What is the zero of f?

Answer:

19/5

Step-by-step explanation:

Aquí, queremos escribir el número total de millas que Hans corrió en forma de una fracción impropia.

Para hacer esto, agregamos todas las millas recorridas.

Matemáticamente, eso sería 3 + 4/5 = 3 4/5 Esta es la forma de fracción mixta.

La fracción impropia es así (5 * 3) + 4/5 = 19/5

The total number of students in Ridgewood Junior High School is 2500 students

It is given that all students in Ridgewood Junior High School either get lunch in the school cafeteria or brought it from home on Tuesday.

No. of students who brought their lunch on Tuesday= 2% = 50 students

Let x be the total number of students in the Ridgewood Junior High School, therefore formulating the equation we get:

2% of x = 50

2/100*x = 50

x = 2500

Total number of students in the school = 2500

Hence, the total number of students in Ridgewood Junior High School is 2500 students

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The most appropriate choice for Quadratic  equation will be given by -

Third option is correct

What is Quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

Here,

\(x^2 +2x=24\\x^2+2x-24=0\\x^2+6x-4x-24=0\\x(x+6)-4(x+6)=0\\(x+6)(x-4)=0\\\)

\(x+ 6 = 0\) or \(x - 4 = 0\)

x = -6 or x = 4

Third option is correct

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Answer:  3/2

Step-by-step explanation:

Answer:

I think it's will be C

Step-by-step explanation:

C I psomes

Answer: C 130%

Step-by-step explanation:

Events, of randomly drawing a King OR a card with an even number describe by a) Mutually Exclusive.

The events of randomly drawing a King and drawing a card with an even number are mutually exclusive. This means that the two events cannot occur at the same time.

In a standard deck of 52 playing cards, there are no Kings that have an even number.

Therefore, if you draw a King, you cannot draw a card with an even number, and vice versa.

The occurrence of one event excludes the possibility of the other event happening.

It is important to note that mutually exclusive events cannot be both independent and conditional. If two events are mutually exclusive, they cannot occur together, making them dependent on each other in terms of their outcomes.

The correct option is (a) Mutually Exclusive.

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Answer:

a = (p - b)/2

Step-by-step explanation:

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and  =

Parenthesis

Exponents (& roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract b from both sides:

p (-b) = 2a + b (-b)

p - b = 2a

2a = p - b

Next, divide 2 from both sides:

(2a)/2 = (p - b)/2

a = (p - b)/2

a = (p - b)/2 is your answer.

~

Answer:

a = (p + b) / 2

Step-by-step explanation:

p = 2a + b

2a - b = p

+b

2a = p + b

/ 2

a = p + b

a = (p + b) / 2

According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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Answer: B

Step-by-step explanation:

Answer:

[2, ∞)

Explanation:

Given f(x) defined below:

Compare the given quadratic function to the vertex form:

The vertex of the function, (h,k)=(-5,2)

What this means is that the minimum value of f(x) is 2.

Therefore, the range of the quadratic function is:

The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

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The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)

The given differential equation is: 2xyy' + (x² - y²) = 0

We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.

Put y = vx and y' = v + xv'

Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x

Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x

Substituting these values in the given differential equation:

2x(v)(v + xv') + (x² - v²x²) = 0

2v + 2x²v' + x - v² = 0

2x²v' + 2v/x - v³/x = -1/x

We can write the above differential equation as:

2x²dv/dx + 2v/x = v³/x - 1/x

Separating the variables and integrating both sides:

∫dx/x = ∫[v/(v² - 2)]dv/x

⇒ ln |x| + ln |v² - 2| + C

⇒ ln |x(v² - 2)| = ln |Cx|

⇒ v² - 2 = Cx² (where C is a constant)

⇒ v = ±√(Cx² + 2)

Putting the value of v in y = vx, we get:

y = x√(Cx² + 2) and y = -x√(Cx² + 2)

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To earn an average grade of 90 student need to score of 116 on a fourth exam.

To find the score needed on the fourth exam for the student to earn an average grade of 90,

we can set up an equation.

Let us denote the score on the fourth exam as x.

The average grade is calculated by summing all the scores and dividing by the number of exams.

Here we have 3 exams with scores of 84, 80, and 80, and we want the average grade to be 90.

(84 + 80 + 80 + x) / 4 = 90

Simplifying the equation,

⇒(244 + x) / 4 = 90

Now, we can solve for x.

⇒244 + x = 90 × 4

⇒ 244 + x = 360

⇒ x = 360 - 244

⇒x = 116

Therefore, the student would need a score of 116 on the fourth exam to earn an average grade of 90.

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Answer: In summary, the sample in this situation is the 30 leaves that the tree enthusiast chose from the oak tree in his backyard. By measuring the length of these leaves, he can estimate the typical length of oak tree leaves in his backyard, which is the population of interest.

The sample in this situation is the 30 leaves that the tree enthusiast chose from the oak tree in his backyard. In statistics, a sample is a subset of individuals or observations from within a statistical population used to draw inferences and conclusions about the population of interest.In this case, the oak tree leaves in the backyard are the population, and the enthusiast is interested in estimating the typical length of these leaves. To do this, he chose a sample of 30 leaves to measure their length and then used this information to draw conclusions about the entire population of oak tree leaves in his backyard. It is important to note that the sample size should be representative of the population for the estimates to be accurate.Answer:In summary, the sample in this situation is the 30 leaves that the tree enthusiast chose from the oak tree in his backyard. By measuring the length of these leaves, he can estimate the typical length of oak tree leaves in his backyard, which is the population of interest. The sample size should be representative of the population for the estimates to be accurate, and it is essential to use statistical methods to ensure the results are reliable.

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ANSWERS

(a) Table:

(b) For x ≥ 6, the table suggests that f(x) is sometimes less than g(x).

EXPLANATION

(a) To fill in this table, we have to substitute x with each value in the first column and solve,

Repeat this for all values of x and we have the table,

(b) Let's analyze the values obtained in the table:

• For x = 6, f(x) is ,less, than g(x).

• For x = 10, f(x) is ,less, than g(x).

• For x = 11, f(x) is greater than g(x).

• For x = 12, f(x) is greater than g(x).

Hence, the table suggests that for x ≥ 6, f(x) is sometimes less than g(x).

Answer:

See below

Step-by-step explanation:

The first part is asking what you would do if f(x)=2 which means how do you solve for x to make the equation come out to be equal to 2.

2 = 8x + 10  simplifying, 8x = 2 - 10 or 8x = -8 and simplified even further,

x =  -1

The second part is asking what the equation would equate to if you replace x with 2.  This gives a totally different answer.

?  = 8(2) + 10  or   ? = 16 + 10  or finally  26

Answer:

The slope of AB is different from the slope of BC is NOT TRUE.

Step-by-step explanation:

AB and BC are on the same straight line, so their slopes are the same.

The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.

The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
     = 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

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The length between these two points on the line graph is approximately 8.60 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given that;

Point (9,3)

Point (2,8)

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 2 - 9 )² + ( 8 - 3 )² )

D = √( ( -7 )² + ( 5 )² )

D = √( 49 + 25 )

D = √74

D = 8.6

Therefore, the distance is approximately 8.60 units.

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Answer:

11. (x, y) -> (7, -3)

14. (x, y) -> (-3, -2)

15. (x, y) -> (-3, 2)

16. (x, y) -> (7,6)

20.(x, y) -> (4, 1)

Step-by-step explanation:

11.

x + 3y = 1

-3x -3y = -15

-2x = -14

/-2    /-2

x = 7

x + 3y = 1

7 + 3y = 1

-7        -7

3y = -6

/3    /3

y = -2

(x, y) -> (7, -3)

14.

-3x + 3y = 3

-5x + y = 13

-5x + y = 13

+5x     +5x

y = 5x + 13

-3x + 3(5x + 13) = 3

-3x + 15x + 39 = 3

12x + 39 = 3

    - 39   -39

12x = -36

/12    /12

x = -3

Now, we solve for y:

-5x + y = 13

-5(-3) + y = 13

15 + y = 13

-15      -15

y = -2

(x, y) -> (-3, -2)

15.

6x + 6y = -6

5x + y = -13

5x + y = -13

-5x         -5x

y = -5x - 13

6x + 6y = -6

6x + 6(-5x - 13) = -6

6x -30x - 78 = -6

-24x - 78 = -6

       + 78  + 78

-24x = 72

/-24     /-24

x = -3

Now, we solve for y:

6x + 6y = -6

6x + 6y = -6

6(-3) + 6y = -6

-18 + 6y = -6

+18       +18

6y = 12

/6   /6

y = 2

(x, y) -> (-3, 2)

16.

2x + y = 20

6x - 5y = 12

2x + y = 20

-2x     -2x

y = -2x + 20

6x - 5y = 12

6x - 5(-2x + 20) = 12

6x + 10x - 100 = 12

16x - 100 = 12

    + 100  +100

16x = 112

/16    /16

x = 7

Now, we solve for y:

2x + y = 20

2(7) + y = 20

14 + y = 20

-14      -14

y = 6

(x, y) -> (7,6)

20.

-2x - y = -9

5x - 2y = 18

-2x - y = -9

+2x     +2x

-y = 2x - 9

/-1    /-1

y = -2x + 9

5x -2y = 18

5x - 2(-2x + 9) = 18

5x + 4x - 18 = 18

9x - 18 = 18

   + 18   + 18

9x = 36

/9  /9

x = 4

Now, we solve for y:

-2(4) - y = -9

-8 - y = -9

+ 8     +8

-y = -1

/-1  /-1

y = 1

(x, y) -> (4, 1)

Hope this helps!

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The rise over run is up 2 right 3 so the slope is 2/3 and yu can see that the y-intercept is 4. So the answer is Choice D.

The probability of an employee randomly selecting three white chocolates out of ten is 0.25028228759765625 or approximately 0.25. Probability is the possibility that an event will occur.

The formula for calculating probability is as follows: P(A) = n(A) / n(S), where n(A) represents the number of favorable outcomes and n(S) represents the number of possible outcomes.

In the case where an employee randomly selects a chocolate, records their selection, and returns the chocolate to the display, selecting 10 chocolates in this way, the possible number of outcomes is 4 * 10 = 40, where the 4 represents the total number of chocolate types and the 10 represents the total number of chocolate selected.

The formula for the binomial distribution is as follows: P(X = x) = \((nCx) p^x (1 - p)^(n - x)\), where n is the total number of trials, x is the total number of successes, p is the probability of success, 1 - p is the probability of failure, and nCx is the binomial coefficient of x in n.

Using the binomial distribution formula, the probability of selecting three white chocolates is:

P(X = 3) = (10C₃) (1/4)^3 \((3/4)^(10 - 3)\) P(X = 3)

= (120) (1/64) (27/64)P(X = 3)

= 0.25028228759765625

Therefore, the probability of an employee randomly selecting three white chocolates out of ten is 0.25028228759765625 or approximately 0.25.

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Answer: The company will make a profit of $1450 by the production of 75 jeans.

Cost functions and revenue

The profit that is gained from the production and selling of the jeans is modeled by the equation;

P = 20x - 50

If 75 jeans are produced, substitute 75 to represent the value of x in the equation.

P = 20(75) - 50 = 1450

Hence, the company will make a profit of $1450 by the production of 75 jeans.

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Step-by-step explanation:

a) two representatives be picked in 5850 ways so that one is a mathematics major and the other is a computer science major. b) one representative be picked in 343 ways who is either a mathematics major or a computer science major.

Product Rule: If one event occurs in m ways and a second event occurs in n ways, the number of ways the two events occur in the sequence is m×n ways.

Sum Rule: If an event occurs either in m ways or in n ways (non-overlapping), the number of ways the event can occur is m+n ways.

according to the question,

Mathematics majors =18 and Computer science majors = 325

A. We need to use the product rule because the first event is picking up a Mathematics major and the second event is picking up a computer science major.

= 18 x 325

= 5850

B. Here sum rule is applicable because the event is picking up a mathematics major or a computer science major.

= 18 + 325

= 343

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(complete question)

there are 18 mathematics majors and 325 computer science majors at a college. a) in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) in how many ways can one representative be picked who is either a mathematics major or a computer science major.

Answer:

273/4

Step-by-step explanation:

We know

A company’s stock opened at 68 3/8 dollars per share

68 3/8 = 547/8

The stock dropped 1 7/8 dollars on Monday

1 7/8 = 15/8

547/8 - 15/8 = 532/8

The stock dropped another 2 1/2 dollars on Tuesday.

2 1/2 = 5/2

532/8 - 5/2 = 532/8 - 20/8 = 512/8

On Wednesday, the stock gained back 4 1/4 dollars.

4 1/4 = 17/4

512/8 + 17/4 = 512/8 + 34/8 = 546/8

546/8 = 273/4

So, the answer is 273/4

Using the combination formula, C₄,₁ = 4, and substituting p = 1/2, q = 1/2, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ, we find that Cₙ,ₓpˣqⁿ⁻ˣ = 1/4.



To evaluate Cₙ,ₓpˣqⁿ⁻ˣ, we can use the combination formula and substitute the given values. The combination formula is given by:

Cₙ,ₓ = n! / (x!(n - x)!)

where n! represents the factorial of n.

Given:

n = 4

x = 1

p = 1/2

First, let's calculate q, which is the complement of p:

q = 1 - p

 = 1 - 1/2

 = 1/2

Now, let's substitute the values into the combination formula:

C₄,₁ = 4! / (1!(4 - 1)!)

     = 4! / (1! * 3!)

Calculating the factorials:

4! = 4 * 3 * 2 * 1 = 24

1! = 1

3! = 3 * 2 * 1 = 6

Substituting the factorials back into the formula:

C₄,₁ = 24 / (1 * 6)

     = 4

Now, let's substitute p, q, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ:

Cₙ,ₓpˣqⁿ⁻ˣ = C₄,₁ * pˣ * q^(n - x)

           = 4 * (1/2)^1 * (1/2)^(4 - 1)

           = 4 * (1/2) * (1/2)^3

           = 4 * 1/2 * 1/8

           = 4/16

           = 1/4

Therefore, Cₙ,ₓpˣqⁿ⁻ˣ evaluates to 1/4.

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Answer:

Step-by-step explanation:

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