−1+5)²

= sqrt of 4+16

= sqrt of 20

=2 sqrt of 5 units

Answer:

The value of x = 17

Step-by-step explanation:

=> 4x + 2 = 70°

=> 4x = 70 - 2

=> 4x = 68

=> x = 68/4

=> x = 17

Answer:

\(3(x-2)=2x+10\\3x-6=2x+10 | +6\\3x=2x+16 | -2x\\x = 16\)

30.

a) \(180^{0} - 134^0-22^0=24^0\)

\(r=24^0\)

b)

\(90^0=2x^0+3x^0\\90^0=5x^0 |:5\\x^0=18^0\)

\(2x^0= 2* 18^0=36^0\)

\(3x^0=3*18^0=54^0\)

Take care!

Answer:

a) 33.33% probability that the respondent is assigned to the guilty state.

b) 35.09% probability that the respondent chooses the stated option (repair the car).

c) 26.32%  probability that the respondent is assigned to the guilty state and chooses the stated option.

d) 40.94% probability that the respondent is assigned to the guilty state or chooses the stated option.

Step-by-step explanation:

A probability is given by the number of desired outcomes divided by the number of total outcomes. We use this concept, along with the given table, to solve the question.

a. Find the probability that the respondent is assigned to the guilty state.

There were 171 participants, and 57 of those were assigned the guilty state. So this probability is \(p = \frac{57}{171} = 0.3333\)

b. Find the probability that the respondent chooses the stated option (repair the car).

There were 171 participants, and 60 of those choose the stated option. So this probability is \(p = \frac{60}{171} = 0.3509\)

c. Find the probability that the respondent is assigned to the guilty state and chooses the stated option.

There were 171 participants, and 45 of those were assigned to the guilty state and choose the stated option. So this probability is \(p = \frac{45}{171} = 0.2632\)

d. Find the probability that the respondent is assigned to the guilty state or chooses the stated option.

Guilty state: 57

Anger or Neutral and stated option: 8 + 7 = 15

Total = 57 + 15 = 72

\(p = \frac{70}{171} = 0.4094\)

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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The length of each side of the square is 16 cm, the perimeter is 64 cm, and the area is 256 cm^2.

Let's solve the problem step by step. We have a square ABCD, and we need to find the length of its sides when the diagonal is 16√2 cm long.

In a square, the diagonal forms a right triangle with the sides. The sides of a square are equal in length, so let's assume the length of one side of the square is 'x' cm.

Using the Pythagorean theorem, we can find the relationship between the side length and the diagonal:

x^2 + x^2 = (16√2)^2

2x^2 = 512

Dividing both sides by 2, we have:

x^2 = 256

Taking the square root of both sides:

x = √256

x = 16 cm

So, the length of each side of the square is 16 cm.

To find the perimeter of the square, we simply multiply the length of one side by 4 since all sides are equal:

Perimeter = 4 * 16 cm = 64 cm

To find the area of the square, we square the length of one side:

Area = (16 cm)^2 = 256 cm^2

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Note the complete question is:

Find the length of side of square ABCD when diagonal is 16√2 cm long. Also find the perimeter and area of the square?

Answer:

6 3/16 in²

Step-by-step explanation:

Area of rectangle = width x length

Given:

width = 2 3/4 in

length = 2 1/4 in

⇒ area = 2 3/4 × 2 1/4 = 11/4 × 9/4 = 99/16 = 6 3/16 in²

As the margin of error decreases, the width of the confidence interval decreases.

So option B is correct option.

A confidence interval is a method used to estimate the population parameter of interest based on a random sample from the population. It is a range of values that contains the true population parameter with a certain degree of confidence.

To determine the accuracy of the estimate, the confidence interval is calculated as a range of values within which we are reasonably certain the true population parameter lies. The confidence interval is calculated based on the sample statistics (e.g. sample mean) and the sample size.

The margin of error (also known as the confidence interval half-width) determines the width of the confidence interval. It is the amount of uncertainty associated with the estimate. It is calculated as the product of the critical value (z*) and the standard error of the statistic.

The width of the confidence interval is inversely related to the margin of error. When the margin of error decreases, the width of the confidence interval decreases, and when the margin of error increases, the width of the confidence interval increases.

Therefore, the correct answer is b. Decreases.

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Answer:

5 units²

Step-by-step explanation:

Area of the triangle = ½ × base × height

base = 2

height = 5

Plug in the values into the formula

Area = ½ × 2 × 5

Area = ½ × 10

Area = 5 units²

Answer:

(2,1)

Step-by-step explanation:

The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.

So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:

4(1) - 2(2) = 0

So the point (2,1) is on the line.

first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)