The Class 2022 had 202 students who took the Statistics course. Their mean score in the Final Test was 80.
a) Suppose a friend of yours concluded 50% of students had a test score higher than 80 with an estimation error of 0.07. Are you skeptical of your friend’s claim? Explain why.
b) For the Class 2023, suppose the mean score of the Final Test is 70. The friend of yours now concludes that Class 2022 did better than Class 2023 in the Final Test. Are you skeptical of your friend’s claim? Explain why.

X = 7 & -7/2

First, use the distributive property to simplify the equation:

2 - 5/(x+7) = -7/(x-3)(x+7)

2(x-3)(x+7) - 5(x-3) = -7(x+7)

2x2 + 7x - 6x - 15 = -7x - 49

2x2 -13x - 49 = 0

This equation can be solved by factoring the binomial:

2x2 -13x - 49 = 0

2x(x-7) - 7(x-7) = 0

(2x-7)(x-7) = 0

Therefore, the solution for x is x = 7 and x = -7/2.

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Answer:

60

Step-by-step explanation:

24 + 36 = 60

You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.

Answer:

A

Step-by-step explanation:

trust

One cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Two cheeseburgers and one small order of fries contain a total of 1420 calories.

Three cheeseburgers and two small orders of fries contain a total of 2290 calories.

let the number of Calories in one cheeseburgers  be x and in one fries be y.

So, the system of Equation is:

2x + y = 1420

3x + 2y= 2290

solving the above two equation

x= 550 and y= 320

So, one cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.

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Answer: Third answer option, [tex]\sqrt{3} *\sqrt{12}[/tex]

Step-by-step explanation:

     Both 3 and 9 are not irrational numbers, so the first option is incorrect.

     The [tex]\sqrt{3}[/tex] is irrational, but 0 is not, so the second option is also incorrect.

     The [tex]\sqrt{3}[/tex] and [tex]\sqrt{12}[/tex] are both irrational. Let us see if they result in a rational number when multiplied together;

                 [tex]\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6[/tex]

      They do, so this answer option is correct.

Answer: I'd say A

Step-by-step explanation:

-1+1=0

We can use the properties of logarithms to evaluate each expression. The properties of logarithms include:

1) loga (xy) = loga (x) + loga (y)

2) loga (x/z) = loga (x) - loga (z)

3) loga (x^p) = p loga (x)

4) loga (square root x) = (1/2) loga (x)

Using these properties, we can evaluate each expression as follows:

(a) loga (xy) = loga (x) + loga (y) = 3.1 + 5.8 = 8.9

(b) loga (x/z) = loga (x) - loga (z) = 3.1 - 1.1 = 2

(c) loga (y^7) = 7 loga (y) = 7 * 5.8 = 40.6

(d) loga (square root y) = (1/2) loga (y) = (1/2) * 5.8 = 2.9

Therefore, the answers are:

(a) loga (xy) = 8.9

(b) loga (x/z) = 2

(c) loga (y^7) = 40.6

(d) loga (square root y) = 2.9

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Answer:

$0.45

Step-by-step explanation:

Answer:

2(−x 2−3)

Simplify the expression

−2x 2−6

Factor the expression

−2(x 2+3)

Answer:

4.2 represents the initial height of the ball.

Step-by-step explanation:

h(x) = -16x² + 24x + 4.2

At x = 0, h(0) = 4.2

4.2 represents the initial height of the ball.

When a point is reflected across the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.

Therefore, to find the coordinates of the reflected point D, we simply change the sign of the y-coordinate of point D.

Given that the coordinates of point D are (3/4,3), its reflected point D' across the x-axis will have the coordinates (3/4, -3).

Therefore, the reflected point D' is located at the point (3/4, -3).

Coordinates are pairs of numbers used to identify the position of a point in a two-dimensional plane. In a Cartesian coordinate system, the two numbers represent the x-coordinate (the horizontal position) and the y-coordinate (the vertical position) of the point.

For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5. This means that the point is located 3 units to the right of the origin (the point where the x- and y-axes intersect) and 5 units above the x-axis. Similarly, the point (-2, -1) has an x-coordinate of -2 and a y-coordinate of -1, which means that it is located 2 units to the left of the origin and 1 unit below the x-axis.

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The following o-fields are equal to each other because they both represent the Borel sigma field on the real line:
i. B= o({(-20,x); r < R})
ii. B2 = o({(-0,2); 2 € R})

Note that the Borel sigma field on the real line is the smallest sigma field containing all the open intervals on the real line. This means that any set that can be constructed from countable unions, intersections, and complements of open intervals is in the Borel sigma field.

In the first o-field, B= o({(-20,x); r < R}), the set {(-20,x); r < R} is an open interval on the real line, so it is in the Borel sigma field. Similarly, in the second o-field, B2 = o({(-0,2); 2 € R}), the set {(-0,2); 2 € R} is also an open interval on the real line, so it is also in the Borel sigma field.

Since both o-fields contain sets that are in the Borel sigma field, they are both equal to the Borel sigma field on the real line. Therefore, B= o({(-20,x); r < R}) = B2 = o({(-0,2); 2 € R}).

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The solutions for the equation 6x²-11x-7=0 are x = -1/2 and x = 7/3

It is important to note that quadratic equations are defined as equations having the highest degree of x as 2.

From the information given, we have that the quadratic equation is given as;

6x²-11x-7=0

Now, multiply the coefficient of x squared with the constant value, then find the pair factors of the product that adds up to given the coefficient of x = -11

We have;

6x² - 14x + 3x - 7 =0

Group the expression in pairs

(6x² - 14x) + (3x - 7) = 0

Factor the expressions

2x(3x - 7) + 1(3x - 7) = 0

Then, we have;

(2x + 1) and (3x - 7) = 0

x = -1/2

x = 7/3

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a)0.1587 (or 15.87%)

b)0.6827 (or 68.27%)

c)0.0228 (or 2.28%)

1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).

2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).

3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).

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Answer: The y-intercept is 30 and the coefficient is -5

Step-by-step explanation:

In the slope-intercept form (y = mx + b) b stands for your y-intercept, in this case, 30.

The coefficient is the number being multiplied by the variable, or in this case, the slope, or -5.

The slope of the linear equation is; 0.5

The y-intercept of the Linear Equation is: 4.75

Yes the equation is proportional

The equation we are given is expressed as;

y = ¹/₂x + 4³/₄

When x = 0,

y = ¹/₂(0) + 4³/₄

y = 4.75

When x = 1,

y = ¹/₂(1) + 4³/₄

y = 5.25

When x = 2,

y = ¹/₂(2) + 4³/₄

y = 5.75

When x = 3,

y = ¹/₂(3) + 4³/₄

y = 6.25

If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5

Thus, slope = 0.5

y-intercept = 4.75

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Answer:

To find the name of the restaurant, we need to find the intersection point of the two streets.

The equation of Second Street is y = (-4/3)x + 4/3.

The equation of Washington Boulevard is y = (3/7)x - 3/7.

To find the intersection point, we can set the two equations equal to each other:

(-4/3)x + 4/3 = (3/7)x - 3/7

Multiplying both sides by 21 (the least common multiple of 3 and 7) to eliminate fractions, we get:

-28x + 28 = 9x - 9

Bringing all the x terms to one side and all the constants to the other side, we get:

-37x = -37

Dividing both sides by -37, we get:

x = 1

Substituting this value of x into either equation, we can find y:

y = (-4/3)(1) + 4/3 = 0

Therefore, the intersection point of Second Street and Washington Boulevard is (1,0), which means the restaurant is located at that point.

Step-by-step explanation:

In response to the query, we have that The two graphs are oriented and coordinates  have the same form in common. The moment where the two graphs come together (1, 2).

A coordinate system is a technique used in geometry to precisely locate points or other geometry objects on a manifold, also including Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional sphere is located using a pair of numbers known as coordinates. The x and y positions are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.

f(1/x) = 2/(1/x) = 2x, where g(x) =

Hence, g(x) = f(1/x) is equivalent to f(x) = 2x.

The values of x and g(x) are as follows:

x= 1 2 3 4 5\sg(x)= 1/8 1/4 1/2 1 2

f(x) = 2x: (1, 2), (2, 4), (3, 6), (4, 8), (5, 10) (5, 10)

g(x) = f(1/x) = 2x: (1, 2), (1/2, 1), (1/3, 2/3), (1/4, 1/2), (1/5, 2/5)

The appropriate choices are thus:

A reflection of the graph of f(x) about the line y = x is the graph of g(x).

The two graphs are oriented and have the same form in common.

The moment where the two graphs come together (1, 2).

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Answer:

The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:

15b = 495 - 4(15)

Simplifying the right-hand side:

15b = 495 - 60

15b = 435

Dividing both sides by 15:

b = 29

So the math coach still needs to deliver 29 boxes of books.

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.

Let's use algebra to solve the problem.

If 19,700 employees represent 22.9% of the company's total number of employees, we can write:

0.229 = 19,700 / Total number of employees

To find the total number of employees, we can isolate the variable on one side of the equation:

Total number of employees = 19,700 / 0.229

Using a calculator, we get:

Total number of employees = 86,026.2

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

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Ezra should increase the stage's dimensions by the following factor in order to make the picture half the size of the original blueprint:

50%.

The modified blueprint will have a perimeter that is half that of the original layout.

When the scale factor is multiplied by the coordinates of an image's vertices, the result is a dilatation, which alters the side lengths of a figure.

The scale factor of the dilation is supplied as follows because, for this issue, we want the updated stage's dimensions to be half those of the original stage.

k = 1/2.

Given that both the perimeter and the side lengths have the same unit, 50%, or half of the original stage's perimeter, will be represented by the updated stage's perimeter.

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Answer:

(-3, -4)

Step-by-step explanation:

Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)

The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

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a)91.44 m

b)51.18 in

c)372.85 W

d)2383186.955 Pa

e)10000 ????????/m3

f)0.4667 T????/ℎ

g)41840 J

300 ft = m

1 ft = 0.3048 m, so 300 ft = 300 * 0.3048 m = 91.44 m



130 cm = in

1 in = 2.54 cm, so 130 cm = 130/2.54 in = 51.18 in



0.5hp = W

1 hp = 745.7 W, so 0.5 hp = 0.5 * 745.7 W = 372.85 W



350psi = Pa

1 psi = 6894.757 Pa, so 350 psi = 350 * 6894.757 Pa = 2383186.955 Pa



10 ????????/????????3 = ????????/m3

1 ????????/????????3 = 1000 ????????/m3, so 10 ????????/????????3 = 10 * 1000 ????????/m3 = 10000 ????????/m3



350 W = ????T????/ℎ

1 W = 0.00134 T????/ℎ, so 350 W = 350 * 0.00134 T????/ℎ = 0.4667 T????/ℎ



10,000 cal = ????

1 cal = 4.184 J, so 10,000 cal = 10,000 * 4.184 J = 41840 J

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1:1.618 (the golden ratio).

To construct a golden spiral that involves a golden rectangle with length 4 meters, first draw a 4 meter long line. Divide it into two segments, such that the longer segment has a ratio of 1:1.618 (the golden ratio) to the shorter segment.

Draw a right angle at the end of the shorter segment. This creates a square that has a side length of 4 meters. Draw an arc centered at the intersection of the two line segments with a radius equal to the shorter segment and connect the ends of the arc. This creates a golden rectangle with a length of 4 meters.

Draw a quarter circle at each corner of the golden rectangle and connect the endpoints. This creates a spiral, and it is a golden spiral if the ratio of the lengths of the two line segments is 1:1.618 (the golden ratio).

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The probability that Ann's score is above 600 is 1 - 0.6628 = 0.3372.

(a) The shape of the sampling distribution of the sample means will be approximately normal. This is because of the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. In this case, the sample size of 35 is large enough for the Central Limit Theorem to apply.

(b) The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 550. The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 120/√35 ≈ 20.28.

(c) To find the probability that the average score of the 35 selected students is above 600, we need to find the z-score for 600 using the mean and standard deviation of the sampling distribution of the sample means. The z-score is (600 - 550)/20.28 ≈ 2.47. Using a z-table, we can find the probability that the z-score is less than 2.47, which is 0.9932. Therefore, the probability that the average score of the 35 selected students is above 600 is 1 - 0.9932 = 0.0068.

(d) To find the probability that Ann's score is above 600, we need to find the z-score for 600 using the mean and standard deviation of the population. The z-score is (600 - 550)/120 ≈ 0.42. Using a z-table, we can find the probability that the z-score is less than 0.42, which is 0.6628.

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The measure that is considered an outlier is the data-set is a measure of 29.5.

The interquartile range is calculated as the difference between the third quartile and the first quartile.

The values that are outliers are given as follows:

The quartiles for this problem are given as follows:

Q1 = 17, Q3 = 22.

Hence the IQR is of:

IQR = 22 - 17

IQR = 5.

Meaning that the outliers are given as follows:

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Answer:

300

Step-by-step explanation:

x(100%-7%)=279

        0.93x=279

                x=300