Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs ...

The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.

In this problem we need to find the solutions of a trigonometric equation, which can be done by means of algebra properties and trigonometric formulas. Now we proceed to present the entire procedure:

Step 1 - Introduce the trigonometric equation:

cos 2x - cos x = - 1

Step 2 - Use the trigonometric formula cos 2x = cos² x - sin ² x:

cos² x - sin ² x - cos x = - 1

Step 3 - Use fundamental trigonometric formula:

cos² x - 1 + cos² x - cos x = - 1

2 · cos² x - cos x = 0

Step 4 - Use algebra properties to factor the expression:

cos x · (2 · cos x - 1) = 0

Step 5 - Find the solutions of the expression:

cos x = 0 → x = {π / 2, 3π / 2}

2 · cos x - 1 = 0

2 · cos x = 1

cos x = 1 / 2 → x = {π / 3, 5π / 3}

The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.

To learn more on trigonometric equations: https://brainly.com/question/22624805

#SPJ1

The percentage of salt in green beans can is 2.89%.

It is important to know about the percentage first, the percentage is a part of the sample in the population. It can be determined by this formula

A% = x / N . 100%

where A% is the percentage, x is the sample and N is the total population

From the question above, we know that :

x = 11.5 grams

N = 14 ounce = 396.89 grams

By substituting the parameter to the equation, we get

A% = x / N . 100%

A% = 11.5 / 396.89 . 100%

A% = 2.89%

Hence, the total salt in the can is 2.89%

Find more percentages at: brainly.com/question/24304697

#SPJ4

Answer:

C, B

Step-by-step explanation:

[tex]x^2+6x+6=0 \\ \\ x=\frac{-6 \pm \sqrt{6^2-4(6)}}{2(1)} \\ \\ x=-3 \pm \sqrt{3} \\ \\ \sqrt{3} \approx 1.7 \implies -5<-3-\sqrt{3}<-4, -2<-3+\sqrt{3}<-1[/tex]

The equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question as:

8x⁴ × 5x³

We have to determine the equivalent fraction of the given expression.

⇒ 8x⁴ × 5x³

⇒ 8 × 5 × x⁴× x³

Multiply the coefficients in the above expression,

⇒ 40 × x⁴× x³

Add the exponents in the above expression,

⇒ 40 × x⁴⁺³

⇒ 40x⁷

Thus, the equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ1

Answer:

  -4, -2, 4

Step-by-step explanation:

You want the roots of the polynomial x³ +2x² -16x -32.

The polynomial can be factored by grouping:

  x³ +2x² -16x -32

  = (x³ +2x²) -(16x +32) . . . . . . group pairs of terms

  = x²(x +2) -16(x +2) . . . . . . . . factor each group

  = (x² -16)(x +2) . . . . . . . . . . . . factor out the common factor

Now, the difference of squares can be factored:

  = (x -4)(x +4)(x +2)

The zero product rule tells us the roots are the values of x that make the factors zero:

  x -4 = 0   ⇒   x = 4

  x +4 = 0   ⇒   x = -4

  x +2 = 0   ⇒   x = -2

The roots of the polynomial are {-4, -2, 4}.

__

Additional comment

The factorization of the difference of squares is a special form:

  a² -b² = (a +b)(a -b)

Answer:

-2, -4, and 4 are the correct answers on edge

Step-by-step explanation:

The given equation written in standard form is 8x - 14y = 26

From the question, we are to write the given linear equation is standard form.

From the given information, the given linear equation is

8x = 26 + 14y

The standard form of linear equation is given as

Ax + By = C

Where x and y are the variables

A, B, and C are the constants

Now, we will write the given equation in standard form

8x = 26 + 14y

Subtract 14y from both sides of the equation

8x - 14y = 26 + 14y - 14y

8x - 14y = 26

Hence, the equation is 8x - 14y = 26

Learn more on Writing an equation in standard form here: https://brainly.com/question/28981240

#SPJ1

a) The smallest number is 2

b) The first quartile Q1 is 12

c) The median is 16

d) Third quartile Q3 is 33

e)The  largest number is 39

What Is Quartile Formula?

To divide a set of observations into four equal pieces, use the quartile formula. The median and the first term are where the first quartile is located. The median represents the middle quartile. The third quartile represents the midway value that falls between the median and the last term.

Given data set:

19, 39, 9, 33, 15, 16, 2, 33, 16

Arrange the data in ascending order:

2, 9 ,15 ,16 ,16 ,19 ,33 ,33 ,39

a) Smallest number: 2

b) The first quartile Q1 :

  number of terms=n=9

Q1= (n+1)/4 th term

Q1= (9+1)/4 = 2.5th terms

This means, Q1=mean of 2nd and 3rd terms= (9+15)/2 = 12

c) Median:

M=(n+1)/2 th term = (9+1)/2 =5th term = 16

d) Third quartile Q3:

Q3= 3[(n+1)/4] th term

Q3= 3[(9+1)/4] = 7.5th terms

This means, Q3=mean of 7th and 8th terms= (33+33)/2 = 33

e) largest number : 39

To learn more about the quartile from the given link

https://brainly.com/question/28168026

#SPJ4

The area of the quadrilateral is = 15 square units.

acc to our quesstion-

hence,The area of the quadrilateral is = 15 square units.

learn more about area of quadrilateral click here:

https://brainly.com/question/22297305

#SPJ1

The mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season or p = 52-43.

According to the question,

We have the following information:

A football team had 52 players at the start of the season, but then some players left the team. After that, the team had 43 players.

Now, let's take the number of players who left the team to be p.

So, we have the following expression:

p = 52-43

p = 9

Hence, the mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season.

To know more about mathematical sentence here

https://brainly.com/question/22248350

#SPJ1

The 42nd term of the sequence is 248

What is Arithmetic Progression?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

The furmula is [tex]a_{n}[/tex]=a + (n - 1 )d

where a = The first form of A.P

n = Number of terms given to find

d = Common difference between each terms

Given,

a = 2

n = 42

d = 6

Now,

[tex]a_{42\\[/tex] = 2 + (42 - 1)6

[tex]a_{42}[/tex] = 2 + (41)6

[tex]a_{42}[/tex] = 2+ 246

Therefore, for 42nd term

[tex]a_{42}[/tex] = 248

Read more about Arithmetic Progression

https://brainly.com/question/29394721

#SPJ1

The answer to following parts are and this can be solved by using probability.

a) 15,890,700 different samples can be chosen

b) 6,523,881 will contain at least one defective chip

c) 41.1%

What is probability?

A probability is the number of desired outcomes divided by the number of total outcomes.

Main body:

The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.

Cₙ,ₓ =[tex]\frac{ n!}{x!(n-x)!}[/tex]

(a) How many different samples can be chosen?

Samples of 6 from a set of 50.

Then

C₅₀,₆ = [tex]\frac{50!}{6!(50-6)!}[/tex] =15,890,700

15,890,700 different samples can be chosen

(b) How many samples will contain at least one defective chip?

Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.

Then

No defective chips:

Four are defective.

So 50-4 = 46 are not.

This is samples of 6 from a set of 46.

C₄₆,₆ = 46!/6!*40!

9,366,819 samples contain no defective chips.

At least one:

9366819 + n = 15890700

n = 6523881

6,523,881 will contain at least one defective chip

(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip

6,523,881 out of 15,890,700

6,523,881/15,890,700 = 0.411

As a percent

41.1%

Hence the answer are as follows.

To learn more about probability click on the link below

https://brainly.com/question/24756209

#SPJ4

The least common denominator for this pair of algebraic fractions: p/4 and p/16 is 16.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In the case, the fraction is illustrated as p/4 and p/16.

It should be noted that the lowest common multiple for 4 and 16 is 16. This is the denominator.

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

The function for the given situation is m=200+0.8t.

Given that, Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the amount of money in Leticia's class fund=m and  the amount of money Leticia has made from selling raffle tickets is t

Now, the function is

m=200+4/5 t

⇒m=200+0.8t

Therefore, the function for the given situation is m=200+0.8t.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ1

Answer:

Step-by-step explanation:

As described in the hint:

The product is:

This is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.

It has a maximum and no minimum value since a < 0.

The x-coordinate of the maximum is the vertex which is x = - b/2a.

The x- coordinate of the vertex is:

The maximum value itself is:

Answer:

10 and 10.

[tex]f(x)=-x^2+20x[/tex]

Maximum value of the function is 100.

Step-by-step explanation:

Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.

Pairs of positive integers whose sum is 20:

The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.  

Therefore the pair of numbers is 10 and 10:

[tex]\implies x = 10[/tex]

[tex]\implies 20 - x = 10[/tex]

Form a quadratic function by multiplying:

[tex]\implies f(x)=x(20-x)[/tex]

[tex]\implies f(x)=20x-x^2[/tex]

[tex]\implies f(x)=-x^2+20x[/tex]

The maximum value of the function is the y-value of its vertex.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

To convert the function to vertex form, complete the square.

Factor out negative 1:

[tex]\implies f(x)=-(x^2-20x)[/tex]

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]

[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]

[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]

Factor the perfect square trinomial:

[tex]\implies f(x)=-(x-10)^2+100[/tex]

Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.

Answer:

(g-7)^3

Step-by-step explanation:

(x-y)^3 = x^3 - y^3

In this case you are solving for y, or 343

The cube root of 343 is 7

g^3 - 7^3 = (g-7)^3

(g-7)^3

Step-by-step explanation:

g³-343=0

g³=343

g=³√343

g=7

g³-7³=0

(g-7)^3=0

Answer:

A = 7.5 in^2

Step-by-step explanation:

the formula for a triangles area is [(h)(b)]/2

2.5 is the h (height) and 6 is the b (base)

first multiply h and b

2.5 * 6 = 15

now divide by 2

15 / 2 = 7.5

that is your answer

Answer:

1.81 inches

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

8x - 21 - 5x = - 15 ( collect like terms on left side )

3x - 21 = - 15 ( add 21 to both sides so numeric values on right side )

3x = 6 ( isolate x by dividing both sides by 3 )

x = 2

The value of m in the angle (6m - 12)° is m = 17 , the correct option is (b) .

In the question ,

it is given that ,

the triangle WZY is cut by the bisector ZX ,

and also given that ZW and ZY are congruent ,

that means ZW = ZY

Based on the characteristics of the triangle given ,

we can conclude that triangle WYZ is an isosceles triangle ,

that means , triangle WXZ = triangle YXZ

So ,  ∠YXZ = ∠WXZ = 90°

given that ∠YXZ = (6m - 12)°

So , (6m - 12)° = 90°

6m - 12 = 90

6m = 90 + 12

6m = 102

m = 102/6

m = 17

Therefore , the value of m in the angle (6m - 12)° is m = 17 .

The given question is incomplete , the complete question is

Triangle W Z Y is cut by bisector Z X. The lengths of sides Z W and Z Y are congruent. ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?

(a) 6

(b) 17

(c) 90

(d) 102

Learn more about Triangles here

https://brainly.com/question/12347204

#SPJ4

Answer:

17

Step-by-step explanation:

i got it right on edge 2022

The basic calculation values are;

1. The largest number is 199

2. The score Vanessa needs is 99 points

3. Each person should raise approximately $471

4. The approximate minimum monthly payment is $374

5. The approximate monthly payment is $55.9

The interest is 123.[tex]\overline {6}[/tex]

Basic mathematical operations includes addition, subtraction, multiplication, division, and combinations of the above operations.

1. Let x represent the number, we have;

x - 46 ≤ 153

x ≤ 153 + 46 = 199

x ≤ 199

The largest integer that could be used for the number is 199

2. Vannesa's current scores are;

81 points, 91 points, 89 points

The score Vannesa requires so as to get an A is 360 points

The score Vannesa needs = 360 - (81+91+89) = 99

Vannesa needs 99 points to get an A

3. The number of members in the band = 105

The amount the band needs to raise = $49,500

The amount each one should raise therefore is 49500 ÷ 105 ≈ 471

Each one needs to raise $471

4. The down payment is $2,000

Number of monthly payment = 48

Least contract amount = $19,940

The monthly payment = (19,940 - 2,000)/48 ≈374

The least monthly payment ≈ $374

5. The cash price for the TV = $1,200

The down payment = $500

The charges = $1,484

Number of monthly payment = 48

Total payment = $1,200 + $1,484 = $2,684

The monthly payment = 2,684 ÷ 48 ≈ 55.9

The monthly payment is approximately $55.9

The interest is therefore;

[tex] \dfrac{1484}{1200}\times 100 = 123.\overline 6 \%[/tex]

Learn more about basic calculations in mathematics here:

https://brainly.com/question/13338580

#SPJ1

The will be A'(0, 20),  B'(20, 10) and  '(-10, 0). Transformation is the  of a point from its to a. Types of transformation are reflection, translation, rotation and dilation.

What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is obtained. Function transformations are very useful for graphing functions without having to start from scratch because they allow you to move, expand, compress, or reflect the curve. In this article, we will examine the guidelines for function transformations as well as examples of how to transform various function types.

Let ABC be a   with coordinates A(0, 2), B(2, 1), C(-1, 0).

The coordinate of points A, B, C will change by below rule

(x, y)↔(10x, 10y)        

where 10 is the scale factor.

∴A(0, 2) ↔A'(0, 20)

B(2, 1) ↔B'(20, 10)

C(-1,0) ↔C'(-10, 0)

Hence,   will be A'(0, 20) ,B'(20, 10)  and C'(-10, 0)

To learn more about transformation
https://brainly.com/question/27895117
#SPJ9

Answer: (6,1), (2,-1) etc

Step-by-step explanation:

Just pick any points on the graph and see if they aren't on the line and if they aren't, then you can pick that one.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

So, inverse of the given statement is "If △ABC is not equilateral , then it is not  isosceles"

We have to find the inverse of the given statement:

" If ∆ABC is equilateral, then it is isosceles."

A triangle is said to be equilateral if all of the three sides are equal in measure and a triangle is said to be isosceles if two sides of a triangle are equal in measure.

To learn more about equilateral visit:https://brainly.com/question/9872652

#SPJ1

Step-by-step explanation:

y + 4 = 8 ( x - 6 )

Multiple 8 by -6 and x

y+4 = 8x -48

Subtract 4 from both sides

y = 8x -52

Take two points from this equation, I took (7,4) and (8,12)

Find the slope with these points, which should give you 8

Step-by-step explanation:

when we have the equation in the form of

y = ax + b

then "a" is the slope.

in our equation

y + 4 = 8(x - 6)

the only thing that contributed to the factor of x is

8(x ...)

so, in the end the equation is (we sit need to bother about the rest)

y = 8x ...

so, the slope is 8.

question 9

this is trickier.

again, we want the form

y = ax + b

we have

6y - 3x = 12

6y = 3x + 12

y = 3/6 x + 2 = 1/2 x + 2

so, the slope is 1/2.

Step-by-step explanation:

[tex]2(x - 3) {}^{2} - 12 = 116 \\ [/tex]

[tex]2 \times ( {x}^{2} - 6x + 9) - 12 = 116[/tex]

[tex] {2x}^{2} - 12x + 18 - 12 = 116[/tex]

[tex] {2x}^{2} - 12x - 110 = 0[/tex]

[tex] {x}^{2} - 6x - 55 = 0[/tex]

[tex] {x}^{2} - 11x + 5x - 55 = 0[/tex]

[tex]x(x - 11) + 5(x - 11) = 0[/tex]

[tex](x +5 )(x - 11) = 0[/tex]

A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.

Here,

From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,

98%C.I. = µ ± z * σ /   n = 98.90 ± 2.33 * 42.30 / sqrt of 16  = 98.90 ± 24.64 = 74.26 to 125.54

The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.

Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

To learn more about the confidence interval from the given link

https://brainly.com/question/26658887

#SPJ4

The equation that would give the amount each month, given a certain number of text messages is 27 + 0.43t.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of text messages be represented as t.

Since BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. The amount will be:

= 27 + (0.43 × t)

= 27 + 0.43t

Learn more about equations on

brainly.com/question/2972832

#SPJ1