mark and kevin own 1/4 and 1/3 of the books on a shelf, respectively lori owns the rest of the books. if kevin owns 9 more books than mark, how many books does lori own ?

The eight types of functions are  Linear Functions, Quadratic Functions, Polynomial Functions, Exponential Functions , Logarithmic Functions, Trigonometric Functions, Rational Functions, Piecewise Functions.

1. Linear Functions: Linear functions are equations of the form y = mx + b, where m and b are constants and x is an independent variable. The equation describes a straight line when graphed. The slope of the line is m, and the y-intercept, where the line crosses the y-axis, is b.

2. Quadratic Functions: Quadratic functions are equations of the form y = ax^2 + bx + c, where a, b, and c are constants and x is an independent variable. These equations describe parabolas when graphed. The vertex of the parabola is the point (x, y) where the curve changes direction and is given by (-b / 2a, c - b^2 / 4a).

3. Polynomial Functions:  Polynomial functions are equations of the form [tex]y = a_nx^n + ... + a_1x + a_0,[/tex] where a_n, ..., a_1, a_0 are constants and x is an independent variable. These equations can describe many different shapes when graphed.

4. Exponential Functions: Exponential functions are equations of the form [tex]y = a^x[/tex], where a is a constant and x is an independent variable. These equations describe exponential growth or decay when graphed. The rate of growth or decay is determined by the value of a.

5. Logarithmic Functions: Logarithmic functions are equations of the form y = log_a x, where a is a constant and x is an independent variable. These equations describe logarithmic curves when graphed. The base of the logarithm is determined by the value of a.

6. Trigonometric Functions: Trigonometric functions are equations of the form y = f(x), where f is a trigonometric function (e.g. sin, cos, tan, cot) and x is an independent variable. These equations describe sine and cosine curves when graphed.

7. Rational Functions: Rational functions are equations of the form y = (ax + b) / (cx + d), where a, b, c, and d are constants and x is an independent variable. These equations can describe many different shapes when graphed.

8. Piecewise Functions: Piecewise functions are equations of the form y = f(x) if x is in a certain interval, and y = g(x) if x is in another interval. These equations can describe many different shapes when graphed.

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Answer: 216 small balls

Step-by-step explanation:

The volume of a ball:

                                [tex]\displaystyle\\V=\frac{4}{3} \pi R^3[/tex]

Let us calculate the volume of a big metallic ball:

[tex]\displaystyle\\V_{big}=\frac{4}{3} (3)(3^3)\\\\ V_{big}=4(27)\\\\V_{big}=108 \ cm^3[/tex]

Now let us calculate the volume of a big small ball:

[tex]\displaystyle\\V_{small}=\frac{4}{3} (3)(0.5^3)\\\\ V_{small}=4(0.125)\\\\V_{small}=0.5 \ cm^3[/tex]

Thus, the number of identical small balls should work:

[tex]\displaystyle\frac{V_{big}}{V_{small}} =\frac{108}{0.5} \\\\\frac{V_{big}}{V_{small}} =216\ units[/tex]

Answer:

1.6

Step-by-step explanation:

Goold helped!!!

Answer: 30 sq ft

Step-by-step explanation: The area of a triangle can be calculated using the formula A = 1/2 * b * h, where A is the area, b is the base, and h is the height. In this case, the base of the triangle is 7 1/2 feet and the height is 8 feet, so the area is calculated as follows: A = 1/2 * 7.5 * 8 = 30 square feet. Therefore, the area of the triangle is 30 square feet.

Answer:

[tex]30sq ft[/tex]

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

At the y-axis intercept, the value of x = 0      <==== put '0' in for 'x' and calculate the y-axis intercept

The age of the son is 10 years old.

Lets simplify the above problem ,

Let assume man's age = a

Let assume son's age = b

If  a man is 4 times as old as his son, then

=> a= 4b

In 5 years, he will only be 3 times as old as his son, then

= a+5

= 3(b+5)

Apply substitution method :

4b+5

=3b+15

b=10

a =40

Hence the son age is 10 years old.

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Answer:

Step-by-step explanation:

[tex]Equation 1\\y-2x=-2\\Equation 2\\8x=-3y-48[/tex]

To begin, solve equation 1 for y:

[tex]y=2x-2[/tex]

Then substitute 2x-2 for y in equation 2:

[tex]8x=-3(2x-2)-48[/tex]

Now solve for x:

[tex]8x=-3(2x-2)-48\\8x=-6x+6-48\\8x=-6x-42\\(8x)+6x=(-6x-42)+6x\\14x=-42\\\frac{14x}{14}=\frac{-42}{14}\\x=-3[/tex]

Substitute this x-value into equation 1:

[tex]y=2x-2\\y=2(-3)-2\\y=-6-2\\y=-8[/tex]

So, the ordered pair that best represents the solution to this system of equations is (-3,-8).  This can be proven by substituting these values for x and y into the original equations:

[tex]y-2x=-2\\(-8)-2(-3)=-2\\-8-(-6)=-2\\-8+6=-2\\-2=-2[/tex]

and

[tex]8x=-3y-48\\8(-3)=-3(-8)-48\\-24=24-48\\-24=-24[/tex]

An equation is given as y=3x+c, an equivalent equation can be created by by solving for c in terms of y and x as y-3x.

An equation is given as y=3x+c , the concept that can be used to find the expression of c is the subject of the formular.

It should be noted that the  subject of a formula is the variable that is being worked out which is been recognised as the letter on its own on one side of the equals sign.

y=3x+c

c= y-3x

Then solving for c in terms of y and x will give us (y-3x)

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A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

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Answer:

  acute, because 10²+12²>15²

Step-by-step explanation:

You want to classify a triangle with sides 10 in, 12 in, and 15 in.

The "form factor" (f) of the triangle can be computed as ...

  f = a² +b² -c²

where a, b, c are the side lengths in increasing order. This is positive for an acute triangle, negative for an obtuse triangle, and zero for a right triangle.

  f = 10² +12² -15² = 100 +144 -225 = 19

  f > 0

That is to say 10² +12² > 15², so the triangle is acute

__

Additional comment

The largest angle in the triangle is arccos(f/(2ab)). In this triangle, that is ...

  arccos(19/(2·10·12)) ≈ 85.46°, an acute angle

The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. The two roots can be calculated using the quadratic formula.

The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. This can be seen by calculating b² - 4ac, which in this case gives (6² - 4*1*9) = 36 - 36 = 0. A discriminant of zero or higher means that the equation has two real roots. The two roots can be calculated using the quadratic formula, which is x = [-b ± Â√(b² - 4ac)] / 2a. In this case, a = 1, b = 6, and c = 9, so the formula becomes x = [-6 ± Â√(6² - 4*1*9)] / 2, which simplifies to x = [-6 ± Â√0] / 2, or x = [-6 ± 0] / 2. So the two roots are x = -3 and x = -3, which means that the equation has two equal real roots.

x² + 6x + 9

b² - 4ac = (6² - 4*1*9) = 36 - 36 = 0

x = [-6 ± Â√(6² - 4*1*9)] / 2

x = [-6 ± Â√0] / 2

x = [-6 ± 0] / 2

x = -3 and x = -3

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The value of y when x = 17 based on y=156 when x=39 is 68

Based on the given task content; the value of y can be determined by using ratio

y = 156 when x = 39

y = ? when x = 17

Equate the ratio of y to x

156 : 39 = y : 17

156/39 = y / 17

cross product

156 × 17 = y × 39

2,652 = 39y

divide both sides by 39

y = 2,652 / 39

= 68

In conclusion, y is 68 when x = 17 when solved with ratio.

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Answer:

m=-2

Step-by-step explanation:

Recall slope (m) can be found using the following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this problem, let:

[tex](x_1,y_1)=(-9,-4)\\(x_2,y_2)=(-3,-16)[/tex]

So,

[tex]m=\frac{(-16)-(-4)}{(-3)-(-9)}\\m=\frac{(-16)+4}{(-3)+9}\\m=\frac{-12}{6}\\m=-2[/tex]

Answer:

x/3

Step-by-step explanation:

like x divided by 3

The term "infinity" in mathematics refers to something that is bigger than a natural number.

Given that,

We have to find what is infinity means.

We know that,

Something that has no beginning is said to be infinite. It is generally something that has no restrictions. It is a condition in which there are no boundaries in terms of time, space, or any other kind of quantity.

Infinity is denoted by ∞.

If there is a one-to-one relationship between a set of numbers and a suitable subset of itself, that set can be said to be infinite.

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a) 7 in

b) 72 steps

Step-by-step explanation:

Angle of elevation formula:  

where  is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.

a)  Given:

b)  Given:

1st floor = 21 feet

2nd floor = 21 feet

⇒ Total height = 21 + 21 = 42 feet

1 foot = 12 inches

⇒ 42 feet = 42 x 12 = 504 inches

Using vertical rise of 7 in per step found in part (a):

Number of steps = 504 ÷ 7 = 72

Increased accuracy

Using unrounded vertical rise of 12tan(32):

Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step

The formula for finding the asymptote of a hyperbola is

y-k =+/- b/a( x-h)

Hyperbola

A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.

An asymptote of the curve y = f(x) or in the implicit form: f(x, y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

In Mathematics, infinity is the concept describing something larger than the natural number. It generally refers to something without any limit. This concept is predominantly used in the field of Physics and Math which is relevant in a number of fields.

The quintessential example of asymptotes are the vertical or horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant.

In the cartesian system, the coordinate plane is divided into four equal parts by the intersection of the x-axis (the horizontal number line) and the y-axis (the vertical number line). These four regions are called quadrants because they each represent one-quarter of the whole coordinate plane.

The formula for finding the asymptote of a hyperbola is

y-k =+/- b/a( x-h)

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An asymptote of the curve y = f(x) or in the implicit form: f(x, y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

The quintessential example of asymptotes are the vertical or horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant.

On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

= n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

= 33 + 50 - 16

= 67

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The reported rate of return is not reasonable i.e. the rate of return on the investment is  -0.20% .

What is Return ?

The annual return on an investment, expressed as a percentage of the initial investment.an investment of $200 earns $12 for a year, so the Rate of Return is 12/200 = 0.06 = 6%.

Given, for an investment of $26,245, a quarterly statement reports that the account balance is $26,192 and rate of return for the same quarter was -0.02 %.

Here, we'll calculate the rate of return as follows:

Rate of return = (change in investment/ Initial investment) × 100

                        = ($26,192 - $26,245)/$26,245 × 100

                        = -53/26245 × 100

                        = - 0.20 %

Hence, The correct rate f return will be -0.20 %, not -0.02%.

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Median is the middlemost value after the data set is sorted in ascending or descending order.

What is median?

The data set's median is the value in the middle.when we will put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them up, and divide by two. Your median will be that value.

so if we given with a data set 2, 1 ,4, 3,2 ,2 ,1

so in order to find the median of a data set we will sort it into ascending order and then find the middle most value as the number of element is odd.

so after sorting the data set is like 1 , 1 , 2 , 2, 2 , 3 , 4 so the middle value is 4 the element which is 2 and hence median of the data set is 2.

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Answer:

its a commutative property becaus its just changing the order

The nature of the roots of a quadratic equation is known by a value known as the discriminant,  which is calculated by seeing the equation and comparing it with the standard equation which is given by -

ax^2 + bx +c , where a , b , c are constants .

The root of the equation is given by -

x= [(-b )± (b^2 - 4ac)] / 2a

Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .

This discriminant is the defining factor of the nature of the roots.

Now, here arise three cases-

(i) If (b^2 - 4ac) > 0, the roots are real and distinct .

(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.

(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.

For example , we have an equation x^2 + 2x + 1.

Here, a =1, b=2 and c=1.

Putting these values in the discriminant , we get -

b^2 - 4ac = 4-4(1)(1) = 0.

So, the roots of the equation are real and equal i.e. x=2,2.

Hence, it is the discriminant which determines the nature of roots.

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Yes,△TSR is Congruent to △QRS ( i.e,△QRS ≅ △TRS) by SAS , because there is all enough information to prove that the triangles are congruent by SAS rule.

The word "congruent" for figures means the same thing in all respects, mainly shape and size. The relationship between two congruent entities is described by congruence. SAS congruence is a term also known as side angle side congruence. According to this rule, two triangles are congruent if two sides of a triangle are equal to two sides of another triangle and the angles formed by those sides of the two triangles are equal. We have two triangles, △TSR and △QRS as we can see in above figure and we get ,

Thus, two sides and one angle of triangle is similar to corresponding sides and angle of other triangle, so SAS Congruence criteria is applicable here. Therefore, △QRS ≅ △TRS by the SAS Congruence Postulate.

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Complete question :

Can TSR and QRS be proven congruent by SAS ? and the triangles are shown above figre.

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example'

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that [tex]X[/tex] is less than or equal to is 0.1,

the probability that [tex]X[/tex] is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that [tex]X[/tex] is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that [tex]X[/tex] is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

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Recall that the transform() and predict() functions only operate on test data, while the fit transform() function only operates on training data.

The mean and standard deviation for a particular feature are calculated using the fit(data) approach and then scaled. Scaling with mean and standard deviation determined by the. fit() method is done using the transform(data) method. The methods fit transform() and transform are both used for fits.

Predict() makes predictions based on the parameters it learned during fit on the testing examples, while the fit() method applies the model to the input training instances. Fit Transform is a mathematical expression that means to calculate, then transform (say calculating the means of columns from some data and then replacing the missing values). In order to alter the training set, you must also calculate it.

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As our sample size is large and grade point average follows normal curve, we use parametric test.

The normal curve is a statistical measurement which refer that the available data presented in a large number close to the mean value.

The test is used to determine an approximate value of a set of data.

hence, we use parametric test for determining an approximate value.

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The correct answer is the error made by the students of statistics is of Type 1 error.

As the question states that,

The news article that claim the number of student who believes that their online courses are as good as  or superior to traditional face-to-face instruction = 90%.

The two types of error known are:

Type I error  :  Reject the null hypothesis when the null hypothesis is true.

Type II error  : Fail to reject the null hypothesis, when the null hypothesis is NOT true.

From the question,

The hypothesis that the student test is H₀ : p = 0.90, Hₐ : p < 0.90 .

Here, p<0.90 means that College student disagree with the statement.

The student had rejected the null hypothesis,

and concluded that p <  0.90 , when in fact the null hypothesis is true .

The correct answer is Type 1 error.

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Answer:

corrine got 66006 vote

bill got 53450 vote

Answer:

Bill Randall= 53450 votes.

Corrine Brown= 66006 votes.

Step-by-step explanation:

Bill Randall = X

Corrine Brown = 1x

Bill Randall= x+1x+12556=119456

2x+12556=119456

2x=119456-12556

2x=106900

x=106900/2

x=53450

Corrine brown = 53450+12556

                        = 66006