In a random sample of 100 students from a large high school, 37 regularly bring a reusable water bottle from home. Which of the following gives the correct value and interpretation of the standard error of the sample proportion? (a) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.095 from the true proportion. (b) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.048 from the true proportion. is ne (c) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.095 from the true proportion.
(d) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion (e) There is not enough information to calculate the standard error.

The equation of the line in point slope form is y + 6 = 3 (x + 3), and the line in slope intercept form is y = 3x + 3.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have the points on the line given.

(-3, -6) and (2, 9)

Slope of the line = (9 - -6) / (2 - -3) = 15/5 = 3

Equation of a line in point slope form is,

y - y₁ = m (x - x₁)

where (x₁, y₁) is a point on the line and m is the slope.

Substituting a point (-3, -6) and the slope = 3, we get,

y - -6 = 3 (x - -3)

y + 6 = 3 (x + 3), which is the point slope form.

Equation of a line in slope intercept form is,

y = mx + c

where m is the slope and c is the y intercept.

Substituting m = 3 and (x, y) = (2, 9),

9 = (3 × 2) + c

c = 9 - 6 = 3

Equation in slope intercept form becomes,

y = 3x + 3

Hence the point slope form and slope intercept form of the given line are y + 6 = 3 (x + 3) and y = 3x + 3 respectively.

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The value of z in the figure is 56⁰.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as the sides of an angle.

In the given figure, there are two pairs of vertically opposite angles.

The vertical opposite angle of 124⁰ is y⁰.

The vertical opposite angle of x⁰ is z⁰.

Thus, 124⁰ = y⁰ and x⁰ = z⁰.

The sum of all angles is 360⁰.

Therefore,

124⁰ + x⁰ +  y⁰ + z⁰ = 360⁰

Putting y⁰ = 124⁰ and x⁰ = z⁰ in the above equation:

124⁰ + z⁰ + 124⁰ + z⁰ = 360⁰

248⁰ + 2z⁰ = 360⁰

Subtract 248⁰ from both sides:

2z⁰ = 360⁰ - 248⁰

2z⁰ = 112⁰

Divide both sides by 2:

z⁰ = 56⁰

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The Spirit Club makes $2.5 profit on each shirt at the end of the year.

What is profit?

Cost price and selling price are better ways to explain profit. Cost price is the actual cost of the good or service, whereas selling price is the price at which it is offered for sale. In this case, the business has made a profit if the selling price of the good is higher than the cost price. Consequently, the profit calculation formula is;

Selling price minus cost price equals profit or gain.

Given that the cost of a shirt for the Spirit Club is $8.

They mark up the shirts 75% to sell in the school store.

The amount that is up on each shirt is $8×75%

= $8×(75/100)

= $8×(3/4)

= $6.

The marked price of each shirt is  $8 + $6 = $14.

They sell the shirts for 25% off at the end of the year.

The discount amount is $14×25%

= $14×(25/100)

= $14×(1/4)

= $3.5

The selling price of each shirt at the end of the year is $14 - $3.5 = $10.5.

The profit is Selling price - cost price = $10.5 - $8 = $2.5

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The number of days it will take for him to kick 100 goals is given as follows:

45 days.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function giving the number of goals on day x is given as follows:

y = 2x + 10.

The number of days for him to score 100 goals is then obtained as follows:

100 = 2x + 10

2x = 90

x = 90/2

x = 45 days.

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the total area of all four square faces:  4 x 60.5 cm² = 242 cm²

To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and then add them up.

The two rectangular faces are congruent, so we only need to calculate one of them and multiply by 2.

The area of one rectangular face is:

6 cm x 5.5 cm = 33 cm²

Multiplying by 2 gives us the total area of both rectangular faces:

2 x 33 cm² = 66 cm²

The other four faces are also congruent, so we only need to calculate one of them and multiply by 4.

The area of one of the square faces is:

11 cm x 5.5 cm = 60.5 cm²

Multiplying by 4 gives us the total area of all four square faces:

4 x 60.5 cm² = 242 cm²

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Answer:

$69

Step-by-step explanation:

25% = 0.25

17.25 ÷ 0.25 = 69

69 × 0.25 = 17.25

The original price of the hammer from the online retailer is $23.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given that,

Discount percentage = 25%

Amount after the discount = $17.25

We have to find the original price of the hammer.

Let x be the original price of the hammer.

x - 25% of x = 17.25

x - 0.25x = 17.25

0.75x = 17.25

x = $23

Hence the original cost of the hammer is $23.

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Terminal point is a term used in mathematics to describe the endpoint of a line segment. It is the point at which the line or curve terminates or comes to an end. It is important to note that a terminal point is not necessarily the same as a vertex or an intersection point; the terminal point is simply the endpoint of the line segment, the point at which it begins and ends.

For example, the terminal points of a line segment that connects the points (3, 5) and (7, 9) are (3, 5) and (7, 9). The line segment does not terminate at any other point.

The reference number is 41, and the given formula is t = 6π.

Therefore, 6π = 41

π = 41/6

π ≈ 6.83

The terminal point is determined by the given formula (r cos θ, r sin θ).

Since r = 1, substitute the values for θ and r into the formula:

(1, cos 6.83, 1, sin 6.83) = (3.5, 2.5)

Therefore, the terminal point determined by the given reference number t = 41 is (3.5, 2.5).

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The solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.

Given that the inequality is:

3|x|+4≥1

Subtract 4 from both sides of the equation:

3|x| + 4 - 4 ≥ 1 - 4

3 |x| ≥ -3

Divide 3 from both sides of the equation:

|x| ≥ -1

We know that, |x| can be written as x and -x thus,

x ≥ -1

-x ≥ -1 or x ≤ 1

Hence, the solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.

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Answer:

D

Step-by-step explanation:

f(x) = 3x - 4

Substituting f(x) into g(x) gives:

g(f(x)) = (3x - 4)^2 - 3

Expanding the squared term, we get:

g(f(x)) = 9x^2 - 24x + 16 - 3

Simplifying, we get:

g(f(x)) = 9x^2 - 24x + 13

The coordinates of point B are (1,2).

How to find Reflection of a point?

When a point is reflected across the X-axis, the x-coordinates remain the same. But the Y-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across X-axis is (x, -y).

The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.

Find the difference between the x and y values of the given points and add that value (distance) to the reflection point.

x-values: 4-3 = 1   y-values: 0-(-2) = 2

Add to reflection point  x: 4-3 = 1     y: 0 -(-2)= 2

Hence, The coordinates of point B are (1,2).

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Answer:

1110

Step-by-step explanation:

Answer:

See My Attached Work For Answer. (POV THIS WAS HARD!!!)

Step-by-step explanation:

The Probability that the student was not a female and did not earn grade C is 34/59.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

                A B C Total

Male 16 18 17 51

Female 19 6 10 35

Total 35 24 27 86

Total number of non-female students who got a A and B : 34

Total number of students who got a A and B: 35+24= 59

So, the probability is

= 34/ 59

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On solving the provided question we can say that at a simple 12% annual percentage rate, it would take approximately 6 years for capital to double.

In mathematics, a ratio or number expressed as a percentage of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." Nonetheless, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100.

The annual rate of return is 12%, so we can calculate:

Time to double = 72 / 12 = 6 years

Therefore, at a simple 12% annual rate, it would take approximately 6 years for capital to double.

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The correct question is -

How long does it take for capital to double at a simple 12% annual rate?

Por lo tanto, el precio original del abrigo era de 72€

Para resolver este problema, primero debemos determinar el precio original del abrigo antes de las rebajas.

Sea x el precio original del abrigo.

Después de aplicar la primera rebaja del 40%, el precio del abrigo sería:

x - 0.4x = 0.6x

Luego, tras la subida del 30%, elprecio se incrementaría al 130% del precio anterior:

1.3(0.6x) = 0.78x

Sabemos que este precio final es de 56,16€, por lo que podemos resolver la ecuación:

0.78x = 56.16

x = 72

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Answer:

Step-by-step explanation:

Let's use A to represent the number of adult tickets sold and C to represent the number of children tickets sold. We can set up two equations based on the information given:

The total number of tickets sold is the sum of adult and children tickets:

A + C = 487

The total proceeds from ticket sales is the product of the number of tickets and their respective prices:

47A + 29C = 17525

We can use the first equation to solve for one of the variables in terms of the other:

C = 487 - A

Substituting this expression for C into the second equation, we get:

47A + 29(487 - A) = 17525

Simplifying and solving for A:

18A + 14123 = 17525

18A = 3402

A = 189

So 189 adult tickets were sold. Using the equation C = 487 - A, we can find the number of children tickets sold:

C = 487 - 189 = 298

Therefore, 189 adult tickets and 298 children tickets were sold for the matinee.

We have discussed what is skewed distribution and how to deal with skewed data as mentioned below.

What is a skewed distribution?

When one tail is longer than the other, the distribution is said to be skewed. The asymmetry of a distribution is defined by skewness. These distributions are asymmetric, in contrast to the well-known normal distribution and its bell-shaped curve. Because the data are not equally distributed on both sides of the distribution peak, the two parts of the distribution are not mirror images.

A) The direction of outliers is revealed by skewness. A distribution curve's tail is longer on the right side when there is a positive skew. As a result, the distribution curve's outliers are more extreme to the right and closer to the mean to the left. Skewness simply conveys the direction of outliers; it does not convey the number of outliers.

B) Lower or upper boundaries on the data frequently cause skewed data. In other words, data with a lower bound are frequently skewed right, whereas data with an upper bound are typically skewed left.

C) One popular method for handling skewed outcome data is to logarithmically transform each observation before conducting the analysis with the resulting values.

D) It is likely that the income distribution curve you plot on a graph will be positively skewed to the right. If the majority of people earn normal earnings and a smaller proportion earn high incomes, then this would happen.

Therefore this is what skewed distribution is and the above mentioned ways are how one deals with skewed data in research.

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Answer:

6

Step-by-step explanation:

Simplifying the expression (2+1)2, we can first perform the operation within the parentheses, which gives us:

(2+1)2 = 3 x 2

Then, we can multiply 3 by 2, which gives us:

3 x 2 = 6

Therefore, the simplified expression for (2+1)2 is 6

Answer:

0.0376 or 3.76%.

Step-by-step explanation:

The probability of drawing a red marble on the first draw is 5/21 because there are 5 red marbles out of 21 total marbles in the bag.

After the first draw, there are only 20 marbles left in the bag, so the probability of drawing a red marble on the second draw, without replacement, is 4/20 or 1/5.

Similarly, after the second draw, there are only 19 marbles left in the bag, so the probability of drawing a red marble on the third draw, without replacement, is 3/19.

To find the probability of all three marbles being red, we need to multiply the probabilities of each individual draw together:

(5/21) x (1/5) x (3/19) = 15/399 or approximately 0.0376.

Therefore, the probability of drawing three red marbles in a row, without replacement, is about 0.0376 or 3.76%.

Answer:

5.85m

Step-by-step explanation:

1 meter is 100 centimeters.

583 divided by 100

The interpretation of the solution of the graph can be: the solution (6, 64) on the graph represents that after 6 minutes, there are 64 gallons of water.

The solution to a system that is plotted on a graph is the coordinates of the point interception of the graph.

Therefore, the solution (6, 64) represents a point on the graph of a relationship between time in minutes (represented by the x-axis) and water in gallons (represented by the y-axis).

The solution tells us that at 6 minutes, the water level is 64 gallons. In other words, (6, 64) on the graph, represents the amount of water in the tank over time.

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Answer:

B. 5

Step-by-step explanation:

The expression "4 to the power of 5" can be written as 4^5. Here, 4 is the base, and 5 is the exponent. So the exponent in the expression 4 to the power of 5 is option B, 5.

To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:

6x²2 - 4xy = 2x(3x - 2y)

What is factorization?

Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.

For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):

x²2 - 4x - 21 = (x - 7)(x + 3)

This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.

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The equations used to calculate the cost of a single tire patch are 22.2 - 4x = 1.9 and 4x + 1.9 + 22.2.

The statistic is said to be in its simplistic definition when divided into its smallest equivalent portion. How to further find the most basic form. Identify common factors in the denominator and the numerator. Verify a fractional integer to verify if it qualifies as a prime number. A remark having two quadrilateral and an identical sign in the middle is called an equation in mathematics. The general form of any issue contains the degrees of all the components in descending order. The basic form of a system of equations is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). Mathematics can be categorized as identity or conditional equations. An identity stands true regardless of the value given to the variables.

given

equations  4x + 1.9 + 22.2

22.2 - 4x = 1.9

It should all total up to $22.20 if you use the undetermined cost of the four tire patches as x, or $1.90 if you're deducting it.

The equations used to calculate the cost of a single tire patch are 22.2 - 4x = 1.9 and 4x + 1.9 + 22.2.

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The domain where fx) is 1-to-1 is x ≥1 , and the inverse there is:

f⁻¹(x) =  √x + 1

Here we have the quadratic function:

f(x) = (x - 1)^2

If we look from the vertex to the right (or the left, is the same) we will have an one to one function.

Here the vertex is at x = 1

f(1) = (1 - 1)^2 = 0

Then for x ≥1 we have an one to one function.

Noe let's find the inverse, if the inverse is f⁻¹(x), then we must have that:

f( f⁻¹(x) ) = x

Solving that:

(f⁻¹(x)  - 1)^2 = x

(f⁻¹(x)  - 1) = √x    (here we only take the positive square root)

f⁻¹(x) =  √x + 1

That is the inverse.

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The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft

The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.

To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.

Therefore, the correct answer is B) 12 ft.

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Answer:

28.6 grams

Step-by-step explanation:

Percentage of cocoa in the chocolate bar = 54%

Weight of the chocolate = 53 grams

Weight of the cocoa = 54% of 53 = 28.62 grams

Rounding off to nearest tenth = 30 grams