4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total

Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation:

Answer:

B) 352

Step-by-step explanation:

45% = 0.45

640 x 0.45= 288

288 is how many students walked to school

So to find how many took the bus to school

640- 288= 352

Answer: y=2

Step-by-step explanation:

We're given x=1 so we can plug this in 3x - y =1 and isolate to solve for y.

[tex]3(1)-y=1\\3-y=1\\-y=-2\\y=2[/tex]

Answer:

The coins are picked without replacement.

The probability of picking at least one Canadian quarter is 1 minus the probability of picking 6 U.S. quarters:

[tex]1 - ( \frac{41}{50} )( \frac{40}{49} )( \frac{39}{48} )( \frac{38}{47} )( \frac{37}{46} )( \frac{36}{45} ) [/tex]

[tex] = 1 - .28296 = .71704[/tex]

So the probability of picking at least one Canadian quarter is about 71.7%.

The values are;

1. x = 6 ,y = 6√2

2. x = 9√2, y = 18

3. x = y = 9

4. x = 12, y = 12√2

5. x = y = 4√2

6. x = y =( 3√2)/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

There are some special angles , in which 45 is part of them.

sin 45 = 1/√2

cos 45 = 1/√2

tan 45 = 1

1. x = 6 ( isosceles triangle)

y = 6 × √2 = 6√2

2. x = 9√2 ( isosceles triangle)

y = 9√2 × √2 = 9×2 = 18

3. x = 9√2/√2 = 9

x = y = 9 ( isosceles triangle)

4. x = 12 ( isosceles triangle)

y = 12×√2 = 12√2

5. x = 8/√2 = 8√2/2 = 4√2

x = y = 4√2( isosceles triangle)

6. x = 3/√2 = (3√2)/2

x = y =( 3√2)/2 ( isosceles triangle)

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[tex]\cfrac{5^7}{5^{-13}}\times\left( \cfrac{4^3}{7^{-2}} \right)^{-2}\implies 5^7\cdot 5^{13}\times \left( \cfrac{7^{-2}}{4^3} \right)^{+2}\implies 5^7\cdot 5^{13}\times\left( \cfrac{7^{-4}}{4^6} \right) \\\\\\ 5^{7+13}\times\left( \cfrac{1}{4^6\cdot 7^4} \right)\implies \cfrac{5^{20}}{4^6\cdot 7^4}\implies \cfrac{95367431640625}{9834496}[/tex]

So, multiple choice algebra questions. the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2[/tex].

To simplify the given expression [tex](3x^4+4x^2) (x^3-2x^2-1)[/tex], we can use the distributive property of multiplication to multiply each term of the first expression by each term of the second expression. This gives us:

[tex](3x^4+4x^2) (x^3-2x^2-1) \\= 3x^4(x^3) + 3x^4(-2x^2) + 3x^4(-1) + 4x^2(x^3) - 4x^2(2x^2) - 4x^2(1)[/tex]

Simplifying each term, we get:

[tex]= 3x^7 - 6x^6 - 3x^4 + 4x^5 - 8x^4 - 4x^2[/tex]

So, the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2.[/tex]

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Since -4 is less than or equal to -2, we use the first part of the definition of f(x) which is f(x) = x + 4 if x ≤ -2. Therefore,

f(-4) = (-4) + 4 = 0.

So, the answer is D. 0.

The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).

Given:

Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285

Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2

Sample size from machine A ([tex]n_1[/tex]) = 35

Sample size from machine B ([tex]n_2[/tex]) = 35

Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]

= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]

= 0.07058061453775912 (rounded to 11 decimal places)

Margin of error (ME) = Critical value * Standard error

= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)

= 0.18765117789861733 (rounded to 11 decimal places)

Confidence interval (CI) = Sample statistic ± Margin of error

= [tex](p_1 - p_2) \pm ME[/tex]

= (0.14285714285714285 - 0.2) ± 0.18765117789861733

= -0.05714285714285715 ± 0.18765117789861733

The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).

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The range of the function in the graph is  6≤e≤12. So correct option is A.

In mathematics, range is a term used to refer to the set of all possible output values of a function. It is the set of values that the function can take as its input varies over its entire domain. In other words, the range of a function is the set of all output values that can be obtained by evaluating the function for all possible input values.

For example, consider the function f(x) = x². The domain of this function is all real numbers, but the range is only non-negative real numbers, since x² is always non-negative for any real number x.

The range of a function can be determined by analyzing its graph, which is a visual representation of the function. The range corresponds to the set of all y-values that appear on the graph. For instance, the range of the function f(x) = sin(x) is the closed interval [-1, 1], since the sine function oscillates between -1 and 1 as its input varies over all real numbers.

Sometimes, it is useful to restrict the domain of a function in order to obtain a specific range. This process is called domain restriction or range selection. For example, the inverse function of f(x) = x² can be obtained by restricting the domain of f to non-negative real numbers, which ensures that the inverse function is also a function. The resulting function is f^-1(x) = √x, whose domain is non-negative real numbers and range is the same as the domain of f.

The range of the function in the graph is  6≤e≤12. So correct option is A.

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Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

In linear equation, 44%  of the shoppers have an e-mail account and 56%  of the shoppers do not have computer access at home.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Total number of the shoppers who were surveyed = 150

a). Number of shoppers who have an e-mail account = Shoppers who have email accounts and computer access at home + Shoppers who have email accounts but no computer access at home

= 44 + 22

= 66

Percentage of the shoppers having an e-mail account = 66/150 * 100

                                                                        = 44%

b). Total number of shoppers who do not have computer access at home

= 7 + 77

=  84

Percentage of the shoppers having computer access at home

                                             = 84/150  * 100   =  56%

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Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is.

[tex]0.1x + 0.2y = 70[/tex]

[tex]y = 3x[/tex]

Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.

Let's define the variables as follows:

Let x be the number of liters of Drink B produced.

Since the company produced 3 times as many liters of Drink A as liters of Drink B, let y be the number of liters of Drink A produced, so y = 3x.

Now, let's write the system of equations:

The total amount of real fruit juice used is 70 liters, so we can write:

[tex]0.1x + 0.2y = 70[/tex]

Substituting y = 3x into the above equation, we get:

[tex]0.1x + 0.2(3x) = 70[/tex]

Simplifying the equation:

[tex]0.1x + 0.6x = 70[/tex]

[tex]0.7x = 70[/tex]

[tex]x = 100[/tex]

So, the company made 100 liters of Drink B and 3 times as many liters of Drink A, or 300 liters of Drink A.

Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is:

[tex]0.1x + 0.2y = 70[/tex]

[tex]y = 3x[/tex]

Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.

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So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.

the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.

In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.

For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.

Let's start by using the formula for the perimeter of a triangle:

[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]

We can also use Heron's formula to find the area of triangle ABC:

[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]

where s is the semi perimeter of the triangle:

[tex]s = (AB + BC + AC) / 2[/tex]

We can use these equations to solve for the side lengths of triangle ABC:

[tex]AB + BC + AC = 65.5[/tex]

[tex]s = (AB + BC + AC) / 2[/tex]

[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]

Solving for AB, BC, and AC gives us:

AB = 15

BC = 20

AC = 30.5

Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.

DE = AB * (5/2) = 37.5

EF = BC * (5/2) = 50

DF = AC * (5/2) = 76.25

Now we can use Heron's formula again to find the area of triangle DEF:

s = (DE + EF + DF) / 2 = 81.875

Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet

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if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.

How to calculate the mean?

To calculate the mean, we add up all the numbers in the list and divide by the total number of values. Before the change, the sum of the numbers is:

164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 523 = 2494

And there are 9 numbers in the list. So the mean is:

2494 / 9 ≈ 277.11

If we change the value of 523 to 424, then the sum becomes:

164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424 = 2465

And there are still 9 numbers in the list. So the new mean is:

2465 / 9 ≈ 273.89

So the mean decreases by approximately 3.22.

To calculate the median, we find the middle value of the list. If the list has an odd number of values, then the median is the middle value. If the list has an even number of values, then the median is the average of the two middle values. In this case, the list has an odd number of values, so the median is:

261

If we change the value of 523 to 424, then the list becomes:

164, 225, 227, 250, 261, 268, 277, 379, 424

And the median is still:

261

So the median stays the same.

In summary, if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.

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Therefore, the volume of the prism is 60 cubic feet.

Volume is the amount of space occupied by a three-dimensional object or the capacity of an object. It is typically measured in cubic units such as cubic meters, cubic feet, or cubic centimeters. The formula for finding the volume of a solid object depends on its shape. In general, the volume of a shape can be found by dividing it into smaller, more easily measured shapes and adding up their volumes. This is known as the method of integration in calculus, and it is used to find the volumes of irregularly shaped objects or fluids. Understanding the concept of volume is important in many fields, such as architecture, engineering, physics, and chemistry. In these fields, volume is used to determine the capacity of containers, the displacement of fluids, and the amount of materials needed for a construction project.

Here,

The volume of a prism is given by the formula:

V = Bh

where B is the area of the base and h is the height of the prism.

Substituting the given values:

V = (20 ft)(3 ft)

V = 60 cubic feet

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Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.

In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.

Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.

Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.

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If the the a is greater than 1, compared to the parent function the C. Stretched vertically.

The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.

If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".

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The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9

From the question, we have the following function that can be used in our computation:

[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]

Next, we set the denominator to 0 and solve for x

So, we have

81 - x²: x = ±9

2x² - 6x: x = 0 and x = 3

x² + 2x - 6x: x = 0 and x = 4

Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9

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The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.

To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.

(sin 2x) / (1 + cos 2x)

(2sin x × cos x) / (1 + (cos²x - sin²x))

(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)

We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:

(2sin x × cos x) / (1 + 2sin x × cos x)

(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)

((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)

(2sin x - 4sin²x) / (1/cos²x - 4sin²x)

Since tan x = sin x / cos x, we can rewrite the expression:

(2tan x - 4tan²x) / (sec²x - 4tan²x)

(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)

(2tan x - 4tan²x) / (1 - 3tan²x)

2tan x × (1 - 2tan²x) / (1 - 3tan²x)

tan x

So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.

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The true statements are:

1. The radius of the circle is 3 units

2. The standard form of the equation is (x-1)^2+y^2=3

3. The center of the circle lies on X-axis

4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9

The given equation is: x^2+y^2-2x-8=0

The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle

The given equation in standard form can be written as

(x^2-2x+1)+y^2-9=0

(x-1)^2+y^2=3^2

Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.

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F(4)=9 is the value for this function.

A function that is defined by numerous smaller functions across various time intervals is known as a piecewise function. The domain of a function is the sum of all the smaller domains, and each sub-function has its own formula and domain. The input value and the function that establishes that interval determine the function's output.

The typical functional notation, which represents the body of a function as an array of functions and related subdomains, can be used to define piecewise functions. Together, these subdomains must encompass the entire domain; frequently, it is also necessary for them to be pairwise disjoint, or constitute a partition of the domain.

x=4 is bigger than or equal to 0 because it.

we use the third function definition

F(x)=x+5.

Therefore, F(4)=4+5=9.

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For all x, P(x) (using universal quantifier ∀) and  It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

1. For all x in S, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

For all x, P(x) (using universal quantifier ∀)

It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

For all x in S, P(x) (using universal quantifier ∀)

It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

1. For all x, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

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The standard form equation of a circle whose diameter endpoints are  (-3,4) (2,1) is [tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5

The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. This equation is derived using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By setting (x - h)² and (y - k)² equal to r² and then combining the two equations, we get the standard form equation of a circle.

The center of the circle lies in the middle of the diameter, so we find the midpoint of the end points:

[tex](\frac{-3+2}{2} , \frac{4+1}{2} )[/tex] = (-0.5, 2.5)

And radius of the circle is half of the diameter, which is:

[tex]\frac{\sqrt{( 2-(-3))^2 + (1-4)^2 )}}{2}[/tex] = [tex]\frac{\sqrt{26}}{2}[/tex]

Therefore, the circle equation is:

[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = [tex](\frac{\sqrt{26} }{2} )^2[/tex] = 26/4 = 6.5

[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5

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Answer: Using the formula i = prt, we have:

i = (104292.12 - 80040) = 24252.12

p = 80040

t = 3

Substituting these values, we get:

24252.12 = 80040 * r * 3

Solving for r, we get:

r = 0.101 or 10.1%

Therefore, the interest rate is 10.1%.

Step-by-step explanation:

This sentence relating to the quotient can be expressed mathematically as:

(30 / x) - 2

This sentence can be expressed mathematically as:

(30 / x) - 2

where x represents the unknown number.

The word "quotient" indicates that we are dividing 30 by the unknown number x. The phrase "is decreased by 2" means that we need to subtract 2 from the quotient.

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Answer:

step by step explanation:

All you have to do is expand and reduce the expressions

then evaluate -2 being a root of the expressions

To do that you need to substitute -2 into the simplified expressions

if the result comes as zero then f(-2) is factor of f(x) according to the factor theorem.

Example 1.

simplify (-5x-2)(7x-4)-2x+3

if you substitute f(x) as f(-2)

then substitute x with -2

when you simply and evaluate the expression you will get that the expression is equal to -137

which means -2 isn't a root since the expression must be equal to 0

-2 is not a root

do the same for the other expressions

The principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.

To calculate the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59%, we first need to calculate the amount of interest that has accrued over the 51 months.

Using the formula:

Interest = Principal x Rate x Time

where Principal = $10,000,

Rate = 12.59% per year,

Time = 51/12 years (since the interest is compounded monthly):

Interest = $10,000 x 0.1259 x (51/12)

= $5,307.13

So the total amount owed after 51 months would be:

Total amount owed = Principal + Interest

= $10,000 + $5,307.13

= $15,307.13

Therefore, the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.

As for recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations, one example is the Black Lives Matter movement, which has brought attention to systemic racism and police brutality in the United States.  Another example is the #MeToo movement, which has raised awareness about sexual harassment and assault and has led to changes in workplace policies and cultural attitudes toward these issues.

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