Karen and Kate have 50 CDs between them. Karen has 6 less than kate. How many each has?

The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.

Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.

For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:

A² + B² + C² = 0

A² = -(B² + C²)

This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.

This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.

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Answer:

≈ 2.76%

Step-by-step explanation:

Price increase

297.9 - 289.7 = 8

% increase

8/289.7 * 100 = 2.7614773904%

≈ 2.76%

Answer:

Parents' income

Step-by-step explanation:

The confounding variable also called the third or lurking variable is usually an unaccounted for variable or factor which may creep into our research, Hence, causing an association or relationship which does not actually exists between the two correlated variables. In the experiment abive, there is no really any actual relationship between increasing percentage of free lunch and less usage of bicycle helmets.

However, We may attribute the change in bicycle helmets used by the children to a swerve or change in the income of the parents of the students, being able to afford a bicycle helmet will depend in the income of the parent and this mightvhave caused the observed association between the variables.

Answer:

parents income

Step-by-step explanation:

Answer:

[tex]x^2+14x-51=0[/tex]

Step-by-step explanation:

Since the entire cabinet door is a rectangle, its area is given by:

[tex]A=w\ell[/tex]

The center of the cabinet door measures 12 inches by 16 inches.

And the border of the cabinet door has a width of x inches.

Therefore, the total width of the cabinet door will be (12 + 2x).

Likewise, the total length of the cabinet door will be (16 + 2x).

Thus, the area of the entire cabinet door will be:

[tex]A=(2x+12)(2x+16)[/tex]

We are given that this entire area is 396 square inches. Thus:

[tex]396=(2x+12)(2x+16)[/tex]

Simplify. We can factor out a two from both of the factors on the right-hand side:

[tex]396=2(x+6)(2)(x+8)[/tex]

So:

[tex]396=4(x+6)(x+8)[/tex]

Dividing both sides by four yields:

[tex]99=(x+6)(x+8)[/tex]

Distribute the right-hand side:

[tex]x^2+14x+48=99[/tex]

Therefore, our equation in standard form is:

[tex]x^2+14x-51=0[/tex]

Edit:

We want to find the width of the board. So, we simply have to solve for x. We previously obtained:

[tex]x^2+14x-51=0[/tex]

We can factor:

[tex](x+17)(x-3)=0[/tex]

By the Zero Product Property:

[tex]x+17=0\text{ or } x-3=0[/tex]

Solve for both cases:

[tex]x=-17\text{ or } x=3[/tex]

Length/width cannot be negative. So, we can reject the first solution.

Thus, our only solution is:

[tex]x=3[/tex]

The width of the border of the cabinet door is 3 inches.

This means that the total length of the cabinet is 16 + 2(3) = 22 inches, and the total width of the cabinet is 12 + 2(3) = 18 inches.

Answer:

84/60

Step-by-step explanation:

1 hour is 60 minutes so 84 minutes /60 gives how much it is in hours

9514 1404 393

Answer:

  y = 3x -7

Step-by-step explanation:

The given point is the y-intercept, so we can write the equation in slope-intercept form.

  y = mx + b . . . . . line with slope m through point (0, b)

For your slope and point, the equation is ...

  y = 3x -7

Answer:

distributive property is your answer

(1). ΔIJH ≅ ΔKHJ, by SSS criterion,

and (2) we need,  ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove  ΔTNS ≅ ΔUHS, by HL criterion.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

We have the triangle:

ΔIJH ≅ ΔKHJ.

To prove the congruent by SSS:

We have to show that three sides of the triangle are congruent to three sides of  the other triangle.

Here,

IJ ≅ KH.

IH ≅ JH, Given.

And both triangles share the same side JH.

So,

JH ≅ JH

So, ΔIJH ≅ ΔKHJ, by SSS criterion.

ΔTNS ≅ ΔUHS.

To prove the congruent by HL:

We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.

So, we need;

ΔTNS and ΔUHS are right-triangles.

S is the mid-point.

So,

SN ≅ SH.

ST ≅ US

So, ΔTNS ≅ ΔUHS, by HL criterion.

Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;

ΔTNS and ΔUHS are right-triangles and S is the mid-point.

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Answer:

Side BC: y = -2x + 10

Side AC: y = 2x + 4

Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.

The product of f(x) and g(x) is always a polynomial. By the definition of

polynomials the product of polynomials is always a polynomial because

the coefficient are real numbers and the exponents are whole

numbers. Real numbers and whole numbers are closed under addition

and subtraction.

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.

Here f(x) and g(x) are two given polynomial,

let f(x) = x+1 ang g(x) = x-1

f(x).g(x) = (x+1)(x-1).

f(x).g(x) = x²-1.

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Find time needed to drive 200 miles:

50 miles = 1 hour

1 mile = 1/50 hour

200 miles = 1/50 x 200 = 4 hours

Find time of arrival:

7:00am + 4 hours = 11am

Answer: She will arrive at 11am

Answer:

The woman will arrive at New York City at 11 am.

Step-by-step explanation:

At an average speed of 50 miles per hour, it will take the woman 4 hours to reach New York City. If she leaves at 7 am, she will arrive at 11 am. Here's the math:

200 miles / 50 miles per hour = <<200/50=4>>4 hours

7 am + 4 hours = 11 am

So the woman will arrive at New York City at 11 am.

Answer:

54°

Step-by-step explanation:

Angles corresponding in parallel lines are the same

The expression in the simplest form is -90p - 102

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given an expression as 9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

Then Rewrite in simplest terms:

9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

2 [ 9(-6p-4)+3(3p-5) ]

Solve the like terms;

2 [-54p - 36 + 9p - 15]

2 [-54p + 9p - 15 -  36]

2 x ( -45p - 51)

-90p - 102

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Answer:

9

Step-by-step explanation:

18/5 ÷ 2/5 = 18/5 x 5/2 = 9

Answer:-4x^2-2x+46.

Step-by-step explanation:

To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:

(-3)(x+4)(x-6)-(x^2+8x-10)

Then, you can distribute the -3 to the terms inside the first set of parentheses:

(-3x-12)(x-6)-(x^2+8x-10)

Then, you can combine like terms:

-3x^2+6x+36-x^2-8x+10

This simplifies to:

-4x^2-2x+46

Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.

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Answer:

Impossible

Step-by-step explanation:

Answer:

1/7778

Step-by-step explanation:

We multiply each event

1/6 x 1/6 x 1/6 x 1/6 x 1/6 =

1/36 x 1/36 x 1/6

= 1/7776

The lines with a slope larger than f(x) are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, you can see that the line crosses the y-axis at y = -4, so the line is something like:

y = a*x - 4

And we can see that it crosses the x-axis at x = 2, then we can write the equation:

0 = a*2 - 4

4 = a*2

4/2 = a

2 = a

So the linear equation on the graph is:

y = 2*x - 4

The slope is 2, the linear equations with a slope larger than that are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

Which can be rewritten as:

y = (5/4)*16x - (5/4)*(1/2)

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Answer:

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{9}{\sqrt{150}} = 1.2[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 40.5 - 1.2 = 39.3 hours

The upper end of the interval is the sample mean added to M. So it is 40.5 + 1.2 = 41.7 hours

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Answer:

C. 1

Step-by-step explanation:

I calculated it logically

Step-by-step explanation:

The correct choice is C

C.1

Answer:

C

Step-by-step explanation:

1 pound sand for 1 2/3 pounds gravel.

1 pound gravel for 2/5 pound cement.

3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =

= 5 pounds gravel.

5 pounds gravel = 5 × 2/5 = 2 pounds of cement

Answer:

cool i think there are 4 questons

Step-by-step explanation:

In the algebraic expression, 6x + 10, x is the variable, 6 is the coefficient and 10 is the constant.

What are algebraic expressions?

Algebraic expressions are mathematical phrases that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They can be used to represent mathematical operations and relationships between numbers.

Examples of algebraic expressions include:

2x + 3 (This is an expression that represents the sum of 2 times the value of x plus 3)

A letter or symbol that denotes an unknowable value is called a variable. The variable here is represented by x.

A coefficient is a number that is multiplied by a variable in an algebraic expression. In this case, 6 is the coefficient of x.

A constant is a value that does not change in an algebraic expression. In this case, 10 is the constant.

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From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0

and solution of these equations are x = -1/2 and y= 15/2

An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.

we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.

From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a  and detect two location of point (1, 6) and (6, 1) for line b.

As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)

hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)

                                                 y-6 = 3(x-5)

                                               y-6 = 3x -15

                                             y-3x -9 = 0

In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)

                                                       y-6 = -1(x-1)

                                                     y-6 = -x+1

                                                   x+ y -7 =0

 now, we get two equations, -3x+ y -9 =0

                                                  x+ y -  7 =0

Solving these two equations by addition method, we get x= -1/2 and y = 15/2

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Answer:

10:12:8

Step-by-step explanation:

so, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. so it would look like this     10:12:8

Answer:

The probability is 0.7449

Step-by-step explanation:

Given

[tex]n = 12[/tex] ---- total

[tex]r = 5[/tex] --- selection

[tex]Genre =\{Rap(4), Country (5), Heavy\ metal (3)\}[/tex]

Required

Probability of buying at least 1 of each genre

First, we calculate the total possible selection.

To select 5 CDs from a total of 12, we use:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

[tex]^{12}C_5 = \frac{12!}{(12 - 5)!5!}[/tex]

[tex]^{12}C_5 = \frac{12!}{7!5!}[/tex]

Expand

[tex]^{12}C_5 = \frac{12*11*10*9*8*7!}{7!*5*4*3*2*1}[/tex]

[tex]^{12}C_5 = \frac{12*11*10*9*8}{5*4*3*2*1}[/tex]

[tex]^{12}C_5 = \frac{95040}{120}[/tex]

[tex]^{12}C_5 = 792[/tex]

So, the total selection is:

[tex]Total = 792[/tex]

To select at least 1 from each genre, there are 6 possible scenarios.

And they are:

[tex]\begin{array}{ccc}{Heavy\ Metal (3)} & {Rap (4)} & {Country(5)} & {3} & {1} & {1} & 2 & {1} & {2} & {2} & {2} & {1}& {1} & {2} & {2}& {1} & {3} & {1}& {1} & {1} & {3} \ \end{array}[/tex]

The possible selections for the given scenario is:

[tex]Possible = ^3C_3* ^4C_1 * ^5C_1 +^3C_2* ^4C_1 * ^5C_2 +^3C_2* ^4C_2 * ^5C_1 +^3C_1* ^4C_2 * ^5C_2 +^3C_1* ^4C_3 * ^5C_1 +^3C_1* ^4C_1 * ^5C_3[/tex]

Using a calculator, we have:

[tex]Possible = 1*4*5 +3*4*10 +3*6*5 +3*6*10+3*4*5+3*4*10[/tex]

[tex]Possible= 20 +120 +90 +180+60+120[/tex]

[tex]Possible = 590[/tex]

The probability is then calculated using:

[tex]Pr = \frac{Possible}{Total}[/tex]

[tex]Pr = \frac{590}{792}[/tex]

[tex]Pr = 0.7449[/tex]

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given  :

=> -x-y=-2

=>  5x + 7y= 28

So ,

=>x = 2-y

thus,

=> 5(2-y) + 7y =28

=> 10 -5y + 7y =28

=> 10 -2y = 28

=> -2y = 18

=> y =-9

and

=> x  = 2 - (-9)

=> x  = 11

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

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Answer:

Step-by-step explanation:

That is not possible.